Application of VMD–CNN–LSTM in mechanical fault diagnosis of pump station units

1 Introduction

The spatial and temporal distribution of water resources in China is uneven; cross-basin water diversion projects have become an important strategic measure to ensure regional water security and support economic and social development (Jun et al., 2023; Enhui et al., 2025). The operational reliability of pump station units, as the core power equipment of such projects, directly affects the safety and efficiency of the entire system (Zhao et al., 2023). However, the units constantly operate under high-load and variable conditions, resulting in frequent mechanical failures. Common failures include rotor misalignment, bearing wear, and rotor-stator rubbing and associated coupling faults (Milošević et al., 2022). Such faults not only occur frequently but also may trigger chain-like equipment damage, causing significant safety risks and economic loss (Qiu et al., 2024). Therefore, developing precise and intelligent fault diagnosis technologies and transforming the operation mode from “regular” to “predictive” maintenance has become an urgent need in the industry (Yong et al., 2024; Li et al., 2021).

The primary challenge for achieving precise diagnosis lies in handling the complex non-stationary vibration signals of pump station units. Traditional signal processing methods have their own limitations: Empirical mode decomposition (EMD) is susceptible to mode aliasing and end effects, affecting the stability of the decomposition (Jun et al., 2020); Wavelet transform’s diagnostic effect largely depends on the selection of the basis function, lacking adaptability (Diao et al., 2023); fast-Fourier transform (FFT) is mainly applicable to stationary signals, and it is difficult to characterize non-stationary features such as fault impacts (Xu et al., 2024). In contrast, variational mode decomposition (VMD) can adaptively decompose the signal into several characteristic intrinsic mode functions (IMF) with limited bandwidth by constructing and solving variational constraint problems, thus effectively suppressing mode aliasing phenomena (Zheng et al., 2019). The superiority of VMD over other adaptive decomposition methods, such as EMD and Hilbert vibration decomposition (HVD), has been systematically validated in the context of vibration-based structural health monitoring. A comparative study by Civera and Surace (2021) demonstrated that VMD exhibits superior robustness to noise and enhanced capability in extracting damage-sensitive features from nonstationary signals, particularly in the presence of structural nonlinearities, which are common in pump station units. Consequently, VMD is increasingly favored in the analysis of hydraulic machinery faults. For example, Ma and Zhang (2025) demonstrated that the VMD method is strongly adaptable in analyzing the characteristics of hydraulic machinery vibration faults and can avoid the mode aliasing problem of EMD. However, the decomposition performance of VMD is highly dependent on the setting of its key parameters (mode number K and penalty factor α). Improper parameters can lead to under-decomposition, over-decomposition, or the inclusion of noise modes, thereby losing key fault information. To address this issue, scholars have explored various parameter optimization strategies. Changwei et al. (2019) proposed an adaptive VMD method based on backtracking algorithm and parameter sensitivity analysis, achieving good results in the analysis of the vibration signal of a hydropower unit. Zhou et al. (2022) used the Pelican algorithm to optimize the VMD parameters and significantly enhanced the extraction ability of the bearing fault features of the motor. These studies collectively point to the conclusion that the optimization of VMD parameters is the core link in improving the effectiveness of fault feature extraction. However, existing optimization algorithms still face challenges such as slow convergence speed and being prone to getting stuck in local optima when dealing with complex scenarios with strong background noise and weak fault features of pump station units. There is, therefore, an urgent need to develop more robust and efficient optimization strategies.

At the level of fault feature identification and classification, data-driven methods represented by deep learning have demonstrated significant advantages. Among them, convolutional neural networks (CNNs) with their powerful ability to automatically extract local features are widely used in mechanical fault diagnosis. For example, Liu Junli and others (Bangcheng et al., 2023) proposed a rolling bearing fault diagnosis method based on improved VMD and CNN, which can effectively extract highly discriminative features and demonstrates good noise resistance while accurately diagnosing various single and compound faults of the bearing. However, CNN is essentially a spatial feature extractor, and its disadvantage lies in its difficulty in effectively modeling the temporal dependency relationships contained in the process of fault occurrence and development (Zhan et al., 2022). Complementary to this, long short-term memory (LSTM) networks, as a special type of recurrent neural network, have a gating mechanism that makes them particularly adept at capturing long-term dependencies in time series. They are widely used in fields such as hydrological forecasting and equipment state time series modeling (Zheng et al., 2023). Liu Shuxi and others (Tian et al., 2023) demonstrated the potential of LSTM in time-series fault diagnosis. They proposed a fault diagnosis method based on improved VMD and LSTM, which was used for the fault diagnosis of sub-module switching tubes in modular multilevel converters, significantly improving diagnostic accuracy and efficiency. These studies, respectively, verify the effectiveness of CNN in spatial feature extraction and LSTM in modeling temporal patterns while also revealing the inherent limitations of a single model: CNN is insensitive to dynamic time series, and LSTM has a relatively weak ability to capture local spatial details.

Therefore, a hybrid model combining CNN and LSTM has become important in current research, aiming to integrate the advantages of both to achieve “spatial–time” joint modeling of fault features. The research of Sun Peng and others (Ren et al., 2023) is representative of this direction. They used the CNN–LSTM model to diagnose the faults of mine transformers, achieving a diagnostic accuracy rate superior to traditional methods and single neural networks. However, a key gap can be identified from the existing research: many studies either focus on optimizing VMD to improve the quality of front-end features, concentrate on building a CNN–LSTM hybrid model to enhance classification performance, or combine VMD with a single LSTM for time-series diagnosis. However, systematically and purposefully integrating “optimized VMD” as a strong anti-noise preprocessing module and deeply coupling it with the “CNN–LSTM” spatiotemporal feature extraction network to construct an end-to-end framework for complex fault diagnosis in a noisy environment is still insufficient. The actual operating environment of pumping station units is complex (including hydraulic, mechanical, electromagnetic, and other noise sources), so directly applying deep learning to the original noisy signal or only the signal after simple decomposition is highly susceptible to interference.

In response to these research gaps and engineering needs, this study proposes a deeply integrated VMD–CNN–LSTM-coupled diagnostic model. The main contributions of this study are threefold.

• A hybrid optimization algorithm (OCSSA) is developed by enhancing the sparrow search algorithm (SSA). It integrates an Osprey optimization algorithm (OA)-inspired global search strategy and a Cauchy mutation operator for local perturbation. This combination is specifically tailored to overcome the limitations of traditional algorithms in adaptively optimizing VMD parameters for signals with strong background noise, thus ensuring the stable and efficient extraction of fault-related IMF components.
• Weak adaptability to extremely low signal-to-noise ratio conditions: existing methods perform well in high signal-to-noise ratio conditions in the laboratory, but in simulated or actual extremely low signal-to-noise ratios (such as ≤ 5 dB) under harsh conditions, the robustness of diagnostic accuracy is not sufficiently verified and guaranteed.
• Balancing model efficiency and engineering practicality: for pumping station units that require real-time or near-real-time monitoring, controlling the computational complexity of the model to meet the real-time requirements of on-site online diagnosis while ensuring high diagnostic accuracy is a key engineering challenge.

In response to these research gaps and engineering needs, this study proposes an innovative, deeply integrated VMD–CNN–LSTM-coupled diagnostic model. The main contribution of this study lies in the following.

• Design of a novel hybrid intelligent optimization algorithm (OCSSA) for the adaptive optimization of VMD parameters. This algorithm combines an improved global search and local perturbation mechanism that aims to overcome the shortcomings of traditional optimization algorithms and ensure stable and efficient decomposition of the key IMF components that represent faults in a strong background noise environment, providing “pure” input for the subsequent deep learning model.
• Construction of an end-to-end diagnostic framework of “adaptive signal purification deep extraction of spatial features → modeling of temporal evolution laws”. This framework is not a simple stacking of technologies but integrates the optimized VMD with CNN–LSTM through the envelope entropy criterion as a bridge. OCSSA–VMD is responsible for noise suppression and feature enhancement, CNN is responsible for extracting the local spatial patterns (such as impact and friction) of faults from the selected IMF, and LSTM is responsible for capturing the evolutionary laws of these patterns over time. The three components form a closed loop of synergistic gain.
• Through systematic comparative experiments, the excellent performance and generalizability of the model under low signal-to-noise ratios were verified. The experimental results on simulated fault datasets with various noise levels and real pump station unit data show that the proposed model can maintain high diagnostic accuracy even at an extremely low signal-to-noise ratio of 5dB, significantly outperforming existing mainstream methods. It also has high training and inference efficiency that provides an effective solution for the reliable intelligent diagnosis of pump station units in actual complex noise environments.

2 Model introduction

The core of the intelligent diagnosis framework proposed here lies in the deep coupling of VMD with the CNN–LSTM hybrid neural network. To adaptively optimize the parameters of VMD, we introduce an enhanced sparrow search algorithm (OCSSA), which incorporates an Osprey-inspired exploration mechanism and a Cauchy mutation operator. The overall technical route follows the logic of “adaptive signal decomposition and purification of spatiotemporal features for deep joint extraction of fault type intelligent classification”. In this section, we will first explain the basic principles of the mature components VMD, CNN, and LSTM (with appropriate citations) and then focus on introducing the improvements, integration methods, and innovative points of our research.

2.1 Variational mode decomposition algorithm

As detailed in the Introduction, VMD (Wang et al., 2018) is employed for its robust performance in decomposing non-stationary signals. Its core idea is that to solve a constrained variational problem, the original signal f t must be decomposed into K intrinsic mode functions (IMF) u k t with limited bandwidths (Equation 1). While VMD effectively mitigates mode mixing issues common in methods such as EMD, its performance is highly dependent on the pre-setting of key parameters—the mode number K and penalty factor α.

min ⁡ u k } , { ω k ∑ k = 1 K ∥ ∂ t δ t + j π t * u k t e − j ω k t ∥ 2 2 , s . t . ∑ k = 1 K u k = f t . (1)

In the abovementioned formula, u _*k* represents the kth IMF, ω k is its center frequency, δ t is the Dirac function, * indicates convolution operation, ∂ t is the time derivative, and j is the imaginary unit.

However, the decomposition performance of VMD is highly dependent on the preset parameters, especially the modal number K and the quadratic penalty factor α. The K value being too small will lead to under-decomposition and an inability to separate the mixed fault features; the K value being too large will generate redundant noise modes and increase the computational burden. Therefore, the parameter adaptive optimization of VMD is a key prerequisite for its effective application in engineering practice. Although some studies have used optimization methods such as the backtracking and the Pelican algorithms for optimization, these methods still have limitations such as being prone to becoming stuck in local optima and having unstable convergence speeds when dealing with high-dimensional and nonlinear optimization problems.

To address these challenges in VMD parameter optimization, this study proposes an enhanced hybrid intelligent optimization algorithm (OCSSA). It is built upon the original SSA and incorporates two substantial improvements to strengthen its global search and local exploitation capabilities, which are detailed in Section 2.3. These enhancements are motivated by the characteristics of strong noise and multiple components in pump station vibration signals.

2.2 Convolutional neural network–long short-term memory network coupling model

CNN and LSTM are both classic network structures in the field of deep learning, each excelling in extracting spatial features and modeling temporal dependency relationships. We adopt a coupling method of CNN and LSTM rather than a simple concatenation—a purposeful structural design based on the characteristics of the pump station failure signals, which combine both local impact patterns and macroscopic evolution laws.

2.2.1 Convolutional neural network

A CNN is a type of feedforward neural network, which has a deep structure and includes convolution computations. The convolutional layer is the core of the CNN, extracting local features from the input data through convolution operations. The mathematical representation of convolution operation is shown in Equation 2

Y = X * W + b . (2)

In the abovementioned formula, W is the weight matrix, X is the input vector, * indicates the convolution operation, b is bias, and Y represents the output feature map.

The pooling layer is mainly used for data dimensionality reduction and computational complexity optimization while maintaining the key information of feature representation. Among them, the pooling operation is the formula as shown in Equation 3.

P o o l k = max m * n x i k . (3)

In the abovementioned formula, Pool (k) represents the output after the pooling layer operation, x i k is the input of layer k, and mn* is the size of the pooling area.

The fully connected layer is responsible for implementing the combined mapping of features and ultimately generating classification results or regression outputs. Its mathematical expression is shown in Equation 4.

Y = X W + b . (4)

The output layer typically uses the softmax activation function for classification tasks. The softmax activation function is shown in Equation 5.

S o f t m a x z j = exp z j ∑ n = 1 N exp z j . (5)

In the abovementioned formula, z j represents the score of each class, and softmax converts the score into probability values.

2.2.2 Long short-term memory network

LSTM excels at capturing long-term dependencies in sequential data, with a memory unit at its core that maintains the “cellular state” at each time step to enable the long-term storage and effective transmission of key historical information. Information flow regulation mainly relies on three gating mechanisms: forgetting, input, and output gates.

The forgetting gate determines which information in the previous moment’s cell state C_t-1 is retained at the current moment and maps the input to the interval [0,1] via the sigmoid activation function to quantitatively adjust the degree of information retention. The function expression is shown in Equation 6.

f t = σ W f h t − 1 , x t + b f (6)

In the formula, f t is the output of the forgetting gate, x t is the input quantity at the current moment, σ is the sigmoid activation function, h t − 1 represents the hidden state of t-1 at the previous moment, W f is the weight matrix of the forgetting gate, and b f is the bias term of the forgetting gate.

The input gate controls the intensity of the current input’s update to the cell state, including a Sigmoid gate (Equation 7) that controls the update position and a Tanh gate (Equation 8) that generates candidate states.

i t = σ W i h t − 1 , x t + b i , (7)

C ∼ t = σ W C h t − 1 , x t + b C . (8)

In the abovementioned formula, i t is the output of the input gate, C ∼ t is a new candidate state for cells, W i is the weight matrix of the input gate, b _*i* is the bias term of the input gate, and W i and b _*C* are, respectively, the weight matrix and the bias term of the candidate states.

The output gate (Equation 9) determines the value of the final output h _*t* (Equation 10). The sigmoid function is first used to determine which cell state parts will be passed to the output, and then the Tanh function is used for modulation.

o t = σ W o h t − 1 , x t + b o , (9)

h t = o t ⁡ tanh C t . (10)

In the abovementioned formula, o t represents the output of the output gate, the cell state at the current moment of C _*t*, h t is the hidden state at the current moment, and W o and b _*o* are, respectively, the weight matrix and the bias term of the output gate.

To achieve efficient and accurate fault classification, this study adopts a model combining CNN and LSTM, fully leveraging the advantages of CNN in feature extraction and the powerful capabilities of LSTM in processing time series data to achieve precise classification of fault signals. The structure of this model is shown in Figure 1.

To ensure that the constructed CNN–LSTM hybrid model achieves best performance and to guarantee the reproducibility of the research process and the comparability of the results, we conducted a systematic grid search and optimization of the network structure hyperparameters and training parameters (Yuan et al., 2024; Xu et al., 2024). All experiments were based on the final configuration obtained through this unified optimization to ensure the fairness of the comparison. The optimization of the network structure hyperparameters aims to balance model complexity and feature expression ability. Based on the design experience of deep learning models and the prior analysis of vibration signals, the search ranges for the following core parameters were defined (Table 1).

TABLE 1. Range of model structure parameter settings.

The complete configuration of the model, the data processing procedure, and the training details are shown in Table 2. This configuration serves as the benchmark for all comparative experiments, thereby ensuring the reliability of the research conclusions.

TABLE 2. Model structure parameter settings.

The final model is a hybrid network composed of a single-layer CNN (with 10 3 × 1 convolutional kernels) and a two-layer LSTM (each layer having 128 units, with a dropout rate of 0.2 between layers). This structure was determined through grid search and cross-validation, achieving the optimal balance between diagnostic performance and generalizability on the validation set. All experiments in this study were strictly based on this unified configuration, ensuring the fairness of method comparisons and the reproducibility of results.

2.3 Enhanced sparrow search algorithm with Osprey and Cauchy mutation

The OCSSA algorithm proposed herein addresses the limitations of the original SSA in optimizing VMD parameters, including limited global exploration ability and a tendency to prematurely converge. Two targeted improvements are introduced to the SSA framework: first, drawing on the “dive and hunt” concept of the Osprey OA to enhance the global exploration ability of the SSA producers; secondly, introducing a Cauchy mutation operator to increase population diversity and help the algorithm escape from local optima. The iterative process and specific formulas of the proposed OCSSA are as follows.

Population optimization: the initial population of sparrows is randomly generated with a uniform distribution to ensure that each sparrow covers the entire solution space (Equation 11).

x i , j 0 = x j , ⁡ min + r 1 · x j , ⁡ max − x j , ⁡ min . (11)

In the abovementioned formula, x i , j 0 represents the position of the ith sparrow in the jth dimension when t = 0 in the initial iteration, x j , ⁡ max , x j , ⁡ min are the upper and lower limits of the jth dimension variable, respectively, and r 1 is a uniformly distributed random number to ensure the diversity of the initial population.

During the producer position update stage, we adopted the “dive-and-catch” dynamic search mechanism of the Fish Eagle OA to replace the simple update method in the SSA. This strategy simulates the behavior of the fish eagle first circling at a high altitude (conducting a wide-range random search) and then diving toward its prey (the potential optimal solution, performing a directional approach) (Equation 12). This enables the algorithm to conduct more effective global exploration in the early iterations and avoid becoming trapped in undesirable local extreme regions.

x i , j t + 1 = x p b e s t , j t · ⁡ exp − t + 1 r 2 · T max + r 3 · C · x j , ⁡ max − x j , ⁡ min , r 4 < S T x p b e s t , j t + C a u c h y 0 , 1 · x i , j t , r 4 ≥ S T . (12)

In the abovementioned formula, x i , j t represents the position of the ith sparrow on the j-dimensional variable during the tth iteration. x p b e s t , j t is the jth dimension of the global optimal position in the tth iteration, T_max represents the maximum number of iterations, r i is a random number belonging to [0,1], ST stands for the safety threshold, Cauchy is the Cauchy variation scale parameter, and C is the step size search factor.

Improved follower position update: followers account for 70%–80% of the total population and follow the producer in foraging. OCSSA introduces a “distance weight” to allow followers closer to the producer to explore more precisely (Equation 13).

x i , j t + 1 = r 5 · x i , j t + C a u c h y 0 , 1 · ∣ x i , j t − x p b e s t , j t ∣ , i > N / 2 x p b e s t , j t + r 6 · ∣ x i , j t − x p b e s t , j t ∣ , i ≤ N / 2 . (13)

In the abovementioned formula, i ≤ N / 2 and i > N / 2 are the followers ranked at the top and bottom, respectively.

Alert person position update: alert persons account for 10%–15% of the total population. They monitor environmental hazards (such as falling into local optimum) (Equation 14). OCSSA retains the original alert mechanism of SSA and adds “fitness judgment”, only updating individuals with poor fitness.

x i , j t + 1 = x j , ⁡ min + r 7 · x j , ⁡ max − x j , ⁡ min , f x i t > f x a v g t x i , j t + r 8 x i , j t − x a v g , j t f x i t − f x a v g t + ω , f x i t < f x a v g t . (14)

In the abovementioned formula, x a v g t , f x a v g t represents the average position and fitness of the population in the tth iteration, respectively, ω avoids the minimum value with a denominator of 0, f x i t > f x a v g t represents the alert with poor fitness, which is directly and randomly reset to a new position in the solution space, and f x i t < f x a v g t is fine-tuned along the direction far from the average position for those with better fitness to maintain population diversity.

The Cauchy mutation operation is applied after every iteration to individuals with lower fitness rankings. Utilizing the long-tail characteristic of the Cauchy distribution to generate large-step perturbations can effectively help the population escape from local optima and increase search diversity, thereby enabling more detailed local exploration in the later iterations (Equation 15).

C a u c h y x ; 0 , 1 = 1 π 1 + x 2 . (15)

For the convergence criterion, repeat steps 2 to 5 until the number of iterations reaches T_max or the change in the global optimal fitness value is less than the preset threshold (Equation 16):

∣ f x p b e s t t + 1 − f x p b e s t t ∣ < δ . (16)

At this point, the iteration terminates and outputs the global optimal position x p b e s t.

The fundamental difference between OCSSA and the original SSA and other traditional optimization algorithms is that it achieves a dynamic balance between global exploration and local exploitation capabilities through the aforementioned mechanism. In this study, OCSSA is specifically used to optimize the [K, α] parameter combination of VMD, with the optimization objective minimizing the envelope entropy of the best IMF component.

2.4 VMD–CNN–LSTM coupling model

Based on the above improvements and designs, the final OCSSA–VMD–CNN–LSTM-coupled model constructed here demonstrates its novelty not only in the improvements of each component but also in the collaborative logic of the entire processing chain. Figure 2 shows the workflow of this model as follows.

• VMD feature extraction. VMD is utilized to decompose complex signals to, thus, obtain multiple intrinsic mode functions (IMFs), each representing a different frequency component in the signal. The center frequency, bandwidth, and other parameters of VMD are adjusted through the OCSSA optimization algorithm to improve the accuracy of the IMF component. Then, the envelope entropy criterion is adopted to screen out the representative IMF components. The best selected IMF contains the key features in the signal, which is helpful for improving the performance of the subsequent classification model.
• Data preprocessing. We standardize the selected optimal IMF components to eliminate scale differences between signals and convert the standardized IMF into a two-dimensional matrix format suitable for CNN input. This step ensures the uniformity and stability of the input data, thereby enhancing the training effect and convergence speed of the model.
• Feature extraction (CNN section). Local features of the signal are extracted through convolutional layers and pooling layers. The convolutional layer extracts spatial information from the signal, while the pooling layer down-samples to reduce the data dimension and highlight significant features, thereby reducing computational complexity. The feature map generated at this stage provides a basis for the subsequent sequence modeling.
• Sequence feature extraction (LSTM part). The feature maps processed by CNN are input into LSTM as time-series data. LSTM can capture the time dependency relationship in the signal and learn the global dependency information of the signal. This process helps the model understand the evolution of faults and extract important temporal features.
• Classification decision. The timing features extracted by LSTM are input into the fully connected layer, and the classification decision of fault types is made through the softmax function. This converts the network’s output into a probability distribution, predicts the probabilities of each fault type, and ultimately outputs the most likely fault category label to achieve precise fault diagnosis.
• Model training and evaluation. We train the CNN–LSTM model using labeled data and evaluate the model’s performance through cross-validation and test sets.

3 Experimental results

3.1 Experimental parameter settings

To ensure the reproducibility of the experimental results, stability of the training process, and reliability of the model performance, this study clarifies the parameter configuration that is unified and suitable for the pump station fault diagnosis scenario for the key links of model training and data processing. The optimizer selects Adam, which has stronger adaptability to the gradient update of non-stationary vibration signals and supports the gradient oscillation by adjusting the momentum parameter. The learning rate adopts a dynamic attenuation strategy to balance convergence speed in the early stage and training accuracy in the later. The combination of the epoch number and the early stop strategy setting not only avoids insufficient training but also prevents overfitting. The batch size matches the memory of the experimental equipment with the sample dimension to ensure training efficiency. At the same time, fixed random seeds eliminate the interference of random factors. The specific parameter configuration and design basis are shown in Table 3.

TABLE 3. Experimental parameter settings.

3.2 Data collection and processing

3.2.1 Data collection

As a special type of rotating power equipment, the operation characteristics of the pumping station unit are essentially different from those of general rotating machinery. This difference is mainly reflected in two ways. First, the unit has been operating in a high-load and variable working condition environment for a long time and must deal with complex hydraulic conditions (including water level fluctuations, flow rate changes, and hydraulic shocks). Second, the vibration signal thereby generated has unique characteristics of frequency modulation and phase change (Rui, 2021). This experimental set-up has three modes: rotor misalignment, rotor-stator friction and collision, and their coupling faults. These faults were simulated at different rotational speeds, and fault signals were collected to construct a fault sample set. The pump station unit test bench is shown in Figure 3. To simulate the parallel misalignment fault, a thin annular gasket only 1.0 mm thick was added to the bearing, resulting in a certain degree of misalignment between the upper and lower rotors. A brass screw was installed above the guide bearing 0.2 mm from the rotor. When the rotor rotates at high speed, if the vibration amplitude exceeds the distance between the screw and the rotor, these will rub against each other, simulating a rubbing fault. In the experiment, the rotational speed range of the unit was 1000–3000 r/min, the sampling frequency was 1000 Hz, and the sampling length was 7200.

To construct a sample set suitable for deep network training, the long-term vibration signals under each fault state were segmented using a sliding window. The specific strategy is as follows. We set the window length to 1024 sampling points and the sliding step size to 512 sampling points, and a series of consecutive signal segments is generated with a 50% overlap rate. To ensure the fairness of model evaluation and prevent data leakage, the original long-term signals under each fault category were first divided into two independent continuous segments on the timeline, which were, respectively, used as the training and test signal segments of that category. Subsequently, the above sliding window was applied only in the training signal segment to generate all training samples, and all test samples were independently generated in the test signal segment. Thus, all overlapping windows from the same original signal only appear in either the training or test set and never simultaneously in both, thus ensuring the complete independence of the training and test sets. Based on this principle, for each fault category listed in Table 4 (with a total of 500 original long sequences), we took the first 60% of the continuous time series as the training signal segment and the last 40% as the test signal segment. We performed sliding window sampling in both segments and generated 300 training samples for each category from the training signal segment and 200 test samples from the test signal segment. In total, a dataset without data leakage containing 3,000 training samples and 2,000 test samples was constructed.

TABLE 4. Fault sample set.

The original vibration signals under different states are shown in Figure 4. We can observe from the figure that the vibration signals of different fault types have certain differences in waveform characteristics. For instance, the vibration signal of the rotor misalignment fault shows relatively obvious periodic fluctuations, while the rotor-stator friction fault is accompanied by instantaneous impact characteristics. The vibration signal of the coupling fault integrates some features of both. After feature extraction, each feature contains 500 samples, totaling 10 features, forming a 5,000 × 10 matrix, and each row of data is labeled. Among them, 1–10 represent different types of faults. The first 300 groups of each feature are divided into the training set, and the last 200 groups are divided into the test set.

3.2.2 Data processing

To comprehensively evaluate the diagnostic robustness of the VMD–CNN–LSTM-coupled model under conditions close to those of actual engineering environments, this study not only injected standard Gaussian white noise but also systematically simulated various complex disturbances commonly encountered at the pump station unit site and of greater practical significance (Hamed et al., 2025). All noises were injected into the original experimental vibration signals additively, and their intensities were controlled by the signal-to-noise ratio (SNR) (Equation 17), which is defined as

S N R d B = 10 ⁡ log 10 P s P n . (17)

In the abovementioned formula, P _*s* and P _*n* represent signal power and noise power, respectively. The specific injected noise and disturbance types, as well as the mathematical model and parameter settings, are as follows.

3.2.2.1 Gaussian white noise

Gaussian white noise is used as the benchmark test to simulate ubiquitous wide-band thermal noise, sensor electronic noise, and other background random disturbances. The noise sequence n GWN t follows a Gaussian distribution with a mean of 0 and a variance of σ 2—that is, n GWN t ∼ N 0 , σ 2. σ 2 is determined based on the target signal-to-noise ratio (SNR = 5, 10, 15, 20 dB).

3.2.2.2 Pulse noise

Pulse noise is used to simulate the sudden sharp disturbances that occur during the operation of the pumping station units due to random impacts (such as foreign objects or bubble collapse), electromagnetic interference, or transient faults in the data acquisition system. Such disturbances seriously contaminate the instantaneous characteristics of the signal. The Bernoulli–Gaussian model was adopted (Equation 18). A pulse position sequence b t following a Bernoulli distribution was first generated, with the pulse occurrence probability being p (pulse index). At the positions where the pulse occurs, the noise amplitude follows a Gaussian distribution with a mean of 0 and variance of σ i 2; otherwise, it is 0. The expression is

n IN t = b t · g t , b t ∼ Bernoulli p , g t ∼ N 0 , σ i 2 . (18)

Parameter settings. We set the pulse index p = 0.01 (approximately 1% of the data points are contaminated by the pulse) and the variance of pulse intensity σ i 2 to ten times the variance of the Gaussian white noise of the same period to simulate strong impulse interference. The overall mixed SNR is still controlled within 5–20 dB (Formula 17).

3.2.2.3 Narrowband interference

Narrowband interference is used to simulate fixed-frequency mechanical resonances, electromagnetic harmonics (Equation 19) (such as power frequency and its multiple frequency interferences), or periodic interferences from adjacent equipment operation. Such interference will form sharp peaks in the spectrum, which are prone to confusion with the characteristic frequencies of faults. The expression is

n NBI t = ∑ m = 1 M A m ⁡ sin 2 π f m t + ϕ m (19)

Parameter settings. We set M = 2 interference frequencies. We simulate interference f 1 = 0.4 × shaft rotational frequency that is close to the fault characteristic frequency band and interference f 2 = 100 Hz of the power frequency harmonic. The phase ϕ m is randomly generated within the range of [0, 2π). The amplitude A m is calculated based on the requirement that the total interference power reaches the target signal-to-noise ratio.

3.2.2.4 Compared with the actual on-site signal segment

To further verify the performance of the model in a completely real and unsimplified complex environment, a segment of vibration signal was extracted from the normal operation monitoring data of the operating units of the project. This segment did not contain any obvious faults but included all natural background noises (such as hydraulic pulsation, electromagnetic interference, and environmental vibration.).

3.3 Optimization process, parameter sensitivity analysis, and stability verification

3.3.1 OCSSA–VMD tuning process

To systematically determine the optimal parameter combination of VMD and ensure the reproducibility of the method and reliability of the engineering deployment, we designed a complete OCSSA–VMD automatic tuning pipeline. The core design elements and configurations of this pipeline are shown in Table 5.

TABLE 5. OCSSA–VMD tuning core configuration.

This pipeline tightly couples the OCSSA intelligent optimization algorithm with the VMD quality assessment, forming a closed-loop automatic optimization process. Its working principle is as follows. The OCSSA algorithm generates parameter combinations [K, log10(α)] within the defined mixed search space. Each evaluation requires a complete VMD and the calculation of the objective function (minimum envelope entropy), thereby guiding the population to evolve toward regions with better decomposition quality. The adoption of the “representative sample optimization” strategy is based on engineering considerations. It makes it possible to perform robust optimization for large-scale datasets with the goal of seeking the global optimal parameters, thereby avoiding overfitting or suboptimal solutions that may result from computational resource limitations.

3.3.2 Parameter sensitivity analysis and convergence characteristics

To quantify the influence of the number of VMD decomposition layers (modal number K) and the parameters of the OCSSA optimization algorithm on the diagnostic performance, a control variable method was adopted to design a control experiment. The experiment fixed other conditions. Under the 5 dB noise condition, the number of modes K (3/5/7), the OCSSA population size N (20/50/100), and the number of iterations T (50/100/200) were, respectively, adjusted. With the minimum envelope entropy and the accuracy of model diagnosis as the core evaluation indicators, the results of parameter sensitivity analysis are shown in Table 6.

TABLE 6. Analysis of the convergence characteristics of OCSSA parameters.

The test results for the number of decomposition layers K show that under the 5 dB low SNR environment (where hydraulic and electromagnetic noise severely interferes with fault feature extraction), when K = 5, the IMF components decomposed by VMD not only fully cover the characteristic frequency bands of faults such as rotor imbalance and collision coupling but also effectively separate noise components from fault-related signals. This is reflected in the minimum envelope entropy (0.32, a key indicator of noise suppression: lower values mean less noise interference in IMF) and the highest corresponding diagnostic accuracy rate (80.95%). When K = 3, under-decomposition of the signal occurs: the high-frequency fault characteristic components (e.g., the impact frequency of rotor-stator friction) are lost, while low-frequency noise (e.g., hydraulic pulsation noise) is retained in the IMF. This leads to a significant increase in envelope entropy (above 0.52) and a decrease in diagnostic accuracy to 72.41% as the model cannot distinguish noise from fault features. When K = 7, over-decomposition introduces redundant noise modes (e.g., high-frequency electromagnetic interference is decomposed into independent IMFs), causing the envelope entropy to rebound to 0.41 and the diagnostic accuracy to decrease to 76.83%—the extra noise modes confuse the model’s feature learning, while training time increases by 37% due to redundant calculations.

In terms of the parameters of the OCSSA optimizer, the optimization of VMD parameters (center frequency and bandwidth) under 5 dB noise directly determines the noise filtering effect; the test results of population size N show that when N = 50, the algorithm’s global search capability is sufficient to explore the optimal VMD parameter space, avoiding the local optimization caused by N = 20 (insufficient search ability leads to suboptimal VMD parameters, resulting in incomplete noise filtering and an envelope entropy of 0.39, which is 12.3% higher than N = 50). Meanwhile, N = 50 avoids the computational redundancy of N = 100 (the envelope entropy only decreases by 0.01 compared with N = 50, but the computing time increases by 35%), achieving a balance between noise suppression and efficiency.

The test results of the number of iterations T show that under 5 dB noise, sufficient iterations ensure that OCSSA converges to the optimal VMD parameters for noise reduction—when T = 100, the optimization process is fully converged, and the VMD parameters (K = 5) are adjusted to the state where noise is maximally filtered, resulting in an envelope entropy of 0.32 and an accuracy of 80.95%. When T = 50, the optimization is incomplete—VMD parameters are not adjusted to the optimal noise-filtering state, so the envelope entropy remains high (0.38), and accuracy decreases to 76.52%. When T = 200, the envelope entropy only slightly decreases by 0.7% (to 0.31), but the calculation time increases by 24%—the marginal gain in noise suppression is negligible, while efficiency is reduced.

In conclusion, under 5 dB low SNR, the parameter combination of K = 5, N = 50, and T = 100 achieves the best balance between noise suppression (minimum envelope entropy), fault feature retention (highest accuracy), and computational efficiency.

The parameter convergence characteristics of the OCSSA algorithm are shown in Figure 1. Figure 5a shows the influence of population size N on the optimization process. When N = 20, the algorithm falls into local optimum due to insufficient search ability. When N = 100, although the final convergence value is slightly better, the convergence speed slows significantly. When N = 50, the algorithm quickly reaches a stable optimal solution after 40 iterations. Figure 5b shows the convergence characteristics of the number of iterations T. When T = 50, the optimization does not fully converge, and the envelope entropy value is relatively high. When T = 200, although the envelope entropy slightly decreases, the convergence efficiency significantly decreases. When T = 100, after approximately 80 iterations, it enters the stable platform area, achieving the best balance between convergence speed and accuracy.

To comprehensively evaluate the core performance of the OCSSA optimization algorithm, this study conducted tests through four standard test functions (F1–F4) and carried out comparative experiments with the SA, ACO, and WOA; the experimental results are shown in Figure 6. The test functions cover different optimization scenarios. F1 (Sphere function) is a simple convex function that contains only a single global optimal solution and is used to test local search accuracy and basic convergence speed. F2 (Rastrigin function) is a multimodal function containing a large number of local optimal solutions, which focus on evaluating the ability of global optimization and jumping out of local extremum. F3 (Griewank function) is a high-dimensional complex function with densely distributed local optimal solutions, used to verify the stability of optimization in high-dimensional spaces. F4 (Michalewicz function) is a high-dimensional multimodal function. The number of local optimal solutions increases exponentially with the dimension, rigorously verifying the optimization potential in complex scenarios. The experiment uniformly sets the population size to 30 and the maximum number of iterations to 100. Taking the fitness value (the minimum value of the function) as the evaluation index, OCSSA basically converges at 40 times on F1, and the final fitness value is significantly lower than that of other algorithms, demonstrating a stronger local fine search ability. In F2, ACO and SA have high fitness values due to their tendency to fall into local optima. Although WOA can escape from local optima to a certain extent, its convergence accuracy is limited. However, OCSSA, through the Fishhawk-dive global search and the Cauchy mutation local escape mechanism, balanced optimization accuracy, convergence speed, and robustness are achieved, verifying its ability to break through local optima. On high-dimensional nonlinear functions such as F3 and F4, the fitness value of OCSSA always remains the lowest, and the convergence curve fluctuates the least. Particularly, in F4, its value is nearly 40% lower than that of the suboptimal WOA, indicating that it can still maintain stable and efficient optimization performance in complex solution spaces.

3.3.3 Stability verification of OCSSA–VMD tuning

To evaluate the stability of the OCSSA–VMD tuning pipeline and prepare for deployment, we conducted rigorous repetitive experiments. We ran the entire optimization process independently using 10 different random seeds (42, 123, 789, 2023, 5555, 8888, 9999, 10001, 31415, 27182), with each run including OCSSA algorithm initialization, VMD parameter optimization, and final CNN–LSTM model training and testing. The results are shown in Table 7.

TABLE 7. OCSSA–VMD tuning with multiple random seeds for stability verification.

The symbol “*” indicates the corresponding fault type based on the measured data.

We conducted rigorous repetitive experiments to evaluate the stability of the OCSSA–VMD tuning pipeline and its applicability to engineering deployment. We independently ran the entire optimization and diagnosis process using 10 different random seeds and quantitatively analyzed the results. In terms of parameter stability, the optimal modal number K* fluctuated mainly between 4 and 5, and 80% of the random seeds converged to K = 5; the average value of the penalty factor α* was 1252, with a standard deviation of 78, and the coefficient of variation was as low as 6.2%. This indicates that the OCSSA algorithm can stably find the performance-closer optimal parameter region within the preset search space and output results with good consistency. In terms of performance stability, the average test accuracy of the models obtained from 10 independent runs was 94.12%, with a standard deviation of only 0.18%. This extremely small performance fluctuation demonstrates that the entire diagnosis process from parameter optimization to model training has a high degree of repeatability and that significant differences are not apparent due to random initialization. The convergence behavior also demonstrates robustness, with an average convergence iteration number of 67 times and a standard deviation of 4.3 times, indicating that the algorithm can effectively converge under different initializations and does not exhibit premature or oscillation phenomena. In summary, the above stability verification has clear deployment readiness, indicating that the proposed OCSSA–VMD–CNN–LSTM diagnosis framework in this study does not rely on a specific random seed. In practical engineering applications, this characteristic ensures that the diagnosis system can stably output high-performance and highly consistent diagnostic results when deployed in different times and computing environments, thus fundamentally meeting the core requirements of the predictive maintenance system for reliability.

3.3.4 Experimental ablation of the OCSSA algorithm components

To analyze the sources of performance improvement of the OCSSA algorithm in depth and quantify the individual contributions of the introduced Osprey-inspired exploration mechanism and the Cauchy mutation operator to VMD parameter optimization, this section designs a systematic ablation study. This research employs three comparison models to contrast with the OCSSA model: the original optimization algorithm SSA, SSA + OA, and SSA + Cauchy. The experiments are conducted in a unified optimization environment, where the optimization objective is to minimize the minimum envelope entropy after VMD. The search space is the modal number K ∈ {3, 4, 5, 6, 7}, the penalty factor α ∈ [50, 3000] (on a logarithmic scale), population size N = 50, the maximum number of iterations T = 100, and the same typical fault signal sample under 5 dB Gaussian white noise is used as the optimization object. Each algorithm runs independently 20 times, and the best envelope entropy, convergence iteration number, and optimization stability obtained by each algorithm are recorded. Subsequently, the optimal parameters (K, α) obtained by each algorithm are applied to the same CNN–LSTM diagnostic model, and diagnostic accuracy is evaluated at 5 dB and 20 dB noise levels to quantify the impact of the front-end parameter optimization on the final diagnostic performance. The experimental results are shown in Table 8.

TABLE 8. Experimental results of the OCSSA algorithm component ablation study.

The results of the ablation experiments on the OCSSA algorithm show that each component makes a clear contribution to the optimization performance. Compared with the baseline SSA algorithm, only introducing the Osprey optimization mechanism to SSA + OA reduces the mean of the best envelope entropy by 18.2%, while the convergence speed is increased by approximately 30%. This verifies that its “dive and hunt” mechanism can significantly enhance the global exploration ability and effectively avoid getting stuck in local stagnation in the early stage of the search. While only introducing the Cauchy variation to SSA + Cauchy reduces the mean of the best envelope entropy by 26.4%, it performs best in terms of improving optimization accuracy, indicating that the long-tail distribution characteristic of the Cauchy variation can effectively assist the population escape from the local optimum in the later iterations and achieve more refined local development. The complete OCSSA algorithm achieves the lowest envelope entropy (0.321) and the highest diagnostic accuracy rate, with the smallest standard deviation of results and best stability. This demonstrates that the Osprey optimization and Cauchy variation have a clear synergistic effect: the OA mechanism drives rapid global exploration in the early and middle stages, laying the foundation for the population distribution, while the Cauchy variation provides refined local search and escape ability in the middle and later stages, with the two complementing each other and jointly achieving the dynamic balance of exploration and development.

Furthermore, the improvement of the front-end parameter optimization effect is strongly positively correlated with the improvement of the back-end diagnostic performance. SSA + OA and SSA + Cauchy independently increased the diagnostic accuracy rate under 5 dB noise by 4.5 and 6.2 percentage points, demonstrating their respective values. The diagnostic performance improvement achieved by the complete OCSSA (8.65 percentage points at 5 dB) exceeded the sum of their independent contributions, which further confirmed the existence of the synergistic gain at the application level. Specifically, under the 20 dB high signal-to-noise ratio condition, OCSSA increased the accuracy rate to 97.50%, indicating that the VMD parameters optimized by OCSSA can purify the fault features to the greatest extent, providing an almost ideal data representation for the subsequent CNN–LSTM network.

In conclusion, the ablation experiments show that the Osprey optimization mechanism and Cauchy variation are the key contributors to the performance improvement of the OCSSA algorithm. The former mainly accelerates global convergence, while the latter mainly improves optimization accuracy and robustness. They are not simply superimposed but form the basis of the excellent performance of the OCSSA algorithm through the collaborative mechanism of “exploration guidance in the early and middle stages and fine-tuning variation in the later stages”; this provides a useful reference for the structural design of intelligent optimization algorithms in complex engineering parameter optimization problems.

3.4 Fault identification effect of the VMD–CNN–LSTM coupling model

In this study, the VMD–CNN–LSTM coupling model is adopted to identify the mechanical fault signals of the pumping station unit, and the effect of the model under different noise levels is evaluated. The recognition performance of the model is visually demonstrated through the confusion matrix and the classification result graph (Figure 7). At a noise level of 5 dB, the classification accuracy of the model exceeds 80%. The confusion matrix shows that most fault types can be accurately identified, but there is still a certain degree of confusion among some. As the signal-to-noise ratio is raised to 10 dB, the diagnostic accuracy of the model further approaches 90%. The confusion matrix shows that the recognition accuracy of various faults has significantly improved, and the classification results are clearer, demonstrating its superior performance in a high-noise environment. At a noise level of 15 dB, the classification accuracy of the model exceeds 90%, and most fault types can be identified with high precision. When the signal-to-noise ratio reaches 20 dB, the model achieves the best recognition effect. The classification accuracy of each fault type is close to 95%, the false diagnosis in the confusion matrix is significantly reduced, and the classification results are almost completely consistent with the real situation.

It is apparent from the above analysis that the VMD–CNN–LSTM-coupled model can maintain high recognition accuracy under different noise levels, especially performing well in environments with higher signal-to-noise ratios. This verifies the effectiveness and robustness of the model in the classification task of complex fault signals, providing reliable technical support for practical applications.

To further evaluate the model performance and align it with engineering operation and maintenance requirements, this section calculates the accuracy, recall rate, and F1 score for each category based on the confusion matrix shown in Figure 7 at a 20 dB signal-to-noise ratio and analyzes the key misclassified pairs. The results are presented in Table 9.

TABLE 9. Various fault diagnosis performance indicators under a 20 dB signal-to-noise ratio.

3.5 Comparison of recognition effects of different models

To comprehensively evaluate the superiority of the proposed model under complex operating conditions, this section compares the OCSSA–VMD–CNN–LSTM model with its variants using different signal decomposition methods under various noise backgrounds. The complete ensemble empirical mode decomposition (CEEMDAN) and Hilbert Vibration Decomposition (HVD) are selected as the comparison benchmarks, based on their wide application and representativeness in the field of signal processing. The test environment covers Gaussian white noise (GWN, 5/20 dB), impulse noise (IN, 5 dB), narrowband interference (NBI, 5 dB), and real field noise collected from actual pumping stations to simulate the complex electromagnetic, hydraulic, and sudden interference during the operation of the unit. In addition to the accuracy rate, the F1 score is also reported to comprehensively evaluate the precision and recall rate. The comprehensive comparison results are shown in Table 10.

TABLE 10. Different model recognition results.

As shown in Table 10, in all tested noise environments, the accuracy and F1 score of the model proposed here (OCSSA–VMD–CNN–LSTM) are significantly and stable and superior to those of the models based on CEEMDAN and HVD. Particularly, in the most challenging real-field noise background, the accuracy of this model (78.63%) is 8.48 and 9.73 percentage points higher than those of CEEMDAN–CNN–LSTM (70.15%) and HVD–CNN–LSTM (68.90%), respectively. This strongly confirms the conclusion of the relevant comparative study, that VMD, with its variational framework’s mathematical rigor, has structural advantages in the orthogonality of decomposed modes and the ability to resist noise interference and can provide purer and more distinguishable features for subsequent deep networks.

By comparing the performance of CEEMDAN–CNN–LSTM and OCSSA–CEEMDAN–CNN–LSTM under various noises (such as an accuracy increase from 74.80% to 77.35% under 5 dB GWN), it can be observed that the OCSSA algorithm itself has general parameter optimization capabilities. However, when OCSSA is combined with VMD, the performance improvement (compared to the unoptimized VMD baseline or the equally optimized CEEMDAN model) is even more significant. This indicates that the OCSSA algorithm plays a decisive role in fully “activating” VMD’s potential under complex conditions. Dynamic and precise optimization enables VMD’s bandwidth constraints and center frequency parameters to adaptively match different noise backgrounds, thereby maximizing the theoretical advantages of VMD into actual diagnostic performance. This is the core technical feature in which the model can achieve a comprehensive leading advantage.

The interpretation of the robustness to different noises reveals the intrinsic mechanism of the model, as follows.

Anti-pulse noise (IN). The suddenness of pulse noise has the greatest impact on the HVD method, which relies on instantaneous amplitude features, resulting in the most significant missed detection. The global optimization characteristic of VMD in the frequency domain enables it to have a certain “isolation” ability against sudden impacts, while the optimization of OCSSA strengthens this characteristic, allowing the model to still maintain the lowest missed detection tendency and the highest F1 score (74.88%) under 5 dB IN—crucial for preventing latent faults caused by sudden impacts.

Anti-narrowband interference (NBI). For fixed-frequency narrowband interference, the preset bandwidth constraint mechanism of VMD shows its advantages. It can effectively limit and compress the energy of narrowband interference within the specific IMF near the center frequency and then separate it from the IMF rich in fault impulses based on the envelope entropy criterion. Therefore, the performance of this model under NBI is the smallest decline, with an accuracy rate (82.15%) that is significantly higher than other models.

Real-field noise adaptability. Real-field noise components are complex, non-Gaussian, and non-stationary, posing the greatest challenge to all models. Under these conditions, this model still maintains the highest diagnostic performance (accuracy rate 78.63%, F1 score 77.25%), indicating that the OCSSA-VMD combination has strong adaptive feature purification capabilities that are able to robustly extract essential fault features from highly mixed backgrounds, thereby demonstrating outstanding engineering generalization potential.

Based on the above analysis, the OCSSA–VMD–CNN–LSTM framework proposed in this study outperforms models based on other mainstream signal decomposition methods (CEEMDAN, HVD) in terms of diagnostic accuracy (accuracy), comprehensive performance (F1-score), and robustness to different types of interference. This aspect verifies the superiority of VMD as a preprocessor. On the other hand, and more importantly, it highlights the indispensability of using the intelligent optimization algorithm (OCSSA) to solve its parameter adaptation problem for fully realizing its potential and enhancing the project’s practicality.

3.6 Comparison of model generalization performance

To verify whether the improvements of OCSSA–VMD can be generalized across datasets, we use the actual monitoring data of Unit 5 of the Zhuchong Pumping Station (horizontal centrifugal pump, model 1200S56) from 2023 to 2024 for verification. This dataset contains samples of six types of states, including normal, rotor misalignment, rubbing, and coupling faults (a total of 4,800). The experimental results are shown in Table 11.

TABLE 11. Generalization verification results of the model based on data from Unit 5 of Zhuchong Pumping Station.

The compared models can be categorized into five groups to facilitate fair comparison: (i) single-network baselines without decomposition (CNN and LSTM); (ii) a hybrid baseline without decomposition (CNN–LSTM); (iii) decomposition-based hybrid models without parameter optimization (EMD–CNN–LSTM, CEEMDAN–CNN–LSTM, HVD–CNN–LSTM, and standard VMD–CNN–LSTM); (iv) optimized VMD-based models using different optimization algorithms (WOA–VMD–CNN–LSTM, ACO–VMD–CNN–LSTM, and the proposed OCSSA–VMD–CNN–LSTM); (v) other complex models for reference (GAT and SVM–CNN).

All training times reported in Table 11 are measured on the same hardware platform (NVIDIA RTX 3090) with identical training settings (epochs = 100, batch size = 32) and averaged over five independent runs to ensure statistical reliability.

The OCSSA–VMD–CNN–LSTM model demonstrates significant comprehensive advantages across all categories. In terms of single-type fault identification, it achieves the highest accuracy for normal states (98.5%), rotor misalignment (96.2%), and rubbing faults (95.8%). Even for the most challenging categories—coupling faults (with the most complex mechanism) and impeller fouling (with the most ambiguous features)—it maintains relatively high accuracies of 92.3% and 90.7%, respectively.

Regarding overall performance, the proposed model achieves an average accuracy of 94.28%, outperforming WOA–VMD–CNN–LSTM (91.60%) by 2.68 percentage points and ACO–VMD–CNN–LSTM (90.92%) by 3.36 percentage points. This confirms that the OCSSA optimization is more suitable for the “mechanical–hydraulic” coupled vibration signals of pumping stations. Compared with decomposition-based models without optimization, the advantages are even more pronounced: the proposed model surpasses SA–CNN–LSTM (87.70%), VMD–CNN–LSTM (84.93%), and EMD–CNN–LSTM (86.00%) by 6.58, 9.35, and 8.28 percentage points, respectively.

In terms of training efficiency, the proposed model requires 18.65 s on average. This is only marginally higher than the single-network baselines (CNN: 16.54 s, LSTM: 18.30 s) and hybrid baseline CNN–LSTM (16.43 s) while being substantially lower than more complex models such as GAT (43.26 s) and SVM–CNN (36.42 s). This indicates that the performance gain achieved by OCSSA–VMD preprocessing does not come at the expense of excessive computational overhead.

The generalization error—defined as the performance drop from the laboratory dataset to the real-world dataset—further validates the model’s robustness. The proposed model achieves the lowest generalization error of 3.22%, significantly lower than VMD–CNN–LSTM (12.57%), EMD–CNN–LSTM (11.50%), CNN–LSTM (13.87%), and SVM–CNN (15.72%). This demonstrates that the performance improvement stems from genuine cross-scenario adaptability rather than overfitting to a single dataset.

In contrast, models such as GAT and SVM–CNN not only yield lower average accuracies (82.3% and 81.2%, respectively) but also exhibit generalization errors exceeding 13%, while their training times are substantially higher, making them less suitable for real-time engineering applications. These results collectively highlight the balanced trade-off achieved by the proposed OCSSA–VMD–CNN–LSTM model between diagnostic accuracy, computational efficiency, and cross-scenario generalization.

4 Discussion

4.1 Limitations of the method

This method and its experimental results still have the following limitations that need to be improved in future research. (1) Insufficient fusion of multi-physics field features. The current model only relies on vibration signals, while the faults of the pumping station unit are actually the result of the coupling effect of multiple physical fields such as hydraulic (e.g., cavitation and flow fluctuations), mechanical (e.g., bearing wear), and electromagnetic (e.g., motor stator faults). Relying solely on vibration signals may miss key information such as pressure pulsation and motor current—for example, the characteristics of cavitation faults are more easily captured through pressure signals, and a single vibration signal may lead to relatively low diagnostic accuracy for such faults. (2) Insufficient verification of generalization capability under actual working conditions. Model training and testing are based on laboratory simulation data. Although noises with different signal-to-noise ratios are added, there are differences from real pumping station sites—the site not only has Gaussian white noise but also complex factors such as frequent load fluctuations (e.g., sudden changes in water diversion flow), equipment aging (e.g., increased bearing clearance), and environmental temperature and humidity interference. Laboratory data is difficult for fully reproducing these scenarios, which may lead to a decrease in model accuracy when deployed on site. (3) The balance between model complexity and real-time performance needs optimization. Although the model’s training efficiency is superior to most comparison models, the series structure of VMD decomposition and CNN–LSTM still has certain computational overhead. To achieve online real-time diagnosis of pumping station units (requiring a response time of ≤1 s), the current model may affect early warning timeliness due to computational delays when processing large amounts of real-time data. (4) Lack of fault-early-warning capability. Existing research focuses on “diagnosis” after faults occur and thus fails to leverage the time-series modeling advantage of LSTM to capture early weak signs of faults (e.g., slight vibration offset in the early stage of rotor misalignment). Thus, it cannot achieve the closed loop of “fault early warning–predictive maintenance,” which aligns with the engineering site’s demand for “early detection and early handling.”

4.2 Core advantages of the VMD–CNN–LSTM coupling model

The core advantage of this model lies in its ability to maintain a diagnostic accuracy rate of 80.95% even in a 5 dB extremely low signal-to-noise ratio environment—an increase of 12.72 percentage points compared to the traditional CNN–LSTM model. This result precisely addresses the core pain points of “strong noise and weak fault characteristics” in the actual operation of pumping station units. In previous studies, Ma and Zhang (2025) achieved higher search efficiency through RIME optimization of VMD but did not conduct performance verification under extremely low signal-to-noise ratios. Zhou et al. (2020) processed the original vibration signals of hydraulic pumps using PSO-VMD, but the accuracy rate was only 91.25%. Zhang and others (Binqiao et al., 2026) constructed the RIME–VMD and TTAO–CNN–LSTM–attention fault diagnosis model. Although they optimized the network structure to enhance its generalization ability, and the fusion of multiple modules solved the problems of overfitting and low accuracy, the accuracy rate under 5 dB noise was only 68.3%. Compared with this, the VMD-CNN-LSTM model optimized by OCSSA proposed here not only shows a higher accuracy rate in the original signal but also has the highest accuracy and F1 score in multiple scenarios such as Gaussian white noise (5 dB), impulse noise, narrowband interference, and real-site noise. This advantage verifies the structural advantages of VMD compared to CEEMDAN and HVD decomposition methods—the mathematical framework based on variational constraints makes the model components more orthogonal. Combined with the parameter optimization of OCSSA, it can more robustly cope with the complex interference in the pumping station site. This model does not rely on cross-domain data transfer and achieves excellent generalization performance through its own preprocessing and modeling mechanism, reducing the data dependency cost in engineering applications. The domain contribution of this study mainly lies in three aspects. First, it quantifies the correlation between VMD parameters (K, α) and the fault diagnosis performance of pumping stations, provides a reusable parameter optimization benchmark through parameter sensitivity analysis, and compensates for the subjective setting of VMD parameters in previous studies. Second, the proposed OCSSA algorithm provided a new solution for complex engineering optimization problems, and its performance in four standard test functions was superior to traditional algorithms such as SA, ACO, and WOA, which can be extended to other signal processing or model optimization scenarios. Third, the end-to-end diagnosis framework constructed promotes the transformation of pumping station unit fault diagnosis from “experience-driven” to “data–model collaborative-driven”, providing a new technical path for the intelligent operation and maintenance of cross-basin water diversion projects.

5 Results

This study addresses the fault diagnosis requirements of the pumping station unit under strong noise and variable operating conditions by proposing the OCSSA–VMD–CNN–LSTM-coupled model. It focuses on optimizing performance, noise resistance, and generalization capabilities in three core dimensions. The main conclusions are as follows.

• The proposed OCSSA demonstrates outstanding optimization performance. By integrating an Osprey-inspired global search strategy with a Cauchy mutation for local perturbation, this enhanced SSA variant effectively overcomes the local optima limitation common in traditional optimization algorithms. It achieves a precise adaptive optimization of VMD parameters (K, α), resulting in a minimum envelope entropy of 0.32 for the fault signal. The optimal parameter combination (K = 5, α = 1252) is determined, resulting in the minimum envelope entropy of the fault signal being reduced to 0.32. Compared with algorithms such as SSA and WOA, OCSSA has lower fitness values in standard test functions, with a 30% increase in convergence speed, providing high-purity IMF components for feature extraction and serving as the core support for improving model performance.
• The proposed framework exhibits exceptional noise resistance and robustness. By synergistically combining the OCSSA–VMD preprocessing module for signal purification with the CNN–LSTM network for spatiotemporal feature extraction, the model maintains high diagnostic accuracy across various complex noise scenarios. As comprehensively demonstrated in Section 3.5 (Table 10), it significantly outperforms benchmark models under low SNR conditions, impulse noise, and narrowband interference while also generalizing effectively to real-site noise. This validates its ability to overcome the multi-source interference prevalent in pumping station environments.
• (3) Significant generalization and engineering practicality. On the real monitoring data of the #5 unit of Zhuchong Pumping Station, the proposed model achieves an average diagnostic accuracy of 94.28% with a generalization error of only 3.22%, which is substantially lower than comparison models such as EMD–CNN–LSTM (11.50%) and GAT (15.18%). Furthermore, its training time (∼18.7 s) remains comparable to the baseline CNN–LSTM (∼16.4 s) and considerably lower than more complex models (e.g., GAT: ∼43 s), demonstrating that the performance gain does not come at the expense of impractical computational overhead. This balance between accuracy and efficiency makes the model suitable for the online predictive maintenance of pumping station units.

In summary, by systematically addressing parameter optimization, noise resilience, and cross-scenario generalization, the proposed OCSSA–VMD–CNN–LSTM model provides a robust and practical technical pathway for the predictive maintenance of pumping station units and has potential for extension to other complex rotating machinery.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Author disclaimer

The statements, opinions, and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of Frontiers and/or the editor(s). Frontiers and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Footnotes

Edited by: Kamil Dimililer, Near East University, Cyprus

Reviewed by: Marco Civera, Polytechnic University of Turin, Italy

Youssef Kassem, Near East University, Cyprus

Shih-Lin Lin, National Changhua University of Education, Taiwan