Fault Diagnosis of Pumped Storage Units—A Novel Data-Model Hybrid-Driven Strategy

Abstract

Pumped storage units serve as a crucial support for power systems to adapt to large-scale and high-proportion renewable energy sources by providing a stable and flexible energy supply. However, due to the coupling effects of electric power load demands and the complex multi-source factors within the water–mechanical–electrical system, the interrelationship between unit parameters becomes more intricate, posing significant threats to the operational reliability and health status of the units. The complexity of fault diagnosis is further aggravated by the intricate and varied nature of fault characteristics, as well as the challenges in signal extraction under conditions of strong electromagnetic interference and high noise levels. To address these issues, this paper proposes a novel data-model hybrid-driven strategy that analyzes vibration signals to achieve rapid and accurate fault diagnosis of the units. Firstly, the spectral kurtosis theory is employed to enhance the traditional empirical mode decomposition, achieving optimal decomposition and noise reduction effects for vibration signals. Secondly, the intrinsic mode functions (IMFs) obtained from the decomposition are reconstructed, and the entropy values of effective IMFs are calculated as fault feature vectors. Subsequently, the CNN-LSTM model is utilized for fault diagnosis. The effectiveness and feasibility of the proposed method are verified through actual operational data from pumped storage units in a specific region. Through analysis, the fault diagnosis accuracy of the method proposed in this paper can be maintained above 95%, demonstrating robustness in complex engineering environments and effectively ensuring the safe and stable operation of pumped storage units.

1. Introduction

Pumped storage power stations play crucial roles in power grids, including peak shaving and valley filling, emergency backup, frequency regulation, and phase modulation. These stations are characterized by rapid startup, flexible and reliable operation, and the ability to respond quickly to sudden changes in load. In addition to peak shaving and valley filling, they are also suitable for tasks such as frequency regulation, phase modulation, and emergency backup, playing a significant role in ensuring the safe and stable operation of power grids and accommodating new energy sources. In 2016, China’s installed hydropower capacity reached 332.07 million kilowatts, accounting for 20.12% of the country’s total installed capacity [1]. With the rapid development of new energy sources such as nuclear power, wind power, and solar power in China, pumped storage, as a mature large-scale energy storage technology, is also gaining increasing attention. As the total installed capacity of pumped storage power stations continues to increase, they become even more important for ensuring the safety and stability of power grids [2].

However, during the operation of pumped storage units, different components interact with each other, and hydraulic, mechanical, and electrical factors are coupled, making the operation process of pumped storage units highly nonlinear, non-stationary, and time varying, which makes it difficult to accurately model them [3,4]. At the same time, due to the complex operating conditions of hydraulic turbines and large variations in water heads, the causes of failures involve multiple uncertain factors, leading to an incomplete understanding of the failure mechanisms of pumped storage units and an inability to accurately describe the fault evolution process. According to statistics, the vibration signals of units can reflect more than 80% of fault characteristics, and different fault types will produce vibrations with different frequencies, amplitudes, and phases in different components of the units [5]. Therefore, how to effectively utilize the vibration signals of units and extract key features that can represent the operating state of the units is currently a research hotspot that focuses on fault diagnosis of pumped storage units.

Currently, the fault diagnosis framework for pumped storage units can be broadly categorized into three interconnected stages: signal processing, feature extraction, and fault classification. In signal processing, the intricate vibration patterns and intensities exhibited by mechanical equipment under diverse operating conditions are mirrored through time-domain statistical attributes of the vibration signals. To address the challenge of extracting subtle fault signatures from planetary gears, the literature [6] innovatively applies maximum kurtosis coupled with deconvolution theory, leveraging the maximum correlated kurtosis deconvolution technique to successfully isolate and enhance weak fault features, yielding promising experimental outcomes. The literature [7] introduces an enhanced energy entropy approach for fault feature extraction, which amplifies differences in energy entropy to bolster the accuracy of bearing fault diagnoses. Meanwhile, the literature [8] proposes a novel multivariate multi-scale fuzzy distribution entropy by refining the coarseness of multi-scale fuzzy distribution entropy, integrating it as a feature vector into a support vector machine for comprehensive classification and identification of diverse bearing, gear, and compound fault signals, achieving remarkable fault diagnosis results. The literature [9] presents an intelligent fault diagnosis methodology that seamlessly fuses vibration data, non-vibration data, and data from vibration monitoring systems, enabling precise localization of typical faults in wind turbine units. The literature [10], on the other hand, combines complementary ensemble adaptive local iterative filtering enhancement with maximum correlated kurtosis deconvolution, dissecting fault signals into intrinsic mode components and subsequently enhancing them to extract periodic impact features, effectively diagnosing wind turbine faults amidst strong noise environments. The literature [11] offers a unique method combining noise subtraction with edge-enhanced squared envelope spectrum analysis. It constructs a time-domain denoised signal in the frequency domain, integrates it into rapid spectral correlation processing, and employs an edge band selection criterion to pinpoint optimal spectral frequencies, excelling at detecting bearing fault characteristic frequencies under high noise conditions. Lastly, the literature [12] develops a data description methodology grounded in cyclic spectrum analysis and semi-supervised support vector machines for bearing fault detection. This approach represents fault information as a bivariate mapping in the frequency domain, feeds the enhanced envelope spectrum of fault signals into a machine learning algorithm, and derives the unit’s health index, offering robust performance in fault warning and degradation detection.

Traditional fault diagnosis methods primarily rely on manual experience and regular equipment inspections, but these methods are inefficient and often fail to detect potential faults. In recent years, various neural network algorithms, such as Probabilistic Neural Networks [13] and Convolutional Neural Networks [14], have gradually been applied to fault diagnosis in various types of machinery. By collecting operational data from machinery units, utilizing intelligent algorithms to process and analyze the data, extracting fault features, and inputting the fault information into a feature classifier, fault diagnosis of machinery units is achieved [15]. The literature [16] utilizes multi-scale entropy combined with an extreme learning machine to realize rapid classification of machinery unit faults. Similarly, the literature [17] extracts characteristic information of machinery unit faults through variational mode decomposition combined with complexity analysis for the classification of fault types. The literature [18] extracts the first three eigenmode functions as characteristic signals through EMD decomposition, calculates energy entropy as input samples for SVM model training, and verifies the method’s high reliability and diagnostic accuracy on a rotor test bench fault vibration dataset. The literature [19] applies intelligent optimization algorithms to SVM parameter selection, combines time–frequency characteristics of vibration patterns, obtains highly sensitive and stable fault features, and improves the accuracy of rolling bearing fault diagnosis. The literature [20] addresses the assessment of the operating health status of high-speed railway motor unit axle boxes by collecting temperature data from various components of the axle box bearings, using SVM to discern the current operating status of the unit after feature dimension reduction, effectively enhancing classification accuracy compared to traditional methods. The literature [21] extracts vibration signal features of pumped storage units in different states, utilizes SVM and neural network classifiers for fault diagnosis of dimension-reduced features, and verifies through examples that multi-dimensional feature input and fused classifier fault diagnosis exhibit higher accuracy. The literature [22] focuses on the issue of local demagnetization faults in permanent magnet synchronous linear motors, analyzes the air gap magnetic flux density distribution characteristics of permanent magnets in local demagnetization modes, integrates magnetic flux density distribution intensities from multiple locations as fault characteristic parameters, and uses neural networks for fault classification, and the experimental results indicate that the accuracy of fault identification exceeds 99%. The literature [23] introduces a stacked denoising autoencoder to achieve data-driven health status recognition of rotating machinery, and examples demonstrate that this method maintains high recognition accuracy even under strong noise interference. The literature [24] targets the operating data of faulty rolling bearings under low loads, uses discrete Fourier transforms and Hilbert transforms to obtain signal features, and inputs them into a neural network to accurately identify bearing fault types under different loads. The literature [25] designs a wavelet neural network model for transformer fault diagnosis and accelerates neural network training speed by combining intelligent optimization algorithms, and the results indicate that the proposed model can effectively fit the nonlinear characteristics of transformer fault symptoms. These methods theoretically enable accurate diagnosis of faults in pumped storage units, but they still face challenges and limitations in practical applications, such as the accuracy and completeness of data collection, which may be interfered with by various factors, as well as inadequate generalization of algorithm models that cannot handle different types and scales of unit faults, leading to low diagnostic accuracy. Despite the achievements made in the current research, several challenges persist.

• Difficulty in effectively identifying early fault characteristics [26]. The condition monitoring of inter-turn short-circuit faults in the windings of pumped storage motors is susceptible to the influence of dynamic/static eccentricities and armature reactions, rendering early fault characteristics inconspicuous and difficult to identify and diagnose effectively.
• Reliance on human experience and a low intelligence level. The current fault diagnosis methods for pumped storage motors primarily rely on on-site diagnosis based on human experience [27,28]. As the complexity of the units increases, it becomes exceedingly challenging to solely rely on specialized technicians to analyze and process the vast amounts of data obtained from the monitoring systems. This approach is not only inefficient but also prone to human factors, leading to inaccurate and untimely diagnostic results.
• Inefficient and unreliable fault diagnosis models. Existing fault diagnosis models often suffer from issues, such as insufficient accuracy and poor generalization capabilities, when dealing with complex faults in pumped storage units involving multiple coupled factors. This results in insufficient guarantees for the accuracy and reliability of fault diagnosis in practical applications [29].

To address the aforementioned issues, this paper introduces a novel data-model hybrid-driven strategy that analyzes vibration signals to achieve rapid and accurate fault diagnosis of the units. The key innovative points are summarized as follows:

(1) This paper comprehensively utilizes both data analysis and model-driven approaches to tackle the complex coupling relationship issues arising from the coupling of power load demands and complex hydro–mechanical–electrical multi-source factors in pumped storage power units.

(2) The traditional EMD is improved in this paper by incorporating spectral kurtosis theory to achieve optimal decomposition and noise reduction effects for vibration signals. The obtained IMFs are reconstructed, and the entropy values of effective IMFs are calculated as fault feature vectors. Finally, an MCNN-LSTM model is employed for fault diagnosis.

2. Basic Introduction to Empirical Mode Decomposition

2.1. The Principle of Empirical Mode Decomposition

Empirical mode decomposition (EMD) is a signal processing method that is suitable for both linear and stationary signals, as well as nonlinear and non-stationary signals. It has been applied in many fields. EMD is a signal decomposition method applicable to the analysis of non-stationary time signals, also known as the Hilbert–Huang Transform. This method is not constrained by the Fourier transform theory. EMD is the core of the Hilbert–Huang Transform, and the essence of the algorithm is a finite-stage filtering process. The essence of EMD is to identify all intrinsic oscillatory modes contained in the signal through characteristic time scales. In this process, the definition of characteristic time scales and intrinsic mode functions (IMFs) possesses a certain empirical and approximate nature. Compared with other signal processing methods, the EMD method is intuitive, indirect, a posteriori, and adaptive. The characteristic time scales used in its decomposition originate from the original signal. EMD is based on the following conditions:

Condition 1: The data must have at least two extrema: one maximum and one minimum.

Condition 2: The local time-domain characteristics of the data are uniquely determined by the time scales between extrema.

Condition 3: If the data have no extrema but have inflection points, extrema can be obtained by differentiating the data once or multiple times, and then the decomposition results can be obtained through integration. The essence of this method is to obtain the intrinsic oscillatory modes through the characteristic time scales of the data and then decompose the data. This decomposition process can be vividly described as a “sifting” process.

2.2. EMD Implementation Steps

The specific decomposition method of EMD is as follows:

(1) Identify all local maxima and minima points of X(t). Use cubic spline interpolation to connect all local maxima points to form the upper envelope $u_0(t)$, and similarly, connect all local minima points to form the lower envelope $l_0(t)$. Here, X(t) represents the current sequence to be decomposed, where t = 0, 1, ..., T.

(2) Calculate the mean of the upper and lower envelopes $m_0(t)$ according to Formula (1) and then subtract this mean $m_0(t)$ from the sequence X(t) to be decomposed according to Formula (2) to obtain the component $h_1(t)$.

$$m_0(t)={\displaystyle \frac{u_0(t)+l_0(t)}{2}}$$

(1)

$$h_1(t)=X(t)-m_0(t)$$

(2)

(3) Judge whether $h_1(t)$ satisfies the conditions of an IMF. If it does, then $h_1(t)$ is the first IMF; otherwise, apply the same processing to $h_1(t)$ as performed to X(t) according to Formula (3). Perform the same judgment and processing on the newly obtained component $h_2(t)$, repeating this until the component $h_k(t)$ satisfies the IMF conditions or reaches the stopping criterion. The stopping criterion is shown in Formula (4) as follows:

$$h_2(t)=h_1(t)-m_0(t)$$

(3)

$$SD={\displaystyle \sum _{t=0}^T\frac{{\left|h_{k-1}(t)-h_k(t)\right|}^2}{h_{k-1}^2(t)}}$$

(4)

When the SD is less than a specific value, the stopping criterion is reached. The specific value is generally selected within the range of [0.2, 0.3]. At this point, the first IMF component, imf₁, is obtained.

The determination of an IMF component needs to satisfy two conditions.

① Within the entire sequence, the number of extrema and the number of zero crossings are the same, or the difference between them does not exceed one.

② At any moment, the average value of the upper and lower envelopes at the extrema points is zero.

(4) Treat the remaining component $r_1(t)=X(t)-im{f}_1$ as the new sequence to be decomposed and repeat the above steps until the component $im{f}_n$ or the remaining component $r_n$ is less than a predetermined value or the remaining component cannot be further decomposed. At this point, Formula (5) holds the following:

$$X(t)={\displaystyle \sum _{k=1}^{n}im{f}_k+r_n}$$

(5)

At this point, the decomposition of the original sequence X(t) is complete. The initial stock logarithmic return sequence X(t) is iteratively decomposed into n mutually orthogonal IMFs and a trend term r_n. The frequency of the IMF components decreases as k increases, meaning that the IMF components decomposed first represent the high-frequency and high-noise parts of the original sequence. The remaining component reflects the trend of the original sequence and is known as the trend term.

2.3. Improved Strategy Based on Spectral Kurtosis Theory

The EMD method can decompose complex signals into a series of sums of IMFs and then reconstruct the IMF components with obvious fault impacts into the signal to be processed. By further envelope demodulation and short-time Fourier transform, fault features can be extracted. The disadvantages of this method are as follows:

1. Potential for over-decomposition. Pseudo-components are often generated in the series of IMF components produced, which can interfere with the extraction of normal characteristic frequencies and must be removed.

2. IMF component synthesis criteria. The selection of IMF components to synthesize the signal to be processed affects the final diagnostic accuracy. If an unreasonable reconstructed signal is chosen, it will increase the difficulty of extracting fault frequencies.

To address the shortcomings of the traditional EMD method, this paper introduces two theories to improve the traditional method, namely, the cross-correlation coefficient criterion and the kurtosis criterion. The cross-correlation coefficient criterion introduces a cross-correlation coefficient indicator based on the characteristic that pseudo-components have small correlation coefficients. The kurtosis criterion introduces a kurtosis indicator based on the characteristic that fault impact signals have large kurtosis values. Combining the above, filtering based on the two criteria can achieve the purpose of signal denoising.

Kurtosis, as a commonly used dimensionless indicator in statistics, is very sensitive to impact characteristics, but it is susceptible to noise signals and loses stability and accuracy, making it difficult to apply in practical engineering. To overcome these defects, researchers have proposed the concept of spectral kurtosis, which analyzes the specific frequency bands where faults occur by obtaining the kurtosis value of each spectral line in the frequency spectrum. The refined EMD algorithm, particularly through the incorporation of spectral kurtosis theory, aims to optimize the performance of traditional EMD in processing nonlinear and non-stationary vibration signals, especially for the vibration analysis of complex mechanical systems, such as pumped storage hydropower units. When signals contain components with close frequencies or at high noise levels, traditional EMD may decompose different frequency components into the same IMF, leading to modal aliasing. Moreover, due to the repeated sifting process involved in the EMD algorithm, boundary effects at the signal’s ends gradually propagate inward, impacting the entire signal processing outcome. The criteria for determining when to stop IMF decomposition, such as residual amplitude or the number of extreme points, possess a degree of subjectivity, potentially causing inconsistency in decomposition results. Spectral kurtosis, an effective tool for detecting transient features and non-Gaussian components in signals, can locate regions of concentrated energy in the frequency domain, particularly those containing transient components. By combining spectral kurtosis with EMD, it becomes feasible to precisely capture and isolate critical fault features within vibration signals. The improved EMD algorithm is thus capable of separating frequency components more effectively, reducing the likelihood of modal aliasing and minimizing interference from irrelevant information.

Define h(t,s) as the time-varying impact response function, and the non-stationary excitation response signal of the signal X(t) is Y(t). Y(t) is decomposed by the Wold–Cramer decomposition as follows:

$$Y(t)={\displaystyle {\int }_{-\infty }^{+\infty }{e}^{j2\pi ft}H(t,f)dX(f)}$$

(6)

In the formula, the time-varying transfer function H(t,f) of the signal Y(t) at frequency f is often expressed in its short-time Fourier transform form as follows:

$$H(t,f)={\displaystyle {\int }_{-\infty }^{+\infty }[x(\tau )\gamma (\tau -t)]e^{j2\pi ft}dt}$$

(7)

In the formula, γ(τ − t) is the window function, whose width is often very small. Spectral kurtosis based on fourth-order spectral cumulants can be defined as follows:

$$C_{4nY}(f)=S_{4nY}(f)-2S_{2nY}^2(f), f\ne 0$$

(8)

In the formula, $S_{2nY}(f)$ represents the 2n-th order time-sequential moment. As an indicator for measuring complex envelope signals, $S_{2nY}(f)$ can be expressed as follows:

$$S_{2nY}(f)=E\left\{{\left|H(t,f)dX(f)\right|}^{2n}\right\}/df$$

(9)

In summary, spectral kurtosis can be defined as the fourth-order spectral cumulant, which is used to represent the peak value of the probability density function H at a certain frequency as follows:

$$K_Y(f)={\displaystyle \frac{C_{4nY}(f)}{S_{2nY}^2(f)}}={\displaystyle \frac{S_{4nY}(f)}{S_{2nY}^2(f)}}-2$$

(10)

After obtaining each independent frequency component, calculate the approximate entropy of each independent sample for subsequent fault diagnosis feature input. Approximate entropy is a metric parameter that describes the internal complex state of time series data, and its calculation formula is as follows:

$$ApEn(T,m,r)={\phi }^m(i)-{\phi }^{m+1}(i)$$

(11)

In the formula, T represents the IMF component; m is the embedding dimension, commonly taken as 2; r is the maximum Euclidean distance matching threshold, often set to 0.2 times the standard deviation; and φ_m(i) is the average value of the logarithm of the matching probability when the embedding dimension is m. By extracting the approximate entropy values of several IMF components obtained from the empirical mode decomposition of the original signal, the multi-scale approximate entropy features of the signal can be obtained. These features reflect the complexity and irregularity of the signal at different scales. When the approximate entropy value is high, it indicates that the signal has high complexity and irregularity, while a low value indicates that the signal is relatively regular and simple.

3. Fault Diagnosis Model Based on CNN-LSTM

3.1. Introduction to Convolutional Neural Networks (CNNs)

In traditional networks, multiple nonlinear activation functions are used to extract features at each level. During training, the characteristics of neural networks are utilized for adaptation, greatly reducing the need for manual feature extraction. However, traditional neural network models are one-dimensional vectors, which can affect the spatial information of features. The CNN is a forward neural network that includes convolution operations. This method uses local connections, shared weights, and other techniques, leveraging convolution and pooling to achieve an efficient representation of raw data. Through convolution and pooling operations, CNNs comprehensively extract local characteristics of images, while pooling operations can expand the receptive field and better extract high-level features. Their basic structure is shown in Figure 1.

The specific descriptions of each layer in the model are as follows.

(1) Convolutional Layer

The convolutional layer is typically located after the input layer of the network and is one of the most important parts of CNNs. Convolution computation involves scanning the input data using a convolution kernel and then locally weighing and combining the data to obtain the corresponding feature map. Convolution kernels of different sizes essentially act as different feature extractors, extracting local features in multiple directions from the input data.

(2) Pooling Layer

The pooling layer, also known as the subsampling layer, is used to select the output features of the convolutional layer. This can significantly reduce the number of parameters in the CNN network and maintain the invariance of the network when slight changes occur in the local region. The pooling layer is generally added after the convolutional layer to reduce the dimension of the feature vector, which can alleviate the problem of overfitting.

(3) Fully Connected Layer

The fully connected layer transmits input information from the front end to the back end of the neurons, representing a highly abstract form of information. On this basis, the neuron nodes are fully connected to all previous regions, and each node corresponds to a weight, achieving dimensionality reduction. At the same time, the output features are used for subsequent processing.

3.2. Introduction to Convolutional Neural Networks (CNNs)

Figure 2 shows a hybrid neural network diagnostic model established using CNN and LSTM neural networks. This model consists of convolutional layers, pooling layers, dropout layers, LSTM layers, and fully connected layers. Firstly, relevant signals are input, and after EMD decomposition, convolutional operations are used for feature extraction to obtain the latent correlations between the data. Pooling methods are employed to compress the number of parameters, further reducing the amount of data. On this basis, dropout layers are added to randomly select network neurons to avoid overfitting. Secondly, LSTM layers are used to process the dimension-reduced features and analyze the data. Finally, the output is produced through the fully connected layer.

To gain a better understanding, a flowchart of fault diagnosis technology for pumped storage units is given in Figure 3.

4. Case Study

This article collects vibration signals of pumped storage units through the following test system. It is important to note that the setting of hyperparameters is a crucial step that directly impacts the model’s performance and training efficiency. As specific hyperparameter values need to be adjusted according to the actual dataset and task complexity, in this paper, the CNN kernel size is set to 5 × 5 based on the characteristics of the input data and the desired scope of local information extraction. The number of convolution filters is 128, with a stride of 1, and the ReLU activation function is used. The pooling type is max pooling, and the pooling window size is 3 × 3. The LSTM hidden state size determines the dimensionality of the internal state of the LSTM unit, and in this paper, it is set to 256. The number of LSTM layers controls the stacking of LSTM units, typically ranging from 1 to 3. Stacking more layers can increase the model’s complexity and learning ability, but it may also lead to overfitting and increased training difficulty, so in this paper, it is set to 2. Bidirectional LSTM can simultaneously consider both forward and backward information in the sequence, which helps improve model performance but increases computational complexity. During training, the learning rate controls the step size of weight updates, typically ranging from 0.001 to 0.01. An excessively high learning rate can lead to unstable training, while an excessively low learning rate can slow down convergence. In this paper, the learning rate is set to 0.005 (note: the original translation of 0.5 seems incorrect for a learning rate in this context). The batch size determines the number of samples used for each training iteration, which is usually adjusted based on the available GPU memory, and in this paper, it is set to 8. The number of epochs represents the number of times the entire training set is traversed, typically ranging from 10 to 100, depending on the size of the dataset and the convergence speed of the model, and in this paper, it is set to 100. Additionally, a learning rate decay strategy is employed to gradually reduce the learning rate during training, which helps improve the stability of the model in later training stages. As an important transmission component in pumped storage units, the gearbox mainly functions to transmit the power of the hydraulic turbine to the generator, enabling it to achieve the corresponding rotational speed. It is one of the key components for converting hydraulic energy into electrical energy. Therefore, the operating state of the gearbox directly affects the performance and stability of the entire pumped storage unit. The internal structure of the gearbox is complex, containing multiple stages of gears, bearings, and other vulnerable components. As shown in Figure 4 and Figure 5, these components are prone to wear, impact, corrosion, and other factors during operation, which can lead to the occurrence of faults. According to statistics, the gearbox is one of the components with a higher failure rate in pumped storage units. Therefore, fault diagnosis of the gearbox is of great significance. This article mainly focuses on collecting vibration signals from the gearbox to perform fault diagnosis. Weak vibration signals are collected through a signal amplifier, filtered for noise, and analyzed for spectrum, and then feature values are extracted for final fault diagnosis. The collected typical vibration signals are shown in the figure below. The collected fault vibration signals are shown in the figure below, with a total of 2100 data sample points. When employing the proposed strategy for fault diagnosis of pumped storage hydro units, the requirements for the vibration signal data format are crucial, as they directly impact the effectiveness of subsequent signal processing and the accuracy of fault diagnosis. The following are the general requirements for the vibration signal data format. The sampling frequency should be sufficiently high to capture the high-frequency components within the vibration signal. Given that the vibration signals of pumped storage hydro units may encompass multiple frequency components, including hydraulic, electromagnetic, and mechanical vibrations, the sampling frequency should be at least twice the highest frequency component present in the signal, adhering to Nyquist’s sampling theorem. The resolution of the data should be high enough to accurately represent subtle changes in the vibration signal. This facilitates more precise extraction of fault features during subsequent signal processing. The vibration signal data should be continuous, without missing or skipping data points. This ensures the continuity and accuracy of signal processing. If the vibration signal data are collected synchronously with other sensor data (such as pressure, temperature, etc.), the timestamps between the datasets should be consistent to facilitate multi-source data fusion and comprehensive analysis. Vibration signal data are typically stored in text files, such as CSV or TXT formats. These files should contain clear timestamps and corresponding vibration signal values. For vibration signal data under different operating conditions or fault states, clear annotations should be provided to facilitate subsequent data processing and fault diagnosis. After collecting the vibration signal data, the noise components in the signals are removed to enhance the signal quality. The amplitude range of the vibration signals is then adjusted to a uniform scale, which facilitates model training. The continuous vibration signals are segmented into fixed-length data segments, with each sample containing sufficient information for subsequent fault diagnosis.

4.1. Verification of the Effectiveness of the Improved EMD Algorithm

To further validate the accuracy of the method proposed in this paper, the optimized EMD algorithm proposed in the literature [15] is selected as the comparison algorithm. This algorithm employs wavelet packet optimization of EMD to achieve fault diagnosis of pumped storage units. Figure 6a,b, respectively, show the spectrum analysis diagrams of the inner and outer rings of the rolling bearing under the traditional EMD algorithm, while Figure 7a,b, respectively, show the spectrum analysis diagrams of the inner and outer rings of the rolling bearing under the improved EMD algorithm. The information in the figures indicates that after applying the improved EMD algorithm, the envelope spectrum of the bearing fault signal accurately represents the fault characteristic frequencies of the inner and outer rings and their multiples, allowing for the determination of whether faults have occurred in the inner and outer rings. However, the interference information in Figure 6 is relatively severe, which increases the difficulty in finding the fault characteristic frequencies. As can be seen in Figure 6a, the characteristic frequencies are not prominent in the spectrum diagram, and in Figure 6b, the first seven multiples of the outer ring fault frequency are relatively clear, but the higher-order multiples after this are obscured by noise interference signals and difficult to find. This indicates that the method still needs improvement in its noise reduction capabilities. Additionally, bandpass filtering enhances the signal-to-noise ratio, making fault signals in the vibration signal more prominent. As can be seen from the fault spectrum analysis diagrams of the inner and outer rings under the algorithm proposed in this paper in Figure 7, the fault characteristic frequencies are more intuitive compared to Figure 6. Specifically, the fault frequency information in Figure 7a is more prominent and almost without interference from noise signal frequencies; compared to Figure 6b, there is also no significant noise interference in Figure 7b. Furthermore, the sixth and seventh multiples of the outer ring are clearly visible. This indicates that the method proposed in this paper can achieve more accurate and clear fault diagnosis results for rolling bearings. In the operation of pumped-storage power units, their vibration signals often contain multiple components, such as hydraulic vibrations, electromagnetic vibrations, and mechanical vibrations. These vibration sources generate frequencies and amplitudes that vary and may interact with each other, resulting in multiple frequency components appearing on the spectrum graph, making it appear complex. During actual measurements, the spectrum graph may contain interfering signals, such as random noise and measurement noise. These noise signals overlap the real vibration signals, further complicating the spectrum graph. Finally, inadequate settings of the measurement equipment’s precision, sampling frequency, resolution, or external disturbances during the measurement process (such as vibrations from nearby equipment) can all lead to inaccurate vibration signal collection, thereby affecting the quality of the spectrum graph.

4.2. Comparative Algorithm and Experimental Result Analysis

After obtaining the characteristic features of typical fault signals, the LSTM-CNN hybrid model is used for fault diagnosis of pumped storage units. To more intuitively demonstrate the effectiveness of the method proposed in this paper, a comparison with traditional methods is made, and the relevant calculation results are shown in

Table 1. Comparison of accuracy between different diagnostic methods.

Method	Accuracy of Inner Race Fault Diagnosis/%	Accuracy of Outer Race Fault Diagnosis/%	Standard Deviation/%
CNN	91.3	91.7	1.7
LSTM	92.6	93.4	2.3
SVM	92.5	94.6	2.6
RNN	91.7	95.2	3.2
The proposed method	95.1	96.8	0.5

below. It should be noted that the standard deviations in the following table are calculated based on the results of 10 fault diagnosis attempts using each method.

Observing the table above, we can find that the diagnostic accuracy of the method proposed in this paper is the highest in all cases, with fault diagnosis accuracy consistently above 95%. The CNN exhibits excellent feature extraction capabilities in signal processing, capable of automatically extracting useful spatial features from raw data, which is highly effective for recognizing image-based data, such as vibration signals from pumped storage units. CNN’s local weight sharing, and parallel processing capabilities reduce network complexity, improve computational efficiency, and avoid the complexity of data reconstruction during feature extraction. LSTM is a variant of the RNN, particularly suited for processing time series data. It can capture long-term dependencies in data, which is crucial for analyzing time series data, such as vibration signals from pumped storage units that vary over time. Through structures like forget gates, input gates, and output gates, LSTM can selectively retain or forget information, effectively solving the gradient vanishing or gradient explosion problems that traditional RNNs often encounter in processing long sequences. The CNN-LSTM hybrid model combines the powerful feature extraction capabilities of the CNN with the excellent time series processing capabilities of LSTM, enabling the model to consider both spatial features and temporal dependencies when processing complex fault data from pumped storage units. The spatial features extracted by the CNN are used as inputs to LSTM, which can further analyze the changes of these features over time, thereby more accurately identifying fault patterns. This combination significantly improves the accuracy of fault diagnosis. Compared to a single CNN, although the CNN performs well in feature extraction, it lacks the ability to process time series data, so it may not fully utilize the temporal information in the data when used alone for fault diagnosis of pumped storage units. Compared to a single SVM, although the SVM is a powerful classifier, it may face challenges when dealing with high-dimensional, nonlinear data, and its performance highly depends on the quality of feature engineering. In contrast, the CNN-LSTM hybrid model can automatically extract features and process time series data, reducing the reliance on manual feature engineering. Compared to the RNN, traditional RNNs are prone to gradient vanishing or gradient explosion when processing long sequence data, while LSTM, as an improved version of the RNN, effectively solves these problems by introducing mechanisms such as forget gates. Therefore, the CNN-LSTM hybrid model is more stable and accurate than a standalone RNN model when processing fault data from pumped storage units. By introducing the spectral kurtosis theory to refine the EMD method, it becomes more effective in identifying and isolating key fault features within vibration signals, while simultaneously reducing noise interference and enhancing the accuracy and reliability of signal decomposition. Utilizing the reconstructed IMFs to calculate entropy values as fault feature vectors enables capturing dynamic changes and nonlinear characteristics within the signals, thereby providing richer and more effective information for subsequent fault diagnosis. Employing the MCNN-LSTM model for fault diagnosis combines the strengths of the CNN in feature extraction and LSTM in capturing long-term dependencies in time series data, improving the accuracy and robustness of fault diagnosis. The proposed method integrates the benefits of both data-driven and model-driven approaches, leveraging the rich information within the data while incorporating prior knowledge and structural information through the model, rendering the entire diagnostic process more comprehensive and intelligent.

However, while the MCNN-LSTM model boasts powerful performance, its computational complexity and resource consumption are relatively high, potentially rendering it unsuitable for scenarios requiring extremely high real-time performance. The method’s performance is highly dependent on the quantity and quality of training data. Insufficient or biased training data may compromise the model’s generalization ability and diagnostic accuracy. Multiple parameters within the model require tuning, such as the CNN’s kernel size, stride, and the number of LSTM units, which significantly impact model performance but can be cumbersome to optimize. While the method excels in diagnosing known fault types, its recognition capabilities may be limited for completely unknown faults, necessitating continuous updates and expansions to the fault feature library. Potential error sources can also contribute to reduced fault diagnosis accuracy. Factors such as sensor accuracy and environmental conditions during vibration signal acquisition may lead to signal distortion or increased noise. Operations like denoising and filtering during preprocessing may introduce errors. Errors in IMF reconstruction and entropy calculation can propagate to the subsequent fault diagnosis model, affecting the accuracy of the diagnostic results. The MCNN-LSTM model’s training process may encounter issues like overfitting and underfitting, degrading its performance on test sets. Additionally, the accuracy of training data labels can impact the model’s training effectiveness.

5. Conclusions

This paper focuses on the important role of pumped storage units as a stable and flexible energy supply in the power system, as well as the challenges they face in terms of operational reliability and health status due to coupling effects from power load demands and complex multi-source factors. A novel data-model hybrid-driven strategy is proposed. This strategy optimizes vibration signal processing through an improved EMD method, combined with entropy-based feature extraction and the CNN-LSTM model, achieving rapid and accurate fault diagnosis of the units. The verification results using actual operational data demonstrate that the proposed method is effective and feasible, providing a new solution for enhancing the operational reliability and health status monitoring of pumped storage units. After a thorough examination, the method introduced in this study has consistently demonstrated a fault diagnosis accuracy exceeding 95%, underscoring its resilience in intricate engineering contexts and efficiently safeguarding the seamless and dependable functioning of pumped storage systems.

Further research will be conducted to explore the application of advanced algorithms, such as deep learning and reinforcement learning, in fault diagnosis for pumped storage units, aiming to enhance the accuracy and efficiency of diagnosis. Additionally, the potential of unsupervised learning algorithms in anomaly detection will be investigated, enabling the automatic discovery of potential fault patterns in the absence of explicit fault labels. Concurrently, efforts will be made to explore how to effectively integrate multi-source data, including vibration signals, temperature, pressure, flow rate, and more, to establish a more comprehensive health monitoring and fault diagnosis system for these units. By leveraging data fusion techniques, the precision and robustness of fault identification will be improved, particularly in complex operating conditions and noisy environments.