A bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning

Abstract

The present invention relates to a bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning, and the method comprises: obtaining a plurality of normal vibration signals, a plurality of outer ring fault vibration signals, a plurality of inner ring fault vibration signals, and a plurality of rolling element fault vibration signals of a rolling bearing; performing VMD preprocessing and CWT processing on each normal vibration signal, outer ring fault vibration signal, inner ring fault vibration signal, and rolling element fault vibration signal in sequence, so as to obtain a data set including a normal matrix, an outer ring fault matrix, an inner ring fault matrix, and a rolling element fault matrix; performing global combination optimization on two parameters of SDAE, namely a learning rate and a batch size, by using SSA, so as to obtain an optimized SDAE; inputting the data set into the optimized SDAE for training; and inputting the collected rolling bearing signal to be detected into the trained SDAE to obtain a fault evaluation and diagnosis result.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial equipment fault diagnosis, and in particular to a bearing fault diagnosis method based on wavelet time-frequency graph and deep learning. Background Art

[0002] Bearings are widely used in transmission systems in aerospace, transportation, and industrial production. Rolling bearing failures can cause significant losses and impacts to transmission equipment. Bearing health monitoring and fault diagnosis are crucial for the stable operation of today's industrial systems.

[0003] The information contained in bearing vibration signals can be used to monitor bearing condition and determine the type of bearing fault. Health monitoring and fault diagnosis primarily involve data acquisition, feature extraction, and pattern recognition. The ability to adaptively extract features from vibration signals is a key criterion for evaluating the quality of fault diagnosis models. Early fault diagnosis relies on experience or simple measurement equipment. This not only requires manual feature extraction and is susceptible to subjective factors, but also results in low diagnostic accuracy and high costs.

[0004] With the development of modern computer technology, fault diagnosis technology based on time-frequency analysis has emerged. In addition, with the continuous development of machine learning, deep neural networks are gradually being used to diagnose bearing faults. Using deep neural networks to diagnose bearing faults can not only achieve end-to-end manual processing, but also improve diagnostic accuracy and save diagnostic time. In view of this, this application combines time-frequency analysis and deep learning to study fault diagnosis models, and provides a bearing fault diagnosis method based on VMD-CWT (wavelet time-frequency diagram) and SSA-SDAE (deep learning). Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning.

[0006] In order to solve the above problems, the technical solution adopted by the present invention is:

[0007] A bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning, the method comprising:

[0008] Acquire multiple normal vibration signals of the rolling bearing in a normal vibration state, multiple outer ring fault vibration signals in an outer ring fault vibration state, multiple inner ring fault vibration signals in an inner ring fault vibration state, and multiple rolling element fault vibration signals in a rolling element fault vibration state;

[0009] After VMD preprocessing and CWT processing are performed on each normal vibration signal, outer race fault vibration signal, inner race fault vibration signal, and rolling element fault vibration signal in sequence, a data set including a normal matrix, an outer race fault matrix, an inner race fault matrix, and a rolling element fault matrix is ​​obtained;

[0010] Use SSA to perform global combined optimization on the learning rate and batch size parameters of SDAE to obtain the optimized SDAE;

[0011] Inputting the data set into the optimized SDAE for training;

[0012] The collected rolling bearing signals to be tested are input into the trained SDAE to obtain fault assessment and diagnosis results.

[0013] As an embodiment of the invention, each normal vibration signal, outer ring fault vibration signal, inner ring fault vibration signal, and rolling element fault vibration signal is subjected to VMD preprocessing and CWT processing in sequence to obtain a data set including a normal matrix, an outer ring fault matrix, an inner ring fault matrix, and a rolling element fault matrix, including:

[0014] After performing VMD preprocessing and CWT processing on each normal vibration signal in sequence, a two-dimensional scale feature matrix corresponding to the normal vibration signal is obtained, and a normal matrix is ​​obtained based on the two-dimensional scale feature matrices corresponding to multiple normal vibration signals;

[0015] After performing VMD preprocessing and CWT processing on each outer ring fault vibration signal in sequence, a two-dimensional scale feature matrix corresponding to the outer ring fault vibration signal is obtained, and an outer ring fault matrix is ​​obtained based on the two-dimensional scale feature matrices corresponding to multiple outer ring fault vibration signals;

[0016] After performing VMD preprocessing and CWT processing on each inner race fault vibration signal in sequence, a two-dimensional scale feature matrix corresponding to the inner race fault vibration signal is obtained, and an inner race fault matrix is ​​obtained based on the two-dimensional scale feature matrices corresponding to the multiple inner race fault vibration signals;

[0017] After performing VMD preprocessing and CWT processing on each rolling element fault vibration signal in sequence, a two-dimensional scale feature matrix corresponding to the rolling element fault vibration signal is obtained, and a rolling element fault matrix is ​​obtained based on the two-dimensional scale feature matrices corresponding to the multiple rolling element fault vibration signals;

[0018] The normal matrix, outer race fault matrix, inner race fault matrix and rolling element fault matrix are saved in the data set.

[0019] As an embodiment of the invention, each normal vibration signal is sequentially subjected to VMD preprocessing and CWT processing to obtain a two-dimensional scale feature matrix corresponding to the normal vibration signal, and a normal matrix is ​​obtained based on the two-dimensional scale feature matrices corresponding to multiple normal vibration signals, including:

[0020] Each normal signal is preprocessed by VMD to obtain multiple BIMFs of different frequencies. The relevant kurtosis value of each BIMF is calculated, and the BIMF corresponding to the maximum relevant kurtosis value is obtained as the key BIMF.

[0021] The key BIMF is processed by CWT to obtain a two-dimensional scale feature matrix corresponding to the normal vibration signal;

[0022] A normal matrix is ​​obtained according to the two-dimensional scale feature matrices corresponding to multiple normal vibration signals.

[0023] As an embodiment of the invention, obtaining a normal matrix based on a two-dimensional scale feature matrix corresponding to a plurality of normal vibration signals includes:

[0024] The two-dimensional scale feature matrices corresponding to the plurality of normal vibration signals form a normal feature matrix;

[0025] Performing dimension reduction and data normalization operations on the normal feature matrix to obtain the normal matrix.

[0026] As an embodiment of the present invention, the following formula is used to calculate the relevant kurtosis value of each BIMF:

[0027]

[0028] Among them, y n is the signal, T is the period of interest, N is the number of sampling points of the signal, and M is the number of shifted periods.

[0029] As an embodiment of the invention, the use of SSA to perform global combined optimization on the two parameters of SDAE, learning rate and batch size, to obtain an optimized SDAE, includes:

[0030] (1) Set the search range of the sparrow group according to the value range of the learning rate and batch size;

[0031] (2) Initialize the parameters related to the sparrow search algorithm, including the number of sparrow populations, the number of producers, and the safety threshold;

[0032] (3) Initialize the sparrow’s position and calculate its fitness, using the cross entropy of the network fine-tuning phase as the sparrow’s fitness;

[0033] (4) Use the sparrow search algorithm for iterative optimization:

[0034] During one iteration, the fitness values ​​are compared and the best and worst positions of the sparrows in the group are recorded. The position of the sparrow with the smallest fitness value is the current global optimal position X. best , the position of the sparrow with the largest fitness is the global worst position X worst ;

[0035] (5) Determine whether the current number of iterations exceeds the upper limit of iterations:

[0036] If yes, the iteration ends and the global optimal result X is output best [α * ,β * ] and its iterative error curve; if not, execute step (6);

[0037] (6) Initialize the sparrows that are out of the search range, the sparrows at the edge of the group move closer to the center, and the sparrows at the center of the group move randomly;

[0038] (7) The parameter combination X[α,β] corresponding to the position of the sparrow is brought into the SDAE network to obtain the cross entropy between the actual value and the predicted value, that is, the fitness of the sparrow; the number of iterations is increased by 1, and the process jumps to step (4).

[0039] As an embodiment of the invention, inputting the data set into the optimized SDAE for training includes:

[0040] Dividing the data set into a plurality of training sets and a plurality of test sets according to the vibration state, each of the training set and the test set carries a label for indicating the vibration state;

[0041] Inputting multiple test sets into the optimized SDAE for training;

[0042] Inputting a plurality of the test sets into the trained SDAE to test the classification effect of the SDAE;

[0043] When it is determined that the classification effect reaches a preset effect, it is determined that the SDAE training is completed.

[0044] As an embodiment of the invention, the step of inputting the collected rolling bearing signal to be detected into the trained SDAE to obtain a fault diagnosis result includes:

[0045] The collected rolling bearing signal to be detected is subjected to VMD preprocessing and CWT processing to obtain a two-dimensional scale feature matrix corresponding to the rolling bearing signal to be detected. The two-dimensional scale feature matrix is ​​input into the trained SDAE for fault diagnosis to obtain fault assessment and diagnosis results.

[0046] The beneficial effects of adopting the above technical solution are:

[0047] The present invention provides a bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning, which obtains multiple normal vibration signals of a rolling bearing in a normal vibration state, multiple outer ring fault vibration signals in an outer ring fault vibration state, multiple inner ring fault vibration signals in an inner ring fault vibration state, and multiple rolling body fault vibration signals in a rolling body fault vibration state; each normal vibration signal, outer ring fault vibration signal, inner ring fault vibration signal and rolling body fault vibration signal is subjected to VMD preprocessing and CWT processing in sequence to obtain a data set including a normal matrix, an outer ring fault matrix, an inner ring fault matrix and a rolling body fault matrix; SSA is used to perform global combination optimization on the two parameters of SDAE, namely the learning rate and batch size, to obtain an optimized SDAE; the data set is input into the optimized SDAE for training to obtain the rolling bearing fault diagnosis model.

[0048] This rolling bearing fault diagnosis model establishment method can achieve complete separability of state features through VMD and CWT processing, and realize that feature information has better aggregation while being separable, which can improve the fault diagnosis accuracy. By using SSA to perform global combination optimization on the learning rate and batch size of SDAE parameters, the adaptive adjustment effect of the network structure is achieved, and the problem of neuron gradient dispersion or disappearance in the fault diagnosis process of traditional SDAE under high noise and variable working conditions is solved, so that the network diagnosis accuracy and training time indicator quality are synergistically improved.

[0049] In addition, the VMD-CWT-SSA-SDAE model provided by the present invention has good generalization for equipment health monitoring and fault diagnosis in multiple working conditions and high-noise environments, basically meeting engineering requirements, and is an ideal model for bearing fault diagnosis in industrial equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a schematic diagram of the autoencoder structure.

[0051] Figure 2 This is a diagram of DAE network training.

[0052] Figure 3 This is a schematic diagram of the stacked denoising autoencoder structure.

[0053] Figure 4 It is a graph showing how the cross entropy value changes with the number of iterations.

[0054] Figure 5 It is the original signal diagram of four bearing conditions.

[0055] Figure 6 This is the signal diagram after VMD processing (inner circle fault).

[0056] Figure 7is the time scale diagram of the vibration signal.

[0057] Figure 8 It is a scatter plot of data feature information extracted by traditional feature extraction.

[0058] Figure 9 It is a scatter plot of data feature information extracted by the algorithm provided in the embodiment of the present invention.

[0059] Figure 10 The accuracy of the 10 experiments of the established model

[0060] Figure 11 This is a comparison chart of multiple algorithms optimizing deep neural networks.

[0061] Figure 12 It is the time domain diagram of the original signal and the aliased signal.

[0062] Figure 13 It is the confusion matrix of fault diagnosis using SVM on network samples after adding noise.

[0063] Figure 14 It is the confusion matrix of fault diagnosis of network samples after adding noise using Non-opt-SDAE.

[0064] Figure 15 It is the confusion matrix of fault diagnosis of network samples after adding noise using SSA-DBN.

[0065] Figure 16 It is the confusion matrix of fault diagnosis of network samples after adding noise using SSA-SDAE. DETAILED DESCRIPTION

[0066] In order to make the objectives, technical solutions and advantages of the present invention more clear, the invention is clearly and completely described below in conjunction with specific embodiments.

[0067] The embodiment of the present invention provides a bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning, specifically a rolling bearing fault diagnosis model establishment method based on VMD-CWT and SSA-SDAE, wherein VMD refers to variational mode decomposition, CWT refers to continuous wavelet transform, SSA refers to sparrow search algorithm, and SDAE refers to a deep neural network composed of multiple denoising autoencoders connected end-to-end.

[0068] Methods include:

[0069] Step S1, obtaining multiple normal vibration signals of the rolling bearing in a normal vibration state, multiple outer ring fault vibration signals in an outer ring fault vibration state, multiple inner ring fault vibration signals in an inner ring fault vibration state, and multiple rolling element fault vibration signals in a rolling element fault vibration state.

[0070] The normal vibration signal, outer ring fault vibration signal, inner ring fault vibration signal and rolling element fault vibration signal can be input by a tester or acquired in real time when the rolling bearing vibrates.

[0071] Step S2: After VMD preprocessing and CWT processing are performed on each normal vibration signal, outer ring fault vibration signal, inner ring fault vibration signal and rolling element fault vibration signal in sequence, a data set including a normal matrix, an outer ring fault matrix, an inner ring fault matrix and a rolling element fault matrix is ​​obtained.

[0072] This step specifically includes:

[0073] Step S201: After performing VMD preprocessing and CWT processing on each normal vibration signal in sequence, a two-dimensional scale feature matrix corresponding to the normal vibration signal is obtained, and a normal matrix is ​​obtained based on the two-dimensional scale feature matrices corresponding to multiple normal vibration signals;

[0074] The process of this step is as follows:

[0075] Step S2011: Perform VMD preprocessing on each normal signal to obtain multiple BIMFs with different frequencies, calculate the relevant kurtosis value of each BIMF, and obtain the BIMF corresponding to the maximum relevant kurtosis value as the key BIMF.

[0076] (1) VMD preprocessing:

[0077] Variational mode decomposition (VMD) can be divided into two processes: variation and solution. The variational process is to process the nonlinear and non-stationary original signal and decompose the original signal into multiple band-limited intrinsic mode functions (BIMF). BIMF is an amplitude-frequency modulation (AM-FM) harmonic signal. k (t), assuming its amplitude is A k (t), with a phase of φ k (t), the mathematical expression can be expressed as:

[0078] u k (t) = A k (t)cos(φ k (t))

[0079] Among them, cos(φ k (t)) is the instantaneous frequency.

[0080] The constraints of the variational process are K modal functions u k The sum of the bandwidths of (t) is the smallest, and the mathematical expression is as follows:

[0081]

[0082] Where, ω k represents the center frequency of the modal component, δ(t) is the Dirac distribution function, t is time, and * represents convolution.

[0083] To ensure that the modal components are absolutely integrable, a quadratic penalty factor α is introduced. The mathematical expression of the augmented Lagrange function is shown in Formula X. The constrained problem of the variational process is transformed into an unconstrained problem.

[0084]

[0085] Where λ is the Lagrange multiplier.

[0086] The solution uses the Alternating Direction Method of Multipilers (ADMM) to find the optimal solution that satisfies the conditions by updating the intrinsic mode functions and the center frequencies of each mode function, thereby obtaining the optimal signal decomposition result. The update functions for both are shown in Formula X.

[0087]

[0088] Where τ is the noise tolerance.

[0089] In this way, a plurality of BIMFs of different frequencies can be obtained based on each normal signal.

[0090] (2) Calculate the relevant kurtosis value of each BIMF:

[0091] To select the modal components that contain the most fault characteristic information (for example, noise interference caused by environmental factors during the acquisition process), the correlation kurtosis, which is more sensitive to the fault impact of the signal, is introduced as an indicator of the presence of fault information in the modal components. The evaluation criterion is based on the maximum kurtosis criterion. That is, when the kurtosis value is small, it indicates that the main component of the vibration signal is Gaussian white noise, the vibration signal is close to a normal distribution, and there is no impact component. When the kurtosis value is large, it indicates that the vibration information contains more impact components and the possibility of rolling bearing failure is high. Therefore, the correlation kurtosis value of each BIMF is calculated using the following formula:

[0092]

[0093] Among them, y nis the signal, T is the period of interest, N is the number of sampling points of the signal, and M is the number of shifted periods;

[0094] The BIMF corresponding to the maximum correlation kurtosis value is obtained as the key BIMF.

[0095] Step S2012: Process the key BIMF through CWT to obtain a two-dimensional scale feature matrix corresponding to the normal vibration signal.

[0096] Continuous wavelet transform CWT can convert the one-dimensional BIMF into a two-dimensional feature matrix, thereby extracting the two-dimensional time scale characteristics of the signal. The two-dimensional time scale feature matrix obtained by time-frequency analysis preprocessing (i.e. VMD and CWT processing) can be used as the input sample of the subsequent deep neural network (SDAE). It should be noted that the wavelet time-frequency graph is the two-dimensional image corresponding to the two-dimensional scale feature matrix. The "wavelet time-frequency graph and deep learning" described in the present invention is based on the two-dimensional scale feature matrix of each signal and the subsequent deep neural network (SDAE), thereby realizing the diagnosis of bearing faults.

[0097] The basic principle of CWT is to combine the signal f(t) and the wavelet function Inner product, get the corresponding wavelet transform coefficient W f (a, b). The greater the similarity between the signal and the wavelet function, the larger the resulting wavelet transform coefficients, and the higher the amplitude of the characteristic energy block clustered somewhere in the time-scale phase plane. Conversely, the lower the amplitude. By adjusting the scale and translation of the wavelet function, we can obtain the two-dimensional time-scale characteristic matrix of the signal f(t).

[0098] Assume that a basic wavelet is and Basic wavelet The wavelet function is obtained by scaling and translating

[0099]

[0100] Where a, b∈R, a≠0, a is the scaling factor, and b is the translation factor. The change of a corresponds to the change of the scale of the wavelet function, and the change of b corresponds to the change of the displacement of the wavelet function.

[0101] For any signal f(t)∈L 2 (R), the continuous wavelet transform of f(t) is:

[0102]

[0103] in, yes The complex conjugate of , <·> represents the inner product.

[0104] Step S2013: Obtain a normal matrix according to the two-dimensional scale features corresponding to the multiple normal vibration signals.

[0105] The method comprises: forming a normal feature matrix from two-dimensional scale features corresponding to a plurality of normal vibration signals; and performing dimension reduction and data normalization operations on the normal feature matrix to obtain the normal matrix.

[0106] Step S202: After performing VMD preprocessing and CWT processing on each outer race fault vibration signal in sequence, a two-dimensional scale feature corresponding to the outer race fault vibration signal is obtained, and an outer race fault matrix is ​​obtained based on the two-dimensional scale features corresponding to the multiple outer race fault vibration signals;

[0107] Step S203: After performing VMD preprocessing and CWT processing on each inner race fault vibration signal in sequence, a two-dimensional scale feature corresponding to the inner race fault vibration signal is obtained, and an inner race fault matrix is ​​obtained based on the two-dimensional scale features corresponding to the multiple inner race fault vibration signals;

[0108] Step S204: performing VMD preprocessing and CWT processing on each rolling element fault vibration signal in sequence to obtain a two-dimensional scale feature corresponding to the rolling element fault vibration signal, and obtaining a rolling element fault matrix based on the two-dimensional scale features corresponding to the multiple rolling element fault vibration signals;

[0109] Among them, the specific process of step S202-step S204 is similar to step S201, the only difference is that the signal to be processed is replaced by the normal vibration signal to the outer ring fault vibration signal, the inner ring fault vibration signal, and the rolling element fault vibration signal, which will not be repeated in this application.

[0110] Step S205: Save the normal matrix, outer race fault matrix, inner race fault matrix and rolling element fault matrix into a data set.

[0111] Step S3: Use SSA to perform global combined optimization on the learning rate and batch size parameters of SDAE to obtain the optimized SDAE.

[0112] (1) Explain the autoencoder and denoising autoencoder DAE

[0113] The autoencoder is the main component of the stacked autoencoder. While minimizing the difference between input and output, the autoencoder performs feature extraction and parameter learning through unsupervised learning. The autoencoder is a feedforward neural network, a fully connected network consisting of a data input layer, a hidden layer, and an output layer. The structure of the autoencoder is as follows: Figure 1 As shown in Figure 2. From the input layer to the hidden layer is the data encoding process, and from the hidden layer to the output layer is the data decoding process.

[0114] Suppose there is a set of D-dimensional samples The encoding unit of the autoencoder takes the weighted sum of the input, adds the bias, and maps it to the feature space through the activation function to obtain the encoding of each sample. The decoding unit uses the same process to obtain the reconstructed samples The reconstruction of the autoencoder is x (n) and x′ (n) The minimum difference is the constraint condition, and the weights and biases are optimized.

[0115] For sample x, the activity value of the middle hidden layer of the autoencoder is the encoding of x, that is: The output of the autoencoder is the reconstructed data: Among them, f a 、f s are the activation functions of the encoder and decoder respectively, is the encoder weight, is the decoder weight. is the encoder bias, is the decoder bias. In order to improve the efficiency of network learning, bundling weights are often used, that is, In addition, the bundled weights play a role of regularization to some extent.

[0116] Given a set of samples x (n) ∈[0,1] D , 1≤n≤n, the autoencoder reconstruction constraint is shown in the following equation. By minimizing the reconstruction error, the network parameters can be effectively learned.

[0117]

[0118] in, λ is the regularization coefficient.

[0119] After the autoencoder training is completed, only the encoder output is retained as the input of the machine learning model.

[0120] In order to improve network performance, reduce overfitting and improve feature extraction capabilities, a denoising auto encoder (DAE) is constructed. Randomly set zeros at the output layer nodes of the auto encoder to add random noise to the input data. The DAE network training diagram is shown below. Figure 2 As shown, the damage data x is obtained by adding noise to the original data n , after the encoding and decoding process of the autoencoder, the reconstructed data x′ is obtained, which is close to the information characteristics of the original data.

[0121] The mathematical expression of the encoding process is: h = f a (w a x n +ba ), the mathematical expression of the decoding process is: x′=f s (w s h+b s ).

[0122] When the reconstruction error obtained through iterative calculations is small, the DAE network can reconstruct the original data from the damaged data. The hidden layer data is a low-dimensional representation of the original data and can serve as an effective fault signature for fault signal diagnosis. DAE can both extract the essential characteristics of the data and effectively reduce the data dimension. This ensures that the reduced-dimensional signal contains the essential characteristics of the fault while removing the redundant components of the high-dimensional signal, accelerating data processing and reducing the possibility of network overfitting.

[0123] (2) Explanation of SDAE

[0124] SDAE is a deep neural network composed of multiple denoising autoencoders connected end-to-end. The diagram of the stacked denoising autoencoder training process is as follows Figure 3 As shown in Figure 2. The training process of SDAE includes two steps: preprocessing and fine-tuning. In the preprocessing stage, multiple DAEs extract features from the data one by one through an end-to-end connection. The input dimension and output dimension of each DAE are the same size. Figure 2 denoted by the same color. The hidden layer features of each DAE serve as the input features of the next DAE. After completing the unsupervised preprocessing process, the outputs of each DAE are chained sequentially. At the end of the supervised fine-tuning process, a softmax classifier is typically added to further regress the extracted features and classify the data. The cross entropy between the actual and predicted values ​​is used as the loss function, as shown in the following formula.

[0125]

[0126] Where y (n) Represents the predicted value of the nth sample, y′ (n) Represents the actual value of the nth sample. (l) is the weight matrix of layer l.

[0127] In the fine-tuning process, the loss function is used as the objective function to fine-tune the weights and biases of the cascade network, and the gradient descent method is used to update the parameters. The parameter update process is as follows:

[0128] ①. For a single sample, calculate the first hidden layer l2 to the output layer The activation value of each node, where the activation value of each node in the output layer is

[0129] ②、Calculate the output layer The residual of each node, the residual formula of node i is shown below.

[0130]

[0131] ③. Calculate the residual of each node in all hidden layers, as shown in the following formula.

[0132]

[0133] ④. For a single sample, calculate the partial derivative of the loss function with respect to parameters W and b. The formula is:

[0134]

[0135] ⑤. For the entire sample set, calculate the partial derivative of the loss function with respect to parameters W and b, and the formula is:

[0136]

[0137] ⑥. Update parameters W and b

[0138]

[0139] Where α is the learning rate.

[0140] (3) In the fine-tuning training process of the aforementioned SDAE, the two parameters of learning rate and batch size have a great influence on the network weight and bias. In the present invention, SSA is used to perform global combined optimization of the two parameters of SDAE, namely, learning rate and batch size, to improve the accuracy and efficiency of SDAE training. In addition, the optimal setting of hyperparameters such as the number of hidden layers and learning rate of SDAE has a huge impact on the fault diagnosis accuracy and generalization performance of the model. The SDAE used in the present invention contains 50 hidden layers, and its diagnostic accuracy is higher and the diagnostic convergence speed is faster.

[0141] The Sparrow Search Algorithm (SSA) is mathematically described as follows: Assume a d-dimensional search space with two types of sparrows, producers and predators, each with different tasks. Producers are responsible for finding food resources and guiding the flock toward resource-rich areas. Predators act more like boosters for producers, constantly monitoring them and seizing opportunities to plunder food. Once a predator's food resources surpass those of the weakest producer, their roles are reversed. In other words, within a flock, the identities of producers and predators change dynamically, but the ratio between them remains constant. The presence of predators motivates producers to continuously search for more abundant food resources, gradually leading the flock toward its optimal state.

[0142] The steps for using SSA to perform global combined optimization of the learning rate and batch size parameters of SDAE are as follows:

[0143] ① Set the search range of the sparrow group according to the value range of the learning rate and batch size;

[0144] The location information of the sparrow group can be represented by array X:

[0145]

[0146] The size of the sparrow's search range is determined by the value ranges of the two parameters, learning rate and batch size. The horizontal axis of the sparrow's position is the learning rate, and the vertical axis is the batch size. Therefore, the search range of the sparrow group can be set according to the value ranges of the initial learning rate and initial batch size.

[0147] ② Initialize the parameters related to the sparrow search algorithm, including the number of sparrow populations, the number of producers, and the safety threshold.

[0148] ③ Initialize the sparrow's position and calculate its fitness, using the cross entropy of the network fine-tuning phase as the sparrow's fitness;

[0149] For any sparrow, its location information can be represented by the vector X[α,β], and the initial fitness of each sparrow is obtained based on the vector X[α,β], and the fitness of all sparrow groups is stored in the vector F x inside:

[0150]

[0151] Training SDAE with different learning rate and batch size combinations yields different cross-entropies between actual and predicted values. The fitness function for each sparrow is the cross-entropy corresponding to its coordinates. The optimization metric for the sparrow search algorithm is to minimize the cross-entropy between actual and predicted values.

[0152] ④. Use the sparrow search algorithm for iterative optimization:

[0153] During one iteration, the fitness values ​​are compared and the best and worst positions of the sparrows in the group are recorded. The position of the sparrow with the smallest fitness value is the current global optimal position X. best , the position of the sparrow with the largest fitness is the global worst position X worst ;

[0154] ⑤. Determine whether the current number of iterations exceeds the upper limit of iterations:

[0155] If yes, the iteration ends and the global optimal result X is output best [α * ,β * ] and its iterative error curve; if not, proceed to step ⑥;

[0156] ⑥ Initialize the sparrows that are out of the search range so that the sparrows at the edge of the group move closer to the center and the sparrows at the center of the group move randomly.

[0157] The following methods can be used to move sparrows:

[0158] In a population, producers make up 10% to 20% of the total population, have higher fitness, and are more capable of foraging. Therefore, they gain a larger foraging range. During each iteration, the producer position is updated according to the following formula.

[0159]

[0160] Among them, t (t = 1, 2, ..., Itera) is the number of iterations of optimization, iter max Is a fixed value, representing the maximum number of iterations. α and Q are both random numbers (α∈(0,1], Q~N(μ,σ 2 )). L is a 1×D matrix with all elements set to 1. R2 is the alert value, and ST is the safety threshold. When R2 ≥ ST, the sparrow colony must immediately migrate to a safe area to avoid the intruder.

[0161] Therefore, the predator updates its position according to the following formula:

[0162]

[0163] Where, X P represents the optimal position among producers. X worst Indicates the worst position in the current range. When i>n / 2, it means that the i-th predator has a very poor fitness and is likely to be in a hungry state.

[0164] The sparrows with alert capabilities update their positions according to the following formula:

[0165]

[0166] When f i =f g When , it indicates that the sparrow has discovered the enemy and is moving closer to other sparrows to avoid being attacked by the enemy.

[0167] ⑦. Substitute the parameter combination X[α,β] corresponding to the sparrow's position into the SDAE network to obtain the cross entropy between the actual value and the predicted value, i.e., the sparrow's fitness. Increase the number of iterations by 1 and jump to step ④.

[0168] (4) This step is described with a specific embodiment:

[0169] SSA is used to globally optimize the learning rate and batch size of SDAE. The search range for the learning rate is [0.011], and the search range for the batch size is [1 90]. The key parameter values ​​of the sparrow search algorithm are shown in Table 1. Figure 4 The cross entropy of the test data changes with the number of iterations. As the number of iterations increases, the cross entropy converges in a step-by-step manner. After the 19th iteration, the cross entropy stabilizes at 0.07, achieving a relatively ideal convergence state. The optimal learning rate and batch size combination found is [0.1776054, 4].

[0170] Table 1 SSA parameter settings

[0171]

[0172] The structural parameters of SDAE are shown in Table 2. The number of nodes in the input layer and the output layer are determined by the input samples and the fault categories, respectively. The SDAE parameter combination settings obtained after SSA global optimization are shown in Table 3.

[0173] Table 2 Parameters of SDAE structure

[0174]

[0175] Table 3 SDAE parameter combination settings

[0176]

[0177] Step S4: input the data set into the optimized SDAE for training.

[0178] It includes:

[0179] Step S401: dividing the data set into multiple training sets and multiple test sets according to the vibration state, each of the training set and the test set carries a label for indicating the vibration state;

[0180] Step S402: input multiple test sets into the optimized SDAE for training;

[0181] Step S403: inputting the plurality of test sets into the trained SDAE to test the classification effect of the SDAE;

[0182] Step S404: When it is determined that the classification effect reaches a preset effect, it is determined that the SDAE training is completed.

[0183] Step S5: Input the collected rolling bearing signal to be detected into the trained SDAE to obtain the fault assessment and diagnosis results.

[0184] The method includes: performing VMD preprocessing and CWT processing on the collected rolling bearing signal to be detected to obtain a two-dimensional scale feature matrix corresponding to the rolling bearing signal to be detected, inputting the two-dimensional scale feature matrix into the trained SDAE for fault diagnosis, and obtaining fault assessment and diagnosis results.

[0185] In addition, compared with the Chinese invention patent "A bearing fault diagnosis method and system based on wavelet time-frequency graph and deep learning" with application number 202111498873.6, the fault diagnosis accuracy of the present invention is higher at 99.7%; the time required for diagnosis is shorter, and multiple tests have found that the diagnostic results of the present invention are more stable.

[0186] The embodiment of the present invention also conducts experimental verification and performance analysis on the rolling bearing fault diagnosis model provided by the present invention.

[0187] (1) Bearing database

[0188] To verify the feasibility of the VMD-CWT-SSA-SDAE model in bearing fault detection and diagnosis, multiple multi-type tests were conducted using the CaseWestern Reserve University (CWRU) bearing dataset. To verify the generalization of the VMD-CWT-SSA-SDAE model, simulation experiments were conducted using the Southeast University induction motor ML bearing dataset.

[0189] (2) Time-frequency feature extraction of original data

[0190] The CWRU dataset was used as the raw data. The bearing data sampling frequency was 12,000 Hz, and the motor speed was 1,730 r / min. The research object was the drive-end bearing under load. Bearings have four different states: normal state, inner ring fault, rolling element fault, and outer ring fault. Fault states are classified as mild, moderate, and severe based on the degree of bearing damage. The fault diameter for mild damage is 0.007 in, the fault diameter for moderate damage is 0.014 in, and the fault diameter for severe damage is 0.021 in (1 in = 2.54 cm). The bearing state table of the CWRU dataset is shown in Table 4.

[0191] Table 4. Bearing test status in the CWRU dataset

[0192]

[0193] Taking a set of data with a fault diameter of 0.004in as an example, the normal signal contains 485643 data points, and the three fault signals each contain 122136 data points. The feature extraction experiment is carried out. The original data points are divided using the window function to obtain the original signal, such as Figure 5The original signal is subjected to variational mode decomposition to obtain multiple band-limited intrinsic mode functions (BIMFs) of different frequencies. Taking the inner race fault signal as an example, the signal after VMD processing is shown in the figure below. Figure 6 shown.

[0194] Taking the inner race fault as an example, the kurtosis calculation results of each BIMF obtained after variational modal decomposition of the vibration signal are shown in Table 5. According to the maximum kurtosis criterion, BIMF3 has the largest relative kurtosis value, which means that BIMF3 contains relatively obvious fault characteristic information.

[0195] Table 5 Kurtosis values ​​of each BIMF after VMD decomposition (inner circle fault)

[0196]

[0197] Performing continuous wavelet transform on the BIMF obtained by decomposing the vibration signals of different bearing states can obtain the two-dimensional time scale feature matrix of multiple bearing vibration signals and draw the corresponding time scale diagram as shown in the figure. Figure 7 As shown. Figure 7 Comparison of the four images reveals significant differences in energy distribution across different bearing states. Therefore, CWT processing can reveal the characteristic information between vibration signals collected under different bearing states.

[0198] In order to further illustrate the effectiveness of the feature extraction process, this paper uses kernel principal component analysis (KPCA) to reduce the high-dimensional features of the samples to three-dimensional space for visualization, and obtains scatter plots of data feature information of samples that have undergone traditional feature extraction and feature extraction using the proposed algorithm. Figure 8 This is a scatter plot of feature information extracted through traditional features. It can be seen that the features of each state have certain clustering properties, but the intra-class distance of each feature is large and the inter-class distance is small. There is a lot of aliasing between features, which is difficult to distinguish. Figure 9 The scatter plot of feature information for samples extracted using the proposed algorithm shows that the state features are completely separable, with larger inter-class distances and smaller intra-class distances. The coordinate system also has a smaller magnitude, indicating that the feature information is both separable and highly aggregated. This comparison demonstrates that the proposed algorithm achieves superior feature extraction performance and can improve fault diagnosis accuracy.

[0199] (3) Diagnostic accuracy test (multiple experiments, multi-algorithm comparison experiments)

[0200] The present invention still uses the CWRU data set as test data. The bearing data set with a fault diameter of 0.004in is divided into 400 original samples, of which each bearing state contains 100 samples. The original samples are subjected to variational modal decomposition to extract the BIMF containing the most fault feature information, and then the continuous wavelet transform is used to obtain the two-dimensional time scale feature matrix of the BIMF. After singular value decomposition dimensionality reduction and data normalization, it constitutes the input sample of the stacked denoising autoencoder. The SDAE with the optimal structure is used for pattern recognition to obtain accurate fault classification results. The diagnosis results of 10 experiments are as follows. Figure 10 The average diagnosis rate can reach 99.7%.

[0201] To verify the superior performance of SSA-SDAE in fault diagnosis, four typical networks—BPNN, SVM, SSA-DBN, and SSA-SDAE—were selected for comparison. The experimental comparisons show that the SSA-SDAE network achieves higher diagnostic accuracy than other networks in both training and testing accuracy. Compared to other deep learning networks, it also exhibits a significant time advantage.

[0202] Table 6 Comparison of the accuracy of fault diagnosis in different networks

[0203]

[0204] In order to prove the superiority of the SSA algorithm in global parameter optimization, GA and PSO algorithms are introduced to adaptively select the hyperparameters of the SDAE network. The fault diagnosis effects of GA-SDAE, PSO-SDAE and SSA-SDAE are compared. The effect comparison chart is as follows: Figure 11 Compared with GA-SDAE and PSO-SDAE, the SSA used in the present invention can find the global optimal parameters of the SDAE network, achieve the reasonable configuration of network hyperparameters, and synergistically improve the quality of indicators such as network diagnosis accuracy and training time.

[0205] (4) Model generalization ability and noise resistance test

[0206] This paper applies the Southeast University induction motor ML bearing dataset to fault diagnosis and validates the generalization capability of the proposed algorithm. The ML bearing data set is selected for a 20 Hz rotation frequency and a load configuration of 2. 1,019,200 sampling points are taken from each data type to obtain the raw signal. The ML dataset contains five bearing states: normal, rolling element fault, inner race fault, outer race fault, and mixed fault. Table 7 describes the sample size and state labels for each of the five bearing states.

[0207] Table 7 Description of samples under five bearing conditions

[0208]

[0209] The vibration signal acquisition environment of rotating mechanical components is accompanied by various noise interferences, which poses a huge challenge to the adaptability of fault diagnosis models. Gaussian white noise is added to the original vibration signal to simulate data collected in a noisy working environment. Fault diagnosis is performed on the noisy vibration signal to evaluate the noise immunity of the fault diagnosis model. The noise level varies in different operating environments of different industrial equipment. The signal-to-noise ratio (SNR) is used to measure the noise level, which is defined as follows:

[0210]

[0211] Where: Ps is the signal power and Pn is the noise power.

[0212] Gaussian white noise with a signal-to-noise ratio of 20dB and a specified signal power of 10dBW is added to the original vibration signals corresponding to the five types of bearing conditions in the ML bearing data set. Taking the outer bearing ring fault as an example, Figure 12 They are the time domain diagram of the original vibration signal, the time domain diagram of Gaussian white noise, and the time domain diagram of the mixed superposition of the vibration signal and white noise.

[0213] SVM, the traditional SDAE (Non-opt-SDAE), SSA-DBN, and SSA-SDAE are used to diagnose network samples after adding noise. The confusion matrix is ​​used to measure the classification ability. The confusion matrix of the fault severity detection result is as follows: Figure 13-16 shown.

[0214] Depend on Figure 13-16 As shown in the figure, even if the data set is changed, the diagnostic accuracy of the SSA-SDAE model provided by the present invention is still between 96.7% and 98.7%, indicating that the model has good generalization. When the original data is contaminated by noise, the diagnostic accuracy of both SVM and the traditional SDAE is greatly affected. The traditional SDAE has the problem of gradient diffusion in a high-noise environment, and the diagnostic accuracy is low and unstable. The diagnostic accuracy of the SSA-DBN model is not greatly affected, but the stability is reduced. Figure 16 As can be seen, the diagnostic accuracy and stability of SSA-SDAE remain high even in high-noise environments, indicating its good noise immunity. This demonstrates that the proposed VMD-CWT-SSA-SDAE model has good generalization for equipment health monitoring and fault diagnosis in multiple operating conditions and high-noise environments, essentially meeting engineering requirements and making it an ideal model for bearing fault diagnosis in industrial equipment.

Claims

1. A bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning, characterized in that: The method comprises: Acquire a plurality of normal vibration signals of the rolling bearing in a normal vibration state, a plurality of outer ring fault vibration signals in an outer ring fault vibration state, a plurality of inner ring fault vibration signals in an inner ring fault vibration state, and a plurality of rolling element fault vibration signals in a rolling element fault vibration state; After each normal vibration signal, outer ring fault vibration signal, inner ring fault vibration signal and rolling element fault vibration signal are subjected to VMD preprocessing and CWT processing in sequence, a data set including a normal matrix, an outer ring fault matrix, an inner ring fault matrix and a rolling element fault matrix is ​​obtained; Use SSA to perform global combined optimization on the two parameters of SDAE, learning rate and batch size, to obtain the optimized SDAE; Inputting the data set into the optimized SDAE for training; The collected rolling bearing signals to be tested are input into the trained SDAE to obtain fault assessment and diagnosis results; After each normal vibration signal, outer ring fault vibration signal, inner ring fault vibration signal and rolling element fault vibration signal are sequentially subjected to VMD preprocessing and CWT processing, a data set including a normal matrix, an outer ring fault matrix, an inner ring fault matrix and a rolling element fault matrix is ​​obtained, including: After performing VMD preprocessing and CWT processing on each normal vibration signal in turn, a two-dimensional scale feature matrix corresponding to the normal vibration signal is obtained, and a normal matrix is ​​obtained according to the two-dimensional scale feature matrices corresponding to multiple normal vibration signals; After performing VMD preprocessing and CWT processing on each outer ring fault vibration signal in turn, a two-dimensional scale feature matrix corresponding to the outer ring fault vibration signal is obtained, and an outer ring fault matrix is ​​obtained according to the two-dimensional scale feature matrices corresponding to multiple outer ring fault vibration signals; After performing VMD preprocessing and CWT processing on each inner ring fault vibration signal in turn, a two-dimensional scale feature matrix corresponding to the inner ring fault vibration signal is obtained, and an inner ring fault matrix is ​​obtained according to the two-dimensional scale feature matrices corresponding to the multiple inner ring fault vibration signals; After performing VMD preprocessing and CWT processing on each rolling element fault vibration signal in turn, a two-dimensional scale feature matrix corresponding to the rolling element fault vibration signal is obtained, and a rolling element fault matrix is ​​obtained according to the two-dimensional scale feature matrices corresponding to the multiple rolling element fault vibration signals; The normal matrix, outer race fault matrix, inner race fault matrix and rolling element fault matrix are saved in the data set; After performing VMD preprocessing and CWT processing on each normal vibration signal in sequence, a two-dimensional scale feature matrix corresponding to the normal vibration signal is obtained, and a normal matrix is ​​obtained according to the two-dimensional scale feature matrices corresponding to multiple normal vibration signals, including: Each normal signal is preprocessed by VMD to obtain multiple BIMFs of different frequencies, and the relevant kurtosis value of each BIMF is calculated. The BIMF corresponding to the maximum relevant kurtosis value is obtained as the key BIMF; the relevant kurtosis value of each BIMF is calculated using the following formula: ； in, y n is the signal, T is the period of interest, N is the number of sampling points of the signal, and M is the number of shifted periods; Processing the key BIMF by CWT to obtain a two-dimensional scale feature matrix corresponding to the normal vibration signal; A normal matrix is ​​obtained according to the two-dimensional scale feature matrix corresponding to a plurality of normal vibration signals; The use of SSA to perform global combined optimization on the two parameters of SDAE, learning rate and batch size, obtains the optimized SDAE, including: (1) Set the search range of the sparrow group according to the value range of the learning rate and batch size; (2) Initialize the parameters related to the sparrow search algorithm, including the number of sparrow populations, the number of producers, and the safety threshold; (3) Initialize the position of the sparrow and calculate the fitness, and use the cross entropy of the network fine-tuning stage as the fitness of the sparrow; (4) Use the sparrow search algorithm for iterative optimization: In one iteration, the fitness values ​​are compared and the best and worst positions in the sparrow group are recorded. The position of the sparrow with the smallest fitness value is the current global optimal position. X best , the position of the sparrow with the highest fitness is the worst position in the world X worst ; (5) Determine whether the current number of iterations exceeds the iteration limit: If yes, the iteration ends and the global optimal result is output X best [α*,β*] and its iterative error curve; if not, execute step (6); (6) Initialize the sparrows that are out of the search range, the sparrows at the edge of the group move closer to the center, and the sparrows at the center of the group move randomly; (7) Combine the parameters corresponding to the sparrow's position X [α, β] is brought into the SDAE network to obtain the cross entropy between the actual value and the predicted value, i.e., the fitness of the sparrow; the number of iterations is increased by 1, and the process jumps to step (4).

2. A bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning according to claim 1, characterized in that: The step of obtaining a normal matrix according to the two-dimensional scale feature matrices corresponding to the plurality of normal vibration signals includes: The two-dimensional scale feature matrices corresponding to the plurality of normal vibration signals are used to form a normal feature matrix; The normal matrix is ​​obtained by performing dimension reduction and data normalization operations on the normal feature matrix.

3. The bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning according to claim 1 is characterized in that: The step of inputting the data set into the optimized SDAE for training comprises: According to the vibration state, the data set is divided into a plurality of training sets and a plurality of test sets, each of the training set and the test set carries a label for indicating the vibration state; Inputting multiple training sets into the optimized SDAE for training; Inputting a plurality of the test sets into the trained SDAE to test the classification effect of the SDAE; When it is determined that the classification effect reaches a preset effect, it is determined that the SDAE training is completed.

4. The bearing fault diagnosis method based on wavelet time-frequency diagram and deep learning according to claim 1 is characterized in that: The step of inputting the collected rolling bearing signal to be detected into the trained SDAE to obtain the fault diagnosis result comprises: The collected rolling bearing signal to be detected is subjected to VMD preprocessing and CWT processing to obtain a two-dimensional scale feature matrix corresponding to the rolling bearing signal to be detected. The two-dimensional scale feature matrix is ​​input into the trained SDAE for fault diagnosis to obtain fault assessment and diagnosis results.

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