CN116858531A - A wind turbine gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt - Google Patents

Abstract

A wind turbine gearbox fault diagnosis method based on data enhancement and CSP‑ResNeXt, including the following steps: using an acceleration sensor installed on the gearbox to collect fault vibration signal data collected from different fault types of the gearbox; using the wavelet packet decomposition method to decompose the collected data Decompose the fault vibration signal to obtain different wavelet packet coefficients. Randomly select a set of wavelet coefficients, distort them and restore them to time domain signals to expand the fault samples and complete the data enhancement operation of the fault samples; through the relative position matrix Relative Position Matrix , RPM converts the time domain signal into a grayscale image and inputs it into the built CSP‑ResNeXt network to train the diagnostic model. Finally, an intelligent fault diagnosis model of the wind turbine gearbox can be obtained, which can be used to input vibration signals collected in real time for fault diagnosis and identification. The present invention uses wavelet packet distortion technology for data enhancement, and at the same time adopts an improved ResNeXt network to achieve accurate fault identification of wind turbine gearboxes when fault sample classes are seriously unbalanced.

Description

A wind turbine gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt

Technical Field

The present invention relates to the technical field of health status monitoring of a wind turbine gearbox, and in particular to a wind turbine gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt.

Background Art

Wind turbines work in extreme temperature, rainstorm, snowstorm, salt spray and other environments for a long time. As the operation time increases, the fatigue strength and operating performance of blades, main bearings, gearboxes, generators and other components continue to decline, causing abnormalities and failures, resulting in abnormal operation or even shutdown of the wind turbine. Analysis of the faulty components shows that the wind turbine gearbox accounts for the highest proportion of all faulty components, so it is very important to establish a fault diagnosis model for the wind turbine gearbox.

Generally, vibration signals are used as signal sources for fault analysis of rotating parts. Strong noise signals are mixed in the signal acquisition process, and the signal itself has nonlinear and non-stationary characteristics, which brings challenges to fault diagnosis. At the same time, the vibration signals collected by the acceleration sensor of the wind turbine are generally normal, and there are few samples of fault signal collection, which makes it difficult to train the fault diagnosis model.

Summary of the invention

The technical problem to be solved by the present invention is to provide a fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt, so as to solve the problem that the energy of the fan gearbox fault vibration signal is weak and is often polluted by strong noise. The traditional fault diagnosis uses time domain and frequency domain analysis methods to extract artificial fault features, which is subjective and has poor diagnostic effect.

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

A wind turbine gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt comprises the following steps:

Step 1, using the acceleration sensor installed on the gearbox to collect fault vibration signal data of different fault types of the gearbox;

Step 2, use wavelet packet distortion to expand the sample data;

Step 3, convert the fault vibration signal into a grayscale image through the relative position matrix;

Step 4: Input the expanded sample data into the improved ResNeXt network, and finally obtain the intelligent fault diagnosis model of the wind turbine gearbox. Use this model to input the real-time collected vibration signal for fault diagnosis and identification.

The specific steps of Step 2 above are as follows:

Step 2.1, use wavelet packet transform to decompose the original vibration signal into two layers;

Step 2.2, randomly select a set of wavelet coefficients for distortion operation;

Step 2.3, restore the wavelet packet decomposition coefficients after the distortion operation to the time domain signal.

In the above Step 2.1, the following function is used to implement the 2-layer decomposition of the original vibration signal:

Where i=0,...,(2j-1), k and l are the sequential indices of the elements, (h,g) is a pair of finite impulse response filters of length L, let wj _,i represent the i-th group of wavelet coefficients of the j-th decomposition layer, and _w0,0 is the original signal.

The distortion function of the distortion operation in Step 2.2 above is:

Where d is the distortion coefficient randomly selected from a preset range, sign is the sign function, which is used to take the sign (positive or negative) of a number in mathematics and computer operations: when x>0, sign(x)=1; when x=0, sign(x)=0; when x<0, sign(x)=-1; abs is the absolute value function, which returns the absolute value of w.

The specific steps of Step 4 above are:

Step 4.1, the input data passes through a preprocessing layer with a convolution kernel of 7×7 field of view, a dimension of 64, and a step size of 2;

The output data of Step 4.2 and Step 4.1 pass through the global maximum pooling layer with a convolution kernel of 3×3 and a step size of 2; the output data of Step 4.3 and Step 4.2 enter the backbone network composed of four ResNeXt residual blocks of different layers.

The structure of the backbone network composed of four ResNeXt residual blocks of different layers in the above Step 4.3 is:

One part consists of 3 layers of residual structures with a base of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally the channels are spliced and output;

The second part consists of 3 layers of residual structures with a base of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally concatenates the channels for output;

The third part consists of 3 layers of residual structures with a base of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally concatenates the channels for output;

The fourth part consists of 3 layers of residual structures with a base size of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally the channels are concatenated and output.

The above four backbone network residual blocks composed of different layers of ResNeXt residual blocks have a stacking structure of 3-4-6-3. A CSP module is inserted into each part of the network structure, and the input channels are grouped when entering each part of the stacked network. Half of the input channels enter the stacked network, and the other half of the input channels enter the CSP module; then the output channel of each part is spliced with the output channel of the CSP module as the total output of each part of the stacked network structure; finally, the output of the fourth part is summarized and enters the global average pooling layer and the fully connected layer with a convolution kernel of 1×1 to realize fault classification.

The above ResNeXt residual block activation function uses the sigmoid function, and its calculation formula is:

Where x is the input and f(x) is the output.

The activation function used in each convolution kernel and transition layer in the above four ResNeXt residual block network parts adopts the Relu activation function, and its calculation formula is:

f(x)＝max(0,x)

Where x is the input and f(x) is the output.

The fully connected layer loss function of the above-mentioned improved ResNeXt network, namely the CSP-ResNeXt network, adopts the cross entropy loss function, and its calculation formula is:

Where p( _xi ) and q( _xi ) represent the true probability distribution and the predicted probability distribution, respectively, and H(p,q) represents the gap between the predicted value and the true value;

The cross entropy loss function is used with the softmax classifier. The output results are processed in the fully connected layer so that the sum of the predicted values of multiple classifications is 1, and then the loss is calculated by cross entropy. The calculation formula of the softmax function is:

Among them, _xi is the output of the previous layer of the model, which serves as the input of the softmax classifier; the output calculation result softmax(x) can be regarded as the confidence that the predicted result is the true result.

The present invention provides a wind turbine gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt, which has the following beneficial effects:

1. Wavelet packet distortion is developed based on wavelet packet transform to increase the number of erroneous training samples. Here, the enhanced samples are similar to the original samples but have different values. This can achieve a balance between classes and improve the sample diversity of the training data set.

2. CSP-ResNeXt introduces the idea of group convolution based on the original Resnet, which makes the network structure have higher classification accuracy under the same complexity. At the same time, in different application scenarios, due to the idea of VGG stacking structure normalization in each residual block, the generalization ability of the model is stronger; after adopting the CSP module, the amount of model calculation is reduced and the gradient combination is richer, which avoids the model from repeatedly learning the same gradient value in the forward gradient propagation and enhances the convergence ability of the model during training.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

FIG1 is a schematic diagram of the overall process of an embodiment of the present invention;

Figure 2 is a residual structure design diagram;

FIG3 is a graph showing a characteristic spectrum of a differential field after conversion in an embodiment;

FIG4 is a schematic diagram of a model training loss function curve in an embodiment;

FIG5 is a schematic diagram of an accuracy curve of the model training of the embodiment.

DETAILED DESCRIPTION

The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and embodiments.

As shown in FIG1-2, a wind turbine gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt includes the following steps:

Step 1, using the acceleration sensor installed on the gearbox to collect fault vibration signal data of different fault types of the gearbox;

Step 2, use wavelet packet distortion to expand the sample data;

Step 3, convert the fault vibration signal into a grayscale image through the relative position matrix;

Step 4: Input the expanded sample data into the improved ResNeXt network, and finally obtain the intelligent fault diagnosis model of the wind turbine gearbox. Use this model to input the real-time collected vibration signal for fault diagnosis and identification.

In Step 1, in terms of vibration signal extraction and original data set construction, at least six types of fault vibration signals, including normal vibration signals, gearbox bearing outer ring fault vibration signals, gearbox bearing inner ring fault vibration signals, broken tooth state fault vibration signals, pitting state fault vibration signals, and wear state fault vibration signals, are taken to form a data set, and the classification labels of the data set are numbered in the form of unique hot encoding to facilitate the subsequent classification of fault diagnosis types using a softmax classifier.

The specific steps of Step 2 above are as follows:

Step 2.1, use wavelet packet transform to decompose the fault vibration signal, the decomposition order is 2, and the wavelet packet decomposition coefficient is obtained;

Step 2.2, randomly select a set of wavelet coefficients for distortion operation;

Step 2.3, restore the time series signal through wavelet packet inverse transformation to complete the data enhancement of the fault vibration signal;

At the same time, in Step 2.3, the data is input into the improved ResNeXt and the available relative position matrix (RPM) is used to convert the data into a two-dimensional image to facilitate the training of the diagnostic model.

As a classic time-frequency domain analysis method, wavelet packet transform can decompose a signal into a set of wavelet coefficients in different frequency bands; on the contrary, the inverse wavelet packet transform can reconstruct and restore the original signal through the wavelet packet decomposition coefficients; if the signal is decomposed and reconstructed according to the same decomposition rule, the reconstructed signal is consistent with the original signal; the present invention performs distortion processing on a set of randomly selected wavelet coefficients so that the reconstructed signal is similar to the original sample but slightly different. The reconstructed signal can be used as an enhanced sample, especially for minority vibration signal samples.

In the above Step 2.1, the following function is used to implement the 2-layer decomposition of the original vibration signal:

Where i=0,...,(2j-1), k and l are the sequential indices of the elements, (h,g) is a pair of finite impulse response filters of length L, let wj _,i represent the i-th group of wavelet coefficients of the j-th decomposition layer, and _w0,0 is the original signal.

The distortion function of the distortion operation in Step 2.2 above is:

Where d is the distortion coefficient randomly selected from a preset range, sign is the sign function, which is used to take the sign (positive or negative) of a number in mathematics and computer operations: when x>0, sign(x)=1; when x=0, sign(x)=0; when x<0, sign(x)=-1; abs is the absolute value function, which returns the absolute value of w.

After distorting some wavelet coefficients, the inverse wavelet packet transform is performed to obtain the output signal v, which is expressed as follows:

in is the distorted wavelet coefficient, v is the reconstructed wavelet coefficient, is a pair of finite impulse response filters of length L, i = 0, ..., (2j-1), k and l are the sequential indices of the elements.

In Step 3, the data is input into the improved ResNeXt and the relative position matrix (RPM) can be used to convert the data into a two-dimensional image to facilitate the training of the diagnostic model. The specific implementation steps are as follows:

The relative position matrix (RPM) contains the redundant features of the original time series , making it easier to capture the similarity information between and within classes in the converted image. For a time series X = (xt, t = 1, 2, ..., N), the RPM graph can be obtained by the following steps:

1) For the original time series, a standard normal distribution Z is obtained by the following z-score standardization method:

Where μ represents the mean of X and σ represents the standard deviation of X.

2)2) Using the piecewise aggregation approximation (PAA) method, select a suitable reduction factor k to generate a new smoothed time series Reduce the dimension N to m:

By calculating the average value of the piecewise constants to reduce the dimension, the approximate trend of the original time series can be maintained, and the new smoothed time series is finally The length is m.

3) Calculate the relative position between the two timestamps and convert the preprocessed time series Convert to a two-dimensional matrix M:

As shown above, the matrix represents the relative position relationship between every two timestamps in the time series; each row and column is referenced to a certain timestamp, further representing the information of the entire sequence.

4) Finally, the minimum-maximum normalization is used to convert M into a gray value matrix, and finally the relative displacement matrix F is obtained:

Finally, the time series vibration signal is converted into a grayscale image through the relative displacement matrix, which can be input into the diagnostic classification model for training.

In the construction of the CSP-ResNeXt network, the following method should be used: the ResNeXt network structure adopts the VGG stacking idea and the Inception split-conversion-merge idea at the same time, and adopts the group convolution method in its basic residual block to keep the topological structure of each aggregation consistent, thereby enhancing the scalability of the model and reducing the difficulty of network structure design for specific data sets; on this basis, the CSP module is introduced to enhance the learning ability of the neural network, eliminate the computing bottleneck to a certain extent, and reduce the memory cost. The introduction of the CSP module in the ResNeXt network can reduce the time spent on reasoning calculations; the CSP module reduces the amount of reasoning calculations by crossing stages, and achieves this function by optimizing the repeated gradient information in the network. It focuses on the variability of gradients by integrating feature maps from the beginning and end of the network stage, enriching and increasing the variety of gradient combinations. Based on the bottleneck layer of ResNet, the group convolution method is introduced, and the original 1×1, 3×3, and 1×1 convolution structures that share convolution kernel parameters are changed to group sharing of convolution kernel parameters within each group to ensure that the amount of calculation is not much different and enhance the learning ability of the network; at the same time, in order to improve the speed of reasoning calculation, the CSP local cross-stage method is introduced to divide the input of the bottleneck layer into two parts, one part is obtained by improving the Resnet block, and the other part is directly spliced with the output obtained by improving the input of the Resnet block to reduce the reuse of redundant gradients; by splitting the gradient flow to make the gradient flow propagate through different network paths, and by switching the cascade and conversion steps, the propagated gradient information can be very different, so as to reduce the reuse of redundant gradients. The residual structure design idea is shown in Figure 2.

The specific steps of Step 4 above are:

Step 4.1, the input data passes through a preprocessing layer with a convolution kernel of 7×7 field of view, a dimension of 64, and a step size of 2;

The output data of Step 4.2 and Step 4.1 pass through the global maximum pooling layer with a convolution kernel of 3×3 and a step size of 2; the output data of Step 4.3 and Step 4.2 enter the backbone network composed of four ResNeXt residual blocks of different layers.

The structure of the backbone network composed of four ResNeXt residual blocks of different layers in the above Step 4.3 is:

One part consists of 3 layers of residual structures with a base of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally the channels are spliced and output;

The second part consists of 3 layers of residual structures with a base of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally concatenates the channels for output;

The third part consists of 3 layers of residual structures with a base of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally concatenates the channels for output;

The fourth part consists of 3 layers of residual structures with a base size of 32 and convolution kernels of 1×1, 3×3, and 1×1, and also includes a residual connection bypass, and finally the channels are concatenated and output.

Four-layer convolution is used for feature extraction. Feature extraction is performed through four convolution layers with the same layer cardinality and convolution kernel, which has a better effect.

The above four backbone network residual blocks composed of different layers of ResNeXt residual blocks have a stacking structure of 3-4-6-3. A CSP module is inserted into each part of the network structure, and the input channels are grouped when entering each part of the stacked network. Half of the input channels enter the stacked network, and the other half of the input channels enter the CSP module; then the output channel of each part is spliced with the output channel of the CSP module as the total output of each part of the stacked network structure; finally, the output of the fourth part is summarized and enters the global average pooling layer and the fully connected layer with a convolution kernel of 1×1 to realize fault classification.

In Step 4, the training set is input into the built CSP-ResNeXt network for training; the hyperparameter batch size is set to 128, and the gradient descent optimization algorithm adopts the adam random optimization algorithm: the learning rate α is set to 0.001, the first-order moment estimation attenuation coefficient _β1 is set to 0.9, the second-order moment estimation attenuation coefficient _β2 is set to 0.999, and the smoothing term ε is set to 1e ^-8 . The specific iteration formula is:

m _t =β ₁ m _t-1 +(1-β ₁ )g _t

Where t is the number of training times; m _t and v _t are the first-order moment estimate and second-order moment estimate of the gradient, respectively, which can be regarded as the approximation of the expected E[g _t ] and E[g _t ² ]; g _t is the gradient value calculated for each parameter θ; and is a correction to m _t and v _t , which can be approximated as an unbiased estimate of the expectation; to prevent the denominator from being 0, a smoothing term ε is set.

The above ResNeXt residual block activation function uses the sigmoid function, and its calculation formula is:

Where x is the input and f(x) is the output.

The activation function used in each convolution kernel and transition layer in the above four ResNeXt residual block network parts adopts the Relu activation function, and its calculation formula is:

f(x)＝max(0,x)

Where x is the input and f(x) is the output.

The fully connected layer loss function of the above-mentioned improved ResNeXt network, namely the CSP-ResNeXt network, adopts the cross entropy loss function, and its calculation formula is:

Where p( _xi ) and q( _xi ) represent the true probability distribution and the predicted probability distribution, respectively, and H(p,q) represents the gap between the predicted value and the true value;

The cross entropy loss function is used with the softmax classifier. The output results are processed in the fully connected layer so that the sum of the predicted values of multiple classifications is 1, and then the loss is calculated by cross entropy. The calculation formula of the softmax function is:

Among them, _xi is the output of the previous layer of the model, which serves as the input of the softmax classifier; the output calculation result softmax(x) can be regarded as the confidence that the predicted result is the true result.

Example:

In order to verify the feasibility of the present invention, the public gearbox data set of Southeast University is used to implement the method of the present invention.

The experimental algorithm processing platform equipment uses Windows 11 as the software environment for high-performance computer model training and testing, Python 3.10 programming language, CUDA 11.8 GPU acceleration library, and Pytorch 2.0.1 deep learning framework.

The experimental data set is divided into five categories, namely healthy, broken teeth, gear surface wear, gear foot cracks, and gear root cracks. The number of samples in each category is 500, and the total number of samples is 2500. After the data set is randomly divided into a training set and a test set at a ratio of 8:2, the number of samples in the training set is 2000 and the number of samples in the validation set is 500.

The model network code is:

An example of a graphic differential field characteristic spectrum converted according to the method of the present invention is shown in FIG3 below.

In terms of model training, the number of model iterations is set to 500, the batch size is set to 8, and the thread is set to 2. The model loss function and accuracy are shown in Figures 4 and 5 below. It can be seen that after 500 iterations of the model, the model basically converges and the accuracy can reach more than 95%.

Claims (10)

1. A fan gear box fault diagnosis method based on data enhancement and CSP-ResNeXt is characterized by comprising the following steps:

step1, collecting fault vibration signal data collected by different fault types of the gear box by using an acceleration sensor arranged on the gear box;

step2, expanding sample data by adopting wavelet packet distortion;

step3, converting the fault vibration signal into a gray level map through a relative position matrix;

step4, inputting the data after sample expansion into an improved ResNeXt network, and finally obtaining an intelligent fault diagnosis model of the fan gear box, and inputting vibration signals acquired in real time by using the model to perform fault diagnosis and identification.

2. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 1, wherein the specific steps of Step2 are as follows:

step2.1, performing 2-layer decomposition on the original vibration signal by adopting wavelet packet transformation;

step2.2, randomly selecting a group of wavelet coefficients to carry out distortion operation;

step2.3, reducing the wavelet packet decomposition coefficient after distortion operation into a time domain signal.

3. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 2, wherein in step2.1, the following function is used to implement 2-layer decomposition of the original vibration signal:

where i=0, (2 j-1), k and L are sequential indices of elements, (h, g) is a pair of finite impulse response filters of length L, let w be _j,i Ith group of wavelet coefficients representing jth decomposition level, w _0,0 Is the original signal.

4. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 2, wherein the distortion function of the distortion operation in the step2.2 is:

wherein d is a distortion coefficient randomly selected from a preset range, sign is a sign function, and in mathematical and computer operations, the function is to take a certain number of signs (positive or negative): when x >0, sign (x) =1; when x=0, sign (x) =0; when x <0, sign (x) = -1; abs is an absolute function, returning the absolute value of the w value.

5. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 1, wherein the Step4 specifically comprises the following steps:

step4.1, the input data passes through a convolution kernel with a field of view of 7×7, a dimension number of 64, and a step length of 2;

the output data of Step4.2 and Step4.1 pass through a global maximum pooling layer with convolution kernel of 3 multiplied by 3 and step length of 2;

the step4.3 and step4.2 output data enter a backbone network consisting of four different layers of ResNeXt residual blocks.

6. The fan gear box fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 5, wherein the four main networks consisting of ResNeXt residual blocks of different layers in the step4.3 have the following composition structure:

one part of the three-layer joint structure consists of 3 layers of residual structures with the base number of 32 and convolution kernels of 1 multiplied by 1,3 multiplied by 3 and 1 multiplied by 1, and comprises a residual connection bypass, and finally, the channels are spliced and output;

the second part is composed of residual structures with 3 layers of convolution kernels of 1 multiplied by 1,3 multiplied by 3 and 1 multiplied by 1, the number of the base numbers of the layers is 32, and the residual structures comprise a residual connection bypass, and finally channels are spliced and output;

the third part is composed of residual structures with 3 layers of convolution kernels of 1 multiplied by 1,3 multiplied by 3 and 1 multiplied by 1, the number of the base numbers of the layers is 32, and the residual structures comprise a residual connection bypass, and finally channels are spliced and output;

the fourth part is composed of a residual structure with 3 layers of convolution kernels of 1×1,3×3 and 1×1 and with a base number of 32, and comprises a residual connection bypass, and finally channels are spliced and output.

7. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 6, wherein the four main network residual blocks formed by ResNeXt residual blocks of different layers are stacked in a structure of 3-4-6-3, CSP modules are inserted into each part of the network structure, input channels are grouped when entering each part of the stacked network, half of the input channels enter the stacked network, and the other half of the input channels enter the CSP modules; then splicing the output channel of each part with the output channel of the CSP module to be used as the total output of each part of stacked network structure; and finally, summarizing the output of the fourth part, and entering a global average pooling layer with the convolution kernel of 1 multiplied by 1 and a full connection layer to realize fault classification.

8. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 7, wherein the ResNeXt residual error block activation function adopts a sigmoid function, and the calculation formula is as follows:

where x is the input and f (x) is the output.

9. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 8, wherein the activation function used by each convolution kernel and transition layer in the four ResNeXt residual block network parts adopts a Relu activation function, and the calculation formula is as follows:

f(x)＝max(0,x)

where x is the input and f (x) is the output.

10. The fan gearbox fault diagnosis method based on data enhancement and CSP-ResNeXt according to claim 9, wherein the improved ResNeXt network, namely the full connection layer loss function of the CSP-ResNeXt network, adopts a cross entropy loss function, and the calculation formula is as follows:

wherein p (x) _i ) And q (x) _i ) Respectively representing a true probability distribution and a predicted probability distribution, and H (p, q) represents the difference between the predicted value and the true value;

the cross entropy loss function is matched with the softmax classifier to be used, the output result is processed at the full connection layer, the sum of the predictive values of a plurality of classifications is 1, and then the loss is calculated through the cross entropy, wherein the softmax function has the calculation formula:

wherein x is _i The output of the upper layer of the model is used as the input of a softmax classifier; the output calculation result softmax (x) may be regarded as the confidence that the predicted result is a true result.