Data-Driven Welding Quality Assessment: Leveraging IoT and Machine Learning in Industrial Practice

Data-Driven Welding Quality Assessment: Leveraging IoT and Machine Learning in Industrial Practice | 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 Data-Driven Welding Quality Assessment: Leveraging IoT and Machine Learning in Industrial Practice Nicola Magaletti, Valeria Notarnicola, Mauro Di Molfetta, Stefano Mariani, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6510362/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 The paper investigates the deployment of data analytics and machine learning to improve welding quality in Tecnomulipast srl, a small-to-medium sized manufacturing firm located in Puglia, Italy. The firm produces food machine components and more recently mechanized its laser welding process with the introduction of an IoT-enabled system integrating photographic control. The investment, underwritten by the Apulia Region under PIA (Programmi Integrati di Agevolazione) allowed Tecnomulipast to not only mechanize its production line but also embark upon wider digital transformation. This involved the creation of internal data analytics infrastructures that have the capability to underpin machine learning and artificial intelligence applications. This paper addresses a prediction of weld bead width (LC) with a dataset of 1,000 observations. Input variables are laser power (PL), pulse time (DI), frequency (FI), beam diameter (DF), focal position (PF), travel speed (VE), trajectory accuracy (TR), laser angle (AN), gas flow (FG), gas purity (PG), ambient temperature (TE), and penetration depth (PE). The parameters were exploited to build and validate some supervised machine learning algorithms like Decision Trees, Random Forest, K-Nearest Neighbors, Support Vector Machines, Neural Networks, and Linear Regression. The performance of the models was measured by MSE, RMSE, MAE, MAPE, and R². Ensemble methods like Random Forest and Boosting performed the highest. Feature importance analysis determined that laser power, gas flow, and trajectory accuracy are the key variables. This project showcases the manner in which Tecnomulipast has benefited from public investment to introduce digital transformation and adopt data-driven strategies within Industry 4.0. Tecnomulipast laser welding machine learning digital transformation Industry 4.0 Figures Figure 1 Figure 2 Figure 3 1. Introduction The increasing adoption of artificial intelligence and data analytics within production operations represents a paradigm shift for how production efficiency and quality are tracked and optimized. Although big industries have driven such developments, their application within small-to-medium enterprises (SMEs) of traditional industries like food machinery production is sparse and underresearched. This research bridges that gap by examining how a Southern Italian SME, Tecnomulipast srl, adopted a data-driven approach for predicting and controlling weld quality within an IoT-enabled laser welding machine. The main research question for this research is: To what extent can machine learning models effectively predict weld bead width (LC) as an essential quality metric from real-time process information observed from a digitally transformed welding machine? Despite the proliferation of sensor-rich production environments, extant research is of little help for SMEs that seek to effectively apply machine learning models for real-time quality prediction, especially for highly specialized processes such as laser welding. Most research tends to target big-industry implementation or is restricted within lab-scale experiments. This research offers a new case study of a regionally funded innovation project (via the Apulia Region’s PIA program) where a full-scale machine learning infrastructure was implemented and validated using 1,000 production samples. By comparing multiple supervised algorithms and selecting the best performing predictor, this research offers actionable findings into how SMEs can converge with Industry 4.0 values through extensive, interpretable, as well as scalable, data science techniques. The article continues as follows, the second section presents the analysis of the literature, the third section presents the data and the variables, the fourth section contains the results of the machine learning regressions, the fifth section shows the results of the network analysis, the sixth section contains the conclusions. 2. Literature Review The following commentary critically examines how recent research in the machine learning and laser welding fields supports and enlightens the Tecnomulipast srl, a small and medium-sized enterprise (SME) located within the region of Apulia, Southern Italy. Tecnomulipast is part of a digital transformation process, investing in the deployment of an automated laser welding system fed by an IoT solution and analytics infrastructure. The chosen articles are theoretically and practically relevant to the challenges and opportunities of the company as aligned with Industry 4.0 philosophies. The research by Wang et al. ( 2025 ) lays a solid groundwork by responding to issues of machine learning model generalizability in intelligent welding systems production within automotive production. Their concern for domain adaptation as well as transferability is of specific relevance for Tecnomulipast, an SME, as it, as many SMEs, will have to adapt advanced algorithms to its unique production process, frequently from less of both the necessary data as well as resources compared to large multinational companies. Their multi-sensor data utilization as well as their concern for robustness is closely aligned with the company’s approach of adopting an interconnected, sensor-intensive welding environment. Ma et al. ( 2025 ) make a contribution by using an innovative hybrid strategy that integrates a Kolmogorov-Arnold Network (KAN) with a genetic algorithm for deep penetration laser welding optimization. Their two-layer approach is a balance between prediction accuracy and interpretability—two considerations fundamental for industrial environments where technicians need to trust as well as comprehend the judgments made by artificial intelligent systems. For Tecnomulipast, the use of interpretable models is essential given the low density of internal data science capabilities, as well as the necessity for actionable, transparent outputs from artificial intelligent systems. The paper by Poornima et al. ( 2024 ) proposes a hybrid DNN-HEVA model for weld quality prediction of duplex stainless steel butt welds. Although specific to one material, the approach—merging deep learning with geometric analysis—is extensible to other applications, including Tecnomulipast production processes. Application of techniques for shape-aware modeling is of particular significance for their vision-based inspection system, given the prevalence of weld bead and joint geometrical information for quality evaluation. Din et al. ( 2024 ) break new ground for visual quality inspection by utilizing Vision Transformers for laser welding image classification. Their multi-model feature aggragation approach presents a direction for Tecnomulipast’s photographic process control, as it already samples images during welding processes. The attention mechanism of the transformer could prove crucial for enhancing defect identification, particularly for detecting subtle visual abnormalities that might be overlooked by standard CNNs. In an applied context, Maculotti et al. ( 2024 ) provide a comparison of machine learning models for optimizing laser welding of deep-drawing steel. Their benchmarking strategy is directly applicable to Tecnomulipast’s project, wherein several supervised learning models (such as Random Forest, SVM, Neural Networks) were compared. The research highlights trade-offs between model interpretability, performance, and computational cost—considerations critical for SMEs balancing innovation with efficiency of operation. Hartung et al. ( 2023 ) provide a machine learning approach for weld geometric reconstruction as part of the overall vision for automation of quality control. Their research can be leveraged further for further development at Tecnomulipast, wherein inline inspection is envisioned as part of the digital transformation journey. Reconstructing weld geometry through sensor readings and regression models is a compelling option for minimizing reliance on human observation and enhancing consistency. Ying-chao et al. ( 2023 ) concentrate on real-time monitoring through emission spectroscopy in laser wire welding. Since Tecnomulipast is not as of yet utilizing spectroscopic techniques, the essential principle—multiple-sensor, real-time weld pool monitoring—is very much relevant. Their research supports the necessity of multistreaming as a means of process control as well as detecting anomalies, consistent with Tecnomulipast’s IoT-capable arrangement. Chianese et al. ( 2022 ) examine the application of photodiodes for weld gap and penetration depth sensing of welding between copper and steel, especially for the welding of battery tabs. Their application of low-cost, high-frequency sensors could motivate cost-effective sensor integration by Tecnomulipast, most notably for real-time weld penetration sensing without the introduction of high-end vision systems. Earlier, Cai et al. ( 2019 ) had shown how high-speed imaging and machine learning could be used for predicting weld bead width. Their findings confirmed the value of temporal imaging and algorithmic comparison, as exemplified by Tecnomulipast’s approach of using photographic information to predict quality factors such as bead width and penetration. Practical deployment of predictive models from image information is one of the key innovations of the Tecnomulipast project. Ozkat et al. ( 2017 ) and Sokolov et al. ( 2020 ) offer insights from the viewpoint of physics-based, as well as hybrid modeling. Ozkat’s multi-physics decoupling addresses variability caused by gaps between parts, while Sokolov’s research on keyhole mapping using optical coherence tomography underpins closed-loop control. Although such methods are complex and appropriate for higher-end manufacturing, they represent longer-term innovation pathways that Tecnomulipast could pursue as its system develops further and its digital infrastructure becomes established. These articles demonstrate the international trend toward machine learning- and IoT-driven smart manufacturing systems. They endorse the notion that integrating data-driven models, interpretable artificial intelligence, real-time sensor input, and visual monitoring can make laser welding processes more adaptable and efficient. For Tecnomulipast srl, they provide both motivation and backing. This company, a small enterprise implementing digital transformation through support from its region of origin (PIA - Regione of Apulia, Italy), is a demonstration that even SMEs can be front-runners in implementing intelligent, data-driven technologies for optimizing production. By aligning its initiatives with the techniques and tenets examined within this advanced study, Tecnomulipast is an example for other small businesses within its region wishing to adopt Industry 4.0 technologies. The intersection of machine learning, autonomous inspection, and digital networking is not only a powerful tool for quality improvement, but for the larger sustainability and competitiveness of small manufacturers within the changing global industrial context (Table 1 ). Table 1 Synthesis of the literature. Macro-theme Reference Key Contribution Relevance to Tecnomulipast Generalizable & Scalable ML for Welding Wang et al. ( 2025 ) Generalizable ML framework for intelligent welding in automotive contexts Supports the transfer of scalable ML models to SME-level environments like Tecnomulipast’s real-world setup Maculotti et al. ( 2024 ) Comparison of ML algorithms for laser welding optimization Helps choose the most efficient and interpretable algorithm given SME constraints and real production data Interpretable & Hybrid AI Models Ma et al. ( 2025 ) Interpretable Kolmogorov-Arnold Network with genetic optimization Offers a transparent model for parameter tuning, suitable for a resource-limited SME Poornima et al. ( 2024 ) Hybrid DNN-HEVA model for weld quality prediction Shows the benefit of combining geometry-aware models with AI, useful in Tecnomulipast’s photo-based inspections Image-Based Monitoring & Vision AI Din et al. ( 2024 ) Vision Transformer with feature aggregation for weld image classification Directly relevant to Tecnomulipast’s photographic system for monitoring welds in real time Cai et al. ( 2019 ) Prediction of weld bead width from high-speed images using various ML algorithms Validates the image-based predictive approach used by Tecnomulipast Inline Quality Control & Process Monitoring Hartung et al. ( 2023 ) Geometry reconstruction using ML for automated weld quality control Useful for extending Tecnomulipast’s inspection system with automated defect detection Ying-chao et al. ( 2023 ) Real-time monitoring via emission spectra in laser wire welding Reinforces the importance of continuous monitoring, even if different sensing tech is used Chianese et al. ( 2022 ) Photodiode-based gap and penetration monitoring in dissimilar metal welding Suggests low-cost sensor strategies for penetration monitoring applicable to SMEs Process Control & Closed-Loop Systems Sokolov et al. ( 2020 ) Optical coherence tomography for closed-loop penetration control Presents a future direction for Tecnomulipast’s system evolution towards real-time adaptive control Ozkat et al. ( 2017 ) Multi-physics simulation accounting for part-to-part gap in laser welding Supports hybrid modeling to complement ML, useful for better understanding material-behavior interaction 3. Data and variables The variables employed for training machine learning models for the prediction of production efficiency of a laser machine within a production firm consist of a mixture of process variables, environmental variables, and quality metrics. The product identifier (PRD2T) provides a distinct reference for each of the produced items, making it possible for them to be traced through the observations. Laser power (PL), pulse duration (DI), and pulse frequency (FI) determine the essential energy and temporal laser welding process specifications, which directly impact thermal input as well as welding stability. Beam diameter (DF) and focal position (PF) capture spatial accuracy as well as energy concentration on the target material, relevant for the stability of consistent weld penetration. The travel speed (VE) captures the speed of laser movement, impacting productivity as well as thermal diffusion. Trajectory and repeatability (TR) capture the mechanical accuracy of the machine, one of the most critical indicators of uniform weld paths as well as minimizing defects. The laser incident angle (AN) impacts energy absorption as well as weld geometry, of higher significance for reflective or complex materials. Gas flow (FG) and gas purity (PG) capture the weld pool shielding conditions, critical for preventing contamination as well as porosity. Ambient temperature (TE) captures context for thermal fluctuations that could affect stability of process. And finally, penetration depth (PE) as well as bead width (LC) are direct quality indicators of the weld as well as can be employed as target variables as well as efficiency as well as consistency proxies within supervised learning models that can predict the efficiency as well as uniformity of the laser machine (Table 2 ). Table 2 Description of Variables. Description Unit of measurement and range Acronym Product Unique identifier for each product produced. It is represented with a progressive number. PRD2T Laser power (W) Energy supplied by the laser to perform the welding. Expressed in Watts (W). Usually variable between 1500 W and 1800 W. PL Pulse duration (ms) Time during which the laser remains active for each pulse. Expressed in milliseconds (ms). Variable between 5 and 8 ms. DI Pulse frequency (Hz) Number of laser pulses per second. Expressed in Hertz (Hz). Typically variable between 2000 and 2300 Hz. FI Beam diameter (µm) Width of the laser beam at the welding point. Expressed in microns (µm). Typically between 100 and 130 µm. DF Focal position (mm) Focal distance from the material surface. Expressed in millimeters (mm). Varies between − 0.5 mm, 0 mm, + 0.5 mm, 1 mm. PF Travel speed (mm/s) Speed ​​with which the laser moves during the welding process. Expressed in mm/s. Varies between 10 and 13 mm/s. VE Trajectory and repeatability Accuracy and repeatability of the laser movement system. Typical values: < ±0.1 mm, < ±0.15 mm, < ±0.2 mm, < ±0.25 mm. TR Laser incidence angle (°) Angle formed by the laser beam from the material surface. Typical values: 75°, 80°, 85°, 90°. AN Gas flow Type of gas used to protect the welding pool and keep it pure. Expressed in l/min for flow FG Gas purity Type of gas used to protect the welding pool and keep it pure. % for purity. PG Ambient temperature (°C) Temperature of the environment in which the welding is performed. Variable between 25°C and 28°C. TE Penetration (mm) Depth of the welding in the material. Expressed in mm. Typically between 1.5 mm and 3.5 mm. PE Bead width (µm) Width of the welding line generated by the laser. Expressed in microns (µm). Typically between 200 µm and 500 µm. LC The information pertains to a company whose welding process is automated by a machine fitted with IoT as well as photographic inspection technologies. All variables have 1000 valid values with no missing values. Values seem normalized with z-score standardization, as evidenced by means near zero and standard deviations near one, making them ready for higher-level statistical analysis or machine learning applications. Both process parameters (laser power, pulse length, frequency, speed, beam width, focal position) as well as output characteristics (bead width, penetration) are the main variables. Their distributions have mild asymmetry and platykurtic behavior, with flatter distribution compared to a normal distribution. This is supported by consistently negative kurtosis values as well as by the Shapiro-Wilk test, whose p-values are lower than 0.001 for all variables, rejecting the normality hypothesis. The most relevant output variables, bead width (LC) and penetration (PE), have negative skewness, meaning that the data have heavier tails on the left side of the distribution and that welds most often have values higher than the mean, although by a minor amount. The machine would seem to have good operating stability, as interquartile ranges are thin, and median absolute deviations are low for all variables, meaning there is little dispersion. Since the non-normal distribution of the data, however, could make classical linear models insufficient for identifying underlying patterns, robust or non-parametric statistical analysis could be needed. Gas-related variables such as gas flow (FG) and gas purity (PG) have higher skewness and modes, perhaps as a consequence of batch variation, as well as of the application of different shielding strategies for different welding contexts. In summary, the data represent a technologically mature, well-maintained system, whose well-regulated parameters, however, have usual variation typical of industrial automation processes (Table 3 ). Table 3 Descriptive Statistics. LC DI FI VE AN TE PL DF PF TR FG PG PE Valid 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Missing 0 0 0 0 0 0 0 0 0 0 0 0 0 Mode 0.731 0.610 -1.607 0.283 -1.315 1.343 1.164 -0.839 1.145 1.096 -1.646 1.192 -1.326 Median 0.277 0.011 -0.039 0.014 -0.010 -0.010 0.057 -0.024 0.278 0.190 -0.099 0.318 0.267 Mean -7.000×10 − 9 1.000×10 − 9 1.400×10 − 8 3.000×10 − 9 5.000×10 − 9 -2.100×10 − 8 2.600×10 − 8 6.000×10 − 9 1.050×10 − 7 7.800×10 − 8 -3.189×10–18 3.900×10 − 8 6.000×10 − 9 Std. Deviation 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 Coefficient of variation -1.429×10 + 8 1.001×10 + 9 7.146×10 + 7 3.335×10 + 8 2.001×10 + 8 -4.764×10 + 7 3.848×10 + 7 1.668×10 + 8 9.529×10 + 6 1.283×10 + 7 -3.138×10 + 17 2.565×10 + 7 1.668×10 + 8 MAD 0.686 0.876 0.871 0.841 0.967 0.861 1.010 0.863 0.867 0.905 0.927 0.829 0.734 MAD robust 1.017 1.298 1.291 1.247 1.434 1.277 1.498 1.280 1.286 1.342 1.375 1.229 1.089 IQR 2.068 1.751 1.758 1.683 1.934 1.699 2.008 1.728 2.169 2.112 1.855 1.883 1.995 Variance 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 Skewness -0.380 0.003 0.076 0.011 0.019 -0.033 0.001 9.900×10 − 4 -0.211 -0.148 0.001 -0.280 -0.353 Std. Error of Skewness 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 Kurtosis -1.473 -1.221 -1.188 -1.170 -1.510 -1.198 -1.931 -1.222 -1.473 -1.651 -1.580 -1.471 -1.392 Std. Error of Kurtosis 0.155 0.155 0.155 0.155 0.155 0.155 0.155 0.155 0.155 0.155 0.155 0.155 0.155 Shapiro-Wilk 0.856 0.953 0.953 0.957 0.913 0.954 0.749 0.954 0.854 0.811 0.895 0.880 0.894 P-value of Shapiro-Wilk < .001 < .001 < .001 < .001 < .001 < .001 < .001 < .001 < .001 < .001 < .001 < .001 < .001 Range 3.173 3.456 3.426 3.494 3.675 3.482 2.330 4.474 2.602 2.414 3.431 3.514 3.734 Minimum -1.838 -1.717 -1.687 -1.739 -1.886 -1.755 -1.166 -2.257 -1.457 -1.318 -1.646 -2.322 -2.085 Maximum 1.335 1.739 1.739 1.755 1.789 1.727 1.164 2.216 1.145 1.096 1.786 1.192 1.649 25th percentile -1.169 -0.876 -0.884 -0.850 -0.964 -0.825 -1.004 -0.875 -1.024 -1.017 -0.925 -0.936 -1.105 50th percentile 0.277 0.011 -0.039 0.014 -0.010 -0.010 0.057 -0.024 0.278 0.190 -0.099 0.318 0.267 75th percentile 0.899 0.875 0.874 0.832 0.970 0.874 1.004 0.853 1.145 1.096 0.930 0.947 0.889 25th percentile -1.169 -0.876 -0.884 -0.850 -0.964 -0.825 -1.004 -0.875 -1.024 -1.017 -0.925 -0.936 -1.105 50th percentile 0.277 0.011 -0.039 0.014 -0.010 -0.010 0.057 -0.024 0.278 0.190 -0.099 0.318 0.267 75th percentile 0.899 0.875 0.874 0.832 0.970 0.874 1.004 0.853 1.145 1.096 0.930 0.947 0.889 Sum -7.000×10 − 6 1.000×10 − 6 1.400×10 − 5 3.000×10 − 6 5.000×10 − 6 -2.100×10 − 5 2.600×10 − 5 6.000×10 − 6 1.050×10 − 4 7.800×10 − 5 -1.665×10–15 3.900×10 − 5 6.000×10 − 6 4. Machine Learning Assessing information on automatic welding within the framework of Industry 4.0 is a strategic action for a small-to-medium company such as Tecnomulipast srl, from Southern Italy operating within the food machinery production industry. IoT technology integration with real-time acquisition systems turns a standard production activity into an intelligent, trackable, and optimizable function. Data analysis from welding enables the company not only to track joint quality with accuracy, minimize process variation, predict anomalies, and enhance overall efficiency, but is critical for raising competitiveness within an industrialized, globalized world. Comparing between machine learning models such as Boosting, Decision Tree, K-Nearest Neighbors, Linear Regression, Neural Networks, Random Forest, Regularized Linear Regression, and Support Vector Machine is of prime relevance as each of the models differs as regards predictive capacity, interpretability, and adaptability to the dataset. Knowing the best-performing algorithm is not only a matter of selecting the best-performing solution, but the one that is stable, efficient, and scalable given available technical and infrastructural capabilities. Technically-scientifically, utilizing the following statistical indicators as evaluation metrics such as MSE (Mean Squared Error), MSE (scaled), RMSE (Root Mean Squared Error), MAE/MAD (Mean Absolute Error / Median Absolute Deviation), MAPE (Mean Absolute Percentage Error), R² (Coefficient of Determination) is methodologically accurate, widely adopted within the industrial data science best practices, and well-accepted within the scientific literature. These metrics enable an integral analysis of model quality by capturing error size (MSE, RMSE), outlier resistance (MAE, MAD), relative error (MAPE), as well as the capacity of the model for variance explanation of the target factor (R²). Their joint utilization enables a balanced, objective, reproducible evaluation that is best practice within industrial-grade data science. We have estimated the following equation: $$\:LC=f(PL,DI,FI,DF,PF,VE,TR,AN,FG,PG,TE,PE)$$ Facing the normalized performance measures of the various machine learning models used for the weld bead width (LC) prediction task, Random Forest is the most precision, stable, and generalization-capacity-rich algorithm. It consistently produces the best outcome for virtually all the evaluation metrics. In particular, it captures the lowest achievable values for MSE, MSE (scaled), RMSE, MAE/MAD, and MAPE—reflecting the smallest prediction error—while also capturing the highest value of R² (1.000) that guarantees perfect adaptability within the normalized framework. Boosting is likewise a highly performing algorithm, ranking second best by the majority of the metrics through an R² value of 0.806 as well as low error values for MSE (0.241), RMSE (0.174), and MAPE (0.116), reflecting high reliability as well as stability. Neural Networks exhibit competitive efficiency through an R² value of 0.758 coupled with relatively low values of MSE as well as MAPE, reflecting their suitability as an alternative. Support Vector Machines as well as Regularized Linear Regression prove mediocre efficiency, whereas K-Nearest Neighbors performs with the worst, through an R² value of 0.000 alongside the highest errors for all the metrics. The Decision Tree model performs better than KNN but not as efficiently as ensemble-based methods through its lower generalization capacity. To sum up, Random Forest is the best choice for the task through precision, stability, as well as generalization, whereas Boosting offers a strong alternative with equivalent reliability within predictive welding analytics (Table 4 ). Table 4 Machine learning analysis results with an indication of the performance of the algorithms. Metric Boosting Decision Tree KNN Linear Regression Neural Net Random Forest Regularized Linear SVM MSE 0.241 0.379 1.000 0.655 0.310 0.000 0.586 0.517 MSE (scaled) 0.179 0.393 1.000 0.393 0.250 0.000 0.536 0.464 RMSE 0.174 0.297 1.000 0.487 0.165 0.000 0.408 0.382 MAE / MAD 0.051 0.000 1.000 0.759 0.228 0.088 0.684 0.620 MAPE 0.116 0.000 1.000 0.312 0.165 0.005 0.803 0.115 R² 0.806 0.645 0.000 0.516 0.758 1.000 0.452 0.581 Selecting Random Forest as our best-performing model, we can analyze the feature importance values to see how much each of the input variables contributes toward predicting weld bead width (LC) most strongly. The table offers three indicators for each of the variables: Mean decrease in accuracy, Total increase in node purity, and Mean dropout loss. These all measure how much each of the variables contributes toward building the model’s predictability. By far the most powerful is clearly PE (penetration depth), with the highest mean decrease in accuracy (0.522), highest increase in node purity (94.680), and highest mean dropout loss (0.598). This is consistent with the expectation that weld penetration is closely correlated with bead width and is a very critical quality determinant of welding in the current scenario. Second is significantly PL (laser power) with a strong decrease in accuracy (0.369), a high node purity (68.918), and a very high dropout loss (0.399). Not unexpectedly, laser power directly controls the energy input during the welding process. Following are FG (gas flow) and PG (gas purity) with values for all metrics rather near-identical. Both of the parameters are crucial for providing a clean welding environment and for preventing defects, so their influence is not surprising. AN (laser angle) and DF (beam diameter) are moderately important, indicating a secondary but still contributary role toward the quality of the weld. Least of all are DI (pulse duration), VE (travel speed), and FI (pulse frequency). Their very low values for all metrics point toward a minor influence on the output within the specific operating window of this dataset. Least of all is TE (ambient temperature), PF (focal position), and TR (trajectory repeatability). These variables are most likely kept relatively constant during operation, or perhaps have previously had their optimal values optimized, so their variability is minimized, and their statistical impact is low. In conclusion, the Random Forest model singles out the penetration depth, laser power, and gas parameters as the prime drivers of bead width of weld during the automated process of Tecnomulipast srl. These findings not only make sense from the welding physics point of view, but they also offer actionable targets for controlling the process, as well as for optimizing the process, within the context of Industry 4.0 (Fig. 1 ). The following is an additive feature attribution output for five test cases, as given by the Random Forest model for predicting weld bead width (LC). The values, presumably created by a SHAP or equivalent interpretability procedure, demonstrate the contribution of each attribute, relative to a set value (the "Base" column, constant at − 0.045 for all cases). In both instances, the value predicted is much less than the base, varying between − 1.226 and − 1.390. This is a decrease from the base because of the cumulative adverse effects of some of the main features, specifically PE (penetration depth), PL (laser power), FG (gas flow), and PG (gas purity). PE is consistently the greatest negative contributor in all cases, ranging from − 0.38 to − 0.384. This is consistent with what is observed in the feature importance as well: the greatest contribution is by penetration depth, significantly pulling the prediction down. PL is seen to have strong negative effect, from − 0.287 to − 0.296. This is consistent with its function of regulating power input—greater power can result in wider bead width, and such deviations from optimal power values would contribute negatively within these given test cases. FG and PG have strong to moderate negative effects, supporting the significance of gas parameters for weld quality. The steady values for all the cases (approximately between − 0.17 and − 0.20 for FG, and between − 0.13 and − 0.15 for PG) demonstrate stable, though considerable, impact on the estimated outcome. The other variables, such as DF (beam diameter) and AN (angle of incidence), have negative contributions across all instances, though less so. Their directional regularity assures constant though secondary impacts on the model's projections. In contrast, variables such as VE (speed of travel) and PF (position of focus) display slight positive or zero effects, occasionally helping raise the prediction by a slight amount. FI (pulse frequency), DI (pulse duration), TR (repeatability of trajectory), and TE (ambient temperature) have near-zero or low effects, consistent with their low values of feature importance. In conclusion, such findings uphold interpretability and internal consistency of the Random Forest model. The most salient features—penetration depth, laser power, and gas flow settings—exhibit the highest and most uniform effects on the predictions for varying test cases. This reflects the model’s capability for yielding trustworthy, understandable information for quality control of welding for applications such as real-time predictive systems within the context of Industry 4.0 (Fig. 2 ). 5. Network analysis After performing a machine learning analysis, it is logical, therefore, to apply network analysis with centrality metrics because machine learning models are good at predicting but do not necessarily capture the internal dynamics of interdependencies among variables. Network analysis offers a structural representation of the relationships, giving further insight into the interplay of variables with each other within the system. By examining centrality metrics like betweenness, closeness, strength, and expected influence, one can determine where variables are central, where they are bridges, and where they are on the periphery. For example, PL (laser power) is ranked highest for all centrality metrics, meaning that it is the most powerful, influencing role within the network of variables. This is as expected given its probable significance within predictive models. DF (beam diameter) and PF (focal position) have significant betweenness, meaning they are connectors between variables, potentially affecting multiple paths even though they are not necessarily the most direct influencers. In contrast, for variables such as DI, FI, and TR, there are negative values for all metrics, suggesting they are not so much central and potentially have isolated effects on the system. Furthermore, network analysis offers the ability to corroborate the machine learning by comparing network metrics with importances from the model, as well as identifying redundant, weakly connected variables, facilitating reduction of dimensions and feature choice. Having the ability to see possible chains of influence among variables improves interpretability of intricate models, such as within industrial environments where behavior of the system is as critical as is predictive accuracy. In all, the combination of network analysis with centrality metrics following machine learning creates a fuller, system-level view that helps interpret models, streamline processes, as well as make informed choices on variable significance as well as role interplay (Fig. 3 ). 6. Conclusions The paper showcases the real-world application value of IoT-enabled data acquisition systems coupled with machine learning methods for improving weld quality prediction for a small-to-medium-sized manufacturing company. In a real-case study of Tecnomulipast srl based in Gravina in Puglia, supported by public funds through the PIA program, the research showcases how a digitalized production environment can make sophisticated predictive analytics available for laser welding. Among the machine learning algorithms applied, Random Forest was identified as the best-performing algorithm, indicating the best prediction accuracy for all the considered performances (MSE, RMSE, MAE, MAPE, and R²). The chosen model not only produced low prediction errors, but for detailed interpretability, feature significance analysis as well as additive contribution methods could be employed. Penetration depth (PE), laser power (PL), and gas flow parameters (FG, PG) were recognized as the main factors affecting weld bead width (LC), yielding actionable insights for process improvement as well as quality control. In addition, the application of network analysis based on centrality indicators provided a complementary view of interdependencies among variables. This methodology disclosed structural interconnections between parameters, corroborating machine learning evidence and allowing for better interpretability of models. Laser power and beam geometry turned out to be central variables within the topology of the system, indicating their decisive impact not only on output quality but on process dynamics as well. Altogether, the research affirms that a union of machine learning with network analysis yields predictive capabilities, as well as systemic insight. For SMEs, looking forward to adapting to Industry 4.0, this dual strategy addresses a scalable, transparent, and efficient framework for optimizing production through data. Declarations Acknowledgement Results obtained in the research and development project "Tecnomulipast" - Codice Pratica 683TK4 - a valere sul Bando Programmi Integrati di Agevolazioni PIA Piccole Imprese (Art 27 Reg. Regionale 17/2014 e smi). References Wang, P. E., Ghassemi-Armaki, H., Pour, M., Zhao, X., Ma, J., Sattari, K., & Carlson, B. (2025). Applicable and generalizable machine learning for intelligent welding in automotive manufacturing. Welding in the World, 1-36. Ma, S., Leng, J., Chen, Z., Du, Y., Zhang, X., & Liu, Q. (2025). Intrinsically and Post-Hoc Interpretable Kolmogorov-Arnold Network and Genetic Algorithm for Laser Deep Penetration Welding Parameters Optimization. IEEE Transactions on Instrumentation and Measurement. Poornima, C. L., Rao, C. S., & Varma, D. N. (2024). Predicting weld quality in duplex stainless steel butt joints during laser beam welding: a hybrid DNN-HEVA approach. Journal of Advanced Manufacturing Systems, 23(04), 801-836. Din, N. U., Zhang, L., Nawaz, M. S., & Yang, Y. (2024). Multi-model feature aggregation for classification of laser welding images with vision transformer. Journal of King Saud University-Computer and Information Sciences, 36(5), 102049. Maculotti, G., Genta, G., & Galetto, M. (2024). Optimisation of laser welding of deep drawing steel for automotive applications by Machine Learning: A comparison of different techniques. Quality and Reliability Engineering International, 40(1), 202-219. Hartung, J., Jahn, A., & Heizmann, M. (2023). Machine learning based geometry reconstruction for quality control of laser welding processes. tm-Technisches Messen, 90(7-8), 512-521. Ying-chao, F., Yi-ming, H., Jin-ping, L., Chen-peng, J., Peng, C., Shao-jie, W., ... & Huan-wei, Y. (2023). On-Line Monitoring of Laser Wire Filling Welding Process Based on Emission Spectrum. SPECTROSCOPY AND SPECTRAL ANALYSIS, 43(6), 1927-1935. Chianese, G., Franciosa, P., Nolte, J., Ceglarek, D., & Patalano, S. (2022). Characterization of photodiodes for detection of variations in part-to-part gap and weld penetration depth during remote laser welding of copper-to-steel battery tab connectors. Journal of Manufacturing Science and Engineering, 144(7), 071004. Cai, W., Wang, J., Cao, L., Mi, G., Shu, L., Zhou, Q., & Jiang, P. (2019). Predicting the weld width from high-speed successive images of the weld zone using different machine learning algorithms during laser welding. Math. Biosci. Eng, 16(5), 5595-5612. Ozkat, E. C., Franciosa, P., & Ceglarek, D. (2017). Development of decoupled multi-physics simulation for laser lap welding considering part-to-part gap. Journal of Laser Applications, 29(2). Sokolov, M., Franciosa, P., Al Botros, R., & Ceglarek, D. (2020). Keyhole mapping to enable closed-loop weld penetration depth control for remote laser welding of aluminum components using optical coherence tomography. Journal of Laser Applications, 32(3). 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. 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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-6510362","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":446772340,"identity":"f361f4a3-96b6-452c-b505-b81c1e0e5b15","order_by":0,"name":"Nicola Magaletti","email":"","orcid":"","institution":"LUM Enterprise s.r.l.","correspondingAuthor":false,"prefix":"","firstName":"Nicola","middleName":"","lastName":"Magaletti","suffix":""},{"id":446772341,"identity":"52f8d3dc-151c-4d87-a930-867d111f1786","order_by":1,"name":"Valeria Notarnicola","email":"","orcid":"","institution":"LUM Enterprise s.r.l.","correspondingAuthor":false,"prefix":"","firstName":"Valeria","middleName":"","lastName":"Notarnicola","suffix":""},{"id":446772342,"identity":"45f864e9-0615-450e-96ef-477de1614e46","order_by":2,"name":"Mauro Di Molfetta","email":"","orcid":"","institution":"LUM Enterprise s.r.l.","correspondingAuthor":false,"prefix":"","firstName":"Mauro","middleName":"Di","lastName":"Molfetta","suffix":""},{"id":446772343,"identity":"c3360824-3dc9-4837-a004-0b6359ef13d9","order_by":3,"name":"Stefano Mariani","email":"","orcid":"","institution":"LUM Enterprise s.r.l.","correspondingAuthor":false,"prefix":"","firstName":"Stefano","middleName":"","lastName":"Mariani","suffix":""},{"id":446772344,"identity":"e5031524-8c90-4dda-8a50-3bcf155d5994","order_by":4,"name":"Angelo Leogrande","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYBACPijN2AAiH4AI9mYQWwKnFjYULQkJQILnIFgLTj1YtEgkgtm4tbA3H35dUXNHtp+B+ZlE4g+bfH7Jh21SNxgs6nBq4TmWZnnm2DPjmQ1sZhIJCWmWM2cntknn4HOYRI6ZYQPb4cQNB3jYgFoOGxjcJqRF/g1Qy7/DifthWuxvHiRkC4/xw8Y2oC0MMFskGAlo4UlLY2zsO2w84zCbsUVCWpqBxJnEZuscAwnJBhxa+NkPH/7Y8O2wbH9788MbH2xsDPjbDx+8nVNRx4/LFrDbwBQziqABHg1AtR/wSo+CUTAKRsEoAABg1U/Q4kxZZwAAAABJRU5ErkJggg==","orcid":"","institution":"LUM Enterprise s.r.l.","correspondingAuthor":true,"prefix":"","firstName":"Angelo","middleName":"","lastName":"Leogrande","suffix":""}],"badges":[],"createdAt":"2025-04-23 08:09:28","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-6510362/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6510362/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81344056,"identity":"fe339ba6-86f4-4e0d-bf85-1b1875efefce","added_by":"auto","created_at":"2025-04-25 04:09:07","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":134313,"visible":true,"origin":"","legend":"\u003cp\u003eFeature Importance Metrics of Random Forest Regression.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6510362/v1/6ebd363799c3e3be1b0184dd.png"},{"id":81344064,"identity":"f7b89804-ce02-4b6e-9e84-c838d75ecf91","added_by":"auto","created_at":"2025-04-25 04:09:07","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":160282,"visible":true,"origin":"","legend":"\u003cp\u003ePredictions using Random Forest Regression.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6510362/v1/6271981c97489eadbe2d34ac.png"},{"id":81344057,"identity":"a3234f71-d5d7-4e53-852e-ee1f7887cbdc","added_by":"auto","created_at":"2025-04-25 04:09:07","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":191356,"visible":true,"origin":"","legend":"\u003cp\u003eNetwork Analysis.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6510362/v1/c649e419dc1229f293b6480f.png"},{"id":81344652,"identity":"d3e5fb6d-c4bc-4d17-a518-48ade94f878d","added_by":"auto","created_at":"2025-04-25 04:25:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1279018,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6510362/v1/382a5a08-b89b-4b00-bbb3-30aca9d72630.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eData-Driven Welding Quality Assessment: Leveraging IoT and Machine Learning in Industrial Practice\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe increasing adoption of artificial intelligence and data analytics within production operations represents a paradigm shift for how production efficiency and quality are tracked and optimized. Although big industries have driven such developments, their application within small-to-medium enterprises (SMEs) of traditional industries like food machinery production is sparse and underresearched. This research bridges that gap by examining how a Southern Italian SME, Tecnomulipast srl, adopted a data-driven approach for predicting and controlling weld quality within an IoT-enabled laser welding machine. The main research question for this research is: To what extent can machine learning models effectively predict weld bead width (LC) as an essential quality metric from real-time process information observed from a digitally transformed welding machine? Despite the proliferation of sensor-rich production environments, extant research is of little help for SMEs that seek to effectively apply machine learning models for real-time quality prediction, especially for highly specialized processes such as laser welding. Most research tends to target big-industry implementation or is restricted within lab-scale experiments. This research offers a new case study of a regionally funded innovation project (via the Apulia Region\u0026rsquo;s PIA program) where a full-scale machine learning infrastructure was implemented and validated using 1,000 production samples. By comparing multiple supervised algorithms and selecting the best performing predictor, this research offers actionable findings into how SMEs can converge with Industry 4.0 values through extensive, interpretable, as well as scalable, data science techniques.\u003c/p\u003e \u003cp\u003eThe article continues as follows, the second section presents the analysis of the literature, the third section presents the data and the variables, the fourth section contains the results of the machine learning regressions, the fifth section shows the results of the network analysis, the sixth section contains the conclusions.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003cp\u003eThe following commentary critically examines how recent research in the machine learning and laser welding fields supports and enlightens the Tecnomulipast srl, a small and medium-sized enterprise (SME) located within the region of Apulia, Southern Italy. Tecnomulipast is part of a digital transformation process, investing in the deployment of an automated laser welding system fed by an IoT solution and analytics infrastructure. The chosen articles are theoretically and practically relevant to the challenges and opportunities of the company as aligned with Industry 4.0 philosophies. The research by Wang et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) lays a solid groundwork by responding to issues of machine learning model generalizability in intelligent welding systems production within automotive production. Their concern for domain adaptation as well as transferability is of specific relevance for Tecnomulipast, an SME, as it, as many SMEs, will have to adapt advanced algorithms to its unique production process, frequently from less of both the necessary data as well as resources compared to large multinational companies. Their multi-sensor data utilization as well as their concern for robustness is closely aligned with the company\u0026rsquo;s approach of adopting an interconnected, sensor-intensive welding environment.\u003c/p\u003e \u003cp\u003eMa et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) make a contribution by using an innovative hybrid strategy that integrates a Kolmogorov-Arnold Network (KAN) with a genetic algorithm for deep penetration laser welding optimization. Their two-layer approach is a balance between prediction accuracy and interpretability\u0026mdash;two considerations fundamental for industrial environments where technicians need to trust as well as comprehend the judgments made by artificial intelligent systems. For Tecnomulipast, the use of interpretable models is essential given the low density of internal data science capabilities, as well as the necessity for actionable, transparent outputs from artificial intelligent systems.\u003c/p\u003e \u003cp\u003eThe paper by Poornima et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) proposes a hybrid DNN-HEVA model for weld quality prediction of duplex stainless steel butt welds. Although specific to one material, the approach\u0026mdash;merging deep learning with geometric analysis\u0026mdash;is extensible to other applications, including Tecnomulipast production processes. Application of techniques for shape-aware modeling is of particular significance for their vision-based inspection system, given the prevalence of weld bead and joint geometrical information for quality evaluation. Din et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) break new ground for visual quality inspection by utilizing Vision Transformers for laser welding image classification. Their multi-model feature aggragation approach presents a direction for Tecnomulipast\u0026rsquo;s photographic process control, as it already samples images during welding processes. The attention mechanism of the transformer could prove crucial for enhancing defect identification, particularly for detecting subtle visual abnormalities that might be overlooked by standard CNNs.\u003c/p\u003e \u003cp\u003eIn an applied context, Maculotti et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) provide a comparison of machine learning models for optimizing laser welding of deep-drawing steel. Their benchmarking strategy is directly applicable to Tecnomulipast\u0026rsquo;s project, wherein several supervised learning models (such as Random Forest, SVM, Neural Networks) were compared. The research highlights trade-offs between model interpretability, performance, and computational cost\u0026mdash;considerations critical for SMEs balancing innovation with efficiency of operation. Hartung et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) provide a machine learning approach for weld geometric reconstruction as part of the overall vision for automation of quality control. Their research can be leveraged further for further development at Tecnomulipast, wherein inline inspection is envisioned as part of the digital transformation journey. Reconstructing weld geometry through sensor readings and regression models is a compelling option for minimizing reliance on human observation and enhancing consistency.\u003c/p\u003e \u003cp\u003eYing-chao et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) concentrate on real-time monitoring through emission spectroscopy in laser wire welding. Since Tecnomulipast is not as of yet utilizing spectroscopic techniques, the essential principle\u0026mdash;multiple-sensor, real-time weld pool monitoring\u0026mdash;is very much relevant. Their research supports the necessity of multistreaming as a means of process control as well as detecting anomalies, consistent with Tecnomulipast\u0026rsquo;s IoT-capable arrangement. Chianese et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) examine the application of photodiodes for weld gap and penetration depth sensing of welding between copper and steel, especially for the welding of battery tabs. Their application of low-cost, high-frequency sensors could motivate cost-effective sensor integration by Tecnomulipast, most notably for real-time weld penetration sensing without the introduction of high-end vision systems.\u003c/p\u003e \u003cp\u003eEarlier, Cai et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) had shown how high-speed imaging and machine learning could be used for predicting weld bead width. Their findings confirmed the value of temporal imaging and algorithmic comparison, as exemplified by Tecnomulipast\u0026rsquo;s approach of using photographic information to predict quality factors such as bead width and penetration. Practical deployment of predictive models from image information is one of the key innovations of the Tecnomulipast project. Ozkat et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Sokolov et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) offer insights from the viewpoint of physics-based, as well as hybrid modeling. Ozkat\u0026rsquo;s multi-physics decoupling addresses variability caused by gaps between parts, while Sokolov\u0026rsquo;s research on keyhole mapping using optical coherence tomography underpins closed-loop control. Although such methods are complex and appropriate for higher-end manufacturing, they represent longer-term innovation pathways that Tecnomulipast could pursue as its system develops further and its digital infrastructure becomes established.\u003c/p\u003e \u003cp\u003eThese articles demonstrate the international trend toward machine learning- and IoT-driven smart manufacturing systems. They endorse the notion that integrating data-driven models, interpretable artificial intelligence, real-time sensor input, and visual monitoring can make laser welding processes more adaptable and efficient. For Tecnomulipast srl, they provide both motivation and backing. This company, a small enterprise implementing digital transformation through support from its region of origin (PIA - Regione of Apulia, Italy), is a demonstration that even SMEs can be front-runners in implementing intelligent, data-driven technologies for optimizing production. By aligning its initiatives with the techniques and tenets examined within this advanced study, Tecnomulipast is an example for other small businesses within its region wishing to adopt Industry 4.0 technologies. The intersection of machine learning, autonomous inspection, and digital networking is not only a powerful tool for quality improvement, but for the larger sustainability and competitiveness of small manufacturers within the changing global industrial context (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSynthesis of the literature.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMacro-theme\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eKey Contribution\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRelevance to Tecnomulipast\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eGeneralizable \u0026amp; Scalable ML for Welding\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWang et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGeneralizable ML framework for intelligent welding in automotive contexts\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSupports the transfer of scalable ML models to SME-level environments like Tecnomulipast\u0026rsquo;s real-world setup\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaculotti et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComparison of ML algorithms for laser welding optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHelps choose the most efficient and interpretable algorithm given SME constraints and real production data\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eInterpretable \u0026amp; Hybrid AI Models\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMa et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2025\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInterpretable Kolmogorov-Arnold Network with genetic optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOffers a transparent model for parameter tuning, suitable for a resource-limited SME\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePoornima et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHybrid DNN-HEVA model for weld quality prediction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShows the benefit of combining geometry-aware models with AI, useful in Tecnomulipast\u0026rsquo;s photo-based inspections\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eImage-Based Monitoring \u0026amp; Vision AI\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDin et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVision Transformer with feature aggregation for weld image classification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDirectly relevant to Tecnomulipast\u0026rsquo;s photographic system for monitoring welds in real time\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCai et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePrediction of weld bead width from high-speed images using various ML algorithms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eValidates the image-based predictive approach used by Tecnomulipast\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cb\u003eInline Quality Control \u0026amp; Process Monitoring\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHartung et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGeometry reconstruction using ML for automated weld quality control\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eUseful for extending Tecnomulipast\u0026rsquo;s inspection system with automated defect detection\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYing-chao et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReal-time monitoring via emission spectra in laser wire welding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReinforces the importance of continuous monitoring, even if different sensing tech is used\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eChianese et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePhotodiode-based gap and penetration monitoring in dissimilar metal welding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSuggests low-cost sensor strategies for penetration monitoring applicable to SMEs\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eProcess Control \u0026amp; Closed-Loop Systems\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSokolov et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOptical coherence tomography for closed-loop penetration control\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePresents a future direction for Tecnomulipast\u0026rsquo;s system evolution towards real-time adaptive control\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOzkat et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2017\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMulti-physics simulation accounting for part-to-part gap in laser welding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSupports hybrid modeling to complement ML, useful for better understanding material-behavior interaction\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"3. Data and variables","content":"\u003cp\u003eThe variables employed for training machine learning models for the prediction of production efficiency of a laser machine within a production firm consist of a mixture of process variables, environmental variables, and quality metrics. The product identifier (PRD2T) provides a distinct reference for each of the produced items, making it possible for them to be traced through the observations. Laser power (PL), pulse duration (DI), and pulse frequency (FI) determine the essential energy and temporal laser welding process specifications, which directly impact thermal input as well as welding stability. Beam diameter (DF) and focal position (PF) capture spatial accuracy as well as energy concentration on the target material, relevant for the stability of consistent weld penetration. The travel speed (VE) captures the speed of laser movement, impacting productivity as well as thermal diffusion. Trajectory and repeatability (TR) capture the mechanical accuracy of the machine, one of the most critical indicators of uniform weld paths as well as minimizing defects. The laser incident angle (AN) impacts energy absorption as well as weld geometry, of higher significance for reflective or complex materials. Gas flow (FG) and gas purity (PG) capture the weld pool shielding conditions, critical for preventing contamination as well as porosity. Ambient temperature (TE) captures context for thermal fluctuations that could affect stability of process. And finally, penetration depth (PE) as well as bead width (LC) are direct quality indicators of the weld as well as can be employed as target variables as well as efficiency as well as consistency proxies within supervised learning models that can predict the efficiency as well as uniformity of the laser machine (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescription of Variables.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnit of measurement and range\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAcronym\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProduct\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnique identifier for each product produced.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIt is represented with a progressive number.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePRD2T\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLaser power (W)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnergy supplied by the laser to perform the welding.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in Watts (W). Usually variable between 1500 W and 1800 W.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePL\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePulse duration (ms)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTime during which the laser remains active for each pulse.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in milliseconds (ms). Variable between 5 and 8 ms.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDI\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePulse frequency (Hz)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of laser pulses per second.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in Hertz (Hz). Typically variable between 2000 and 2300 Hz.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFI\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBeam diameter (\u0026micro;m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWidth of the laser beam at the welding point.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in microns (\u0026micro;m). Typically between 100 and 130 \u0026micro;m.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDF\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFocal position (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFocal distance from the material surface.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in millimeters (mm). Varies between \u0026minus;\u0026thinsp;0.5 mm, 0 mm, +\u0026thinsp;0.5 mm, 1 mm.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePF\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTravel speed (mm/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpeed ​​with which the laser moves during the welding process.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in mm/s. Varies between 10 and 13 mm/s.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVE\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTrajectory and repeatability\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAccuracy and repeatability of the laser movement system.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTypical values: \u0026lt; \u0026plusmn;0.1 mm, \u0026lt; \u0026plusmn;0.15 mm, \u0026lt; \u0026plusmn;0.2 mm, \u0026lt; \u0026plusmn;0.25 mm.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTR\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLaser incidence angle (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAngle formed by the laser beam from the material surface.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTypical values: 75\u0026deg;, 80\u0026deg;, 85\u0026deg;, 90\u0026deg;.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAN\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGas flow\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eType of gas used to protect the welding pool and keep it pure.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in l/min for flow\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFG\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGas purity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eType of gas used to protect the welding pool and keep it pure.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e% for purity.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePG\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAmbient temperature (\u0026deg;C)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTemperature of the environment in which the welding is performed.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVariable between 25\u0026deg;C and 28\u0026deg;C.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTE\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePenetration (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDepth of the welding in the material.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in mm. Typically between 1.5 mm and 3.5 mm.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePE\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBead width (\u0026micro;m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWidth of the welding line generated by the laser.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExpressed in microns (\u0026micro;m). Typically between 200 \u0026micro;m and 500 \u0026micro;m.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe information pertains to a company whose welding process is automated by a machine fitted with IoT as well as photographic inspection technologies. All variables have 1000 valid values with no missing values. Values seem normalized with z-score standardization, as evidenced by means near zero and standard deviations near one, making them ready for higher-level statistical analysis or machine learning applications. Both process parameters (laser power, pulse length, frequency, speed, beam width, focal position) as well as output characteristics (bead width, penetration) are the main variables. Their distributions have mild asymmetry and platykurtic behavior, with flatter distribution compared to a normal distribution. This is supported by consistently negative kurtosis values as well as by the Shapiro-Wilk test, whose p-values are lower than 0.001 for all variables, rejecting the normality hypothesis. The most relevant output variables, bead width (LC) and penetration (PE), have negative skewness, meaning that the data have heavier tails on the left side of the distribution and that welds most often have values higher than the mean, although by a minor amount. The machine would seem to have good operating stability, as interquartile ranges are thin, and median absolute deviations are low for all variables, meaning there is little dispersion. Since the non-normal distribution of the data, however, could make classical linear models insufficient for identifying underlying patterns, robust or non-parametric statistical analysis could be needed. Gas-related variables such as gas flow (FG) and gas purity (PG) have higher skewness and modes, perhaps as a consequence of batch variation, as well as of the application of different shielding strategies for different welding contexts. In summary, the data represent a technologically mature, well-maintained system, whose well-regulated parameters, however, have usual variation typical of industrial automation processes (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive Statistics.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"14\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003ePL\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eDF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003ePF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eTR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eFG\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003ePG\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c14\"\u003e \u003cp\u003ePE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMissing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMode\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.731\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.607\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.283\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.315\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.164\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.839\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-1.646\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e-1.326\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMedian\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.039\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.318\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.267\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-7.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.400\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.100\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.600\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.050\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e7.800\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-3.189\u0026times;10\u0026ndash;18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e3.900\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e6.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStd. Deviation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoefficient of variation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.429\u0026times;10\u0026thinsp;+\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.001\u0026times;10\u0026thinsp;+\u0026thinsp;9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.146\u0026times;10\u0026thinsp;+\u0026thinsp;7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.335\u0026times;10\u0026thinsp;+\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.001\u0026times;10\u0026thinsp;+\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-4.764\u0026times;10\u0026thinsp;+\u0026thinsp;7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.848\u0026times;10\u0026thinsp;+\u0026thinsp;7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.668\u0026times;10\u0026thinsp;+\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e9.529\u0026times;10\u0026thinsp;+\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.283\u0026times;10\u0026thinsp;+\u0026thinsp;7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-3.138\u0026times;10\u0026thinsp;+\u0026thinsp;17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e2.565\u0026times;10\u0026thinsp;+\u0026thinsp;7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.668\u0026times;10\u0026thinsp;+\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.686\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.876\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.841\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.863\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.867\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.905\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.927\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.829\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.734\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAD robust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.298\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.291\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.247\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.434\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.229\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.089\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIQR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.751\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.758\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.683\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.934\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.699\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e2.169\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2.112\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.855\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.883\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.995\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSkewness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e9.900\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-0.211\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-0.148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e-0.280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e-0.353\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStd. Error of Skewness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKurtosis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.221\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.188\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.510\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.198\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.931\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-1.222\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1.473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1.651\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-1.580\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e-1.471\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e-1.392\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStd. Error of Kurtosis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShapiro-Wilk\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.856\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.953\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.953\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.957\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.913\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.954\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.749\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.954\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.854\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.895\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.880\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.894\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP-value of Shapiro-Wilk\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e\u0026lt;\u0026nbsp;.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRange\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.456\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.426\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.494\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.675\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4.474\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e2.602\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2.414\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e3.431\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e3.514\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e3.734\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.838\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.717\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.687\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.886\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.755\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.166\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-2.257\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1.457\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1.318\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-1.646\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e-2.322\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e-2.085\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.335\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.755\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.789\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.727\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.164\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.216\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.786\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1.649\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25th percentile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.169\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.876\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.884\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.850\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.964\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.825\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-0.925\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e-0.936\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e-1.105\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50th percentile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.039\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.318\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.267\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75th percentile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.899\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.832\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.970\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.853\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.930\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.947\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.889\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25th percentile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.169\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.876\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.884\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.850\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.964\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.825\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-0.925\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e-0.936\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e-1.105\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50th percentile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.039\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.318\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.267\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75th percentile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.899\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.832\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.970\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.853\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.930\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.947\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.889\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-7.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.400\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.100\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.600\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.050\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e7.800\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-1.665\u0026times;10\u0026ndash;15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e3.900\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e6.000\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4. Machine Learning","content":"\u003cp\u003eAssessing information on automatic welding within the framework of Industry 4.0 is a strategic action for a small-to-medium company such as Tecnomulipast srl, from Southern Italy operating within the food machinery production industry. IoT technology integration with real-time acquisition systems turns a standard production activity into an intelligent, trackable, and optimizable function. Data analysis from welding enables the company not only to track joint quality with accuracy, minimize process variation, predict anomalies, and enhance overall efficiency, but is critical for raising competitiveness within an industrialized, globalized world. Comparing between machine learning models such as Boosting, Decision Tree, K-Nearest Neighbors, Linear Regression, Neural Networks, Random Forest, Regularized Linear Regression, and Support Vector Machine is of prime relevance as each of the models differs as regards predictive capacity, interpretability, and adaptability to the dataset. Knowing the best-performing algorithm is not only a matter of selecting the best-performing solution, but the one that is stable, efficient, and scalable given available technical and infrastructural capabilities. Technically-scientifically, utilizing the following statistical indicators as evaluation metrics such as MSE (Mean Squared Error), MSE (scaled), RMSE (Root Mean Squared Error), MAE/MAD (Mean Absolute Error / Median Absolute Deviation), MAPE (Mean Absolute Percentage Error), R\u0026sup2; (Coefficient of Determination) is methodologically accurate, widely adopted within the industrial data science best practices, and well-accepted within the scientific literature. These metrics enable an integral analysis of model quality by capturing error size (MSE, RMSE), outlier resistance (MAE, MAD), relative error (MAPE), as well as the capacity of the model for variance explanation of the target factor (R\u0026sup2;). Their joint utilization enables a balanced, objective, reproducible evaluation that is best practice within industrial-grade data science.\u003c/p\u003e \u003cp\u003eWe have estimated the following equation:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:LC=f(PL,DI,FI,DF,PF,VE,TR,AN,FG,PG,TE,PE)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFacing the normalized performance measures of the various machine learning models used for the weld bead width (LC) prediction task, Random Forest is the most precision, stable, and generalization-capacity-rich algorithm. It consistently produces the best outcome for virtually all the evaluation metrics. In particular, it captures the lowest achievable values for MSE, MSE (scaled), RMSE, MAE/MAD, and MAPE\u0026mdash;reflecting the smallest prediction error\u0026mdash;while also capturing the highest value of R\u0026sup2; (1.000) that guarantees perfect adaptability within the normalized framework. Boosting is likewise a highly performing algorithm, ranking second best by the majority of the metrics through an R\u0026sup2; value of 0.806 as well as low error values for MSE (0.241), RMSE (0.174), and MAPE (0.116), reflecting high reliability as well as stability. Neural Networks exhibit competitive efficiency through an R\u0026sup2; value of 0.758 coupled with relatively low values of MSE as well as MAPE, reflecting their suitability as an alternative. Support Vector Machines as well as Regularized Linear Regression prove mediocre efficiency, whereas K-Nearest Neighbors performs with the worst, through an R\u0026sup2; value of 0.000 alongside the highest errors for all the metrics. The Decision Tree model performs better than KNN but not as efficiently as ensemble-based methods through its lower generalization capacity. To sum up, Random Forest is the best choice for the task through precision, stability, as well as generalization, whereas Boosting offers a strong alternative with equivalent reliability within predictive welding analytics (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMachine learning analysis results with an indication of the performance of the algorithms.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoosting\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDecision Tree\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKNN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLinear Regression\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNeural Net\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRandom Forest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRegularized Linear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eSVM\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.241\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.379\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.655\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.310\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.586\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.517\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMSE (scaled)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.393\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.393\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.536\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.464\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.174\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.297\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.487\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.165\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.408\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.382\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAE / MAD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.759\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.228\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.088\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.620\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.165\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.803\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.115\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.516\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.758\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.452\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.581\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eSelecting Random Forest as our best-performing model, we can analyze the feature importance values to see how much each of the input variables contributes toward predicting weld bead width (LC) most strongly. The table offers three indicators for each of the variables: Mean decrease in accuracy, Total increase in node purity, and Mean dropout loss. These all measure how much each of the variables contributes toward building the model\u0026rsquo;s predictability. By far the most powerful is clearly PE (penetration depth), with the highest mean decrease in accuracy (0.522), highest increase in node purity (94.680), and highest mean dropout loss (0.598). This is consistent with the expectation that weld penetration is closely correlated with bead width and is a very critical quality determinant of welding in the current scenario. Second is significantly PL (laser power) with a strong decrease in accuracy (0.369), a high node purity (68.918), and a very high dropout loss (0.399). Not unexpectedly, laser power directly controls the energy input during the welding process. Following are FG (gas flow) and PG (gas purity) with values for all metrics rather near-identical. Both of the parameters are crucial for providing a clean welding environment and for preventing defects, so their influence is not surprising. AN (laser angle) and DF (beam diameter) are moderately important, indicating a secondary but still contributary role toward the quality of the weld. Least of all are DI (pulse duration), VE (travel speed), and FI (pulse frequency). Their very low values for all metrics point toward a minor influence on the output within the specific operating window of this dataset. Least of all is TE (ambient temperature), PF (focal position), and TR (trajectory repeatability). These variables are most likely kept relatively constant during operation, or perhaps have previously had their optimal values optimized, so their variability is minimized, and their statistical impact is low. In conclusion, the Random Forest model singles out the penetration depth, laser power, and gas parameters as the prime drivers of bead width of weld during the automated process of Tecnomulipast srl. These findings not only make sense from the welding physics point of view, but they also offer actionable targets for controlling the process, as well as for optimizing the process, within the context of Industry 4.0 (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe following is an additive feature attribution output for five test cases, as given by the Random Forest model for predicting weld bead width (LC). The values, presumably created by a SHAP or equivalent interpretability procedure, demonstrate the contribution of each attribute, relative to a set value (the \"Base\" column, constant at \u0026minus;\u0026thinsp;0.045 for all cases).\u003c/p\u003e \u003cp\u003eIn both instances, the value predicted is much less than the base, varying between \u0026minus;\u0026thinsp;1.226 and \u0026minus;\u0026thinsp;1.390. This is a decrease from the base because of the cumulative adverse effects of some of the main features, specifically PE (penetration depth), PL (laser power), FG (gas flow), and PG (gas purity).\u003c/p\u003e \u003cp\u003ePE is consistently the greatest negative contributor in all cases, ranging from \u0026minus;\u0026thinsp;0.38 to \u0026minus;\u0026thinsp;0.384. This is consistent with what is observed in the feature importance as well: the greatest contribution is by penetration depth, significantly pulling the prediction down.\u003c/p\u003e \u003cp\u003ePL is seen to have strong negative effect, from \u0026minus;\u0026thinsp;0.287 to \u0026minus;\u0026thinsp;0.296. This is consistent with its function of regulating power input\u0026mdash;greater power can result in wider bead width, and such deviations from optimal power values would contribute negatively within these given test cases.\u003c/p\u003e \u003cp\u003eFG and PG have strong to moderate negative effects, supporting the significance of gas parameters for weld quality. The steady values for all the cases (approximately between \u0026minus;\u0026thinsp;0.17 and \u0026minus;\u0026thinsp;0.20 for FG, and between \u0026minus;\u0026thinsp;0.13 and \u0026minus;\u0026thinsp;0.15 for PG) demonstrate stable, though considerable, impact on the estimated outcome.\u003c/p\u003e \u003cp\u003eThe other variables, such as DF (beam diameter) and AN (angle of incidence), have negative contributions across all instances, though less so. Their directional regularity assures constant though secondary impacts on the model's projections.\u003c/p\u003e \u003cp\u003eIn contrast, variables such as VE (speed of travel) and PF (position of focus) display slight positive or zero effects, occasionally helping raise the prediction by a slight amount. FI (pulse frequency), DI (pulse duration), TR (repeatability of trajectory), and TE (ambient temperature) have near-zero or low effects, consistent with their low values of feature importance. In conclusion, such findings uphold interpretability and internal consistency of the Random Forest model. The most salient features\u0026mdash;penetration depth, laser power, and gas flow settings\u0026mdash;exhibit the highest and most uniform effects on the predictions for varying test cases. This reflects the model\u0026rsquo;s capability for yielding trustworthy, understandable information for quality control of welding for applications such as real-time predictive systems within the context of Industry 4.0 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Network analysis","content":"\u003cp\u003eAfter performing a machine learning analysis, it is logical, therefore, to apply network analysis with centrality metrics because machine learning models are good at predicting but do not necessarily capture the internal dynamics of interdependencies among variables. Network analysis offers a structural representation of the relationships, giving further insight into the interplay of variables with each other within the system. By examining centrality metrics like betweenness, closeness, strength, and expected influence, one can determine where variables are central, where they are bridges, and where they are on the periphery. For example, PL (laser power) is ranked highest for all centrality metrics, meaning that it is the most powerful, influencing role within the network of variables. This is as expected given its probable significance within predictive models. DF (beam diameter) and PF (focal position) have significant betweenness, meaning they are connectors between variables, potentially affecting multiple paths even though they are not necessarily the most direct influencers. In contrast, for variables such as DI, FI, and TR, there are negative values for all metrics, suggesting they are not so much central and potentially have isolated effects on the system. Furthermore, network analysis offers the ability to corroborate the machine learning by comparing network metrics with importances from the model, as well as identifying redundant, weakly connected variables, facilitating reduction of dimensions and feature choice. Having the ability to see possible chains of influence among variables improves interpretability of intricate models, such as within industrial environments where behavior of the system is as critical as is predictive accuracy. In all, the combination of network analysis with centrality metrics following machine learning creates a fuller, system-level view that helps interpret models, streamline processes, as well as make informed choices on variable significance as well as role interplay (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eThe paper showcases the real-world application value of IoT-enabled data acquisition systems coupled with machine learning methods for improving weld quality prediction for a small-to-medium-sized manufacturing company. In a real-case study of Tecnomulipast srl based in Gravina in Puglia, supported by public funds through the PIA program, the research showcases how a digitalized production environment can make sophisticated predictive analytics available for laser welding. Among the machine learning algorithms applied, Random Forest was identified as the best-performing algorithm, indicating the best prediction accuracy for all the considered performances (MSE, RMSE, MAE, MAPE, and R\u0026sup2;). The chosen model not only produced low prediction errors, but for detailed interpretability, feature significance analysis as well as additive contribution methods could be employed. Penetration depth (PE), laser power (PL), and gas flow parameters (FG, PG) were recognized as the main factors affecting weld bead width (LC), yielding actionable insights for process improvement as well as quality control.\u003c/p\u003e \u003cp\u003eIn addition, the application of network analysis based on centrality indicators provided a complementary view of interdependencies among variables. This methodology disclosed structural interconnections between parameters, corroborating machine learning evidence and allowing for better interpretability of models. Laser power and beam geometry turned out to be central variables within the topology of the system, indicating their decisive impact not only on output quality but on process dynamics as well. Altogether, the research affirms that a union of machine learning with network analysis yields predictive capabilities, as well as systemic insight. For SMEs, looking forward to adapting to Industry 4.0, this dual strategy addresses a scalable, transparent, and efficient framework for optimizing production through data.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgement\u003c/h2\u003e \u003cp\u003eResults obtained in the research and development project \"Tecnomulipast\" - Codice Pratica 683TK4 - a valere sul Bando Programmi Integrati di Agevolazioni PIA Piccole Imprese (Art 27 Reg. Regionale 17/2014 e smi).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eWang, P. E., Ghassemi-Armaki, H., Pour, M., Zhao, X., Ma, J., Sattari, K., \u0026amp; Carlson, B. (2025). Applicable and generalizable machine learning for intelligent welding in automotive manufacturing. Welding in the World, 1-36.\u003c/li\u003e\n \u003cli\u003eMa, S., Leng, J., Chen, Z., Du, Y., Zhang, X., \u0026amp; Liu, Q. (2025). Intrinsically and Post-Hoc Interpretable Kolmogorov-Arnold Network and Genetic Algorithm for Laser Deep Penetration Welding Parameters Optimization. IEEE Transactions on Instrumentation and Measurement.\u003c/li\u003e\n \u003cli\u003ePoornima, C. L., Rao, C. S., \u0026amp; Varma, D. N. (2024). Predicting weld quality in duplex stainless steel butt joints during laser beam welding: a hybrid DNN-HEVA approach. Journal of Advanced Manufacturing Systems, 23(04), 801-836.\u003c/li\u003e\n \u003cli\u003eDin, N. U., Zhang, L., Nawaz, M. S., \u0026amp; Yang, Y. (2024). Multi-model feature aggregation for classification of laser welding images with vision transformer. Journal of King Saud University-Computer and Information Sciences, 36(5), 102049.\u003c/li\u003e\n \u003cli\u003eMaculotti, G., Genta, G., \u0026amp; Galetto, M. (2024). Optimisation of laser welding of deep drawing steel for automotive applications by Machine Learning: A comparison of different techniques. Quality and Reliability Engineering International, 40(1), 202-219.\u003c/li\u003e\n \u003cli\u003eHartung, J., Jahn, A., \u0026amp; Heizmann, M. (2023). Machine learning based geometry reconstruction for quality control of laser welding processes. tm-Technisches Messen, 90(7-8), 512-521.\u003c/li\u003e\n \u003cli\u003eYing-chao, F., Yi-ming, H., Jin-ping, L., Chen-peng, J., Peng, C., Shao-jie, W., ... \u0026amp; Huan-wei, Y. (2023). On-Line Monitoring of Laser Wire Filling Welding Process Based on Emission Spectrum. SPECTROSCOPY AND SPECTRAL ANALYSIS, 43(6), 1927-1935.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eChianese, G., Franciosa, P., Nolte, J., Ceglarek, D., \u0026amp; Patalano, S. (2022). Characterization of photodiodes for detection of variations in part-to-part gap and weld penetration depth during remote laser welding of copper-to-steel battery tab connectors. Journal of Manufacturing Science and Engineering, 144(7), 071004.\u003c/li\u003e\n \u003cli\u003eCai, W., Wang, J., Cao, L., Mi, G., Shu, L., Zhou, Q., \u0026amp; Jiang, P. (2019). Predicting the weld width from high-speed successive images of the weld zone using different machine learning algorithms during laser welding. Math. Biosci. Eng, 16(5), 5595-5612.\u003c/li\u003e\n \u003cli\u003eOzkat, E. C., Franciosa, P., \u0026amp; Ceglarek, D. (2017). Development of decoupled multi-physics simulation for laser lap welding considering part-to-part gap. Journal of Laser Applications, 29(2).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eSokolov, M., Franciosa, P., Al Botros, R., \u0026amp; Ceglarek, D. (2020). Keyhole mapping to enable closed-loop weld penetration depth control for remote laser welding of aluminum components using optical coherence tomography. Journal of Laser Applications, 32(3).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"Tecnomulipast, laser welding, machine learning, digital transformation, Industry 4.0","lastPublishedDoi":"10.21203/rs.3.rs-6510362/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6510362/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe paper investigates the deployment of data analytics and machine learning to improve welding quality in Tecnomulipast srl, a small-to-medium sized manufacturing firm located in Puglia, Italy. The firm produces food machine components and more recently mechanized its laser welding process with the introduction of an IoT-enabled system integrating photographic control. The investment, underwritten by the Apulia Region under PIA (Programmi Integrati di Agevolazione) allowed Tecnomulipast to not only mechanize its production line but also embark upon wider digital transformation. This involved the creation of internal data analytics infrastructures that have the capability to underpin machine learning and artificial intelligence applications. This paper addresses a prediction of weld bead width (LC) with a dataset of 1,000 observations. Input variables are laser power (PL), pulse time (DI), frequency (FI), beam diameter (DF), focal position (PF), travel speed (VE), trajectory accuracy (TR), laser angle (AN), gas flow (FG), gas purity (PG), ambient temperature (TE), and penetration depth (PE). The parameters were exploited to build and validate some supervised machine learning algorithms like Decision Trees, Random Forest, K-Nearest Neighbors, Support Vector Machines, Neural Networks, and Linear Regression. The performance of the models was measured by MSE, RMSE, MAE, MAPE, and R\u0026sup2;. Ensemble methods like Random Forest and Boosting performed the highest. Feature importance analysis determined that laser power, gas flow, and trajectory accuracy are the key variables. This project showcases the manner in which Tecnomulipast has benefited from public investment to introduce digital transformation and adopt data-driven strategies within Industry 4.0.\u003c/p\u003e","manuscriptTitle":"Data-Driven Welding Quality Assessment: Leveraging IoT and Machine Learning in Industrial Practice","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-25 04:09:03","doi":"10.21203/rs.3.rs-6510362/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":"8bd783af-4ef0-42e0-823a-b1317eec47b0","owner":[],"postedDate":"April 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-04-25T04:09:03+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-25 04:09:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6510362","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6510362","identity":"rs-6510362","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}