Single-domain generalizable and physically interpretable bearing fault diagnosis method
Through amplitude normalization and angle domain resampling, time-frequency diagrams are generated and fault pattern recognition is combined with convolutional neural networks, the single domain generalization and physical interpretability problems of bearing fault diagnosis in the prior art are solved, and reliable diagnosis is achieved in the unknown target domain.
Patent Information
- Application Number
- CN202510417224.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-03
- Publication Date
- 2025-08-01
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
The existing bearing fault diagnosis method based on deep learning has deteriorated performance under operating conditions or noise differences, and the decision-making process is opaque, making it difficult to achieve single-domain generalization and physically interpretable fault diagnosis.
The bearing vibration signals are processed through amplitude normalization and angle domain resampling, a time-frequency diagram is generated, and a convolutional neural network is combined to identify fault patterns, and a heat map is used to generate a heat map to explain the diagnostic results.
The bearing fault diagnosis generalized to unknown target domains in a single source domain is realized, eliminating the impact of speed changes, providing explainable fault feature recognition, and improving the reliability and transparency of the diagnosis.
Smart Images
Figure CN120408398A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of bearing fault diagnosis, and particularly relates to a bearing fault diagnosis method that is single-domain generalizable and physically interpretable. Background Art
[0002] Rolling bearings are the core components of rotating machinery, used to reduce friction and improve operating efficiency. However, they are long-term affected by corrosion, insufficient lubrication, and load, with a failure rate as high as 30% of the total mechanical failures, seriously threatening equipment safety and increasing operation and maintenance costs.
[0003] In the prior art, diagnostic methods based on deep learning extract features through signal processing (such as time-frequency analysis) and combine convolutional neural networks (CNNs) to achieve fault classification. Although they perform well in specific scenarios, there are some defects. Traditional methods rely on the consistency of the training and test data distributions. In practice, due to differences in working conditions (speed, load) or noise, the performance drops significantly. Domain adaptation methods require simultaneous acquisition of source domain and target domain data, making it difficult to handle unknown or continuously changing industrial scenarios. Moreover, the decision-making process of deep learning models is opaque and has weak physical interpretability. Existing interpretation techniques only visualize the data activation patterns and cannot associate with the physical characteristics (such as characteristic frequencies) of bearing faults, resulting in users being unable to verify the reliability of decisions and being prone to misjudgments due to domain shifts. Therefore, there is an urgent need for a diagnostic solution that can be generalized from a single source domain to an unknown target domain and provide interpretable results based on physical characteristics to improve the reliability and adaptability of industrial applications. Summary of the Invention
[0004] To solve the deficiencies of the prior art and achieve the purposes of improving fault diagnosis performance, expanding the applicable industrial scenarios, enhancing fault transparency and interpretability, and avoiding misjudgments, the present invention adopts the following technical solutions:
[0005] A bearing fault diagnosis method that is single-domain generalizable and physically interpretable, comprising the following steps:
[0006] Perform amplitude normalization and angular domain resampling on the acquired bearing vibration signal to address domain differences, enabling domain-invariant representations in the time domain and frequency domain, achieving single-domain generalization (SDG), and obtaining a preprocessed signal;
[0007] Perform envelope analysis on the preprocessed signal and generate a time-frequency diagram based on the obtained envelope spectrum;
[0008] Construct a neural network to perform pattern recognition of the fault mode sequence on the time-frequency diagram to classify bearing faults.
[0009] Further, in order to eliminate the influence of angular velocity on the vibration signal, the original bearing vibration signal is divided by the square of the rotational frequency, then normalized to zero mean and unit standard deviation, and a standardized bearing vibration signal v n (t) is generated based on the zero mean and unit standard deviation.
[0010] Further, since the bearing vibration signal v n (t) varies with the rotational speed and the frequency of the impact excitation signal also varies with time, resulting in domain differences in the frequency domain. In order to obtain impact excitation signals with equal intervals and balance the calculation cost and accuracy, the cubic spline interpolation method is adopted. A cubic polynomial is used for interpolation between every two data points, while ensuring the continuity of the first and second derivatives. A smooth and continuous estimated value is calculated at each target angle sampling point to obtain an angle resampled signal v n (θ):
[0011] v n (θ) = Interpolate{θ(t), v n (t)}
[0012] where, v n (t) represents the bearing vibration signal, and θ(t) represents the angle signal;
[0013] The angle domain conversion makes the signal no longer affected by the rotational speed change. The fault impact characteristic order is stable, and different bearing faults will generate specific characteristic orders. The specific formulas are as follows:
[0014]
[0015] where, OBPFO, OBPFI, and OBSF respectively represent the outer race fault order, inner race fault order, and ball fault order of the bearing; f BPFO , f BPFI and f BSF respectively represent the outer race fault frequency, inner race fault frequency, and ball fault frequency of the bearing; f r represents the rotational speed; D b , D c respectively represent the rolling element diameter and pitch diameter of the bearing; N b represents the number of rolling elements, and α represents the contact angle;
[0016] In the angle domain, the peak value based on the characteristic order does not change with the rotational speed, and fault identification can be directly carried out.
[0017] Furthermore, when the bearing fails, the low-frequency impact excitation signal is affected by the amplitude modulation of the high-frequency carrier signal caused by the natural vibration of the bearing. Envelope analysis is an effective method that can extract the modulation frequency components and eliminate the carrier signal, so that the impact excitation signal of the characteristic fault sequence can be detected. Based on the Hilbert transform, the envelope spectrum is obtained from the resampled signal v n (θ) as follows:
[0018]
[0019] where θ and represent the angle and the Hilbert transform of the angle resampled signal v n (θ) respectively. By taking v n (θ) as the real part and as the imaginary part, the complex signal z(θ) is calculated:
[0020]
[0021] The envelope spectrum e n (θ) is obtained by calculating the magnitude of z(θ).
[0022] Based on the short-time Fourier transform, the envelope spectrum is converted into a short-time Fourier transform time-frequency diagram.
[0023] Based on the envelope spectrum of the original signal, without signal preprocessing, due to the centrifugal force and the change of rotational speed, the vibration amplitude and frequency change within the sampling time. Therefore, even if the bearing fault labels are the same, the input signals are always different, resulting in the domain shift problem. In contrast, the short-time Fourier transform time-frequency diagram after preprocessing shows that the amplitude and frequency distributions are evenly aligned, indicating that these signals are domain-invariant.
[0024] However, it is still difficult to accurately extract the information related only to the fault impact excitation signal in all data by signal preprocessing alone; for example, the obtained vibration signal not only contains the impact excitation signal caused by the bearing fault, but also includes other impact excitation signals reflecting machine characteristics such as mechanical looseness and imbalance. Therefore, the harmonics of the rotational speed order may be larger in amplitude than those of the characteristic fault order; in addition, due to the complexity of various modulation signals caused by the ball fault, it is more difficult to extract the characteristic ball fault order OBSF. To overcome this problem, further, the present invention calculates the contribution correlation score of the input node to the prediction output of the convolutional neural network based on the hierarchical relevance propagation technique, and generates a heat map based on the contribution correlation score to reflect the contribution degree of the input node to the classification result of the convolutional neural network output.
[0025] Furthermore, the neural network uses a convolutional neural network (CNN) as its backbone structure. At the input layer, the image data is processed through multiple convolutional layers. Each convolutional operation uses a 3×3 convolutional kernel to gradually extract features from the image. In the first convolutional layer (Conv.C1), the network first generates 32 feature maps through convolutional operations. These feature maps mainly extract low-level features in the input image, such as edges and textures. Then, in the second convolutional layer (Conv.C2), the convolutional operation generates 64 feature channels to continue extracting higher-level features. Finally, the third convolutional layer (Conv.C3) further generates 128 feature channels to extract more abstract and complex image features. Through these convolutional and pooling layers, the model gradually extracts hierarchical features from the input image. Low-level features such as edges and textures are extracted in the previous layers, while more advanced and complex features are captured in the subsequent layers. The extracted features are processed through a fully connected layer (Dense D1). This layer flattens the feature maps extracted by the convolutional and pooling operations and outputs a feature vector of length 625 to represent the final features of the input image. After each convolutional layer, the model uses pooling layers (Pooling P1, P2, P3). Each pooling layer uses a 2×2 max-pooling kernel to reduce the spatial dimension of the image, lower the computational complexity, and enhance the robustness of the model. These pooling operations help reduce overfitting while extracting features. The neural network outputs the result through a classification layer. This layer converts the feature vector into probability values for four categories through the Softmax activation function, representing "Normal", "Inner race", "Outer race", and "Ball" respectively. Each category corresponds to a probability indicating the probability of the input image belonging to that category.
[0026] Furthermore, to explain the deep neural network, the present invention adopts layer-wise relevance propagation (LRP). First, the contribution correlation score R(x) of each input node or pixel to the predicted output f(x) of the convolutional neural network CNN is calculated. Then, these correlations are aggregated into the total correlation score of the features. Finally, a heatmap is generated to explain the model prediction. The correlation score represents the predicted output f(x) through Taylor expansion:
[0027]
[0028] where a represents the root point of the Taylor series, f(a) represents the function value at the expansion point, d represents the dimension of the variable, f represents the prediction function, x represents the input time-frequency diagram, and ∈ represents the error term of the higher-order terms of the Taylor series.
[0029] Further, since the second term on the right side represents the contribution of each input to the output, when using the ReLU activation function, f(a) and ∈ can be removed, resulting in the following formula:
[0030]
[0031] where w i , b, and R i represent the weight, bias, and relevance score of the i-th node, respectively.
[0032] By adding a hierarchical relevance preservation constraint, the relevance score is propagated from the output layer to the input layer:
[0033]
[0034] where V(l) represents the total number of neurons in the l-th layer, and R d represents the relevance score of the d-th neuron.
[0035] Further, determine the contribution degree of the input node to the classification result of the convolutional neural network output. The contribution degree is represented by the relevance score R i . After redistributing the relevance score based on the first rule and further optimizing the relevance score based on the second rule, a heatmap is generated based on the optimized relevance score.
[0036] Further, the relevance score R i is calculated by the following formula:
[0037]
[0038] where f(x) represents the classification probability value output by the neural network, w i represents the weight, x i represents the input node, b represents the bias, R i represents the relevance score of the i-th node, and d represents the total number of input nodes;
[0039] Use the first rule and the second rule to redistribute the relevance. The first rule is the z+ rule;
[0040]
[0041] where R i represents the final relevance score obtained by the i-th node in the input layer; R j represents the relevance score of the j-th neuron in the upper layer, x i represents the activation value of the i-th node in the lower layer, that is, the input signal, Denotes the connection weight from the lower-layer node i to the upper-layer node j, representing the positive part of the weight.
[0042] The second rule is z B Rule; after redistributing the relevance scores based on the first rule and further optimizing the relevance scores based on the second rule, the specific formula is as follows:
[0043]
[0044] where z ij = x i w ij , representing the product of the activation value of node i and the corresponding weight, i.e., the contribution to node j; l i and h i respectively represent the lower bound and upper bound of the activation values of the lower-layer nodes, and respectively represent the positive part and negative part of the weight w ij .
[0045] The advantages and beneficial effects of the present invention are as follows:
[0046] A single-domain generalizable and physically interpretable bearing fault diagnosis method of the present invention can solve the domain differences, achieve single-domain generalization, eliminate the influence of angular velocity on vibration signals, and avoid domain differences in the frequency domain; through angular domain conversion, the signal is no longer affected by the rotational speed change, making the fault impact characteristic order stable, and through envelope analysis, the modulation frequency components are extracted and the carrier signal is eliminated, so that the impact excitation signal of the characteristic fault order can be detected; through the hierarchical relevance propagation technology, the contribution relevance scores of the input nodes to the predicted output of the convolutional neural network are calculated, and a heat map is generated based on the contribution relevance scores to reflect the contribution degree of the input nodes to the classification result of the convolutional neural network output, so as to extract as much information as possible that is only related to the fault impact excitation signal for fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS
[0047] Figure 1 is the flowchart of the method of the embodiment of the present invention.
[0048] Figure 2 is the structural schematic diagram of the modules involved in the method of the embodiment of the present invention.
[0049] Figure 3 is the schematic diagram showing the differences between the single-domain generalization problem and the domain adaptation and domain generalization problems in the embodiment of the present invention.
[0050] Figure 4 is the schematic diagram of the domain-invariant representation embedding prior knowledge in the embodiment of the present invention.
[0051] Figure 5It is a flowchart of the signal preprocessing process in an embodiment of the present invention.
[0052] Figure 6 It is a schematic structural diagram of a convolutional neural network in an embodiment of the present invention.
[0053] Figure 7 It is a schematic diagram of the working effect of hierarchical relevance propagation in an embodiment of the present invention. Detailed implementation manners
[0054] The following will describe in detail the specific implementation manners of the present invention with reference to the accompanying drawings. It should be understood that the specific implementation manners described herein are only for explaining and illustrating the present invention, and are not used to limit the present invention.
[0055] As Figure 1 shown, a single-domain generalizable and physically interpretable bearing fault diagnosis method specifically includes the following steps:
[0056] Step 101: Divide the bearing vibration signal by the square of the rotation frequency and then perform normalization processing, and perform angular domain resampling processing on the normalized bearing vibration signal to obtain a preprocessing signal;
[0057] Step 102: Perform envelope analysis and short-time Fourier transform on the preprocessing signal to obtain an STFT time-frequency diagram;
[0058] Step 103: Perform fault mode classification on the STFT time-frequency diagram based on a convolutional neural network;
[0059] Step 104: Calculate the contribution correlation score of the input nodes to the prediction output of the convolutional neural network based on hierarchical relevance propagation technology, and generate a heat map based on the contribution correlation score; the heat map is used to reflect the contribution degree of the input nodes to the classification result output by the convolutional neural network.
[0060] The execution process of its overall module is as Figure 2 shown. The vibration signal of the acquisition device is sent into two modules, namely signal preprocessing domain generalization (SPDG) and domain interpretation signal preprocessing (SPDI), to obtain an STFT time-frequency diagram, and then the time-frequency diagram is sent into a convolutional neural network for fault classification, and finally a heat map is obtained through hierarchical relevance propagation for the prediction result.
[0061] As Figure 3 shown, the domain-adaptive training data consists of a small part of the source domain (S) and the target domain (T), and the test data only comes from T. S∩∪T<>T means that the intersection of the training data and the test data is small or almost none; the domain generalization training data consists of multiple different but related source domains (S1, S2...), and the test data comes from a new target domain that has not been seen before. The formula S i ∪S j >Si / j Combining multiple source domains is shown to provide more generalization ability than a single source domain. Single-domain generalization methods aim to train a model that can learn from one source domain and improve its generalization ability to unknown target domains. Different from traditional domain adaptation methods, single-domain generalization does not rely on the data distribution information of the target domain, but trains using data from multiple source domains S to enhance the stability and robustness of the model when facing unknown target domains.
[0062] To solve single-domain generalization, the present invention adopts a way of embedding prior knowledge. Under different operating conditions, the distribution differences between source domain data (S) and target domain data (T), especially the data distributions at different rotational speeds (increasing, constant, and decreasing), are as Figure 4 shown. Each region contains different types of samples, reflecting that the signals of the same fault may exhibit different characteristics at different rotational speeds, which leads to significant data differences between the source domain and the target domain. Under the invariant space of the region, the differences between the source domain and the target domain are minimized by signal processing and learning the domain-invariant subspace. The signal processing method uses domain prior knowledge to optimize feature extraction, making the data distributions of the source domain and the target domain more consistent. In the domain-invariant subspace, the data is no longer affected by operating conditions (such as rotational speed changes), becomes more shared, and can be effectively classified in the same space.
[0063] First, signal preprocessing domain generalization (SPDG) is defined, as Figure 5 shown, which consists of amplitude normalization and angular domain recovery to address domain differences and achieve domain-invariant representations in the time domain and frequency domain. This method allows the proposed method to achieve single-domain generalization (SDG), unlike existing domain generalization (DG) methods that require a large amount of data under various working conditions to ensure stable statistical convergence.
[0064] The vibration amplitude changes with the rotational speed, and this change is caused by centrifugal force:
[0065] F = mrω 2 ∝ mf r (t) 2 / r
[0066] where m, ω, and r are the mass, angular velocity, and radius of the circle respectively, and f r (t) represents the rotational frequency. To eliminate the influence of angular velocity on the vibration signal, the present invention divides the original bearing vibration signal by f r (t) 2 , obtains the vibration signal v(t), and then obtains the standardized bearing vibration signal v n (t) by normalizing v(t) to zero mean and unit standard deviation, which is expressed as:
[0067]
[0068] Among them, μ and σ represent the mean and standard deviation of v(t), respectively.
[0069] Since v n (t) varies with the rotational speed, the frequency of the impact excitation signal also varies with time, resulting in domain differences in the frequency domain. To obtain impact excitation signals with equal intervals and balance the calculation cost and accuracy, this method uses cubic spline interpolation. Cubic spline interpolation uses a cubic polynomial for interpolation between every two data points while ensuring the continuity of the first and second derivatives, calculating a smooth and continuous estimated value at each target angle sampling point, and obtaining the signal v n sampled uniformly in angle, that is:
[0070] v n (θ) = Interpolate{θ(t), v n (t)}
[0071] The angle domain conversion makes the signal no longer affected by the rotational speed change. The fault impact characteristic order is stable, and different bearing faults will generate specific characteristic orders. The specific formulas are as follows:
[0072]
[0073]
[0074] Among them, O BPFO , O BPFI and O BSF are the characteristic orders of outer race faults, inner race faults, and ball faults respectively; f BPFO , f BPFI and f BSF are the outer race fault frequency, inner race fault frequency, and ball fault frequency respectively; D b , D c are the rolling element diameter and pitch diameter respectively; N b is the number of rolling elements, and α is the contact angle. In the angle domain, the peaks of these characteristic orders do not change with the rotational speed, so they can be directly used for fault identification.
[0075] Secondly, it is the domain interpretation signal preprocessing (SPDI) module. As Figure 5 shown, when the bearing fails, the low-frequency impact excitation signal will be amplitude-modulated by the high-frequency carrier signal caused by the natural vibration of the bearing. Envelope analysis is an effective method that can extract the modulation frequency components and eliminate the carrier signal, so that the impact excitation signal of the characteristic fault order can be detected. Using the Hilbert transform on the given v nThe envelope spectrum is obtained from v(θ) as follows:
[0076]
[0077] where θ and represent the angle and the Hilbert transform of v(θ), respectively. By taking v(θ) as the real part and n as the imaginary part, the complex signal z(θ) is calculated: n
[0078]
[0079] The envelope spectrum e(θ) is obtained by calculating the magnitude of z(θ). n
[0080] Based on the envelope spectrum of the original signal, without signal preprocessing, due to centrifugal force and speed changes, the vibration amplitude and frequency change within the sampling time. Therefore, even if the bearing fault labels are the same, the input signals are always different, resulting in the domain shift problem. In contrast, the preprocessed STFT time-frequency diagram shows that the amplitude and frequency distributions are evenly aligned, indicating that these signals are domain-invariant. However, it is still difficult to accurately extract the information related only to the fault impact excitation signal from all the data by signal preprocessing alone. For example, the obtained vibration signal not only contains the impact excitation signal caused by bearing faults but also includes other impact excitation signals reflecting machine characteristics such as mechanical looseness and imbalance. Therefore, the harmonics of the rotational speed order may be larger in amplitude than those of the characteristic fault order. In addition, due to the complexity of various modulation signals caused by ball faults, it is more difficult to extract the characteristic ball fault order OBSF. To overcome this problem, the preprocessed STFT time-frequency diagram will be input into a deep learning network to achieve pattern recognition of the characteristic fault order.
[0081] The present invention requires being able to identify the impact excitation signal of each fault and providing confidence for the diagnosis of out-of-distribution data. As Figure 6 As shown, the Convolutional Neural Network (CNN) is used as the backbone structure. At the input layer, the image data is processed through three convolutional layers. Each convolutional operation uses a 3×3 convolutional kernel to gradually extract features from the image. In the first convolutional layer (Conv.C1), the network generates 32 feature maps through the convolutional operation. These feature maps mainly extract low-level features in the input image, such as edges and textures. Then, in the second convolutional layer (Conv.C2), the convolutional operation generates 64 feature channels to continue extracting higher-level features. The third convolutional layer (Conv.C3) further generates 128 feature channels to extract more abstract and complex image features. Through these convolutional and pooling layers, the model gradually extracts hierarchical features from the input image. Low-level features such as edges and textures are extracted in the previous layers, while more advanced and complex features are captured in the subsequent layers. The extracted features are processed through the fully connected layer (Dense D1). This layer flattens the feature maps extracted by the convolutional and pooling operations and outputs a feature vector with a length of 625, representing the final features of the input image.
[0082] After each convolutional layer, the model uses pooling layers (Pooling P1, P2, P3). Each pooling layer uses a 2×2 max pooling kernel. The purpose is to reduce the spatial dimension of the image, lower the computational complexity, and enhance the robustness of the model. These pooling operations help reduce overfitting while extracting features.
[0083] The neural network outputs the results through the classification layer. This layer converts the feature vector into probability values for four categories through the Softmax activation function, representing "Normal", "Inner race", "Outer race", and "Ball" respectively. Each category corresponds to a probability, indicating the probability that the input image belongs to that category.
[0084] To explain the deep neural network, the present invention selects Layer-wise Relevance Propagation (LRP), as Figure 7 shown. First, the contribution relevance score R(x) of each input node or pixel to the predicted output f(x) of the CNN is calculated. Then, these relevances are aggregated into the total relevance score of the features. Finally, a heatmap is generated to explain the model prediction. The relevance score represents the predicted output f(x) through Taylor expansion:
[0085]
[0086] Where a represents the root point of the Taylor series, f(a) represents the function value at the expansion point, d represents the dimension of the variable, f represents the prediction function, x represents the time-frequency graph of the input, and ∈ represents the error term of the higher-order term of the Taylor series. Since the second term on the right represents the contribution of each input to the output, f(a) and ∈ can be removed when using the ReLU activation function. Therefore, the formula can be rewritten as:
[0087]
[0088] Among them, w i , b and R i are the weight, bias, and relevance score of the i-th node, respectively. Finally, the relevance score is propagated from the output layer to the input layer by adding a “layer-level relevance preservation constraint”:
[0089]
[0090] Among them, V(l) represents the total number of neurons in layer l, R d represents the relevance score of the d-th neuron.
[0091] The present invention uses a first rule and a second rule to redistribute the correlation, and the first rule may specifically be a z+ rule;
[0092]
[0093] Among them, R i Represents the final relevance score of the i-th node in the input layer. j represents the relevance score of the j-th neuron in the upper layer. Defined as x i is the activation value (input signal) of the i-th node in the lower layer. is the connection weight from the lower layer node i to the upper layer node j, and represents the positive part of the weight.
[0094] The second rule can be specifically z B After redistributing the relevance scores based on the first rule, the relevance scores are further optimized based on the second rule, as shown in the following formula:
[0095]
[0096] Among them, z ij Defined as z ij =x i w ij , represents the product of the activation value of node i and the corresponding weight, that is, the contribution to node j. i and h i Respectively represent the lower and upper bounds of the activation values of the lower layer nodes, and represent the positive and negative parts of the weight w ij respectively.
[0097] Generate a heatmap based on the optimized correlation score. The model shows that the higher the positive correlation of the input node, the greater its impact on classification, and the correlation is 0 if there is no impact. Therefore, when LRP is combined with SPDI, only the information related to each bearing fault impact excitation signal will be displayed in the heatmap, excluding any other signals, enabling users to understand the diagnostic results from a physical perspective.
[0098] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A single-domain generalizable and physically interpretable bearing fault diagnosis method, characterized in that It includes the following steps: Based on the acquired bearing vibration signal, perform amplitude normalization and angular domain resampling to achieve domain-invariant representation in the time domain and frequency domain, and obtain a preprocessed signal; Perform envelope analysis on the preprocessed signal, and generate a time-frequency diagram according to the obtained envelope spectrum; By constructing a neural network, perform pattern recognition of the fault mode sequence on the time-frequency diagram to classify bearing faults.
2. The single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, characterized in that: After dividing the original bearing vibration signal by the square of the rotation frequency, normalize it to zero mean and unit standard deviation, and generate a standardized bearing vibration signal based on the zero mean and unit standard deviation.
3. A single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, characterized in that: Using the cubic spline interpolation method, a cubic polynomial is used for interpolation between every two data points, while ensuring the continuity of the first-order and second-order derivatives, and a smooth and continuous estimated value is calculated at each target angle sampling point to obtain the angle resampling signal v n (θ): v n (θ) = Interpolate{θ(t), v n (t)} where v n (t) represents the bearing vibration signal, and θ(t) represents the angle signal; Different bearing faults will generate specific characteristic orders, and the specific formula is as follows: Among them, OBPFO, OBPFI, and OBSF respectively represent the outer ring fault order, inner ring fault order, and ball fault order of the bearing; f BPFO , f BPFI , and f BSF respectively represent the outer ring fault frequency, inner ring fault frequency, and ball fault frequency of the bearing; f r represents the rotational speed; D b , D c respectively represent the rolling element diameter and pitch diameter of the bearing; N b represents the number of rolling elements, and α represents the contact angle; In the angular domain, based on the fact that the peak value of the characteristic order does not change with the rotational speed, directly perform fault identification.
4. A single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, characterized in that: Resample the signal v from a given angle based on the Hilbert transform to obtain the envelope spectrum in n (θ) as follows: n (θ) as follows: where θ and represent the angle and the Hilbert transform of the angle resampled signal v n (θ), respectively, by taking v n (θ) as the real part and as the imaginary part to calculate the complex signal z(θ): The envelope spectrum e n (θ) is obtained by calculating the magnitude of z(θ).
5. A single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, characterized in that: Calculate the contribution correlation score of the input nodes to the prediction output of the convolutional neural network based on the hierarchical relevance propagation technique, and generate a heat map based on the contribution correlation score to reflect the contribution degree of the input nodes to the classification result of the convolutional neural network output.
6. The single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, wherein: The neural network uses a convolutional neural network as the backbone structure. In the input layer, the image data is processed through multiple convolutional layers, and the features in the image are gradually extracted. First, the low-level features in the input image, such as edges and textures, are extracted; then, continue to extract higher-level features. Finally, more abstract and complex image features are extracted; the hierarchical features in the input image are gradually extracted, and the extracted features will be flattened through the fully connected layer, and the output feature vector represents the final features of the input image; After each layer of convolution, the model uses a pooling layer to reduce the spatial dimension of the image, reduce the computational complexity, and enhance the robustness of the model; the neural network outputs the result through the classification layer, and converts the feature vector into the probability representing the category of the input image.
7. A single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, characterized in that: Adopt hierarchical relevance propagation (LRP). First, calculate the contribution correlation score R(x) of each input node or pixel to the prediction output f(x) of the convolutional neural network, then summarize these correlations into the total correlation score of the features, and finally generate a heat map to explain the model prediction; the correlation score represents the prediction output f(x) through Taylor expansion: Among them, a represents the root point of the Taylor series, f(a) represents the function value at the expansion point, d represents the dimension of the variable, f represents the prediction function, x represents the input time-frequency diagram, and ∈ represents the error term of the higher-order term of the Taylor series.
8. A single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 7, characterized in that: When using the ReLU activation function, f(a) and ∈ can be removed, and the following formula is obtained: where, w i , b, and R i respectively represent the weight, bias, and relevance score of the i-th node; By adding hierarchical relevance preservation constraints, propagate the correlation score from the output layer to the input layer: Among them, V(l) represents the total number of neurons in the l-th layer, and R d represents the relevance score of the d-th neuron.
9. The single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, characterized in that: Determine the contribution degree of the input node to the classification result of the convolutional neural network output, and the contribution degree is represented by the correlation score R i After redistributing the correlation scores based on the first rule, further optimize the correlation scores based on the second rule, and generate a heat map based on the optimized correlation scores.
10. A single-domain generalizable and physically interpretable bearing fault diagnosis method according to claim 1, characterized in that: Relevance score R i Calculated by the following formula: Among them, f(x) represents the classification probability value output by the neural network, w i represents the weight, x i represents the input node, b represents the bias, R i represents the relevance score of the i-th node, and d represents the total number of input nodes; Use the first rule and the second rule to reallocate the relevance, and the first rule is the z+ rule; Among them, R i represents the final obtained relevance score of the i-th node in the input layer; R j represents the relevance score of the j-th neuron in the upper layer, x i represents the activation value of the i-th node in the lower layer, that is, the input signal, represents the connection weight from the lower layer node i to the upper layer node j; The second rule is z B The rule further optimizes the relevance score, as shown in the following formula: where z ij = x i w ij , representing the product of the activation value of node i and the corresponding weight, i.e., the contribution to node j; l i and h i represent the lower and upper bounds of the activation values of the lower-layer nodes respectively, and represent the positive and negative parts of the weight w ij respectively.