Hierarchical fault classification method based on stacked autoencoder

Abstract

The application discloses a hierarchical fault classification method based on a stacked autoencoder. Firstly, according to prior knowledge of an industrial process and correlation between variables, the whole process is divided into several sub-blocks; secondly, fault types prone to misclassification in each sub-block are treated as a composite class to avoid misclassification; a fault diagnosis model based on SAE is trained to realize preliminary classification of faults. Then, an improved D-S evidence theory is proposed to fuse multiple SAE classification results, handle conflicts between the multiple SAE classification results and improve accuracy of fault diagnosis. Finally, the SAE classification model is used to classify fault types that cannot be classified by decision fusion. The application reduces complexity of the model and improves accuracy of the SAE classification model, and has important significance for fault diagnosis of the industrial process.

Description

Technical Field

[0001] This invention relates to the field of data-driven fault classification methods, and in particular to a hierarchical fault classification method based on stacked autoencoders for nonlinear large-scale chemical processes. Background Technology

[0002] With the increasing complexity of modern industrial processes, the challenge of ensuring their safe and stable operation is also growing. Fault detection and diagnosis (FDD) technology plays a crucial role in improving the reliability and safety of chemical processes. Fault classification is an important aspect of FDD. Fault classification involves categorizing fault samples. Fault classification methods include model-based methods, knowledge-based methods, and data-driven methods. Due to the development of computer and sensor technologies, a large amount of historical industrial process data can be collected and stored, leading to widespread attention being paid to data-driven methods.

[0003] Multivariate statistical analysis is a data-driven approach. Methods such as Principal Component Analysis (PCA) and Fisher Discriminant Analysis (FDA) have been successfully applied to fault classification. For nonlinear data, kernel PCA and kernel FDA have been proposed. To consider the multimodal nature of industrial process data and emphasize key fault variables, sparse local FDA has been proposed. However, multivariate statistical methods can only extract shallow features, which may negatively impact fault classification performance. Deep neural networks, composed of multiple hidden layers, can extract deep, nonlinear features of the data. Fault classification methods based on deep neural networks have received increasing attention. Deep belief networks (DBNs), convolutional neural networks (CNNs), and stacked autoencoders (SAEs) have been applied to fault classification. SAEs, an unsupervised model, have been successfully applied to fault classification in industrial processes. To improve the performance of SAEs in industrial process fault classification, many improved SAE models have been proposed, such as Discriminant Information-based Autoencoders (DIAEs), Autoencoders Embedded Dictionary Learning (AEDLs), and Stacked Supervised Autoencoders (SSAEs). However, modern industrial processes are often large-scale, consisting of multiple operational units. Therefore, establishing only a single fault classification model may be detrimental to the fault classification performance of large-scale industrial processes. Summary of the Invention

[0004] To improve fault classification performance in large-scale industrial processes, this invention proposes a hierarchical fault classification method based on stacked autoencoders. Considering the large scale of industrial processes, the entire process is divided into several sub-blocks using prior knowledge and correlations. Then, to avoid misclassification of fault types, fault types prone to misclassification in each sub-block are treated as a composite class. Based on this, an SAE-Softmax classification model is established for each sub-block. Next, to handle conflicts between multiple SAE-Softmax classification results, an improved DS evidence theory is proposed to perform decision fusion on the classification results of multiple sub-blocks, thereby improving the accuracy of decision fusion. Finally, an SAE-Softmax model is established to classify fault samples that cannot be classified by decision fusion.

[0005] The hierarchical fault classification method based on stacked autoencoders is characterized by the following steps:

[0006] A. Offline phase:

[0007] 1) Obtain historical data as training data X∈R n×m Where n represents the total number of samples and m represents the number of variables included in the samples, the mean of the training data under normal conditions is calculated. The standardized training data X is obtained by summing the standard deviation S.

[0008]

[0009] 2) Based on the B operational units of the industrial process, the standardized training data... The variables are divided into B sub-blocks, and the datasets corresponding to these B sub-blocks are as follows: in b represents the b-th sub-block. express For the i-th variable, to consider the correlation between sub-blocks, mutual information is used to evaluate the correlation between two variables, and the variables in the b-th sub-block are calculated. Other variables Mutual information values ​​between

[0010]

[0011] in express Marginal probability density, express marginal probability density, express and Calculate the joint probability density The mutual information values ​​between the variables in the b-th sub-block and all variables in the b-th sub-block are used to obtain a one-dimensional vector. Where j = 1, 2, ..., m b By calculating the mutual information values ​​between all variables outside the b-th sub-block and the variables within the b-th sub-block, we can obtain m–m. b One-dimensional vectors: Calculate m–m b The mean of a one-dimensional vector is obtained in for The mean, if it exists Then variable If it is a related variable of the b-th sub-block, then... If added to the b-th sub-block, then the b-th sub-block after adding the relevant variables will be updated as follows: Where m b Let ' be the number of variables in the b-th sub-block, and m b ′>m b k > 1 is a manually set parameter, the purpose of which is to avoid the sub-block containing too many variables;

[0012] 3) Build an SAE model for each sub-block separately:

[0013] To avoid misclassification of fault types, the fault types that are prone to misclassification in each sub-block are first treated as a composite class, and the fault category of the fault sample is the label. An SAE classification model is trained for each sub-block using composite class data and fault data that are less prone to misclassification. The SAE consists of L autoencoders (AEs) capable of extracting deep features. Each AE consists of an input layer, a hidden layer, and an output layer. The hidden layer outputs the features extracted by the AE. The input and hidden layers form the encoder, and the hidden and output layers form the decoder. The input layer of each AE is the hidden layer of the previous AE. The encoder and decoder of an AE can be represented as:

[0014] h=f(Wx+b) (3)

[0015]

[0016] Where x represents the input of the AE, and h represents the features extracted by the AE. Let represent the output of AE, W represent the weight matrix from the input layer to the hidden layer, and b represent the bias vector of the hidden layer. This represents the weight matrix from the hidden layer to the output layer. Let f(·) represent the bias vector of the output layer, f(·) represent the activation function of the hidden layer, and g(·) represent the activation function of the output layer. encoder,l (·) represents the encoder of the l-th AE in SAE, f decoder,l (·) represents the decoder of the l-th AE in the SAE. Then, the decoding and encoding parts of the SAE built for the b-th sub-block can be represented as follows:

[0017]

[0018]

[0019] Among them, H b The input is Features extracted by SAE at that time The input is The output of the SAE is displayed. To achieve fault classification, a Softmax layer is connected after the encoding part of the SAE. The training of the SAE is divided into two stages: pre-training and fine-tuning. In the pre-training stage, each AE in the SAE is trained separately using the mean squared error loss function, which can be expressed as:

[0020]

[0021] Where, x (i) Let represent the input of the i-th sample of AE. Let represent the output of the i-th sample of the AE. During the fine-tuning phase, since the composite class contains multiple fault types, and the number of samples for each fault type is the same, the composite class has more samples than other fault types, thus causing a sample imbalance problem. To address this imbalance, the SAE model is trained using the idea of ​​a weighted cross-entropy loss function. The loss function used can be expressed as:

[0022]

[0023] Where y j This indicates the true label of the sample, i.e., the fault category. This represents the predicted label of Softmax, where w is the weight, and when y j When the true label is a composite class, w = 1, and when y j When the actual label is not a composite class, w = n c +1, n c The number of fault types contained in the composite class;

[0024] 4) A Softmax layer is connected after the SAE encoding part to classify fault samples. DS evidence theory is used to fuse the classification results of multiple SAE-Softmax layers. DS evidence theory can fuse inaccurate and incomplete information and has been applied in the field of fault diagnosis. Θ={A1,A2,...,A... p} is the identification framework, where each element is a pairwise mutually exclusive probability hypothesis. In this method, Θ is the set of all fault categories. The basic probability assignment (BPA), also known as the m-function, can be expressed as:

[0025] m:2 Θ →[0,1] (9)

[0026] The m-function satisfies the following conditions:

[0027]

[0028] For B pieces of evidence E1, E2, ..., E B The m functions are m1, m2, ..., m B The DS evidence combination rule can be expressed as:

[0029]

[0030] in For the result of combining B pieces of evidence, K, the normalization coefficient, can be expressed as:

[0031]

[0032] 1–K represents the degree of conflict between evidence bodies, where 0 < 1–K < 1. A larger 1–K indicates greater conflict between evidence bodies; conversely, a 1–K close to 1 may result in an incorrect combination. In this method, B SAE-Softmax values ​​represent B evidence bodies, the set of fault types forms the recognition frame, and the output of Softmax, i.e., the probability of the fault category of the fault sample, is used as the m-function. However, when there is a high degree of conflict between the outputs of multiple SAE-Softmax values, the DS evidence theory may yield unreasonable decision fusion results. To more effectively handle the conflict between multiple classifiers, the DS evidence theory is improved. First, the m-function is modified:

[0033]

[0034] Where q is the number of possible fault categories on each sub-block, and m′(A i () represents the improved m-function, mean m Let m(A1), m(A2), ..., m(Aq The mean and max of ) m Let m(A1), m(A2), ..., m(A) be the bases for the values ​​of A1, A2, ..., A2. q To further improve the accuracy of decision fusion, the DS combination rule is improved by calculating the normalization coefficient E between the two evidence bodies. i and E j The normalization coefficients between them are expressed as follows:

[0035]

[0036] For evidence E i E can be obtained i The mean of B-1 normalized coefficients between the evidence and other evidence is obtained by taking the average of these coefficients.

[0037]

[0038] Where K i The larger E is i The less conflict with other evidence, the better. i The higher the credibility, according to K i Calculate E i weight w i :

[0039]

[0040] When performing decision fusion, utilize w i For E i If the evidence is weighted by the m-function, the improved DS combination rule can be expressed as:

[0041]

[0042] Where K′ can be represented as:

[0043]

[0044] 5) After using the DS evidence theory to perform decision fusion on the classification results of multiple SAE-Softmax, there may be fault samples that cannot be classified. These fault types are then treated as composite classes, and an SAE-Softmax classification model is trained for these fault types, denoted as the B+1th SAE-Softmax.

[0045] B. Online Phase:

[0046] 1) Collect online sample X′, and standardize X′ to obtain

[0047]

[0048] in Let S be the mean of the training data X, and S be the standard deviation of the training data X, which is the same as in formula (1). Equal to S;

[0049] 2) To Variable partitioning is performed to obtain

[0050] 3) Input the SAE-Softmax model of the b-th sub-block in offline modeling to obtain the classification result of the b-th SAE-Softmax model;

[0051] 4) Decision fusion is performed on the classification results of B SAE-Softmax using the improved DS evidence theory;

[0052] 5) If the decision fusion result is a composite class, then the classification is achieved using the (B+1)th SAE-Softmax. If the decision fusion result is not a composite class, then the fusion result is the classification result.

[0053] Beneficial effects

[0054] This invention targets nonlinear large-scale industrial processes, dividing the entire industrial process into multiple sub-blocks and establishing SAE-Softmax classification models for each, thereby reducing the complexity of the SAE classification model and improving the accuracy of the SAE-Softmax classification model, which is of great significance for fault diagnosis of industrial processes. Attached Figure Description

[0055] Figure 1 The flowchart shown is a process of the method of the present invention;

[0056] Figure 2 The diagram shown is a schematic of AE;

[0057] Figure 3 The diagram shown is a flowchart of the TE process;

[0058] Figure 4 The results shown are the SAE-Softmax classification results for the five sub-blocks.

[0059] Figure 5 The figure shows the fusion result of the improved DS evidence theory; Detailed Implementation

[0060] TE processes are simulations of real chemical processes and are often used to verify the performance of fault diagnosis methods. For example... Figure 3The flowchart of the TE process is shown. The TE process can simulate normal conditions and 21 fault conditions, collecting 52 variables. This experiment uses 33 of these variables. The TE process contains 5 operating units: input unit, reactor, separator, stripper, and compressor. The variables contained in each unit are shown in Table 1. The dataset used in this experiment consists of 18 fault conditions: faults 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, and 21. The training data contains 480 samples per fault condition, and the test data contains 800 samples per fault condition.

[0061] Variables for each cell in Table 1

[0062]

[0063] Based on the above description, and in accordance with the invention, the specific process is implemented as follows:

[0064] A. Offline phase:

[0065] 1) For training data X∈R 500×33 Standardize and calculate the mean of X. The sum and standard deviation S are obtained by standardizing X using formula (1).

[0066] 2) According to Table 1, The variables were partitioned to obtain 5 subsets, which are as follows: Among them To account for the correlation between sub-blocks, mutual information is used to evaluate the correlation between two variables, and the variables within the b-th sub-block are calculated. Other variables Mutual information values ​​between

[0067]

[0068] in express marginal probability density, express marginal probability density, Represent the joint probability density, calculate The mutual information values ​​between the variables in the b-th sub-block and all variables in the b-th sub-block are used to obtain a one-dimensional vector. Where j = 1, 2, ..., m b By calculating the mutual information values ​​between all variables outside the b-th sub-block and the variables within the b-th sub-block, we can obtain m–m. b One-dimensional vectors: Calculate m–mb The mean of a one-dimensional vector is obtained in for The mean, if it exists Then variable If it is a related variable of the b-th sub-block, then... If added to the b-th sub-block, then the b-th sub-block after adding the relevant variables is: Where m b Let ' be the number of variables in the b-th sub-block, and m b ′>m b k = 1.04. Table 2 shows the results of sub-block division and the fault types occurring in each sub-block, where [·] represents a composite class. In Table 2, only fault 19 occurs only in the 5th sub-block. Therefore, when only the 5th sub-block detects an anomaly, the fault can be identified as fault 19. Only fault 20 occurs in the 3rd, 4th, and 5th sub-blocks. Therefore, when the 3rd, 4th, and 5th sub-blocks detect an anomaly, the fault can be identified as fault 20. Thus, fault 19 and fault 20 can be identified without SAE. A sliding window with a window width of 40 is taken for each sub-block to obtain dynamic data.

[0069] Table 2 shows the results of sub-block partitioning and the types of faults occurring in each sub-block.

[0070]

[0071]

[0072] 3) with Five SAE-Softmax models were trained using training data. The structures of the five SAE-Softmax models are shown in Table 3, where "Number of Neurons" represents the number of neurons in each layer of the SAE-Softmax model. Each of the five SAE-Softmax models has three hidden layers, and the output layer is a Softmax layer. The activation functions for the three hidden layers and the output layer of the five SAEs are Gaussian function-linear function-linear function-Sofmax, respectively. The Gaussian function and the linear function are expressed as follows:

[0073]

[0074] f Linear (z)=z (22)

[0075] Where z represents the input vector, and all SAEs use the Adam optimizer with a learning rate of 0.001.

[0076] Table 3 shows the structure of the five sub-blocks of SAE.

[0077]

[0078] 4) DS evidence theory is used to fuse classification results from multiple SAEs. DS evidence theory can fuse inaccurate and incomplete information and has been applied in the field of fault diagnosis. The identification framework is Θ={f1,f2,f4,f5,f6,f7,f8,f... 10 ,f 11 ,f 12 ,f 13 ,f 14 ,f 16 ,f 17 ,f 18 ,f 21}, where f1 represents fault 1, f2 represents fault 2, ..., f 21 For fault 21, the output value of Softmax is used as the value of the basic probability assignment function, i.e., the m-function value. Improvements are made to the m-function as follows:

[0079]

[0080] Where F i The possible classification results for SAE-Softmax are (i = 1, 2, ..., q), where q is the number of possible failure categories in SAE-Softmax, and m′(F i () represents the improved m-function, mean m Let m(F1), m(F2), ..., m(F q The mean and max of ) m Let m(F1), m(F2), ..., m(F q To improve the accuracy of decision fusion, an improved DS combination rule is proposed, which finds the maximum value of DS.

[0081]

[0082] Where F is a fault type in Θ. For the merged m-function, F i Let K′ be the normalization coefficient, representing the fault type occurring in the i-th sub-block.

[0083]

[0084] w i For m i The weights of the ′ function can be obtained using the following formula.

[0085]

[0086] Where K i,jK represents the normalization coefficient between the i-th and j-th SAE-Softmax classification results. i The mean of the normalized coefficients between the i-th SAE-Softmax classification result and other SAE-Softmax classification results;

[0087] 5) Since faults 11 and 14 occur in the second sub-block and both belong to the composite class, decision fusion cannot distinguish between these two faults. These two faults are denoted as f. c 1. Since faults 5, 8, 10, 12, 13, 16, and 18 occur in 5 sub-blocks and are all fault types within the composite class, decision fusion cannot distinguish these faults. These faults are denoted as f. c 2. The sixth SAE-Softmax classification model was trained using dynamic data of faults 5, 8, 10, 11, 12, 13, 14, 16, and 18. The dynamic data was obtained by taking a sliding window with a width of 40 from the training data of faults 5, 8, 10, 11, 12, 13, 14, 16, and 18. Each sample in the training data has 33 variables. The model consists of one input layer, three hidden layers, and one input layer. The number of neurons is 1320, 660, 330, 165, and 16, respectively. The activation functions of the three hidden layers and the output layer are Gaussian function, linear function, linear function, and Softmax, respectively. The optimizer is Adam optimizer, and the learning rate is 0.001.

[0088] B. Online Phase:

[0089] 1) Collect online sample X′, and standardize X′ using formula (1) to obtain

[0090] 2) According to Table 2 Variable partitioning is performed to obtain right Dynamic data is obtained by using a sliding window with a width of 40.

[0091] 3) Input the SAE-Softmax model of the b-th sub-block in offline modeling to obtain the classification result of the b-th SAE-Softmax model;

[0092] 4) Decision fusion of the classification results of 5 SAE-Softmaxes is performed using the improved DS evidence theory;

[0093] 5) If the decision fusion result is f c 1 or f c 2, then Fault classification is achieved by inputting the data into the 6th SAE-Softmax classification model; otherwise, the decision fusion result is the fault classification result.

[0094] The above steps illustrate the specific application of this method in TE process fault classification. This experiment uses the Fault Diagnosis Rate (FDR) to evaluate the method's performance. FDR refers to the ratio of the number of samples correctly classified as class c to the total number of class c samples; a higher FDR indicates better method performance. Figure 4 The SAE-Softmax classification results are for 5 sub-blocks, where 22, 23, 24, 25, and 26 represent composite classes. Figure 5 To improve the fusion results of DS evidence theory and demonstrate the effectiveness of our method, we compared it with SAE-Softmax, Linear Discriminant Analysis (LDA), and Support Vector Machine (SVM). Table 4 shows the FDRs of our method, SAE-Softmax, LDA, and SVM for 16 faults in the TE process. SAE-Softmax consists of one input layer, three hidden layers, and one output layer, with 1320, 660, 330, 165, and 16 neurons respectively, and the activation function is Gaussian function-linear function-linear function-Softmax. Our method achieved higher FDRs for faults 8, 10, 11, 12, 13, 16, 17, and 18 than the other three methods, and its mean FDRs were the highest among the four methods. Therefore, our method improves the performance of fault classification. Furthermore, the structure of the SAE-Softmax model established by our method is simpler than that of a single SAE-Softmax model, meaning that our method is more suitable for fault classification in large-scale industrial processes. Therefore, this method not only simplifies the structure of the SAE-Softmax classification model but also improves the classification performance of the SAE model.

[0095] Table 4. FDRs of 16 faults in the TE process using this method, SAE, LDA, and SVM.

[0096]

[0097]

Claims

1. A hierarchical fault classification method based on stacked autoencoders, characterized in that Comprising the following steps: A. Offline stage: 1) Obtain historical data as training data X ∈ R n×m where n represents the total amount of samples, m represents the number of variables contained in the sample, the mean value of the training data under normal conditions is calculated and the standard deviation S, and the standardized training data X is obtained 2) According to B operation units of the industrial process, the standardized training data is divided into B sub-blocks, and the data set corresponding to the B sub-blocks is Wherein b represents the bth sub-block, represents the ith variable in the bth sub-block, in order to consider the correlation between the sub-blocks, the mutual information is used to evaluate the correlation between two variables, and the mutual information value between the variable and other variables in the bth sub-block is calculated where denotes the marginal probability density of denotes the marginal probability density of denotes the joint probability density of and , and is calculated as the mutual information between all variables in the bth sub-block, and a one-dimensional vector where j = 1, 2,..., m b is obtained. The mutual information between all variables outside the bth sub-block and the variables in the bth sub-block is calculated, and m - m b one-dimensional vectors are obtained: The mean of the m - m b one-dimensional vectors is calculated to obtain where is the mean of If there exists , the variable is a relevant variable of the bth sub-block. The bth sub-block is updated by adding to the bth sub-block. The bth sub-block after adding the relevant variable is where m b ' is the number of variables in the bth sub-block, and m b ' > m b , and k > 1 is a parameter artificially set to avoid the sub-block containing too many variables.​​ 3) Establish SAE model for each sub-block respectively: In order to avoid misclassification of fault categories, first, the fault types that are easy to misclassify in each sub-block are taken as a composite class, and the composite class data and fault data that are not easy to misclassify are used to train SAE classification model for each sub-block. SAE is composed of L autoencoders (AE), which has the ability to extract non-linear deep features. Each AE is composed of an input layer, a hidden layer and an output layer. The hidden layer output is the feature extracted by AE. The input layer and the hidden layer are encoders, and the hidden layer and the output layer are decoders. The input layer of each AE is the hidden layer of the previous AE. The encoder and decoder of AE are represented as: h = f(Wx + b) (3) where x denotes the input of the AE, h denotes the features extracted by the AE, denotes the output of the AE, W denotes the weight matrix from the input layer to the hidden layer, b denotes the bias vector of the hidden layer, denotes the weight matrix from the hidden layer to the output layer, denotes the bias vector of the output layer, f(·) denotes the activation function of the hidden layer, g(·) denotes the activation function of the output layer, f encoder,l (·) denotes the encoder of the l-th AE in the SAE, f decoder,l (·) denotes the decoder of the l-th AE in the SAE, the decoding part and the encoding part of the SAE established for the b-th sub-block are denoted as: where H b is the input is the features extracted by SAE, is the output of SAE when the input is In order to realize fault classification, a Softmax layer is connected after the encoding part of SAE, and the training of SAE is divided into two stages of pre-training and fine-tuning. In the pre-training stage, each AE in SAE is trained separately, and the AE is trained by using a mean square error loss function, and the mean square error loss function is expressed as: where x (i) represents the input of the i-th sample of the AE, represents the output of the i-th sample of the AE, in the fine-tuning stage, since the composite class contains multiple fault types, and the number of samples of each fault type is consistent, the number of samples of the composite class is more than that of other fault types, so there is a problem of sample imbalance. In view of the sample imbalance, the SAE model is trained by using the idea of weighted cross-entropy loss function, and the loss function adopted is represented as: where y j represents the true label of the sample, i.e., the failure class, represents the predicted label of Softmax, w is the weight, when y j the true label of y is a compound class, w = 1, when y j the true label of y is not a compound class, w = n c + 1, n c is the number of failure types contained in the compound class; 4) Connect a Softmax layer after the encoding part of SAE to realize the classification of fault samples. The output of Softmax is the probability of fault category. The fault category with the maximum probability is the classification result of SAE-Softmax classifier. The classification results of multiple SAE-Softmax may conflict. In order to deal with the conflict of multiple classifiers, D-S evidence theory is used to decision fusion of the classification results of multiple SAE-Softmax. When there is a high conflict between the classification results of multiple SAE-Softmax, D-S evidence theory may get unreasonable decision fusion results. In order to more effectively deal with the conflict of multiple classifiers, an improved D-S evidence theory is proposed, which is represented as: wherein K' is the improved normalization coefficient, B is the number of evidences, i.e., the number of SAE-Softmax classifiers, A is the fault type, A i is the fault type identified by the i th SAE-Softmax, m'(A i ) is the improved basic probability assignment function, w i is the weight of m'(A i ), is the result of the improved basic probability assignment function of the fusion of p SAE-Softmaxes, i.e., the probability that the fault sample is the fault type A, and K' is represented as: An improved basic probability assignment function m'(A i ) is expressed as: where q is the number of failure classes that can occur on each sub-block, m(A i ) is the basic probability assignment function, i.e. the probability that a failure sample is of failure type A i , mean m is the mean of m(A1), m(A2),..., m(A q ), max m is the maximum of m(A1), m(A2),..., m(A q ), and the weight w i is calculated by the following: first, the normalization coefficient between two evidence bodies is calculated, the normalization coefficient between the ith classifier and the jth classifier is represented as: For the i-th classifier, B-1 normalized coefficients between the classifiers can be obtained. The average of the B-1 normalized coefficients can be obtained as: where K i The greater the K, the smaller the conflict of the ith SAE-Softmax with other evidences, and the higher the reliability of the classification result of the ith SAE-Softmax, according to K i Calculate E i The weight w i : 5) After decision fusion of the classification results of multiple SAE-Softmax using the improved D-S evidence theory, there may be fault types that cannot be classified. These fault types are taken as a composite class, and an SAE-Softmax classification model is trained for these fault types, which is denoted as the B+1-th SAE-Softmax classification model; B. Online stage: 1) Collecting an online sample X', normalizing X' to obtain wherein is the mean of the training data X, S is the standard deviation of the training data X, and and S are equal to those in equation (1). 2) on Variable partitioning gives 3) to input the SAE-Softmax model of the bth sub-block in the offline modeling, and obtain the classification result of the bth SAE-Softmax. 4) Decision fusion of the classification results of B SAE-Softmax is carried out using the improved D-S evidence theory; 5) If the decision fusion result is a composite class, the B+1-th SAE-Softmax classification model is used to realize classification. If the decision fusion result is not a composite class, the fusion result is the classification result.

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