Rolling bearing fault diagnosis algorithm based on improved VMD optimized CNN-GRU neural network

Abstract

The invention provides a rolling bearing fault diagnosis algorithm based on an improved VMD optimized CNN-GRU neural network. The rolling bearing fault diagnosis algorithm aims at solving the problem that early faults of a rolling bearing are difficult to recognize under complex working conditions. The method comprises the steps of providing an OCSSA algorithm fusing an eagle algorithm and a Cauchy variation strategy, realizing adaptive optimization of VMD parameters, remarkably relieving modal aliasing, and improving signal decomposition precision; according to the method, the CNN-GRU end-to-end deep diagnosis framework is constructed, time-frequency fusion features are automatically extracted, time sequence dependence is modeled, and dependence on artificial features is reduced; the model performance is verified on a CWRU bearing data set, the average recognition accuracy rate reaches 98.67%, compared with a mainstream model, the precision and operation efficiency are obviously improved, and the good generalization ability and engineering application potential are achieved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of mechanical fault diagnosis, and more particularly to a rolling bearing fault diagnosis algorithm based on an improved VMD optimized CNN-GRU neural network. BACKGROUND

[0002] When rolling bearings are operated under harsh conditions such as high load and variable load, problems such as wear, corrosion and damage are prone to occur. Bearing faults account for more than 40% of all motor faults. If the rolling bearing faults in the motor cannot be detected in time, the consequences are that the equipment will be shut down, causing economic losses to the enterprise, or even threatening human health and life, and causing negative social impact. Therefore, it is of great significance to carry out high-precision, intelligent and low-delay fault diagnosis on rolling bearings.

[0003] In recent years, the research on rolling bearing fault diagnosis mainly focuses on signal processing, machine learning and deep learning. Signal processing techniques include time domain, frequency domain and time-frequency analysis. Due to the nonlinear and non-stationary characteristics of rolling bearing fault vibration signals under complex working conditions, time-frequency analysis methods are often used for fault diagnosis. Typical methods include short-time Fourier transform (STFT), wavelet analysis, empirical mode decomposition (EMD), variational mode decomposition (VMD) and singular value decomposition (SVD). With a significant increase in the amount of mechanical equipment fault data, relying solely on expert subjective analysis of signal features will result in unsatisfactory diagnostic accuracy. Bearing fault signals have significant time series correlation, and traditional methods have obvious shortcomings in establishing long-term dependence models. Single model architectures (such as GRU, LSTM and CNN) have inherent limitations in terms of diagnostic accuracy and computational efficiency. Although CNN performs well in automatic feature extraction through local convolution operations, its modeling capability for long-term dependencies in time series (such as the periodic evolution characteristics of impact waveforms) is limited, making it difficult to effectively capture the gradual development of faults. On the other hand, when GRU directly processes original high-dimensional vibration signals, it lacks the ability to extract fine local time-frequency features, making it susceptible to background noise interference and thus affecting classification performance. In addition, GRU has an early key information forgetting phenomenon when processing long time series, further restricting the correlation analysis of cross-period fault features.

[0004] These studies show that the integration of efficient feature extraction, strong robustness and lightweight model structure will be an important development direction for future fault diagnosis systems. Although existing methods have made some progress in fault diagnosis performance, they still generally face limitations such as complex model structure, strong parameter dependence, high risk of modal aliasing and low computational efficiency, making it difficult to balance accuracy, robustness and practicality.

[0005] To address the above problems, this paper proposes a rolling bearing fault diagnosis algorithm based on an improved VMD optimized CNN-GRU neural network for high-precision intelligent diagnosis of rolling bearing faults. Summary of the invention:

[0006] To achieve efficient and accurate identification of bearing faults, this paper constructs a rolling bearing fault diagnosis algorithm based on an improved VMD-optimized CNN-GRU neural network. This model fully integrates the advantages of signal decomposition, deep feature extraction, and time series modeling. First, an OCSSA algorithm is designed that combines the global optimization capabilities of Osprey search with the Cauchy mutation local perturbation mechanism to achieve adaptive optimization of the penalty factor and number of modes in variational mode decomposition (VMD), effectively suppressing modal aliasing. Subsequently, an end-to-end deep diagnostic framework is constructed, using a CNN to extract time-frequency fusion features from the decomposed signal, and introducing a gated recurrent unit (GRU) to model long-term dependencies in the sequence, thereby improving the ability to identify weak fault signatures.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A rolling bearing fault diagnosis algorithm based on an improved VMD optimized CNN-GRU neural network includes the following specific steps:

[0009] 1. Signal preprocessing and parameter optimization.

[0010] 2. Feature component selection and frequency feature acquisition.

[0011] 3. Deep feature extraction.

[0012] 4. Timing modeling and fault classification.

[0013] Here is a complete process introduction.

[0014] Preferably, the signal preprocessing and parameter optimization are performed in step 1. The specific process is as follows:

[0015] After normalizing and preprocessing the collected raw vibration signals, the Osprey–Cauchy–Sparrow search algorithm (OCSSA) is introduced to adaptively optimize the key parameters in VMD—the penalty factor α and the modal number K. The optimal parameter combination is determined by minimizing the fitness function value and substituted into the VMD for signal decomposition.

[0016] The improved sparrow search algorithm, Osprey-Cauchy-Sparrow Search Algorithm (OCSSA), is a new hybrid intelligent optimization algorithm based on the traditional Sparrow Search Algorithm (SSA)

[13] , the Osprey Optimization Algorithm (OOA)

[14] and the Cauchy Mutation strategy. The algorithm aims to overcome the problems of the original SSA, such as being easily trapped in local optimum and unstable convergence speed, so as to improve the optimization performance in high-dimensional complex search space. Specifically, the following three improvements are made to the sparrow algorithm:

[0017] 1) Population initialization stage: In order to improve the diversity and uniformity of the initial population, this paper introduces the Logistic chaotic mapping as the population initialization strategy. Chaotic mapping has ergodicity and randomness, which helps to expand the coverage of the solution space and enhance the global search ability of the algorithm.

[0018] Logistic chaotic mapping is a typical complex nonlinear behavior method, and its formula is as follows:

[0019]

[0020] Where μ is the parameter that determines the mapping behavior, is the chaotic mapping between .

[0021] 2) Global exploration stage (first stage):

[0022] The position updating method of the "discoverer" individual in the traditional SSA is replaced by the updating mechanism of the Osprey Optimization Algorithm. The Osprey Algorithm simulates the movement of the Osprey in the air to track the prey, which can perform a jump search in the solution space and avoid the problem of over-reliance on the position of the previous generation of individuals in the SSA. Specifically, the Osprey Algorithm updates the position of the search individual in multiple directions by introducing random detection and attacking the food source position, and its position updating formula is as follows:

[0023]

[0024] Where is the new position of the nth Osprey in the first stage, is the new position of the nth Osprey in the first stage in the m-dimensional space, is the objective function in the m-dimensional space, SF n is the fish selected by the nth Osprey, SF n,m is the m-dimensional space, r n,m ∈[0,1] is a random number, I n,mis a random number. This strategy significantly enhances the algorithm's ability to escape local traps and cover the solution space in the early stages of the search.

[0025] 3) Local development stage (second stage): The Cauchy mutation strategy

[15] is used to replace the position update method of the "follower" individual in the original SSA. The new position of the follower is updated as follows.

[0026]

[0027] where cauchy(0, 1) is a standard Cauchy distribution function, denotes multiplication.

[0028] The Cauchy distribution function is a continuous probability distribution function used to describe certain types of random variables. Its probability density function (PDF) is as follows:

[0029]

[0030] where x0 is the location parameter representing the center of the distribution, and γ is the scale parameter representing the width of the distribution.

[0031] Compared with the standard normal distribution, the Cauchy distribution has a smaller probability density at the origin, a more gentle distribution on both sides, and a longer tail, so it has greater perturbation ability. The introduction of the Cauchy distribution into the individual position perturbation can effectively expand the search range and improve the algorithm's ability to escape local optimal traps, thereby enhancing the algorithm's global convergence and robustness.

[0032] Preferably, the feature component selection in step 2 is combined with frequency feature acquisition. The specific process is as follows:

[0033] The minimum envelope entropy is used to construct the fitness function, evaluate all IMF components, and select the most representative modal component to obtain the key frequency feature.

[0034] Preferably, the deep feature extraction in step 3 is as follows:

[0035] The CNN is used to perform multi-scale convolution operation on the signal after VMD decomposition, extract its time-frequency domain fusion features, and effectively capture local waveform changes and key pattern information.

[0036] Preferably, the time series modeling and fault classification in step 4 are as follows:

[0037] The feature sequence output by the CNN is input into the GRU network to model the time dependence in the fault data, and to realize classification and prediction of the fault type.

[0038] Compared with the prior art, the rolling bearing fault diagnosis algorithm based on the improved VMD optimized CNN-GRU neural network provided in the technical solution has the characteristics that the intelligent optimization algorithm and the deep fusion modeling are combined, the feature learning ability and the robustness are strong, and the diagnosis precision and the response speed under complex working conditions can be effectively improved. Time series modeling and classification: the time dependence relationship in the fault data is modeled by using the GRU network, and the classification of the fault type is realized; the intelligent optimization algorithm and the deep learning model are combined, the high-precision and high-efficiency diagnosis of the early fault of the rolling bearing is realized, and the engineering practicability and the popularization value are strong. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 : OCSSA-VMD-CNN-GRU fault diagnosis model flow chart

[0040] Figure 2 : Case Western Reserve University bearing test bench schematic diagram

[0041] Figure 3 : OCSSA optimized VMD iteration convergence curve

[0042] Figure 4 : IMF component diagram after VMD decomposition

[0043] Figure 5 : Comparison of confusion matrix diagrams of the same model

[0044] Figure 6 : Comparison of classification result diagrams of different models DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0046] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application. Figures 1-6 The present application will be further described in detail, and a rolling bearing fault diagnosis algorithm based on an improved VMD optimized CNN-GRU neural network is proposed, which includes the following steps: 1, signal preprocessing and parameter optimization; 2, feature component selection and frequency feature acquisition; 3, deep feature extraction; 4, time series modeling and fault classification. The OCSSA-VMD-CNN-GRU fault diagnosis model flow chart is as shown in Figure 1 .

[0047] Step 1, signal preprocessing and parameter optimization.

[0048] Step 2, feature component selection and frequency feature acquisition.

[0049] Step 3, deep feature extraction.

[0050] Step 4, time series modeling and fault classification.

[0051] In step 1, signal preprocessing and parameter optimization. The specific process is as follows:

[0052] After normalizing and preprocessing the collected original vibration signals, the Osprey-Cauchy-Sparrow Search Algorithm (OCSSA) is introduced to adaptively optimize the key parameters in VMD, namely the penalty factor α and the modal number K. The optimal parameter combination is determined by the minimum fitness function value, and it is substituted into VMD for signal decomposition.

[0053] The improved Sparrow Search Algorithm, Osprey-Cauchy-Sparrow Search Algorithm (OCSSA), is a new hybrid intelligent optimization algorithm based on the traditional Sparrow Search Algorithm (SSA), combining the Osprey Optimization Algorithm (OOA) and the Cauchy Mutation strategy. This algorithm aims to overcome the problems of the original SSA, such as being easily trapped in local optima and unstable convergence speed, thereby improving the optimization performance in high-dimensional complex search space. Specifically, the following three improvements are made based on the Sparrow Algorithm:

[0054] 1) Population initialization stage: To improve the diversity and uniformity of the initial population, this paper introduces the Logistic chaotic mapping as the population initialization strategy. Chaotic mapping has ergodicity and randomness, which helps to expand the coverage of the solution space, thereby enhancing the global search ability of the algorithm.

[0055] Logistic chaotic mapping is a typical complex nonlinear behavior method, and its formula is as follows:

[0056]

[0057] where μ is the parameter that determines the mapping behavior, isthe chaotic mapping between

[0058] 2) Global exploration stage (first stage):

[0059] The position updating method of the "discoverer" individual in the traditional SSA is replaced by the updating mechanism of the fish eagle optimization algorithm. The fish eagle algorithm can perform a jump global search in the solution space by simulating the movement trajectory of the fish eagle in the air to track prey, and avoid the problem of over-reliance on the position of the previous generation of individuals in SSA. Specifically, the fish eagle algorithm updates the position of the search individual in a multi-directional propulsion manner by introducing random detection and attack of food source positions, and its position updating formula is as follows:

[0060]

[0061] wherein is the new position of the nth fish eagle in the first stage, is the new position of the nth fish eagle in the first stage in the m dimension, is the objective function in the m dimension, SF n is the fish selected by the nth fish eagle, SF n,m is the m dimension, r n,m ∈[0,1] is a random number, I n,m ∈{1,2} is a random number. This strategy significantly enhances the ability of the algorithm to jump out of the local and the coverage range of the solution space in the early search stage.

[0062] 3) Local development stage (second stage): The position updating method of the "follower" individual in the original SSA is replaced by the Cauchy mutation strategy. The new position of the follower is updated as follows.

[0063]

[0064] wherein cauchy(0,1) is a standard Cauchy distribution function, denotes multiplication.

[0065] The Cauchy distribution function is a continuous probability distribution function used to describe certain types of random variables. Its probability density function (PDF) is as follows:

[0066]

[0067] wherein x0 is a location parameter representing the center of the distribution, and γ is a scale parameter representing the width of the distribution.

[0068] Compared with the standard normal distribution, the Cauchy distribution has a smaller probability density at the origin, a more gentle distribution on both sides, and a longer tail, so it has greater disturbance ability. Introducing the Cauchy distribution into individual position disturbance can effectively expand the search range and improve the algorithm's ability to jump out of the local optimal trap, thereby enhancing the algorithm's global convergence and robustness. The following are the specific improvements of the improved sparrow search algorithm (OCSSA). After normalizing and preprocessing the collected original vibration signals, the fish-eagle-Cauchy-sparrow search algorithm (OCSSA) is introduced to adaptively optimize the key parameters of VMD, namely the penalty factor α and the modal number K. The optimal parameter combination is determined by the minimum fitness function value, and it is substituted into VMD for signal decomposition. The improved sparrow search algorithm, fish-eagle-Cauchy-sparrow search algorithm (OCSSA), is a new hybrid intelligent optimization algorithm based on the traditional sparrow search algorithm (Sparrow Search Algorithm, SSA) and the fusion of the Osprey Optimization Algorithm (OOA) and the Cauchy Mutation strategy. The algorithm aims to overcome the problems of the original SSA, such as easy to fall into local optimum and unstable convergence speed, thereby improving the optimization performance in high-dimensional complex search space.

[0069] The experimental data used in this study were from a public dataset, and the experimental platform was as shown in Figure 2 In this study, the rolling bearing used in the experiment was the drive end bearing (bearing model 6205-2RSJEMSKF), and the data acquisition frequency was 12 kHz. In the experiment, ten fault categories were established, including four types of states: normal bearing, rolling element fault, outer ring fault, and inner ring fault. According to the fault diameters 0.007, 0.014, and 0.021 in, each fault state was further classified, and three fault types were selected in each fault diameter, resulting in nine different states representing different degrees of fault. A total of 120 samples were collected for each state, and the data length of each sample was 1x2048 points. At the same time, in the experimental setup, 90 samples were allocated for model training, and 30 samples were reserved for model testing.

[0070] S11: Specific implementation case:

[0071] The specific experimental conditions are shown in Table 1:

[0072] Table 1: Ten fault types

[0073] Failure Sequence Number Failure Diameter / inch Failure Type 1 0 Normal 2 0.007 Inner Ring Failure 3 0.007 Rolling Element Failure 4 0.007 Outer Ring Failure 5 0.014 Inner Ring Failure 6 0.014 Rolling Element Failure 7 0.014 Outer Ring Failure 8 0.021 Inner Ring Failure 9 0.021 Rolling Element Failure 10 0.021 Outer Ring Failure

[0074] The VMD-CNN-LSTM, VMD-CNN-GRU, OCSSA-VMD-CNN-BiLSTM and OCSSA-VMD-CNN-GRU models are compared in the comparative experiment, and the training set and test set are divided in a ratio of 8:2. In this experiment, from the perspective of whether the early weak fault of the rolling bearing can be identified, the performance of the OCCSA-VMD-CNN-GRU model for the multi-level classification problem of the rolling bearing fault is verified.

[0075] Meanwhile, the OCSSA algorithm is used to globally optimize the key parameters (penalty factor a and mode number K) of VMD to determine the optimal parameter combination, from Figure 3 As can be seen from the figure, the VMD variational mode decomposition is optimized using OCSSA, and gradually converges with the increase of the number of iterations. Figure 4 The figure shows the VMD mode decomposition after the optimal parameters and penalty factors obtained by using OCSSA optimization, which is decomposed into the following 10 imf components.

[0076] In step 2, feature component selection and frequency feature acquisition: use the minimum envelope entropy to construct the fitness function, evaluate all IMF components, and select the most representative modal component to obtain the key frequency feature. The specific process is as follows:

[0077] Calculate the envelope entropy of each IMF component, construct the fitness function and parameter optimization, select the representative IMF component, and extract the key frequency feature.

[0078] In step 3, deep feature extraction: use CNN to perform multi-scale convolution operation on the signal decomposed by VMD, extract its time-frequency domain fusion feature, and effectively capture local waveform changes and key pattern information. The specific process is as follows:

[0079] Through multi-scale convolution and feature fusion, fine feature extraction of bearing fault signal is realized, which provides high-discrimination input for subsequent GRU time series modeling, and finally achieves industry-leading diagnostic performance on the CWRU dataset.

[0080] In step 4, time series modeling and fault classification: input the feature sequence output by CNN into GRU network to model the time dependence in fault data, realize the classification and prediction of fault type. The specific process is as follows:

[0081] In order to evaluate the performance of OCSSA-VMD-CNN-GRU, the model proposed in this paper is compared with other three models. Figure 5 and Figure 6The confusion matrix and classification results of fault diagnosis of the four models are shown. After repeated verification, the OCSSA-VMDCNN-GRU model shows superior performance, with an identification accuracy of 96.7% for normal bearings and 100% for all other 9 types of faults. The overall identification accuracy for 10 types of faults is 99.67%. In addition, the identification speed of the OCSSA-VMD-CNN-GRU model has also been significantly improved, proving its effectiveness in fault diagnosis. Deep learning methods such as CNN-LSTM, CNN-GRU and VMD-CNN-GRU perform very well in fault identification, usually with higher accuracy than traditional machine learning methods. The combination of technologies such as VMD and OCSSA further improves the accuracy of fault identification. This analysis shows that the method combining deep learning and optimization technology has a significant advantage in multi-class fault identification tasks, providing strong support for practical engineering applications.

[0082] At the same time, Table 2 lists the average running time data of each model under the same hardware and experimental conditions. The results show that the traditional VMD-CNN-LSTM model has a long running time (6.71 seconds), while the introduction of the OCSSA optimization strategy and the GRU architecture significantly improves the computational efficiency of the model. In summary, the proposed model has high precision while maintaining fast response capability, and has strong engineering practicability and deployment value.

[0083] Table 2 Specific running time comparison

[0084] Model Running Time / s VMD-CNN-LSTM 6.706626 VMD-CNN-GRU 4.476807 OCSSA-VMD-CNN-BiLSTM 4.272857 OCSSA-VMD-CNN-GRU 3.919142

[0085] The present application proposes a rolling bearing fault diagnosis method combining variational mode decomposition and deep learning model, which decomposes, optimizes and reconstructs the data signal by variational mode decomposition. Then the adaptive feature extraction ability of CNN and the long-term and short-term dependence of GRU are used, while avoiding the complexity of manual feature extraction and the problem of gradient disappearance or gradient descent. Because GRU has a simpler structure than LSTM, GRU dynamically adjusts the fusion of historical information and current input through update gate and reset gate, realizing long-term dependence modeling of time series features. Therefore, this method simplifies the network structure, speeds up the training speed and improves the accuracy. The proposed method is verified on the XJTU-SY rolling bearing dataset, proving its effectiveness in rolling bearing fault diagnosis. The present application first introduces GRU into the VMD-CNN diagnosis model, combines OCSSA parameter optimization, and realizes the balance between accuracy and efficiency in rolling bearing fault diagnosis. The present application can provide technical support for online monitoring systems of key equipment such as wind turbines and high-speed rail bearings, and is especially suitable for industrial scenarios with strict real-time requirements.

[0086] The foregoing description of the disclosed embodiments enables one skilled in the art to make or use the application. Numerous modifications of those embodiments can be apparent to those skilled in the art, and the generic principles defined herein can be applied to other embodiments without the use of the innovation falling outside the spirit and scope of the application. Therefore, the application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. Rolling bearing fault diagnosis algorithm based on improved VMD optimized CNN-GRU neural network. Characterized by: The method includes the following steps: To achieve efficient and accurate identification of bearing faults, this paper constructs a rolling bearing fault diagnosis algorithm based on an improved VMD-optimized CNN-GRU neural network. This model fully integrates the advantages of signal decomposition, deep feature extraction, and time series modeling, and includes the following steps:

1. Signal preprocessing and parameter optimization.

2. Feature component selection and frequency feature acquisition.

3. Deep feature extraction.

4. Timing modeling and fault classification. in: In step 1, signal preprocessing and parameter optimization are performed. The specific process is as follows: After normalizing and preprocessing the collected raw vibration signals, the Osprey–Cauchy–Sparrow search algorithm (OCSSA) is introduced to adaptively optimize the key parameters in VMD—the penalty factor α and the modal number K. The optimal parameter combination is determined by minimizing the fitness function value and substituted into the VMD for signal decomposition. The improved Sparrow Search Algorithm, the Osprey-Cauchy-Sparrow Search Algorithm (OCSSA), is a novel hybrid intelligent optimization algorithm built on the traditional Sparrow Search Algorithm (SSA) by integrating the Osprey Optimization Algorithm (OOA) with the Cauchy Mutation strategy. This algorithm aims to overcome the problems of the original SSA, such as its tendency to fall into local optima and unstable convergence speed, thereby improving optimization performance in high-dimensional complex search spaces. Specifically, this paper improves the Sparrow Search Algorithm in the following three aspects: 1) Population Initialization: To improve the diversity and distribution uniformity of the initial population, this paper introduces the Logistic Chaos Map as a population initialization strategy. The chaotic map is ergodic and random, which helps expand the solution space coverage, thereby enhancing the algorithm's global search capability. Logical chaos mapping is a typical complex nonlinear behavior method, and its formula is as follows: where μ is a parameter that determines the mapping behavior, yes Chaotic mapping between . 2) Global Exploration Phase (Phase I): The position update mechanism of the "discoverer" individual in traditional SSA is replaced with the update mechanism of the Osprey optimization algorithm. By simulating the trajectory of an osprey tracking its prey in mid-air, the Osprey algorithm performs a leap-like global search in the solution space, avoiding the over-reliance on the individual's previous generation position in SSA. Specifically, the Osprey algorithm introduces random detection and attack on the location of food sources, guiding the searcher to update in a multi-directional manner. Its position update formula is as follows: in is the new position of the nth osprey in the first phase, is the new position of the nth osprey in the m dimension in the first stage, is the objective function in its m-dimension, SF n It is the fish chosen by the nth osprey, SF n,n is its m dimension, r n,m ∈[0,1] is a random number, I n,m ∈{1,2} is a random number. This strategy significantly enhances the algorithm’s ability to escape locality and the coverage of the solution space in the early stages of the search. 3) Local development phase (second phase): The Cauchy mutation strategy is used to replace the position update method of the "follower" individual in the original SSA. The new position update of the follower is as follows. Where cauchy(0,1) is the standard Cauchy distribution function, Represents multiplication. The Cauchy distribution is a continuous probability distribution function used to describe certain types of random variables. Its probability density function (PDF) is as follows: Where x0 is the location parameter representing the center of the distribution, and γ is the scale parameter representing the width of the distribution. Compared to the standard normal distribution, the Cauchy distribution has a lower probability density at the origin, a flatter distribution, and a longer tail, resulting in greater perturbation resistance. Introducing the Cauchy distribution into individual position perturbations effectively expands the search range and improves the algorithm's ability to escape local optima, thereby enhancing its global convergence and robustness. The specific process of feature component selection and frequency feature acquisition in step 2 is as follows: The fitness function is constructed using the minimum envelope entropy to evaluate all IMF components, and the most representative modal components are selected to obtain the key frequency characteristics. The depth feature extraction in step 3 is as follows: CNN is used to perform multi-scale convolution operations on the signal after VMD decomposition to extract its time-frequency domain fusion features and effectively capture local waveform changes and key pattern information. The specific process of timing modeling and fault classification in step 4 is as follows: The feature sequence output by CNN is input into the GRU network to model the temporal dependency in the fault data and realize the classification and prediction of the fault type. This paper proposes a rolling bearing fault diagnosis method that combines variational mode decomposition with a deep learning model. This method uses variational mode decomposition to decompose, optimize, and reconstruct data signals. The method then leverages the adaptive feature extraction capabilities of CNNs and the long- and short-term dependencies of GRUs, avoiding the complexity of manual feature extraction and the problem of vanishing gradients or gradient descent. Because GRUs have a simpler structure than LSTMs, they dynamically adjust the fusion of historical information and current inputs through update and reset gates, modeling the long-term dependencies of temporal features. Consequently, this method simplifies the network structure, accelerates training, and improves accuracy. The proposed method was validated on the XJTU-SY rolling bearing dataset, demonstrating its effectiveness in rolling bearing fault diagnosis. This method, based on the first introduction of GRUs into the VMD-CNN diagnostic model and combined with OCSSA parameter optimization, achieves a balance between accuracy and efficiency in rolling bearing fault diagnosis. This method can provide technical support for online monitoring systems for key equipment such as wind turbines and high-speed rail bearings, and is particularly suitable for industrial scenarios with stringent real-time requirements.

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