Fault diagnosis method of aero-engine bearing based on DeiT model

Abstract

The invention discloses a fault diagnosis method for an aero-engine bearing based on a DeiT model, and belongs to the technical field of bearing fault diagnosis, and the method comprises the following steps: obtaining vibration displacement data of the aero-engine bearing in different health states; preprocessing the acquired data, and drawing a two-dimensional grayscale image of the vibration signal; performing data enhancement on the image; embedding the image blocks after data enhancement into a DeiT model, adding position codes and extracting global features; the DeiT model uses a pre-trained RegNetY-160 network to learn richer feature information, and the loss is optimized; and outputting a bearing health state classification result by using a full connection layer classifier. The beneficial effects of the invention are that the method can achieve the precise and rapid recognition of the health state of the rolling bearing, is high in classification precision, is high in model training speed, can accurately judge which health state the bearing belongs to in a short time, effectively prevents the occurrence of potential faults, and provides a reliable basis for the subsequent maintenance decision.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft engine bearing fault diagnosis, in particular to an aircraft engine bearing fault diagnosis method based on a DeiT model. Background Art

[0002] Bearings are key components of aircraft engine systems and play a vital role in ensuring the stable operation of the system. Since bearings usually work in harsh working environments, they are prone to various faults, which reduce the reliability and safety of the equipment. If serious bearing faults are not discovered in time, they may lead to immeasurable accidents. Traditional fault detection methods mostly rely on the collection and analysis of signals such as vibration, temperature, acoustic emission, oil and current. Although these methods are effective, they often rely on manual experience and have certain limitations in the detection of complex fault modes. With the development of data science and machine learning, methods such as image classification and vibration analysis based on deep learning have gradually become a trend.

[0003] However, it is difficult for traditional deep learning image classification technology to improve the accuracy of bearing fault diagnosis while making the model train faster. For example, traditional deep learning image classification technology has low data utilization efficiency. It is difficult to achieve more accurate fault diagnosis when the training time is short. If the training time is longer, it is difficult to make a more accurate judgment on the health status of the bearing in a timely manner. Therefore, there is an urgent need for an aircraft engine bearing fault diagnosis technology that can accurately identify the health status in a shorter training time to improve the efficiency and accuracy of fault detection. Summary of the invention

[0004] The purpose of the present invention is to provide an aircraft engine bearing fault diagnosis method based on the DeiT model, which can realize aircraft engine bearing fault diagnosis that accurately identifies the health state in a shorter training time and improve the efficiency and accuracy of fault detection.

[0005] The purpose of the present invention is achieved through the following technical solutions: The fault diagnosis method of aircraft engine bearing based on DeiT model includes the following steps: S1. Obtain vibration displacement data of aircraft engine bearings under different health conditions; S2, preprocessing the acquired data and drawing a two-dimensional grayscale image of the vibration signal; S3, perform data enhancement on the image; S4, embed the data-enhanced image blocks into the DeiT model, add position encoding and extract global features; S5. The DeiT model uses the pre-trained RegNetY-160 network to learn richer feature information and optimize the loss; S6. Use the fully connected layer classifier to output the bearing health status classification results.

[0006] Furthermore, the vibration displacement data under different health states include a normal state data set, an inner race fault data set and an outer race fault data set.

[0007] Furthermore, in step S2, the preprocessing step includes: (1) Normalize the data: , In the formula, X is the original data, X min is the minimum value in the original data, X max is the maximum value in the original data, X norm is the normalized data; (2) Multiply the normalized data by 255 and map the value to a grayscale value: .

[0008] Furthermore, in step S3, data enhancement includes sequentially performing data enhancement on the image by randomly cropping and scaling the image, randomly changing the brightness and contrast of the image, automatically enhancing the image, and randomly erasing the image.

[0009] Furthermore, in step S4, embedding the image blocks after data enhancement into the DeiT model includes: (1) The input image is divided into multiple blocks of fixed size. Divide into multiple small blocks, each block is P×P in size, and each block contains P 2 The number of pixels divided into blocks is: , (2) Flatten each small block into a vector. Define the image as having C channels. Then the size of each small block after the pixel value is flattened into a vector is P. 2 ×C, and then embedded through a fully connected layer so that each block is mapped to a fixed dimension D: , In the formula, represents the linear transformation matrix, represents the pixel value of the i-th block after flattening, b is the bias vector, and after the embedding transformation, the embedding vectors of all image blocks form a sequence: ' In the formula, , and add [CLS] token as the aggregation point of global features, and its embedding vector size is , the input sequence is: ; (3) Adding position coding includes: defining the position coding matrix , each block has its position code PE i , add the positional encoding to the embedding vector to get the final input of the Transformer , the formula is: , (4) Extracting global features includes: using the Transformer encoder to complete the extraction of global features. In the self-attention mechanism of the Transformer encoder, each input embedding vector and position encoding is mapped into three vectors: query, key and value. The formula for calculating the attention weight is: , Where Q is the query vector, K is the key vector, and V is the value vector, all of which are linear transformations of the input embeddings. k is the dimension of the key vector. After being processed by the self-attention mechanism, the new representation of each block is: , (5) The output of the self-attention module is processed by the feed-forward network, and the formula is: , In the formula, represents the input, σ is the nonlinear activation function, is the weight matrix of the first layer, which is used to map the input feature dimension from D to a higher dimension D hidden , is the bias vector of the first layer, is the weight matrix of the second layer, which converts the dimension D of the hidden layer of the feedforward network into hidden Projected back to the input feature dimension D, is the bias vector of the second layer; (6) The DeiT model extracts global features from the image by stacking multiple self-attention layers and feed-forward network layers.

[0010] Furthermore, the steps of step S5 include: (1) Use hard labels and hard predictions to calculate the cross entropy loss of hard labels. The formula is: , Where, L CE is the cross entropy loss of the hard label, which is used to guide the model to learn the classification task under the real label, y hardis the hard label, that is, the true label of the category, y hard-prediction It is a hard prediction. In the DeiT model, the student model outputs hard predictions through classification tokens, that is, the probability distribution of the predicted category; (2) Using soft labels and soft predictions, the KL divergence is used to calculate the distillation loss. The formula is: , Where, L distill is the distillation loss of the soft label, which is used to guide the prediction distribution of the student model to be closer to the teacher model; soft is the soft prediction of the student model, i.e., the probability distribution generated by the distilled tokens; y soft-prediction is the output of the teacher model, which comes from the pre-trained RegNetY-160 network; (3) Using L CE and L distill Calculate the final loss, the formula is: , Where L is the total loss of the student model and α is a hyperparameter used to control the weight of hard label loss and soft label loss.

[0011] Furthermore, the steps of step S6 include: (1) The output features of the [CLS] token processed by the Transformer encoder are considered as the global representation of the entire image: , In the formula, CLS Token feature is the output feature of the [CLS] token after being processed by the Transformer encoder, h cls is the global representation of the entire image, and d is the hidden dimension of Transformer; (2) The fully connected layer converts h cls Mapping from hidden dimension d to number of categories C: , Where W is the weight matrix; b is the bias vector; (3) Apply the softmax function to the output z of the fully connected layer to obtain the probability distribution of each category: , Where P (yi) is the probability that the predicted image belongs to the i-th category, exp(zi) is the exponential function of the score of category i output by the model in the last fully connected layer, is the sum of the indexed scores for all categories.

[0012] The present invention has the following advantages: by introducing a special DistillationToken in the DeiT model, the knowledge from the teacher model is integrated into the student model training, so that the student model can learn effective representations faster, thereby accelerating the training speed of the DeiT model and improving the classification accuracy. Combining the real label and soft label optimization loss, the model can not only use the precise supervision of the real label, but also learn richer category correlations from the teacher model, thereby improving the classification performance and training efficiency of the model, and can accurately determine which health state the bearing belongs to in a relatively short time, effectively prevent the occurrence of potential faults, and provide a reliable basis for subsequent maintenance decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the present invention; Figure 2 It is a principle block diagram of the present invention; Figure 3 The following is a waveform diagram of the bearing vibration under normal conditions of the present invention (the first 160,000 data points); Figure 4 This is a grayscale image of the bearing vibration under normal conditions of the present invention; Figure 5 The vibration waveform of the bearing under the inner ring fault state of the present invention (the first 160,000 data points); Figure 6 It is a grayscale image of the bearing vibration under the inner ring fault state of the present invention; Figure 7 The vibration waveform of the bearing under the outer ring fault state of the present invention (the first 160,000 data points); Figure 8 It is a grayscale image of the bearing vibration under the outer ring fault state of the present invention; Fig. 9 This is a graph showing the classification accuracy changes of the DeiT model of the present invention and the traditional deep learning image classification model under the same training rounds. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0015] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0016] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0017] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0018] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside", etc. indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, or the positions or positional relationships in which the product of the invention is usually placed when in use, or the positions or positional relationships commonly understood by those skilled in the art, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0019] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0020] refer to Figure 1-9 As shown, one embodiment of the present invention is: The fault diagnosis method of aircraft engine bearing based on DeiT model includes the following steps: S1. Obtain vibration displacement data of aircraft engine bearings under different health conditions.

[0021] The vibration data comes from Journal of Dynamics, Monitoring and Diagnostics, 2023,2, 228-242. Harbin Institute of Technology established a test bench based on an aircraft engine prototype. Two eddy current sensors were installed on the test bench to measure the horizontal and vertical vibration displacement responses of the low-pressure rotor, and four acceleration sensors were installed to measure the vibration acceleration response. The test was carried out 5 times, and 5 data sets of 3 health states of the bearing were obtained and stored in the form of time series. Each data set is stored as a three-dimensional array, and the original data is a long time series sampled for 15 seconds with a sampling frequency of 25000Hz. The original data is segmented and truncated, containing a short time series of 20480 data points. The present invention selects three vibration displacement data sets under different health states: a normal state data set (data1), an inner ring fault data set (data3), and an outer ring fault data set (data5) for bearing fault diagnosis.

[0022] S2. Preprocess the acquired data, and draw a two-dimensional grayscale image of the vibration signal with 2500 processed data points as a group.

[0023] The preprocessing steps include: (1) Normalize the data: , In the formula, X is the original data, X min is the minimum value in the original data, X max is the maximum value in the original data, X norm is the normalized data; (2) Multiply the normalized data by 255 and map the value to a grayscale value: .

[0024] Normalizing different types of bearing fault data to [0, 1] and then multiplying by 255 can map the data to the standard pixel range of the grayscale image [0, 255], which is convenient for intuitively displaying different fault characteristics and enhancing data contrast. In classification tasks, the value ranges of different features are often different. For example, the value range of one feature is 2000-4000, and the value range of another feature is 2-4. Without normalization, features with larger values ​​will dominate the calculation process, causing the model to assign it a higher weight. This weight bias will affect the accuracy of the classification results because features with smaller values ​​may be more helpful for classification decisions. Through normalization, the feature values ​​are compressed to the same range, ensuring that the model fairly considers the impact of each feature. After preprocessing, the first 160,000 vibration displacement data of the three data sets are as follows: Figure 3 , Figure 5 , Figure 7 shown.

[0025] The 2500 data points are reshaped into a 50×50 matrix, and then these data are mapped to the pixel values ​​of the grayscale image, and the grayscale image is drawn using the image display tool. After the data of the three data sets are preprocessed, the grayscale image drawn is as follows Figure 4 , Figure 6 , Figure 8 shown.

[0026] S3, perform data enhancement on the image, the steps include: (1) Randomly crop and scale the image: Randomly crop a region from the input grayscale image and then scale the region to the target size to simulate changes in multiple viewing angles and sizes, thereby enhancing the model’s robustness to targets of different sizes and locations. (2) Randomly change the brightness and contrast of the image; (3) Automatic enhancement: Automatically select a variety of enhancement strategies (such as flipping, rotation, and shearing) and apply them to images to enhance data diversity, reduce model overfitting, and be suitable for small data sets; (4) Random erasing: Randomly block a rectangular area in the image and fill it with random values ​​or zeros to simulate sensor failure or noise occlusion and improve the robustness of the model.

[0027] S4. The data-enhanced image is divided into blocks and embedded into the DeiT model, position encoding is added and global features are extracted.

[0028] Among them, the image block embedding DeiT model after data enhancement includes: (1) The input image is divided into multiple blocks of fixed size. Divide into multiple small blocks, each block is P×P in size, and each block contains P 2 Pixel points, the number of blocks obtained by division is: , (2) Flatten each small block into a vector. Define the image as having C channels. Then the size of each small block after the pixel value is flattened into a vector is P. 2 ×C, and then embedded through a linear layer (fully connected layer) so that each block is mapped to a fixed dimension D: , In the formula, represents the linear transformation matrix, represents the pixel value of the i-th block after flattening, and b is the bias vector. After the embedding transformation, the embedding vectors of all image blocks form a sequence: , In the formula, , and add [CLS] token as the aggregation point of global features, and its embedding vector size is , the input sequence is: ; (3) Adding position coding includes: defining the position coding matrix , each block has its position code PE i , add the positional encoding to the embedding vector to get the final input of the Transformer , the formula is: , (4) Extracting global features includes: using the Transformer encoder to complete the extraction of global features. In the self-attention mechanism of the Transformer encoder, each input embedding vector and position encoding is mapped into three vectors: query, key and value. The formula for calculating the attention weight is: , Where Q is the query vector, K is the key vector, and V is the value vector, all of which are linear transformations of the input embeddings. k is the dimension of the key vector. After being processed by the self-attention mechanism, the new representation of each block is: ; (5) The output of the self-attention module is processed by the feed-forward network, and the formula is: , In the formula, represents the input, σ is the nonlinear activation function, is the weight matrix of the first layer, which is used to map the input feature dimension from D to a higher dimension D hidden , helps to capture more complex features; is the bias vector of the first layer, is the weight matrix of the second layer, which converts the dimension D of the hidden layer of the feedforward network into hidden Project back to the input feature dimension D to ensure that the input and output dimensions of the Transformer are consistent; is the bias vector of the second layer.

[0029] (6) By stacking multiple self-attention layers and feed-forward network layers, the DeiT model can effectively extract global features from the image.

[0030] S5. The DeiT model uses the pre-trained RegNetY-160 network to learn richer feature information and optimize the loss. The process steps include: (1) Use hard labels and hard predictions to calculate the cross entropy loss of hard labels. The formula is: , Where, L CE is the cross entropy loss of the hard label, which is used to guide the model to learn the classification task under the real label and ensure the basic classification performance of the model; hard is a hard label, that is, the true label of the category; y hard-prediction It is a hard prediction. In the DeiT model, the student model outputs hard predictions through classification tokens, that is, the probability distribution of the predicted category; (2) Using soft labels and soft predictions, the KL divergence is used to calculate the distillation loss. The formula is: , Where, L distill is the distillation loss of the soft label, which can help the student model learn the implicit relationship between categories from the teacher model, namely the RegNetY-160 network, and learn richer feature information, which is used to guide the prediction distribution of the student model to be closer to the teacher model, thereby improving the model performance and optimizing the generalization ability; soft is the soft prediction of the student model, i.e., the probability distribution generated by the distilled tokens; y soft-prediction is the output of the teacher model, which is the probability distribution of the teacher model's category predictions for the input data, and comes from the pre-trained RegNetY-160 network; (3) Using L CE and L distill Calculate the final loss, the formula is: , In the formula, L is the total loss of the student model, and α is a hyperparameter used to control the weight of the hard label loss and the soft label loss. That is, by adjusting α, the model can be controlled to rely more on the true label or the soft label of the teacher model, thereby optimizing the loss.

[0031] S6. Use the fully connected layer classifier to output the classification result of the bearing health status. The steps include: (1) The output features of the [CLS] token processed by the Transformer encoder are considered as the global representation of the entire image: , In the formula, CLS Token feature is the output feature of the [CLS] token after being processed by the Transformer encoder, h cls is the global representation of the entire image, and d is the hidden dimension of Transformer; (2) The fully connected layer converts h clsMapping from hidden dimension d to number of categories C: , Where W is the weight matrix; b is the bias vector; (3) Apply the softmax function to the output z of the fully connected layer to obtain the probability distribution of each category: , Where, P (yi) is the probability that the predicted image belongs to the i-th category; exp(zi) is the exponential function of the score of category i output by the model in the last fully connected layer, reflecting the model’s “confidence” in category i; It is the sum of the indexed scores of all categories. Through step S1, the vibration displacement data points of the three data sets data1, data3, and data5 are obtained, which are 10321920, 10321920, and 9216000 respectively. After processing in step S2, 4128, 4128 and 3686 grayscale images are obtained respectively. In order to ensure the balance of the data set, the present invention finally selects the first 3686 images of the data1 and data3 image data sets. The processed data set is divided into a training set and a test set according to a ratio of 8:2. The number of training rounds is 200, and the accuracy rate reaches 98.74%. In comparison, the traditional deep learning model is used for image classification. The corresponding parameters and classification results are shown in Table 1. The classification accuracy changes under the same training rounds are as shown in Table 1. Fig. 9 As shown, it can be seen that the classification accuracy of the present invention is the highest.

[0032] Table 1 Comparison of the results of DeiT model and traditional deep learning image classification model Model Name Batch size Optimizer Learning Rate Number of training rounds Time required (s) Accuracy (%) Dei 64 AdamW 0.0005 200 3736 98.74 ViT 64 SGD 0.00001 200 8670 91.19 Transformer 64 SGD 0.0005 200 2996 88.21 Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A fault diagnosis method for aircraft engine bearings based on the DeiT model, characterized in that: The following steps are involved: S1. Obtain vibration displacement data of aircraft engine bearings under different health conditions; S2, preprocessing the acquired data and drawing a two-dimensional grayscale image of the vibration signal; S3, perform data enhancement on the image; S4, embed the data-enhanced image blocks into the DeiT model, add position encoding and extract global features; S5. The DeiT model uses the pre-trained RegNetY-160 network to learn richer feature information and optimize the loss; S6. Use the fully connected layer classifier to output the bearing health status classification results.

2. The fault diagnosis method of aircraft engine bearing based on DeiT model according to claim 1 is characterized in that: The vibration displacement data under different health states include a normal state data set, an inner ring fault data set and an outer ring fault data set.

3. The fault diagnosis method of aircraft engine bearing based on DeiT model according to claim 1 is characterized in that: In step S2, the pre-processing step includes: (1) Normalize the data: , In the formula, X is the original data, X min is the minimum value in the original data, X max is the maximum value in the original data, X norm is the normalized data; (2) Multiply the normalized data by 255 and map the value to a grayscale value: 。 4. The fault diagnosis method of aircraft engine bearing based on DeiT model according to claim 1 is characterized in that: In step S3, data enhancement includes sequentially performing data enhancement on the image by randomly cropping and scaling the image, randomly changing the brightness and contrast of the image, automatically enhancing the image, and randomly erasing the image.

5. The fault diagnosis method of aircraft engine bearing based on DeiT model according to claim 1 is characterized in that: In step S4, embedding the image blocks after data enhancement into the DeiT model includes: (1) The input image is divided into multiple blocks of fixed size. Divide into multiple small blocks, each block is P×P in size, and each block contains P 2 The number of pixels divided into blocks is: ， (2) Flatten each small block into a vector. Define the image as having C channels. Then the size of each small block after the pixel value is flattened into a vector is P. 2 ×C, and then embedded through a fully connected layer so that each block is mapped to a fixed dimension D: ， In the formula, represents the linear transformation matrix, represents the pixel value of the i-th block after flattening, b is the bias vector, and after the embedding transformation, the embedding vectors of all image blocks form a sequence: ， In the formula, And add [CLS] token as the aggregation point of global features, and its embedding vector size is , the input sequence is: ， (3) Adding position coding includes: defining the position coding matrix , each block has its position code PE i , add the positional encoding to the embedding vector to get the final input of the Transformer , the formula is: ； (4) Extracting global features includes: using the Transformer encoder to complete the extraction of global features. In the self-attention mechanism of the Transformer encoder, each input embedding vector and position encoding is mapped into three vectors: query, key and value. The formula for calculating the attention weight is: , Where Q is the query vector, K is the key vector, and V is the value vector, all of which are linear transformations of the input embeddings. k is the dimension of the key vector. After being processed by the self-attention mechanism, the new representation of each block is: ， (5) The output of the self-attention module is processed by the feed-forward network, and the formula is: ， In the formula, represents the input, σ is the nonlinear activation function, is the weight matrix of the first layer, which is used to map the input feature dimension from D to a higher dimension D hidden , is the bias vector of the first layer, is the weight matrix of the second layer, which converts the dimension D of the hidden layer of the feedforward network into hidden Projected back to the input feature dimension D, is the bias vector of the second layer; (6) The DeiT model extracts global features from the image by stacking multiple self-attention layers and feed-forward network layers.

6. The fault diagnosis method of aircraft engine bearing based on DeiT model according to claim 1 is characterized in that: The steps of step S5 include: (1) Use hard labels and hard predictions to calculate the cross entropy loss of hard labels. The formula is: ， Where, L CE is the cross entropy loss of the hard label, which is used to guide the model to learn the classification task under the real label, y hard is the hard label, that is, the true label of the category, y hard-prediction It is a hard prediction. In the DeiT model, the student model outputs hard predictions through classification tokens, that is, the probability distribution of the predicted category; (2) Using soft labels and soft predictions, the KL divergence is used to calculate the distillation loss. The formula is: ， Where, L distill is the distillation loss of the soft label, which is used to guide the prediction distribution of the student model to be closer to the teacher model; soft is the soft prediction of the student model, i.e., the probability distribution generated by the distilled tokens; y soft-prediction is the output of the teacher model, which comes from the pre-trained RegNetY-160 network; (3) Using L CE and L distill Calculate the final loss, the formula is: ， Where L is the total loss of the student model and α is a hyperparameter used to control the weight of hard label loss and soft label loss.

7. The fault diagnosis method of aircraft engine bearing based on DeiT model according to claim 5 is characterized in that: The steps of step S6 include: (1) The output features of the [CLS] token processed by the Transformer encoder are considered as the global representation of the entire image: ， In the formula, CLS Token feature is the output feature of the [CLS] token after being processed by the Transformer encoder, h cls is the global representation of the entire image, and d is the hidden dimension of Transformer; (2) The fully connected layer converts h cls Mapping from hidden dimension d to number of categories C: ， Where W is the weight matrix; b is the bias vector; (3) Apply the softmax function to the output z of the fully connected layer to obtain the probability distribution of each category: ， Where, P (yi) is the probability that the predicted image belongs to the i-th category, exp(zi) is the exponential function of the score of category i output by the model in the last fully connected layer, is the sum of the indexed scores for all categories.

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