Fault diagnosis method of variable speed bearings based on wavelet-driven physically interpretable networks

Abstract

The present invention relates to the technical field of bearing faults, and in particular to a variable speed bearing fault diagnosis method using a wavelet-driven physically interpretable network. The method comprises using an acceleration sensor to collect bearing fault signal samples, employing a short-time Fourier transform to calculate a time-frequency diagram of the vibration signal; employing a local peak search algorithm to extract the instantaneous speed from the time-frequency diagram of the vibration signal; employing a fast Fourier transform (FFT) to convert the time-domain fault vibration signal into a frequency-domain signal; constructing and training a learnable wavelet-driven physically interpretable network (LWPI) based on the extracted instantaneous speed information; and implementing fault diagnosis using the trained LWPI network. The present invention utilizes signal processing technology to impart a certain physical meaning to a convolutional neural network, while integrating speed information into the construction of the convolutional neural network, thereby improving the accuracy of bearing fault diagnosis under variable speed conditions and enhancing the efficiency of research and economic production.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing failures, and in particular to a variable speed bearing failure diagnosis method based on a wavelet-driven physically interpretable network. Background Art

[0002] With the development of Industry 4.0, Predictive Health Management (PHM) of rotating machinery has attracted widespread attention in academia and industry, and equipment fault diagnosis plays a key role in PHM. As a key component of rotating machinery, the health of rolling bearings is crucial to the safe and stable operation of the equipment. Furthermore, in practical engineering, bearings often operate under variable speed conditions. Therefore, bearing fault diagnosis under variable speed conditions has attracted widespread attention.

[0003] Vibration signals contain rich state signals of mechanical equipment. Fault diagnosis methods based on vibration signal analysis can reliably identify the fault type based on the fault mechanism, so its diagnostic process has certain physical significance. Wavelet analysis, as a typical representative of traditional signal processing methods, has achieved remarkable results in bearing fault diagnosis. Li et al. proposed a mechanical fault diagnosis method based on empirical wavelet transform. Zhang et al. used orthogonal wavelet basis to transform vibration signals into the time-scale domain and performed envelope refinement spectrum analysis on the wavelet coefficients in the high-frequency scale domain to achieve rolling bearing fault diagnosis. However, traditional wavelet analysis methods require various parameters to be pre-set according to the diagnostic objectives and professional knowledge. In addition, most methods are applicable to rotating machinery with a fixed speed, and their diagnostic accuracy is greatly affected by speed changes. One of the more significant drawbacks is that traditional signal analysis methods have difficulty processing massive fault data.

[0004] Data-driven deep learning methods can not only adaptively mine fault features from raw data but also process massive amounts of data. However, deep learning methods extract local features using randomly initialized kernels within convolutional layers. Furthermore, their internal decision-making process operates as a "black box," making it difficult to interpret the physical meaning of the extracted features. To imbue neural networks with physical meaning, Li et al. employed a continuous wavelet convolutional layer as the first convolutional layer of a convolutional neural network and validated the robustness of their approach using various gearbox data. Jiang et al. designed a multi-wavelet kernel convolutional layer as the first layer of a neural network to localize and detect mechanical faults. Liu et al. leveraged bearing failure mechanisms to demodulate fault signals into multiple modal components, designed multiple filters, and combined these with the powerful feature extraction capabilities of neural networks to extract fault features and achieve fault classification. These studies provide significant research value in imbuing convolutional neural networks with physical meaning. However, due to the complex structure and operating environment of rotating machinery, vibration signals are often affected by speed fluctuations and interference from vibration signals of other components, which can reduce the performance of fault diagnosis models. These interpretable networks ignore the influence of operating speed, limiting their application in variable-speed bearing fault diagnosis. Deepening the network layer may improve the impact of speed fluctuations and enhance diagnostic capabilities, but the higher the network layer, the more abstract and difficult to interpret the feature graph, and its internal decision-making process is more difficult to understand. Summary of the Invention

[0005] The present invention discloses a bearing fault diagnosis method based on a learnable wavelet physics interpretability network. The specific method is as follows:

[0006] An interpretable network is constructed with Morlet wavelet multi-wavelet filter layer as the first layer and CNN convolution block as the second layer;

[0007] Obtain historical time domain vibration signals when bearing fails;

[0008] The historical time-domain vibration signal is processed by Fourier transform to obtain the historical frequency-domain vibration signal;

[0009] Train an interpretability network using historical frequency-domain vibration signals;

[0010] The current time domain vibration signal of the bearing is collected by the acceleration sensor, and the variable speed bearing fault is diagnosed using the trained interpretable network.

[0011] Furthermore, the key parameters of the interpretability network are determined by the historical time-domain vibration signal as follows:

[0012] The historical time-domain vibration signal is processed by short-time Fourier transform to obtain the historical time-frequency diagram, and the historical speed information is extracted from the historical time-frequency diagram using an improved local peak search algorithm.

[0013] The key parameters of the Morlet wavelet and multi-wavelet filter layers are fitted based on the historical speed information.

[0014] Furthermore, an improved local peak search algorithm is used to extract historical speed information from the historical time-frequency graph. The specific method is as follows:

[0015] The speed value μ(t1) at the first time point t1 in the historical time-frequency diagram is screened, and the frequency corresponding to the main spectrum peak is found according to the local maximum peak. The frequency obtained from the smallest to the largest frequency is μ(t1)=[μ 11 ,μ 12 ,…,μ 1n ], taking into account the interference of noise and nearby components in the time-frequency diagram, a penalty function is added to the local peak search algorithm:

[0016]

[0017] Among them, the local maximum peak of the time-frequency graph is:

[0018] P(t,μ(t))=|TFD(t,μ(t)| 2

[0019] The final penalty function of the local peak search algorithm is:

[0020]

[0021] Through the final penalty function of the local peak search algorithm, find the instantaneous rotation frequency corresponding to the minimum penalty function:

[0022]

[0023] in, is the instantaneous rotation frequency finally extracted at the i-th moment; is the lower limit of frequency search; is the upper limit of frequency search; c1, c2 are constants, μ(t k ) is the frequency value at time point i within the frequency search range; μ(t j ) is the instantaneous frequency extracted from time i and all previous times.

[0024] Furthermore, the key parameters of the Morlet wavelet multi-wavelet filter layer are fitted according to the historical speed information. The specific method is as follows:

[0025] According to the extracted instantaneous rotation frequency, the Morlet wavelet multi-wavelet filter layer is designed. The frequency domain expression of the Morlet wavelet is:

[0026]

[0027] Among them, β is the bandwidth parameter, which controls the width of the wavelet window in the frequency domain; f0 is the center frequency, which determines the position of the wavelet window on the frequency axis; f is the set frequency range;

[0028] When constructing the Morlet wavelet multi-wavelet filter layer, the bandwidth parameter β i and center frequency f i Obtained by fitting the extracted rotation frequency ridge:

[0029]

[0030] in, is the median frequency of the i-th time interval; n is the time interval divided when extracting the instantaneous rotation frequency; κ i0 , κ i1 , c i They are the bandwidth parameters β i and center frequency f i The fitting coefficient of the Morlet wavelet multi-wavelet filter layer is:

[0031]

[0032] The feature expression of the extraction of the i-th filter kernel is:

[0033] L i =ψ i (f)*F[x]

[0034] Where x is the original vibration signal and F[·] represents the Fourier transform.

[0035] Furthermore, the CNN convolution block consists of a convolution layer, a BN layer, a global pooling layer GAP and an activation function ReLU, which is expressed as:

[0036] Z = GAP(BN(ReLU(W×L+b)))

[0037] Where W and b are the weight and bias of the convolution layer, respectively; L is the fault feature extracted by the Morlet wavelet multi-wavelet filter layer; Z is the high-dimensional feature output by the convolution block;

[0038] The fully connected layer flattens the fault features extracted by the convolutional layer, and the expression is:

[0039] Z←flattening(Z)

[0040] q=ω z Z+b z

[0041] Among them, ω z and b zare the weights and biases of the classifier. The softmax function is used to classify the input features. The expression is:

[0042]

[0043] Among them, S is the number of fault categories, o i is the predicted probability of the i-th category;

[0044] The cross-entropy loss is used to measure the distribution of predicted labels and true labels, and its expression is:

[0045]

[0046] Among them, r i is the true probability of fault category i.

[0047] Furthermore, the interpretability network is trained with historical frequency-domain vibration signals. The specific method is as follows:

[0048] The historical frequency domain vibration signals are randomly divided into training set and test set;

[0049] During the training process, according to the chain rule, the weights of the convolution kernel and the key coefficients of the Morlet wavelet and multi-wavelet filter layers are optimized in the back-propagation process to obtain a trained interpretable network.

[0050] Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

[0051] The present invention uses signal processing technology to give the convolutional neural network a certain physical meaning, and at the same time integrates speed information into the construction of the convolutional neural network, thereby improving the accuracy of bearing fault diagnosis under variable speed conditions and improving the efficiency of research and economic production.

[0052] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings of the present invention are described below.

[0054] Figure 1 Construct graph for Morlet wavelet multiwavelet filter layer;

[0055] Figure 2 It is a schematic diagram of the overall process of the present invention;

[0056] Figure 3Diagnostic accuracy diagram of different diagnostic models on a self-made variable speed bearing dataset;

[0057] Figure 4 This is a diagram demonstrating the physical meaning of the features extracted by the Morlt wavelet filter layer at a speed of 500 rpm;

[0058] Figure 5 This is a diagram demonstrating the physical meaning of the features extracted by the Morlt wavelet filter layer at a speed of 1000 rpm;

[0059] Figure 6 This is a diagram demonstrating the physical meaning of the features extracted by the Morlt wavelet filter layer at a speed of 1500 rpm;

[0060] Figure 7 The results of extracting the rotation frequency using the local peak search algorithm for IA-2 under accelerated conditions before and after improvement.

[0061] Figure 8 The rotation frequency extraction results of OB-2 under deceleration conditions before and after the improvement of the local peak search algorithm. DETAILED DESCRIPTION

[0062] The present invention will be further described below with reference to the accompanying drawings and examples.

[0063] A bearing fault diagnosis method based on learnable wavelet physics interpretability network, such as Figure 2 The specific steps are as follows:

[0064] S1. Obtain the historical time domain vibration signal when the bearing fails.

[0065] In step S1, a variable speed vibration signal is collected by an acceleration sensor.

[0066] S2. Use short-time Fourier transform to process the time-domain vibration signal to obtain a time-frequency diagram, and use a local peak search algorithm to extract the speed information from the time-frequency diagram. The specific method is as follows:

[0067] The speed value μ(t1) at the first time point t1 in the time-frequency diagram (TFD) is screened, and the frequency corresponding to the main spectrum peak is found according to the local maximum peak. The frequency obtained from the smallest to the largest frequency is μ(t1) = [μ 11 ,μ 12 ,…,μ 1n Taking into account the interference of noise and nearby components in the time-frequency diagram, a penalty function is added to the local peak search algorithm:

[0068]

[0069] Among them, the local maximum peak of the time-frequency graph is:

[0070] P(t,μ(t))=|TFD(t,μ(t)| 2 (2)

[0071] Combining formulas (1) and (2), the final penalty function of the local peak search algorithm is:

[0072]

[0073] From formula (1) and formula (3), the penalty function of the local peak search algorithm can be obtained as:

[0074]

[0075] in, is the instantaneous rotation frequency finally extracted at the i-th moment; is the lower limit of frequency search; is the upper limit of frequency search; c1, c2 are constants, μ(t k ) is the frequency value at time point i within the frequency search range; μ(t j ) is the instantaneous frequency extracted from time i and all previous times.

[0076] S3. According to the historical speed information, the key parameters of Morlet wavelet are fitted and constructed as follows Figure 1 The specific method is as follows:

[0077] According to the extracted instantaneous rotation frequency, the Morlet wavelet multi-wavelet filter layer is designed. The frequency domain expression of the Morlet wavelet is:

[0078]

[0079] Among them, β is the bandwidth parameter, which controls the width of the wavelet window in the frequency domain; f0 is the center frequency, which determines the position of the wavelet window on the frequency axis; f is the set frequency range;

[0080] When constructing the Morlet wavelet multi-wavelet filter layer, the bandwidth parameter β i and center frequency f i Obtained by fitting the extracted rotation frequency ridge:

[0081]

[0082] in, is the median frequency of the i-th time interval; n is the time interval divided when extracting the instantaneous rotation frequency; κ i0 , κ i1 , c i They are the bandwidth parameters β i and center frequency f iThe fitting coefficient of the Morlet wavelet multi-wavelet filter layer is:

[0083]

[0084] The feature expression of the extraction of the i-th filter kernel is:

[0085] L i =ψ i (f)*F[x]

[0086] Where x is the original vibration signal and F[·] represents the Fourier transform.

[0087] S4. Use Fourier transform to process the historical time domain vibration signal to obtain the historical frequency domain vibration signal.

[0088] S5. The designed Morlet wavelet multi-wavelet filter layer is used as the first layer of LWPI, and the convolution block is used as the second layer. The CNN convolution block includes a convolution layer, a BN layer, a global pooling layer GAP and an activation function ReLU to form a convolution block, and its expression is:

[0089] Z = GAP(BN(ReLU(W×L+b)))

[0090] Where W and b are the weight and bias of the convolution layer, respectively; L is the fault feature extracted by the Morlet wavelet multi-wavelet filter layer; Z is the high-dimensional feature output by the convolution block;

[0091] The fully connected layer flattens the fault features extracted by the convolutional layer, and the expression is:

[0092] Z←flattening(Z)

[0093] q=ω z Z+b z

[0094] Among them, ω z and b z are the weights and biases of the classifier. The softmax function is used to classify the input features. The expression is:

[0095]

[0096] Among them, S is the number of fault categories, o i is the predicted probability of the i-th category;

[0097] The cross-entropy loss is used to measure the distribution of predicted labels and true labels, and its expression is:

[0098]

[0099] Among them, r i is the true probability of fault category i.

[0100] The historical frequency domain vibration signal information is randomly divided into a training set and a test set;

[0101] During the training process, according to the chain rule, the weights of the convolution kernel and the key coefficients of the Morlet wavelet multi-wavelet filter are optimized in the back-propagation process to obtain the trained LWPI network model.

[0102] The test set is input into the trained LWPI network model to achieve fault diagnosis.

[0103] S6. Collect the current time domain vibration signal of the bearing through the acceleration sensor; use Fourier transform to process the current time domain vibration signal to obtain the current frequency domain vibration signal; use the designed Morlet wavelet to process the current frequency domain vibration signal and extract the current preliminary diagnosis signal; use the trained CNN convolution block to identify the current preliminary diagnosis signal and obtain the final diagnosis result.

[0104] To verify the effectiveness, the method was validated on two datasets: a self-made variable-speed bearing dataset and an Ottawa variable-speed bearing dataset. The self-made bearing dataset consists of two experimental datasets: one conducted at time-varying speeds and the other at different constant speeds, including 500, 1000, and 1500 rpm. In both experiments, eight health categories were identified: 1) ball fault (BF); 2) combined fault of the inner raceway and ball (IB); 3) inner raceway fault (IF); 4) combined fault of the inner and outer raceways (IO); 5) normal (NO); 6) combined fault of the outer raceway and ball (OB); 7) outer raceway fault (OF); and 8) combined fault of the ball, inner raceway, and outer raceway (BIO). In the first experiment, vibration signals were collected from the eight healthy bearings during the acceleration (T1) and deceleration (T2) phases. A sensor was used to acquire the vibration signals, with a sampling frequency of 12 kHz. For each health category, the bearing vibration signal was divided into a total of 3656 samples using a sliding window technique with a window width of 3072 points. These time-domain signals are converted into spectra using Fast Fourier Transform (FFT). Considering the conjugate property of FFT data, the first half of the FFT data points are used as input. The ratio of training samples to test samples is set to 7:3.

[0105] In order to further verify the superiority of the model, five classic and cutting-edge models were compared: MWA-CNN, GTFE-Net, Morlet-LeNet and Morlet-AlexNet and MA1DCNN. At the same time, two ablation experimental models were constructed. One is the Morlet wavelet in the Morlet wavelet filter layer without parameter learning function FF-CNN, and the other is the entire network structure without Morlet wavelet filter layer FL-CNN. The diagnostic results of different models under two variable speed conditions are shown in Figure 2. Figure 3 As shown in the figure, it can be seen that the diagnostic accuracy of the proposed network structure LWPI is higher than that of the five classic and cutting-edge models, and it can effectively improve the accuracy of bearing fault diagnosis under variable speed. The physical meaning of the features extracted by the Morlet wavelet multi-wavelet filter layer is as follows Figures 4 to 6 As shown, Figures 4 to 6 The Morlet wavelet filter layer extraction results at different constant speeds are given. As can be seen from the figure, the vibration signals extracted at different constant speeds all have obvious fault characteristic frequencies, which shows that the features extracted by the Morlet wavelet filter layer have significant physical significance. Therefore, the convolutional neural network can be given a certain physical meaning.

[0106] To further verify the generalization of the model, further validation was conducted on the Ottawa variable-speed bearing dataset. Vibration signals collected from the dataset under acceleration (XA-2) and deceleration (XB-2) conditions were used. In this dataset, diagnostic experiments used four types of bearings: inner raceway fault, outer raceway fault, ball bearing fault, and normal. Under each health state, acceleration signals were collected for 10 seconds at a sampling frequency of 20 kHz. The signals were then segmented into 650 non-overlapping samples, each with a length of 3072. The training and test sets were also split in a 7:3 ratio.

[0107] The diagnostic accuracy of different models under two variable speed conditions is shown in the following table:

[0108]

[0109] The experimental results show that the proposed model has higher diagnostic accuracy than the five classical and cutting-edge models, further verifying the effectiveness and superiority of the proposed model. In addition, the local peak search algorithm before and after the improvement is also compared on this dataset, such as Figure 7 and Figure 8 As shown, Figure 7 and Figure 8The figures show the rotation frequency extraction results of the improved local peak search algorithm under the acceleration XA-2 and deceleration XB-2 speed conditions. It can be seen from the figure that the improved local peak search algorithm can effectively avoid the interference of noise and adjacent components and accurately extract the rotation frequency.

[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A variable speed bearing fault diagnosis method based on wavelet-driven physically interpretable network, characterized in that: The specific method is as follows: An interpretable network is constructed with Morlet wavelet multi-wavelet filter layer as the first layer and CNN convolution block as the second layer; Obtain historical time domain vibration signals when bearing fails; The historical time-domain vibration signal is processed by Fourier transform to obtain the historical frequency-domain vibration signal; Train an interpretability network using historical frequency-domain vibration signals; The current time-domain vibration signal of the bearing is collected by the acceleration sensor, and the variable speed bearing fault is diagnosed using the trained interpretable network. The key parameters of the interpretability network are determined by the historical time-domain vibration signal as follows: The historical time-domain vibration signal is processed by short-time Fourier transform to obtain the historical time-frequency diagram, and the historical speed information is extracted from the historical time-frequency diagram using an improved local peak search algorithm. The key parameters of the Morlet wavelet and multi-wavelet filter layers are fitted based on the historical speed information; The improved local peak search algorithm is used to extract historical speed information from the historical time-frequency graph. The specific method is as follows: The speed value μ(t1) at the first time point t1 in the historical time-frequency diagram is screened, and the frequency corresponding to the main spectrum peak is found according to the local maximum peak. The frequency obtained from the smallest to the largest frequency is μ(t1)=[μ 11 ,μ 12 ,…,μ 1n ], taking into account the interference of noise and nearby components in the time-frequency diagram, a penalty function is added to the local peak search algorithm: Among them, the local maximum peak of the time-frequency graph is: P(t,μ(t))=|TFD(t,μ(t)| 2 The final penalty function of the local peak search algorithm is: Through the final penalty function of the local peak search algorithm, find the instantaneous rotation frequency corresponding to the minimum penalty function: in, is the instantaneous rotation frequency finally extracted at the i-th moment; is the lower limit of frequency search; is the upper limit of frequency search; c1, c2 are constants, μ(t k ) is the frequency value at time point i within the frequency search range; μ(t j ) is the instantaneous frequency extracted from time i and all previous times.

2. The variable speed bearing fault diagnosis method based on wavelet-driven physical interpretable network according to claim 1 is characterized in that: The key parameters of the Morlet wavelet and multi-wavelet filter layers are fitted based on the historical speed information. The specific method is as follows: According to the extracted instantaneous rotation frequency, the Morlet wavelet multi-wavelet filter layer is designed. The frequency domain expression of the Morlet wavelet is: Among them, β is the bandwidth parameter, which controls the width of the wavelet window in the frequency domain; f0 is the center frequency, which determines the position of the wavelet window on the frequency axis; f is the set frequency range; When constructing the Morlet wavelet multi-wavelet filter layer, the bandwidth parameter β i and center frequency f i Obtained by fitting the extracted rotation frequency ridge: in, is the median frequency of the i-th time interval; n is the time interval divided when extracting the instantaneous rotation frequency; κ i0 , κ i1 , c i They are the bandwidth parameters β i and center frequency f i The fitting coefficient of the Morlet wavelet multi-wavelet filter layer is: The feature expression of the extraction of the i-th filter kernel is: L i =ψ i (f)*F[x] Where x is the original vibration signal and F[·] represents the Fourier transform.

3. The variable speed bearing fault diagnosis method based on wavelet-driven physically interpretable network according to claim 1 is characterized in that: The CNN convolution block consists of a convolution layer, a BN layer, a global pooling layer GAP and an activation function ReLU, which is expressed as: Z = GAP(BN(ReLU(W×L+b))) Among them, ω z and b z are the weights and biases of the classifier, L is the fault feature extracted by the Morlet wavelet multi-wavelet filter layer; Z is the high-dimensional feature output by the convolution block; The fully connected layer flattens the fault features extracted by the convolutional layer, and the expression is: Z←flattening(Z) q=ω z Z+b z Among them, W z and b z are the weights and biases of the classifier. The softmax function is used to classify the input features. The expression is: Among them, S is the number of fault categories, o i is the predicted probability of the i-th category; The cross-entropy loss is used to measure the distribution of predicted labels and true labels, and its expression is: Among them, r i is the true probability of fault category i.

4. The variable speed bearing fault diagnosis method based on wavelet-driven physically interpretable network according to claim 3 is characterized in that: The interpretability network is trained with historical frequency-domain vibration signals. The specific method is as follows: The historical frequency domain vibration signals are randomly divided into training set and test set; During the training process, according to the chain rule, the weights of the convolution kernel and the key coefficients of the Morlet wavelet and multi-wavelet filter layers are optimized in the back-propagation process to obtain a trained interpretable network.

Images