Bearing system fault diagnosis method based on depth time-frequency domain adaptive network

Abstract

The invention discloses a bearing system fault diagnosis method based on a deep time-frequency domain adaptive network, and the method comprises the steps: collecting multi-domain vibration signals of a bearing with different fault modes, building a cross-domain data set, constructing the deep time-frequency domain adaptive network, initializing the deep time-frequency domain adaptive network through employing a parameter theta, and carrying out the fault diagnosis of the bearing system. And preparing hyper-parameter tuning according to the selected data set, training the deep time-frequency domain adaptive network by using cross-domain training sets Ds and Dt, outputting a classification result of the optimized deep time-frequency domain adaptive network on the test set Dtest, and counting and analyzing the result. According to the method, the depth time-frequency domain adaptive network is applied to fault diagnosis, and the robustness and accuracy in a cross-domain fault diagnosis scene are improved.

Description

Technical Field

[0001] The present invention relates to the field of bearing system fault diagnosis, and in particular to a bearing system fault diagnosis method based on a deep time-frequency domain adaptive network. Background Art

[0002] Rotating machinery is an essential component of many industries, including manufacturing, transportation, and energy. Bearings are essential components of rotating machinery and are subject to large loads at high speeds, which makes them susceptible to malfunctions and failures. Therefore, bearing fault diagnosis is critical to the safe, reliable, and stable operation of rotating equipment.

[0003] In recent years, fault diagnosis has made significant progress due to the development of intelligent technology, especially the increasing popularity of deep learning. A large number of studies have explored the applicability of various deep learning architectures, including convolutional networks (CNNs), recurrent convolutional networks (RNNs), Transformers, etc. in the field of fault diagnosis. However, traditional deep learning has poor cross-domain generalization ability because it assumes the consistency of data distribution, which is not always guaranteed in practice. Insufficient labeled data of the target object and changes in operating conditions further limit the applicability of these methods and hinder the use of historical data. This limitation is particularly important in fault diagnosis because mechanical equipment may exhibit different degradation modes and fault characteristics. Therefore, conducting cross-domain fault diagnosis research has greater practical significance.

[0004] Deep transfer learning techniques, especially domain adaptation methods, have been shown to be successful in improving fault diagnosis in cross-domain scenarios. Although domain adaptation methods have significantly improved the cross-domain generalization of fault diagnosis by reducing the differences in feature distributions, some challenges still exist. For example, a unique feature of time series data for fault diagnosis is that feature shifts occur in both the time and frequency domains. While existing models use traditional structures such as convolutional neural networks to process time domain signals or time-frequency transformed data, these structures lack dedicated learning architectures for spectral representation. This limitation can limit the model's ability to learn physical features from the spectrum. Second, few studies have explored domain invariance and reducing feature shifts in the spectral and time domains. In complex variable scenarios, data mining in the time domain feature space is difficult to handle cross-domain generalization, resulting in negative transfer. Therefore, it is necessary to design a learning architecture for time-frequency spectrum representation that achieves domain adaptation in both the time and spectral spaces to further improve the cross-domain generalization of fault diagnosis. Summary of the invention

[0005] In order to overcome the shortcomings and deficiencies of the prior art, the present invention provides a bearing system fault diagnosis method based on a deep time-frequency domain adaptive network.

[0006] A bearing system fault diagnosis method based on a deep time-frequency domain adaptive network, the method comprising:

[0007] Step S1, data set preparation: collect multi-domain vibration signals of bearings with different failure modes and establish a cross-domain data set, including the annotated source data set D s , unlabeled target dataset D t And the test dataset D test ;

[0008] Step S2, model initialization: construct a deep time-frequency domain adaptive network, and use parameter θ to initialize the deep time-frequency domain adaptive network, and then prepare hyperparameter tuning according to the selected data set;

[0009] Step 3S, model parameter optimization: using cross-domain training set D s and D t Training the deep time-frequency domain adaptive network;

[0010] Step S4, test verification: output the optimized deep time-frequency domain adaptive network to the test set D test The classification results are collected and analyzed.

[0011] Furthermore, the construction of a deep time-frequency domain adaptive network includes: obtaining a spectrum representation using discrete Fourier transform, spectrum neural layer calculation, and calculating Sinkhorn divergence through an iterative data solution.

[0012] Furthermore, the spectrum representation is obtained by discrete Fourier transform. For a given time series sample x∈R containing C channels and t time points, C×T , perform a 1D discrete Fourier transform on each channel to obtain f = F(x)∈C C×T , the expression is:

[0013]

[0014] Where k represents the kth frequency index and c represents the cth channel. (c) Represents the signal x (c) The discrete Fourier transform result, F(x (c) ) is also a signal x (c) The discrete Fourier transform result, x (c) represents the original signal of the cth channel, t represents each discrete time point in the time series, and T represents the signal x (c) The total number of samples, e is the natural constant Euler number, which is used as the base of the exponential function in Fourier transform, j is the imaginary unit, 2π is the coefficient in the exponential function, and C represents the total number of channels.

[0015] Furthermore, the spectrum neural layer calculation includes: spectrum convolution, spectrum pooling, spectrum activation, and spectrum batch normalization;

[0016] The spectral convolution adopts the complex convolution type. Given a complex input vector x=u+iv∈C, a complex filter matrix W=A+iB∈C is used for convolution, where u and v∈R are real vectors, A and B∈R are real matrices, and the complex convolution calculation expression is:

[0017] W*x=(A*uB*v)+i(B*uA*v)

[0018] Among them, W*x represents the product between vector x and matrix W, the symbol * represents the convolution operation, W is a complex matrix containing real and imaginary parts, and x is a complex vector; A and B represent linear transformations acting on u and v respectively, u and v represent the real and imaginary parts of the complex vector x respectively, and i represents the imaginary unit.

[0019] The matrix form expression is:

[0020]

[0021] in, represents the real part of the above complex expression W*x, Represents the imaginary part of the above complex expression W*x.

[0022] The spectrum pooling is usually performed based on the importance of frequency components to retain the main frequency information. The spectrum pooling process expression is:

[0023]

[0024] Among them, Y is the output after pooling, Pool represents the pooling operation, x(t) is the time domain signal, and f is the frequency.

[0025] The spectrum activation adopts a complex activation function based on ReLU, that is, the zReLU activation function. Given a complex input x∈C, zReLU only retains the value of the first quadrant, and the expression is:

[0026]

[0027] Among them, θ x represents the phase of x, which satisfies the Cauchy-Riemann equation, except for the set Any point in .

[0028] The spectral batch normalization is to avoid gradient vanishing by batch normalization and to accelerate training. Given a small batch where x i∈C, this task is regarded as a whitened two-dimensional vector, expressed as:

[0029]

[0030] in, represents the normalized data, E[X] represents the expected value of the matrix X, and V represents the covariance matrix. The expression is:

[0031]

[0032] Among them, V rr , V ri , V ir and V ii Respectively represent the specific elements in the covariance matrix V, and denote the real and imaginary parts of the matrix X, respectively, and Cov denotes the covariance operator, which ensures that Standard complex distribution with mean μ = 0, covariance Γ = 1 and pseudo-covariance Γ = 0; the expressions for mean, covariance and pseudo-covariance are:

[0033]

[0034] Among them, μ represents the data , Γ represents the covariance, Π represents the pseudo-covariance, and i represents the imaginary unit.

[0035] Spectral batch normalization has two parameters, including the shift parameter β and the scaling parameter γ, both of which are complex. There are three degrees of freedom to ensure that the variance of the two original principal components is 1. The translation parameter β = β r +iβ i There are two trainable values ​​corresponding to the real and imaginary parts. Spectral Batch Normalization (SBN) is defined as:

[0036]

[0037] Where SBN represents the result of the batch normalization operation, β is the shift parameter, and γ is the scaling parameter. γ ri =β r =β i =0.

[0038] Furthermore, the Sinkhorn divergence is calculated by iterative data solution, and the specific steps are as follows: first, initialize two input distributions, namely the characteristic data distribution and the fault mode distribution of the bearing system, and then perform optimization calculations through the Sinkhorn divergence, gradually adjust these distributions so that they are minimized under a certain metric, and finally obtain the calculated Sinkhorn divergence to measure the difference between the two distributions. This regularization is known to be equivalent to limiting the search space and has the following scaling form:

[0039] P 0 =diag(u)Kdiag(v)

[0040] Among them, P 0 represents the value obtained after matrix transformation, diag(u) performs diagonal matrix operation on vector u, matrix K = exp(-C / η) is the Gibbs kernel, and diag(v) performs diagonal matrix operation on vector v. Note that exp(·) here represents element-by-element operation. Starting from the selected initial value, the fixed point is solved by the following iterative method:

[0041]

[0042] Among them, u (l+1) represents the updated value of vector u in the l+1th iteration, v (l+1) represents the updated value of vector v in the l+1th iteration, u (l) and v (l) They represent the current value in the lth iteration, u s Represents the result of nonlinear transformation of vector u, u t represents the transposed form of vector u, t is the time step, s represents the index value, K T Represents the transposed matrix of matrix K.

[0043] After L iterations, the best pairing is P (L) =diag(u (L) )Kdiag(v (L) ). Therefore, the final divergence is:

[0044]

[0045] in, represents the calculation result of the final divergence, η represents the regularization parameter, C is a matrix, P (L) It also represents a matrix, L is the current number of layers of the matrix, c ij represents the element in the i-th row and j-th column of the matrix C, n s Indicates that s The number of samples involved, n tIndicates that t The number of samples involved, and Respectively represent vector u s and u t The i-th and j-th vector elements in the L-th layer, K ij Represents the element in the i-th row and j-th column of matrix K.

[0046] In order to achieve the task goal of fault diagnosis, the output features of the deep time-frequency domain adaptive network are mapped to various fault categories, and a fully connected layer with a SoftMax activation function is used as a classifier to output category probabilities.

[0047] Furthermore, the goal of the deep time-frequency domain adaptive network is to minimize the structural risk of the network in the target domain, which is expressed as:

[0048]

[0049] Among them, θ * represents the optimal parameter in the optimization process, θ is the network parameter, ε t represents the objective function, Pr[·] represents the data distribution in the training dataset, D represents the dataset containing the input feature x and the corresponding label y, t is the time step, c(·) is the loss function, g(x) represents the predicted value generated by the model for the input x, and y is the target variable to be predicted by the model during training.

[0050] The objective function of the deep time-frequency domain adaptive network minimizes both the empirical risk in the source domain and the difference between domains. The former is expressed as the classification error based on supervised learning, namely:

[0051]

[0052] in, Indicates the calculated value, n s is the number of samples, C represents the total number of categories, is the calculation symbol of the cross entropy loss function, i and s are index variables, is the i-th sample x in the dataset i The sth subset of represents the i-th sample y i The sth subset of .

[0053] The objective function expression of the deep time-frequency domain adaptive network is:

[0054]

[0055] Among them, θ *represents the optimal parameter in the optimization process, θ is the network parameter, argmin represents the minimization operation, is the objective function, is the calculation result of the final divergence, η represents the regularization parameter, and λ represents the trade-off coefficient.

[0056] Beneficial effects:

[0057] The present invention proposes a bearing system fault diagnosis method based on a deep time-frequency domain adaptive network. The method first designs a spectral feature learning structure including multiple spectral neural layers to process complex spectral values. Secondly, the time-domain feature extraction branch is combined with the spectral feature extraction branch to form a time-frequency domain adaptive network; wherein, the time-frequency spectrum representation process of the time-frequency domain adaptive network is completed by using the regularized optimal transmission distance, namely, Si nkhorn divergence. Finally, an end-to-end fault diagnosis architecture based on the time-frequency domain adaptive network is proposed. The architecture aligns the time-frequency domain from both the time domain and the spectral space by learning representation, thereby achieving more robust and more accurate performance. The method extracts more discriminative features from the perspectives of the time domain and the spectrum. The spectral feature branch of the deep time-frequency domain adaptive network includes operations such as spectral convolution and spectral pooling to process complex spectral representations. The designed deep time-frequency domain adaptive method performs source-target alignment on the extracted time-frequency domain spectral representation, and uses Si nkhorn divergence to learn more domain-invariant representations. The deep time-frequency domain adaptive network is applied to fault diagnosis, and the method improves the robustness and accuracy in cross-domain fault diagnosis scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a flow chart of the method steps of the present invention;

[0059] Figure 2 A spectrum representation diagram including a one-dimensional discrete Fourier transform of the present invention;

[0060] Figure 3 A spectrum convolution diagram of the present invention including a complex convolution type;

[0061] Figure 4 The one-dimensional and two-dimensional spectrum pooling graphs including complex convolution operations of the present invention;

[0062] Figure 5 Detailed structural diagram of the deep time-frequency domain adaptive network of the present invention. DETAILED DESCRIPTION

[0063] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application may be combined with each other. The present application is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0064] like Figure 1 As shown, a bearing system fault diagnosis method based on a deep time-frequency domain adaptive network, the method includes:

[0065] Step S1, data set preparation: collect multi-domain vibration signals of bearings with different failure modes and establish a cross-domain data set, including the annotated source data set D s , unlabeled target dataset D t And the test dataset D test ;

[0066] Specifically, this step includes the first step of the fault diagnosis method, which first needs to collect bearing vibration signals with different fault modes. The diversity of the data set is the key to the success of this method, so the collected vibration signals should cover different fault conditions, such as normal operation, slight wear, severe damage, etc. These signals not only come from multiple fields, but also need to be collected for different working conditions to ensure the breadth and representativeness of the data. The collected signals will constitute a cross-domain data set, including: Source data set D s , which is a labeled training dataset, containing vibration signals and corresponding labels under different fault modes. Basic data used for training the algorithm. Target dataset D t This is an unlabeled dataset that simulates the lack of labeling in actual applications and is usually used to test the generalization ability of the algorithm. test ,This dataset contains bearing vibration signals used for model validation, verifying the classification accuracy of the deep time-frequency domain adaptive network.

[0067] Step S2, model initialization: construct a deep time-frequency domain adaptive network, and use parameter θ to initialize the deep time-frequency domain adaptive network, and then prepare hyperparameter tuning according to the selected data set;

[0068] Specifically, this step includes, in the model initialization stage, first constructing a deep time-frequency domain adaptive network, which is used to simultaneously learn the characteristics of vibration signals from the time and frequency domains. The network structure usually includes a time-frequency feature extraction layer, a fusion layer, and a classifier. During the initialization process, the network is initialized using the parameter θ. These parameters control the structure and weight of the network. On this basis, in order to ensure that the algorithm can be optimized on different data sets, hyperparameters are tuned. The purpose of hyperparameter tuning is to select appropriate parameters such as learning rate, regularization coefficient, and training rounds to ensure that the model will not overfit or underfit during the training process. This step is of great significance for subsequent model training and optimization.

[0069] Step 3S, model parameter optimization: using cross-domain training set D s and D t Training the deep time-frequency domain adaptive network;

[0070] Specifically, this step includes using the cross-domain training set D in the model parameter optimization stage. s and D t To train the deep time-frequency domain adaptive network. The goal of training is to enable the network to learn useful features from the source dataset and have good generalization ability on the target dataset. To achieve this goal, a cross-domain training method is used to enhance the learning ability of the model by using the labeled information of the source dataset and the unlabeled information of the target dataset. This process is carried out through iterative optimization, constantly adjusting the weights and biases in the network to minimize the loss function (such as cross entropy loss) and achieve accurate fault diagnosis.

[0071] Step S4, test verification: output the optimized deep time-frequency domain adaptive network to the test set D test The classification results are collected and analyzed.

[0072] Specifically, this step includes entering the test verification phase after the model training is completed. At this point, the trained deep time-frequency domain adaptive network will be used to test the test set D test By statistically analyzing the classification results of the test data, the performance of the model in practical applications can be evaluated. The test indicators include classification accuracy, recall rate, F1 value, etc., which aim to comprehensively evaluate the effectiveness of the model in fault diagnosis tasks. In this step, further optimization and adjustment can be made based on the performance of the model to ensure that the model can be stably applied to actual bearing fault detection.

[0073] Construct a deep time-frequency domain adaptive network, including: using discrete Fourier transform to obtain spectrum representation, spectrum neural layer calculation, and calculating Sinkhorn divergence through iterative data solution.

[0074] The deep time-frequency domain adaptive network proposed in this application is composed of (1) a feature extractor g(·) and (2) a classifier c(·). The structural characteristics are that the feature extractor contains two branches, namely, the time domain g τ (·) and frequency domain g s (·), which learn feature representations from the time domain and frequency domain respectively. The time domain branch uses a traditional 1D convolutional neural network, which contains four 1D convolutional layers and two maximum pooling layers, each of which is followed by a BN layer and a ReLU activation function.

[0075] At the same time, the frequency domain branch uses the 1D frequency domain convolutional network designed by this application, which includes four 1D convolutional layers and two frequency domain pooling layers, and the frequency domain BN layer and zReLU activation function are also placed in it. In order to construct a frequency domain feature extractor corresponding to the time domain branch, this application proposes the following spectral representation, spectral neural layer, and calculates the Sinkhorn divergence through an iterative data solution.

[0076] The first step of frequency domain learning is to obtain the spectrum representation using discrete Fourier transform. For a given time series sample x∈R containing C channels and t time points C×T ,like Figure 2 As shown in the figure, a signal processing process based on a deep time-frequency domain adaptive network is shown, especially for the processing of vibration signals in bearing system fault diagnosis. The content of the figure involves the operation of converting the input signal from the time domain to the frequency domain. The specific details include: 1). The input signal is a vibration signal obtained through multiple channels (each channel may correspond to a different sensor or data source). These signals change over time and contain different time-frequency information, which can reveal the working status or potential failure mode of the equipment. In the figure, these signals are arranged at time point T in different channels (expressed as C). 2). On the left side of the figure, the input signal is presented as time domain data, where each row represents the data of a channel, and the vertical arrangement represents the change of the signal at time point T. At this time, the signal is mainly processed according to the time dimension, but the information contained in it is far more than that, so further processing is required to extract frequency domain features. 3). The figure uses the symbol F(·) to represent the process of Fourier transforming the input time domain signal. Fourier transform converts the time domain signal into the frequency domain signal, which can capture the characteristics of the signal from the perspective of frequency. On the right side of the figure, each column shows the distribution of the signal at different frequencies. After Fourier transform, the time domain information of the signal is converted into frequency domain information, which helps to extract content that is very sensitive to frequency characteristics in the fault diagnosis process. 4). After conversion to the frequency domain, the signal not only contains time information, but also expresses frequency components, which is crucial for analyzing mechanical faults such as bearing damage or wear. Frequency domain signals can clearly reveal the characteristics of different frequency bands and help analyze the type and severity of faults. Through a deep time-frequency domain adaptive network, the network can simultaneously learn information in the time domain and frequency domain to more comprehensively capture the operating status of the bearing system. 5). In the signal after frequency domain conversion, the network further extracts and optimizes key features, and finally applies them to fault diagnosis tasks. Through deep learning, the network can accurately identify different fault modes and achieve accurate classification and prediction. Perform a 1D discrete Fourier transform on each channel to obtain f=F(x)∈C C×T ,Right now

[0077]

[0078] Where k represents the kth frequency index, c represents the cth channel, and f (c) Represents the signal x (c) The discrete Fourier transform result, F(x (c) ) is also a signal x (c) The discrete Fourier transform result, x (c) represents the original signal of the cth channel, t represents each discrete time point in the time series, and T represents the signal x (c) The total number of samples, e is the natural constant Euler number, which is used as the base of the exponential function in Fourier transform, j is the imaginary unit, 2π is the coefficient in the exponential function, and C represents the total number of channels.

[0079] Spectral neural layer calculation, the spectral neural layer designed by this application includes spectral convolution, spectral pooling, spectral activation, and spectral batch normalization. Spectral convolution uses a complex convolution type to retain as much information as possible in the frequency domain. Given a complex input vector x = u + iv ∈ C, this application convolves it with a complex filter matrix W = A + iB ∈ C, where u and v ∈ R are real vectors, and A and B ∈ R are real matrices. The complex convolution calculation is as follows:

[0080] W*x=(A*uB*v)+i(B*uA*v)

[0081] Among them, W*x represents the product between vector x and matrix W, the symbol * represents the convolution operation, W is a complex matrix containing real and imaginary parts, and x is a complex vector; A and B represent linear transformations acting on u and v respectively, u and v represent the real and imaginary parts of the complex vector x respectively, and i represents the imaginary unit.

[0082] like Figure 3 As shown in the figure, a complex matrix and vector operation process is shown. The core task is to perform specific transformations on the signal in order to extract useful features. This process involves the operation of complex matrices and vectors. Through this method, the algorithm can perform complex transformations between the time domain and the frequency domain, helping to improve the performance of the fault diagnosis model. The following is a detailed description of the process: 1). Initialization of complex matrices and vectors. Figure 3 At the top, matrices A and B are two complex matrices, where A represents the real part matrix, B represents the imaginary part matrix, and i is the imaginary unit. This matrix will be used in subsequent calculations to operate on the input signal. Vector u is the real part of the input signal, and v is the imaginary part of the input signal. The complex vector provides rich time domain and frequency domain features by combining the real part u and the imaginary part v. 2). Figure 3 The second layer is the multiplication of two complex matrices and a vector, which is mainly used as the product of a matrix and a vector to extract features from time domain signals. 3). Figure 3 The last layer calculates the complex result and finally obtains the complex result, where the real part is A*uB*v and the imaginary part is B*uA*v. The result of this step is to combine all the previous matrix and vector multiplication results through subtraction and addition to obtain the complex signal. The real part and the imaginary part represent the features of different levels in the signal, which are used for subsequent fault diagnosis. Its matrix form expression is:

[0083]

[0084] in, represents the real part of the above complex expression W*x, Represents the imaginary part of the above complex expression W*x.

[0085] The spectrum pooling is usually performed based on the importance of frequency components to retain the main frequency information. The spectrum pooling process expression is:

[0086]

[0087] Among them, Y is the output after pooling, Pool represents the pooling operation, x(t) is the time domain signal, and f is the frequency.

[0088] In addition, the spectrum pooling designed in this application can be regarded as Figure 4 The low-pass filter shown here has two main benefits: 1) Due to the uneven distribution of information density with respect to frequency, more information can be retained at the same size. 2) The scale of the representation can be scaled down more flexibly without suffering the drastic reduction of traditional pooling. Figure 4 The upper part of the figure shows the dimension transformation process of the matrix, and the lower part is the two-dimensional matrix transformation. Through the representation of this two-dimensional matrix, multiple feature dimensions of the signal can be taken into account at the same time. In this step, the elements in the matrix are compressed or converted through certain operations (such as pooling, convolution, etc.) and transformed into a target matrix. Finally, the final result is the features extracted in the height and width directions. This process extracts the core features of the signal through matrix transformation and provides valuable information for subsequent calculations and fault diagnosis. Through the extraction of this high-dimensional information, the algorithm can identify potential patterns or anomalies in the signal, thereby helping to make more accurate fault diagnosis. It can be seen that Figure 4The processing process demonstrated uses multiple matrix transformations, compression, and feature extraction to deeply learn and process the time domain and frequency domain information in the signal. Each step of the matrix transformation is to ensure that the signal features can be effectively extracted and provide accurate information for subsequent classification or prediction. This process combines multiple operations such as matrix transposition, compression, and dimensionality adjustment to optimize the representation of the signal, and can effectively mine potential fault modes and features in complex signals, thereby improving the accuracy and efficiency of fault diagnosis.

[0089] In addition, the present application uses a complex activation function based on ReLU for the spectrum activation of neuron units, namely the zReLU activation function. Given a complex input x∈C, zReLU only retains the value of the first quadrant, which is expressed as follows:

[0090]

[0091] where θx represents the phase of x, which satisfies the Cauchy-Riemann equation except for the set Any point in .

[0092] Finally, batch normalization is used to avoid gradient vanishing and speed up training. Given a small batch Where xi∈C, this application regards this task as a whitened two-dimensional vector, expressed as follows:

[0093]

[0094] in, represents the normalized data, E[X] represents the expected value of the matrix X, and V represents the covariance matrix. The expression is:

[0095]

[0096] Among them, V rr , V ri , V ir and V ii Respectively represent the specific elements in the covariance matrix V, and denote the real and imaginary parts of the matrix X, respectively, and Cov denotes the covariance operator, which ensures that Standard complex distribution with mean μ = 0, covariance Γ = 1 and pseudo-covariance Γ = 0; the expressions for mean, covariance and pseudo-covariance are:

[0097]

[0098] Among them, μ represents the data , Γ represents the covariance, Π represents the pseudo-covariance, and i represents the imaginary unit.

[0099] Spectral batch normalization has two parameters, including the shift parameter β and the scaling parameter γ, both of which are complex. There are three degrees of freedom to ensure that the variance of the two original principal components is 1. The translation parameter β = β r +iβ i There are two trainable values ​​corresponding to the real and imaginary parts. Spectral batch normalization SBN can be defined as:

[0100]

[0101] Where SBN represents the result of the batch normalization operation, β is the shift parameter, and γ is the scaling parameter. γ ri =β r =β i =0.

[0102] The Sinkhorn divergence is calculated by iterative data solution, which provides a computationally efficient way to approximate the optimal transmission and make the loss function differentiable. This regularization is known to be equivalent to restricting the search space and has the following scaling form:

[0103] P 0 =diag(u)Kdiag(v)

[0104] Among them, P 0 represents the value obtained after matrix transformation, diag(u) performs diagonal matrix operation on vector u, matrix K = exp(-C / η) is the Gibbs kernel, and diag(v) performs diagonal matrix operation on vector v. Note that exp(·) here represents element-by-element operation. Starting from the selected initial value, the fixed point is solved by the following iterative method:

[0105]

[0106] Among them, u (l+1) represents the updated value of vector u in the l+1th iteration, v (l+1) represents the updated value of vector v in the l+1th iteration, u (l) and v (l) They represent the current value in the lth iteration, u s Represents the result of nonlinear transformation of vector u, u t represents the transposed form of vector u, t is the time step, s represents the index value, K T Represents the transposed matrix of matrix K.

[0107] After L iterations, the best pairing is P (L) =diag(u(L) )Kdiag(v (L) ). Therefore, the final divergence is:

[0108]

[0109] in, represents the calculation result of the final divergence, η represents the regularization parameter, C is a matrix, P (L) It also represents a matrix, L is the current number of layers of the matrix, c ij represents the element in the i-th row and j-th column of the matrix C, n s Indicates that s The number of samples involved, n t Indicates that t The number of samples involved, and Respectively represent vector u s and u t The i-th and j-th vector elements in the L-th layer, K ij Represents the element in the i-th row and j-th column of matrix K.

[0110] In order to achieve the task goal of fault diagnosis, the output features of the deep time-frequency domain adaptive network are mapped to various fault categories, and a fully connected layer with a SoftMax activation function is used as a classifier to output category probabilities.

[0111] In addition, the classifier of the present application is a fully connected layer with a SoftMax activation function, and the detailed structure of the deep time-frequency domain adaptive network is as follows: Figure 5 shown. Figure 5 The paper shows a specific implementation process of a deep time-frequency domain adaptive network for bearing system fault diagnosis. The core of this method is to perform fault diagnosis by extracting features in the time and frequency domains, combining Sinkhorn divergence and classifiers. Figure 5It mainly includes: 1). Input of source domain and target domain data, which are vibration signals collected from different bearing fault modes. In practical applications, source domain data is usually labeled data, while target domain data is unlabeled data. The input data will be processed by different feature extraction modules. 2). Time domain feature extraction, the time domain feature extractor consists of multiple convolutional layers, ReLU activation functions and batch normalization layers. Through these layers, the model can extract meaningful time domain features from the original signal. For example, the convolutional layer extracts the local features of the signal, the ReLU activation function introduces nonlinear transformations, and the batch normalization layer helps accelerate the training process and prevent overfitting. 3). Frequency domain feature extraction, this part is similar to the time domain feature extractor, and is also composed of convolutional layers, ReLU activation functions and batch normalization layers. In the frequency domain, the change of the signal can more intuitively reflect the frequency characteristics. Especially when processing the fault signal of the bearing, the frequency domain features can often reveal subtle fault modes. 4). Time domain and frequency domain feature fusion, this process is to enhance the comprehensive discrimination ability of the model by combining feature information from different sources, thereby improving the accuracy of fault diagnosis. 5). The fused features are further calculated by Sinkhorn divergence. In this process, the model attempts to reduce the distribution difference between the source domain and the target domain by minimizing the Sinkhorn divergence, thereby improving the classification performance on the target domain. 6). Classifier and classification loss. After feature fusion and adjustment through Sinkhorn divergence, the final feature vector will be input into the classifier for fault mode prediction. The classifier is usually a fully connected layer with a SoftMax activation function, which is responsible for mapping the extracted features to the label of the fault type. It can be seen that Figure 5 A complete deep time-frequency domain adaptive network framework is presented, which includes multiple modules such as time domain and frequency domain feature extraction, feature fusion, Sinkhorn divergence calculation, classifier and classification loss. This method combines the time domain and frequency domain and uses the feature differences between the source domain and the target domain for transfer learning, thereby improving the accuracy of bearing system fault diagnosis. In practical applications, this algorithm can effectively cope with the challenges brought by the differences in data distribution in different fields and ensure efficient diagnostic capabilities on unlabeled target domain data. The goal of the network is to minimize the structural risk of the network in the target domain, which is expressed as follows:

[0112]

[0113] Among them, θ * represents the optimal parameter in the optimization process, θ is the network parameter, ε trepresents the objective function, Pr[·] represents the data distribution in the training dataset, D represents the dataset containing the input feature x and the corresponding label y, t is the time step, c(·) is the loss function, g(x) represents the predicted value generated by the model for the input x, and y is the target variable to be predicted by the model during training.

[0114] Therefore, its objective function minimizes both the empirical risk in the source domain and the difference between domains. The former is expressed as the classification error based on supervised learning, namely:

[0115]

[0116] in, Indicates the calculated value, n s is the number of samples, C represents the total number of categories, is the calculation symbol of the cross entropy loss function, i and s are index variables, is the i-th sample x in the dataset i The sth subset of represents the i-th sample y i The sth subset of .

[0117] Finally, the objective function of the network described in this application is expressed as follows:

[0118]

[0119] Among them, θ * represents the optimal parameter in the optimization process, θ is the network parameter, argmin represents the minimization operation, is the objective function, is the calculation result of the final divergence, η represents the regularization parameter, and λ represents the trade-off coefficient.

[0120] The present invention proposes a bearing system fault diagnosis method based on a deep time-frequency domain adaptive network. The method first designs a spectral feature learning structure containing multiple spectral neural layers to process complex spectral values. Secondly, the time domain feature extraction branch is combined with the spectral feature extraction branch to form a time-frequency domain adaptive network; wherein, the time-frequency spectrum representation process of the time-frequency domain adaptive network is completed based on the regularized optimal transmission distance, namely, the Si nkhorn divergence. The method has the following advantages:

[0121] 1. Joint extraction of time-frequency domain features: This method combines the feature extraction branches of the time domain and the frequency domain to form a time-frequency domain adaptive network. This method can simultaneously utilize time domain and spectrum information to extract more discriminative features and improve the accuracy of fault diagnosis.

[0122] 2. Adaptive time-frequency spectrum representation: By introducing the Si nkhorn divergence (regularized optimal transmission distance), this method can effectively align the time-frequency spectrum representations of the source and target domains, ensuring the adaptability and robustness of the model on different data sources.

[0123] 3. Spectral feature processing: The designed spectral feature learning structure includes operations such as spectral convolution and spectral pooling, which can effectively process complex spectral representations and further improve the performance of fault diagnosis.

[0124] 4. End-to-end architecture: This method proposes an end-to-end fault diagnosis architecture based on a time-frequency domain adaptive network, which can automatically learn the features extracted from the time domain and spectrum domain without manually designing features, simplifying the processing flow.

[0125] 5. Cross-domain robustness: This method can maintain high robustness and accuracy in cross-domain fault diagnosis scenarios, and is particularly suitable for fault diagnosis between different operating conditions or devices.

[0126] 6. Domain-invariant feature learning: By introducing the Sinkhorn divergence, the model can learn domain-invariant features, so that the model can maintain consistent performance when facing data from different sources.

[0127] Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A bearing system fault diagnosis method based on deep time-frequency domain adaptive network, characterized in that , the method comprises: Step S1, data set preparation: collect multi-domain vibration signals of bearings with different failure modes and establish a cross-domain data set, including the annotated source data set D s , unlabeled target dataset D t And the test dataset D test ; Step S2, model initialization: construct a deep time-frequency domain adaptive network, and use parameter θ to initialize the deep time-frequency domain adaptive network, and then prepare hyperparameter tuning according to the selected data set; Step 3S, model parameter optimization: using cross-domain training set D s and D t Training the deep time-frequency domain adaptive network; Step S4, test verification: output the optimized deep time-frequency domain adaptive network to the test set D test The classification results are collected and analyzed.

2. A bearing system fault diagnosis method based on deep time-frequency domain adaptive network as claimed in claim 1, characterized in that: The construction of the deep time-frequency domain adaptive network includes: obtaining spectrum representation by discrete Fourier transform, spectrum neural layer calculation, and calculating Sinkhorn divergence by iterative data solution.

3. A bearing system fault diagnosis method based on deep time-frequency domain adaptive network as claimed in claim 2, characterized in that: The spectrum representation is obtained by discrete Fourier transform. For a given time series sample x∈R containing C channels and t time points, C×T , perform a 1D discrete Fourier transform on each channel to obtain f = F(x)∈C C×T , the expression is: Where k represents the kth frequency index, c represents the cth channel, and f (c) Represents the signal x (c) The discrete Fourier transform result, F(x (c) ) is also a signal x (c) The discrete Fourier transform result, x (c) represents the original signal of the cth channel, t represents each discrete time point in the time series, and T represents the signal x (c) The total number of samples, e is the natural constant Euler number, which is used as the base of the exponential function in Fourier transform, j is the imaginary unit, 2π is the coefficient in the exponential function, and C represents the total number of channels.

4. A bearing system fault diagnosis method based on deep time-frequency domain adaptive network as claimed in claim 2, characterized in that: The spectrum neural layer calculation includes: spectrum convolution, spectrum pooling, spectrum activation, and spectrum batch normalization; The spectral convolution adopts the complex convolution type. Given a complex input vector x=u+iv∈C, a complex filter matrix W=A+iB∈C is used for convolution, where u and v∈R are real vectors, A and B∈R are real matrices, and the complex convolution calculation expression is: W*x=(A*uB*v)+i(B*uA*v) Where W*x represents the product between vector x and matrix W, the symbol * represents the convolution operation, W is a complex matrix containing real and imaginary parts, and x is a complex vector; A and B represent linear transformations acting on u and v respectively, u and v represent the real and imaginary parts of the complex vector x respectively, and i represents the imaginary unit; The matrix form expression is: in, represents the real part of the complex expression W*x, Represents the imaginary part of the complex expression W*x; The spectrum pooling is performed based on the importance of frequency components to retain the main frequency information. The spectrum pooling process is expressed as: Where Y is the output after pooling, Pool represents the pooling operation, x(t) is the time domain signal, and f is the frequency; The spectrum activation adopts a complex activation function based on ReLU, that is, the zReLU activation function. Given a complex input x∈C, zReLU only retains the value of the first quadrant, and the expression is: Among them, θ x represents the phase of x, which satisfies the Cauchy-Riemann equation, except for the set Any point in ; The spectral batch normalization is to avoid gradient vanishing by batch normalization and to accelerate training. Given a small batch where x i ∈C, this task is regarded as a whitened two-dimensional vector, expressed as: in, represents the normalized data, E[X] represents the expected value of the matrix X, and V represents the covariance matrix. The expression is: Among them, V rr , V ri , V ir and V ii Respectively represent the specific elements in the covariance matrix V, and Represent the real and imaginary parts of the matrix X respectively, Cov represents the covariance operator symbol, which is used to determine Save Standard complex distribution with mean μ = 0, covariance Γ = 1 and pseudo-covariance Γ = 0; the expressions for mean, covariance and pseudo-covariance are: Among them, μ represents the data The expected value or mean of , Γ represents the covariance, Π represents the pseudo-covariance, and i represents the imaginary unit; Spectral batch normalization has two parameters, including the shift parameter β and the scaling parameter γ, both of which are complex. There are three degrees of freedom to ensure that the variances of the two original principal components are 1, and the translation parameter β = β r +iβ i With two trainable values ​​corresponding to the real and imaginary parts, Spectral Batch Normalization (SBN) is defined as: Among them, SBN represents the result of batch normalization operation, β is the shift parameter, γ is the scaling parameter, and the initialization γ ri =β r =β i =0.

5. A bearing system fault diagnosis method based on deep time-frequency domain adaptive network as claimed in claim 2, characterized in that: The Sinkhorn divergence is calculated by iterative data solution, and two input distributions are initialized, namely, the characteristic data distribution and the fault mode distribution of the bearing system. The optimization calculation is performed by Sinkhorn divergence, and these distributions are gradually adjusted so that they are minimized under a certain metric. The calculated Sinkhorn divergence is obtained to measure the difference between the two distributions. Regularization is known to be equivalent to limiting the search space, and has a scaling form of: P0=diag(u)Kdiag(v) Where P0 represents the value obtained after matrix transformation, diag(u) performs a diagonal matrix operation on the vector u, the matrix K = exp(-Cη) is the Gibbs kernel, diag(v) performs a diagonal matrix operation on the vector v, and exp(·) represents an element-by-element operation. Starting from the selected initial value, the fixed point is solved by the following iterative method: Among them, u (l+1) represents the updated value of vector u in the l+1th iteration, v (l+1) represents the updated value of vector v in the l+1th iteration, u (l) and v (l) Respectively represent the current value in the lth iteration, u s Represents the result of nonlinear transformation of vector u, u t represents the transposed form of vector u, t is the time step, s represents the index value, K T represents the transposed matrix of matrix K; After L iterations, the best pairing is P( L) =diag(u (L) )Kdiag(v (L) ), the final divergence is: in, represents the calculation result of the final divergence, η represents the regularization parameter, C is a matrix, P (L) It also represents a matrix, L is the current number of layers of the matrix, c ij represents the element in the i-th row and j-th column of the matrix C, n s Indicates that s The number of samples involved, n t Indicates that t The number of samples involved, and Respectively represent vector u s and u t The i-th and j-th vector elements in the L-th layer, K ij Represents the element in the i-th row and j-th column of the matrix K; The output features of the deep time-frequency domain adaptive network are mapped to various fault categories, and a fully connected layer with a SoftMax activation function is used as a classifier to output category probabilities.

6. A bearing system fault diagnosis method based on deep time-frequency domain adaptive network as claimed in claim 2, characterized in that: The goal of the deep time-frequency domain adaptive network is to minimize the structural risk of the network in the target domain, which is expressed as: Among them, θ * represents the optimal parameter in the optimization process, θ is the network parameter, ε t represents the objective function, Pr[·] represents the data distribution in the training dataset, D represents the dataset containing the input feature x and the corresponding label y, t is the time step, c(·) is the loss function, g(x) represents the predicted value generated by the model for the input x, and y is the target variable to be predicted by the model during training; The objective function of the deep time-frequency domain adaptive network minimizes both the empirical risk in the source domain and the difference between domains. The former is expressed as the classification error based on supervised learning, namely: in, Indicates the calculated value, n s is the number of samples, C represents the total number of categories, is the calculation symbol of the cross entropy loss function, i and s are index variables, is the i-th sample x in the dataset i The sth subset of represents the i-th sample y i The sth subset of ; The objective function expression of the deep time-frequency domain adaptive network is: Among them, θ * represents the optimal parameter in the optimization process, θ is the network parameter, argmin represents the minimization operation, is the objective function, is the calculation result of the final divergence, η represents the regularization parameter, and λ represents the trade-off coefficient.

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