CN114266339A - Rolling bearing fault diagnosis method based on small sample and GAF-DCGAN - Google Patents

Abstract

The invention discloses a rolling bearing fault diagnosis method based on a small sample and GAF-DCGAN, which comprises the steps of firstly carrying out wavelet denoising on a vibration signal of a noisy rolling bearing, obtaining a reconstructed vibration signal, and then converting the reconstructed vibration signal into a two-dimensional image by utilizing a Gemlar Angular Field (GAF); inputting the two-dimensional image into a depth convolution generation countermeasure network model for image generation; then, the generated image and the original image are mixed, and the expanded data is input into a fault diagnosis model for training, so that the problem of small samples is solved; and finally, inputting the fault image to be diagnosed into the trained fault diagnosis model to diagnose the fault of the rolling bearing. The invention also provides a judgment standard for adding the softmax layer, and after judgment, the image is input into the DCGAN fault diagnosis model added with the softmax layer for training. Finally, the accuracy of fault diagnosis is improved.

Description

Rolling bearing fault diagnosis method based on small sample and GAF-DCGAN

Technical Field

The invention belongs to the field of bearing fault diagnosis, and particularly relates to a fault diagnosis method for a rolling bearing of industrial field equipment based on a small sample and GAF-DCGAN.

Background

The rolling bearing is one of the core components of the industrial equipment and is also the main cause of system failure, and statistics shows that 45% -55% of equipment failure is caused by bearing damage, so whether the failure affects the normal operation, performance, efficiency and even safety of the whole industrial equipment system. In order to ensure the operational safety of industrial equipment, it is of great importance to perform effective fault diagnosis on rolling bearings. At present, most of fault diagnosis for the rolling bearing is to analyze and research one-dimensional vibration signals of the rolling bearing, and with the rapid development of deep learning, an intelligent fault diagnosis algorithm adopting the deep learning is widely applied to the field of fault diagnosis for the rolling bearing. Although these methods have achieved good results, the basis of most research is established in the case of sufficient fault data. In the actual production process of industrial equipment, the acquired fault data has two problems, namely, the probability of equipment failure is very low, the fault data is far insufficient, namely, the fault data belongs to small sample data, and therefore, the research on the fault diagnosis method of the small sample data is more in line with the practical application; the second aspect is that the collected data has the problem of complicated noise types, so the research on wavelet denoising of the rolling bearing fault data is particularly important.

In the prior art, the one-dimensional time series data is converted into a two-dimensional image through the GAF and then is input into a Convolutional Neural Network (CNN) model to realize fault diagnosis, but the problems that an actual fault data set contains noise and the number of samples is small are not fully considered only for western storage data. In addition, singular spectrum analysis is also performed on the vibration signal of the noisy faulty bearing to obtain a reconstructed vibration signal, and the reconstructed vibration signal is input into a WDCNN fault diagnosis model for fault diagnosis, but the advantages of CNN in the aspect of image feature extraction are not fully utilized, and the fault diagnosis accuracy rate cannot be well improved. In addition, Xulin, Zhengtong, Pabo, Tiange, Motor bearing fault diagnosis method [ J ] based on improved GAN algorithm, university of northeast China (Nature science edition), 2019,40(12): 1679-. However, the diagnostic process still has some defects, the two-dimensional image converted by the continuous wavelet transform processing vibration signal is a gray image, and the included characteristic information is incomplete, so that the fault diagnosis accuracy of the rolling bearing is influenced.

Disclosure of Invention

The invention aims to provide a rolling bearing fault diagnosis method based on a small sample and GAF-DCGAN, which is how to more accurately diagnose the fault of a bearing under the environment of the small sample under the condition of lacking of rolling bearing fault data in the actual production process of industrial equipment.

The technical solution for realizing the purpose of the invention is as follows:

a rolling bearing fault diagnosis method based on GAF-DCGAN is used for judging whether a bearing is in fault and the type of the fault by analyzing a bearing vibration signal acquired on site, and comprises the following steps:

step 1, processing the collected bearing data set: collecting bearing vibration data to form a sample data set comprising a fault data set and a normal data set;

step 2, denoising the bearing sample data set to obtain a denoised one-dimensional bearing data set;

step 3, converting the denoised one-dimensional bearing data set into a two-dimensional fault image set;

step 4, establishing a DCGAN bearing data generation model: training a pre-constructed DCGAN model by using a two-dimensional fault image set to obtain a bearing data generation model; the generator and the discriminator in the DCGAN structure are both composed of a convolutional neural network. The discriminator structure sequentially comprises an input layer, a first layer of convolution layer, batch standardization, a second layer of convolution layer, batch standardization, a third layer of convolution layer, batch standardization, a fourth layer of convolution layer, batch standardization, a global pooling layer, a Flatten layer, a Dense layer and an output layer; the generator mainly comprises an input layer, a shape change layer, a first layer of transposition convolution layer, a second layer of transposition convolution layer, a third layer of transposition convolution layer, a fourth layer of transposition convolution layer and an output layer;

step 5, initializing DCGAN fault data generation model parameters, training a DCGAN bearing data generation model through a two-dimensional fault image set, calculating an evaluation value for an image obtained by each training, wherein the evaluation value represents the comprehensive distance between a generated image and an original image, and the evaluation standard after training is that the evaluation value reaches a set threshold value, so that a trained DCGAN fault data generation model is finally obtained;

step 6, judging whether the evaluation value is larger than a set threshold value, if so, adding a SoftMax layer behind an output layer of a discriminant of the trained DCGAN fault data generation model, so that the model has classification capability, and the DCGAN fault data generation model is converted into a DCGAN fault diagnosis model; if the threshold value is smaller than the threshold value, turning to the step 5;

and 7, mixing the generated image which accords with the evaluation value in the step 6 with the original image data set to form an expanded sample data set, training the model by taking the sample data set as the input of the DCGAN fault diagnosis model, and judging whether the training of the model is finished by calculating whether the loss value is converged or not to finally obtain the trained bearing fault diagnosis model.

Compared with the prior art, the invention has the following remarkable advantages:

(1) according to the invention, the one-dimensional time sequence fault vibration data is converted into the two-dimensional image through the Gemlra angular field, and because the generator and the discriminator in the GAN model both comprise the convolution layer, and the convolution layer has the great advantage of image feature extraction, compared with the one-dimensional time sequence signal, the two-dimensional image can enable the model to extract more complete features, so that more feature information is learned, an image with higher similarity is generated, the problem of fault data shortage in the actual production process of industrial equipment is well solved, and the purpose of improving the fault diagnosis accuracy is finally achieved.

(2) The invention provides a formula for calculating the comprehensive distance between a generated image and a real image, the value calculated by the formula can well judge whether the training of a data generation network model is finished or not, and also provides reference for when the model starts to train a fault diagnosis model, and finally, whether the GAN reaches Nash balance or not can be judged according to whether the comprehensive distance tends to a fixed value or not.

Drawings

FIG. 1 is a process flow diagram.

FIG. 2 is a block diagram of the algorithm.

FIG. 3 is a comparison graph before and after wavelet denoising of fault data.

FIG. 4 is X_f，rLogic diagram for judging value.

Fig. 5 is a diagram illustrating an example of a two-dimensional failure image.

FIG. 6 is a data-generating network model hierarchy diagram of the GAF-DCGAN.

FIG. 7 is a hierarchy diagram of a GAF-DCGAN fault diagnosis network model.

FIG. 8 is a graph of fault diagnosis model loss value curves and accuracy.

Detailed Description

The invention is further described with reference to the following figures and embodiments.

With reference to fig. 1 and fig. 2, the rolling bearing fault diagnosis method based on the small sample and the GAF-DCGAN of the present embodiment includes the following steps:

step 1: the collected bearing data set is processed. The test object of this example is a motor drive end cylindrical roller bearing, model No. TMB-N209M. The diagnosed bearing has 3 fault locations: outer lane trouble, rolling element trouble, inner circle trouble, every fault location contains 3 fault degree: the number of early faults, light faults and serious faults is 9, and the fault types can be distinguished according to the damage diameter. And finally, the collected data are arranged to form a bearing data set which comprises a fault data set and a normal data set.

Aiming at the non-damage rolling bearing and each type of rolling bearing with damage, the vibration signals of the rolling bearing in each type of state under the action of load are collected through a sensor deployed on the rolling bearing, a sample data set with a fault type label is formed, and the sampling frequency of the system is 10 kHz. Because the characteristic frequencies of the inner ring, the outer ring and the rolling body of the rolling bearing are obtained by different formulas, the specific formula is as follows:

TABLE 1 formula for calculating failure frequency at each position

Wherein f is_rThe relative rotation frequency of the inner and outer rings is shown, and Z is the number of balls.

Because the characteristic frequency of the fault can be analyzed in the vibration signal, the fault type can be determined by comparing the analyzed value with the value calculated by the formula. Therefore, the bearing vibration signal is collected by the invention. Because the sample data set of this step is acquired in the industrial field and contains noise, the noise reduction process needs to be performed on the sample set, i.e., step 2.

Step 2: and (3) denoising the bearing sample data set acquired in the step (1) by using a wavelet threshold denoising method. Wavelets are functions that have both volatility and tight support. The basic idea of wavelet denoising is to decompose the obtained noisy signal through a proper base wavelet, then set a proper threshold to process a high-frequency wavelet coefficient, and finally reconstruct the original signal according to the wavelet coefficient obtained by wavelet denoising. The method comprises the following specific steps:

(1) the wavelet basis functions and the number of wavelet decomposition levels are selected. The present invention employs Daubechies-based wavelet functions. The number of decomposition layers was 3.

(2) A threshold function is selected as well as a threshold. Thresholds that are commonly used in practice include hard thresholds and soft thresholds. The invention uses threshold to select general threshold, the threshold function uses soft threshold function, the concrete mathematical model is as follows:

wherein the content of the first and second substances,

is a threshold, σ is the noise mean square error, N is the noisy signal sequence length, γ is the wavelet coefficient,

and T_hBoth (γ, t) are expressed as threshold functions.

The denoised signal and original signal time domain curve pair is shown in fig. 3.

And step 3: the one-dimensional time series vibration data is converted into a two-dimensional image using a Grammide Angular Field (GAF). Because the fault data collected in step 1 is time sequence vibration data belonging to one dimension, the conversion principle of the GAF is satisfied. The specific GAF implementation principle steps are as follows: firstly, the numerical scaling is performed, i.e. the time series data is scaled to [ -1,1], which is realized by the following formula:

wherein the content of the first and second substances,

is a one-dimensional time sequence signal, x, after the numerical scaling of the ith time_iThe signal value at the ith time in the one-dimensional time sequence signal, max (X) is the maximum value in the one-dimensional time sequence signal, and min (X) is the minimum value in the one-dimensional time sequence signal.

Then, the time stamp is encoded as a radius using a coordinate transformation formula, representing the rescaled time series in a polar coordinate system

The formula is as follows:

wherein, t_iIs a time stamp, N is a constant factor for adjusting the span of the polar coordinate system, phi is a polar coordinate angle,

is a one-dimensional time sequence signal after the numerical value scaling at the ith moment, r is a polar coordinate radius,

is a rescaled time sequence.

This is one method of representing a time series based on polar coordinates, with the corresponding values twisting between different angular points on the spanning circle as time increases. The coding mapping of the above formula has two important properties. The first property is that: it is bijective in that when φ ∈ [0, π ], cos (φ) is a monotonic function, i.e., given a time series, the mapping produces a unique result in polar coordinates and has a unique inverse mapping; the second property is as follows: in contrast to cartesian coordinates, a polar coordinate system maintains an absolute time relationship. After converting the rescaled time series to a polar coordinate system, we can identify the time dependencies in different time intervals by taking into account the triangles and/or differences between each point to exploit the angular perspective. The Gramian sum angle field (GASF) is defined as follows:

wherein the content of the first and second substances,

in order to perform a numerically scaled timing signal,

is composed of

I is a unit vector, phi_i，φ_jRespectively the corresponding angles of the two time points.

The invention uses a faulty two-dimensional image dataset generated by the GASF. Dividing a training sample set, a verification sample set and a test sample set for each type of fault image, wherein the training sample set x_trainVerifying the sample set x_validAnd test sample set x_testThe division ratio of (1) is 7: 2: 1.

and 4, step 4: establishing a DCGAN bearing data generation model: and training a pre-constructed DCGAN model by using a two-dimensional fault image set to obtain a bearing data generation model for generating a two-dimensional fault image. The generator and the discriminator in the DCGAN structure are both composed of a convolutional neural network. The discriminator structure sequentially comprises an input layer, a first layer of convolution layer, batch standardization, a second layer of convolution layer, batch standardization, a third layer of convolution layer, batch standardization, a fourth layer of convolution layer, batch standardization, a global pooling layer, a Flatten layer, a Dense layer and an output layer; the generator is mainly composed of an input layer, a shape change layer, a first layer of transposition convolution layer, a second layer of transposition convolution layer, a third layer of transposition convolution layer, a fourth layer of transposition convolution layer and an output layer. The input of the model of the invention is divided into two parts, the first is that the input of the generator is random noise conforming to the gaussian distribution, and the second is that the input of the discriminator is the two-dimensional image dataset in step 3. The output of the model is a two-dimensional image containing fault features.

And 5: and initializing DCGAN fault data generation model parameters, and setting the sample number Batch _ size, the maximum iteration sample number MaxEpoch and the maximum iteration step number MaxStep of single training. The training relationship between the generator and the discriminator needs to be set: TrainStep is 2, indicating that when the generator is trained once, the arbiter will be trained twice. Training a DCGAN bearing data generation model through a two-dimensional fault image set, calculating an evaluation value for an image obtained by each training, wherein the evaluation value represents the comprehensive distance between a generated image and an original image, and the evaluation standard of training completion is that the evaluation value reaches a set threshold value, so that a trained DCGAN fault data generation model is finally obtained;

5.1 formula for calculating comprehensive distance

If the generated image is used for fault diagnosis, the similarity between the generated image and the original image needs to be judged, namely, the numerical level judgment needs to be carried out by calculating the Structural Similarity (SSIM), the peak signal-to-noise ratio (PSNR) and the FrecheInclusion distance (FID value) between the generated image and the original image. Wherein SSIM is taken to be [0,1]]The larger the SSIM value is, the more similar the two images are; the larger the PSNR value is, the more diverse the generated images are; the smaller the FID value is, the better the quality of the model is, and the stronger the capability of outputting diversity and high-quality images is. By combining the three judgment standards, the invention designs a value X capable of being comprehensively evaluated_f，r，X_f，rThe larger the generated image is, the more similar the generated image is to the original image. The calculation formula is as follows:

Xf_，r＝αx_ssim+βX_psnr-γX_fid+δ

wherein, X_f，rFor the sum of the distances, X, of the real image and the generated image_ssimFor structural similarity of real and generated images, X_psnrIs the peak signal-to-noise ratio, X_fidThe Frechet initiation distance, alpha, beta and gamma are constants larger than 0 and are used for adjusting the specific gravity of three factors, and delta is other factors (such as a Mode fraction, an initiation fraction and the like) influencing the comprehensive distance.

5.2 Freehet Inclusion Distance (FID)

To overcome the drawbacks of the IS method, the formula for calculating the FID score IS as follows (4-23):

wherein mu is the mean value of multivariate normal distribution, sigma is covariance, r and g subscripts respectively represent a real image and a generated image, and T_rRepresents the synthesis of elements on the diagonal of the matrix, i.e., the "trace".

The lower the FID score, the better the quality of the description model, and the greater its ability to output a diverse, high quality image.

5.3 Structural Similarity (SSIM)

The structural similarity is an index for measuring the similarity of two images, and can be used for judging the generated image and the real image of the GAN network. The value interval of SSIM is [0,1], and the larger the SSIM value is, the more similar the two images are. The formula for SSIM is as follows:

wherein, mu_x，μ_yIs the pixel value of the image, delta_x，δ_yIs the standard deviation, delta, of the image pixel values_xyIs the covariance of x and y points, C₁，C₂，C₃Is a constant.

5.4 Peak Signal-to-noise ratio (PSNR)

The peak signal-to-noise ratio PSNR is calculated according to the following formula (4-29):

where MSE is the mean square error of the image, MAX_IThe maximum value of the pixel point color is represented. The larger the PSNR, the more diverse the generated images.

Step 6: judging X calculated in the step 5_f，rWhether the value is greater than a set threshold. If greater than the set threshold, and X_f，rAnd (3) approaching to a fixed value, namely reaching nash balance, adding a Softmax layer after an output layer of a discriminant of the trained DCGAN data generation model, so that the model has classification capability, and the DCGAN fault data generation model is converted into a DCGAN fault diagnosis model, wherein the specific logic is shown in FIG. 4. If the value is less than the threshold value, the step 5 is carried out.

6.1 Nash balance

Nash balance results from the problem of the game theory of zero-sum games, i.e., the loss of revenue on one side equals the loss of revenue on the other. The zero-sum game has a nash balance point, i.e., neither party can improve their results in any way of effort. The following two conditions are met, and the GAN reaches nash equilibrium:

(1) the pseudo fault image generated by the generator is consistent with the real image in the training set;

(2) the discriminator can only randomly guess whether a particular sample is true or false, i.e., the probability of true and false is 50%.

And 7: matching X in step 6_f，rAnd mixing the generated image of the values with the original image data set to form an expanded data set, and taking the sample data set as the input of the DCGAN fault diagnosis model. And training the model, and judging whether the model is trained or not by calculating whether the loss value is converged or not. After the training is finished, the model takes the bearing fault data as input and outputs the diagnosis result of the fault type and the fault position. The loss value is calculated as follows.

8.1 loss function

In the process of classifying faults, the loss function of the discriminator aims to reduce the difference between a real sample and a prediction sample, and the formula of the loss function is as follows:

wherein the content of the first and second substances,

for the expected value of the original sample, Softmax () represents the Softmax function, D (x) represents the network of discriminators, λ | | W | Wy²Denoted L2 regularization, the parameters of the contribution are all weights of the discriminators.

The loss function of the generator is used for measuring the distance between the generated image generated by the generator and the real image, and the corresponding loss function formula is as follows:

wherein the content of the first and second substances,

representing the expected value of the input random gaussian noise, and g (z) represents the generator network.

8.2 generating error function of countermeasure network

From the principle of GAN, it follows that the generator and the discriminator model are competing, with L (G, D) representing the impairment function, where the discrimination model tries to minimize the error and the generator model tries to maximize the error, and the final error function is formulated as follows:

example 1

The rolling bearing fault diagnosis method based on the small sample and the GAF-DCGAN is utilized to carry out test verification.

Step 1: the test object of the test is a cylindrical roller bearing at the driving end of the motor, and the model is TMB-N209M. The diagnosed bearing has 3 fault locations: outer lane trouble, rolling element trouble, inner circle trouble, every fault location contains 3 fault degree: early failure (damage diameter of 0.42 inch), minor failure (damage diameter of 0.70 inch), major failure (damage diameter of 0.98 inch), totaling 9 failure types. And finally, the collected data are arranged to form a bearing data set which comprises a fault data set and a normal data set. Specifically, the following table 1 shows.

TABLE 1 Fault location Table

Step 2: and (3) denoising the bearing sample data set in the step (1) by using a wavelet denoising method. The first step is to carry out wavelet decomposition on signals by adopting a selected Daubechies base wavelet function and a 3-layer decomposition scale; selecting a general threshold and a soft threshold function; and finally, reconstructing the original data according to the wavelet coefficient obtained by wavelet de-noising. The specific processing result pairs are shown in fig. 3.

And step 3: and (3) converting the one-dimensional bearing data set processed in the step (2) into polar coordinate representation by utilizing a Grarami angle field, and further obtaining a two-dimensional fault image set with the size of 64x 64. The ratio of each type of fault in the image set is 7: 2: 1, the training sample set, the verification sample set, and the test sample set are divided as shown in table 2 below. An example of a specific converted two-dimensional image is shown in fig. 5.

TABLE 2 partitioning of sample sets

And 4, step 4: and (3) establishing a DCGAN bearing data generation model, wherein the layer structure of the DCGAN bearing data generation model is shown in FIG. 6.

And 5: and initializing DCGAN data generation model parameters. Setting the single sample number as Batch _ size 128, the maximum iteration number MaxEpoch as 10, the maximum iteration step number MaxStep as 100, and the threshold value X of the integrated distance between the generated image and the original image as 23. The training relationship TrainStep of the generator and the discriminator is set to be 2, which means that when the generator is trained once, the discriminator will be trained twice. Calculating X of the generated image for each iteration_f，rThe value is obtained. And finally obtaining a trained DCGAN fault data generation model.

Step 6: judgment of X_f，rWhether the value is greater than a set threshold value X. If the DCGAN data generation model is larger than the set threshold, adding a Softmax layer behind the output layer of the discriminant of the trained DCGAN data generation model, so that the model has classification capability, and the DCGAN data generation network model is converted into a fault diagnosis model; if the value is less than the set value, the step 5 is carried out.

And 7: and (3) establishing a DCGAN bearing fault diagnosis model, wherein the layer structure of the DCGAN bearing fault diagnosis model is shown in figure 7. Matching X in step 6_f，rGeneration map of valuesThe image is blended with the original image data set to form an expanded data set as input to the DCGAN fault diagnosis model, and the expanded sample set partitioning criteria are shown in table 3 below. And training the DCGAN fault diagnosis model.

Table 3 partitioning table for extended sample set

Since it is the discriminator that performs the fault diagnosis, the loss value is calculated using the loss function of the discriminator. Further judging whether the model is converged, and if so, finishing the training of the DCGAN fault diagnosis model; if the model does not converge, the training continues. And importing a test sample set into the trained DCGAN fault diagnosis model for testing, and obtaining a result output by the full connection layer as a diagnosis basis of fault diagnosis. The loss value curve represents the speed of the test set that the model tends to converge in the process of model iteration, and the loss value curve is shown in the following figure 8 (a). The fault diagnosis model can be analyzed, with the input of the extended sample set, the diagnosis accuracy of the model can be up to 99.6% finally, and the accuracy curve is shown in fig. 8(b) below.

Claims (7)

1. A rolling bearing fault diagnosis method based on GAF-DCGAN is used for judging whether a bearing is in fault and the type of the fault by analyzing a bearing vibration signal acquired on site, and is characterized by comprising the following steps:

step 1, processing the collected bearing data set: collecting bearing vibration data to form a sample data set comprising a fault data set and a normal data set;

step 2, denoising the bearing sample data set to obtain a denoised one-dimensional bearing data set;

step 3, converting the denoised one-dimensional bearing data set into a two-dimensional fault image set;

step 4, establishing a DCGAN bearing data generation model: training a pre-constructed DCGAN model by using a two-dimensional fault image set to obtain a bearing data generation model; the generator and the discriminator in the DCGAN structure are both composed of a convolutional neural network. The discriminator structure sequentially comprises an input layer, a first layer of convolution layer, batch standardization, a second layer of convolution layer, batch standardization, a third layer of convolution layer, batch standardization, a fourth layer of convolution layer, batch standardization, a global pooling layer, a Flatten layer, a Dense layer and an output layer; the generator mainly comprises an input layer, a shape change layer, a first layer of transposition convolution layer, a second layer of transposition convolution layer, a third layer of transposition convolution layer, a fourth layer of transposition convolution layer and an output layer;

step 5, initializing DCGAN fault data generation model parameters, training a DCGAN bearing data generation model through a two-dimensional fault image set, calculating an evaluation value for an image obtained by each training, wherein the evaluation value represents the comprehensive distance between a generated image and an original image, and the evaluation standard after training is that the evaluation value reaches a set threshold value, so that a trained DCGAN fault data generation model is finally obtained;

step 6, judging whether the evaluation value is larger than a set threshold value, if so, adding a SoftMax layer behind an output layer of a discriminant of the trained DCGAN fault data generation model, so that the model has classification capability, and the DCGAN fault data generation model is converted into a DCGAN fault diagnosis model; if the threshold value is smaller than the threshold value, turning to the step 5;

and 7, mixing the generated image which accords with the evaluation value in the step 6 with the original image data set to form an expanded sample data set, training the model by taking the sample data set as the input of the DCGAN fault diagnosis model, and judging whether the training of the model is finished by calculating whether the loss value is converged or not to finally obtain the trained bearing fault diagnosis model.

2. The GAF-DCGAN-based rolling bearing failure diagnosis method according to claim 1, wherein the specific calculation formula of the evaluation value in step 5 is as follows:

X_f，r＝αx_ssim+βX_psnr-γX_fid+δ

wherein, X_f，rFor the combined distance, X, of the original image and the generated image_ssimFor structural similarity of the original image and the generated image, X_psnrIs the peak signal-to-noise ratio, X_fidThe Frechet increment distance is a constant which is larger than 0 for alpha, beta and gamma, and delta is a constant.

3. The GAF-DCGAN-based rolling bearing fault diagnosis method according to claim 1, wherein the specific process of determining whether the DCGAN fault data generation model is completed in step 5 is as follows:

and if the evaluation value reaches a set threshold value and tends to a fixed value, the DCGAN network model reaches Nash balance, and further the model training is determined to be finished.

4. The GAF-DCGAN-based rolling bearing fault diagnosis method according to claim 3, wherein said Nash balance satisfies the following condition:

(1) the pseudo fault image generated by the generator is consistent with the real image in the training set;

(2) the discriminator can only randomly guess whether a particular sample is true or false, i.e., the probability of true and false is 50%.

5. The GAF-DCGAN-based rolling bearing fault diagnosis method according to claim 1, wherein the denoising processing of the bearing sample data set in step 2 adopts a wavelet threshold denoising method, specifically comprising the steps of:

2.1, selecting wavelet basis functions and wavelet decomposition layer numbers.

2.2, selecting a threshold function and a threshold.

6. The GAF-DCGAN-based rolling bearing fault diagnosis method according to claim 1, wherein the step 3 of converting the denoised one-dimensional bearing data set into a two-dimensional fault image set comprises the following steps:

3.1, performing numerical scaling, i.e. scaling the time series data to [ -1,1], and realizing the following formula:

wherein the content of the first and second substances,

is a one-dimensional time sequence signal, x, after the numerical scaling of the ith time_iThe signal value at the ith time in the one-dimensional time sequence signal, max (X) is the maximum value in the one-dimensional time sequence signal, and min (X) is the minimum value in the one-dimensional time sequence signal.

3.2 then encoding the timestamp as a radius using a coordinate transformation formula, representing the rescaled time series in a polar coordinate system

The formula is as follows:

wherein, t_iIs a time stamp, N is a constant factor for adjusting the span of the polar coordinate system, phi is a polar coordinate angle,

is a one-dimensional time sequence signal after the numerical value scaling at the ith moment, r is a polar coordinate radius,

is a rescaled time sequence.

3.3, identifying temporal correlations in different time intervals by exploiting the angular perspective by considering the trigonometry and/or the difference between each point. The Gramian sum angle field (GASF) is defined as follows:

wherein the content of the first and second substances,

in order to perform a numerically scaled timing signal,

is composed of

I is a unit vector, phi_i，φ_jRespectively the corresponding angles of the two time points.

7. The GAF-DCGAN-based rolling bearing fault diagnosis method according to claim 1, wherein the loss value calculation formula in step 7 is:

wherein the content of the first and second substances,

for the expected value of the original sample, Softmax () represents the Softmax function, D (x) represents the network of discriminators, λ | | W | Wy²It is indicated that the L2 regularization,

representing the expected value of the input random gaussian noise, and g (z) represents the generator network.

Images