A Hydraulic Turbine Fault Diagnosis Method Based on Synchrosqueezed Wavelet Transform and SE-ResNet

Abstract

To tackle the challenges associated with conventional methods of diagnosing hydraulic turbine faults, which depend heavily on expert knowledge and exhibit low efficiency and precision, a model for detecting hydraulic turbine faults has been developed that integrates the synchrosqueezed wavelet transform (SWT) with SE-ResNet. Initially, a 1D non-stationary vibration signal is converted into a high-frequency time–frequency representation in two dimensions using SWT, which then acts as the input for the convolutional neural network. Secondly, a model based on SE-ResNet is designed, incorporating an attention mechanism that enhances the extraction of features from two-dimensional images, thereby increasing the emphasis on crucial features and bolstering the model’s representation capabilities. Finally, results related to fault detection are produced via the softmax layer. To evaluate the proposed model’s efficiency, two datasets were utilized for the experiments conducted, one sourced from Case Western Reserve University and the other from hydraulic turbine vibration signals. Compared to conventional approaches, this technique demonstrates significant practicality and effective convergence characteristics, offering considerable value in real-world applications.

1. Introduction

As a rotating machine, the hydraulic turbine is the core equipment in the energy conversion process of hydropower stations. Due to the coupling effects of hydraulic, mechanical, electrical, and other interference factors, the monitoring signals of hydropower units exhibit obvious nonlinear and non-stationary characteristics, and there is a complex mapping relationship between faults and symptoms [1,2]. Traditional methods are no longer able to meet the current demand for accurate analysis of unit operation status. Therefore, researching new state analysis theories and methods has important engineering application value for improving the accuracy of unit fault diagnosis and trend prediction, and ensuring stable operation of units.

Fault detection in rotating machines has evolved through three primary phases: classical signal processing techniques, machine learning approaches, and deep learning methodologies [3]. Traditional signal analysis involves transforming the acquired signals into a time–frequency domain, employing techniques such as wavelet transforms, empirical mode decomposition (EMD), and variational mode decomposition (VMD) for examination. For instance, EMD was utilized by Lu et al. in their study to isolate and refine the vibration signal waveform, leading to the extraction of approximation coefficients for various fault signals [4]. An enhanced version of the parameter-adaptive VMD was introduced by Miao et al., which was utilized for diagnosing both individual mechanical faults and multiple fault scenarios [5]. Cui et al. integrated the VMD technique with maximum correlation kurtosis deconvolution (MCKD) to analyze weak fault signals for identifying fault frequencies, which facilitated the diagnosis of rolling element failures in bearings [6]. Conventional techniques for fault diagnosis often necessitate human monitoring and assessment, relying heavily on essential prior knowledge and the expertise of specialists. These methods often lack a solid theoretical and technical basis, making it challenging to achieve accurate diagnostics, which significantly hinders their application in real-world scenarios.

The process of machine learning is typically divided into four key phases, starting with the analysis of signals, extracting characteristics of the reduction in feature dimensions, and the identification of faults [7,8,9]. Over the past few years, with the swift advancement of machine learning techniques and smart optimization methods, a variety of advanced classification techniques have been utilized for diagnosing mechanical faults, leading to notable achievements [10,11]. Among the currently favored methods for intelligent fault diagnosis are support vector machines (SVMs), random forest, extreme learning machines, and artificial neural networks [12,13,14]. For instance, Shan et al. introduced a novel approach that integrates improved variational mode decomposition (IVMD) with a hybrid artificial sheep algorithm (HASA) to optimize support vector machines (SVM) for diagnosing faults in rotating machinery [15]. Tian et al. developed a method known as multi-domain entropy random forest (MDERF) aimed at diagnosing inter-shaft bearing faults [16]. Similarly, Wang et al. formulated a fault diagnosis methodology that incorporates an enhanced bat algorithm to fine-tune extreme learning machines (ELM) [17]. In the domain of machine learning, the majority of implementations still depend on expert feature identification and manual encoding tailored to specific domains and data types. Among the frequently employed techniques in machine learning, SVM is well suited for datasets with a limited number of samples; however, its effectiveness diminishes when faced with large datasets and complex fault categorization tasks. Certain models, including feedforward neural networks and extreme learning machines, demonstrate adaptive and nonlinear capabilities that allow for them to handle large datasets effectively. Nevertheless, their approach to parameter fine-tuning, which relies on empirical risk minimization, often results in challenges related to local optima and issues with convergence. Decision trees in ensemble learning are effective for analyzing data that are both high-dimensional and unbalanced, and the nodes generated during training can serve as valuable insights. Nonetheless, they are significantly influenced by the presence of noisy data, which may result in overfitting issues [18,19].

As computing technologies have advanced, deep learning has gradually received attention from researchers [20,21,22]. Models such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have found extensive use within the realm of artificial intelligence. Although this area is considered a subset of machine learning, in contrast to conventional machine learning techniques, advanced neural network architectures in deep learning exhibit enhanced capabilities for feature extraction across various dimensions [23,24,25,26]. These methods are capable of automatically obtaining features across multiple levels, as well as multidimensional and complex patterns from large datasets, and their capacity is enhanced to accommodate various data contexts. The integration of deep learning techniques in fault diagnosis makes some limitations become apparent. For instance, as the complexity of the model increases with additional layers and parameters, successfully training a sizable deep learning network from inception necessitates a substantial quantity of data, computing power, and time. Acquiring an extensive dataset for fault diagnosis poses considerable challenges. To address these limitations in deep learning, approaches utilizing transfer learning techniques have been employed in the area of diagnosing mechanical faults. This can involve either a single source domain or a combination of multiple source domains for the transfer learning process. the effectiveness of model transfer training tends to be enhanced when it occurs under identical working conditions. Nevertheless, when adapting to alternative working conditions, particularly in cases where there is an absence of training examples for varying operational environments, the outcome of the training will be far from ideal.

To overcome the above limitations, a novel technique for diagnosing hydraulic turbine faults is introduced, which utilizes an enhanced residual neural network based on an attention mechanism. This approach is characterized by several key features:

(a)

The technique synchrosqueezed wavelet transform (SWT) enables the conversion of one-dimensional signals into their corresponding representations within the time–frequency realm. Unlike the commonly used continuous wavelet transform (CWT), the synchrosqueezed wavelet transform provides enhanced precision in time–frequency analysis, which significantly contributes to a deeper insight and investigation of signal behaviors.

(b)

Utilizing transfer learning approaches, residual neural networks facilitate the direct application of samples across various operational scenarios within two-dimensional time–frequency domain imagery. In other words, the model undergoes training focused on specific operational scenarios before being evaluated in different conditions. In contrast to conventional methods that involve partitioning datasets based on varying operational environments into separate training and testing sets, the network introduced in this research exhibits enhanced adaptability.

(c)

The optimization of residual neural networks has been enhanced by incorporating squeeze and excitation networks (SENet), which are based on attention mechanisms.

The latter portion of the document is organized in the following manner: In the subsequent section, a succinct overview of the pertinent knowledge base is provided; Section 3 presents an in-depth discussion of the proposed method’s framework; Section 4 covers the validation, practical implementation, and comparative evaluation of the proposed technique; in Section 5, an overview of the research findings is presented.

2. Theoretical Background

2.1. Synchrosqueezed Wavelet Transform

Synchrosqueezed wavelet transform, introduced by Daubechies et al. in 2011 [27], serves as a method for analyzing signals in the time–frequency domain. This technique proves beneficial for the examination of signals comprising multiple oscillatory elements, such as those found in speech patterns, mechanical vibrations, and biological signals. Numerous real-life signals exhibiting oscillatory behavior can also be described as combinations of components that are both amplitude- and frequency-modulated. A comprehensive representation for these categories of signals that consist of composite elements is

$$f\left(t\right)={\displaystyle \sum _{i=1}^N{f}_i\left(t\right)}={\displaystyle \sum _{i=1}^N{A}_i\left(t\right)}\cos \left(2\pi {\varphi }_i\left(t\right)\right)$$

(1)

where A_i(t) represents the gradual change in amplitude and ϕ_i(t) denotes the phase at a given moment.

The approach of wavelet transformation can be viewed as a method within the realm of time–frequency analysis, where the energy from a signal is reallocated among various frequency ranges. This modification tackles the scattering effects associated with the initial wavelet employed. Unlike other techniques for reallocating time–frequency components, synchrosqueezing predominantly aims at reallocating energy strictly within the frequency dimension, thus preserving the signal’s time attributes. The reversed application of synchrosqueezing allows for an accurate rebuild of the original signal while preserving its temporal characteristics. In synchrosqueezing applications, it is crucial to classify each component of the combined signal as a function of intrinsic mode type (IMT).

The SWT algorithm can be divided into these main steps:

(a) Select an analytical wavelet ψ(t). In the context of synchrosqueezing, utilizing a complex-valued wavelet for the continuous wavelet transform (CWT) is essential for effectively capturing the information regarding instantaneous frequency.

(b) To acquire the continuous wavelet transform (CWT) of the given input signal f(t), utilize the wavelet:

$$W_{\psi }f(s,u)={\int }_R{e}^{2\pi i\omega u}\hspace{0.17em}\widehat{f}(\omega )\overline{\hspace{0.17em}\widehat{\psi }(s\omega )}\hspace{0.17em}d\omega$$

(2)

The variables s and u denote the scale and translation parameters, respectively.

(c) Utilize a phase transform to obtain the instantaneous frequencies from the output of the continuous wavelet transform (CWT), denoted as ω_f. This phase transformation is directly related to the first-order derivative of the CWT concerning the variable u:

$${\omega }_f\left(s,u\right)=-i{\left[2\pi W_{\psi }f\left(s,u\right)\right]}^{-1}{\displaystyle \frac{\partial }{\partial u}}{W}_{\psi }f\left(s,u\right)$$

(3)

The scales are defined as s = ω₀/ω, where ω₀ is the peak frequency of the wavelet and ω is the frequency.

(d) The process involves ‘squeezing’ the continuous wavelet transform (CWT) in areas where the phase transformation remains unchanged. The instantaneous frequency value obtained is then assigned to a singular point located at the centroid of the CWT’s time–frequency area. This method of reassignment leads to a more refined output from the synchrosqueezed transformation than what is achieved with the CWT.

2.2. Residual Network

With an increase in the depth of a neural network, the challenge of effectively training it escalates, and this can result in a plateauing of training accuracy and, ultimately, a decline in network performance. To address this challenge, a structure known as a residual network (ResNet) was introduced by He et al. [28]. An efficient connection technique is employed to layer multiple residual components, facilitating identity mapping within the network’s architecture.

The architecture of the residual block emphasizes the principle of mapping residuals rather than adhering to the direct mappings typically observed in the multiple layers stacked within a network. Assuming the original input is x and the ideal mapping fitted by multiple stacked network layers is H (x), the mapping fitted by the residual network is F (x) := H (x) − x. The original operation may be represented as F (x) + x. The difference of normal block and residual block is shown in Figure 1.

This rephrasing arises from the unexpected issues related to the degradation phenomenon. Should the additional layers be designed to function as identity mappings, a model with greater depth ought to exhibit a training error that is equal to or less than that of its shallower equivalent. The issue of degradation indicates that the methods may struggle to replicate identity mappings through several nonlinear layers. Through the reformulation involving residual learning, in scenarios where identity mappings prove to be preferable, the solvers could effectively adjust the weights of various nonlinear layers towards zero to attain those mappings.

In practical situations, it is not very probable that identity mappings represent the best option; however, the proposed reformulation could assist in setting a better foundation for tackling the problem. When the ideal function resembles an identity mapping more than it does a zero mapping, it may facilitate the solver’s ability to identify adjustments by referring to the identity mapping, rather than requiring the function to be understood from scratch. Within the residual structure, the flow of data can be enhanced through connections between layers. This method offers a considerable reduction in the difficulties related to mapping, while also enhancing the speed at which the model converges.

3. The Proposed Approach

3.1. SENet

The concept of the attention mechanism draws inspiration from the way humans focus their attention to perceive their surroundings, with the goal of identifying more significant information while disregarding less relevant data. Various deep learning challenges, such as generating images, classifying them, semantic segmentation, and responding to visual inquiries, extensively utilize the attention mechanism. The swift progress in attention mechanisms can be primarily linked to two factors: first, they represent one of the most innovative and efficient approaches for addressing multi-classification challenges in recent years, leading to a significant enhancement in the accuracy of the foundational models; moreover, by emphasizing certain features, attention mechanisms contribute to a deeper comprehension of learning tasks, thereby enhancing model interpretability for researchers. Consequently, the SENet attention module is utilized in this study to improve the performance of the ResNet architecture.

The concept of SENet was introduced by Hu et al. in the 2017 ImageNet competition [29], with its architecture illustrated in Figure 2. Unlike traditional CNN approaches, this method improves upon earlier feature extraction by implementing a dual process termed squeeze and excitation. The first stage is the squeeze operation, which reduces the dimensionality of the features across the spatial axes by transforming each 2D feature channel into a singular real-valued number. This enables layers closer to the input to gain a broad understanding. The algorithm can be defined by the following equation:

$$F_{sq}(x_i)={\displaystyle \frac{1}{h\times w}}{\displaystyle \sum _a^h{\displaystyle \sum _b^w{x}_i(a,b)}}$$

(4)

where x_i is the i-th feature map with size h × w.

Following that is the mechanism of excitation, which is primarily comprises two dense layers alongside two activation functions. The formula is

$$y_i=F_{ex}[F_{sq}\left(x_i\right),\omega ]=\sigma \left.\left\{{\omega }_2\delta \left[{\omega }_1{F}_{sq}\left(x_i\right)\right]\right.\right\}$$

(5)

where σ denotes the rectified linear unit (ReLU) activation function; δ denotes the sigmoid activation function; ω₁ denotes the first fully connected layer; ω₂ denotes the second fully connected layer; F_sq (x_i) is the output value after the exception operation.

The rectified linear unit function refers to the slope function in mathematics, that is [30]:

$$f(x)=\max (0,x)$$

(6)

3.2. The Architecture of SE-ResNet18

Currently, deep learning stands out as a prominent subject, with deeper networks exhibiting superior feature extraction capabilities compared to their shallower counterparts. As a result, numerous researchers have turned to deep neural networks for effective fault diagnosis. This study focuses on enhancing diagnostic precision by utilizing ResNet18 as the foundational architecture and integrating SENet to create an advanced diagnostic framework. The configuration of the model is illustrated in Figure 3, while its specifications can be found in

Table 1. ResNet model detailed parameters.

Layer Name	Output Size	18-Layer
Conv1	112 × 112	7 × 7, 64
Residual Block1	56 × 56	3 × 3 max pool $\left[\begin{array}{c}3\times 3,\hspace{0.33em}64\\ 3\times 3,\hspace{0.33em}64\end{array}\right]\times 2$
Residual Block2	28 × 28	$\left[\begin{array}{c}3\times 3,\hspace{0.33em}128\\ 3\times 3,\hspace{0.33em}128\end{array}\right]\times 2$
Residual Block3	14 × 14	$\left[\begin{array}{c}3\times 3,\hspace{0.33em}256\\ 3\times 3,\hspace{0.33em}256\end{array}\right]\times 2$
Residual Block4	7 × 7	$\left[\begin{array}{c}3\times 3,\hspace{0.33em}512\\ 3\times 3,\hspace{0.33em}512\end{array}\right]\times 2$
	1 × 1	average pool, fc, softmax
FLOPs		1.8 × 109
Total learnables		11,260,810

.

3.3. The Procedure of the Proposed Method

The key phases associated with this method are described below:

(a)

Acquire vibration data from sensors located at the drive end, capturing both normal and defective signals across various operational scenarios.

(b)

Vibration signals are segmented into several sample signals, and these samples are utilized to create time–frequency domain images using a synchrosqueezed wavelet transform, resulting in the formation of an image dataset. The gathered dataset undergoes normalization and is then split into training and testing subsets in a specified ratio.

(c)

The SE-ResNet18 model receives the training dataset, and the cross-entropy loss corresponding to the diagnostic output of the network is calculated following each iteration. The parameters of the network are optimized using the Adam algorithm until reaching the specified maximum iterations.

(d)

The trained SE ResNet18 model is utilized to evaluate the samples from the test set and effectively identify the various states.

4. Experimental Verification

This research employs two separate datasets to illustrate the efficacy of the suggested approach for diagnosing faults. The configuration of the experimental setup comprises a MECHREVO (Beijing, China) laptop with AMD R9-7945HX CPU, a GeForce GTX 4070 GPU, and 32 GB of memory.

4.1. Experiment Analysis with the CWRU Dataset

4.1.1. Experimental Setup

The rolling elements in the dataset provided by CWRU originate from SKF, specifically featuring models 6205 and 6203, which were specifically designed for the evaluation of fault diagnosis techniques [31]. This research focused on employing defective data originating from the bearing at the drive end, collected at a frequency of 12 kHz, as shown in Figure 4; data on vibrations were collected from rolling bearings subjected to four different operating conditions, with each scenario being characterized by power levels of 0, 1, 2, or 3 horsepower (hp), with corresponding rotational speeds of 1797, 1772, 1750, and 1730 rpm. Each fault diagnosis encompasses three distinct diameters (0.007, 0.014, and 0.021 inch) of the inner race fault, issues with rolling components, alongside the issue pertaining to the outer race located at the bottom position. A corresponding diagram is provided in Figure 5.

After calculation, it is necessary to ensure that a sample contains all the information within one cycle of bearing rotation, and there must be at least 400 sampling points in a sample. In this experiment, a sample contains 2048 sampling points, with 80 samples for each fault type. Therefore, the data size is 80 × 2048 = 163,840, and the total number of samples at each speed is 10 × 80 = 800, as shown in

Table 2. Details of the CWRU dataset.

Fault Type	Fault Size/Inch	Data Description	Rotating Speed/rpm	Label
Normal		4 × 80	1797/1772/1750/1730	1
Ball	0.007	4 × 80		2
	0.014	4 × 80		3
	0.021	4 × 80		4
Inner ring	0.007	4 × 80		5
	0.014	4 × 80		6
	0.021	4 × 80		7
Outer ring	0.007	4 × 80		8
	0.014	4 × 80		9
	0.021	4 × 80		10

.

4.1.2. Experiment Results and Discussion

Experiments on transfer learning utilizing the CWRU dataset were carried out to provide further validation of the findings. The results highlighting the effectiveness of transfer learning are illustrated in Figure 6 and

Table 3. Comparison of accuracy of different methods.

Task	1	2	3	4	5	6	7	8	9	10	11	12
	0→1	0→2	0→3	1→0	1→2	1→3	2→0	2→1	2→3	3→0	3→1	3→2
SE-ResNet18	98.38	97	88.62	97.5	99	92.26	94.37	98.5	97.5	86.25	94.75	97.5
ResNet18	94.5	88.5	76.4	95.5	98.75	89.39	93.13	97	90.39	77.62	96.25	96.12
AlexNet	97.25	97.88	80.65	97.5	97.5	85.14	92.25	94.75	87.27	91.5	88.38	97.5
VGG16	92.37	95.5	67.17	87.5	99	71.79	79.75	88.12	82	66.37	77.38	90

, where the notation 0→1 implies that the data from the 0 hp payload serve as the source domain while the 1 hp payload data act as the target domain. The findings revealed that SE-ResNet18 achieved superior accuracy across the majority of tasks, on the other hand, AlexNet excelled in tasks 0→2 and 3→0. Furthermore, the larger the variation in operational environments, the effectiveness of transfer learning diminishes. For instance, the accuracy rate of transfer learning for the 0-1 task stands at 98.38%; the performance of the 0-3 task falls below 90%, accounting for 88.62%.

The Friedman test was conducted for statistical significance testing. It is a rank-based test that assumes that the mean ranking of all samples is equal [32]. Specifically, different algorithms are first ranked on each dataset, and then the mean ranking of each algorithm on all datasets is calculated. If all algorithms have no performance difference, their average ranking of performance should be equal, so that we can choose a specific confidence interval to determine whether the difference is significant. The result of the Friedman test is p = 2.7883905124644845 × 10⁻⁵ < 0.05, which means there is significant difference between the four algorithms. The Nemenyi test was then performed for further analysis. As shown in

Table 4. The results of Nemenyi test.

p	SE-ResNet18	ResNet18	AlexNet	VGG16
SE-ResNet18	1	0.036176	0.044941	0.000008
ResNet18	0.036176	1	0.999823	0.142184
AlexNet	0.044941	0.999823	1	0.119495
VGG16	0.000008	0.142184	0.119495	1

, the results demonstrate that there are significant differences between the proposed model and every other models.

The influence of the proximity between the source and target domains on transfer learning outcomes is clearly demonstrated in Table 3. It suggests that domains positioned closer to each other yield superior performance in transfer learning and enhanced accuracy levels. Additionally, tasks related to 3 hp exhibit comparatively lower accuracy metrics. For instance, the transfer rate for the 0-2 task stands at 97%, whereas the 1-3 task achieves an accuracy of 92.26%.

Task 1/4, Task 2/5, and Tasks 3 and 6 represent two comparative experimental cohorts sharing identical inter-domain distances. The findings indicate that utilizing the 0 hp condition for transfer training from the initial dataset to the 1/2/3 hp settings leads to effective outcomes. there are 0/1/3 labels with an accuracy below 90, and when the source and target domains are exchanged, there are 1/2/3 labels with an accuracy below 90, as shown in Figure 7. The greatest inaccuracies are associated with experiments that involve three distinct working conditions for the horsepower. It can be inferred that a decrease in load correlates with an increase in the precision of transfer learning, indicating that a greater number of characteristics have been effectively conveyed.

4.2. Experiment Analysis with Hydraulic Turbine Vibration Signals

4.2.1. Experimental Setup

This section uses the cavitation erosion failure of a hydraulic turbine as a typical case to verify the practicality of the proposed method. Cavitation and cavitation erosion are common faults in the flow-passing components of hydropower units, which directly lead to a degradation in unit performance and reductions in runner blade life, while causing severe unit vibration and noise [33]. The cavitation process of the turbine usually covers the entire process of bubble accumulation, flow, splitting, and collapse. Cavitation erosion is the direct consequence of cavitation, which generally occurs on solid boundaries and often results in material damage on the surface of flow-passing components [34].

This experiment selected Unit 2 of a hydropower plant as the analysis object, and cavitation signals were collected through acoustic emission sensors installed on the guide vane connecting rod, top cover X and Y directions, and draft tube gate. The frequency response range of the sensors was 50 kHz to 400 kHz, and the sampling frequency was 1 MHz. Figure 8 shows the scenario of collecting cavitation signals on site using sensors installed at the guide vane connecting rod. The experimental data include signals collected under normal operating conditions of the turbine, as well as cavitation signals collected under three operating conditions: 0 load, 30% opening of guide vanes, and full load. Detailed information is shown in

Table 5. Detailed information on cavitation signal of hydraulic turbine.

Type		Sample Dimension	Number of Samples	Label
Normal		1024	25	A
Cavitation	0 load condition	1024	25	B
	30% opening of guide vanes condition	1024	25	C
	Full load condition	1024	25	D

. The time domain waveforms of signals under different operating conditions are show in Figure 9.

4.2.2. Experiment Results and Discussion

Initially, the experimental platform’s vibration data are segmented into samples of 1024 points each, and the time–frequency domain representations are generated by applying the synchrosqueezed wavelet transform to these time series data. Figure 10 displays the images generated through synchrosqueezed wavelet transformation and continuous wavelet transformation for various fault conditions and normal states across different speeds. This comparison illustrates that the SWT images, in contrast to the CWT images, significantly minimize the presence of unnecessary energy in the time–frequency spectrum, thereby mitigating issues such as frequency crossover and aliasing. This results in enhanced frequency line clarity, effectively emphasizing fault information more distinctly.

Following the application of synchrosqueezed wavelet transformation, each speed level is associated with a total of 100 image samples. A random distribution is employed to partition the data into training and testing sets, utilizing a 7:3 ratio, and the model for diagnosing faults is developed and evaluated. Figure 11 illustrates the confusion matrices, indicating a high level of accuracy in the evaluation results.

In order to validate the effectiveness of the suggested approach, a series of comparative experiments was performed. The SWT approach was utilized by SWT-SE-ResNet18, SWT-ResNet18, SWT-VGG16, and SWT-AlexNet for transforming one-dimensional raw signals into two-dimensional representations, whereas the CWT-SE-ResNet18 technique employed CWT for processing the raw data to generate images in the time–frequency domain. Furthermore, the VGG16 network was adopted by SWT-VGG16 as its feature extraction component, which employs a 3 × 3 kernel consistently across all layers. The transition from large convolutional filters to a series of 3 × 3 filters not only diminishes the number of parameters but also enhances the capacity to learn. The SWT variant of AlexNet incorporates the original AlexNet architecture for feature extraction, notably enhancing its performance by integrating a dropout layer that mitigates the risk of overfitting.

The results of the comparative experiments illustrated in Figure 12 and

Table 6. Comparison of different methods.

Method	SWT-SE-ResNet18	SWT-ResNet18	SWT-VGG16	SWT-AlexNet	CWT-SE-ResNet18
Accuracy/%	100	96.43	67.86	92.86	92.86
Time/s	126	100	480	108	125

revealed that SWT-SE-ResNet18 excelled in classification tasks across samples at varying speeds with slightly more time consumption, whereas SWT-VGG16 exhibited the least effective performance with a lot of time consumption. The performance metrics reveal that SWT-SE-ResNet18 surpasses both SWT-ResNet18 and CWT-SE-ResNet18 in terms of precision, suggesting that the integration of the SE module enhances the accuracy of the ResNet18 model slightly, while SWT also outperforms CWT in testing accuracy. Figure 13 shows the convergence behavior of the proposed method. It can be seen that the proposed method converges quickly.

5. Conclusions

This paper introduces a novel method for diagnosing hydraulic turbine failures that integrates the synchrosqueezed wavelet transform (SWT) with a deep residual neural network. The main conclusions are as follows:

(a)

The vibration signal undergoes preprocessing, transforming the original one-dimensional data into a detailed two-dimensional time–frequency representation via synchrosqueezed wavelet transform. This process minimizes the impact of extraneous information, allowing for more pronounced fault frequencies and clearer distinctions between them.

(b)

An attention mechanism was integrated to develop the SE-ResNet18 model, enhancing the overall effectiveness of the network architecture. Analysis of various datasets reveals that employing the SWT technique results in superior diagnostic efficacy compared to the CWT approach.

(c)

The integration of the SE module significantly enhances the performance of the ResNet framework. The implemented model demonstrates effective diagnostic capabilities in identifying hydraulic turbine faults, showing superior accuracy compared to alternative techniques, and offers significant practical implications, thereby opening up new avenues for industrial fault diagnosis applications.

Nonetheless, insufficient labeled fault data continue to pose a significant challenge in diagnosing failures under varying operational conditions within practical engineering settings. Moreover, experiments indicated that the effectiveness of transfer learning was not up to expectations when there were considerable variations in operational conditions. Consequently, to enhance the precision of diagnosing faults under varying operating conditions, additional investigation should concentrate on addressing this challenge.