Wear fault diagnosis in hydro-turbine via the incorporation of the IWSO algorithm optimized CNN-LSTM neural network

Wear fault diagnosis in hydro-turbine via the incorporation of the IWSO algorithm optimized CNN-LSTM neural network | 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 Article Wear fault diagnosis in hydro-turbine via the incorporation of the IWSO algorithm optimized CNN-LSTM neural network Fang Dao, Yun Zeng, Yidong Zou, Jing Qian This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3975472/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract Diagnosing hydro-turbine wear fault is crucial for the safe and stable operation of hydropower units. A hydro-turbine wear fault diagnosis method based on improved WT (wavelet threshold algorithm) preprocessing combined with IWSO (improved white shark optimizer) optimized CNN-LSTM (convolutional neural network-long-short term memory) is proposed. The improved WT algorithm is utilized for denoising the preprocessing of the original signals. The CNN-LSTM hydro-turbine wear fault diagnosis model is constructed. Aiming at the problem that the WSO algorithm quickly falls into local optimum and premature convergence, tent chaotic mapping is used to initialize the population and birds flock search behavior. The cosine elite variation strategy is introduced to improve convergence speed and accuracy. Hyperparameter tuning of CNN-LSTM model based on IWSO algorithm. The experimental results show that the accuracy of the proposed method reaches 96.2%, which is 8.9% higher than that of the IWSO-CNN-LSTM model without denoising. The study also found that the diagnostic accuracy of hydro-turbine wear faults increased with increasing sediment concentration in the water. This study can supplement the existing hydro-turbine condition monitoring and fault diagnosis system. Meanwhile, diagnosing wear faults in hydro-turbines can improve power generation efficiency and quality and minimize resource consumption. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Introduction As a critical pillar of human productivity, energy plays a vital role in global development 1 . Hydropower has become an indispensable part of the global energy system due to its renewability, environmental characteristics, economy, and excellent performance in regulating the power system 2 . As an essential link in hydropower energy development, the stability and safety of hydropower station operation are crucial for power supply 3 . However, during the operation of hydropower stations, the hydro-turbines of hydropower stations generally face challenges such as sediment abrasion, which is particularly prominent in some rivers with high sediment content 4,5 . Accurate and timely diagnosis of hydro-turbine wear-related faults is essential 6 . It ensures the sustainable operation of hydropower stations. It also maintains the stability of the energy supply. The constant impact and friction of sediments such as mud and sand causes wear and damage to the surface of the hydro-turbine runner 7 . Wear leads to changes in the trajectory of the internal water flow, which cuts down the unit's efficiency and makes the conversion of hydropower energy less efficient. In addition, damage to the hydro-turbine runner makes the hydropower unit less stable, and the resulting instability triggers safety uncertainty in operation and increases the noise level during the operation of the hydropower station 8 . The manifestation of extensive wear and tear issues can precipitate mechanical breakdown in hydro-turbines, thereby imperiling the operational integrity of hydropower units and the safety of the personnel involved 9 . Consequently, the diagnostic of wear-related faults within hydro-turbines assumes paramount importance. Scholarly inquiry into the phenomenon of sediment erosion affecting hydro-turbine runners has predominantly centered on the subsequent pivotal domains: (1) reducing sediment loading, (2) improving the erosion resistance of runners, and (3) conducting erosion simulation studies. Several technical means have been adopted to reduce sediment loading, including sediment monitoring for runner intake ports 10 , temporary hydro-turbine shutdowns during flood season, and filtration and sedimentation methods like sedimentation ponds to reduce erosion sources 11 . Applying specific coating processes on hydro-turbine overflow elements' surfaces can enhance their resistance to sediment erosion and prolong their service life 12,13 . Considering the fluctuating sediment concentrations across seasons and the intricate configurations characterizing hydropower station infrastructure, numerous investigations about the erosion of hydro-turbine runner blades by sediment have embraced methodologies entailing simulation and analysis of solid-liquid two-phase flow dynamics. This research requires modeling erosion and wear 14 or analyzing sediment particles' shape and kinematic properties 15 . However, there needs to be more research on using deep learning models to analyze sediment wear failures in hydro-turbines. This area holds great promise, and exploring the potential applications of deep learning in solving this problem is worthwhile. Deep learning theories have excellent modeling and data processing capabilities, providing unique data analysis solutions for various industries 16,17 . The fault diagnosis and identification field has also benefited 18 . It excels at solving complex problems. These problems are challenging to solve using traditional analytical modeling or empirical knowledge alone. Deep learning is known for its high accuracy, robustness, and excellent generalization capabilities 19,20 . Convolutional neural networks (CNNs) have been widely used in rotating machinery fault diagnosis due to their powerful ability for automatic feature extraction 21 . The network has demonstrated excellent performance in recognizing the health condition of rotating machinery. The convolutional weight-sharing structure of CNN stands out as a notable feature, effectively mitigating neural network complexity and parameter count, thus serving as a preventive measure against overfitting 22 . Nonetheless, CNNs exhibit an inherent limitation in their capability to address static features within datasets, thereby disregarding prolonged temporal dependencies intrinsic to time series data. This constraint presents a challenge, particularly in addressing protracted time series problems 23 . Recurrent Neural Networks (RNNs) are adept at capturing prolonged dependencies within temporal datasets, making them well-suited for addressing classification and regression tasks involving time series data 24 . Nevertheless, data points distant from the present moment present complexities that hinder their effective utilization as references for input-output mapping, resulting in issues such as gradient vanishing and explosion 25 . To address these challenges, Hochreiter et al. introduced the Long Short-Term Memory (LSTM) network, an upgraded version of Recurrent Neural Networks (RNNs) specifically designed to handle time-series data 26 . The LSTM excels at retaining long-term memories and learning dependencies, effectively addressing gradient vanishing and exploding issues, resulting in superior performance and outcomes compared to RNNs 27 . Increasing the number of nodes and layers of the neural network can effectively improve the learning and fitting effectiveness. However, it also significantly increases the number of hyperparameters 28 . These hyperparameters, including the number of nodes per layer, the initial learning rate, and the number of iterations, are pre-set before model training begins 29 . Assessing each combination of hyperparameters necessitates numerous iterative computations, leading to significant time and effort expenditure. Therefore, optimization of hyperparameters is essential. The white shark optimizer (WSO) algorithm is an emerging meta-heuristic algorithm proposed by Braik and other researchers 30 . The algorithm imitates white sharks, which use their superior perceptual abilities to sense complex information while hunting in the deep sea 31 . The basic idea of the white shark optimization algorithm is to model and simulate three primary behaviors: rapid movement of white sharks towards prey, movement towards the best prey, and flocking behavior. This algorithm can efficiently handle optimization problems of high complexity 32 . However, like most population-based algorithms, the WSO algorithm must improve its convergence accuracy and tends to converge when dealing with complex optimization problems. In the operational context of hydro-turbine environments, the acoustic vibration signal generated by the interaction of water flow with the turbine runner becomes entangled with significant levels of noise, incorporating hydraulic, electromagnetic, and mechanical vibrations 33 . Directly using the raw data for fault identification will significantly impact the identification results, so it is necessary to de-noise the collected signals for pre-processing. The wavelet threshold (WT) algorithm was first proposed by Donoho in 1995 34 . It has been widely used in noise reduction with its excellent discriminative ability and ability to adapt to time-varying signal processing 35 . Central to the wavelet threshold denoising algorithm are pivotal threshold determination and quantization considerations. Traditional threshold functions primarily comprise the hard and soft threshold functions. Although the hard threshold function offers computational simplicity, it introduces discontinuities in the processed signal, thereby instigating signal reconstruction oscillations. Conversely, the soft threshold function preserves overall continuity 36 . Nevertheless, in scenarios where the signal magnitude is substantial, the attenuating influence of the wavelet may precipitate a persistent deviation in the processed signal. Within the domain of wavelet threshold denoising, selecting an appropriate threshold function emerges as a critical consideration necessitating meticulous deliberation 37 . Based on the above analysis, this paper proposes a hydro-turbine wear fault diagnosis method based on improved WT preprocessing combined with improved white shark optimization (IWSO) optimized CNN-LSTM. Improved WT denoising preprocessing is first performed on the collected data to enhance the accuracy of fault features extracted by the subsequent neural network. The amalgamation of CNN and LSTM neural network models yields the CNN-LSTM fault diagnosis model. Addressing challenges associated with low convergence accuracy and premature convergence in complex optimization problems, the WSO algorithm incorporates Tent chaotic mapping for population initialization while enhancing convergence speed and accuracy by integrating bird flocking search behavior and the cosine elite variation strategy. IWSO optimizes the constructed CNN-LSTM deep learning model to improve the fault diagnosis accuracy of CNN-SLTM. The effectiveness of the method proposed in this paper is verified by building a hydro-turbine fault experimental bench and collecting hydro-turbine fault signals from different working conditions for identification. In summary, the principal innovations of this study can be categorized as follows: Design of hydro-turbine wear fault diagnosis model based on improved WT denoising combined with IWSO optimized CNN-LSTM; An improved WT denoising is proposed. To overcome the limitations associated with conventional threshold functions in the wavelet threshold algorithm, a novel threshold function is formulated; An improved white shark optimization algorithm is proposed. Use Tent chaotic mapping to initialize the population, introduce bird flock search behavior and cosine elite variation strategy to improve its convergence speed and accuracy; Designed and built a Fault experimental bench. Simulate the sand-containing working condition of hydro-turbine to verify the effectiveness of the method proposed in this paper; The frequency characteristics of sand-laden water flow through runner blades are analyzed from an acoustic vibration signal perspective. The rest of the discussion is as follows: Section 2 elaborates on the principle of the proposed method. Section 3 explains the WSO algorithm and its improvement method in detail. The experiments and data description are carried out in section 4. In section 5, the proposed method is verified and analyzed based on the experiments. Section 6 of this paper synthesizes the principal findings and offers insights into future research directions. Principles of the proposed method Improved wavelet threshold algorithm. Based on wavelet transform principles, the WT algorithm accurately extracts effective signals by leveraging significant differences between proper signals and noise signals in wavelet coefficients. This algorithm, with excellent performance, is widely used in many fields, especially in signal noise reduction and feature extraction. The core idea of the WT algorithm is the ability of wavelet transform to decompose a signal into wavelet coefficients at various frequencies and scales. Valuable and noisy signals usually behave significantly differently on these coefficients. By selecting a suitable threshold value, the wavelet thresholding algorithm can remove or reduce noise in the wavelet coefficients while preserving or enhancing the valuable signal component. It helps improve the signal quality, reduce noise interference, and make the signal easier to analyze and interpret effectively by subsequent processing methods. The WT algorithm has a relatively small amount of computation. It can quickly complete the processing, making it suitable for real-time or large-scale data processing tasks. Secondly, it is easy to implement as its principle is relatively simple and does not require a complex mathematical background. Threshold processing encompasses two key components: threshold selection and threshold function selection. Commonly utilized thresholds include the Sqtwolog , Rigrsure , Heursure , and Minimaxi thresholds. Sqtwolog threshold is used with a small computational effort, but if the signal-to-noise ratio of the signal is low, it will reduce its stability. Heursure threshold is stable, but the computational effort is enormous and requires iterative computation. Minimaxi threshold has an excellent theoretical basis and stable performance, but the computational effort is enormous, and the noise denoising effect is average. The present investigation utilizes the unbiased risk estimation threshold, selected for its moderate computational demands relative to the alternative thresholds. Furthermore, this threshold is chosen to maximize the retention of valid signals characterized by small modal values. Another crucial aspect in the WT denoising pertains to the choice of the threshold function. The hard and soft threshold functions emerge as the predominant options. The expression of soft threshold function is: $${\widehat{\omega }}_{j,k}=\left\{\begin{array}{c}{sgn(\omega }_{j,k}\left)\right(\left|{\omega }_{j,k}\right|-\lambda ), \left|{\omega }_{j,k}\right|\ge \lambda \\ 0, \left|{\omega }_{j,k}\right|<\lambda \end{array}\right.$$ 1 The expression of hard threshold function is: $${\widehat{\omega }}_{j,k}=\left\{\begin{array}{c}{\omega }_{j,k}, \left|{\omega }_{j,k}\right|\ge \lambda \\ 0, \left|{\omega }_{j,k}\right|<\lambda \end{array}\right.$$ 2 The hard threshold function exhibits discontinuities at thresholds \(\lambda\) and \(-\lambda\) . Consequently, the wavelet inverse transform introduces a pseudo-Gibbs effect, resulting in local signal oscillations that adversely impact reconstruction quality. In contrast, the soft threshold function maintains continuity at thresholds \(\lambda\) and \(-\lambda\) . promoting smoother signal waveforms. However, when \(\left|{\omega }_{j,k}\right|\ge \lambda\) , \({\widehat{\omega }}_{j,k}\) consistently differs from \({\omega }_{j,k}\) by \(\lambda\) . This creates an inherent bias between the reconstructed signal and the original signal, leading to distortion in the reconstructed signal. While the conventional threshold function offers certain advantages, there are inevitable drawbacks that affect noise reduction. To address the limitations of both the soft and hard threshold functions in noise reduction, the study proposes a novel threshold function as follows: $${\widehat{\omega }}_{j,k}=\left\{\begin{array}{c}\left(1-\mu \right){\omega }_{j,k}+\mu \bullet {sgn(\omega }_{j,k})\left[\left|{\omega }_{j,k}\right|-\frac{\mu \lambda }{exp\left(\frac{\left|{\omega }_{j,k}\right|}{{\lambda }^{2}}\right)}\right], \left|{\omega }_{j,k}\right|\ge \lambda \\ 0, \left|{\omega }_{j,k}\right|<\lambda \end{array}\right.$$ 3 In the above, \(\mu =\frac{\lambda }{\left|{\omega }_{j,k}\right|\bullet \text{e}\text{x}\text{p}(\left|\frac{{\omega }_{j,k}}{\lambda }\right|-1)}\) ; \({\omega }_{j,k}\) is the wavelet coefficient; sgn (*) is the sign function; and \(\lambda\) is the threshold value. ( 1 ) Continuity analysis When \({\omega }_{j,k}=\lambda\) , the left limit of \({\widehat{\omega }}_{j,k}\) at \(\lambda\) is: $$\underset{{\omega }_{j,k\to {\lambda }^{-}}}{\text{lim}}{\omega }_{j,k}=\underset{{\omega }_{j,k\to {\lambda }^{-}}}{\text{lim}}\left(0\right)=0$$ 4 The right limit of \({\widehat{\omega }}_{j,k}\) at \(\lambda\) is: $$\underset{{\omega }_{j,k\to {\lambda }^{+}}}{\text{lim}}\left(\left(1-\mu \right){\omega }_{j,k}+\mu \bullet {sgn(\omega }_{j,k})\left[\left|{\omega }_{j,k}\right|-\frac{\mu \lambda }{exp\left(\frac{\left|{\omega }_{j,k}\right|}{{\lambda }^{2}}\right)}\right]\right)=0$$ 5 When \(\left|{\omega }_{j,k}\right|={\lambda }\) , \(\mu =1, {\widehat{\omega }}_{j,k}\left({\lambda }\right)=0\) . The improved threshold function is continuous. ( 2 ) Asymptote analysis When \(\left|{\omega }_{j,k}\right|\) increases, the constructor \(\text{F}={\widehat{\omega }}_{j,k}-{\omega }_{j,k}\) , which collapses: $$\text{F}=-\frac{{{\lambda }}^{2}}{{\omega }_{j,k}\bullet \text{e}\text{x}\text{p}(\frac{{\omega }_{j,k}}{{\lambda }}-1)\left(\frac{\left|{\omega }_{j,k}\right|}{{\lambda }^{2}}\right)}$$ 6 As \({\omega }_{j,k}\to \infty\) , \(\text{F}\to 0\) , indicating that \({\widehat{\omega }}_{j,k}\) gradually converges to \({\omega }_{j,k}\) as \({\omega }_{j,k}\) increases. Replacing \({\omega }_{j,k}\) by x and deriving F(x) yields \({F}^{{\prime }}\left(x\right)>0\) , indicating that F(x) is monotonically increasing. The improved function maintains continuity at the threshold \(\lambda\) . As the parameter \(\mu\) approaches 0 or 1, the improved threshold function gradually converges towards the conventional threshold function, eventually aligning with it. Figure 1 illustrates the curves of the new, hard, and soft threshold functions. The new threshold function offers two key advantages. It addresses the constant deviation issue found in the soft threshold function and mitigates the intermittency problem present in the hard threshold function. Convolutional Neural Network. A convolutional neural network (CNN) is a mathematical model that focuses on performing linear discrete convolutional operations. It has excellent feature learning capabilities and exhibits excellent robustness and fault tolerance. It maintains its performance even in the face of translation, scaling, and distortion transformations. Figure 2 illustrates a typical CNN architecture. The CONV serves as the central component of CNN, executing convolutional operations on input data and forwarding the output to subsequent network layers. Within the CONV layer, a convolutional kernel functions as the receptive field, traversing the entire input set with a specified stride. Often, activation functions are employed to extract the nonlinear features inherent in the output data to enhance the model's expressive power. Activation functions are categorized into saturated nonlinear functions and unsaturated nonlinear functions. Compared to saturated nonlinear functions, using unsaturated nonlinear functions helps overcome the challenges of gradient explosion and gradient vanishing and improves the convergence speed of the model. The Rectified Linear Unit (ReLU) is a widely adopted unsaturated nonlinear activation function in CNN models. Its advantages, such as rapid convergence and straightforward gradient computation, significantly contribute to its widespread adoption and appeal within the field. In order to facilitate the extraction of an adequate number of feature vectors, the output dimension of the convolutional layer is typically substantial. However, a diminutive dimensionality may engender overfitting challenges. Introducing a pooling layer into the model effectively reduces the number of parameters and helps mitigate overfitting while maintaining essential features of the output data. Standard pooling methods include average pooling and maximum pooling. The maximum pooling layer is good for preserving the main features, so this study uses it as a pooling method. The fully connected layer serves as the final classification module in the CNN model, responsible for applying nonlinear activation to the extracted features and generating the probability distribution for each class. In this layer, each neuron is connected to all neurons in the preceding layer, establishing a mapping relationship between input features and output categories through learning weights and biases. The output of the fully connected layer is subjected to an activation function, which yields the probability distribution of the classification outcomes. Consequently, the model can make precise classification predictions for input samples. Long Short-Term Memory. The comprehensive architecture of the LSTM network, delineated in Fig. 3 , encompasses five principal constituents: the unit state, hidden state, input gate, forgetting gate, and output gate. Among the unique features of LSTM is the introduction of three gating structures: an input gate, an output gate, and a forget gate. The architectural incorporation of gating mechanisms within LSTM networks affords a heightened degree of control over information acceptance, retention, and dissemination. This characteristic renders LSTM networks particularly well-suited for addressing time series classification. The state of the last moments can be retained in the state of the current LSTM unit, which is controlled through the forgetting gate. The forgetting gate serves as a mechanism to filter the memory content, thereby discerning which information warrants retention and which should be discarded. The LSTM can efficiently manage and update its internal state by calculating the forgetting gate. Its calculation is as follows: $${\varvec{f}}_{t}=\sigma \left({\varvec{W}}_{xf}{\varvec{x}}_{t}+{\varvec{W}}_{hf}{\varvec{h}}_{t-1}+{\varvec{b}}_{f}\right)$$ 7 In the above, \({\varvec{W}}_{xf}\) is the weight matrix between the current input and the forgetting gate, \(\sigma\) denotes the chosen activation function, specifically the Sigmoid function with an output range of 0 to 1, utilized to signify the extent of the gate's openness, \({\varvec{f}}_{t}\) is the output of the forgetting gate, \({\varvec{h}}_{t-1}\) is the output state at the last moment \({\varvec{x}}_{t}\) is the current input state, \({\varvec{b}}_{f}\) is the bias term of the forgetting gate, and \({\varvec{W}}_{hf}\) is the weight matrix between the historical output and the forgetting gate. The input gate updates the LSTM cell's state, determining whether new input information should be memorized. This gating structure generates an output value between 0 and 1 by passing the state of the previous time step and the current input information to an activation function. This output value is used to quantify how much information has been updated. Proximity of the output value to 0 suggests insignificance of the input information. In contrast, when the output value is close to 1, it indicates that the input information is essential. Simultaneously, the tanh function processes the preceding state and current input data, compressing them into − 1 to 1 to produce the candidate cell state. Consequently, the LSTM's internal state can be updated, leveraging the input gate outputs and candidate cell states. This mechanism empowers the LSTM network to effectively regulate the acceptance and integration of new information, facilitating modeling and learning from sequential data. The output is then calculated based on this processed information: $${\varvec{i}}_{t}=\sigma \left({\varvec{W}}_{xi}{\varvec{x}}_{t}+{\varvec{W}}_{hi}{\varvec{h}}_{t-1}+{\varvec{b}}_{i}\right)$$ 8 In the above, \({\varvec{i}}_{t}\) is the input gate output, \({\varvec{W}}_{hi}\) is the weight matrix between the historical output and the input gate, \({\varvec{W}}_{xi}\) is the weight matrix between the input and the input gate, and \({\varvec{b}}_{i}\) is the bias term of the input gate. The candidate cell status is: $${\widehat{\varvec{c}}}_{t}=\text{t}\text{a}\text{n}\text{h}({\varvec{W}}_{xc}{\varvec{x}}_{t}+{\varvec{W}}_{hc}{\varvec{h}}_{t-1}+{\varvec{b}}_{c})$$ 9 In the above, \({\varvec{W}}_{xc}\) is the weight matrix between the input and cell state, \({\widehat{\varvec{c}}}_{t}\) is the candidate cell state, \({\varvec{b}}_{c}\) represents the bias term of the cell state, wherein the application of the hyperbolic tangent (tanh) function facilitates scaling of the value, \({\varvec{W}}_{hc}\) is the weight matrix between the historical output and cell state. With the outputs of the forgetting gate and the input gate, the current LSTM cell state \({\varvec{C}}_{t}\) can be determined to consist of two parts. The forgetting gate multiplies the previous cell state to determine the retained information, allowing it to selectively control the forgetting of specific information from the previous state. Second, the output of the input gate is multiplied by the current candidate cell state, which determines the part of the information to be added. This way, the input gate can determine how much the newly input information affects the current state. The updated LSTM unit state \({\varvec{C}}_{t}\) is obtained by adding these two parts. In this way, the LSTM achieves selective memory and the addition of information through the gating mechanism. The cell state is expressed as: $${\varvec{C}}_{t}={\varvec{f}}_{t}{\varvec{C}}_{t-1}+{\varvec{i}}_{t}{\widehat{\varvec{c}}}_{t}$$ 10 The final output of the control unit status is located at the output gate. Multiply the current unit state information with the output of the output gate. Tanh function operation is performed on the result to get the output value of the unit. The expression for the output gate can be expressed as: $${\varvec{o}}_{t}={\sigma }({\varvec{W}}_{xo}{\varvec{x}}_{t}+{\varvec{W}}_{ho}{\varvec{h}}_{t-1}+{\varvec{b}}_{o})$$ 11 In the above, \({\varvec{W}}_{ho}\) is the weight matrix between the historical output and output gates, \({\varvec{W}}_{xo}\) is the weight matrix between the input and output gates, and \({\varvec{b}}_{o}\) the bias term of the output gate. The expression for the unit status output is: $${\varvec{h}}_{t}={\varvec{o}}_{t}tanh\left({\varvec{C}}_{t}\right)$$ 12 Wear fault diagnosis model of the CNN-LSTM. CNN and LSTM represent disparate feature extraction methodologies, each endowed with distinct characteristics. CNN is mainly used to capture spatially correlated features efficiently through convolutional kernels, which is suitable for processing image and spatial data. LSTM combines memory cells and gating mechanisms, mainly used to capture temporal correlation, which is suitable for processing time-series data, e.g., natural language text or sensor data. However, CNNs have some limitations in dealing with the temporal correlation of input variables. In contrast, LSTMs can learn and capture the dependencies between the previous and subsequent time steps in sequential data, leading to better temporal correlation feature processing. This study introduces a hybrid CNN-LSTM model for diagnosing hydro-turbine wear faults. This model integrates both CNN and LSTM architectures. This integration utilizes LSTM's strong temporal feature-capturing capability. It aims to compensate for the limitations of CNN when handling the temporal correlation of input variables. The proposed model can comprehensively analyze the input data through this combination strategy. Capturing both spatial and temporal correlation features enhances the reliability and accuracy of hydro-turbine fault diagnosis systems. Within the CNN-LSTM fault diagnosis model, CNN undertakes the task of extracting spatial features from input data and reducing its dimensionality. Conversely, LSTM reveals latent temporal features within the data, leveraging its inherent long-term memory property to enhance data classification processes. The comprehensive model is depicted in Fig. 4 . Through a synergistic integration of CNN and LSTM; the model can effectively harness their respective strengths, thereby facilitating the diagnosis of hydro-turbine wear faults. The primary stages of the diagnostic procedure involve: ( 1 ) Acquire the acoustic vibration signals related to wear faults in hydro-turbines, categorize and segment the signals, and compile a standardized dataset of segmented data samples; ( 2 ) The processed dataset is fed into the CONV, and the fault features are dynamically extracted using a convolutional kernel; ( 3 ) After the CONV, the extracted features are maximally pooled in order to reduce the dimensionality of the feature set; ( 4 ) The feature data, after dimensionality reduction, will serve as the input for training the neural network within the LSTM layer, allowing for automatic learning of fault characteristics; ( 5 ) Classification of features related to hydro-turbine faults using Softmax functions. The procedures above delineate the core methodology of CNN-LSTM modeling for fault diagnosis in hydro-turbines. Through comprehensive utilization of the strengths inherent in CNN and LSTM, alongside their complementary capacities for spatial and temporal feature extraction, acoustic vibration signals are subjected to feature extraction processes followed by fault classification. Improved white shake optimizer White shake optimizer. The white shark is one of the world's most dangerous and powerful predatory sharks. In its natural environment, the white shark relies on its sensitive vision, hearing, smell, and electromagnetic field perception to sense subtle changes in the external environment and to receive and process a wide range of complex information. Figure 5 shows the perception range of different sensory systems of the white shark. The white shark optimization algorithm is designed for three typical behaviors of white sharks: movement speed toward prey, movement toward the best prey, and fish school behavior 30 . ( 1 ) Movement speed toward prey The great white shark relies on its keen senses to track prey, detecting the prey's movements that create water ripples. It identifies the prey's location based on the sound of these ripples and approaches it in a wave-like manner, swimming at a speed of: $${v}_{k+1}^{i}=\mu \left[{v}_{k}^{i}+{p}_{1}\left({w}_{g{best}_{k}}-{w}_{k}^{i}\right)\times {c}_{1}+{p}_{2}\left({\varvec{w}}_{best}^{{v}_{k}^{i}}-{w}_{k}^{i}\right)\times {c}_{2}\right]$$ 13 In the above, i is the white shark population, \(i=1, 2,\dots ..,n\) ; \(\mu\) is the contraction factor, which enhances the robustness of the algorithm, and the expression is as in Eq. ( 15 ); \({v}_{k}^{i}\) is the speed of the i -th white shark in the k -th iteration; \({p}_{1}\) and \({p}_{2}\) are scaling parameters controlling \({w}_{g{best}_{k}}\) and \({\varvec{w}}_{best}^{{v}_{k}^{i}}\) , defined by Eq. ( 15 ) and Eq. ( 16 ), respectively; \({w}_{g{best}_{k}}\) is the white shark in the k -th iteration optimal position; \({w}_{k}^{i}\) is the position of the i -th white shark in the k -th iteration; \({c}_{1}\) and \({c}_{2}\) are random numbers with values in the range of \(\left[\text{0,1}\right]\) ; \({\varvec{w}}_{best}^{{v}_{k}^{i}}\) is the vector of the i -th optimal position of the population; \({v}^{i}\) is the vector of the ith index of the white shark in the optimal position as shown in Eq. ( 18 ). $$\mu =\frac{2}{\left|2-\tau -\sqrt{{\tau }^{2}-4\tau }\right|}$$ 14 $${p}_{1}={p}_{max}+\left({p}_{max}-{p}_{min}\right)\times {e}^{{-\left(4k/K\right)}^{2}}$$ 15 $${p}_{1}={p}_{min}+\left({p}_{max}-{p}_{min}\right)\times {e}^{{-\left(4k/K\right)}^{2}}$$ 16 $$v=⌊n\times rand\left(\text{0,1}\right)⌋+1$$ 17 In Eqs. ( 14 )-( 17 ), \(\tau\) is the acceleration coefficient, which takes the value of 4.125; \({p}_{max}\) and \({p}_{min}\) are the maximum and initial velocities for white sharks to achieve good locomotion, respectively; k and K are the numbers of current iterations, and the maximum number of iterations, respectively; n is the population size of the white sharks; \(rand\left(\text{0,1}\right)\) denotes the n random numbers generated in the range of [0,1] that obey the uniform distribution. ( 2 ) Moving toward the best prey The white shark usually spends much time looking for potential prey, so its position is constantly changing. When a white shark hears waves produced by prey or smells prey during its search, it moves toward the prey's location. In some cases, the prey will move away from the original position. The white shark then tracks the prey again based on the scent it leaves behind or the waves it creates by swimming. In this case, the position update strategy of the white shark moving toward the prey is expressed as: $${w}_{k+1}^{i}=\left\{\begin{array}{c}{w}_{k}^{i}\bullet \neg ⨁{\varvec{w}}_{0}+u\bullet a+l\bullet b ;rand<mv\\ {w}_{k}^{i}+\raisebox{1ex}{${v}_{k}^{i}$}\!\left/ \!\raisebox{-1ex}{$f$}\right. ;rand\ge mv\end{array}\right.$$ 18 In the above, \({w}_{k+1}^{i}\) is the new position of the ith white shark at the (k+1) -th iteration; \(\neg\) is the inverse operator; \({\varvec{w}}_{0}\) is a logic vector, which is defined according to Eq. ( 19 ); u and l denote the upper and lower bounds of the search space, respectively; a and b are one-dimensional binary vectors, which are defined according to Eqs. ( 20 ) and ( 21 ); f denotes the frequency of fluctuating movement of white sharks, which is defined in Eq. ( 21 ); rand denotes the random number generated in the range of [0,1] obeying the uniform distribution; mv denotes the sensory intensity of white sharks, which is increasing with increasing the number of iterations, which is defined in Eq. ( 30 ). $${\varvec{w}}_{0}=⨁(\varvec{a},\varvec{b})$$ 19 In the above, \(⨁\) denotes the different-or operation. $$\varvec{a}=sgn\left({w}_{k}^{i}-u\right)>0$$ 20 $$\varvec{b}=sgn\left({w}_{k}^{i}-l\right)<0$$ 21 In the above, sgn denotes the symbolic operator; Eqs. ( 19 )-( 21 ) are the steps of integrating the dimensions in that \({w}_{k}^{i}\) are beyond the upper and lower boundaries into the upper and lower boundaries of the search space, which is crucial to help white sharks explore potential regions. $$f={f}_{min}+\frac{{f}_{max}-{f}_{min}}{{f}_{max}+{f}_{min}}$$ 22 In the above, \({f}_{max}\) and \({f}_{min}\) are the maximum and minimum frequencies of the white shark's fluctuating motions, respectively, and generally take the values of 0.75 and 0.07. $$mv=\frac{1}{\left({a}_{0}+{e}^{\left(K/2-k\right)/{a}_{1}}\right)}$$ 23 In the above, \({a}_{0}\) and \({a}_{1}\) are two constants that take values of 6.25 and 100, they are generally used to manage exploration and exploitation behavior. When mv takes a smaller value, the WSO algorithm performs a smaller localized search in the vicinity of \({w}_{k+1}^{i}\) . When mv takes a larger value, the WSO algorithm performs a larger search in the region away from \({w}_{k+1}^{i}\) . ( 3 ) fish school behavior White sharks are highly social animals and cooperative when hunting, with the group moving towards the white shark closest to the prey. Eq. ( 24 ) simulates the behavior of a group of white sharks moving toward the best white shark position: $${w}_{k+1}^{{\prime }i}={w}_{g{best}_{k}}+{r}_{1}{\overrightarrow{D}}_{w}sgn\left({r}_{2}-0.5\right) ; {r}_{3}<{S}_{s}$$ 24 In the above, \({w}_{k+1}^{{\prime }i}\) is the new position of the i -th white shark iterated to the (k+1) -th iteration relative to the prey position; \({r}_{1}\) , \({r}_{2}\) , and \({r}_{3}\) are random numbers in the range of [0,1], respectively; \(sgn\left({r}_{2}-0.5\right)\) controls the direction and randomness of the localized search and is taken to be the same with the probability of 1 and − 1; \({\overrightarrow{D}}_{w}\) is the distance between the prey and white sharks distance, defined by Eq. ( 25 ); \({S}_{s}\) denotes the olfactory and visual parameters when the white shark group locks on to the best positioned white shark defined by Eq. ( 26 ). $${\overrightarrow{D}}_{w}=\left|rand\times \left({w}_{g{best}_{k}}-{w}_{k}^{i}\right)\right|$$ 25 $${S}_{s}=\left|1-{e}^{\left(-{a}_{2}\times k/K\right)}\right|$$ 26 In the above, \({a}_{2}\) is a constant that takes the value 0.0005. Simulate the behavior of a white shark population. This simulation retains the optimal solution. The optimal solution accounts for the speed at which the white shark moves toward its prey and the specific prey it targets. Update the positions of other white sharks based on the optimal positions obtained: $${w}_{k+1}^{i}=\frac{{w}_{k}^{i}+{w}_{k+1}^{{\prime }i}}{2\times rand}$$ 27 Improved white shake optimizer . ( 1 ) Initial population optimization The WSO algorithm excels in low-dimensional optimization problems. However, it needs to exhibit higher convergence accuracy in high-dimensional optimization problems. It is easy to fall into local extremes and converge prematurely. This paper proposes an improved WSO (IWSO) algorithm to improve the optimization-seeking speed and accuracy of the original algorithm. Chaotic mapping algorithms are characterized by sensitivity to initial conditions and chaotic traversal. The chaotic optimization algorithm is evolved according to these characteristics. Chaotic optimization algorithms can filter out the local optimal solution and converge quickly during optimization. The WSO algorithm's initial population is generated randomly, which causes the initial solution to be unevenly distributed and lack diversity in the search domain. For this reason, this paper introduces a tent chaotic optimization algorithm to initialize the population and replace the selection process of random values to improve the convergence and local search ability of the WSO algorithm. The expression of tent chaotic mapping is shown in Eq. ( 35 ), where the chaotic mapping of each particle follows the order depicted in Fig. 6 . $${x}_{k+1}=\left\{\begin{array}{c}\frac{{x}_{k}}{0.7},{x}_{k}<0.7 \\ \frac{10}{3}\left(1-{x}_{k}\right), {x}_{k}\ge 0.7\end{array}\right.$$ 28 ( 2 ) Velocity update optimization In the WSO algorithm, the velocity update of the white shark's movement toward the prey relies on an overall scaling by a contraction factor \(\mu\) . The value of \(\mu\) depends on the acceleration coefficient \(\tau\) . In practice,, \(\mu\) is a constant, \(\mu =0.70346\) 30 . This result suggests that the scaling to the velocity is constant, which leads to inactivation of the white shark population. The WSO algorithm suffers from convergence stagnation during the global search. A bird-flock search strategy was introduced to optimize the scaling factor. The inertial weights of the flight speeds of the bird flocks are brought into Eq. ( 13 ): $${w}_{k+1}^{i}=\left\{\begin{array}{c}B\times \text{cos}\left(\alpha \right)\bullet {w}_{g{best}_{k}} ;rand<em\\ {w}_{k}^{i}\bullet \neg ⨁{\varvec{w}}_{0}+u\bullet a+l\bullet b ;rand\ge em\end{array}\right.$$ 29 In the above, g is the inertia weight parameter, defined by Eq. ( 30 ): $$g={g}_{max}-\left[\frac{\left({g}_{max}-{g}_{min}\right)}{K}\right]\bullet k$$ 30 In the above, \({g}_{max}\) is the upper bound of the inertia weights; \({g}_{min}\) is the lower bound of the inertia weights; as the number of iterations increases, g dynamically decreases, which facilitates probing again for the optimal solution among the ones already found. ( 3 ) Elite White Shark Optimization Each white shark group will have a white shark closest to the prey, called the elite white shark. Refining the search in the local space near it can enhance the probability of searching for the optimal solution and improve convergence accuracy. For this reason, the cosine variation strategy is introduced in the white shark moving toward the best prey stage. The periodic oscillation of the cosine function is utilized to drive the WSO algorithm to search in the local space near the elite white shark. As the search proceeds, it makes the elite white shark closer and closer to its prey. The expression of the process is as follows: $${w}_{k+1}^{i}=\left\{\begin{array}{c}B\times \text{cos}\left(\alpha \right)\bullet {w}_{g{best}_{k}} ;rand<em\\ {w}_{k}^{i}\bullet \neg ⨁{\varvec{w}}_{0}+u\bullet a+l\bullet b ;rand\ge em\end{array}\right.$$ 31 In the above, B is the amplitude of \(\text{cos}\left(\alpha \right)\) , which is calculated by Eq. ( 31 ); \(\alpha \in \left[\text{0,2}\pi \right]\) ; and em denotes the cosine variance control parameter, it taken as 0.2. $$B={e}^{\left(-\gamma \times \left(k/K\right)\right)}$$ 32 In the above, \(\gamma\) is the shape control coefficient; as the number of iterations increases, the value of B decreases. Modeling architecture for wear fault in Hydro-turbines Materials and methods Fault experimental bench . In this study, an experimental bench for hydro-turbine failure analysis was designed and constructed. The experimental bench, illustrated in Fig. 7 , consists of a pressure pump, hydroelectric generator unit, submersible pump, water tank, and corresponding pipe. The sensor captures signals of wear faults in the hydroelectric generator unit. The tank and return tank are first filled with water, then the pressure and submersible pumps are activated simultaneously. The pressure pump facilitates the transfer of water from the tank through a network of pipes that ultimately impinge on the rotor blades within the hydro-turbine. After passing through the hydro-turbine, the water flowed back to the tank, and the submersible pump pumped the water back to the tank to ensure water circulation. Throughout the experiment, sediment was added to the tank to simulate conditions in the natural environment. After a period of operation of the failure test bed, when the signal amplitude region captured by the sensor stabilizes and no longer increases, it indicates that the water and sediments within the cycle have been adequately mixed. At this time, start recording signal data. Figure 8 depicts the assembled fault experimental bench. The acoustic vibration signals of the three conditions of the hydro-turbine, normal working conditions, and sediment concentrations \(0.73\text{k}\text{g}/{\text{m}}^{3}\) and \(1.4\text{k}\text{g}/{\text{m}}^{3}\) were collected for processing and analysis. Data description. The signal acquisition apparatus incorporates the utilization of the noise sensor (CRY2301), which is characterized as a compact industrial-grade real-time spectrum analyzer featuring an advanced DSP processor. This device integrates essential components such as a microphone, preamplifier, and data acquisition card within a tightly arranged structure, ensuring precise and efficient data processing. Table 1 provides an overview of the parameters associated with the noise sensor. Table 1 Parameters of the noise sensor Parameters Specification Unit Sample rate 48 kHz Standard measuring range 25–130 dBA Dynamic measuring range \(\ge 110\) dBA Frequency measuring range 10-20000 Hz communication interface USB Audio + USB HID Size \({\phi }25\times 115\) mm The collected acoustic vibration signals are shown in Fig. 9 . Data collected from each operational condition are structured and segmented, with each segment sample comprising 1024 data points. There are a total of 70 sample sets for each operational condition. The samples were randomly selected to divide the training and test sets to form the final data set, as shown in Table 2 . Table 2 Parameters of the noise sensor Working condition of the hydro-turbine Sample size Label Training sets Test sets Normal 49 21 1 Sand concentration of \(0.73\text{k}\text{g}/{\text{m}}^{3}\) 49 21 2 Sand concentration of \(1.4\text{k}\text{g}/{\text{m}}^{3}\) 49 21 3 Modeling architecture . In hydro-turbines' practical operational settings, the acoustic vibration signal arising from water flow impacting the runner is frequently marred by substantial noise contamination. Directly using the raw data for fault diagnosis will significantly impact the diagnosis results, so it is necessary to de-noise the collected signals first for pre-processing. This paper uses the improved WT algorithm to denoise the original signal, maximizing the signal characteristics of different working conditions to be retained. The IWSO algorithm is introduced and combined with the constructed CNN-LSTM fault diagnosis model, and the CNN-LSTM hydro-turbine fault diagnosis model is optimized through IWSO integration. The introduction of the IWSO algorithm can improve the convergence and convergence accuracy of the model and effectively solve the problem of hyperparameter adjustment inherent in deep learning models. The structure of the hydro-turbine wear fault diagnosis model based on improved WT denoising and IWSO-optimized CNN-LSTM is shown in Fig. 10 . Experimental validation and analysis Data preprocessing . The improved WT denoising is performed on three raw signals collected in 4.2.1. Since the raw signal data is vast, if the denoising results of all signals in the same working condition are shown, it will lead to a relatively close denoising effect graph. In order to show the denoising effect more intuitively, this section selects ten groups of data in each working condition as the result display. The db4 wavelet basis and a four-layer decomposition are selected to decompose the simulated signal. The threshold size of the wavelet coefficients is established through Stein's unbiased estimation of the threshold function. Following this determination, the signals undergo processing utilizing soft, hard, and novel thresholding techniques. Subsequently, the wavelet coefficients are reconstructed post-thresholding operation. Figure 11 juxtaposes the signals processed employing soft, hard, and novel thresholding methods across three distinct operational conditions. Figure 11. Comparison of three threshold denoising Noise-denoising operations using different threshold functions will result in producing different graphical results. All three different threshold functions effectively reduce the noise level of the original signal. Across the three distinct operating conditions, the resulting curve following the application of the hard threshold function exhibits roughness and contains a higher level of high-frequency noise. Conversely, the noise reduction curve produced by the soft threshold function appears comparatively smoother. However, in signal decomposition, part of the useful signal is misjudged as noise and filtered, thus leading to a certain degree of distortion. On the other hand, the noise reduction operation using the new threshold function can obtain a smoother noise reduction curve and maximize the retention of the useful signal, thus making the noise-denoising signal closer to the original signal. Figure 12 illustrates the signal spectra processed using soft threshold, hard threshold, and new threshold for three operating conditions. All three thresholding methods successfully removed some of the high-frequency noise components. However, it should be noted that the signal processed by the soft threshold function shows significant distortion in the low-frequency band, which indicates that the method misjudges a part of the useful signal as noise and rejects it in the denoising process. On the contrary, the signal processed by the hard threshold function showed more burrs in the high-frequency band, meaning its denoising effect is relatively poor. However, after the noise reduction by the new threshold function, the spectrum exhibits higher smoothness in the high-frequency band and better preservation of the useful signal. Hence, the new threshold function performs well in maintaining signal integrity. To assess the denoising effectiveness further, the outcomes were evaluated utilizing the root mean square error (RMSE) and signal-to-noise ratio (SNR), expressed as follows: $$RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^{n}{\left[f\left(n\right)-\widehat{f}\left(n\right)\right]}^{2}}$$ 33 $$SNR=10{\text{log}}_{10}\left\{\frac{\frac{1}{n}\sum _{i=1}^{n}{f}^{2}\left(n\right)}{\frac{1}{n}\sum _{i=1}^{n}{\left[f\left(n\right)-\widehat{f}\left(n\right)\right]}^{2}}\right\}$$ 34 In the above, n is the signal length; \(f\left(n\right)\) is the noise-containing signal; and \(\widehat{f}\left(n\right)\) is the noise-canceled signal. A smaller RMSE value indicates a more effective noise-canceling effect, while a more considerable SNR value also signifies improved noise cancellation. Following processing, the RMSE and SNR for various working conditions are illustrated in Fig. 13. Notably, the new threshold function exhibits the highest SNR and the lowest RMSE. It indicates that the noise reduction effect of the new threshold function exceeds the performance of the traditional threshold function. IWSO-based optimized CNN-LSTM model for hydro-turbine wear fault diagnosis . The hyperparameters of the CNN-LSTM model are first optimized. The IWSO and WSO algorithms are used to operate this optimization process. Their convergence iteration process curves are shown in Fig. 14 . With the continuous updating of speed and position, the population evolves, and the value of the fitness function of the optimal individual decreases. After 50 iterations of computation, the IWSO algorithm can complete convergence in less than ten iterations. The unoptimized WSO algorithm, on the other hand, needs about 13 iterations to complete convergence, which is more than the IWSO algorithm. Moreover, the WSO algorithm falls into local optimality. The figure shows that the IWSO algorithm can have higher efficiency and more accurate calculation results. In summary, the IWSO algorithm offers an effective and dependable approach for hyperparameter selection in CNN-LSTM models, mitigating issues such as time loss and model instability that may arise from manual hyperparameter adjustments. The output of the optimal combination of hyperparameters is feature_num=[27,93], LayerSizes = 47, Stride = 2. The IWSO-optimized CNN-LSTM model was employed for fault diagnosis across three operational conditions. To underscore the efficacy of the proposed approach delineated in this study, CNN, LSTM, and CNN-LSTM models were chosen as comparison benchmarks. An additional dataset without undergoing wavelet threshold denoising is included for diagnostic purposes in the IWSO-CNN-LSTM model. Figure 15 illustrates the training curves for the five distinct methods. The accuracy and function loss rate curves of the five models CNN, LSTM, CNN-LSTM, IWSO-CNN-LSTM, and the proposed method are shown in Fig. 15. The accuracy of all five models can reach more than 65%. Notably, the LSTM model has the lowest accuracy of 68.7%. The curve fluctuates more in the model, and the smoothness is poor. Upon incorporating the LSTM model, the CNN-LSTM model achieves an accuracy of 83.7%. It shows that adding LSTM overcomes CNN's limitations in handling long sequences and enhances the model's stability and accuracy. The accuracy of the IWSO-CNN-LSTM model is 89.1%, which exceeds the CNN, LSTM, and CNN-LSTM models. By denoising the raw data with the improved WT algorithm, the IWSO-CNN-LSTM model achieves a diagnostic accuracy of 97.2%, 8.1% better than the un-denoised model. This result illustrates the importance of data denoising preprocessing to improve the diagnostic accuracy of the model. As shown in Fig. 15(b), the function loss rate of the WT-IWSO-CNN-LSTM model is 0.38, which is lower than the other four models, thereby substantiating its superior performance. The proposed method distinguishes itself with exceptional fault diagnosis capabilities. The model demonstrates enhanced accuracy and stability by integrating the distinctive features inherent in CNN and LSTM architectures, leveraging the IWSO algorithm to determine optimal hyperparameter configurations. Figure 16 presents a comparative analysis of the five models' actual and diagnostic recognition outcomes. The proposed methodology demonstrates the most congruence between diagnostic outcomes and actual results, thus affirming its superior accuracy and reliability in diagnosing wear faults. Further, from the confusion matrices of the five model training, the diagnostic accuracy of the models for condition 3 is all the better than the diagnostic accuracy of condition 2. In order to evaluate the diagnostic results of the test set more comprehensively, this paper introduces Accuracy, Precision, Recall, and F1-score as the evaluation indexes of the fault diagnostic results. Each evaluation index is expressed as: $$\left\{\begin{array}{c}Accuracy=\frac{TP+TN}{TP+FP+TN+FN}\\ Precsion=\frac{TP}{TP+FP}\\ Recall=\frac{TP}{TP+TN}\\ F1score=\frac{\left(1+{\beta }^{2}\right)TP}{\left(1+{\beta }^{2}\right)TP+FP+FN}\end{array}\right.$$ 35 True positive (TP) signifies the count of signals accurately identified as normal conditions. True negative (TN) signifies the count of signals correctly identified as faults. False negative (FN) indicates the count of signals erroneously classified as normal conditions. False positive (FP) denotes the count of signals inaccurately classified as faults. The test sets of the three working conditions are brought into the trained model for diagnosis. The evaluation metrics of the diagnostic results are shown in Fig. 17 . The results indicate that the proposed method model achieves the highest evaluation score among the recognition outcomes of the five models. The LSTM model exhibits the lowest evaluation score. Conversely, the recognition outcomes of the proposed method model outperform those of the other four models across all four evaluation metrics. Compared to the other four methods, the proposed model demonstrates superior performance and enhanced stability, enabling more comprehensive recognition and diagnosis of hydro-turbine wear fault signals. Figure 18 illustrates the fault diagnosis performance of the five models on the test dataset. Notably, all five models exhibit commendable accuracy levels for Case 1 and Case 3. However, the LSTM model demonstrates a notably lower accuracy of 65.3% and needs to improve in diagnosing condition 2. Conversely, the CNN model achieves an accuracy of 77.8%, significantly higher than that of the LSTM model. The CNN-LSTM model attains an accuracy of 84.2%. Upon employing the White Shark Optimization (WSO) algorithm to optimize the CNN-LSTM model, the accuracy of the resulting IWSO-CNN-LSTM model improves to 87.3%, representing a notable enhancement in diagnostic accuracy across all three operating conditions. Particularly noteworthy is the superior performance of the proposed method, which achieves an accuracy of 96.2% and attains 100% accuracy in diagnosing both working condition 1 and working condition 3. This outcome serves to validate the exceptional performance of the proposed method. Similar to the training set results, in the test set, the diagnostic accuracies of the five models for condition 3 are higher than that of condition 2, which indicates that the accuracy of hydro-turbine wear fault diagnosis increases with the increase of sediment concentration in the water. This phenomenon is caused by increased sediment concentration, which substantially impacts the hydro-turbine runner more. Consequently, the amplitude of the collected fault signals undergoes a notable increase, thereby rendering the fault characteristics more conspicuous and enhancing diagnostic accuracy effectively. Conclusion This paper proposes a hydro-turbine wear fault diagnosis method based on improved WT preprocessing combined with IWSO-based optimized CNN-LSTM. The new threshold function is first constructed, and the traditional wavelet threshold algorithm is improved. The improved wavelet threshold algorithm is utilized to denoise the acquired signals' preprocessing. This step enhances the accuracy of the neural network for feature extraction. In response to the limitations encountered by the CNN model in managing lengthy sequence complexities, the CNN-LSTM model is formulated, integrating the LSTM model to address the shortcomings inherent in the CNN algorithm concerning capturing temporal correlations. Due to the excessive number of nodes in the CNN-LSTM model, there is the problem of hyperparameter tuning, and the IWSO is introduced for hyperparameter tuning. For the problem that the WSO algorithm quickly falls into local optimum and premature convergence, tent chaotic mapping is used to initialize the population, and bird flock search behavior and cosine elite variation strategy are introduced to improve its convergence speed and accuracy. According to the training outcomes, the proposed method surpasses the CNN, LSTM, CNN-LSTM, and IWSO-CNN-LSTM models regarding accuracy and function loss rate, achieving 97.2% and 0.38, respectively. Furthermore, it exhibits the most excellent concordance between diagnostic outcomes and actual results. In the test findings, the proposed approach attains an accuracy of 96.2%, surpassing that of CNN, LSTM, and CNN-LSTM models. Compared to the IWSO-CNN-LSTM model, the proposed methodology demonstrates an improvement in accuracy by 8.9%. Notably, the diagnostic accuracy of hydro-turbine wear faults has escalated with escalating sediment concentration. Diagnosing wear faults in hydro-turbines improves efficiency and power generation quality, reduces maintenance costs, and minimizes resource consumption. This study is valuable to the extant hydro-turbine condition monitoring and fault diagnosis systems. Hydro-turbines have different structures and collect different fault signals. At the same time, the characteristics of different river sediments, such as grain size gradation, hardness, and sediment composition during the flooding period, are complicated. Therefore, it is more valuable to carry out targeted research and analysis in the next step for engineering application. Declarations Credit author contribution statement Fang Dao : Methodology, Software, Writing - Original Draft, Writing - Editing. Yun Zeng : Conceptualization, Supervision, Funding acquisition. Yidong Zou : Conceptualization , Validation. Jing Qian : Investigation, Resources. Data availability The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is supported by grants from the National Natural Science Foundation of China (52079059) and the National Natural Science Foundation of China (No: 52269020). References Tariq, G. et al. 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Cite Share Download PDF Status: Published Journal Publication published 25 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 25 Jul, 2024 Reviews received at journal 01 Jul, 2024 Reviewers agreed at journal 26 Jun, 2024 Reviews received at journal 06 May, 2024 Reviewers agreed at journal 26 Apr, 2024 Reviewers agreed at journal 26 Apr, 2024 Reviewers invited by journal 26 Apr, 2024 Editor assigned by journal 25 Apr, 2024 Editor invited by journal 07 Mar, 2024 Submission checks completed at journal 07 Mar, 2024 First submitted to journal 21 Feb, 2024 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. 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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-3975472","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":277913403,"identity":"1e6b9197-b46a-423c-b667-921d0b6bb2eb","order_by":0,"name":"Fang Dao","email":"","orcid":"","institution":"Kunming University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Fang","middleName":"","lastName":"Dao","suffix":""},{"id":277913404,"identity":"dd50560c-0c9c-4ecf-b050-9f7962156fb7","order_by":1,"name":"Yun Zeng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYBADHjZm5gMHPvwgQYscPztb4sGZPSRoMZbs5zE+zMFGhFL59t7Dr3nb7iRuOMzz4TADD4M8v9gB/FoYe86lWfO2PQNq4d1wuMCCwXDm7AT8WpglcsyMedsOQ7TM4GFIMLhNQAub/BuYFp4Hh3nYiNDCI8Fj/BioxViymYeBOC0SPDlmjHPOHZbjZ2YzAAayBGG/yLefMf7wpgxoPv/hxx8+/LCR55cmoAXkHSkeJFsJKgcB5o+kJJNRMApGwSgYgQAA/OFD8QWlq6wAAAAASUVORK5CYII=","orcid":"","institution":"Kunming University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Yun","middleName":"","lastName":"Zeng","suffix":""},{"id":277913405,"identity":"157fc716-43d0-4010-9d4f-f880c4119f21","order_by":2,"name":"Yidong Zou","email":"","orcid":"","institution":"Wuhan University","correspondingAuthor":false,"prefix":"","firstName":"Yidong","middleName":"","lastName":"Zou","suffix":""},{"id":277913406,"identity":"6d6457b2-c260-44e5-bb43-d8aaa2a3cbf7","order_by":3,"name":"Jing Qian","email":"","orcid":"","institution":"Kunming University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jing","middleName":"","lastName":"Qian","suffix":""}],"badges":[],"createdAt":"2024-02-21 12:44:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3975472/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3975472/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-77251-7","type":"published","date":"2024-10-25T15:58:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":52414723,"identity":"02e66944-73b6-4663-8660-208551d78892","added_by":"auto","created_at":"2024-03-11 11:06:34","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":55560,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of three threshold functions\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/8150819822f698c2f079435f.png"},{"id":52414729,"identity":"e20272be-fd6c-456b-982e-d5f0c0e4c55a","added_by":"auto","created_at":"2024-03-11 11:06:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":365108,"visible":true,"origin":"","legend":"\u003cp\u003eTypical architecture of the CNN\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/fcfa552072d1b0e66b8a99a6.png"},{"id":52414740,"identity":"397a8700-06b2-490d-8e49-66dcc9351ed5","added_by":"auto","created_at":"2024-03-11 11:06:39","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":88838,"visible":true,"origin":"","legend":"\u003cp\u003eStructure of the LSTM\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/ad728699ab3a4b326713976a.png"},{"id":52414724,"identity":"5773563b-4bb4-4b04-9eda-aaf222f30a0e","added_by":"auto","created_at":"2024-03-11 11:06:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":649877,"visible":true,"origin":"","legend":"\u003cp\u003eThe CNN-LSTM model\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/9fbb3929e35eb9ea15359c24.png"},{"id":52414732,"identity":"b8f167df-d8cd-41d3-ba35-4a05e9b15cc3","added_by":"auto","created_at":"2024-03-11 11:06:38","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":399258,"visible":true,"origin":"","legend":"\u003cp\u003eSensory system of the white shark\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/00e7009409220f4292a0aebf.png"},{"id":52414730,"identity":"d752480b-017d-4f2e-80bb-4dede21ee128","added_by":"auto","created_at":"2024-03-11 11:06:36","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":81395,"visible":true,"origin":"","legend":"\u003cp\u003echaotic sequence diagram\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/5e87f848cfff2705ae15cea1.png"},{"id":52414728,"identity":"7f347b4d-bb3d-41b8-8a48-0dddbaa8854e","added_by":"auto","created_at":"2024-03-11 11:06:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":473257,"visible":true,"origin":"","legend":"\u003cp\u003eThe operation process of hydro-turbine failure experimental bench\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/9b366cd12da723abcc7e4783.png"},{"id":52414733,"identity":"9662427a-15e2-4061-aaee-0bf88f6715ec","added_by":"auto","created_at":"2024-03-11 11:06:38","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":547848,"visible":true,"origin":"","legend":"\u003cp\u003eFailure experimental bench of the hydro-turbine\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/5d495cf8f572608d040774ba.png"},{"id":52414727,"identity":"5a8361c5-8768-4357-9e8b-4c552b5e2ae4","added_by":"auto","created_at":"2024-03-11 11:06:36","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":86090,"visible":true,"origin":"","legend":"\u003cp\u003eSignals of the three 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0.73kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003e(c) Sand of 1.4kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/1737f70ddf1c51d98c78943e.png"},{"id":52414739,"identity":"2a711c3f-7ae6-4bc4-be2a-3821dc5c5d15","added_by":"auto","created_at":"2024-03-11 11:06:39","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":1117069,"visible":true,"origin":"","legend":"\u003cp\u003eSpectrums of three threshold denoising\u003c/p\u003e\n\u003cp\u003e(a) Normal\u003c/p\u003e\n\u003cp\u003e(b) Sand of 0.73kg/m\u003csup\u003e3\u0026nbsp;\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003e(c) Sand of 1.4kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/08757a4e9c9775268aff95ea.png"},{"id":52414738,"identity":"5c26caf5-a8a0-4058-921e-21e728de1098","added_by":"auto","created_at":"2024-03-11 11:06:39","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":125869,"visible":true,"origin":"","legend":"\u003cp\u003eSNR and RMSE\u003c/p\u003e\n\u003cp\u003e(a) Normal\u003c/p\u003e\n\u003cp\u003e(b) Sand of 0.73kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003e(c) Sand of 1.4kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/a5822f717cab4a4996e58edb.png"},{"id":52414726,"identity":"e4beb68b-a4b1-4a89-bbd0-d576ea67e277","added_by":"auto","created_at":"2024-03-11 11:06:36","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":13243,"visible":true,"origin":"","legend":"\u003cp\u003eOptimization Iteration Process Curve\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/83e2ad6a42b115ff0f977bdf.png"},{"id":52414735,"identity":"1fa2d409-3994-4786-8f64-ac6350bf0633","added_by":"auto","created_at":"2024-03-11 11:06:39","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":405419,"visible":true,"origin":"","legend":"\u003cp\u003eTraining curve\u003c/p\u003e\n\u003cp\u003e(a) Accuracy\u003c/p\u003e\n\u003cp\u003e(b) Loss\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/59dc82df101d96caf1350bab.png"},{"id":52414900,"identity":"a9965790-8bcb-4497-ba50-c3544d902181","added_by":"auto","created_at":"2024-03-11 11:14:39","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":905446,"visible":true,"origin":"","legend":"\u003cp\u003eConfusion matrix for the five models\u003c/p\u003e\n\u003cp\u003e(a) CNN\u003c/p\u003e\n\u003cp\u003e(b) LSTM\u003c/p\u003e\n\u003cp\u003e(c) CNN-LSTM\u003c/p\u003e\n\u003cp\u003e(d) IWSO-CNN-LSTM\u003c/p\u003e\n\u003cp\u003e(e) The proposed method\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/c3eb719b7161fb2fedee5047.png"},{"id":52414725,"identity":"3d1f6262-2b46-4291-bf01-6d6429cd5a74","added_by":"auto","created_at":"2024-03-11 11:06:35","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":79261,"visible":true,"origin":"","legend":"\u003cp\u003eEvaluation indicator\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/54a61f827cf77bb3a6fc2fac.png"},{"id":52414736,"identity":"1e951b4f-c86d-418a-a057-0111d303a70b","added_by":"auto","created_at":"2024-03-11 11:06:39","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":165210,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of test set diagnostic results\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/adca534906efd73e281e74ce.png"},{"id":67682016,"identity":"c2b3ce73-5052-402a-ad07-495a45cc121e","added_by":"auto","created_at":"2024-10-28 16:12:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10499836,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3975472/v1/2dbb7729-746a-4a22-bdd1-0763fe2184db.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Wear fault diagnosis in hydro-turbine via the incorporation of the IWSO algorithm optimized CNN-LSTM neural network","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAs a critical pillar of human productivity, energy plays a vital role in global development\u0026nbsp;\u003csup\u003e1\u003c/sup\u003e. Hydropower has become an indispensable part of the global energy system due to its renewability, environmental characteristics, economy, and excellent performance in regulating the power system\u0026nbsp;\u003csup\u003e2\u003c/sup\u003e. As an essential link in hydropower energy development, the stability and safety of hydropower station operation are crucial for power supply\u0026nbsp;\u003csup\u003e3\u003c/sup\u003e. However, during the operation of hydropower stations, the hydro-turbines of hydropower stations generally face challenges such as sediment abrasion, which is particularly prominent in some rivers with high sediment content\u0026nbsp;\u003csup\u003e4,5\u003c/sup\u003e. Accurate and timely diagnosis of hydro-turbine wear-related faults is essential\u0026nbsp;\u003csup\u003e6\u003c/sup\u003e. It ensures the sustainable operation of hydropower stations. It also maintains the stability of the energy supply.\u003c/p\u003e\n\u003cp\u003eThe constant impact and friction of sediments such as mud and sand causes wear and damage to the surface of the hydro-turbine runner\u0026nbsp;\u003csup\u003e7\u003c/sup\u003e. Wear leads to changes in the trajectory of the internal water flow, which cuts down the unit\u0026apos;s efficiency and makes the conversion of hydropower energy less efficient. In addition, damage to the hydro-turbine runner makes the hydropower unit less stable, and the resulting instability triggers safety uncertainty in operation and increases the noise level during the operation of the hydropower station\u0026nbsp;\u003csup\u003e8\u003c/sup\u003e. The manifestation of extensive wear and tear issues can precipitate mechanical breakdown in hydro-turbines, thereby imperiling the operational integrity of hydropower units and the safety of the personnel involved\u0026nbsp;\u003csup\u003e9\u003c/sup\u003e. Consequently, the diagnostic of wear-related faults within hydro-turbines assumes paramount importance.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eScholarly inquiry into the phenomenon of sediment erosion affecting hydro-turbine runners has predominantly centered on the subsequent pivotal domains: (1) reducing sediment loading, (2) improving the erosion resistance of runners, and (3) conducting erosion simulation studies. Several technical means have been adopted to reduce sediment loading, including sediment monitoring for runner intake ports\u0026nbsp;\u003csup\u003e10\u003c/sup\u003e, temporary hydro-turbine shutdowns during flood season, and filtration and sedimentation methods like sedimentation ponds to reduce erosion sources\u0026nbsp;\u003csup\u003e11\u003c/sup\u003e. Applying specific coating processes on hydro-turbine overflow elements\u0026apos; surfaces can enhance their resistance to sediment erosion and prolong their service life\u0026nbsp;\u003csup\u003e12,13\u003c/sup\u003e. Considering the fluctuating sediment concentrations across seasons and the intricate configurations characterizing hydropower station infrastructure, numerous investigations about the erosion of hydro-turbine runner blades by sediment have embraced methodologies entailing simulation and analysis of solid-liquid two-phase flow dynamics. This research requires modeling erosion and wear\u0026nbsp;\u003csup\u003e14\u003c/sup\u003e or analyzing sediment particles\u0026apos; shape and kinematic properties\u0026nbsp;\u003csup\u003e15\u003c/sup\u003e. However, there needs to be more research on using deep learning models to analyze sediment wear failures in hydro-turbines. This area holds great promise, and exploring the potential applications of deep learning in solving this problem is worthwhile.\u003c/p\u003e\n\u003cp\u003eDeep learning theories have excellent modeling and data processing capabilities, providing unique data analysis solutions for various industries\u0026nbsp;\u003csup\u003e16,17\u003c/sup\u003e. The fault diagnosis and identification field has also benefited\u0026nbsp;\u003csup\u003e18\u003c/sup\u003e. It excels at solving complex problems. These problems are challenging to solve using traditional analytical modeling or empirical knowledge alone. Deep learning is known for its high accuracy, robustness, and excellent generalization capabilities\u0026nbsp;\u003csup\u003e19,20\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eConvolutional neural networks (CNNs) have been widely used in rotating machinery fault diagnosis due to their powerful ability for automatic feature extraction\u0026nbsp;\u003csup\u003e21\u003c/sup\u003e. The network has demonstrated excellent performance in recognizing the health condition of rotating machinery. The convolutional weight-sharing structure of CNN stands out as a notable feature, effectively mitigating neural network complexity and parameter count, thus serving as a preventive measure against overfitting\u0026nbsp;\u003csup\u003e22\u003c/sup\u003e. Nonetheless, CNNs exhibit an inherent limitation in their capability to address static features within datasets, thereby disregarding prolonged temporal dependencies intrinsic to time series data. This constraint presents a challenge, particularly in addressing protracted time series problems\u0026nbsp;\u003csup\u003e23\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eRecurrent Neural Networks (RNNs) are adept at capturing prolonged dependencies within temporal datasets, making them well-suited for addressing classification and regression tasks involving time series data\u0026nbsp;\u003csup\u003e24\u003c/sup\u003e. Nevertheless, data points distant from the present moment present complexities that hinder their effective utilization as references for input-output mapping, resulting in issues such as gradient vanishing and explosion\u0026nbsp;\u003csup\u003e25\u003c/sup\u003e. To address these challenges, Hochreiter et al. introduced the Long Short-Term Memory (LSTM) network, an upgraded version of Recurrent Neural Networks (RNNs) specifically designed to handle time-series data\u0026nbsp;\u003csup\u003e26\u003c/sup\u003e. The LSTM excels at retaining long-term memories and learning dependencies, effectively addressing gradient vanishing and exploding issues, resulting in superior performance and outcomes compared to RNNs\u0026nbsp;\u003csup\u003e27\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIncreasing the number of nodes and layers of the neural network can effectively improve the learning and fitting effectiveness. However, it also significantly increases the number of hyperparameters\u0026nbsp;\u003csup\u003e28\u003c/sup\u003e. These hyperparameters, including the number of nodes per layer, the initial learning rate, and the number of iterations, are pre-set before model training begins\u0026nbsp;\u003csup\u003e29\u003c/sup\u003e. Assessing each combination of hyperparameters necessitates numerous iterative computations, leading to significant time and effort expenditure. Therefore, optimization of hyperparameters is essential.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe white shark optimizer (WSO) algorithm is an emerging meta-heuristic algorithm proposed by Braik and other researchers\u0026nbsp;\u003csup\u003e30\u003c/sup\u003e. The algorithm imitates white sharks, which use their superior perceptual abilities to sense complex information while hunting in the deep sea\u0026nbsp;\u003csup\u003e31\u003c/sup\u003e. The basic idea of the white shark optimization algorithm is to model and simulate three primary behaviors: rapid movement of white sharks towards prey, movement towards the best prey, and flocking behavior. This algorithm can efficiently handle optimization problems of high complexity\u0026nbsp;\u003csup\u003e32\u003c/sup\u003e. However, like most population-based algorithms, the WSO algorithm must improve its convergence accuracy and tends to converge when dealing with complex optimization problems.\u003c/p\u003e\n\u003cp\u003eIn the operational context of hydro-turbine environments, the acoustic vibration signal generated by the interaction of water flow with the turbine runner becomes entangled with significant levels of noise, incorporating hydraulic, electromagnetic, and mechanical vibrations\u0026nbsp;\u003csup\u003e33\u003c/sup\u003e. Directly using the raw data for fault identification will significantly impact the identification results, so it is necessary to de-noise the collected signals for pre-processing. The wavelet threshold (WT) algorithm was first proposed by Donoho in 1995\u0026nbsp;\u003csup\u003e34\u003c/sup\u003e. It has been widely used in noise reduction with its excellent discriminative ability and ability to adapt to time-varying signal processing\u0026nbsp;\u003csup\u003e35\u003c/sup\u003e. Central to the wavelet threshold denoising algorithm are pivotal threshold determination and quantization considerations. Traditional threshold functions primarily comprise the hard and soft threshold functions. Although the hard threshold function offers computational simplicity, it introduces discontinuities in the processed signal, thereby instigating signal reconstruction oscillations. Conversely, the soft threshold function preserves overall continuity\u0026nbsp;\u003csup\u003e36\u003c/sup\u003e. Nevertheless, in scenarios where the signal magnitude is substantial, the attenuating influence of the wavelet may precipitate a persistent deviation in the processed signal. Within the domain of wavelet threshold denoising, selecting an appropriate threshold function emerges as a critical consideration necessitating meticulous deliberation\u0026nbsp;\u003csup\u003e37\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBased on the above analysis, this paper proposes a hydro-turbine wear fault diagnosis method based on improved WT preprocessing combined with improved white shark optimization (IWSO) optimized CNN-LSTM. Improved WT denoising preprocessing is first performed on the collected data to enhance the accuracy of fault features extracted by the subsequent neural network. The amalgamation of CNN and LSTM neural network models yields the CNN-LSTM fault diagnosis model. Addressing challenges associated with low convergence accuracy and premature convergence in complex optimization problems, the WSO algorithm incorporates Tent chaotic mapping for population initialization while enhancing convergence speed and accuracy by integrating bird flocking search behavior and the cosine elite variation strategy. IWSO optimizes the constructed CNN-LSTM deep learning model to improve the fault diagnosis accuracy of CNN-SLTM. The effectiveness of the method proposed in this paper is verified by building a hydro-turbine fault experimental bench and collecting hydro-turbine fault signals from different working conditions for identification. In summary, the principal innovations of this study can be categorized as follows:\u003c/p\u003e\n\u003col start=\"12\"\u003e\n \u003cli\u003eDesign of hydro-turbine wear fault diagnosis model based on improved WT denoising combined with IWSO optimized CNN-LSTM;\u003c/li\u003e\n \u003cli\u003eAn improved WT denoising is proposed. To overcome the limitations associated with conventional threshold functions in the wavelet threshold algorithm, a novel threshold function is formulated;\u003c/li\u003e\n \u003cli\u003eAn improved white shark optimization algorithm is proposed. Use Tent chaotic mapping to initialize the population, introduce bird flock search behavior and cosine elite variation strategy to improve its convergence speed and accuracy;\u003c/li\u003e\n \u003cli\u003eDesigned and built a Fault experimental bench. Simulate the sand-containing working condition of hydro-turbine to verify the effectiveness of the method proposed in this paper;\u003c/li\u003e\n \u003cli\u003eThe frequency characteristics of sand-laden water flow through runner blades are analyzed from an acoustic vibration signal perspective.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThe rest of the discussion is as follows: Section 2 elaborates on the principle of the proposed method. Section 3 explains the WSO algorithm and its improvement method in detail. The experiments and data description are carried out in section 4. In section 5, the proposed method is verified and analyzed based on the experiments. Section 6 of this paper synthesizes the principal findings and offers insights into future research directions.\u0026nbsp;\u003c/p\u003e"},{"header":"Principles of the proposed method","content":"\u003cp\u003e \u003cb\u003eImproved wavelet threshold algorithm.\u003c/b\u003e Based on wavelet transform principles, the WT algorithm accurately extracts effective signals by leveraging significant differences between proper signals and noise signals in wavelet coefficients. This algorithm, with excellent performance, is widely used in many fields, especially in signal noise reduction and feature extraction.\u003c/p\u003e \u003cp\u003eThe core idea of the WT algorithm is the ability of wavelet transform to decompose a signal into wavelet coefficients at various frequencies and scales. Valuable and noisy signals usually behave significantly differently on these coefficients. By selecting a suitable threshold value, the wavelet thresholding algorithm can remove or reduce noise in the wavelet coefficients while preserving or enhancing the valuable signal component. It helps improve the signal quality, reduce noise interference, and make the signal easier to analyze and interpret effectively by subsequent processing methods. The WT algorithm has a relatively small amount of computation. It can quickly complete the processing, making it suitable for real-time or large-scale data processing tasks. Secondly, it is easy to implement as its principle is relatively simple and does not require a complex mathematical background.\u003c/p\u003e \u003cp\u003eThreshold processing encompasses two key components: threshold selection and threshold function selection. Commonly utilized thresholds include the \u003cem\u003eSqtwolog\u003c/em\u003e, \u003cem\u003eRigrsure\u003c/em\u003e, \u003cem\u003eHeursure\u003c/em\u003e, and \u003cem\u003eMinimaxi\u003c/em\u003e thresholds.\u003c/p\u003e \u003cp\u003e \u003cem\u003eSqtwolog\u003c/em\u003e threshold is used with a small computational effort, but if the signal-to-noise ratio of the signal is low, it will reduce its stability. \u003cem\u003eHeursure\u003c/em\u003e threshold is stable, but the computational effort is enormous and requires iterative computation. Minimaxi threshold has an excellent theoretical basis and stable performance, but the computational effort is enormous, and the noise denoising effect is average. The present investigation utilizes the unbiased risk estimation threshold, selected for its moderate computational demands relative to the alternative thresholds. Furthermore, this threshold is chosen to maximize the retention of valid signals characterized by small modal values.\u003c/p\u003e \u003cp\u003eAnother crucial aspect in the WT denoising pertains to the choice of the threshold function. The hard and soft threshold functions emerge as the predominant options.\u003c/p\u003e \u003cp\u003eThe expression of soft threshold function is:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\widehat{\\omega }}_{j,k}=\\left\\{\\begin{array}{c}{sgn(\\omega }_{j,k}\\left)\\right(\\left|{\\omega }_{j,k}\\right|-\\lambda ), \\left|{\\omega }_{j,k}\\right|\\ge \\lambda \\\\ 0, \\left|{\\omega }_{j,k}\\right|\u0026lt;\\lambda \\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe expression of hard threshold function is:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${\\widehat{\\omega }}_{j,k}=\\left\\{\\begin{array}{c}{\\omega }_{j,k}, \\left|{\\omega }_{j,k}\\right|\\ge \\lambda \\\\ 0, \\left|{\\omega }_{j,k}\\right|\u0026lt;\\lambda \\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe hard threshold function exhibits discontinuities at thresholds \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(-\\lambda\\)\u003c/span\u003e\u003c/span\u003e. Consequently, the wavelet inverse transform introduces a pseudo-Gibbs effect, resulting in local signal oscillations that adversely impact reconstruction quality. In contrast, the soft threshold function maintains continuity at thresholds \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(-\\lambda\\)\u003c/span\u003e\u003c/span\u003e. promoting smoother signal waveforms. However, when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|{\\omega }_{j,k}\\right|\\ge \\lambda\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{\\omega }}_{j,k}\\)\u003c/span\u003e\u003c/span\u003e consistently differs from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{j,k}\\)\u003c/span\u003e\u003c/span\u003e by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e. This creates an inherent bias between the reconstructed signal and the original signal, leading to distortion in the reconstructed signal.\u003c/p\u003e \u003cp\u003eWhile the conventional threshold function offers certain advantages, there are inevitable drawbacks that affect noise reduction. To address the limitations of both the soft and hard threshold functions in noise reduction, the study proposes a novel threshold function as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${\\widehat{\\omega }}_{j,k}=\\left\\{\\begin{array}{c}\\left(1-\\mu \\right){\\omega }_{j,k}+\\mu \\bullet {sgn(\\omega }_{j,k})\\left[\\left|{\\omega }_{j,k}\\right|-\\frac{\\mu \\lambda }{exp\\left(\\frac{\\left|{\\omega }_{j,k}\\right|}{{\\lambda }^{2}}\\right)}\\right], \\left|{\\omega }_{j,k}\\right|\\ge \\lambda \\\\ 0, \\left|{\\omega }_{j,k}\\right|\u0026lt;\\lambda \\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu =\\frac{\\lambda }{\\left|{\\omega }_{j,k}\\right|\\bullet \\text{e}\\text{x}\\text{p}(\\left|\\frac{{\\omega }_{j,k}}{\\lambda }\\right|-1)}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{j,k}\\)\u003c/span\u003e\u003c/span\u003eis the wavelet coefficient; \u003cem\u003esgn\u003c/em\u003e(*) is the sign function; and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e is the threshold value.\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) Continuity analysis\u003c/p\u003e \u003cp\u003eWhen \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{j,k}=\\lambda\\)\u003c/span\u003e\u003c/span\u003e, the left limit of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{\\omega }}_{j,k}\\)\u003c/span\u003e\u003c/span\u003e at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e is:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\underset{{\\omega }_{j,k\\to {\\lambda }^{-}}}{\\text{lim}}{\\omega }_{j,k}=\\underset{{\\omega }_{j,k\\to {\\lambda }^{-}}}{\\text{lim}}\\left(0\\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe right limit of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{\\omega }}_{j,k}\\)\u003c/span\u003e\u003c/span\u003e at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e is:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\underset{{\\omega }_{j,k\\to {\\lambda }^{+}}}{\\text{lim}}\\left(\\left(1-\\mu \\right){\\omega }_{j,k}+\\mu \\bullet {sgn(\\omega }_{j,k})\\left[\\left|{\\omega }_{j,k}\\right|-\\frac{\\mu \\lambda }{exp\\left(\\frac{\\left|{\\omega }_{j,k}\\right|}{{\\lambda }^{2}}\\right)}\\right]\\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhen \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|{\\omega }_{j,k}\\right|={\\lambda }\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu =1, {\\widehat{\\omega }}_{j,k}\\left({\\lambda }\\right)=0\\)\u003c/span\u003e\u003c/span\u003e. The improved threshold function is continuous.\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) Asymptote analysis\u003c/p\u003e \u003cp\u003eWhen \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|{\\omega }_{j,k}\\right|\\)\u003c/span\u003e\u003c/span\u003e increases, the constructor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{F}={\\widehat{\\omega }}_{j,k}-{\\omega }_{j,k}\\)\u003c/span\u003e\u003c/span\u003e, which collapses:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\text{F}=-\\frac{{{\\lambda }}^{2}}{{\\omega }_{j,k}\\bullet \\text{e}\\text{x}\\text{p}(\\frac{{\\omega }_{j,k}}{{\\lambda }}-1)\\left(\\frac{\\left|{\\omega }_{j,k}\\right|}{{\\lambda }^{2}}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAs \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{j,k}\\to \\infty\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{F}\\to 0\\)\u003c/span\u003e\u003c/span\u003e, indicating that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{\\omega }}_{j,k}\\)\u003c/span\u003e\u003c/span\u003e gradually converges to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{j,k}\\)\u003c/span\u003e\u003c/span\u003e as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{j,k}\\)\u003c/span\u003e\u003c/span\u003e increases. Replacing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{j,k}\\)\u003c/span\u003e\u003c/span\u003e by x and deriving \u003cem\u003eF(x)\u003c/em\u003e yields \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}^{{\\prime }}\\left(x\\right)\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, indicating that \u003cem\u003eF(x)\u003c/em\u003e is monotonically increasing. The improved function maintains continuity at the threshold \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e. As the parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e approaches 0 or 1, the improved threshold function gradually converges towards the conventional threshold function, eventually aligning with it.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates the curves of the new, hard, and soft threshold functions. The new threshold function offers two key advantages. It addresses the constant deviation issue found in the soft threshold function and mitigates the intermittency problem present in the hard threshold function.\u003c/p\u003e \u003cp\u003e \u003cb\u003eConvolutional Neural Network.\u003c/b\u003e A convolutional neural network (CNN) is a mathematical model that focuses on performing linear discrete convolutional operations. It has excellent feature learning capabilities and exhibits excellent robustness and fault tolerance. It maintains its performance even in the face of translation, scaling, and distortion transformations. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates a typical CNN architecture.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe CONV serves as the central component of CNN, executing convolutional operations on input data and forwarding the output to subsequent network layers. Within the CONV layer, a convolutional kernel functions as the receptive field, traversing the entire input set with a specified stride.\u003c/p\u003e \u003cp\u003eOften, activation functions are employed to extract the nonlinear features inherent in the output data to enhance the model's expressive power. Activation functions are categorized into saturated nonlinear functions and unsaturated nonlinear functions. Compared to saturated nonlinear functions, using unsaturated nonlinear functions helps overcome the challenges of gradient explosion and gradient vanishing and improves the convergence speed of the model. The Rectified Linear Unit (ReLU) is a widely adopted unsaturated nonlinear activation function in CNN models. Its advantages, such as rapid convergence and straightforward gradient computation, significantly contribute to its widespread adoption and appeal within the field.\u003c/p\u003e \u003cp\u003eIn order to facilitate the extraction of an adequate number of feature vectors, the output dimension of the convolutional layer is typically substantial. However, a diminutive dimensionality may engender overfitting challenges. Introducing a pooling layer into the model effectively reduces the number of parameters and helps mitigate overfitting while maintaining essential features of the output data. Standard pooling methods include average pooling and maximum pooling. The maximum pooling layer is good for preserving the main features, so this study uses it as a pooling method.\u003c/p\u003e \u003cp\u003eThe fully connected layer serves as the final classification module in the CNN model, responsible for applying nonlinear activation to the extracted features and generating the probability distribution for each class. In this layer, each neuron is connected to all neurons in the preceding layer, establishing a mapping relationship between input features and output categories through learning weights and biases. The output of the fully connected layer is subjected to an activation function, which yields the probability distribution of the classification outcomes. Consequently, the model can make precise classification predictions for input samples.\u003c/p\u003e \u003cp\u003e \u003cb\u003eLong Short-Term Memory.\u003c/b\u003e The comprehensive architecture of the LSTM network, delineated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, encompasses five principal constituents: the unit state, hidden state, input gate, forgetting gate, and output gate. Among the unique features of LSTM is the introduction of three gating structures: an input gate, an output gate, and a forget gate. The architectural incorporation of gating mechanisms within LSTM networks affords a heightened degree of control over information acceptance, retention, and dissemination. This characteristic renders LSTM networks particularly well-suited for addressing time series classification.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe state of the last moments can be retained in the state of the current LSTM unit, which is controlled through the forgetting gate. The forgetting gate serves as a mechanism to filter the memory content, thereby discerning which information warrants retention and which should be discarded. The LSTM can efficiently manage and update its internal state by calculating the forgetting gate. Its calculation is as follows:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$${\\varvec{f}}_{t}=\\sigma \\left({\\varvec{W}}_{xf}{\\varvec{x}}_{t}+{\\varvec{W}}_{hf}{\\varvec{h}}_{t-1}+{\\varvec{b}}_{f}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{xf}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the current input and the forgetting gate, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e denotes the chosen activation function, specifically the Sigmoid function with an output range of 0 to 1, utilized to signify the extent of the gate's openness, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{f}}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the output of the forgetting gate, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{h}}_{t-1}\\)\u003c/span\u003e\u003c/span\u003eis the output state at the last moment \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{x}}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the current input state, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{b}}_{f}\\)\u003c/span\u003e\u003c/span\u003e is the bias term of the forgetting gate, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{hf}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the historical output and the forgetting gate.\u003c/p\u003e \u003cp\u003eThe input gate updates the LSTM cell's state, determining whether new input information should be memorized. This gating structure generates an output value between 0 and 1 by passing the state of the previous time step and the current input information to an activation function. This output value is used to quantify how much information has been updated. Proximity of the output value to 0 suggests insignificance of the input information. In contrast, when the output value is close to 1, it indicates that the input information is essential.\u003c/p\u003e \u003cp\u003eSimultaneously, the tanh function processes the preceding state and current input data, compressing them into \u0026minus;\u0026thinsp;1 to 1 to produce the candidate cell state. Consequently, the LSTM's internal state can be updated, leveraging the input gate outputs and candidate cell states. This mechanism empowers the LSTM network to effectively regulate the acceptance and integration of new information, facilitating modeling and learning from sequential data. The output is then calculated based on this processed information:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${\\varvec{i}}_{t}=\\sigma \\left({\\varvec{W}}_{xi}{\\varvec{x}}_{t}+{\\varvec{W}}_{hi}{\\varvec{h}}_{t-1}+{\\varvec{b}}_{i}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{i}}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the input gate output,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{hi}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the historical output and the input gate, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{xi}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the input and the input gate, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{b}}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the bias term of the input gate.\u003c/p\u003e \u003cp\u003eThe candidate cell status is:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$${\\widehat{\\varvec{c}}}_{t}=\\text{t}\\text{a}\\text{n}\\text{h}({\\varvec{W}}_{xc}{\\varvec{x}}_{t}+{\\varvec{W}}_{hc}{\\varvec{h}}_{t-1}+{\\varvec{b}}_{c})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{xc}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the input and cell state, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{\\varvec{c}}}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the candidate cell state, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{b}}_{c}\\)\u003c/span\u003e\u003c/span\u003e represents the bias term of the cell state, wherein the application of the hyperbolic tangent (tanh) function facilitates scaling of the value, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{hc}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the historical output and cell state.\u003c/p\u003e \u003cp\u003eWith the outputs of the forgetting gate and the input gate, the current LSTM cell state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{C}}_{t}\\)\u003c/span\u003e\u003c/span\u003ecan be determined to consist of two parts. The forgetting gate multiplies the previous cell state to determine the retained information, allowing it to selectively control the forgetting of specific information from the previous state. Second, the output of the input gate is multiplied by the current candidate cell state, which determines the part of the information to be added. This way, the input gate can determine how much the newly input information affects the current state. The updated LSTM unit state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{C}}_{t}\\)\u003c/span\u003e\u003c/span\u003e is obtained by adding these two parts. In this way, the LSTM achieves selective memory and the addition of information through the gating mechanism. The cell state is expressed as:\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$${\\varvec{C}}_{t}={\\varvec{f}}_{t}{\\varvec{C}}_{t-1}+{\\varvec{i}}_{t}{\\widehat{\\varvec{c}}}_{t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe final output of the control unit status is located at the output gate. Multiply the current unit state information with the output of the output gate. Tanh function operation is performed on the result to get the output value of the unit. The expression for the output gate can be expressed as:\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$${\\varvec{o}}_{t}={\\sigma }({\\varvec{W}}_{xo}{\\varvec{x}}_{t}+{\\varvec{W}}_{ho}{\\varvec{h}}_{t-1}+{\\varvec{b}}_{o})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{ho}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the historical output and output gates, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{W}}_{xo}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix between the input and output gates, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{b}}_{o}\\)\u003c/span\u003e\u003c/span\u003e the bias term of the output gate.\u003c/p\u003e \u003cp\u003eThe expression for the unit status output is:\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$${\\varvec{h}}_{t}={\\varvec{o}}_{t}tanh\\left({\\varvec{C}}_{t}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003eWear fault diagnosis model of the CNN-LSTM.\u003c/b\u003e CNN and LSTM represent disparate feature extraction methodologies, each endowed with distinct characteristics. CNN is mainly used to capture spatially correlated features efficiently through convolutional kernels, which is suitable for processing image and spatial data. LSTM combines memory cells and gating mechanisms, mainly used to capture temporal correlation, which is suitable for processing time-series data, e.g., natural language text or sensor data. However, CNNs have some limitations in dealing with the temporal correlation of input variables. In contrast, LSTMs can learn and capture the dependencies between the previous and subsequent time steps in sequential data, leading to better temporal correlation feature processing.\u003c/p\u003e \u003cp\u003eThis study introduces a hybrid CNN-LSTM model for diagnosing hydro-turbine wear faults. This model integrates both CNN and LSTM architectures. This integration utilizes LSTM's strong temporal feature-capturing capability. It aims to compensate for the limitations of CNN when handling the temporal correlation of input variables. The proposed model can comprehensively analyze the input data through this combination strategy. Capturing both spatial and temporal correlation features enhances the reliability and accuracy of hydro-turbine fault diagnosis systems.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWithin the CNN-LSTM fault diagnosis model, CNN undertakes the task of extracting spatial features from input data and reducing its dimensionality. Conversely, LSTM reveals latent temporal features within the data, leveraging its inherent long-term memory property to enhance data classification processes. The comprehensive model is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Through a synergistic integration of CNN and LSTM; the model can effectively harness their respective strengths, thereby facilitating the diagnosis of hydro-turbine wear faults. The primary stages of the diagnostic procedure involve:\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) Acquire the acoustic vibration signals related to wear faults in hydro-turbines, categorize and segment the signals, and compile a standardized dataset of segmented data samples;\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) The processed dataset is fed into the CONV, and the fault features are dynamically extracted using a convolutional kernel;\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) After the CONV, the extracted features are maximally pooled in order to reduce the dimensionality of the feature set;\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) The feature data, after dimensionality reduction, will serve as the input for training the neural network within the LSTM layer, allowing for automatic learning of fault characteristics;\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e) Classification of features related to hydro-turbine faults using Softmax functions.\u003c/p\u003e \u003cp\u003eThe procedures above delineate the core methodology of CNN-LSTM modeling for fault diagnosis in hydro-turbines. Through comprehensive utilization of the strengths inherent in CNN and LSTM, alongside their complementary capacities for spatial and temporal feature extraction, acoustic vibration signals are subjected to feature extraction processes followed by fault classification.\u003c/p\u003e"},{"header":"Improved white shake optimizer","content":"\u003cp\u003e \u003cb\u003eWhite shake optimizer.\u003c/b\u003e The white shark is one of the world's most dangerous and powerful predatory sharks. In its natural environment, the white shark relies on its sensitive vision, hearing, smell, and electromagnetic field perception to sense subtle changes in the external environment and to receive and process a wide range of complex information. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the perception range of different sensory systems of the white shark. The white shark optimization algorithm is designed for three typical behaviors of white sharks: movement speed toward prey, movement toward the best prey, and fish school behavior \u003csup\u003e30\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) Movement speed toward prey\u003c/p\u003e \u003cp\u003eThe great white shark relies on its keen senses to track prey, detecting the prey's movements that create water ripples. It identifies the prey's location based on the sound of these ripples and approaches it in a wave-like manner, swimming at a speed of:\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$${v}_{k+1}^{i}=\\mu \\left[{v}_{k}^{i}+{p}_{1}\\left({w}_{g{best}_{k}}-{w}_{k}^{i}\\right)\\times {c}_{1}+{p}_{2}\\left({\\varvec{w}}_{best}^{{v}_{k}^{i}}-{w}_{k}^{i}\\right)\\times {c}_{2}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cem\u003ei\u003c/em\u003e is the white shark population, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i=1, 2,\\dots ..,n\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e is the contraction factor, which enhances the robustness of the algorithm, and the expression is as in Eq.\u0026nbsp;(\u003cspan refid=\"Equ15\" class=\"InternalRef\"\u003e15\u003c/span\u003e); \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({v}_{k}^{i}\\)\u003c/span\u003e\u003c/span\u003e is the speed of the \u003cem\u003ei\u003c/em\u003e-th white shark in the \u003cem\u003ek\u003c/em\u003e-th iteration; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{2}\\)\u003c/span\u003e\u003c/span\u003eare scaling parameters controlling \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{g{best}_{k}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{w}}_{best}^{{v}_{k}^{i}}\\)\u003c/span\u003e\u003c/span\u003e, defined by Eq.\u0026nbsp;(\u003cspan refid=\"Equ15\" class=\"InternalRef\"\u003e15\u003c/span\u003e) and Eq.\u0026nbsp;(\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e16\u003c/span\u003e), respectively; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{g{best}_{k}}\\)\u003c/span\u003e\u003c/span\u003e is the white shark in the \u003cem\u003ek\u003c/em\u003e-th iteration optimal position; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{k}^{i}\\)\u003c/span\u003e\u003c/span\u003e is the position of the \u003cem\u003ei\u003c/em\u003e-th white shark in the \u003cem\u003ek\u003c/em\u003e-th iteration; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({c}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({c}_{2}\\)\u003c/span\u003e\u003c/span\u003e are random numbers with values in the range of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left[\\text{0,1}\\right]\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{w}}_{best}^{{v}_{k}^{i}}\\)\u003c/span\u003e\u003c/span\u003e is the vector of the \u003cem\u003ei\u003c/em\u003e-th optimal position of the population; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({v}^{i}\\)\u003c/span\u003e\u003c/span\u003e is the vector of the ith index of the white shark in the optimal position as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ18\" class=\"InternalRef\"\u003e18\u003c/span\u003e).\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$\\mu =\\frac{2}{\\left|2-\\tau -\\sqrt{{\\tau }^{2}-4\\tau }\\right|}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$${p}_{1}={p}_{max}+\\left({p}_{max}-{p}_{min}\\right)\\times {e}^{{-\\left(4k/K\\right)}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ16\" name=\"EquationSource\"\u003e\n$${p}_{1}={p}_{min}+\\left({p}_{max}-{p}_{min}\\right)\\times {e}^{{-\\left(4k/K\\right)}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ17\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ17\" name=\"EquationSource\"\u003e\n$$v=\u0026lfloor;n\\times rand\\left(\\text{0,1}\\right)\u0026rfloor;+1$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e17\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn Eqs.\u0026nbsp;(\u003cspan refid=\"Equ14\" class=\"InternalRef\"\u003e14\u003c/span\u003e)-(\u003cspan refid=\"Equ17\" class=\"InternalRef\"\u003e17\u003c/span\u003e), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau\\)\u003c/span\u003e\u003c/span\u003e is the acceleration coefficient, which takes the value of 4.125; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{max}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{min}\\)\u003c/span\u003e\u003c/span\u003e are the maximum and initial velocities for white sharks to achieve good locomotion, respectively; \u003cem\u003ek\u003c/em\u003e and \u003cem\u003eK\u003c/em\u003e are the numbers of current iterations, and the maximum number of iterations, respectively; n is the population size of the white sharks; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(rand\\left(\\text{0,1}\\right)\\)\u003c/span\u003e\u003c/span\u003e denotes the n random numbers generated in the range of [0,1] that obey the uniform distribution.\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) Moving toward the best prey\u003c/p\u003e \u003cp\u003eThe white shark usually spends much time looking for potential prey, so its position is constantly changing. When a white shark hears waves produced by prey or smells prey during its search, it moves toward the prey's location. In some cases, the prey will move away from the original position. The white shark then tracks the prey again based on the scent it leaves behind or the waves it creates by swimming. In this case, the position update strategy of the white shark moving toward the prey is expressed as:\u003cdiv id=\"Equ18\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ18\" name=\"EquationSource\"\u003e\n$${w}_{k+1}^{i}=\\left\\{\\begin{array}{c}{w}_{k}^{i}\\bullet \\neg ⨁{\\varvec{w}}_{0}+u\\bullet a+l\\bullet b ;rand\u0026lt;mv\\\\ {w}_{k}^{i}+\\raisebox{1ex}{${v}_{k}^{i}$}\\!\\left/ \\!\\raisebox{-1ex}{$f$}\\right. ;rand\\ge mv\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e18\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{k+1}^{i}\\)\u003c/span\u003e\u003c/span\u003e is the new position of the ith white shark at the \u003cem\u003e(k+1)\u003c/em\u003e-th iteration; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\neg\\)\u003c/span\u003e\u003c/span\u003e is the inverse operator; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{w}}_{0}\\)\u003c/span\u003e\u003c/span\u003e is a logic vector, which is defined according to Eq.\u0026nbsp;(\u003cspan refid=\"Equ19\" class=\"InternalRef\"\u003e19\u003c/span\u003e); \u003cem\u003eu\u003c/em\u003e and \u003cem\u003el\u003c/em\u003e denote the upper and lower bounds of the search space, respectively; \u003cb\u003ea\u003c/b\u003e and \u003cb\u003eb\u003c/b\u003e are one-dimensional binary vectors, which are defined according to Eqs.\u0026nbsp;(\u003cspan refid=\"Equ20\" class=\"InternalRef\"\u003e20\u003c/span\u003e) and (\u003cspan refid=\"Equ21\" class=\"InternalRef\"\u003e21\u003c/span\u003e); \u003cem\u003ef\u003c/em\u003e denotes the frequency of fluctuating movement of white sharks, which is defined in Eq.\u0026nbsp;(\u003cspan refid=\"Equ21\" class=\"InternalRef\"\u003e21\u003c/span\u003e); rand denotes the random number generated in the range of [0,1] obeying the uniform distribution; \u003cem\u003emv\u003c/em\u003e denotes the sensory intensity of white sharks, which is increasing with increasing the number of iterations, which is defined in Eq.\u0026nbsp;(\u003cspan refid=\"Equ30\" class=\"InternalRef\"\u003e30\u003c/span\u003e).\u003cdiv id=\"Equ19\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ19\" name=\"EquationSource\"\u003e\n$${\\varvec{w}}_{0}=⨁(\\varvec{a},\\varvec{b})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e19\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(⨁\\)\u003c/span\u003e\u003c/span\u003e denotes the different-or operation.\u003cdiv id=\"Equ20\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ20\" name=\"EquationSource\"\u003e\n$$\\varvec{a}=sgn\\left({w}_{k}^{i}-u\\right)\u0026gt;0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e20\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ21\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ21\" name=\"EquationSource\"\u003e\n$$\\varvec{b}=sgn\\left({w}_{k}^{i}-l\\right)\u0026lt;0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e21\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cem\u003esgn\u003c/em\u003e denotes the symbolic operator; Eqs.\u0026nbsp;(\u003cspan refid=\"Equ19\" class=\"InternalRef\"\u003e19\u003c/span\u003e)-(\u003cspan refid=\"Equ21\" class=\"InternalRef\"\u003e21\u003c/span\u003e) are the steps of integrating the dimensions in that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{k}^{i}\\)\u003c/span\u003e\u003c/span\u003e are beyond the upper and lower boundaries into the upper and lower boundaries of the search space, which is crucial to help white sharks explore potential regions.\u003cdiv id=\"Equ22\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ22\" name=\"EquationSource\"\u003e\n$$f={f}_{min}+\\frac{{f}_{max}-{f}_{min}}{{f}_{max}+{f}_{min}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e22\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{max}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{min}\\)\u003c/span\u003e\u003c/span\u003e are the maximum and minimum frequencies of the white shark's fluctuating motions, respectively, and generally take the values of 0.75 and 0.07.\u003cdiv id=\"Equ23\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ23\" name=\"EquationSource\"\u003e\n$$mv=\\frac{1}{\\left({a}_{0}+{e}^{\\left(K/2-k\\right)/{a}_{1}}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e23\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{0}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{1}\\)\u003c/span\u003e\u003c/span\u003e are two constants that take values of 6.25 and 100, they are generally used to manage exploration and exploitation behavior.\u003c/p\u003e \u003cp\u003eWhen \u003cem\u003emv\u003c/em\u003e takes a smaller value, the WSO algorithm performs a smaller localized search in the vicinity of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{k+1}^{i}\\)\u003c/span\u003e\u003c/span\u003e. When mv takes a larger value, the WSO algorithm performs a larger search in the region away from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{k+1}^{i}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) fish school behavior\u003c/p\u003e \u003cp\u003eWhite sharks are highly social animals and cooperative when hunting, with the group moving towards the white shark closest to the prey. Eq.\u0026nbsp;(\u003cspan refid=\"Equ24\" class=\"InternalRef\"\u003e24\u003c/span\u003e) simulates the behavior of a group of white sharks moving toward the best white shark position:\u003cdiv id=\"Equ24\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ24\" name=\"EquationSource\"\u003e\n$${w}_{k+1}^{{\\prime }i}={w}_{g{best}_{k}}+{r}_{1}{\\overrightarrow{D}}_{w}sgn\\left({r}_{2}-0.5\\right) ; {r}_{3}\u0026lt;{S}_{s}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e24\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{k+1}^{{\\prime }i}\\)\u003c/span\u003e\u003c/span\u003e is the new position of the \u003cem\u003ei\u003c/em\u003e-th white shark iterated to the \u003cem\u003e(k+1)\u003c/em\u003e-th iteration relative to the prey position; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{2}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{3}\\)\u003c/span\u003e\u003c/span\u003e are random numbers in the range of [0,1], respectively; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(sgn\\left({r}_{2}-0.5\\right)\\)\u003c/span\u003e\u003c/span\u003e controls the direction and randomness of the localized search and is taken to be the same with the probability of 1 and \u0026minus;\u0026thinsp;1; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\overrightarrow{D}}_{w}\\)\u003c/span\u003e\u003c/span\u003e is the distance between the prey and white sharks distance, defined by Eq.\u0026nbsp;(\u003cspan refid=\"Equ25\" class=\"InternalRef\"\u003e25\u003c/span\u003e); \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({S}_{s}\\)\u003c/span\u003e\u003c/span\u003e denotes the olfactory and visual parameters when the white shark group locks on to the best positioned white shark defined by Eq.\u0026nbsp;(\u003cspan refid=\"Equ26\" class=\"InternalRef\"\u003e26\u003c/span\u003e).\u003cdiv id=\"Equ25\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ25\" name=\"EquationSource\"\u003e\n$${\\overrightarrow{D}}_{w}=\\left|rand\\times \\left({w}_{g{best}_{k}}-{w}_{k}^{i}\\right)\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e25\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ26\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ26\" name=\"EquationSource\"\u003e\n$${S}_{s}=\\left|1-{e}^{\\left(-{a}_{2}\\times k/K\\right)}\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e26\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{2}\\)\u003c/span\u003e\u003c/span\u003e is a constant that takes the value 0.0005.\u003c/p\u003e \u003cp\u003eSimulate the behavior of a white shark population. This simulation retains the optimal solution. The optimal solution accounts for the speed at which the white shark moves toward its prey and the specific prey it targets. Update the positions of other white sharks based on the optimal positions obtained:\u003cdiv id=\"Equ27\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ27\" name=\"EquationSource\"\u003e\n$${w}_{k+1}^{i}=\\frac{{w}_{k}^{i}+{w}_{k+1}^{{\\prime }i}}{2\\times rand}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e27\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003eImproved white shake optimizer\u003c/b\u003e. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) Initial population optimization\u003c/p\u003e \u003cp\u003eThe WSO algorithm excels in low-dimensional optimization problems. However, it needs to exhibit higher convergence accuracy in high-dimensional optimization problems. It is easy to fall into local extremes and converge prematurely. This paper proposes an improved WSO (IWSO) algorithm to improve the optimization-seeking speed and accuracy of the original algorithm.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eChaotic mapping algorithms are characterized by sensitivity to initial conditions and chaotic traversal. The chaotic optimization algorithm is evolved according to these characteristics. Chaotic optimization algorithms can filter out the local optimal solution and converge quickly during optimization. The WSO algorithm's initial population is generated randomly, which causes the initial solution to be unevenly distributed and lack diversity in the search domain. For this reason, this paper introduces a tent chaotic optimization algorithm to initialize the population and replace the selection process of random values to improve the convergence and local search ability of the WSO algorithm. The expression of tent chaotic mapping is shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ35\" class=\"InternalRef\"\u003e35\u003c/span\u003e), where the chaotic mapping of each particle follows the order depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003cdiv id=\"Equ28\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ28\" name=\"EquationSource\"\u003e\n$${x}_{k+1}=\\left\\{\\begin{array}{c}\\frac{{x}_{k}}{0.7},{x}_{k}\u0026lt;0.7 \\\\ \\frac{10}{3}\\left(1-{x}_{k}\\right), {x}_{k}\\ge 0.7\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e28\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) Velocity update optimization\u003c/p\u003e \u003cp\u003eIn the WSO algorithm, the velocity update of the white shark's movement toward the prey relies on an overall scaling by a contraction factor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e. The value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e depends on the acceleration coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau\\)\u003c/span\u003e\u003c/span\u003e. In practice,, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e is a constant, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu =0.70346\\)\u003c/span\u003e\u003c/span\u003e \u003csup\u003e30\u003c/sup\u003e. This result suggests that the scaling to the velocity is constant, which leads to inactivation of the white shark population. The WSO algorithm suffers from convergence stagnation during the global search. A bird-flock search strategy was introduced to optimize the scaling factor. The inertial weights of the flight speeds of the bird flocks are brought into Eq.\u0026nbsp;(\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e13\u003c/span\u003e):\u003cdiv id=\"Equ29\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ29\" name=\"EquationSource\"\u003e\n$${w}_{k+1}^{i}=\\left\\{\\begin{array}{c}B\\times \\text{cos}\\left(\\alpha \\right)\\bullet {w}_{g{best}_{k}} ;rand\u0026lt;em\\\\ {w}_{k}^{i}\\bullet \\neg ⨁{\\varvec{w}}_{0}+u\\bullet a+l\\bullet b ;rand\\ge em\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e29\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cem\u003eg\u003c/em\u003e is the inertia weight parameter, defined by Eq.\u0026nbsp;(\u003cspan refid=\"Equ30\" class=\"InternalRef\"\u003e30\u003c/span\u003e):\u003cdiv id=\"Equ30\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ30\" name=\"EquationSource\"\u003e\n$$g={g}_{max}-\\left[\\frac{\\left({g}_{max}-{g}_{min}\\right)}{K}\\right]\\bullet k$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e30\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({g}_{max}\\)\u003c/span\u003e\u003c/span\u003e is the upper bound of the inertia weights; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({g}_{min}\\)\u003c/span\u003e\u003c/span\u003e is the lower bound of the inertia weights; as the number of iterations increases, \u003cem\u003eg\u003c/em\u003e dynamically decreases, which facilitates probing again for the optimal solution among the ones already found.\u003c/p\u003e \u003cp\u003e(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) Elite White Shark Optimization\u003c/p\u003e \u003cp\u003eEach white shark group will have a white shark closest to the prey, called the elite white shark. Refining the search in the local space near it can enhance the probability of searching for the optimal solution and improve convergence accuracy. For this reason, the cosine variation strategy is introduced in the white shark moving toward the best prey stage. The periodic oscillation of the cosine function is utilized to drive the WSO algorithm to search in the local space near the elite white shark. As the search proceeds, it makes the elite white shark closer and closer to its prey. The expression of the process is as follows:\u003cdiv id=\"Equ31\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ31\" name=\"EquationSource\"\u003e\n$${w}_{k+1}^{i}=\\left\\{\\begin{array}{c}B\\times \\text{cos}\\left(\\alpha \\right)\\bullet {w}_{g{best}_{k}} ;rand\u0026lt;em\\\\ {w}_{k}^{i}\\bullet \\neg ⨁{\\varvec{w}}_{0}+u\\bullet a+l\\bullet b ;rand\\ge em\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e31\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cem\u003eB\u003c/em\u003e is the amplitude of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{cos}\\left(\\alpha \\right)\\)\u003c/span\u003e\u003c/span\u003e, which is calculated by Eq.\u0026nbsp;(\u003cspan refid=\"Equ31\" class=\"InternalRef\"\u003e31\u003c/span\u003e); \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha \\in \\left[\\text{0,2}\\pi \\right]\\)\u003c/span\u003e\u003c/span\u003e; and em denotes the cosine variance control parameter, it taken as 0.2.\u003cdiv id=\"Equ32\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ32\" name=\"EquationSource\"\u003e\n$$B={e}^{\\left(-\\gamma \\times \\left(k/K\\right)\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e32\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\gamma\\)\u003c/span\u003e\u003c/span\u003e is the shape control coefficient; as the number of iterations increases, the value of \u003cem\u003eB\u003c/em\u003e decreases.\u003c/p\u003e"},{"header":"Modeling architecture for wear fault in Hydro-turbines","content":"\n\u003ch3\u003eMaterials and methods\u003c/h3\u003e\n\u003cp\u003e \u003cb\u003eFault experimental bench\u003c/b\u003e. In this study, an experimental bench for hydro-turbine failure analysis was designed and constructed. The experimental bench, illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, consists of a pressure pump, hydroelectric generator unit, submersible pump, water tank, and corresponding pipe.\u003c/p\u003e \u003cp\u003eThe sensor captures signals of wear faults in the hydroelectric generator unit. The tank and return tank are first filled with water, then the pressure and submersible pumps are activated simultaneously. The pressure pump facilitates the transfer of water from the tank through a network of pipes that ultimately impinge on the rotor blades within the hydro-turbine. After passing through the hydro-turbine, the water flowed back to the tank, and the submersible pump pumped the water back to the tank to ensure water circulation. Throughout the experiment, sediment was added to the tank to simulate conditions in the natural environment.\u003c/p\u003e \u003cp\u003eAfter a period of operation of the failure test bed, when the signal amplitude region captured by the sensor stabilizes and no longer increases, it indicates that the water and sediments within the cycle have been adequately mixed. At this time, start recording signal data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e depicts the assembled fault experimental bench. The acoustic vibration signals of the three conditions of the hydro-turbine, normal working conditions, and sediment concentrations \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.73\\text{k}\\text{g}/{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(1.4\\text{k}\\text{g}/{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e were collected for processing and analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eData description.\u003c/b\u003e The signal acquisition apparatus incorporates the utilization of the noise sensor (CRY2301), which is characterized as a compact industrial-grade real-time spectrum analyzer featuring an advanced DSP processor. This device integrates essential components such as a microphone, preamplifier, and data acquisition card within a tightly arranged structure, ensuring precise and efficient data processing. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e provides an overview of the parameters associated with the noise sensor.\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\u003eParameters of the noise sensor\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpecification\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ekHz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStandard measuring range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25\u0026ndash;130\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003edBA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDynamic measuring range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ge 110\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003edBA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrequency measuring range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10-20000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecommunication interface\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUSB Audio\u0026thinsp;+\u0026thinsp;USB HID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSize\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\phi }25\\times 115\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003emm\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 collected acoustic vibration signals are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eData collected from each operational condition are structured and segmented, with each segment sample comprising 1024 data points. There are a total of 70 sample sets for each operational condition. The samples were randomly selected to divide the training and test sets to form the final data set, as shown in 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\u003eParameters of the noise sensor\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=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eWorking condition\u003c/p\u003e \u003cp\u003eof the hydro-turbine\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eSample size\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLabel\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTraining sets\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTest sets\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNormal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSand concentration of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.73\\text{k}\\text{g}/{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSand concentration of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(1.4\\text{k}\\text{g}/{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3\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\u003e \u003cb\u003eModeling architecture\u003c/b\u003e. In hydro-turbines' practical operational settings, the acoustic vibration signal arising from water flow impacting the runner is frequently marred by substantial noise contamination. Directly using the raw data for fault diagnosis will significantly impact the diagnosis results, so it is necessary to de-noise the collected signals first for pre-processing. This paper uses the improved WT algorithm to denoise the original signal, maximizing the signal characteristics of different working conditions to be retained.\u003c/p\u003e \u003cp\u003eThe IWSO algorithm is introduced and combined with the constructed CNN-LSTM fault diagnosis model, and the CNN-LSTM hydro-turbine fault diagnosis model is optimized through IWSO integration. The introduction of the IWSO algorithm can improve the convergence and convergence accuracy of the model and effectively solve the problem of hyperparameter adjustment inherent in deep learning models. The structure of the hydro-turbine wear fault diagnosis model based on improved WT denoising and IWSO-optimized CNN-LSTM is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Experimental validation and analysis","content":"\u003cp\u003e\u003cstrong\u003eData preprocessing\u003c/strong\u003e. The improved WT denoising is performed on three raw signals collected in 4.2.1. Since the raw signal data is vast, if the denoising results of all signals in the same working condition are shown, it will lead to a relatively close denoising effect graph. In order to show the denoising effect more intuitively, this section selects ten groups of data in each working condition as the result display.\u003c/p\u003e\n\u003cp\u003eThe db4 wavelet basis and a four-layer decomposition are selected to decompose the simulated signal. The threshold size of the wavelet coefficients is established through Stein\u0026apos;s unbiased estimation of the threshold function. Following this determination, the signals undergo processing utilizing soft, hard, and novel thresholding techniques. Subsequently, the wavelet coefficients are reconstructed post-thresholding operation. Figure\u0026nbsp;11 juxtaposes the signals processed employing soft, hard, and novel thresholding methods across three distinct operational conditions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 11.\u003c/strong\u003e Comparison of three threshold denoising\u003c/p\u003e\n\u003cp\u003eNoise-denoising operations using different threshold functions will result in producing different graphical results. All three different threshold functions effectively reduce the noise level of the original signal. Across the three distinct operating conditions, the resulting curve following the application of the hard threshold function exhibits roughness and contains a higher level of high-frequency noise. Conversely, the noise reduction curve produced by the soft threshold function appears comparatively smoother. However, in signal decomposition, part of the useful signal is misjudged as noise and filtered, thus leading to a certain degree of distortion. On the other hand, the noise reduction operation using the new threshold function can obtain a smoother noise reduction curve and maximize the retention of the useful signal, thus making the noise-denoising signal closer to the original signal.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;12 illustrates the signal spectra processed using soft threshold, hard threshold, and new threshold for three operating conditions. All three thresholding methods successfully removed some of the high-frequency noise components. However, it should be noted that the signal processed by the soft threshold function shows significant distortion in the low-frequency band, which indicates that the method misjudges a part of the useful signal as noise and rejects it in the denoising process. On the contrary, the signal processed by the hard threshold function showed more burrs in the high-frequency band, meaning its denoising effect is relatively poor. However, after the noise reduction by the new threshold function, the spectrum exhibits higher smoothness in the high-frequency band and better preservation of the useful signal. Hence, the new threshold function performs well in maintaining signal integrity.\u003c/p\u003e\n\u003cp\u003eTo assess the denoising effectiveness further, the outcomes were evaluated utilizing the root mean square error (RMSE) and signal-to-noise ratio (SNR), expressed as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ33\"\u003e\n \u003cdiv id=\"FileID_Equ33\" name=\"EquationSource\"\u003e$$RMSE=\\sqrt{\\frac{1}{n}\\sum _{i=1}^{n}{\\left[f\\left(n\\right)-\\widehat{f}\\left(n\\right)\\right]}^{2}}$$\u003c/div\u003e\n \u003cdiv\u003e33\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ34\"\u003e\n \u003cdiv id=\"FileID_Equ34\" name=\"EquationSource\"\u003e$$SNR=10{\\text{log}}_{10}\\left\\{\\frac{\\frac{1}{n}\\sum _{i=1}^{n}{f}^{2}\\left(n\\right)}{\\frac{1}{n}\\sum _{i=1}^{n}{\\left[f\\left(n\\right)-\\widehat{f}\\left(n\\right)\\right]}^{2}}\\right\\}$$\u003c/div\u003e\n \u003cdiv\u003e34\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn the above, \u003cem\u003en\u003c/em\u003e is the signal length; \u003cspan\u003e\u003cspan\u003e\\(f\\left(n\\right)\\)\u003c/span\u003e\u003c/span\u003e is the noise-containing signal; and \u003cspan\u003e\u003cspan\u003e\\(\\widehat{f}\\left(n\\right)\\)\u003c/span\u003e\u003c/span\u003e is the noise-canceled signal.\u003c/p\u003e\n\u003cp\u003eA smaller RMSE value indicates a more effective noise-canceling effect, while a more considerable SNR value also signifies improved noise cancellation. Following processing, the RMSE and SNR for various working conditions are illustrated in Fig.\u0026nbsp;13. Notably, the new threshold function exhibits the highest SNR and the lowest RMSE. It indicates that the noise reduction effect of the new threshold function exceeds the performance of the traditional threshold function.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eIWSO-based optimized CNN-LSTM model for hydro-turbine wear fault diagnosis\u003c/strong\u003e. The hyperparameters of the CNN-LSTM model are first optimized. The IWSO and WSO algorithms are used to operate this optimization process. Their convergence iteration process curves are shown in Fig. \u003cspan\u003e14\u003c/span\u003e. With the continuous updating of speed and position, the population evolves, and the value of the fitness function of the optimal individual decreases. After 50 iterations of computation, the IWSO algorithm can complete convergence in less than ten iterations. The unoptimized WSO algorithm, on the other hand, needs about 13 iterations to complete convergence, which is more than the IWSO algorithm. Moreover, the WSO algorithm falls into local optimality. The figure shows that the IWSO algorithm can have higher efficiency and more accurate calculation results.\u003c/p\u003e\n\u003cp\u003eIn summary, the IWSO algorithm offers an effective and dependable approach for hyperparameter selection in CNN-LSTM models, mitigating issues such as time loss and model instability that may arise from manual hyperparameter adjustments. The output of the optimal combination of hyperparameters is feature_num=[27,93], LayerSizes\u0026thinsp;=\u0026thinsp;47, Stride\u0026thinsp;=\u0026thinsp;2.\u003c/p\u003e\n\u003cp\u003eThe IWSO-optimized CNN-LSTM model was employed for fault diagnosis across three operational conditions. To underscore the efficacy of the proposed approach delineated in this study, CNN, LSTM, and CNN-LSTM models were chosen as comparison benchmarks. An additional dataset without undergoing wavelet threshold denoising is included for diagnostic purposes in the IWSO-CNN-LSTM model. Figure\u0026nbsp;15 illustrates the training curves for the five distinct methods.\u003c/p\u003e\n\u003cp\u003eThe accuracy and function loss rate curves of the five models CNN, LSTM, CNN-LSTM, IWSO-CNN-LSTM, and the proposed method are shown in Fig.\u0026nbsp;15. The accuracy of all five models can reach more than 65%. Notably, the LSTM model has the lowest accuracy of 68.7%. The curve fluctuates more in the model, and the smoothness is poor. Upon incorporating the LSTM model, the CNN-LSTM model achieves an accuracy of 83.7%. It shows that adding LSTM overcomes CNN\u0026apos;s limitations in handling long sequences and enhances the model\u0026apos;s stability and accuracy. The accuracy of the IWSO-CNN-LSTM model is 89.1%, which exceeds the CNN, LSTM, and CNN-LSTM models. By denoising the raw data with the improved WT algorithm, the IWSO-CNN-LSTM model achieves a diagnostic accuracy of 97.2%, 8.1% better than the un-denoised model. This result illustrates the importance of data denoising preprocessing to improve the diagnostic accuracy of the model.\u003c/p\u003e\n\u003cp\u003eAs shown in Fig.\u0026nbsp;15(b), the function loss rate of the WT-IWSO-CNN-LSTM model is 0.38, which is lower than the other four models, thereby substantiating its superior performance. The proposed method distinguishes itself with exceptional fault diagnosis capabilities. The model demonstrates enhanced accuracy and stability by integrating the distinctive features inherent in CNN and LSTM architectures, leveraging the IWSO algorithm to determine optimal hyperparameter configurations.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;16 presents a comparative analysis of the five models\u0026apos; actual and diagnostic recognition outcomes. The proposed methodology demonstrates the most congruence between diagnostic outcomes and actual results, thus affirming its superior accuracy and reliability in diagnosing wear faults. Further, from the confusion matrices of the five model training, the diagnostic accuracy of the models for condition 3 is all the better than the diagnostic accuracy of condition 2.\u003c/p\u003e\n\u003cp\u003eIn order to evaluate the diagnostic results of the test set more comprehensively, this paper introduces Accuracy, Precision, Recall, and F1-score as the evaluation indexes of the fault diagnostic results. Each evaluation index is expressed as:\u003c/p\u003e\n\u003cdiv id=\"Equ35\"\u003e\n \u003cdiv id=\"FileID_Equ35\" name=\"EquationSource\"\u003e$$\\left\\{\\begin{array}{c}Accuracy=\\frac{TP+TN}{TP+FP+TN+FN}\\\\ Precsion=\\frac{TP}{TP+FP}\\\\ Recall=\\frac{TP}{TP+TN}\\\\ F1score=\\frac{\\left(1+{\\beta }^{2}\\right)TP}{\\left(1+{\\beta }^{2}\\right)TP+FP+FN}\\end{array}\\right.$$\u003c/div\u003e\n \u003cdiv\u003e35\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eTrue positive (TP) signifies the count of signals accurately identified as normal conditions. True negative (TN) signifies the count of signals correctly identified as faults. False negative (FN) indicates the count of signals erroneously classified as normal conditions. False positive (FP) denotes the count of signals inaccurately classified as faults.\u003c/p\u003e\n\u003cp\u003eThe test sets of the three working conditions are brought into the trained model for diagnosis. The evaluation metrics of the diagnostic results are shown in Fig. \u003cspan\u003e17\u003c/span\u003e. The results indicate that the proposed method model achieves the highest evaluation score among the recognition outcomes of the five models. The LSTM model exhibits the lowest evaluation score. Conversely, the recognition outcomes of the proposed method model outperform those of the other four models across all four evaluation metrics. Compared to the other four methods, the proposed model demonstrates superior performance and enhanced stability, enabling more comprehensive recognition and diagnosis of hydro-turbine wear fault signals.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;18 illustrates the fault diagnosis performance of the five models on the test dataset. Notably, all five models exhibit commendable accuracy levels for Case 1 and Case 3. However, the LSTM model demonstrates a notably lower accuracy of 65.3% and needs to improve in diagnosing condition 2. Conversely, the CNN model achieves an accuracy of 77.8%, significantly higher than that of the LSTM model. The CNN-LSTM model attains an accuracy of 84.2%. Upon employing the White Shark Optimization (WSO) algorithm to optimize the CNN-LSTM model, the accuracy of the resulting IWSO-CNN-LSTM model improves to 87.3%, representing a notable enhancement in diagnostic accuracy across all three operating conditions. Particularly noteworthy is the superior performance of the proposed method, which achieves an accuracy of 96.2% and attains 100% accuracy in diagnosing both working condition 1 and working condition 3. This outcome serves to validate the exceptional performance of the proposed method.\u003c/p\u003e\n\u003cp\u003eSimilar to the training set results, in the test set, the diagnostic accuracies of the five models for condition 3 are higher than that of condition 2, which indicates that the accuracy of hydro-turbine wear fault diagnosis increases with the increase of sediment concentration in the water. This phenomenon is caused by increased sediment concentration, which substantially impacts the hydro-turbine runner more. Consequently, the amplitude of the collected fault signals undergoes a notable increase, thereby rendering the fault characteristics more conspicuous and enhancing diagnostic accuracy effectively.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis paper proposes a hydro-turbine wear fault diagnosis method based on improved WT preprocessing combined with IWSO-based optimized CNN-LSTM. The new threshold function is first constructed, and the traditional wavelet threshold algorithm is improved. The improved wavelet threshold algorithm is utilized to denoise the acquired signals' preprocessing. This step enhances the accuracy of the neural network for feature extraction. In response to the limitations encountered by the CNN model in managing lengthy sequence complexities, the CNN-LSTM model is formulated, integrating the LSTM model to address the shortcomings inherent in the CNN algorithm concerning capturing temporal correlations. Due to the excessive number of nodes in the CNN-LSTM model, there is the problem of hyperparameter tuning, and the IWSO is introduced for hyperparameter tuning. For the problem that the WSO algorithm quickly falls into local optimum and premature convergence, tent chaotic mapping is used to initialize the population, and bird flock search behavior and cosine elite variation strategy are introduced to improve its convergence speed and accuracy.\u003c/p\u003e \u003cp\u003eAccording to the training outcomes, the proposed method surpasses the CNN, LSTM, CNN-LSTM, and IWSO-CNN-LSTM models regarding accuracy and function loss rate, achieving 97.2% and 0.38, respectively. Furthermore, it exhibits the most excellent concordance between diagnostic outcomes and actual results. In the test findings, the proposed approach attains an accuracy of 96.2%, surpassing that of CNN, LSTM, and CNN-LSTM models. Compared to the IWSO-CNN-LSTM model, the proposed methodology demonstrates an improvement in accuracy by 8.9%. Notably, the diagnostic accuracy of hydro-turbine wear faults has escalated with escalating sediment concentration. Diagnosing wear faults in hydro-turbines improves efficiency and power generation quality, reduces maintenance costs, and minimizes resource consumption. This study is valuable to the extant hydro-turbine condition monitoring and fault diagnosis systems.\u003c/p\u003e \u003cp\u003eHydro-turbines have different structures and collect different fault signals. At the same time, the characteristics of different river sediments, such as grain size gradation, hardness, and sediment composition during the flooding period, are complicated. Therefore, it is more valuable to carry out targeted research and analysis in the next step for engineering application.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCredit author contribution statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFang Dao\u003c/strong\u003e: Methodology, Software, Writing - Original Draft, Writing - Editing. \u003cstrong\u003eYun Zeng\u003c/strong\u003e: Conceptualization, Supervision, Funding acquisition. \u003cstrong\u003eYidong Zou\u003c/strong\u003e: Conceptualization\u003cstrong\u003e,\u0026nbsp;\u003c/strong\u003eValidation.\u003cstrong\u003e\u0026nbsp;Jing Qian\u003c/strong\u003e: Investigation, Resources.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of competing interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is supported by grants from the National Natural Science Foundation of China (52079059) and the National Natural Science Foundation of China (No: 52269020). \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eTariq, G.\u003cem\u003e et al.\u003c/em\u003e Influence of green technology, green energy consumption, energy efficiency, trade, economic development and FDI on climate change in South Asia. \u003cem\u003eSCIENTIFIC REPORTS\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, doi:10.1038/s41598-022-20432-z (2022).\u003c/li\u003e\n\u003cli\u003eSayed, E. 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Gear fault diagnosis based on a new wavelet adaptive threshold de-noising method. \u003cem\u003eIndustrial Lubrication and Tribology\u003c/em\u003e \u003cstrong\u003e71\u003c/strong\u003e, 40-47 (2019).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3975472/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3975472/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Diagnosing hydro-turbine wear fault is crucial for the safe and stable operation of hydropower units. A hydro-turbine wear fault diagnosis method based on improved WT (wavelet threshold algorithm) preprocessing combined with IWSO (improved white shark optimizer) optimized CNN-LSTM (convolutional neural network-long-short term memory) is proposed. The improved WT algorithm is utilized for denoising the preprocessing of the original signals. The CNN-LSTM hydro-turbine wear fault diagnosis model is constructed. Aiming at the problem that the WSO algorithm quickly falls into local optimum and premature convergence, tent chaotic mapping is used to initialize the population and birds flock search behavior. The cosine elite variation strategy is introduced to improve convergence speed and accuracy. Hyperparameter tuning of CNN-LSTM model based on IWSO algorithm. The experimental results show that the accuracy of the proposed method reaches 96.2%, which is 8.9% higher than that of the IWSO-CNN-LSTM model without denoising. The study also found that the diagnostic accuracy of hydro-turbine wear faults increased with increasing sediment concentration in the water. This study can supplement the existing hydro-turbine condition monitoring and fault diagnosis system. Meanwhile, diagnosing wear faults in hydro-turbines can improve power generation efficiency and quality and minimize resource consumption.","manuscriptTitle":"Wear fault diagnosis in hydro-turbine via the incorporation of the IWSO algorithm optimized CNN-LSTM neural network","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-11 11:06:28","doi":"10.21203/rs.3.rs-3975472/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-25T12:33:46+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-01T06:09:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"142137511410044943039199003909189816894","date":"2024-06-26T12:34:46+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-06T13:49:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"88d5ca22-3d5f-4d3b-beeb-6196b5411a73","date":"2024-04-26T15:44:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"0da3c0fd-556a-4095-92ba-624096016e8b","date":"2024-04-26T11:00:46+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-04-26T10:26:40+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-25T06:08:38+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-03-07T14:12:05+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-07T14:02:30+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-02-21T12:35:28+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6a18ef0c-3d69-420b-88b6-00aacd0866ad","owner":[],"postedDate":"March 11th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-10-28T16:04:40+00:00","versionOfRecord":{"articleIdentity":"rs-3975472","link":"https://doi.org/10.1038/s41598-024-77251-7","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-10-25 15:58:05","publishedOnDateReadable":"October 25th, 2024"},"versionCreatedAt":"2024-03-11 11:06:28","video":"","vorDoi":"10.1038/s41598-024-77251-7","vorDoiUrl":"https://doi.org/10.1038/s41598-024-77251-7","workflowStages":[]},"version":"v1","identity":"rs-3975472","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3975472","identity":"rs-3975472","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}