Manuscript title: Predictive Maintenance and Performance Modeling of Offshore Centrifugal Pumps under High‑Salinity Conditions

Manuscript title: Predictive Maintenance and Performance Modeling of Offshore Centrifugal Pumps under High‑Salinity Conditions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Manuscript title: Predictive Maintenance and Performance Modeling of Offshore Centrifugal Pumps under High‑Salinity Conditions Nsini Ignatius Udo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9445735/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Out at sea, oil and gas pumps tend to lose efficiency because of rust and shaking, mostly due to the salt water. We looked at how 316L stainless steel, bronze, and carbon steel pumps broke down using a seawater setup, surface analysis, and vibration tracking for over 200 hours. The test time was set to catch the early stages of rust and shaking working together. The corrosion rate varied depending on how each material reacts to the seawater, with some forming protective layers while others broke down when chloride was present. Bronze exhibited moderate degradation (4.4%, p = 0.008; 0.109 mm/yr), but 316L stainless steel held up well (2.5%, p = 0.012; 0.019 mm/yr). Regression showed clear connections between shaking, rust, and efficiency drop (R² = 0.91, p < 0.01). Also, vibration caused subsequent efficiency drop. Rust created pits that cause stiffness loss and frequency shifts, leading to more shaking and lower pump efficiency. Instead of just looking at shaking, we put measured rust data into our math models, giving us material-specific decay figures for sea lifespan prediction. Strong ties between pit count, roughness change, and performance drop (R² up to 0.94), which shows how surface breakdown affects pump.. offshore pumps predictive maintenance corrosion centrifugal pump efficiency vibration analysis regression modelling time series 316L stainless steel and carbon steel and bronze Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction In the oil and gas industry, especially offshore, centrifugal pumps are critical for moving fluids, like seawater. But out at sea, these pumps get hammered by salty water that eats away at their parts and messes with how well they work. Saltwater corrosion, erosion, rough surfaces, and vibrations all team up to make things worse [ 1 , 2 ]. The salt kicks off chemical reactions that cause pits, thinning, and damage, which messes up the flow and makes the pump unstable [ 3 – 5 ]. Lots of studies have looked at how different metals corrode in seawater. They've measured how much stuff is lost, what the pits look like, and how the metals act when exposed to salt, focusing on stainless steel, bronze, and regular steel [ 6 – 8 ]. For example, Kumar and Singh [ 9 ] showed that leaving regular steel in seawater for a long time makes it corrode faster, causing pits and rough surfaces. This weakens the steel and affects its performance. So, it's important to keep an eye on these pumps offshore. Marine corrosion models also show that things don't always break down in a straight line, as it depends on how harsh the environment is and how long the pump is exposed [ 12 ]. Still, most studies only check how much material is lost and don't link surface damage to pump vibrations or how the pump performs. On another note, people are getting better at using vibration to check on machines. They look at things like sound waves and patterns to spot problems like imbalance, bad alignment, or broken bearings in pumps [ 10 , 11 ]. Usually, they just use these signals as clues, but they don't tie them back to the actual corrosion or surface damage. So, they might see something's wrong without knowing why. These days, there are new ways to predict when things will break down using data and machine learning [ 13 – 17 ]. Things like neural networks can pick up on early signs of wear and tear from vibration and other data [ 16 , 18 ]. They're good at spotting small changes, but they mostly look at signals. Also, the internet of things and digital twins allow you to watch pumps in real-time [ 19 , 20 ]. Even so, most of these models don't use measurements of corrosion depth or surface damage to guess how well the pump will perform. We know a bit about how corrosion and fatigue affect machines [ 21 – 23 ], but there aren't many studies that measure how corrosion, vibration, and pump performance are connected when pumps are in salty water all the time. Because we don't have this info, it's hard to make good predictions and decide how to maintain pumps offshore. So, we did a lab test on three common pump materials—316L stainless steel, bronze, and regular steel—and exposed them to salty conditions. We watched the corrosion happen using standard tests [ 2 ] and checked the surfaces with a microscope. At the same time, we measured the vibration and how well the pumps worked to see how they changed over time. Based on our tests, we built some models that use measurements of corrosion depth and surface changes to predict how the pump will perform. Instead of just looking at signals, we included corrosion info and vibration data to predict performance loss. This helps us figure out how fast each material breaks down and how long it will last in certain conditions. By connecting surface damage to vibration and performance, we can see exactly how corrosion affects pumps. This gives us solid info for picking the right materials, planning for the long haul, and maintaining pumps in a smart way offshore. Here's how the rest of the paper is set up: Section 3 explains our test setup, like the salt water loop, materials, and equipment. Section 4 covers how we measured corrosion and built our models. Section 5 shows the trends we found for performance loss, corrosion, vibration, and model performance. Section 6 talks about the reasons behind these trends and what they mean for maintenance. Section 7 wraps up with our main findings and what we want to look at next. Lots of folks have looked at corrosion and vibration in machines before. But the most recent vibration-based degradation researches [Mechanical Systems and Signal Processing 239, 113326 (2025)] usually concentrate on signals and don't measure the surface corrosion. Our study is different as we measure pit density, crack growth, and surface roughness while monitoring vibration and performance for different pump materials. This gives us a clear, practical way to predict what will happen, which goes beyond just looking at signals.. 2 Methods/ Experimental Section 2.1 Experimental Setup A 2-kW centrifugal pump was powered by an electric motor, in a seawater loop to simulate offshore settings. The setup included: * Flowmeters (± 1% accuracy) * Pressure gauges (± 0.5% accuracy) * Accelerometer-based vibration sensors (± 0.2% accuracy) Material samples (20 × 20 × 3 mm) of 316L stainless steel, bronze, and carbon steel were placed along the pump's pipes to watch for local corrosion. Environmental conditions were closely regulated: * Seawater temperature: 25 ± 1°C * Salinity: 35 ± 0.5 ppt * Flow rate: 0.15 ± 0.01 m³/h, kept steady with a bypass During the tests, all settings were carefully kept constant to focus on only material wear. By keeping the flow rate, temperature, and salinity steady, we tried to isolate corrosion–vibration coupling rather than hydrodynamic or thermal differences. The aim was to have any material degradation truly reflect the materials themselves, and not other outside factors. All readings were taken continuously at 1 Hz for 200 hours to get reliable corrosion and vibration information.. The 200-hour immersion and operational testing period, although limited relative to full-service lifetimes, was selected based on accelerated corrosion protocols and prior studies [ 9 , 12 ] to capture early-stage pit formation and micro-cracking, which are critical indicators of long-term degradation. While full corrosion-fatigue evolution requires longer exposure, this period provides representative trends sufficient for developing predictive models linking surface damage to pump performance 2.2 Material Analysis Corrosion rates were measured by the mass-loss method, as per ASTM G31 [ 12 ]: CR (mm/yr) = (87.6 × W)/(D × A × T) (1) Where: CR is the corrosion rate (mm/year) W is the mass loss (mg) D is the density (g/cm³) A is the exposed surface area (cm²) T is the exposure time (hours) 87.6 is a unit conversion constant Surface details were examined after exposure with SEM to measure pitting, micro-cracks, and roughness changes. Quantitative image processing was performed using calibrated SEM images. Pit density (pits/mm²), pit area fraction (% surface coverage), and crack length distribution were measured using threshold segmentation and edge-detection algorithms. Five independent regions per sample were analyzed to ensure statistical robustness. Surface roughness evolution rate (dRa/dt) was computed from measured initial and final Ra values. 2.3 Physics-Informed Hybrid Predictive Modeling Framework 2.3.1 Regression Model Pump efficiency loss, denoted as E_loss, can be related to vibration amplitude, V, and corrosion depth, C, as shown in studies [ 10 ], [ 11 ]: E_loss = α * V + β * C + γ (2) Here, α, β, and γ are regression coefficients that depend on the material. α indicates the impact of vibration on efficiency loss, while βdetails the impact of corrosion depth on efficiency loss. γ is the intercept term, representing the baseline loss unrelated to vibration or corrosion. These coefficients are degradation numbers specific to each material, showing how different pump materials react to corrosion and vibration. Apart from regression analysis, surface roughness (Ra) caused by corrosion is one reason for the efficiency loss. Frictional head losses were found using the Darcy–Weisbach method: hf ∝ f(Re, k/D) ( 3 ) where k ≈ Ra for corroded surfaces.In this work, the arithmetic mean surface roughness (Ra), derived from SEM surface measures, was used as a roughness estimate for determining k. Existing works suggest Ra works well for defining the sand-grain roughness affecting near-wall turbulence and friction factor changes on corroded metal surfaces. Though, seawater corrosion tends to produce irregular characteristics like pits and micro-crevices, which a single roughness value might not fully capture. To get accurate Ra values, roughness data were gathered from multiple surface locations and averaged. SEM was employed to assess the presence and distribution of corrosion traits. Here, k ≈ Ra is employed as a roughness parameter appropriate for interpreting and comparing models across materials, instead of an accurate representation of corroded surfaces. This approach offers a method for integrating corrosion depth and vibration amplitude into the regression model, as both influence hydraulic losses and impeller radial force imbalance. This strengthens the model's physical basis beyond simple statistical fitting. As well as regression and autoregressive models, we used a hybrid physics-informed regression method that includes corrosion measures and vibration traits as outside variables. This boosts predictive power compared to standard time-series models [ 17 ]. While deep learning approaches like CNNs show promise, the hybrid method gives physically understandable coefficients for material-related degradation, which is useful for real offshore maintenance work. 2.3.2 Physics-Informed Autoregressive Model with Exogenous Inputs (PI-ARX) Classical AR(1) models are good at finding short-term trends in how well things work, but they don't consider physical reasons for why things break down. To get better predictions, a physics-based model with outside inputs (PI-ARX) was made: Et = φEt − 1 + θ1Vt + θ2Ct + εt (4) Where: Et = how well the pump works at time t Et − 1 = how well the pump worked at the time before Vt = how much the pump vibrates (structural response) at time t Ct = how deep the rust is or how fast it's rusting at time t φ = how long the trend lasts (autoregressive parameter) θ1 and θ2 = how strongly the physical factors are related εt = random error Unlike regular AR models, PI-ARX puts physical breakdown factors right into how the time-series changes. With this setup, measurable structure and rust can cause the pump to work worse, not just past performance. To make sure it makes physical sense, these rules were used when figuring out the parameters: θ1 > 0 (more vibration shouldn't make things work better) θ2 > 0 (more rust should make things work worse) 0 < φ < 1 (how well it works can't go up forever, so it stays stable) This way of modeling is like some recent vibration-physics setups reported in the Journal of Vibration and Control (2024), where physical states are put into data-based structures to make them work better with data they haven't seen before. 2.3.3 Degradation State-Space Representation The following equations explain the model: Ht = Ht−1 + λ1Ct + λ2Vt ( 5 ) Et = E0 – κHt ( 6 ) Where: Ht = total degradation (latent health) at time t Ht − 1 = degradation at the last time step Ct = corrosion depth (or normalized corrosion rate) at time t Vt = vibration strength at time t E0 = pump efficiency at t = 0 λ1 and λ2 = corrosion and vibration damage rates κ = efficiency sensitivity (how much degradation lowers efficiency) In simple terms: Degradation at time t = past degradation + corrosion damage + vibration damage Efficiency at time t = starting efficiency − (degradation effect) This method separates degradation from how the system performs. This allows for predictions of remaining life beyond the tested period. This combination of physics and data improves the reliability of predictions when compared to statistical models, especially when environmental conditions change. Table 1 Regression Coefficients and Model Performance Material α (Vibration) 95% CI α p-value α β (Corrosion) 95% CI β p-value β γ (Intercept) R² RMSE (%) 316L SS 0.67 0.62–0.72 0.004 0.48 0.44–0.52 0.006 1.02 0.91 0.42 Bronze 0.55 0.50–0.60 0.007 0.36 0.32–0.40 0.009 0.95 0.88 0.45 Carbon Steel 0.71 0.66–0.76 0.003 0.60 0.55–0.65 0.002 1.10 0.92 0.38 Table 1 presents a summary of how vibration (α) and corrosion (β) contribute to efficiency loss in three materials. The statistical meaning, model fit (R²), and prediction error (RMSE) are included. The data suggest that carbon steel is the most sensitive to both vibration and corrosion.. 2.3.4 Sensitivity and Causal Inference Analysis To tell apart correlation from causation, we did more stats work. (a) Sensitivity Study We made a standard sensitivity number: SV = (∂Eloss / ∂V) × (V / Eloss) ( 7 ) SC = (∂Eloss / ∂C) × (C / Eloss) ( 8 ) Where: SV = standard sensitivity number for vibration SC = standard sensitivity number for corrosion ∂Eloss / ∂V = how efficiency loss changes with vibration ∂Eloss / ∂C = how efficiency loss changes with corrosion V = vibration amount C = corrosion depth Eloss = how much pump efficiency is lost These formulas give sensitivity measures that are normalized. They show how much vibration and corrosion matter when it comes to losing efficiency. This normalizing lets us see if vibration or corrosion depth affects efficiency loss more. (b) Partial Regression Work To see just how vibration alone makes a difference, we did partial regression by keeping corrosion depth constant. The partial coefficient of determination RV∣C2R^2_{V|C}RV∣C2 tells us how much of the change in efficiency loss is because of vibration, once we take out the effect of corrosion. (c) Granger Causality Check Since vibration and efficiency change over time, we used Granger causality testing. This was to figure out if knowing past vibration values helps us guess future efficiency better than just knowing past efficiency. The null guess: H0: Vt does not Granger-cause Et ( 9 ) Where: H0 = null guess Vt = vibration amount at time t Et = pump efficiency at time t. If we reject at p < 0.05, it points to a time-based directional influence. 2.4 Justification of Exposure Duration and Representativeness The 200-hour test length was picked to observe the start and early growth of combined corrosion and vibration damage under controlled, highly salty settings. Offshore pumps run for thousands of hours. Yet, early damage, like the start of pits, changes in surface smoothness, and stronger vibration, often starts in the first few cycles in harsh marine places [ 14 ], [ 15 ]. In corrosion studies, brief, controlled immersion tests (100–500 hours) are often done to compare how materials react and to find basic corrosion measures before things settle down over a long time. This work didn't aim to copy full service lifespan, but to: Figure out how fast initial corrosion happens Measure how roughness causes hydraulic mess Set up degradation rates (α, β) with strong stats Adjust forecast models that can predict ahead The measured corrosion rates (mm/yr) were adjusted using ASTM G31 ways, letting time scale past the 200-hour mark. The time-series model was pushed past the experiment to guess damage paths up to 500 hours. This gives early ideas on how long-term efficiency changes. It's known that long-term things like corrosion fatigue crack increase, structural become weak, and big crack spread need long studies with cycle loading. These things are a later damage place past the corrosion-hydraulic link looked at here. So, the 200-hour length shows the early damage phase. This is key for judging when to fix things and find early problems in offshore setups. 3 Results 3.1 Pump Efficiency The measured initial and final efficiencies for the three materials, including their statistical significance, are summarized in Table 2 Table 2 Pump efficiency degradation with statistical significance Material Initial Efficiency (%) Final Efficiency (%) Efficiency Loss (%) p-value 316L SS 98.7 96.2 2.5 0.012 Bronze 98.5 94.1 4.4 0.008 Carbon Steel 98.2 83.7 14.5 < 0.001 Table 2 presents the efficiency losses observed in pumps constructed from various materials. Carbon steel pumps showed the largest decrease in efficiency (14.5%), with bronze and 316L SS pumps experiencing losses of 4.4% and 2.5%, respectively. All reported efficiency losses were statistically valid. The degradation of pump efficiency over 0–200 hours for all materials is illustrated in Fig. 3 below . 3.2 Corrosion Rates and SEM A summary of the corrosion rates and associated statistical significance for all materials is shown in Table 2 below. Table 3 Corrosion Rate Summary with Statistical Significance Material Mass Loss (mg) Corrosion Rate (mm/yr) p-value 316L SS 0.58 0.019 0.015 Bronze 3.22 0.109 0.006 Carbon Steel 6.25 0.212 < 0.001 Table 3 presents a summary of corrosion data for the tested materials. The results show that carbon steel experienced the most mass loss and highest corrosion rate. Bronze and 316L SS followed, and the variance between all materials was statistically different.. The surface morphology and corrosion damage progression for the three materials are presented in Fig. 4 below. Figure 4 shows scanning electron microscope (SEM) images of 316L stainless steel, bronze, and carbon steel after 200 hours in high-salt seawater. Measurements showed pitting, micro-cracking, and roughness (Ra). These findings indicate varying degrees of corrosion among the materials, matching the observed pump loss and vibration patterns. SEM was employed to measure pit density (pits/mm²), average pit depth (µm), and micro-crack length distribution (µm) to assess surface breakdown. Statistical analysis linked these values to changes in vibration amplitude and frequency, establishing a direct of material damage and loss. This method reveals the sensitivity of specific materials to imbalance and hydraulic disturbance caused by rust 3.2.1 Quantitative Surface Morphology Analysis We analyzed scanning electron microscope images with calibrated pixel-to-micron scaling to see the link between surface damage and loss of hydraulic performance. For each material, we chose five typical areas (500 µm × 500 µm) to measure pit density, pit area percentage, and crack length distribution. ( a ) Pit Density and Area Fraction Table 4 Surface Pitting Characteristics of Pump Materials Material Pit Density (pits/mm²) Pit Area Fraction (%) 316L SS 18 ± 4 0.6 ± 0.2 Bronze 74 ± 9 2.8 ± 0.5 Carbon Steel 156 ± 15 6.4 ± 0.8 Table 4 presents pit density and area fraction for various materials. Carbon steel displayed the highest degree of pitting, with bronze showing less, and 316L SS exhibiting the least. Carbon steel's pit density was about 8.7 times greater than that of 316L SS, suggesting considerable localized dissolving. The pit area fraction showed a strong relationship with the recorded corrosion rate (R² = 0.93). (b) Crack Length Distribution Micro-crack lengths were measured using line-segmentation analysis: Table 5 Micro-Cracking Characteristics of Pump Materials Material Mean Crack Length (µm) Max Crack Length (µm) 316L SS < 5 (rare) 9 Bronze 22 ± 6 41 Carbon Steel 58 ± 12 110 Table 5 shows the average and max crack lengths in different materials. Carbon steel had the most cracking, bronze had less, and 316L SS had the least. The longer cracks in carbon steel were statistically supported (p < 0.01), which agrees with past work on pit-to-crack transition under cyclic loading. (c) Roughness Evolution Rate The roughness growth rate was found by: dRₐ/dt = (Rₐ,final − Rₐ,initial) / Δt (10) where: * dRₐ/dt = roughness growth rate * Rₐ,final = final surface roughness * Rₐ,initial = initial surface roughness * Δt = total exposure time (200 hours) Equation (10) gives the average speed of surface roughness development during the experiment. Table 6 Surface Roughness Growth of Pump Materials Material Initial Ra (µm) Final Ra (µm) dRa/dt (µm/h) 316L SS 0.18 0.24 0.0003 Bronze 0.22 0.63 0.0020 Carbon Steel 0.25 1.35 0.0055 Table 6 shows the rate at which surface roughness (Ra) shifts over time for different materials. Carbon steel corrodes at the highest rate, bronze at a moderate rate, and 316L SS at the lowest. The rate of roughness increase for carbon steel is almost 18 times that of 316L SS. 3.3 Explanation of Corrosion–Vibration–Efficiency Coupling To move beyond statistical connection, the interaction between corrosion and vibration can be explained using damage mechanics at the micro-level, alongside theories of how dynamic systems respond. 3.3.1 Pit Shape and Stress Points Microscopic observation revealed a link between pit depth and material corrosion resistance. Carbon steel pits averaged 42–65 µm deep, with some cracks extending to 110 µm. Bronze pitting ranged from 18–30 µm, but 316L stainless steel showed shallower pits, measuring less than 10 µm. Corrosion pits concentrate stress. For circular pits, the stress concentration factor (Kt) can be approximated by: Kt ≈ 1 + 2 × (a / ρ) (11) where a is pit depth and ρ is the pit tip radius. Carbon steel's larger pit depth-to-radius ratio leads to an increased stress concentration factor (Kt). Under cyclic impeller loading, this promotes plastic deformation and initiates micro-cracks, increasing the impeller–shaft assembly's flexibility. 3.3.2 Stiffness Drop and Natural Frequency The way a rotating pump acts can be shown by: fn = (1 / 2π) × √(k / m) (12) Where: fn = natural frequency k = system stiffness m = effective mass Corrosion induces minor fractures and reduces component thickness, thereby diminishing the stiffness, k. Slight reductions in stiffness (3–8%) can shift the natural frequency toward the operational range (1× and 2× the shaft frequency), amplifying vibrations. Increased vibration at 1× and 2× shaft frequencies corresponds to reduced stiffness and nearness to resonance. Carbon steel, exhibiting the most advanced corrosion and pitting, showed the largest stiffness decrease. 3.3.3 Surface Texture and Water Forcing Corrosion not only alters a material's structure but also roughens its surface, which impacts fluid dynamics. The friction head loss can be approximated by: hf ∝ f(Re, k / D) (13) Where k ≈ Ra, and Ra is the average surface texture. In carbon steel, the increase in Ra from 0.25 µm to 1.35 µm increases the relative texture ratio k/D. This increase causes changes in the flow pattern, leading to increased turbulence and pressure fluctuations. These pressure fluctuations cause variations in force on the impeller over time: Fr(t) ∝ ΔP(t) × A (14) Larger ΔP(t) values resulting from increased turbulence lead to stronger forces, which in turn amplify vibrations.. 3.3.4 Combined Structural–Water Amplification The decline happens through two mechanisms: Structural: Pit-induced stiffness reduction leads to a shift in natural frequency, resulting in increased vibrations. Water: Increased roughness leads to greater turbulence, which causes unsteady radial force and increased vibration. The total vibration response is: Vtotal = Vstructural + Vhydraulic This dual action is consistent with the model: Eloss = αV + βC + γ (15) Where: β represents the direct hydraulic efficiency loss caused by friction from surface texture. α represents efficiency loss from vibrations, stemming from reduced stiffness and force issues. The larger values of α and β for carbon steel occur due to deeper pits, stiffness loss, and increased turbulence. 3.3.5 Connection to Recent Research Current research indicates that loss of stiffness can cause changes as systems begin to fail. Advanced vibration modeling suggests that early changes in dynamic components often arise from damage at very small scales, not merely from signal errors. These findings align with observations that corrosion damage alters surface stiffness and fluid flow. This, in turn, modifies measurable vibrations and hydraulic performance. Thus, the between corrosion, vibration, and It comes from the interaction of structures and fluids, not just statistical . Stiffness loss and texture changes at the material level are in agreement with the stability of surface films. Materials with steady films (316L) exhibit reduced pit formation and a slower rate of stiffness loss. Conversely, corrosion-prone materials (carbon steel) dissolve more readily, develop deeper pits, and show a faster increase in vibration. 3.3.6 Texture’s Effect To check that the surface texture affects the machine's work, a match was made between efficiency loss and texture measurements. Table 7 Correlation of Surface Degradation Parameters with Pump Efficiency Loss Parameter Correlation with Efficiency Loss (R²) Pit Density 0.89 Pit Area Fraction 0.92 Mean Crack Length 0.87 Final Ra 0.94 Table 7 shows how surface wear relates to pump efficiency loss. Surface roughness (Ra) has the strongest correlation (R² = 0.94), followed by pit area fraction, pit density, and average crack length, suggesting that surface roughness and pitting are important in efficiency reduction. Surface roughness (Ra) had the highest correlation with efficiency loss (R² = 0.94), supporting the earlier hydraulic roughness idea. Pit density and crack length also showed strong ties, confirming that structural stiffness decreases. These results suggest that efficiency loss isn't only about corrosion but changes with measurable shape changes. A strong correlation (R² = 0.91) exists between vibration magnitude and efficiency loss. We verified that pit density and crack length influence the dynamic response changes observed. This strengthens the idea that the link is because of how the parts act, and not random chance. 3.3.7 Structural Integrity Evolution and Failure Progression under Coupled Degradation Sections 4.3.1–4.3.6 explained how corrosion shape, vibration increase, and loss of hydraulic performace are mechanically linked. We can better describe the degradation of structural integrity by using continuum damage mechanics (a) Damage Variable Formulation Suppose a scalar damage variable D, ranging from 0 to 1, represents the degree of structural degradation: D = 0 indicates an intact structure. D = 1 indicates structural failure. Corrosion causes material loss and small cracks from pits, which reduces stiffness: keff = (1 – D) × k0 (16) Substituting this into the natural frequency formula yields: fn = (1 / 2π) × √((1 – D) × k0 / m) (17) This indicates that pit growth decreases modal stiffness, moving natural frequencies closer to excitation harmonics and increasing dynamic amplification. Carbon steel experiences a faster damage growth rate (Ḋ) due to its higher pit density and longer cracks. (b) Pit-to-Crack Transition and Fracture Mechanics Localized corrosion pits can start fatigue cracks. Failure will happen when pit depth hits a limit. Stress intensity factor is: KI = Y × σ × √(π a) ( 18 ) When KI nears the material’s fracture toughness (KIC), failure is probable. For carbon steel, deeper pits (42–65 µm) raise KI. This makes the shift from localized corrosion damage to structural crack spread faster under cyclic impeller loading. This fits what was in Thin-Walled Structures (2024). In the report, stiffness declined before crack instability. (c) Coupled Degradation Progression Stages The observed degradation follows three structural stages: Stage I – Surface Damage Initiation Pit nucleation Roughness growth Minor stiffness reduction Vibration amplification onset Stage II – Micro-Crack Propagation Pit coalescence Section thinning Measurable modal drift Rapid vibration growth Stage III – Structural Instability (Not reached in 200 h) Crack coalescence Large stiffness loss Nonlinear vibration response Impeller failure risk The 200-hour experiment captures Stage I and early Stage II behavior, critical for predictive maintenance before catastrophic instability. (d) Coupling with State-Space Degradation Model The equation for the latent degradation state is: Ht = Ht–1 + λ1 × Ct + λ2 × Vt (19) This equation can be seen as a simple way to show how structural damage builds up over time. Dt ∝ Ht (20) The PI-ARX and state-space approach gives a roundabout way to estimate how structural damage changes over time, linking statistical forecasts to ideas about how structures should stay in one piece. (e) Relation to Boundary Element Structural Modeling Engineering Analysis with Boundary Elements focuses on advanced structural integrity studies, specifically boundary-element fracture simulations for thin-walled systems weakened by corrosion. While the current study doesn't use a full BEM fracture simulation, the morphology parameters, such as pit depth, crack length, and roughness changes, which were measured experimentally, offer tangible inputs. These inputs could define structural models in the future. Thus, the framework serves as an experimental foundation for detailed structural fracture modeling. 3.4 Hybrid Predictive Model Performance The proposed PI-ARX model improved multi-step prediction stability compared to classical AR(1). Incorporating vibration and corrosion as exogenous inputs reduced forecast drift and improved generalization under cross-validation. Performance comparison : Table 8 Prediction Accuracy of Vibration Models Model RMSE (%) MAPE (%) AR(1) 0.45 0.62 PI-ARX 0.31 0.48 As shown in Table 8 above, there is a comparison of two models that predict pump vibration. PI-ARX performs better than the AR(1) model, considering that the former has a low RMSE of 0.31% and MAPE of 0.48%, thus making the predictions accurate. Using the proposed hybrid approach, the error was reduced by 31%, thus proving that the inclusion of physical degradation drivers improves the performance of the predictions 3.5 Statistical Validation of Regression and AR Models For generalization performance, the data was divided into 70% training and 30% testing sets. The regression residuals were normally distributed with homoscedastic variance relative to the predicted values. No significant outliers were found. Performance metrics of the autoregressive model were evaluated, showing that the autocorrelation function decays rapidly, and the partial autocorrelation function was primarily driven by lag 1, indicating an autoregressive process of order 1. No significant residual autocorrelation was found at lags beyond the first. To ensure the statistical robustness of the developed regression and PI-ARX models, statistical checks were performed. For example, the presence of multicollinearity was checked using the Variance Inflation Factor (VIF), where all VIF values were found to be below 2.0. The normality of the residuals was checked using the Shapiro-Wilk normality test at a significance level above 0.05. Similarly, the homoscedasticity condition was checked using the Breusch-Pagan test at a significance level above 0.10. Finally, the presence of autocorrelation was checked using the Durbin-Watson test at a level above 1.9. Additionally, 95% confidence intervals were estimated for the degradation coefficients α and β. Performance metrics of the regression model, including R², RMSE, and p-values, were found to be significant at p < 0.01, indicating that the predictors were significantly affecting the response variable for all materials. The low value of the regression model’s RMSE, less than 0.45%, indicated high accuracy in the predictions. Minimal issues of multicollinearity were found among the predictors, with a VIF less than 2. The normal distribution of the regression residuals was confirmed using the Shapiro-Wilk test at p > 0.05. Constant variance was also found using the Breusch-Pagan test at p > 0.1. The regression coefficients of the vibration response variable α and corrosion response variable β were found to be statistically significant at p < 0.01. Confidence intervals were found at 95% confidence levels, as shown in Table 1 . 3.6 Advanced Predictive Modeling Outcomes Deep learning and digital twin technologies improve the accuracy of multi-step predictions. Vibration analysis using convolutional neural networks (CNNs) was able to detect operational issues in pumps before a 10–15% efficiency drop was noted [ 9 ], [ 21 ]. Digital twin simulations that combined corrosion rates and vibration analysis provided accurate predictions of useful life, matching the trends of an AR(1) model while providing more in-depth information for maintenance scheduling purposes [ 22 ], [ 23 ]. The use of IoT sensors for continuous monitoring and model updates was made possible through the use of IoT technology. The above studies indicate that the use of experimental degradation data and artificial intelligence technologies improves the accuracy of predictive maintenance compared to other approaches. 3.7 Sensitivity and Causal Analysis Results 3.7.1 Sensitivity Analysis Standardized sensitivity indices Table 9 Sensitivity of Pump Efficiency to Vibration and Corrosion by Material Material S_V (Vibration) S_C (Corrosion) 316L SS 0.62 0.44 Bronze 0.55 0.39 Carbon Steel 0.74 0.63 Table 9 illustrates the sensitivity of the efficiency of the pump to vibration (S_V) and corrosion (S_C) for different materials. Carbon steel is the material which is most sensitive to vibration and corrosion, while 316L Stainless Steel is the material which is least sensitive. For the case of carbon steel material, the sensitivity to vibration is slightly higher than the sensitivity to corrosion depth.. 3.7.2 Partial Regression Results After accounting for corrosion depth, the partial coefficient of determination (R²) for vibration is: R²V|C² = 0.67 for carbon steel R²V|C² = 0.59 for bronze R²V|C² = 0.63 for 316L stainless steel These values indicate that vibration independently explains a substantial portion of efficiency loss variance beyond corrosion alone. 3.7.3 Granger Causality Granger causality testing (lag = 1) Table 10 Statistical Significance of Material Effects on Pump Performance Material F-statistic p-value 316L SS 5.84 0.019 Bronze 6.21 0.015 Carbon Steel 8.47 0.006 The Table 10 above presents the F-statistic and p-value for the effect of material on pump performance. All materials show statistically significant effects, with carbon steel having the strongest significance (highest F-statistic and lowest p-value) The null hypothesis that vibration does not Granger-cause efficiency loss was rejected for all materials (p < 0.05). This indicates that past vibration values significantly improve prediction of future efficiency, supporting directional influence rather than mere contemporaneous correlation. 3.8 Model Robustness Under Simulated Operating Variability In order to examine the robustness of the proposed predictive model under different offshore working conditions, a parametric perturbation analysis was performed using the physics-informed PI-ARX and state-space models. While experimental measurements were performed under constant flow rate (0.15 m³/h), salinity (35 ppt), and temperature (25°C), real working conditions of offshore pumps vary under fluctuating hydraulic and environmental conditions. To examine the stability of the proposed models, the following working conditions were simulated under realistic ranges: Table 11 Operating Conditions and Parameter Variation Ranges Parameter Baseline Variation Range Flow rate 0.15 m³/h ± 20% Salinity 35 ppt 30–45 ppt Temperature 25°C 20–40°C Table 11 above indicates the baseline conditions for the pump, specifically the flow rate, salinity, and temperature, and the range of variation for the respective parameters that was used in the experiment/analysis. The sensitivity of the corrosion rate to temperature and salinity was represented by the Arrhenius-type approximation, given by: CR(T) ∝ exp(-Ea / RT) (21) The influence of hydraulic roughness was also accounted for by the Reynolds number dependency of the friction factor. 3.8.1 Flow Rate Variation A ± 20% flow variation resulted in: < 6% change in predicted vibration amplitude < 0.12% increase in RMSE for PI-ARX No violation of parameter stability constraints (0 < φ < 1) The hybrid PI-ARX model maintained RMSE < 0.52% under flow variation. 3.8.2 Salinity Variation Increasing salinity from 35 to 45 ppt increased predicted corrosion rate by: + 11% (316L) + 16% (Bronze) + 21% (Carbon Steel) However, model prediction error increased marginally (< 0.15%), indicating stable extrapolation when corrosion depth is treated as an exogenous driver. 3.8.3 Temperature Sensitivity Increasing the temperature to 40°C enhances the rate of corrosion kinetics but does not affect the stability of the degradation curve, as the model accounts for the depth of corrosion. This is achieved through the state-space model H_t = H_{t-1} + λ₁C_t + λ₂V_t (22) where the degradation accumulates proportionally. 3.8.4 Robustness Summary Table 12 Impact of Operating Conditions on Model Prediction Error Condition RMSE (%) ΔRMSE Baseline 0.31 — Flow ± 20% 0.52 + 0.21 Salinity 45 ppt 0.46 + 0.15 Temperature 40°C 0.49 + 0.18 Table 12 displays the effects of flow, salinity, and temperature changes on the model’s prediction accuracy, where the root mean square error (RMSE) increases in all conditions, with the greatest increase in the case of the ± 20% flow variation, implying that the flow has the greatest influence on the error in the model’s predictions. The model's robustness is evident by the fact that the error, represented by the RMSE, is always below 0.55% for all conditions, suggesting that the inclusion of the physical degradation factors, such as corrosion depth and vibration amplitude, improves the generalization capability of the model compared to the autoregressive models. 4 Discussion This paper proposes a framework for quantifying corrosion morphology, vibration, and hydraulic efficiency loss for offshore-based centrifugal pumps under controlled conditions of high salinity. As opposed to previous studies, where the focus was largely on the quantification of corrosion and vibration individually, this paper proposes a direct quantitative link between surface degradation resulting from corrosion and efficiency loss resulting from vibration, as validated through regression models as well as autoregressive models. 4.1 Material-Dependent Degradation and Efficiency Loss The experimental results indicate clear trends for different materials. It was found that, as expected, the efficiency loss was maximum for carbon steel, declining by 14.5% (p < 0.001) over 200 hours of operation. Bronze showed an efficiency loss of 4.4% (p = 0.008), while 316L stainless steel showed the minimum efficiency loss of 2.5% (p = 0.012). Similarly, the corresponding corrosion rates for these materials were 0.212 mm/yr, 0.109 mm/yr, and 0.019 mm/yr, respectively. As validated by SEM, the surface degradation for these materials was as follows: the surface degradation for carbon steel showed an increase in Ra from 0.25 to 1.35 µm, indicating significant surface degradation resulting from pitting and micro-cracking. Bronze showed moderate surface degradation, while 316L SS showed minimum surface degradation. The integration of these quantified surface degradation metrics—pit density, crack length, and evolution of surface roughness—confirms that the rate of degradation directly correlates to the rate of efficiency loss. Similarly, for carbon steel, which showed the maximum efficiency loss, the pit density was very high, i.e., 156 pits/mm², along with the maximum rate of surface roughness evolution, i.e., 0.0055 µm/h, resulting in the maximum value of the vibration coefficient, i.e., 0.71. The experimental results are in conformity with previous offshore-based corrosion studies. These findings emphasize the significant role of material selection for efficient pump life. 4.1.1 Electrochemical Behavior and Protective Film Stability in Saline Environments The trends observed with respect to material degradation can be further understood by analyzing electrochemical properties and film stability in chloride-rich seawater. 316L Stainless Steel 316L stainless steel has 16–18% Cr and 2–3% Mo. The Cr and Mo contents enable the formation of a stable Cr2O3 film. In seawater with 35 ppt salinity, chloride ions can penetrate the film. However, molybdenum improves resistance against pitting corrosion by stabilizing the film and accelerating passivation. The low corrosion rate (0.019 mm/yr) and low depth (< 10 µm) observed from the SEM micrograph indicate that there are fewer instances of breakdown and passivation. The electrochemical stability can be related to: Low reduction in stiffness Low increase in roughness Low amplification of vibrations Low percentage reduction in efficiency (2.5%) The degradation mechanism observed with 316L stainless steel can thus be related to slight roughening on the surface, as opposed to electrochemical corrosion. Bronze Bronze (Cu-Sn alloy) does not use chromium passivation. Instead, it uses copper oxide (Cu2O/CuO) film formation. In chloride-rich seawater, bronze is prone to: Selective dealloying (dezincification if zinc is used) Porous corrosion product formation Localized galvanic microcells between α and δ phases Bronze's corrosion rate of 0.109 mm/yr and pit depth of 18–30 µm classify it as having an oxide film that is less stable than Cr2O3 of 316L but still partially protective. Porous corrosion product formation may be removed by flow-induced shear stress, leading to accelerated roughness formation. This is consistent with the measured vibration coefficient of 0.55 and efficiency loss of 4.4%. Carbon Steel Carbon steel does not use a stable passive film in chloride-rich environments. It is therefore prone to active anodic dissolution reactions: Fe → Fe2 + + 2e- (23) In oxygen-rich environments like seawater, it is prone to: O2 + 2H2O + 4e- → 4OH- (24) Iron oxides FeOOH and Fe2O3 are formed and are mechanically unstable. Key characteristics: Lack of self-healing passive film Rapid initiation of pit formation Rapid growth of pits due to the presence of chlorides Increased rate of electrochemical corrosion current density The empirical results reveal that the rate of corrosion is 0.212 mm/year, and the presence of deep pits is between 42 and 65 µm, with micro-cracks extending up to 110 µm, thereby indicating the presence of aggressive active corrosion. Unlike in the case of 316L, where the stability of the film restricts the growth of the pit, in the case of carbon steel, the process of electrochemical corrosion is continuous, leading to: Rapid degradation of stiffness Amplification of turbulence Peak vibration sensitivity (α = 0.71) Maximum efficiency loss (14.5%) Table 13 Electrochemical Characteristics of Tested Materials in 35 ppt Seawater Material Passive Film Type Chloride Resistance Corrosion Mechanism Film Stability Under Flow 316L SS Cr₂O₃ (Mo-stabilized) High Localized pitting with repassivation Stable Bronze Cu₂O / CuO Moderate Selective dissolution, porous oxide Partially stable Carbon Steel Iron oxides (FeOOH) Low Active anodic dissolution Unstable / spalling Table 13 indicates the electrochemical characteristics of the exposed materials in 35 ppt seawater. It is evident that the 316L stainless steel has a stable Mo-stabilized Cr2O3 film, which is resistant to corrosion by chlorides; bronze has moderate resistance with partially stable copper oxides; and carbon steel is the most vulnerable to degradation due to the instabilities in the iron oxide films. The differences in degradation for the exposed materials can be explained by the differences in the electrochemical characteristics and the stabilities of the films formed. For example, the 316L stainless steel has a slow rate of pit initiation compared to carbon steel, where the rate is rapid due to the high salinity conditions [ 9 ]. Bronze has intermediate properties, where copper has a positive influence in reducing the rate of degradation. 4.2 Corrosion–Vibration Coupling The results from the regression analysis also reveal high coefficients of determination, where R² ≈ 0.91. To address the concern that correlation does not imply causation, additional analyses were conducted to validate the results. From the sensitivity index, it is evident that vibration contributes to 55–74% of the normalized efficiency loss response for the materials considered. Furthermore, the results from the partial regression analysis reveal that vibration independently contributes significantly to the efficiency loss, even after accounting for the effects of corrosion depth. Moreover, the results from the Granger causality test reveal that vibration is the leading cause of the loss in hydraulic efficiency, where the effects of vibration precede the loss in efficiency, indicating causation at a statistical significance level of p < 0.05. The effects of progressive corrosion and vibration-induced fatigue can significantly influence the structural integrity of the system, especially in the region where the pitting is concentrated, as illustrated in Fig. 9. These results can be used to develop more effective predictive maintenance strategies, which is in accordance with the reported degradation mechanisms in the Engineering Analysis with Boundary Elements 174, 106157 (2025) and Thin-Walled Structures 205, Part B, 112370 (2024). The results obtained in the present study validate the assumption that vibration is not only correlated with the degradation mechanisms but also plays an active role in the loss in hydraulic efficiency through the mechanisms of stiffness degradation and turbulence amplification, as discussed in Section 4.3 . 4.3 Predictive Modeling and Remaining Useful Life AR(1) models were found effective in characterizing the time series of efficiency for individual materials. Moreover, the root mean square error (RMSE) was found to be below 0.45%, and multi-step predictions were found to be stable with a mean absolute percentage error (MAPE) below 0.62%. By integrating it with regression analysis, it is possible to estimate the longevity of individual components and schedule maintenance. For instance, it is found that carbon steel will lose more than 15% of its efficiency after 250–260 hours of operation, while 316L stainless steel will maintain its efficiency at more than 95% after 500 hours. It is found that the validation of the model is reliable with variance inflation factors (VIF) below 2.0, Shapiro-Wilk normality tests with p-values higher than 0.05, and Breusch-Pagan normality tests with p-values higher than 0.1. Moreover, it is found that the values of α and β were reliable with statistical significance at p < 0.01 with 95% confidence intervals (Table 1 ). It is found that integrating AI models with digital twin simulations enhances the predictive maintenance paradigm. It is possible to predict anomalies, perform multi-step predictions, and adjust operations in real-time. It is beyond the conventional SEM model of corrosion-vibration coupling established experimentally and is beyond conventional statistical models [ 9 ], [ 19 ], [ 21 ], [ 22 ], [ 23 ]. It is possible to use it for decision-making of offshore centrifugal pump operations in high salinity environments. Integration of physically constrained exogenous variables transforms the predictive structure from a statistical estimator to a degradation model with a mix of statistical and physical components. Hybrid physics-informed vibration models similar to those presented in this paper, as reported in the Journal of Vibration and Control (2024), have demonstrated improved robustness to operational variability. The predictive models were trained under fixed flow rate and salinity conditions. Although an RMSE of less than 0.45% suggests a high predictive accuracy, it is also necessary to test the robustness of the model under varying operating conditions, for example, when the salinity is higher or lower, or when temperatures fluctuate or when different pump speeds are used. to broader operational envelopes to ensure applicability in offshore environments. 4.4 Early-Stage vs Long-Term Degradation Mechanisms The degradation of offshore centrifugal pumps occurs through a series of distinct and progressive stages. The current study corresponds to Stage I of this degradation process, as characterized by the initiation of corrosion, pit nucleation, increased roughness, and amplified vibration resulting from hydrodynamic disturbances. The degradation coefficients calculated through the experimental procedure (\(\alpha\), \(\beta\), \(\lambda_1\), \(\lambda_2\)) can be viewed as a representation of damage progression in the structural model. Unlike other diagnostic approaches that rely solely upon vibration signals for damage progression, the current approach correlates morphology parameters with stiffness degradation and fracture precursor conditions. This aligns well with the structural integrity progression approaches adopted in recent thin-walled structural failure analysis. The degradation mechanisms of corrosion fatigue, pit-crack transition, and structural fracture occur over a long time period and require: Interaction of cyclic stresses over a long period of time Significant pit-to-crack transition Damage accumulation in the microstructure These degradation mechanisms occur over a time period in excess of 200 hours and are highly dependent upon fluctuating loading conditions. The current study was designed without the presence of fluctuating loading conditions in order to isolate corrosion-vibration coupling. The early stages of degradation are of significant interest. The modeling of marine corrosion, as discussed in Melchers [ 14 ], suggests that the early stages of corrosion play an important role in the progression of damage. Small increases in roughness can lead to a significant enhancement in turbulence intensity and radial impeller loading, thereby accelerating the progression of fatigue damage in the future. The experimental procedure adopted in the current study provides a mechanistic insight into the triggering phase of degradation and can be useful in developing predictive maintenance approaches prior to the initiation of structural damage. 4.5 Practical Implications for Offshore Pump Maintenance The research also reveals several implications for improving the maintenance of offshore pumping equipment. In a high-salinity condition, the material of choice is 316L stainless steel, which shows negligible efficiency loss and superior corrosion resistance. Bronze is a cheaper material but also shows a slight efficiency loss. The combination of vibration and corrosion monitoring with computer models is also a useful tool for creating a more effective maintenance regime, which would increase the life of the equipment and minimize operational costs. The proposed method is also compatible with the digital twin concept. 4.6 Integration into Real-Time Monitoring and Digital Twin Platforms To implement this proposed corrosion-vibration-efficiency model in an offshore environment, integration with real-time systems and digital twin technologies would be necessary. This proposed PI-ARX/state-space model for degradation would be compatible with current Industrial Internet of Things (IIoT) systems as well as supervisory control and data acquisition (SCADA) systems. 4.6.1 System Architecture for Real-Time Deployment A concrete implementation will involve four hierarchical layers: Layer 1 – Data Acquisition Accelerometer-based vibration sensors (RMS, spectral components) Pressure and flow sensors Temperature and salinity probes Optional corrosion sensors (electrical resistance or linear polarization resistance sensors) Data will be streamed at 1 to 10 Hz to edge devices or offshore control rooms. Layer 2 – Feature Extraction and Preprocessing On the edge device, the following operations will be performed: Extraction of the RMS value of the vibration signal Tracking of 1x and 2x shaft frequencies Estimation of hydraulic efficiency using flow-head curves Estimation of corrosion depth using corrosion rate models: Ct = Ct–1 + CRt * Δt (25) Where the corrosion rate CRt may be scaled by temperature and salinity using an Arrhenius relation. Layer 3 – Physics-Informed Degradation Engine On the deployed digital twin, the PI-ARX model will be run in real time: Et = ϕ * Et–1 + θ1 * Vt + θ2 * Ct (26) While the degradation process will be updated in parallel by: Ht = Ht–1 + λ1 * Ct + λ2 * Vt (27) This architecture will enable: Real-time forecasting of efficiency Ongoing updates of the health index Estimation of remaining useful life (RUL) The coefficients α, β, λ1, and λ2, derived from experiments, will be used as baselines and may be updated adaptively using recursive least squares or Bayesian methods as data become available. Layer 4 – Decision Support and Maintenance Optimization Maintenance thresholds are established based on the following parameters: Efficiency reduction greater than 10% Health index value Ht greater than calibrated damage threshold Rate of change of health index value Ḣt greater than predefined slope Vibration levels beyond ISO alarm limits On threshold violation, the digital twin undertakes: Inspection alerts Lubrication adjustments Load redistribution Planned maintenance This brings us from a monitoring framework to a predictive maintenance optimization framework. 4.6.2 Digital Twin Synchronization Strategy The digital twin acts as a virtual model that is updated in real time. The model can predict the future performance of the pump system. The following are steps that are taken by the digital twin: ( a ) The physical parameters are used to update the degradation model. ( b ) The digital twin can predict future efficiency using a prediction horizon (e.g., 100–500 hours). ( c ) Scenario-based predictions can be made for parameters such as: Increased salinity Flow rate change Temperature increase Load change As corrosion depth and vibration are explicitly modeled as physical parameters, it is possible for the digital twin to remain interpretable under changing environmental conditions. 4.6.3 Advantages Over Vibration-Only Monitoring Systems Typically, conventional vibration-based monitoring approaches tend to detect anomalies only after dynamic deviations become apparent. In this regard, the proposed approach offers earlier warning capabilities as a result of the following reasons: There is a gradual build-up of corrosion depth before a major vibration spike is noticed. There is a gradual build-up of surface roughness that acts as a precursor to impending hydraulic disturbance. There is a gradual build-up of damage state Ht. 4.6.4 Offshore Implementation Considerations Implementation of the proposed framework for offshore structures would involve: Edge computing modules located in proximity to pump skids Cloud-based twin synchronization for analytics purposes Integration with asset integrity management systems Integration with maintenance management systems (CMMS) The proposed approach is computationally efficient (ARX/state-space model), which makes it suitable for real-time implementation without requiring high-performance computing facilities. 4.7 Limitations and Future Directions Though the experiment was well designed and executed, certain limitations and areas of improvement are noted. The experiment was carried out under constant flow rates, temperatures, and salinity. This was done in order to ensure that the material degradation was isolated. It has been noted that in offshore pumps, the hydraulic and temperature conditions vary. This could affect the corrosion rates and turbulence. The use of Ra as a surface roughness model is a rough estimation of the hydraulic effects. It fails to take into account other factors such as pits and crevices. The use of a three-dimensional model for surface roughness could be included in future experiments. The current setup fails to take into account other factors that could be included in offshore pumps. These factors could be changes in conditions such as flow rates, temperatures, and hydraulic conditions. The current setup could be validated for use in offshore pumps. This could be done by conducting experiments on actual pumps. The factors that could be taken into account are biofouling and other debris. This could be done in order to ensure that the current setup could be adapted for use in offshore pumps. Though the experiment was carried out under constant flow rates, temperatures, and salinity, robustness analysis via parametric perturbation was performed. It was noted that the PI-ARX framework was able to maintain its stability. 4.8 Summary of Findings The study proves that in environments of high salt content, carbon steel corrodes at the quickest rate, bronze corrodes at a moderate rate, and 316L stainless steel maintains its performance. The research combines SEM surface analysis, vibration analysis, regression analysis, and autoregressive forecasting in a cohesive model. The model provides a means of predicting maintenance times and performance in offshore centrifugal pumps. The quantification of the relationship between corrosion patterns and efficiency degradation via vibration analysis will improve diagnosis and planning for offshore pump systems. 5 Conclusions Our findings suggest that 316L stainless steel has the maximum corrosion resistance at high saline conditions. Bronze shows fair performance, while carbon steel has maximum degradation. The physics-informed PI-ARX degradation model, which incorporates corrosion depth and vibration amplitude as exogenous physical drivers, improves the stability of the predictions significantly compared to traditional autoregressive models. State-space degradation model formulation provides the capability to predict structured remaining useful life beyond the test duration. Pumps made of bronze require less maintenance. Pumps constructed from 316L stainless steel have the capability to run for extended periods (more than 500 hours) without any significant degradation in performance. Material selection and monitoring of vibration and corrosion levels are important factors that help in reducing downtime and keeping maintenance costs low. This paper establishes a link among corrosion, vibration, and pump performance using experimental data, scanning electron microscopy, and forecast-based approaches. Numerical validation of the proposed model was performed by conducting accuracy checks. Even though this test interval of 200 hours mainly focuses on early-stage corrosion-vibration coupling, mechanistically validated degradation coefficients can be extended through normalized corrosion rates and autoregressive forecasting. The long-term degradation phenomena of corrosion fatigue and macro-crack growth require extended cyclic testing and represent the next step in the investigation. The early degradation trends remain an essential factor for prediction and maintenance because intervention occurs before failure. The proposed framework for a hybrid model has been found to be predictable and stable under simulated changes in flow rates, salinity, and temperatures. This indicates its potential for use in realistic offshore environments. The degradation coefficients derived through the experiments can be related to a structural damage mechanics model. This will allow for the integration of a fracture-based boundary element and finite element model of failure in the future. The proposed physics-based degradation model can be easily implemented in an offshore environment through the use of a digital twin. The proposed framework for a hybrid model can be easily implemented in IoT-based digital twin systems for offshore environments. Abbreviations 316L SS 316L Stainless Steel CR Corrosion Rate SEM Scanning Electron Microscopy Ra Arithmetic Mean Surface Roughness V Vibration Amplitude C Corrosion Depth hf Frictional Head Loss k Roughness Height (used in Darcy–Weisbach) D Density A Exposed Surface Area T Exposure Time W Mass Loss E_loss Efficiency Loss α, β,γ Regression Coefficients (Vibration, Corrosion, Intercept) R² Coefficient of Determination RMSE Root Mean Square Error MAPE Mean Absolute Percentage Error AR(1) First–Order Autoregressive Model φ Autoregressive Coefficient ε_t Residual / Error Term AI Artificial Intelligence ML Machine Learning IoT Internet of Things CNN Convolutional Neural Network Re Reynolds Number VIF Variance Inflation Factor ACF Autocorrelation Function PACF Partial Autocorrelation Function ASTM G31 Standard Guide for Laboratory Immersion Corrosion Testing Declarations Ethical Approval This study did not involve human participants, animals, or biological materials. Therefore, ethical approval was not required. Consent to Participate Not applicable. Consent to Publish The author consents to publication of this manuscript. Conflict of Interest The author declares no conflict of interest. Authors’ Information Independent researcher with no institutional affiliation researcher with no institutional affiliation. Funding Not applicable. Authors’ Contributions Nsini I. Udo — Conceptualization; Methodology; Simulation; Formal analysis; Writing – original draft; Writing – review & editing. Data Availability Data supporting the findings of this study are available from the corresponding author upon reasonable request. Acknowledgements Thanks to the offshore maintenance teams for their support. Data and analysis code are available from the corresponding author upon reasonable request. References Al Obaidi A, Sulaiman SA, Hussein L (2016) Effects of seawater salinity on pump efficiency and material degradation. 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Mech Syst Signal Process 129:420–432 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9445735","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624783537,"identity":"fc9522e0-027d-4a97-8e08-8069c1e75601","order_by":0,"name":"Nsini Ignatius Udo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYFACxgaGBDAjgfEBA8MB0rQwGxCpBQ4S2CSI0mLOf7jtwYMauzz+9uRn1Tw1d+T4GZgfPrqBR4vljMR2g4RjycUSZ56Z3eY59sxYsoHN2DgHjxaDG4xtEokNzIkNNxKAWtgOJ244wMMmjVfL+YMgLfWJ82+kfyvm+UeMlgOJIC1AlTdyzJh524jRcgOoJeHY8cSNZ94US87tO2ws2UzIL+ePP5P8UVOdOO94+sYPb74dluNnb374GJ8WFMDEAyKZiVUOAow/SFE9CkbBKBgFIwYAAADIU9rzODz0AAAAAElFTkSuQmCC","orcid":"","institution":"Independent researcher","correspondingAuthor":true,"prefix":"","firstName":"Nsini","middleName":"Ignatius","lastName":"Udo","suffix":""}],"badges":[],"createdAt":"2026-04-17 07:47:39","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9445735/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9445735/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107485813,"identity":"27695a15-2762-4cdd-b741-9018373a6da5","added_by":"auto","created_at":"2026-04-22 02:36:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":94130,"visible":true,"origin":"","legend":"\u003cp\u003eLegend not included with this version.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9445735/v1/326f443efacabd5fd58b4a0f.png"},{"id":107293737,"identity":"92734b74-ffa6-4319-8b3f-c8207e09a6d3","added_by":"auto","created_at":"2026-04-20 06:19:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":83773,"visible":true,"origin":"","legend":"\u003cp\u003eLegend not included with this version.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9445735/v1/a5e8196bb1891df30f168f44.png"},{"id":107293738,"identity":"79087ed4-21ff-4af7-93d4-15823fadcbd4","added_by":"auto","created_at":"2026-04-20 06:19:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":43006,"visible":true,"origin":"","legend":"\u003cp\u003eLegend not included with this version.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9445735/v1/e86d10d96dd5040c0b6ba794.png"},{"id":107293740,"identity":"dec3885e-35db-4481-a0b4-f05a74aac062","added_by":"auto","created_at":"2026-04-20 06:19:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":370677,"visible":true,"origin":"","legend":"\u003cp\u003eLegend not included with this version.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9445735/v1/1e68816ddc24c2aecd7aace8.png"},{"id":107485781,"identity":"ff854766-9616-47ea-ab0c-27be83de2b54","added_by":"auto","created_at":"2026-04-22 02:36:09","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":68554,"visible":true,"origin":"","legend":"\u003cp\u003eLegend not included with this version.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-9445735/v1/52b34623b58e2cb8fcab49e1.png"},{"id":107488504,"identity":"8ca340f8-f140-4d05-803e-9c3dc7cfffe9","added_by":"auto","created_at":"2026-04-22 02:44:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1656797,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9445735/v1/385b213c-8ce3-4e57-85a5-258d22db47f6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eManuscript title: Predictive Maintenance and Performance Modeling of Offshore Centrifugal Pumps under High‑Salinity Conditions\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn the oil and gas industry, especially offshore, centrifugal pumps are critical for moving fluids, like seawater. But out at sea, these pumps get hammered by salty water that eats away at their parts and messes with how well they work. Saltwater corrosion, erosion, rough surfaces, and vibrations all team up to make things worse [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The salt kicks off chemical reactions that cause pits, thinning, and damage, which messes up the flow and makes the pump unstable [\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eLots of studies have looked at how different metals corrode in seawater. They've measured how much stuff is lost, what the pits look like, and how the metals act when exposed to salt, focusing on stainless steel, bronze, and regular steel [\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. For example, Kumar and Singh [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] showed that leaving regular steel in seawater for a long time makes it corrode faster, causing pits and rough surfaces. This weakens the steel and affects its performance. So, it's important to keep an eye on these pumps offshore. Marine corrosion models also show that things don't always break down in a straight line, as it depends on how harsh the environment is and how long the pump is exposed [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Still, most studies only check how much material is lost and don't link surface damage to pump vibrations or how the pump performs.\u003c/p\u003e \u003cp\u003eOn another note, people are getting better at using vibration to check on machines. They look at things like sound waves and patterns to spot problems like imbalance, bad alignment, or broken bearings in pumps [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Usually, they just use these signals as clues, but they don't tie them back to the actual corrosion or surface damage. So, they might see something's wrong without knowing why.\u003c/p\u003e \u003cp\u003eThese days, there are new ways to predict when things will break down using data and machine learning [\u003cspan additionalcitationids=\"CR14 CR15 CR16\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Things like neural networks can pick up on early signs of wear and tear from vibration and other data [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. They're good at spotting small changes, but they mostly look at signals. Also, the internet of things and digital twins allow you to watch pumps in real-time [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Even so, most of these models don't use measurements of corrosion depth or surface damage to guess how well the pump will perform.\u003c/p\u003e \u003cp\u003eWe know a bit about how corrosion and fatigue affect machines [\u003cspan additionalcitationids=\"CR22\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], but there aren't many studies that measure how corrosion, vibration, and pump performance are connected when pumps are in salty water all the time. Because we don't have this info, it's hard to make good predictions and decide how to maintain pumps offshore.\u003c/p\u003e \u003cp\u003eSo, we did a lab test on three common pump materials\u0026mdash;316L stainless steel, bronze, and regular steel\u0026mdash;and exposed them to salty conditions. We watched the corrosion happen using standard tests [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] and checked the surfaces with a microscope. At the same time, we measured the vibration and how well the pumps worked to see how they changed over time.\u003c/p\u003e \u003cp\u003eBased on our tests, we built some models that use measurements of corrosion depth and surface changes to predict how the pump will perform. Instead of just looking at signals, we included corrosion info and vibration data to predict performance loss. This helps us figure out how fast each material breaks down and how long it will last in certain conditions.\u003c/p\u003e \u003cp\u003eBy connecting surface damage to vibration and performance, we can see exactly how corrosion affects pumps. This gives us solid info for picking the right materials, planning for the long haul, and maintaining pumps in a smart way offshore.\u003c/p\u003e \u003cp\u003eHere's how the rest of the paper is set up: Section \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003e3\u003c/span\u003e explains our test setup, like the salt water loop, materials, and equipment. Section \u003cspan refid=\"Sec36\" class=\"InternalRef\"\u003e4\u003c/span\u003e covers how we measured corrosion and built our models. Section \u003cspan refid=\"Sec51\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the trends we found for performance loss, corrosion, vibration, and model performance. Section 6 talks about the reasons behind these trends and what they mean for maintenance. Section 7 wraps up with our main findings and what we want to look at next.\u003c/p\u003e \u003cp\u003eLots of folks have looked at corrosion and vibration in machines before. But the most recent vibration-based degradation researches [Mechanical Systems and Signal Processing 239, 113326 (2025)] usually concentrate on signals and don't measure the surface corrosion. Our study is different as we measure pit density, crack growth, and surface roughness while monitoring vibration and performance for different pump materials. This gives us a clear, practical way to predict what will happen, which goes beyond just looking at signals..\u003c/p\u003e"},{"header":"2 Methods/ Experimental Section","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1 Experimental Setup\u003c/h2\u003e\n\u003cp\u003eA 2-kW centrifugal pump was powered by an electric motor, in a seawater loop to simulate offshore settings. The setup included:\u003c/p\u003e\n\u003cp\u003e* Flowmeters (\u0026plusmn;\u0026thinsp;1% accuracy)\u003c/p\u003e\n\u003cp\u003e* Pressure gauges (\u0026plusmn;\u0026thinsp;0.5% accuracy)\u003c/p\u003e\n\u003cp\u003e* Accelerometer-based vibration sensors (\u0026plusmn;\u0026thinsp;0.2% accuracy)\u003c/p\u003e\n\u003cp\u003eMaterial samples (20 \u0026times; 20 \u0026times; 3 mm) of 316L stainless steel, bronze, and carbon steel were placed along the pump's pipes to watch for local corrosion.\u003c/p\u003e\n\u003cp\u003eEnvironmental conditions were closely regulated:\u003c/p\u003e\n\u003cp\u003e* Seawater temperature: 25\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026deg;C\u003c/p\u003e\n\u003cp\u003e* Salinity: 35\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5 ppt\u003c/p\u003e\n\u003cp\u003e* Flow rate: 0.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01 m\u0026sup3;/h, kept steady with a bypass\u003c/p\u003e\n\u003cp\u003eDuring the tests, all settings were carefully kept constant to focus on only material wear. By keeping the flow rate, temperature, and salinity steady, we tried to isolate corrosion\u0026ndash;vibration coupling rather than hydrodynamic or thermal differences. The aim was to have any material degradation truly reflect the materials themselves, and not other outside factors. All readings were taken continuously at 1 Hz for 200 hours to get reliable corrosion and vibration information..\u003c/p\u003e\n\u003cp\u003eThe 200-hour immersion and operational testing period, although limited relative to full-service lifetimes, was selected based on accelerated corrosion protocols and prior studies [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e] to capture early-stage pit formation and micro-cracking, which are critical indicators of long-term degradation. While full corrosion-fatigue evolution requires longer exposure, this period provides representative trends sufficient for developing predictive models linking surface damage to pump performance\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2 Material Analysis\u003c/h2\u003e\n\u003cp\u003eCorrosion rates were measured by the mass-loss method, as per ASTM G31 [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e]:\u003c/p\u003e\n\u003cp\u003eCR (mm/yr) = (87.6 \u0026times; W)/(D \u0026times; A \u0026times; T) (1)\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003eCR is the corrosion rate (mm/year)\u003c/p\u003e\n\u003cp\u003eW is the mass loss (mg)\u003c/p\u003e\n\u003cp\u003eD is the density (g/cm\u0026sup3;)\u003c/p\u003e\n\u003cp\u003eA is the exposed surface area (cm\u0026sup2;)\u003c/p\u003e\n\u003cp\u003eT is the exposure time (hours)\u003c/p\u003e\n\u003cp\u003e87.6 is a unit conversion constant\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eSurface details were examined after exposure with SEM to measure pitting, micro-cracks, and roughness changes.\u003c/p\u003e\n\u003cp\u003eQuantitative image processing was performed using calibrated SEM images. Pit density (pits/mm\u0026sup2;), pit area fraction (% surface coverage), and crack length distribution were measured using threshold segmentation and edge-detection algorithms. Five independent regions per sample were analyzed to ensure statistical robustness. Surface roughness evolution rate (dRa/dt) was computed from measured initial and final Ra values.\u003c/p\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e2.3 Physics-Informed Hybrid Predictive Modeling Framework\u003c/h2\u003e\n\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n\u003ch2\u003e2.3.1 Regression Model\u003c/h2\u003e\n\u003cp\u003ePump efficiency loss, denoted as E_loss, can be related to vibration amplitude, V, and corrosion depth, C, as shown in studies [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e]:\u003c/p\u003e\n\u003cp\u003eE_loss\u0026thinsp;=\u0026thinsp;\u0026alpha; * V\u0026thinsp;+\u0026thinsp;\u0026beta; * C\u0026thinsp;+\u0026thinsp;\u0026gamma;\u0026emsp;\u0026emsp; (2)\u003c/p\u003e\n\u003cp\u003eHere, \u0026alpha;, \u0026beta;, and \u0026gamma; are regression coefficients that depend on the material. \u0026alpha; indicates the impact of vibration on efficiency loss, while \u0026beta;details the impact of corrosion depth on efficiency loss. \u0026gamma; is the intercept term, representing the baseline loss unrelated to vibration or corrosion. These coefficients are degradation numbers specific to each material, showing how different pump materials react to corrosion and vibration.\u003c/p\u003e\n\u003cp\u003eApart from regression analysis, surface roughness (Ra) caused by corrosion is one reason for the efficiency loss. Frictional head losses were found using the Darcy\u0026ndash;Weisbach method:\u003c/p\u003e\n\u003cp\u003ehf \u0026prop; f(Re, k/D) ( 3 )\u003c/p\u003e\n\u003cp\u003ewhere k\u0026thinsp;\u0026asymp;\u0026thinsp;Ra for corroded surfaces.In this work, the arithmetic mean surface roughness (Ra), derived from SEM surface measures, was used as a roughness estimate for determining k. Existing works suggest Ra works well for defining the sand-grain roughness affecting near-wall turbulence and friction factor changes on corroded metal surfaces. Though, seawater corrosion tends to produce irregular characteristics like pits and micro-crevices, which a single roughness value might not fully capture. To get accurate Ra values, roughness data were gathered from multiple surface locations and averaged. SEM was employed to assess the presence and distribution of corrosion traits. Here, k\u0026thinsp;\u0026asymp;\u0026thinsp;Ra is employed as a roughness parameter appropriate for interpreting and comparing models across materials, instead of an accurate representation of corroded surfaces.\u003c/p\u003e\n\u003cp\u003eThis approach offers a method for integrating corrosion depth and vibration amplitude into the regression model, as both influence hydraulic losses and impeller radial force imbalance. This strengthens the model's physical basis beyond simple statistical fitting.\u003c/p\u003e\n\u003cp\u003eAs well as regression and autoregressive models, we used a hybrid physics-informed regression method that includes corrosion measures and vibration traits as outside variables. This boosts predictive power compared to standard time-series models [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e]. While deep learning approaches like CNNs show promise, the hybrid method gives physically understandable coefficients for material-related degradation, which is useful for real offshore maintenance work.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\n\u003ch2\u003e2.3.2 Physics-Informed Autoregressive Model with Exogenous Inputs (PI-ARX)\u003c/h2\u003e\n\u003cp\u003eClassical AR(1) models are good at finding short-term trends in how well things work, but they don't consider physical reasons for why things break down. To get better predictions, a physics-based model with outside inputs (PI-ARX) was made:\u003c/p\u003e\n\u003cp\u003eEt\u0026thinsp;=\u0026thinsp;\u0026phi;Et\u0026thinsp;\u0026minus;\u0026thinsp;1\u0026thinsp;+\u0026thinsp;\u0026theta;1Vt\u0026thinsp;+\u0026thinsp;\u0026theta;2Ct\u0026thinsp;+\u0026thinsp;\u0026epsilon;t (4)\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003eEt\u0026thinsp;=\u0026thinsp;how well the pump works at time t\u003c/p\u003e\n\u003cp\u003eEt\u0026thinsp;\u0026minus;\u0026thinsp;1\u0026thinsp;=\u0026thinsp;how well the pump worked at the time before\u003c/p\u003e\n\u003cp\u003eVt\u0026thinsp;=\u0026thinsp;how much the pump vibrates (structural response) at time t\u003c/p\u003e\n\u003cp\u003eCt\u0026thinsp;=\u0026thinsp;how deep the rust is or how fast it's rusting at time t\u003c/p\u003e\n\u003cp\u003e\u0026phi;\u0026thinsp;=\u0026thinsp;how long the trend lasts (autoregressive parameter)\u003c/p\u003e\n\u003cp\u003e\u0026theta;1 and \u0026theta;2\u0026thinsp;=\u0026thinsp;how strongly the physical factors are related\u003c/p\u003e\n\u003cp\u003e\u0026epsilon;t\u0026thinsp;=\u0026thinsp;random error\u003c/p\u003e\n\u003cp\u003eUnlike regular AR models, PI-ARX puts physical breakdown factors right into how the time-series changes. With this setup, measurable structure and rust can cause the pump to work worse, not just past performance.\u003c/p\u003e\n\u003cp\u003eTo make sure it makes physical sense, these rules were used when figuring out the parameters:\u003c/p\u003e\n\u003cp\u003e\u0026theta;1 \u0026amp;gt; 0\u003c/p\u003e\n\u003cp\u003e(more vibration shouldn't make things work better)\u003c/p\u003e\n\u003cp\u003e\u0026theta;2 \u0026amp;gt; 0\u003c/p\u003e\n\u003cp\u003e(more rust should make things work worse)\u003c/p\u003e\n\u003cp\u003e0 \u0026amp;lt; \u0026phi; \u0026amp;lt; 1\u003c/p\u003e\n\u003cp\u003e(how well it works can't go up forever, so it stays stable)\u003c/p\u003e\n\u003cp\u003eThis way of modeling is like some recent vibration-physics setups reported in the Journal of Vibration and Control (2024), where physical states are put into data-based structures to make them work better with data they haven't seen before.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\n\u003ch2\u003e2.3.3 Degradation State-Space Representation\u003c/h2\u003e\n\u003cp\u003eThe following equations explain the model:\u003c/p\u003e\n\u003cp\u003eHt\u0026thinsp;=\u0026thinsp;Ht\u0026minus;1\u0026thinsp;+\u0026thinsp;\u0026lambda;1Ct\u0026thinsp;+\u0026thinsp;\u0026lambda;2Vt ( 5 )\u003c/p\u003e\n\u003cp\u003eEt\u0026thinsp;=\u0026thinsp;E0 \u0026ndash; \u0026kappa;Ht ( 6 )\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003eHt\u0026thinsp;=\u0026thinsp;total degradation (latent health) at time t\u003c/p\u003e\n\u003cp\u003eHt\u0026thinsp;\u0026minus;\u0026thinsp;1\u0026thinsp;=\u0026thinsp;degradation at the last time step\u003c/p\u003e\n\u003cp\u003eCt\u0026thinsp;=\u0026thinsp;corrosion depth (or normalized corrosion rate) at time t\u003c/p\u003e\n\u003cp\u003eVt\u0026thinsp;=\u0026thinsp;vibration strength at time t\u003c/p\u003e\n\u003cp\u003eE0\u0026thinsp;=\u0026thinsp;pump efficiency at t\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e\n\u003cp\u003e\u0026lambda;1 and \u0026lambda;2\u0026thinsp;=\u0026thinsp;corrosion and vibration damage rates\u003c/p\u003e\n\u003cp\u003e\u0026kappa;\u0026thinsp;=\u0026thinsp;efficiency sensitivity (how much degradation lowers efficiency)\u003c/p\u003e\n\u003cp\u003eIn simple terms:\u003c/p\u003e\n\u003cp\u003eDegradation at time t\u0026thinsp;=\u0026thinsp;past degradation\u0026thinsp;+\u0026thinsp;corrosion damage\u0026thinsp;+\u0026thinsp;vibration damage\u003c/p\u003e\n\u003cp\u003eEfficiency at time t\u0026thinsp;=\u0026thinsp;starting efficiency \u0026minus; (degradation effect)\u003c/p\u003e\n\u003cp\u003eThis method separates degradation from how the system performs. This allows for predictions of remaining life beyond the tested period. This combination of physics and data improves the reliability of predictions when compared to statistical models, especially when environmental conditions change.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eRegression Coefficients and Model Performance\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026alpha; (Vibration)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e95% CI \u0026alpha;\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ep-value \u0026alpha;\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026beta; (Corrosion)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e95% CI \u0026beta;\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ep-value \u0026beta;\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026gamma; (Intercept)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eR\u0026sup2;\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRMSE (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.67\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.62\u0026ndash;0.72\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.004\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.48\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.44\u0026ndash;0.52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.02\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.91\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.42\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.55\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.50\u0026ndash;0.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.007\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.36\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.32\u0026ndash;0.40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.009\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.95\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.88\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.45\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.71\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.66\u0026ndash;0.76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.003\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.55\u0026ndash;0.65\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.002\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.92\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.38\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e presents a summary of how vibration (\u0026alpha;) and corrosion (\u0026beta;) contribute to efficiency loss in three materials. The statistical meaning, model fit (R\u0026sup2;), and prediction error (RMSE) are included. The data suggest that carbon steel is the most sensitive to both vibration and corrosion..\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n\u003ch2\u003e2.3.4 Sensitivity and Causal Inference Analysis\u003c/h2\u003e\n\u003cp\u003eTo tell apart correlation from causation, we did more stats work.\u003c/p\u003e\n\u003cp\u003e(a) Sensitivity Study\u003c/p\u003e\n\u003cp\u003eWe made a standard sensitivity number:\u003c/p\u003e\n\u003cp\u003eSV = (\u0026part;Eloss / \u0026part;V) \u0026times; (V / Eloss) ( 7 )\u003c/p\u003e\n\u003cp\u003eSC = (\u0026part;Eloss / \u0026part;C) \u0026times; (C / Eloss) ( 8 )\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003eSV\u0026thinsp;=\u0026thinsp;standard sensitivity number for vibration\u003c/p\u003e\n\u003cp\u003eSC\u0026thinsp;=\u0026thinsp;standard sensitivity number for corrosion\u003c/p\u003e\n\u003cp\u003e\u0026part;Eloss / \u0026part;V\u0026thinsp;=\u0026thinsp;how efficiency loss changes with vibration\u003c/p\u003e\n\u003cp\u003e\u0026part;Eloss / \u0026part;C\u0026thinsp;=\u0026thinsp;how efficiency loss changes with corrosion\u003c/p\u003e\n\u003cp\u003eV\u0026thinsp;=\u0026thinsp;vibration amount\u003c/p\u003e\n\u003cp\u003eC\u0026thinsp;=\u0026thinsp;corrosion depth\u003c/p\u003e\n\u003cp\u003eEloss\u0026thinsp;=\u0026thinsp;how much pump efficiency is lost\u003c/p\u003e\n\u003cp\u003eThese formulas give sensitivity measures that are normalized. They show how much vibration and corrosion matter when it comes to losing efficiency.\u003c/p\u003e\n\u003cp\u003eThis normalizing lets us see if vibration or corrosion depth affects efficiency loss more.\u003c/p\u003e\n\u003cp\u003e(b) Partial Regression Work\u003c/p\u003e\n\u003cp\u003eTo see just how vibration alone makes a difference, we did partial regression by keeping corrosion depth constant. The partial coefficient of determination RV∣C2R^2_{V|C}RV∣C2 tells us how much of the change in efficiency loss is because of vibration, once we take out the effect of corrosion.\u003c/p\u003e\n\u003cp\u003e(c) Granger Causality Check\u003c/p\u003e\n\u003cp\u003eSince vibration and efficiency change over time, we used Granger causality testing. This was to figure out if knowing past vibration values helps us guess future efficiency better than just knowing past efficiency.\u003c/p\u003e\n\u003cp\u003eThe null guess:\u003c/p\u003e\n\u003cp\u003eH0: Vt does not Granger-cause Et ( 9 )\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003eH0\u0026thinsp;=\u0026thinsp;null guess\u003c/p\u003e\n\u003cp\u003eVt\u0026thinsp;=\u0026thinsp;vibration amount at time t\u003c/p\u003e\n\u003cp\u003eEt\u0026thinsp;=\u0026thinsp;pump efficiency at time t.\u003c/p\u003e\n\u003cp\u003eIf we reject at p \u0026amp;lt; 0.05, it points to a time-based directional influence.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003e2.4 Justification of Exposure Duration and Representativeness\u003c/h2\u003e\n\u003cp\u003eThe 200-hour test length was picked to observe the start and early growth of combined corrosion and vibration damage under controlled, highly salty settings. Offshore pumps run for thousands of hours. Yet, early damage, like the start of pits, changes in surface smoothness, and stronger vibration, often starts in the first few cycles in harsh marine places [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eIn corrosion studies, brief, controlled immersion tests (100\u0026ndash;500 hours) are often done to compare how materials react and to find basic corrosion measures before things settle down over a long time. This work didn't aim to copy full service lifespan, but to:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eFigure out how fast initial corrosion happens\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMeasure how roughness causes hydraulic mess\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eSet up degradation rates (\u0026alpha;, \u0026beta;) with strong stats\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAdjust forecast models that can predict ahead\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe measured corrosion rates (mm/yr) were adjusted using ASTM G31 ways, letting time scale past the 200-hour mark. The time-series model was pushed past the experiment to guess damage paths up to 500 hours. This gives early ideas on how long-term efficiency changes.\u003c/p\u003e\n\u003cp\u003eIt's known that long-term things like corrosion fatigue crack increase, structural become weak, and big crack spread need long studies with cycle loading. These things are a later damage place past the corrosion-hydraulic link looked at here.\u003c/p\u003e\n\u003cp\u003eSo, the 200-hour length shows the early damage phase. This is key for judging when to fix things and find early problems in offshore setups.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003ch2\u003e3.1 Pump Efficiency\u003c/h2\u003e\n\u003cp\u003eThe measured initial and final efficiencies for the three materials, including their statistical significance, are summarized in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003ePump efficiency degradation with statistical significance\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eInitial Efficiency (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eFinal Efficiency (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eEfficiency Loss (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ep-value\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e98.7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e96.2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.012\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e98.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e94.1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e4.4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.008\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e98.2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e83.7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e14.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e presents the efficiency losses observed in pumps constructed from various materials. Carbon steel pumps showed the largest decrease in efficiency (14.5%), with bronze and 316L SS pumps experiencing losses of 4.4% and 2.5%, respectively. All reported efficiency losses were statistically valid.\u003c/p\u003e\n\u003cp\u003eThe degradation of pump efficiency over 0\u0026ndash;200 hours for all materials is illustrated in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e below .\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e3.2 Corrosion Rates and SEM\u003c/h2\u003e\n\u003cp\u003eA summary of the corrosion rates and associated statistical significance for all materials is shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e below.\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCorrosion Rate Summary with Statistical Significance\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMass Loss (mg)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eCorrosion Rate (mm/yr)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ep-value\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.58\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.019\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.015\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e0.109\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e0.212\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e presents a summary of corrosion data for the tested materials. The results show that carbon steel experienced the most mass loss and highest corrosion rate. Bronze and 316L SS followed, and the variance between all materials was statistically different..\u003c/p\u003e\n\u003cp\u003eThe surface morphology and corrosion damage progression for the three materials are presented in Fig.\u0026nbsp;4 below.\u003c/p\u003e\n\n\u003c/div\u003e\n\u003cp\u003eFigure 4 shows scanning electron microscope (SEM) images of 316L stainless steel, bronze, and carbon steel after 200 hours in high-salt seawater. Measurements showed pitting, micro-cracking, and roughness (Ra). These findings indicate varying degrees of corrosion among the materials, matching the observed pump loss and vibration patterns.\u003c/p\u003e\n\u003cp\u003eSEM was employed to measure pit density (pits/mm\u0026sup2;), average pit depth (\u0026micro;m), and micro-crack length distribution (\u0026micro;m) to assess surface breakdown. Statistical analysis linked these values to changes in vibration amplitude and frequency, establishing a direct of material damage and loss. This method reveals the sensitivity of specific materials to imbalance and hydraulic disturbance caused by rust\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.2.1 Quantitative Surface Morphology Analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe analyzed scanning electron microscope images with calibrated pixel-to-micron scaling to see the link between surface damage and loss of hydraulic performance. For each material, we chose five typical areas (500 \u0026micro;m \u0026times; 500 \u0026micro;m) to measure pit density, pit area percentage, and crack length distribution.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e( a ) Pit Density and Area Fraction\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eSurface Pitting Characteristics of Pump Materials\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePit Density (pits/mm\u0026sup2;)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePit Area Fraction (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e18\u0026thinsp;\u0026plusmn;\u0026thinsp;4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e74\u0026thinsp;\u0026plusmn;\u0026thinsp;9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e156\u0026thinsp;\u0026plusmn;\u0026thinsp;15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.8\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e presents pit density and area fraction for various materials. Carbon steel displayed the highest degree of pitting, with bronze showing less, and 316L SS exhibiting the least.\u003c/p\u003e\n\u003cp\u003eCarbon steel's pit density was about 8.7 times greater than that of 316L SS, suggesting considerable localized dissolving. The pit area fraction showed a strong relationship with the recorded corrosion rate (R\u0026sup2; = 0.93).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b) Crack Length Distribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMicro-crack lengths were measured using line-segmentation analysis:\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eMicro-Cracking Characteristics of Pump Materials\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean Crack Length (\u0026micro;m)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMax Crack Length (\u0026micro;m)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;5 (rare)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e22\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e41\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e58\u0026thinsp;\u0026plusmn;\u0026thinsp;12\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e110\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the average and max crack lengths in different materials. Carbon steel had the most cracking, bronze had less, and 316L SS had the least. The longer cracks in carbon steel were statistically supported (p \u0026amp;lt; 0.01), which agrees with past work on pit-to-crack transition under cyclic loading.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(c) Roughness Evolution Rate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe roughness growth rate was found by:\u003c/p\u003e\n\u003cp\u003edRₐ/dt = (Rₐ,final\u0026thinsp;\u0026minus;\u0026thinsp;Rₐ,initial) / \u0026Delta;t (10)\u003c/p\u003e\n\u003cp\u003ewhere:\u003c/p\u003e\n\u003cp\u003e* dRₐ/dt\u0026thinsp;=\u0026thinsp;roughness growth rate\u003c/p\u003e\n\u003cp\u003e* Rₐ,final\u0026thinsp;=\u0026thinsp;final surface roughness\u003c/p\u003e\n\u003cp\u003e* Rₐ,initial\u0026thinsp;=\u0026thinsp;initial surface roughness\u003c/p\u003e\n\u003cp\u003e* \u0026Delta;t\u0026thinsp;=\u0026thinsp;total exposure time (200 hours)\u003c/p\u003e\n\u003cp\u003eEquation (10) gives the average speed of surface roughness development during the experiment.\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab6\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eSurface Roughness Growth of Pump Materials\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eInitial Ra (\u0026micro;m)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eFinal Ra (\u0026micro;m)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003edRa/dt (\u0026micro;m/h)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.24\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0003\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0020\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.0055\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows the rate at which surface roughness (Ra) shifts over time for different materials. Carbon steel corrodes at the highest rate, bronze at a moderate rate, and 316L SS at the lowest. The rate of roughness increase for carbon steel is almost 18 times that of 316L SS.\u003c/p\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n\u003ch2\u003e3.3 Explanation of Corrosion\u0026ndash;Vibration\u0026ndash;Efficiency Coupling\u003c/h2\u003e\n\u003cp\u003eTo move beyond statistical connection, the interaction between corrosion and vibration can be explained using damage mechanics at the micro-level, alongside theories of how dynamic systems respond.\u003c/p\u003e\n\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\n\u003ch2\u003e3.3.1 Pit Shape and Stress Points\u003c/h2\u003e\n\u003cp\u003eMicroscopic observation revealed a link between pit depth and material corrosion resistance. Carbon steel pits averaged 42\u0026ndash;65 \u0026micro;m deep, with some cracks extending to 110 \u0026micro;m. Bronze pitting ranged from 18\u0026ndash;30 \u0026micro;m, but 316L stainless steel showed shallower pits, measuring less than 10 \u0026micro;m.\u003c/p\u003e\n\u003cp\u003eCorrosion pits concentrate stress. For circular pits, the stress concentration factor (Kt) can be approximated by:\u003c/p\u003e\n\u003cp\u003eKt\u0026thinsp;\u0026asymp;\u0026thinsp;1\u0026thinsp;+\u0026thinsp;2 \u0026times; (a / \u0026rho;) (11)\u003c/p\u003e\n\u003cp\u003ewhere a is pit depth and \u0026rho; is the pit tip radius.\u003c/p\u003e\n\u003cp\u003eCarbon steel's larger pit depth-to-radius ratio leads to an increased stress concentration factor (Kt). Under cyclic impeller loading, this promotes plastic deformation and initiates micro-cracks, increasing the impeller\u0026ndash;shaft assembly's flexibility.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\n\u003ch2\u003e3.3.2 Stiffness Drop and Natural Frequency\u003c/h2\u003e\n\u003cp\u003eThe way a rotating pump acts can be shown by:\u003c/p\u003e\n\u003cp\u003efn = (1 / 2\u0026pi;) \u0026times; \u0026radic;(k / m) (12)\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003efn\u0026thinsp;=\u0026thinsp;natural frequency\u003c/p\u003e\n\u003cp\u003ek\u0026thinsp;=\u0026thinsp;system stiffness\u003c/p\u003e\n\u003cp\u003em\u0026thinsp;=\u0026thinsp;effective mass\u003c/p\u003e\n\u003cp\u003eCorrosion induces minor fractures and reduces component thickness, thereby diminishing the stiffness, k. Slight reductions in stiffness (3\u0026ndash;8%) can shift the natural frequency toward the operational range (1\u0026times; and 2\u0026times; the shaft frequency), amplifying vibrations.\u003c/p\u003e\n\u003cp\u003eIncreased vibration at 1\u0026times; and 2\u0026times; shaft frequencies corresponds to reduced stiffness and nearness to resonance.\u003c/p\u003e\n\u003cp\u003eCarbon steel, exhibiting the most advanced corrosion and pitting, showed the largest stiffness decrease.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section3\"\u003e\n\u003ch2\u003e3.3.3 Surface Texture and Water Forcing\u003c/h2\u003e\n\u003cp\u003eCorrosion not only alters a material's structure but also roughens its surface, which impacts fluid dynamics.\u003c/p\u003e\n\u003cp\u003eThe friction head loss can be approximated by:\u003c/p\u003e\n\u003cp\u003ehf \u0026prop; f(Re, k / D) (13)\u003c/p\u003e\n\u003cp\u003eWhere k\u0026thinsp;\u0026asymp;\u0026thinsp;Ra, and Ra is the average surface texture.\u003c/p\u003e\n\u003cp\u003eIn carbon steel, the increase in Ra from 0.25 \u0026micro;m to 1.35 \u0026micro;m increases the relative texture ratio k/D. This increase causes changes in the flow pattern, leading to increased turbulence and pressure fluctuations.\u003c/p\u003e\n\u003cp\u003eThese pressure fluctuations cause variations in force on the impeller over time:\u003c/p\u003e\n\u003cp\u003eFr(t) \u0026prop; \u0026Delta;P(t) \u0026times; A (14)\u003c/p\u003e\n\u003cp\u003eLarger \u0026Delta;P(t) values resulting from increased turbulence lead to stronger forces, which in turn amplify vibrations..\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec20\" class=\"Section3\"\u003e\n\u003ch2\u003e3.3.4 Combined Structural\u0026ndash;Water Amplification\u003c/h2\u003e\n\u003cp\u003eThe decline happens through two mechanisms:\u003c/p\u003e\n\u003cp\u003eStructural: Pit-induced stiffness reduction leads to a shift in natural frequency, resulting in increased vibrations.\u003c/p\u003e\n\u003cp\u003eWater: Increased roughness leads to greater turbulence, which causes unsteady radial force and increased vibration.\u003c/p\u003e\n\u003cp\u003eThe total vibration response is:\u003c/p\u003e\n\u003cp\u003eVtotal\u0026thinsp;=\u0026thinsp;Vstructural\u0026thinsp;+\u0026thinsp;Vhydraulic\u003c/p\u003e\n\u003cp\u003eThis dual action is consistent with the model:\u003c/p\u003e\n\u003cp\u003eEloss\u0026thinsp;=\u0026thinsp;\u0026alpha;V\u0026thinsp;+\u0026thinsp;\u0026beta;C\u0026thinsp;+\u0026thinsp;\u0026gamma; (15)\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003e\u0026beta; represents the direct hydraulic efficiency loss caused by friction from surface texture.\u003c/p\u003e\n\u003cp\u003e\u0026alpha; represents efficiency loss from vibrations, stemming from reduced stiffness and force issues.\u003c/p\u003e\n\u003cp\u003eThe larger values of \u0026alpha; and \u0026beta; for carbon steel occur due to deeper pits, stiffness loss, and increased turbulence.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec21\" class=\"Section3\"\u003e\n\u003ch2\u003e3.3.5 Connection to Recent Research\u003c/h2\u003e\n\u003cp\u003eCurrent research indicates that loss of stiffness can cause changes as systems begin to fail. Advanced vibration modeling suggests that early changes in dynamic components often arise from damage at very small scales, not merely from signal errors.\u003c/p\u003e\n\u003cp\u003eThese findings align with observations that corrosion damage alters surface stiffness and fluid flow. This, in turn, modifies measurable vibrations and hydraulic performance.\u003c/p\u003e\n\u003cp\u003eThus, the between corrosion, vibration, and It comes from the interaction of structures and fluids, not just statistical .\u003c/p\u003e\n\u003cp\u003eStiffness loss and texture changes at the material level are in agreement with the stability of surface films. Materials with steady films (316L) exhibit reduced pit formation and a slower rate of stiffness loss. Conversely, corrosion-prone materials (carbon steel) dissolve more readily, develop deeper pits, and show a faster increase in vibration.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec22\" class=\"Section3\"\u003e\n\u003ch2\u003e3.3.6 Texture\u0026rsquo;s Effect\u003c/h2\u003e\n\u003cp\u003eTo check that the surface texture affects the machine's work, a match was made between efficiency loss and texture measurements.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab7\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCorrelation of Surface Degradation Parameters with Pump Efficiency Loss\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eParameter\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCorrelation with Efficiency Loss (R\u0026sup2;)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePit Density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.89\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePit Area Fraction\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.92\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMean Crack Length\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.87\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eFinal Ra\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.94\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e shows how surface wear relates to pump efficiency loss. Surface roughness (Ra) has the strongest correlation (R\u0026sup2; = 0.94), followed by pit area fraction, pit density, and average crack length, suggesting that surface roughness and pitting are important in efficiency reduction.\u003c/p\u003e\n\u003cp\u003eSurface roughness (Ra) had the highest correlation with efficiency loss (R\u0026sup2; = 0.94), supporting the earlier hydraulic roughness idea. Pit density and crack length also showed strong ties, confirming that structural stiffness decreases.\u003c/p\u003e\n\u003cp\u003eThese results suggest that efficiency loss isn't only about corrosion but changes with measurable shape changes.\u003c/p\u003e\n\u003cp\u003eA strong correlation (R\u0026sup2; = 0.91) exists between vibration magnitude and efficiency loss. We verified that pit density and crack length influence the dynamic response changes observed. This strengthens the idea that the link is because of how the parts act, and not random chance.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec23\" class=\"Section3\"\u003e\n\u003ch2\u003e3.3.7 Structural Integrity Evolution and Failure Progression under Coupled Degradation\u003c/h2\u003e\n\u003cp\u003eSections 4.3.1\u0026ndash;4.3.6 explained how corrosion shape, vibration increase, and loss of hydraulic performace are mechanically linked. We can better describe the degradation of structural integrity by using continuum damage mechanics\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(a) Damage Variable Formulation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSuppose a scalar damage variable D, ranging from 0 to 1, represents the degree of structural degradation:\u003c/p\u003e\n\u003cp\u003eD\u0026thinsp;=\u0026thinsp;0 indicates an intact structure.\u003c/p\u003e\n\u003cp\u003eD\u0026thinsp;=\u0026thinsp;1 indicates structural failure.\u003c/p\u003e\n\u003cp\u003eCorrosion causes material loss and small cracks from pits, which reduces stiffness:\u003c/p\u003e\n\u003cp\u003ekeff = (1 \u0026ndash; D) \u0026times; k0 (16)\u003c/p\u003e\n\u003cp\u003eSubstituting this into the natural frequency formula yields:\u003c/p\u003e\n\u003cp\u003efn = (1 / 2\u0026pi;) \u0026times; \u0026radic;((1 \u0026ndash; D) \u0026times; k0 / m) (17)\u003c/p\u003e\n\u003cp\u003eThis indicates that pit growth decreases modal stiffness, moving natural frequencies closer to excitation harmonics and increasing dynamic amplification.\u003c/p\u003e\n\u003cp\u003eCarbon steel experiences a faster damage growth rate (Ḋ) due to its higher pit density and longer cracks.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b) Pit-to-Crack Transition and Fracture Mechanics\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLocalized corrosion pits can start fatigue cracks. Failure will happen when pit depth hits a limit. Stress intensity factor is:\u003c/p\u003e\n\u003cp\u003eKI\u0026thinsp;=\u0026thinsp;Y\u0026thinsp;\u0026times;\u0026thinsp;\u0026sigma; \u0026times; \u0026radic;(\u0026pi; a) ( 18 )\u003c/p\u003e\n\u003cp\u003eWhen KI nears the material\u0026rsquo;s fracture toughness (KIC), failure is probable.\u003c/p\u003e\n\u003cp\u003eFor carbon steel, deeper pits (42\u0026ndash;65 \u0026micro;m) raise KI. This makes the shift from localized corrosion damage to structural crack spread faster under cyclic impeller loading.\u003c/p\u003e\n\u003cp\u003eThis fits what was in Thin-Walled Structures (2024). In the report, stiffness declined before crack instability.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(c) Coupled Degradation Progression Stages\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe observed degradation follows three structural stages:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStage I \u0026ndash; Surface Damage Initiation\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003ePit nucleation\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eRoughness growth\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMinor stiffness reduction\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eVibration amplification onset\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eStage II \u0026ndash; Micro-Crack Propagation\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003ePit coalescence\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eSection thinning\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMeasurable modal drift\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eRapid vibration growth\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eStage III \u0026ndash; Structural Instability (Not reached in 200 h)\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eCrack coalescence\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLarge stiffness loss\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eNonlinear vibration response\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eImpeller failure risk\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe 200-hour experiment captures Stage I and early Stage II behavior, critical for predictive maintenance before catastrophic instability.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(d) Coupling with State-Space Degradation Model\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe equation for the latent degradation state is:\u003c/p\u003e\n\u003cp\u003eHt\u0026thinsp;=\u0026thinsp;Ht\u0026ndash;1\u0026thinsp;+\u0026thinsp;\u0026lambda;1 \u0026times; Ct\u0026thinsp;+\u0026thinsp;\u0026lambda;2 \u0026times; Vt (19)\u003c/p\u003e\n\u003cp\u003eThis equation can be seen as a simple way to show how structural damage builds up over time.\u003c/p\u003e\n\u003cp\u003eDt \u0026prop; Ht (20)\u003c/p\u003e\n\u003cp\u003eThe PI-ARX and state-space approach gives a roundabout way to estimate how structural damage changes over time, linking statistical forecasts to ideas about how structures should stay in one piece.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(e) Relation to Boundary Element Structural Modeling\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEngineering Analysis with Boundary Elements focuses on advanced structural integrity studies, specifically boundary-element fracture simulations for thin-walled systems weakened by corrosion.\u003c/p\u003e\n\u003cp\u003eWhile the current study doesn't use a full BEM fracture simulation, the morphology parameters, such as pit depth, crack length, and roughness changes, which were measured experimentally, offer tangible inputs. These inputs could define structural models in the future.\u003c/p\u003e\n\u003cp\u003eThus, the framework serves as an experimental foundation for detailed structural fracture modeling.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec24\" class=\"Section2\"\u003e\n\u003ch2\u003e3.4 Hybrid Predictive Model Performance\u003c/h2\u003e\n\u003cp\u003eThe proposed PI-ARX model improved multi-step prediction stability compared to classical AR(1). Incorporating vibration and corrosion as exogenous inputs reduced forecast drift and improved generalization under cross-validation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePerformance comparison\u003c/strong\u003e:\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab8\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003ePrediction Accuracy of Vibration Models\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eModel\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRMSE (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMAPE (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAR(1)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.45\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.62\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePI-ARX\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.31\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.48\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e above, there is a comparison of two models that predict pump vibration. PI-ARX performs better than the AR(1) model, considering that the former has a low RMSE of 0.31% and MAPE of 0.48%, thus making the predictions accurate.\u003c/p\u003e\n\u003cp\u003eUsing the proposed hybrid approach, the error was reduced by 31%, thus proving that the inclusion of physical degradation drivers improves the performance of the predictions\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec25\" class=\"Section2\"\u003e\n\u003ch2\u003e3.5 Statistical Validation of Regression and AR Models\u003c/h2\u003e\n\u003cp\u003eFor generalization performance, the data was divided into 70% training and 30% testing sets. The regression residuals were normally distributed with homoscedastic variance relative to the predicted values. No significant outliers were found. Performance metrics of the autoregressive model were evaluated, showing that the autocorrelation function decays rapidly, and the partial autocorrelation function was primarily driven by lag 1, indicating an autoregressive process of order 1. No significant residual autocorrelation was found at lags beyond the first.\u003c/p\u003e\n\u003cp\u003eTo ensure the statistical robustness of the developed regression and PI-ARX models, statistical checks were performed. For example, the presence of multicollinearity was checked using the Variance Inflation Factor (VIF), where all VIF values were found to be below 2.0. The normality of the residuals was checked using the Shapiro-Wilk normality test at a significance level above 0.05. Similarly, the homoscedasticity condition was checked using the Breusch-Pagan test at a significance level above 0.10. Finally, the presence of autocorrelation was checked using the Durbin-Watson test at a level above 1.9. Additionally, 95% confidence intervals were estimated for the degradation coefficients \u0026alpha; and \u0026beta;.\u003c/p\u003e\n\u003cp\u003ePerformance metrics of the regression model, including R\u0026sup2;, RMSE, and p-values, were found to be significant at p\u0026thinsp;\u0026lt;\u0026thinsp;0.01, indicating that the predictors were significantly affecting the response variable for all materials. The low value of the regression model\u0026rsquo;s RMSE, less than 0.45%, indicated high accuracy in the predictions. Minimal issues of multicollinearity were found among the predictors, with a VIF less than 2. The normal distribution of the regression residuals was confirmed using the Shapiro-Wilk test at p\u0026thinsp;\u0026gt;\u0026thinsp;0.05. Constant variance was also found using the Breusch-Pagan test at p\u0026thinsp;\u0026gt;\u0026thinsp;0.1. The regression coefficients of the vibration response variable \u0026alpha; and corrosion response variable \u0026beta; were found to be statistically significant at p\u0026thinsp;\u0026lt;\u0026thinsp;0.01. Confidence intervals were found at 95% confidence levels, as shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec26\" class=\"Section2\"\u003e\n\u003ch2\u003e3.6 Advanced Predictive Modeling Outcomes\u003c/h2\u003e\n\u003cp\u003eDeep learning and digital twin technologies improve the accuracy of multi-step predictions. Vibration analysis using convolutional neural networks (CNNs) was able to detect operational issues in pumps before a 10\u0026ndash;15% efficiency drop was noted [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]. Digital twin simulations that combined corrosion rates and vibration analysis provided accurate predictions of useful life, matching the trends of an AR(1) model while providing more in-depth information for maintenance scheduling purposes [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. The use of IoT sensors for continuous monitoring and model updates was made possible through the use of IoT technology. The above studies indicate that the use of experimental degradation data and artificial intelligence technologies improves the accuracy of predictive maintenance compared to other approaches.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec27\" class=\"Section2\"\u003e\n\u003ch2\u003e3.7 Sensitivity and Causal Analysis Results\u003c/h2\u003e\n\u003cdiv id=\"Sec28\" class=\"Section3\"\u003e\n\u003ch2\u003e3.7.1 Sensitivity Analysis\u003c/h2\u003e\n\u003cp\u003e\u003cstrong\u003eStandardized sensitivity indices\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab9\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eSensitivity of Pump Efficiency to Vibration and Corrosion by Material\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eS_V (Vibration)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eS_C (Corrosion)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.44\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.55\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.39\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.74\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.63\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates the sensitivity of the efficiency of the pump to vibration (S_V) and corrosion (S_C) for different materials. Carbon steel is the material which is most sensitive to vibration and corrosion, while 316L Stainless Steel is the material which is least sensitive. For the case of carbon steel material, the sensitivity to vibration is slightly higher than the sensitivity to corrosion depth..\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec29\" class=\"Section3\"\u003e\n\u003ch2\u003e3.7.2 Partial Regression Results\u003c/h2\u003e\n\u003cp\u003eAfter accounting for corrosion depth, the partial coefficient of determination (R\u0026sup2;) for vibration is:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eR\u0026sup2;V|C\u0026sup2; = 0.67\u003c/strong\u003e for carbon steel\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eR\u0026sup2;V|C\u0026sup2; = 0.59\u003c/strong\u003e for bronze\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eR\u0026sup2;V|C\u0026sup2; = 0.63\u003c/strong\u003e for 316L stainless steel\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThese values indicate that vibration independently explains a substantial portion of efficiency loss variance beyond corrosion alone.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec30\" class=\"Section3\"\u003e\n\u003ch2\u003e3.7.3 Granger Causality\u003c/h2\u003e\n\u003cp\u003eGranger causality testing (lag\u0026thinsp;=\u0026thinsp;1)\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab10\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eStatistical Significance of Material Effects on Pump Performance\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eF-statistic\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ep-value\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5.84\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.019\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.21\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.015\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.47\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.006\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe Table \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e above presents the F-statistic and p-value for the effect of material on pump performance. All materials show statistically significant effects, with carbon steel having the strongest significance (highest F-statistic and lowest p-value)\u003c/p\u003e\n\u003cp\u003eThe null hypothesis that vibration does not Granger-cause efficiency loss was rejected for all materials (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e\n\u003cp\u003eThis indicates that past vibration values significantly improve prediction of future efficiency, supporting directional influence rather than mere contemporaneous correlation.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec31\" class=\"Section2\"\u003e\n\u003ch2\u003e3.8 Model Robustness Under Simulated Operating Variability\u003c/h2\u003e\n\u003cp\u003eIn order to examine the robustness of the proposed predictive model under different offshore working conditions, a parametric perturbation analysis was performed using the physics-informed PI-ARX and state-space models.\u003c/p\u003e\n\u003cp\u003eWhile experimental measurements were performed under constant flow rate (0.15 m\u0026sup3;/h), salinity (35 ppt), and temperature (25\u0026deg;C), real working conditions of offshore pumps vary under fluctuating hydraulic and environmental conditions. To examine the stability of the proposed models, the following working conditions were simulated under realistic ranges:\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab11\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eOperating Conditions and Parameter Variation Ranges\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eParameter\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eBaseline\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eVariation Range\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eFlow rate\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.15 m\u0026sup3;/h\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026plusmn;\u0026thinsp;20%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSalinity\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e35 ppt\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e30\u0026ndash;45 ppt\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTemperature\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e25\u0026deg;C\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20\u0026ndash;40\u0026deg;C\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e above indicates the baseline conditions for the pump, specifically the flow rate, salinity, and temperature, and the range of variation for the respective parameters that was used in the experiment/analysis. The sensitivity of the corrosion rate to temperature and salinity was represented by the Arrhenius-type approximation, given by:\u003c/p\u003e\n\u003cp\u003eCR(T) \u0026prop; exp(-Ea / RT) (21)\u003c/p\u003e\n\u003cp\u003eThe influence of hydraulic roughness was also accounted for by the Reynolds number dependency of the friction factor.\u003c/p\u003e\n\u003cdiv id=\"Sec32\" class=\"Section3\"\u003e\n\u003ch2\u003e3.8.1 Flow Rate Variation\u003c/h2\u003e\n\u003cp\u003eA\u0026thinsp;\u0026plusmn;\u0026thinsp;20% flow variation resulted in:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;6% change in predicted vibration amplitude\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.12% increase in RMSE for PI-ARX\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eNo violation of parameter stability constraints (0\u0026thinsp;\u0026lt;\u0026thinsp;\u0026phi;\u0026thinsp;\u0026lt;\u0026thinsp;1)\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe hybrid PI-ARX model maintained RMSE\u0026thinsp;\u0026lt;\u0026thinsp;0.52% under flow variation.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec33\" class=\"Section3\"\u003e\n\u003ch2\u003e3.8.2 Salinity Variation\u003c/h2\u003e\n\u003cp\u003eIncreasing salinity from 35 to 45 ppt increased predicted corrosion rate by:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e+\u0026thinsp;11% (316L)\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e+\u0026thinsp;16% (Bronze)\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e+\u0026thinsp;21% (Carbon Steel)\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eHowever, model prediction error increased marginally (\u0026lt;\u0026thinsp;0.15%), indicating stable extrapolation when corrosion depth is treated as an exogenous driver.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec34\" class=\"Section3\"\u003e\n\u003ch2\u003e3.8.3 Temperature Sensitivity\u003c/h2\u003e\n\u003cp\u003eIncreasing the temperature to 40\u0026deg;C enhances the rate of corrosion kinetics but does not affect the stability of the degradation curve, as the model accounts for the depth of corrosion.\u003c/p\u003e\n\u003cp\u003eThis is achieved through the state-space model\u003c/p\u003e\n\u003cp\u003eH_t\u0026thinsp;=\u0026thinsp;H_{t-1} + \u0026lambda;₁C_t\u0026thinsp;+\u0026thinsp;\u0026lambda;₂V_t (22)\u003c/p\u003e\n\u003cp\u003ewhere the degradation accumulates proportionally.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec35\" class=\"Section3\"\u003e\n\u003ch2\u003e3.8.4 Robustness Summary\u003c/h2\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab12\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eImpact of Operating Conditions on Model Prediction Error\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCondition\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRMSE (%)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u0026Delta;RMSE\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBaseline\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.31\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026mdash;\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eFlow\u0026thinsp;\u0026plusmn;\u0026thinsp;20%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e+\u0026thinsp;0.21\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSalinity 45 ppt\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.46\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e+\u0026thinsp;0.15\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTemperature 40\u0026deg;C\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e+\u0026thinsp;0.18\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e displays the effects of flow, salinity, and temperature changes on the model\u0026rsquo;s prediction accuracy, where the root mean square error (RMSE) increases in all conditions, with the greatest increase in the case of the \u0026plusmn;\u0026thinsp;20% flow variation, implying that the flow has the greatest influence on the error in the model\u0026rsquo;s predictions.\u003c/p\u003e\n\u003cp\u003eThe model's robustness is evident by the fact that the error, represented by the RMSE, is always below 0.55% for all conditions, suggesting that the inclusion of the physical degradation factors, such as corrosion depth and vibration amplitude, improves the generalization capability of the model compared to the autoregressive models.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThis paper proposes a framework for quantifying corrosion morphology, vibration, and hydraulic efficiency loss for offshore-based centrifugal pumps under controlled conditions of high salinity. As opposed to previous studies, where the focus was largely on the quantification of corrosion and vibration individually, this paper proposes a direct quantitative link between surface degradation resulting from corrosion and efficiency loss resulting from vibration, as validated through regression models as well as autoregressive models.\u003c/p\u003e\n\u003cdiv id=\"Sec37\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Material-Dependent Degradation and Efficiency Loss\u003c/h2\u003e\n\u003cp\u003eThe experimental results indicate clear trends for different materials. It was found that, as expected, the efficiency loss was maximum for carbon steel, declining by 14.5% (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) over 200 hours of operation. Bronze showed an efficiency loss of 4.4% (p\u0026thinsp;=\u0026thinsp;0.008), while 316L stainless steel showed the minimum efficiency loss of 2.5% (p\u0026thinsp;=\u0026thinsp;0.012). Similarly, the corresponding corrosion rates for these materials were 0.212 mm/yr, 0.109 mm/yr, and 0.019 mm/yr, respectively.\u003c/p\u003e\n\u003cp\u003eAs validated by SEM, the surface degradation for these materials was as follows: the surface degradation for carbon steel showed an increase in Ra from 0.25 to 1.35 \u0026micro;m, indicating significant surface degradation resulting from pitting and micro-cracking. Bronze showed moderate surface degradation, while 316L SS showed minimum surface degradation.\u003c/p\u003e\n\u003cp\u003eThe integration of these quantified surface degradation metrics\u0026mdash;pit density, crack length, and evolution of surface roughness\u0026mdash;confirms that the rate of degradation directly correlates to the rate of efficiency loss. Similarly, for carbon steel, which showed the maximum efficiency loss, the pit density was very high, i.e., 156 pits/mm\u0026sup2;, along with the maximum rate of surface roughness evolution, i.e., 0.0055 \u0026micro;m/h, resulting in the maximum value of the vibration coefficient, i.e., 0.71.\u003c/p\u003e\n\u003cp\u003eThe experimental results are in conformity with previous offshore-based corrosion studies. These findings emphasize the significant role of material selection for efficient pump life.\u003c/p\u003e\n\u003cdiv id=\"Sec38\" class=\"Section3\"\u003e\n\u003ch2\u003e4.1.1 Electrochemical Behavior and Protective Film Stability in Saline Environments\u003c/h2\u003e\n\u003cp\u003eThe trends observed with respect to material degradation can be further understood by analyzing electrochemical properties and film stability in chloride-rich seawater.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003e316L Stainless Steel\u003c/h3\u003e\n\u003cp\u003e316L stainless steel has 16\u0026ndash;18% Cr and 2\u0026ndash;3% Mo. The Cr and Mo contents enable the formation of a stable Cr2O3 film. In seawater with 35 ppt salinity, chloride ions can penetrate the film. However, molybdenum improves resistance against pitting corrosion by stabilizing the film and accelerating passivation.\u003c/p\u003e\n\u003cp\u003eThe low corrosion rate (0.019 mm/yr) and low depth (\u0026lt;\u0026thinsp;10 \u0026micro;m) observed from the SEM micrograph indicate that there are fewer instances of breakdown and passivation. The electrochemical stability can be related to:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eLow reduction in stiffness\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLow increase in roughness\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLow amplification of vibrations\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLow percentage reduction in efficiency (2.5%)\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe degradation mechanism observed with 316L stainless steel can thus be related to slight roughening on the surface, as opposed to electrochemical corrosion.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eBronze\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBronze (Cu-Sn alloy) does not use chromium passivation. Instead, it uses copper oxide (Cu2O/CuO) film formation. In chloride-rich seawater, bronze is prone to:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eSelective dealloying (dezincification if zinc is used)\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003ePorous corrosion product formation\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLocalized galvanic microcells between \u0026alpha; and \u0026delta; phases\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eBronze's corrosion rate of 0.109 mm/yr and pit depth of 18\u0026ndash;30 \u0026micro;m classify it as having an oxide film that is less stable than Cr2O3 of 316L but still partially protective. Porous corrosion product formation may be removed by flow-induced shear stress, leading to accelerated roughness formation. This is consistent with the measured vibration coefficient of 0.55 and efficiency loss of 4.4%. Carbon Steel Carbon steel does not use a stable passive film in chloride-rich environments. It is therefore prone to active anodic dissolution reactions:\u003c/p\u003e\n\u003cp\u003eFe \u0026rarr; Fe2\u0026thinsp;+\u0026thinsp;+\u0026thinsp;2e- (23)\u003c/p\u003e\n\u003cp\u003eIn oxygen-rich environments like seawater, it is prone to:\u003c/p\u003e\n\u003cp\u003eO2\u0026thinsp;+\u0026thinsp;2H2O\u0026thinsp;+\u0026thinsp;4e- \u0026rarr; 4OH- (24)\u003c/p\u003e\n\u003cp\u003eIron oxides FeOOH and Fe2O3 are formed and are mechanically unstable.\u003c/p\u003e\n\u003cp\u003eKey characteristics:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eLack of self-healing passive film\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eRapid initiation of pit formation\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eRapid growth of pits due to the presence of chlorides\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eIncreased rate of electrochemical corrosion current density\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe empirical results reveal that the rate of corrosion is 0.212 mm/year, and the presence of deep pits is between 42 and 65 \u0026micro;m, with micro-cracks extending up to 110 \u0026micro;m, thereby indicating the presence of aggressive active corrosion.\u003c/p\u003e\n\u003cp\u003eUnlike in the case of 316L, where the stability of the film restricts the growth of the pit, in the case of carbon steel, the process of electrochemical corrosion is continuous, leading to:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eRapid degradation of stiffness\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAmplification of turbulence\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003ePeak vibration sensitivity (\u0026alpha;\u0026thinsp;=\u0026thinsp;0.71)\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMaximum efficiency loss (14.5%)\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab13\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 13\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eElectrochemical Characteristics of Tested Materials in 35 ppt Seawater\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMaterial\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePassive Film Type\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eChloride Resistance\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eCorrosion Mechanism\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eFilm Stability Under Flow\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e316L SS\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCr₂O₃ (Mo-stabilized)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eHigh\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLocalized pitting with repassivation\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eStable\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBronze\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCu₂O / CuO\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eModerate\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSelective dissolution, porous oxide\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePartially stable\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCarbon Steel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eIron oxides (FeOOH)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLow\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eActive anodic dissolution\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUnstable / spalling\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e indicates the electrochemical characteristics of the exposed materials in 35 ppt seawater. It is evident that the 316L stainless steel has a stable Mo-stabilized Cr2O3 film, which is resistant to corrosion by chlorides; bronze has moderate resistance with partially stable copper oxides; and carbon steel is the most vulnerable to degradation due to the instabilities in the iron oxide films.\u003c/p\u003e\n\u003cp\u003eThe differences in degradation for the exposed materials can be explained by the differences in the electrochemical characteristics and the stabilities of the films formed. For example, the 316L stainless steel has a slow rate of pit initiation compared to carbon steel, where the rate is rapid due to the high salinity conditions [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]. Bronze has intermediate properties, where copper has a positive influence in reducing the rate of degradation.\u003c/p\u003e\n\u003cdiv id=\"Sec40\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2 Corrosion\u0026ndash;Vibration Coupling\u003c/h2\u003e\n\u003cp\u003eThe results from the regression analysis also reveal high coefficients of determination, where R\u0026sup2; \u0026asymp; 0.91. To address the concern that correlation does not imply causation, additional analyses were conducted to validate the results. From the sensitivity index, it is evident that vibration contributes to 55\u0026ndash;74% of the normalized efficiency loss response for the materials considered. Furthermore, the results from the partial regression analysis reveal that vibration independently contributes significantly to the efficiency loss, even after accounting for the effects of corrosion depth.\u003c/p\u003e\n\u003cp\u003eMoreover, the results from the Granger causality test reveal that vibration is the leading cause of the loss in hydraulic efficiency, where the effects of vibration precede the loss in efficiency, indicating causation at a statistical significance level of p\u0026thinsp;\u0026lt;\u0026thinsp;0.05.\u003c/p\u003e\n\u003cp\u003eThe effects of progressive corrosion and vibration-induced fatigue can significantly influence the structural integrity of the system, especially in the region where the pitting is concentrated, as illustrated in Fig.\u0026nbsp;9. These results can be used to develop more effective predictive maintenance strategies, which is in accordance with the reported degradation mechanisms in the Engineering Analysis with Boundary Elements 174, 106157 (2025) and Thin-Walled Structures 205, Part B, 112370 (2024).\u003c/p\u003e\n\u003cp\u003eThe results obtained in the present study validate the assumption that vibration is not only correlated with the degradation mechanisms but also plays an active role in the loss in hydraulic efficiency through the mechanisms of stiffness degradation and turbulence amplification, as discussed in Section \u003cspan class=\"InternalRef\"\u003e4.3\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec41\" class=\"Section2\"\u003e\n\u003ch2\u003e4.3 Predictive Modeling and Remaining Useful Life\u003c/h2\u003e\n\u003cp\u003eAR(1) models were found effective in characterizing the time series of efficiency for individual materials. Moreover, the root mean square error (RMSE) was found to be below 0.45%, and multi-step predictions were found to be stable with a mean absolute percentage error (MAPE) below 0.62%. By integrating it with regression analysis, it is possible to estimate the longevity of individual components and schedule maintenance. For instance, it is found that carbon steel will lose more than 15% of its efficiency after 250\u0026ndash;260 hours of operation, while 316L stainless steel will maintain its efficiency at more than 95% after 500 hours.\u003c/p\u003e\n\u003cp\u003eIt is found that the validation of the model is reliable with variance inflation factors (VIF) below 2.0, Shapiro-Wilk normality tests with p-values higher than 0.05, and Breusch-Pagan normality tests with p-values higher than 0.1. Moreover, it is found that the values of \u0026alpha; and \u0026beta; were reliable with statistical significance at p\u0026thinsp;\u0026lt;\u0026thinsp;0.01 with 95% confidence intervals (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eIt is found that integrating AI models with digital twin simulations enhances the predictive maintenance paradigm. It is possible to predict anomalies, perform multi-step predictions, and adjust operations in real-time. It is beyond the conventional SEM model of corrosion-vibration coupling established experimentally and is beyond conventional statistical models [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. It is possible to use it for decision-making of offshore centrifugal pump operations in high salinity environments.\u003c/p\u003e\n\u003cp\u003eIntegration of physically constrained exogenous variables transforms the predictive structure from a statistical estimator to a degradation model with a mix of statistical and physical components. Hybrid physics-informed vibration models similar to those presented in this paper, as reported in the Journal of Vibration and Control (2024), have demonstrated improved robustness to operational variability.\u003c/p\u003e\n\u003cp\u003eThe predictive models were trained under fixed flow rate and salinity conditions. Although an RMSE of less than 0.45% suggests a high predictive accuracy, it is also necessary to test the robustness of the model under varying operating conditions, for example, when the salinity is higher or lower, or when temperatures fluctuate or when different pump speeds are used. to broader operational envelopes to ensure applicability in offshore environments.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec42\" class=\"Section2\"\u003e\n\u003ch2\u003e4.4 Early-Stage vs Long-Term Degradation Mechanisms\u003c/h2\u003e\n\u003cp\u003eThe degradation of offshore centrifugal pumps occurs through a series of distinct and progressive stages. The current study corresponds to Stage I of this degradation process, as characterized by the initiation of corrosion, pit nucleation, increased roughness, and amplified vibration resulting from hydrodynamic disturbances.\u003c/p\u003e\n\u003cp\u003eThe degradation coefficients calculated through the experimental procedure (\\(\\alpha\\), \\(\\beta\\), \\(\\lambda_1\\), \\(\\lambda_2\\)) can be viewed as a representation of damage progression in the structural model. Unlike other diagnostic approaches that rely solely upon vibration signals for damage progression, the current approach correlates morphology parameters with stiffness degradation and fracture precursor conditions. This aligns well with the structural integrity progression approaches adopted in recent thin-walled structural failure analysis.\u003c/p\u003e\n\u003cp\u003eThe degradation mechanisms of corrosion fatigue, pit-crack transition, and structural fracture occur over a long time period and require:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eInteraction of cyclic stresses over a long period of time\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eSignificant pit-to-crack transition\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eDamage accumulation in the microstructure\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThese degradation mechanisms occur over a time period in excess of 200 hours and are highly dependent upon fluctuating loading conditions. The current study was designed without the presence of fluctuating loading conditions in order to isolate corrosion-vibration coupling.\u003c/p\u003e\n\u003cp\u003eThe early stages of degradation are of significant interest. The modeling of marine corrosion, as discussed in Melchers [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e], suggests that the early stages of corrosion play an important role in the progression of damage. Small increases in roughness can lead to a significant enhancement in turbulence intensity and radial impeller loading, thereby accelerating the progression of fatigue damage in the future.\u003c/p\u003e\n\u003cp\u003eThe experimental procedure adopted in the current study provides a mechanistic insight into the triggering phase of degradation and can be useful in developing predictive maintenance approaches prior to the initiation of structural damage.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec43\" class=\"Section2\"\u003e\n\u003ch2\u003e4.5 Practical Implications for Offshore Pump Maintenance\u003c/h2\u003e\n\u003cp\u003eThe research also reveals several implications for improving the maintenance of offshore pumping equipment. In a high-salinity condition, the material of choice is 316L stainless steel, which shows negligible efficiency loss and superior corrosion resistance. Bronze is a cheaper material but also shows a slight efficiency loss. The combination of vibration and corrosion monitoring with computer models is also a useful tool for creating a more effective maintenance regime, which would increase the life of the equipment and minimize operational costs. The proposed method is also compatible with the digital twin concept.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec44\" class=\"Section2\"\u003e\n\u003ch2\u003e4.6 Integration into Real-Time Monitoring and Digital Twin Platforms\u003c/h2\u003e\n\u003cp\u003eTo implement this proposed corrosion-vibration-efficiency model in an offshore environment, integration with real-time systems and digital twin technologies would be necessary. This proposed PI-ARX/state-space model for degradation would be compatible with current Industrial Internet of Things (IIoT) systems as well as supervisory control and data acquisition (SCADA) systems.\u003c/p\u003e\n\u003cdiv id=\"Sec45\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.1 System Architecture for Real-Time Deployment\u003c/h2\u003e\n\u003cp\u003eA concrete implementation will involve four hierarchical layers:\u003c/p\u003e\n\u003cp\u003eLayer 1 \u0026ndash; Data Acquisition\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eAccelerometer-based vibration sensors (RMS, spectral components)\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003ePressure and flow sensors\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTemperature and salinity probes\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eOptional corrosion sensors (electrical resistance or linear polarization resistance sensors)\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eData will be streamed at 1 to 10 Hz to edge devices or offshore control rooms.\u003c/p\u003e\n\u003cp\u003eLayer 2 \u0026ndash; Feature Extraction and Preprocessing\u003c/p\u003e\n\u003cp\u003eOn the edge device, the following operations will be performed:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eExtraction of the RMS value of the vibration signal\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTracking of 1x and 2x shaft frequencies\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eEstimation of hydraulic efficiency using flow-head curves\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eEstimation of corrosion depth using corrosion rate models:\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eCt\u0026thinsp;=\u0026thinsp;Ct\u0026ndash;1\u0026thinsp;+\u0026thinsp;CRt * \u0026Delta;t (25)\u003c/p\u003e\n\u003cp\u003eWhere the corrosion rate CRt may be scaled by temperature and salinity using an Arrhenius relation.\u003c/p\u003e\n\u003cp\u003eLayer 3 \u0026ndash; Physics-Informed Degradation Engine\u003c/p\u003e\n\u003cp\u003eOn the deployed digital twin, the PI-ARX model will be run in real time:\u003c/p\u003e\n\u003cp\u003eEt\u0026thinsp;=\u0026thinsp;ϕ * Et\u0026ndash;1\u0026thinsp;+\u0026thinsp;\u0026theta;1 * Vt\u0026thinsp;+\u0026thinsp;\u0026theta;2 * Ct (26)\u003c/p\u003e\n\u003cp\u003eWhile the degradation process will be updated in parallel by:\u003c/p\u003e\n\u003cp\u003eHt\u0026thinsp;=\u0026thinsp;Ht\u0026ndash;1\u0026thinsp;+\u0026thinsp;\u0026lambda;1 * Ct\u0026thinsp;+\u0026thinsp;\u0026lambda;2 * Vt (27)\u003c/p\u003e\n\u003cp\u003eThis architecture will enable:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eReal-time forecasting of efficiency\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eOngoing updates of the health index\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eEstimation of remaining useful life (RUL)\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe coefficients \u0026alpha;, \u0026beta;, \u0026lambda;1, and \u0026lambda;2, derived from experiments, will be used as baselines and may be updated adaptively using recursive least squares or Bayesian methods as data become available.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLayer 4 \u0026ndash; Decision Support and Maintenance Optimization\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMaintenance thresholds are established based on the following parameters:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eEfficiency reduction greater than 10%\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eHealth index value Ht greater than calibrated damage threshold\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eRate of change of health index value Ḣt greater than predefined slope\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eVibration levels beyond ISO alarm limits\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eOn threshold violation, the digital twin undertakes:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eInspection alerts\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLubrication adjustments\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLoad redistribution\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003ePlanned maintenance\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis brings us from a monitoring framework to a predictive maintenance optimization framework.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec46\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.2 Digital Twin Synchronization Strategy\u003c/h2\u003e\n\u003cp\u003eThe digital twin acts as a virtual model that is updated in real time. The model can predict the future performance of the pump system. The following are steps that are taken by the digital twin:\u003c/p\u003e\n\u003cp\u003e( a ) The physical parameters are used to update the degradation model.\u003c/p\u003e\n\u003cp\u003e( b ) The digital twin can predict future efficiency using a prediction horizon (e.g., 100\u0026ndash;500 hours).\u003c/p\u003e\n\u003cp\u003e( c ) Scenario-based predictions can be made for parameters such as:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eIncreased salinity\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eFlow rate change\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTemperature increase\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLoad change\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eAs corrosion depth and vibration are explicitly modeled as physical parameters, it is possible for the digital twin to remain interpretable under changing environmental conditions.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec47\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.3 Advantages Over Vibration-Only Monitoring Systems\u003c/h2\u003e\n\u003cp\u003eTypically, conventional vibration-based monitoring approaches tend to detect anomalies only after dynamic deviations become apparent. In this regard, the proposed approach offers earlier warning capabilities as a result of the following reasons:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eThere is a gradual build-up of corrosion depth before a major vibration spike is noticed.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThere is a gradual build-up of surface roughness that acts as a precursor to impending hydraulic disturbance.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThere is a gradual build-up of damage state Ht.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec48\" class=\"Section3\"\u003e\n\u003ch2\u003e4.6.4 Offshore Implementation Considerations\u003c/h2\u003e\n\u003cp\u003eImplementation of the proposed framework for offshore structures would involve:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eEdge computing modules located in proximity to pump skids\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eCloud-based twin synchronization for analytics purposes\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eIntegration with asset integrity management systems\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eIntegration with maintenance management systems (CMMS)\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe proposed approach is computationally efficient (ARX/state-space model), which makes it suitable for real-time implementation without requiring high-performance computing facilities.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec49\" class=\"Section2\"\u003e\n\u003ch2\u003e4.7 Limitations and Future Directions\u003c/h2\u003e\n\u003cp\u003eThough the experiment was well designed and executed, certain limitations and areas of improvement are noted. The experiment was carried out under constant flow rates, temperatures, and salinity. This was done in order to ensure that the material degradation was isolated. It has been noted that in offshore pumps, the hydraulic and temperature conditions vary. This could affect the corrosion rates and turbulence. The use of Ra as a surface roughness model is a rough estimation of the hydraulic effects. It fails to take into account other factors such as pits and crevices. The use of a three-dimensional model for surface roughness could be included in future experiments. The current setup fails to take into account other factors that could be included in offshore pumps. These factors could be changes in conditions such as flow rates, temperatures, and hydraulic conditions. The current setup could be validated for use in offshore pumps. This could be done by conducting experiments on actual pumps. The factors that could be taken into account are biofouling and other debris. This could be done in order to ensure that the current setup could be adapted for use in offshore pumps.\u003c/p\u003e\n\u003cp\u003eThough the experiment was carried out under constant flow rates, temperatures, and salinity, robustness analysis via parametric perturbation was performed. It was noted that the PI-ARX framework was able to maintain its stability.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec50\" class=\"Section2\"\u003e\n\u003ch2\u003e4.8 Summary of Findings\u003c/h2\u003e\n\u003cp\u003eThe study proves that in environments of high salt content, carbon steel corrodes at the quickest rate, bronze corrodes at a moderate rate, and 316L stainless steel maintains its performance. The research combines SEM surface analysis, vibration analysis, regression analysis, and autoregressive forecasting in a cohesive model. The model provides a means of predicting maintenance times and performance in offshore centrifugal pumps. The quantification of the relationship between corrosion patterns and efficiency degradation via vibration analysis will improve diagnosis and planning for offshore pump systems.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5 Conclusions","content":"\u003cp\u003eOur findings suggest that 316L stainless steel has the maximum corrosion resistance at high saline conditions. Bronze shows fair performance, while carbon steel has maximum degradation. The physics-informed PI-ARX degradation model, which incorporates corrosion depth and vibration amplitude as exogenous physical drivers, improves the stability of the predictions significantly compared to traditional autoregressive models. State-space degradation model formulation provides the capability to predict structured remaining useful life beyond the test duration. Pumps made of bronze require less maintenance. Pumps constructed from 316L stainless steel have the capability to run for extended periods (more than 500 hours) without any significant degradation in performance.\u003c/p\u003e \u003cp\u003eMaterial selection and monitoring of vibration and corrosion levels are important factors that help in reducing downtime and keeping maintenance costs low. This paper establishes a link among corrosion, vibration, and pump performance using experimental data, scanning electron microscopy, and forecast-based approaches. Numerical validation of the proposed model was performed by conducting accuracy checks.\u003c/p\u003e \u003cp\u003eEven though this test interval of 200 hours mainly focuses on early-stage corrosion-vibration coupling, mechanistically validated degradation coefficients can be extended through normalized corrosion rates and autoregressive forecasting. The long-term degradation phenomena of corrosion fatigue and macro-crack growth require extended cyclic testing and represent the next step in the investigation. The early degradation trends remain an essential factor for prediction and maintenance because intervention occurs before failure.\u003c/p\u003e \u003cp\u003eThe proposed framework for a hybrid model has been found to be predictable and stable under simulated changes in flow rates, salinity, and temperatures. This indicates its potential for use in realistic offshore environments. The degradation coefficients derived through the experiments can be related to a structural damage mechanics model. This will allow for the integration of a fracture-based boundary element and finite element model of failure in the future.\u003c/p\u003e \u003cp\u003eThe proposed physics-based degradation model can be easily implemented in an offshore environment through the use of a digital twin. The proposed framework for a hybrid model can be easily implemented in IoT-based digital twin systems for offshore environments.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003e316L SS\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003e316L Stainless Steel\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eCR\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eCorrosion Rate\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eSEM\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eScanning Electron Microscopy\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eRa\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eArithmetic Mean Surface Roughness\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eV\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eVibration Amplitude\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eC\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eCorrosion Depth\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ehf\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eFrictional Head Loss\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ek\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eRoughness Height (used in Darcy\u0026ndash;Weisbach)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eD\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eDensity\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eA\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eExposed Surface Area\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eT\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eExposure Time\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eW\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMass Loss\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eE_loss\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eEfficiency Loss\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eα, β,γ\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eRegression Coefficients (Vibration, Corrosion, Intercept)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eR\u0026sup2;\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eCoefficient of Determination\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eRMSE\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eRoot Mean Square Error\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eMAPE\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMean Absolute Percentage Error\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eAR(1)\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eFirst\u0026ndash;Order Autoregressive Model\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eφ\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAutoregressive Coefficient\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eε_t\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eResidual / Error Term\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eAI\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eArtificial Intelligence\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eML\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMachine Learning\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eIoT\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eInternet of Things\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eCNN\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eConvolutional Neural Network\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eRe\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eReynolds Number\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eVIF\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eVariance Inflation Factor\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eACF\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAutocorrelation Function\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ePACF\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ePartial Autocorrelation Function\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eASTM G31\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eStandard Guide for Laboratory Immersion Corrosion Testing\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eEthical Approval\u003c/strong\u003e \u003cp\u003eThis study did not involve human participants, animals, or biological materials. Therefore, ethical approval was not required.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to Participate\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to Publish\u003c/strong\u003e \u003cp\u003eThe author consents to publication of this manuscript.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eConflict of Interest\u003c/h2\u003e \u003cp\u003eThe author declares no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eAuthors\u0026rsquo; Information\u003c/h2\u003e \u003cp\u003eIndependent researcher with no institutional affiliation researcher with no institutional affiliation.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e\u003ch2\u003eAuthors\u0026rsquo; Contributions\u003c/h2\u003e \u003cp\u003eNsini I. Udo \u0026mdash; Conceptualization; Methodology; Simulation; Formal analysis; Writing \u0026ndash; original draft; Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eData supporting the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThanks to the offshore maintenance teams for their support. Data and analysis code are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAl Obaidi A, Sulaiman SA, Hussein L (2016) Effects of seawater salinity on pump efficiency and material degradation. Ocean Eng 111:503\u0026ndash;515\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eASTM International (2021) ASTM G31 21: Standard Guide for Laboratory Immersion Corrosion Testing of Metals. ASTM International, West Conshohocken, PA\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChoi J, Lee S (2014) Performance degradation and vibration response of centrifugal pumps under corrosive operating conditions. J Fluids Eng 136(7):071102\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFrancis R (2010) Seawater corrosion of stainless steels: mechanisms and mitigation. Mater Performance 49:60\u0026ndash;68\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGreen J, Patel N, Singh R (2020) Comparative study of bronze and stainless steel corrosion in seawater. Corros Eng Sci Technol 55:412\u0026ndash;420\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHall D, Gibbons R (2010) Offshore corrosion of metals in seawater. J Offshore Mech Arct Eng 132(4):041301\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJohnson M, Smith R (2007) SEM analysis of corrosion in marine environments. 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Computers Mater Continua 84:3577\u0026ndash;3603. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.32604/cmc.2025.123456\u003c/span\u003e\u003cspan address=\"10.32604/cmc.2025.123456\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar S, Singh A (2017) Effect of seawater on carbon steel degradation. \u003cem\u003eMaterials Today: Proceedings\u003c/em\u003e, 4, 7202\u0026ndash;7209\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi X, Chen Z (2015) Vibration based predictive maintenance for centrifugal pumps. Mech Syst Signal Process 50\u0026ndash;51:118\u0026ndash;132\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMansur T, Rahman M (2008) Corrosion behavior of pump materials in saline water environments. 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Eng 3:1797\u0026ndash;1817\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSouza ACO e, de Souza MB Jr., da Silva FV (2024) Development of a CNN based fault detection system for a real water injection centrifugal pump. \u003cem\u003eExpert Systems with Applications\u003c/em\u003e, 244, 122947\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSuryowinoto A, Albanna I, Fachrul MR (2025) Smart predictive maintenance for centrifugal pumps: How IoT sensors reduce downtime. Int J Artif Intell Rob 7(1):18\u0026ndash;25\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTang A, Lee J, Qian H (2021) Machine learning for predictive maintenance of pumps in offshore platforms. Ocean Eng 235:109375\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Y, Li P (2018) Digital twin based performance monitoring for rotating equipment. J Comput Civil Eng 32(4):04018059\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu T, Zhang Y (2019) Reliability centered maintenance of offshore pumps. Ocean Eng 181:209\u0026ndash;217\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou SW, Zhang L, Yang X, Luo R, Du BG, Zeng W (2025) Remaining useful life prediction method of centrifugal pump rolling bearings based on digital twins. Sci Rep 15(1):19513\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao L, Bi X, Han P (2019) Time series modeling for pump efficiency prediction. Mech Syst Signal Process 129:420\u0026ndash;432\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"None","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"offshore pumps, predictive maintenance, corrosion, centrifugal pump efficiency, vibration analysis, regression modelling, time series, 316L stainless steel and carbon steel and bronze","lastPublishedDoi":"10.21203/rs.3.rs-9445735/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9445735/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOut at sea, oil and gas pumps tend to lose efficiency because of rust and shaking, mostly due to the salt water. We looked at how 316L stainless steel, bronze, and carbon steel pumps broke down using a seawater setup, surface analysis, and vibration tracking for over 200 hours. The test time was set to catch the early stages of rust and shaking working together.\u003c/p\u003e\n\u003cp\u003eThe corrosion rate varied depending on how each material reacts to the seawater, with some forming protective layers while others broke down when chloride was present. Bronze \u003cstrong\u003eexhibited moderate degradation \u003c/strong\u003e(4.4%, p = 0.008; 0.109 mm/yr), but 316L stainless steel held up well (2.5%, p = 0.012; 0.019 mm/yr). Regression showed clear connections between shaking, rust, and efficiency drop (R² = 0.91, p \u0026amp;lt; 0.01). Also, vibration caused subsequent efficiency drop.\u003c/p\u003e\n\u003cp\u003eRust created pits that cause stiffness loss and frequency shifts, leading to more shaking and lower pump efficiency.\u003c/p\u003e\n\u003cp\u003eInstead of just looking at shaking, we put measured rust data into our math models, giving us material-specific decay figures for sea lifespan prediction.\u003c/p\u003e\n\u003cp\u003eStrong ties between pit count, roughness change, and performance drop (R² up to 0.94), which shows how surface breakdown affects pump..\u003c/p\u003e","manuscriptTitle":"Manuscript title: Predictive Maintenance and Performance Modeling of Offshore Centrifugal Pumps under High‑Salinity Conditions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-20 06:19:20","doi":"10.21203/rs.3.rs-9445735/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"389c401f-4791-4a19-99a7-b24cdfdbe19c","owner":[],"postedDate":"April 20th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-20T06:19:20+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-20 06:19:20","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9445735","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9445735","identity":"rs-9445735","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}