Rolling bearing fault diagnosis method based on Koopman operator and CWT

Abstract

The invention discloses a rolling bearing fault diagnosis method based on a Koopman operator and CWT, and belongs to the field of mechanical fault diagnosis, and the method comprises a denoising module, a CWT time-frequency feature extraction module and a CNN-GRU classification module. The denoising module performs dynamic modeling and denoising on the signals through a residual network based on a Koopman operator, and extracts main dynamic characteristics of the signals after noise separation; the CWT time-frequency feature extraction module performs multi-scale time-frequency analysis on the denoised signals, captures transient features and local modes of fault signals, and generates a time-frequency feature matrix; the CNN-GRU classification module fully extracts a space and time dependency relationship in the time-frequency features and maps the space and time dependency relationship into a fault category through a full connection layer. According to the method, the noise interference in the vibration signal is remarkably reduced, and the dynamic feature extraction capability and the fault diagnosis accuracy when the model processes the complex nonlinear fault signal are improved.

Description

Technical Field

[0001] The present invention relates to the field of mechanical fault diagnosis, and in particular to a rolling bearing fault diagnosis method based on Koopman operator and CWT. Background Art

[0002] Rolling bearings are core components of rotating machinery, and their fault diagnosis plays a key role in ensuring safe equipment operation and reducing maintenance costs. Currently, bearing fault diagnosis methods are primarily based on deep learning algorithms, which are mainly divided into two categories: those based on convolutional neural networks and those based on time series modeling and attention mechanisms.

[0003] Methods based on convolutional neural networks primarily leverage their local feature extraction capabilities to automatically learn the time-frequency domain features of bearing vibration signals. These methods typically convert one-dimensional vibration signals into two-dimensional time-frequency images through methods such as short-time Fourier transforms and wavelet transforms. They then use the convolutional and pooling layers of the convolutional neural network to abstract the local features and global structure of the image layer by layer, thereby identifying different types of bearing faults. However, these methods are relatively weak in capturing long-range dependencies in time series signals, while bearing fault signals often contain rich time series dynamic characteristics. When processing fault signals under non-stationary conditions, incomplete feature extraction can occur, resulting in reduced diagnostic accuracy.

[0004] Methods based on time series modeling and attention mechanisms focus on the time series characteristics of bearing vibration signals, modeling long-term dependencies in time series data through recurrent neural networks such as LSTM and GRU, or models such as Transformer. At the same time, the introduction of the attention mechanism enables the model to adaptively focus on key time points or key features in the fault signal, suppressing the interference of irrelevant noise, thereby improving the accuracy of fault diagnosis. However, in bearing fault diagnosis, fault features are often relatively weak and easily overwhelmed by strong background noise. The attention mechanism may lead to diagnostic bias due to learning the wrong key features. In addition, this type of method usually has high computational complexity and has high requirements for data volume and computing resources. In actual engineering applications, there may be problems with insufficient real-time performance.

[0005] To address the limitations of these two approaches, researchers have explored improvements. In the area of ​​convolutional neural networks, some studies have combined CNNs with long short-term memory (LSTM) networks to form hybrid CNN-LSTM models. These models leverage the advantages of CNNs for local feature extraction while capturing the long-term dependencies of temporal signals through LSTMs. In the area of ​​temporal modeling and attention mechanisms, researchers have designed lightweight attention modules (such as channel attention and temporal attention) to balance computational efficiency and feature focusing capabilities.

[0006] However, existing methods still have some issues that need to be addressed. First, bearing vibration signals in industrial sites are often mixed with background noise interference such as gear meshing noise, motor electromagnetic noise, and structural resonance noise, which makes it difficult to accurately identify bearing fault characteristics and affects the accuracy of fault diagnosis. In addition, when bearings operate under dynamic conditions such as variable speed and load, the fault signal exhibits nonlinear time-varying characteristics such as frequency modulation and amplitude modulation. The non-stationary nature of the signal can lead to misdiagnosis and missed diagnosis. Summary of the Invention

[0007] The purpose of the present invention is to propose a rolling bearing fault diagnosis method based on the Koopman operator and CWT. The method aims to improve the fault diagnosis model's denoising ability for the original vibration signal and the feature extraction ability for the non-stationary signal by constructing a denoising module based on the Koopman operator, a CWT time-frequency feature extraction module and a CNN-GRU classification module, thereby improving the accuracy of fault diagnosis.

[0008] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0009] The rolling bearing fault diagnosis method based on Koopman operator and CWT includes the following steps:

[0010] Step 1. Preprocess the raw bearing vibration data to construct a data set for training the rolling bearing fault diagnosis model based on the Koopman operator and CWT in step 2 below;

[0011] Step 2. Build a rolling bearing fault diagnosis model based on the Koopman operator and CWT, including a denoising module, a CWT time-frequency feature extraction module, and a CNN-GRU classification module;

[0012] The denoising module consists of four Koopmanblocks;

[0013] First, the original input signal is processed by the first Koopman block, and a linear dynamic processing based on the Koopman operator is performed to extract the main dynamic features of the signal. The original input signal is then subtracted from the output signal of the first Koopman block to generate a first residual signal.

[0014] Then, the residual signal is optimized through a multi-stage iterative method, the first residual signal is input into a second Koopman block for processing to generate a second processed signal; the first residual signal and the second processed signal are subjected to a difference operation to generate a second residual signal; the second residual signal is input into a third Koopman block for processing to generate a third processed signal; the second residual signal and the third processed signal are subjected to a difference operation to generate a third residual signal; the third residual signal is input into a fourth Koopman block for processing to generate a fourth processed signal; the third residual signal and the fourth processed signal are subjected to a difference operation to generate a fourth residual signal; the original input signal and the fourth residual signal are subjected to a difference operation to obtain a denoised reconstructed signal;

[0015] Finally, the denoised reconstructed signal is subjected to continuous wavelet transform to extract time-frequency features to generate a two-dimensional time-frequency feature matrix containing real and imaginary features. The fault type corresponding to the signal is obtained through the CNN-GRU classification network.

[0016] Step 3. Based on the data set established in step 1, the rolling bearing fault diagnosis model established in step 2 is trained to obtain a trained fault diagnosis model, and the trained bearing fault diagnosis model is used to determine the bearing fault type.

[0017] Compared with the existing technology, the rolling bearing fault diagnosis method of the present application uses a residual network based on the Koopman operator to dynamically model and denoise the vibration signal, reducing the interference of background noise; combined with CWT to perform multi-scale analysis of the denoised signal, it can capture the transient characteristics and local patterns of the fault signal and highlight the non-stationary nonlinear characteristics of the signal; through the CNN-GRU classification model, the joint extraction of local spatial features and temporal dynamic features is realized, improving the classification performance under complex conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 1 is an overall flow chart of a rolling bearing fault diagnosis method based on Koopman operator and CWT in an embodiment of the present invention;

[0019] Figure 2 This is a network structure diagram of the denoising module in this embodiment;

[0020] Figure 3 This is a network structure diagram of Koopmanblock in an embodiment of the present invention;

[0021] Figure 4 This is a network structure diagram of the CNN-GRU classification module in an embodiment of the present invention; DETAILED DESCRIPTION

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0023] This embodiment proposes a rolling bearing fault diagnosis method based on the Koopman operator and CWT to address issues such as susceptibility to noise interference and insufficient extraction of non-stationary, nonlinear features of the signal in existing methods. Specifically, the bearing fault diagnosis method reconstructs the current signal using a residual network based on the Koopman operator to reduce the impact of noise. It then uses the CWT to perform time-frequency analysis on the denoised signal to capture the nonlinear, time-varying features in the fault signal, improving the ability to extract non-stationary features. The CNN-GRU classification module is then used to capture local impact features in the time-frequency graph and their evolution over time, thereby improving the accuracy of fault diagnosis.

[0024] In this embodiment, the rolling bearing fault diagnosis method based on the Koopman operator and CWT includes the following steps:

[0025] Step 1. Obtain a public dataset and preprocess the raw bearing vibration data to construct a dataset for training the rolling bearing fault diagnosis model based on the Koopman operator and CWT in the following step 2.

[0026] The public dataset is the rolling bearing dataset of Case Western Reserve University. The sampling frequency of the selected original vibration data is 48kHz. It includes normal state and three fault types: inner ring fault, outer ring fault, and ball fault. The training set and test set are divided into 7:3 ratios.

[0027] First, the length of the original vibration data of the bearing is read to determine that the sample signal length is 1024. The original vibration data of the bearing is re-divided using a sliding window method with a sliding window overlap rate of 0.5. When the length is less than 1024, the last 1024 signals are taken as a sample signal.

[0028] Then save the resampled vibration signal in a new Excel table, with each row corresponding to a sample, and add a fault type label at the beginning of each row. The normal state label is 0, the 0.1778 mm inner ring fault label is 1, the 0.3556 mm inner ring fault label is 2, the 0.5334 mm inner ring fault label is 3, the 0.1778 mm outer ring fault label is 4, the 0.3556 mm outer ring fault label is 5, the 0.5334 mm outer ring fault label is 6, the 0.1778 mm ball fault label is 7, the 0.3556 mm ball fault label is 8, and the 0.5334 mm ball fault label is 9. The data after preprocessing is recorded as Where N is the number of samples and T is the number of time steps.

[0029] Step 2. Build a rolling bearing fault diagnosis model based on Koopman operator and CWT.

[0030] like Figure 1 As shown, the rolling bearing fault diagnosis method constructed in this embodiment includes a denoising module, a CWT time-frequency feature extraction module and a CNN-GRU classification module.

[0031] The denoising module consists of four Koopman blocks. Figure 2 As shown in the figure, the processing flow of the denoising module based on the Koopman operator is as follows:

[0032] First input signal After the first Koopmanblock processing, the linear dynamic processing based on the Koopman operator is performed to extract the main dynamic features of the signal, and the input signal is converted to Process the signal X with the output of the first Koopmanblock pred,1 Perform difference operation to generate the first residual signal R1=XX pred,1 .

[0033] Then, the residual signal is optimized by a four-level iterative method, and the first residual signal R1 is input into the second Koopman block for processing to generate a second processed signal X pred,2 ; The first residual signal R1 and the second processed signal X pred,2 Perform difference operation to generate the second residual signal R2 = R1-X pred,2 The second residual signal R2 is input to the third Koopman block for processing to generate a third processed signal X pred,3 ; The second residual signal R2 and the third processed signal X pred,3 Perform difference operation to generate the third residual signal R3 = R2-X pred,3 ; Input the third residual signal R3 to the fourth Koopman block for processing to generate a fourth processed signal X pred,4 ; The third residual signal R3 and the fourth processed signal X pred,4 Perform difference operation to generate the fourth residual signal R4 = R3-X pred,4 ; Perform a difference operation on the input signal X and the fourth residual signal R4 to obtain the denoised reconstructed signal X enhanced =X-R4.

[0034] Finally, the denoised reconstructed signal X enhanced The time-frequency features are extracted by CWT to generate a two-dimensional time-frequency feature matrix containing real and imaginary features, and the fault type corresponding to the signal is obtained through the CNN-GRU classification network.

[0035] like Figure 3 As shown, Koopmanblock includes an encoder, a Koopman operator, and a decoder, and its processing flow is as follows:

[0036] The input signal X is processed by an encoder composed of a multi-layer perceptron. Through linear transformation and nonlinear activation function (ReLU), the input signal X is mapped to a high-dimensional feature space to obtain a feature representation. Where d is the feature dimension, which is set to 128 in this method.

[0037] Then, by the formula Z pred =κ·Z modeling feature evolution process, where is the Koopman operator.

[0038] Then the decoder composed of a multi-layer perceptron is used for processing, and the formula X pred =Decoder(Z pred ) and X recon =Decoder(Z) reconstructs the high-dimensional features back to the signal space. The decoder has a symmetrical structure with the encoder.

[0039] In this process, the parameters of the encoder, Koopman operator and decoder are optimized simultaneously by the back propagation algorithm to minimize the total loss L = α·L dynmic +β·L recon Realize the feature extraction, prediction and reconstruction of nonlinear dynamic signals, where α and β are weight coefficients, L dynmic =||ZZ pred || 2 is the dynamic loss, L recon =||XX recon || 2 is the reconstruction loss.

[0040] The processing flow of the CWT time-frequency feature extraction module is as follows:

[0041] The reconstructed signal X after denoising enhanced Perform CWT processing: Save the real and imaginary parts of the CWT coefficients separately, denoted as and Where W(s,τ) represents the CWT coefficient at scale s and time displacement τ; X enhanced,t is the input signal; * (t) is the complex conjugate of the mother wavelet function. Morlet wavelet is selected in this method. S is the scale parameter, which is set to 5 to control the expansion and contraction of the wavelet and affect the frequency resolution. τ is the time displacement parameter, which controls the position of the wavelet on the signal.

[0042] like Figure 4 As shown, the processing flow of the CNN-GRU classification model is as follows:

[0043] First, the real part characteristics Imaginary part characteristics Perform 2D convolution operations separately and extract local time-frequency features in the same way and The processing process is expressed as:

[0044] F real =Conv2D(W real ), F imag =Conv2D(W imag ), where the convolution kernel size is 3×3, the stride is 1, the padding is 1, and the number of channels C' is 32. The process also includes a batch normalization layer, a ReLU activation function layer, and a maximum pooling layer.

[0045] Then the convolution output F real and F imag Merge along the channel dimension to obtain And using 1×1 convolution to reduce the number of channels from 64 to 16 we get This reduces computational complexity.

[0046] In order to convert the spatiotemporal features output by CNN into the sequence format required by GRU, the channel and scale dimensions are first moved to the time dimension, and the spatial dimension is flattened, and the channel and scale are merged into the feature dimension to obtain

[0047] Send it into the three-layer stacked GRU network structure and take the last time step hidden state of the third layer GRU As a global time series feature, the hidden state dimension is 64 and the activation function is tanh.

[0048] Then the global time series features are fed into the fully connected layer to map the 64-dimensional features output by the GRU to 10 types of fault spaces. The calculation process is expressed as:

[0049]

[0050] Finally, the classification probability is obtained through the Softmax activation function.

[0051] In this process, the cross entropy loss is defined to optimize the goal of minimizing the difference between the predicted distribution and the true label.

[0052] The above description is merely a preferred embodiment of the present invention, and the present invention is not limited to the above-mentioned embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the substantive scope of this specification and should be protected by the present invention.

Claims

1. A rolling bearing fault diagnosis method based on Koopman operator and CWT, characterized in that: The following steps are involved: Step 1. Preprocess the raw bearing vibration data to construct a data set for training the rolling bearing fault diagnosis model based on the Koopman operator and CWT in step 2 below; Step 2. Build a rolling bearing fault diagnosis model based on the Koopman operator and CWT, including a denoising module, a CWT time-frequency feature extraction module, and a Conv-GRU classification module; The denoising module consists of four Koopmanblocks; First, the original input signal is processed by the first Koopman block, and a linear dynamic processing based on the Koopman operator is performed to extract the main dynamic features of the signal. The original input signal is then subtracted from the output signal of the first Koopman block to generate a first residual signal. Then, the residual signal is optimized through a multi-stage iterative method, the first residual signal is input into a second Koopman block for processing to generate a second processed signal; the first residual signal and the second processed signal are subjected to a difference operation to generate a second residual signal; the second residual signal is input into a third Koopman block for processing to generate a third processed signal; the second residual signal and the third processed signal are subjected to a difference operation to generate a third residual signal; the third residual signal is input into a fourth Koopman block for processing to generate a fourth processed signal; the third residual signal and the fourth processed signal are subjected to a difference operation to generate a fourth residual signal; the original input signal and the fourth residual signal are subjected to a difference operation to obtain a denoised reconstructed signal; Finally, the denoised reconstructed signal is subjected to continuous wavelet transform to extract time-frequency features to generate a two-dimensional time-frequency feature matrix containing real and imaginary features, and the fault type corresponding to the signal is obtained through the Conv-GRU classification network; Step 3. Based on the data set established in step 1, the rolling bearing fault diagnosis model established in step 2 is trained to obtain a trained fault diagnosis model, and the trained bearing fault diagnosis model is used to determine the bearing fault type.

2. The rolling bearing fault diagnosis method based on Koopman operator and CWT according to claim 1 is characterized in that: The Koopmanblock processing flow includes: First, a multi-layer perceptron is used as an encoder to perform nonlinear mapping on the input signal X to generate a high-dimensional feature space representation Z; Then, the Koopman operator is applied in the high-dimensional feature space to perform a linear transformation on the current high-dimensional feature Z to generate the predicted feature Z pred ; Finally, the multi-layer perceptron is used as a decoder to predict the feature Z pred Decode back to the original dimension to generate the decoded signal X recon ; The parameters of the encoder, Koopman operator and decoder are optimized simultaneously by the back propagation algorithm to minimize the total loss L = α·L dynmic +β·L recon Realize the feature extraction, prediction and reconstruction of nonlinear dynamic signals, where α and β are weight coefficients, L dynmic is the dynamic loss, L dynmic =||ZZ pred || 2 , L recon is the reconstruction loss, L recon =||XX recon || 2 .

3. The rolling bearing fault diagnosis method based on Koopman operator and CWT according to claim 1 is characterized in that: The Conv-GRU classification module processing flow includes: Performing a two-dimensional convolution operation on the real part and the imaginary part of the time-frequency feature matrix to extract local spatial features; Apply the ReLU activation function to introduce nonlinear transformation; Reduce the dimension of the feature map through the maximum pooling layer to retain the salient features; Use the Dropout layer to randomly discard some neuron outputs to alleviate overfitting; The real and imaginary features are concatenated and channel dimension reduction is performed through 1×1 convolution to generate comprehensive features; Expand the comprehensive features along the time dimension and input them into a 3-layer stacked GRU network to extract global temporal features; The global time series features are linearly transformed through a fully connected layer, and then the probability distribution of each fault category is generated through a softmax function to determine the fault type corresponding to the original input signal.

4. The rolling bearing fault diagnosis method based on Koopman operator and CWT according to claim 1, characterized in that: The pretreatment includes: The bearing vibration signal data comes from the CWRU bearing fault dataset; First, read the length of the original bearing vibration data and determine that the sample signal length is 1024. Then, use a sliding window method to re-divide the original bearing vibration data. The sliding window overlap rate is 0.

5. When the length is less than 1024, the last 1024 signals are taken as a sample signal. Then save the resampled strictly faulty signal in a new Excel spreadsheet, with each row corresponding to one sample, and add a fault type label at the beginning of each row; Fault types include normal state, inner ring fault, outer ring fault, and ball fault. Each fault type includes three cases with fault diameters of 0.1778 mm, 0.3556 mm, and 0.5334 mm. The fault labels are recorded as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 respectively.

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