Multi-modal process fault detection method based on SKDPC-RS-MSDAE

Abstract

The invention provides a multi-modal process fault detection method based on SKDPC-RS-MSDAE, which is used for solving the problems that multi-modal division depends on experience knowledge, the detection precision of tiny faults is low and the like. The method comprises the following steps: firstly, collecting original data of a TE multi-mode process, and mining deep information of the original data by using ResNet; secondly, a DPC modal identification method based on path selection is designed, local density and relative distance are reconstructed through path selection and kNN, an optimal clustering number judgment criterion based on a contour coefficient is constructed, and a DPC based on the contour coefficient and path selection is designed; secondly, establishing an MSDAE detection model for each steady state, and obtaining a corresponding fault probability; and finally, designing a Bayesian reasoning probability index BIP based on multi-probability fusion. Experimental verification is carried out through the TE process, compared with other methods, the overall fault detection rate is improved, and the detection performance of tiny faults is improved.

Claims

1. A multi-modal process fault detection method based on SKDPC-RS-MSDAE, characterized in that, The steps are as follows: S1: Collect the historical sample data of the normal Tennessee Eastman process to construct a multi-modal training set and perform standardization processing. Use the standardized training data to train the residual neural network ResNet, and use the trained residual neural network ResNet to extract the historical sample features; S2: Improve density peak clustering by combining the k-nearest neighbor algorithm, path selection method, and silhouette coefficient method, and establish the SKDPC-RS modal partitioning method. Use the SKDPC-RS modal partitioning method to perform modal partitioning on the offline data: S3: Construct an MSDAE offline model based on each steady-state data after SKDPC-RS modal partitioning and calculate the offline SPE. Determine each steady-state control limit using the KDE method based on the offline SPE; S4: Obtain the online samples of the TE process and perform standardization processing. Extract the online sample features by passing the online samples through the offline ResNet network, calculate the posterior probability of the online sample features, and determine the mode to which the online samples belong; S5: Input the online sample features into the MSDAE offline model and calculate the online SPE. Calculate the failure probability of the online SPE using each steady-state control limit; S6: Calculate the global Bayesian joint probability index by combining the failure probability of the online SPE and the posterior probability of the online sample features, and perform fault discrimination based on the Bayesian joint probability index.

2. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to claim 1, characterized in that The SKDPC-RS modal partitioning method is as follows: S2.1: Use the k-nearest neighbor algorithm to update the local density of density peak clustering; S2.2: Use the path selection method to update the relative distance of density peak clustering; S2.3: Use the silhouette coefficient method to obtain the optimal number L of historical sample feature clustering centers; S2.4: Use the local density and relative distance to construct a scatter decision diagram with the local density as the abscissa and the relative distance as the ordinate. In the scatter decision diagram, according to the optimal number L of historical sample feature clustering centers, select the top L points with both high local density and relative distance as the optimal clustering centers of historical sample features. By calculating the Euclidean distance between the remaining historical sample features and the optimal clustering centers, assign the remaining historical sample features to the corresponding clustering center with the nearest Euclidean distance, thereby realizing modal partitioning and obtaining the modal classification labels to which each historical sample feature belongs.

3. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to claim 2, wherein The method for using the k-nearest neighbor algorithm to update the local density of density peak clustering is as follows: Calculate each sample feature x i The kNN set in the entire training set: kNN(x i ) = {x j ∈ X | d ij ≤ d(x i , NN k (x i ))} Among them, x i represents the sample feature obtained by the residual neural network ResNet, and kNN(x i ) represents the set of k nearest neighbors containing the sample feature xi. X represents the set of sample features extracted by the residual neural network ResNet. NN k (x i ) represents the k-th nearest neighbor of the sample feature x i . The Euclidean distance between d(x i , NN k (x i )) represents the sample feature x i and the k-th nearest neighbor NN k (x i ); Local density updated according to the kNN set kNN(x i ): where d ij represents the Euclidean distance between the sample feature x i and the neighboring feature x j , and ||·||2 represents the 2-norm.

4. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to claim 2, characterized in that The method for updating the relative distance of density peak clustering using the path selection method is as follows: For the sample feature x i , based on the Euclidean distance d of the sample feature ij , define the threshold T that determines the path direction ij ; According to the threshold T ij , calculate the adaptive term Dis of the distance penalty a and the basic term Dis b respectively. Sum the adaptive term Dis a and the basic term Dis b to obtain the updated relative distance δ(x i ); The formula is: T ij = T r · d ij δ(x i ) = Dis a + Dis b where n is the number of points on the path, T r and P r are the threshold ratio and the penalty factor respectively, Dis a is the adaptive term of the distance penalty, N ij is the number of connections, representing the number of sample features in the shortest path among all paths, Dis b is the basic term, representing the maximum value among the averages of all distances d ij where the distance between any two adjacent points on each path among all paths is less than the threshold T k , mean(·) represents the average function, and χ(·) represents the intercept kernel.

5. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to any one of claims 2 to 4, characterized in that, The method for using the silhouette coefficient method to obtain the optimal number of clustering centers is as follows: Initialize different numbers of clustering centers, and based on the DPC algorithm, loop to calculate the average silhouette coefficient of all sample features corresponding to each number of clustering centers. Draw a relationship diagram between the average silhouette coefficient and the number of clustering centers, and select the number of clustering centers L corresponding to the maximum average silhouette coefficient value as the optimal number of clustering centers.

6. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to claim 5, characterized in that The calculation method of the silhouette coefficient for each sample feature is as follows: Calculate the average distance between the sample feature x i and other sample features x j within the same cluster, as well as the average distance between the sample feature x i and sample features x j in other clusters. Calculate the silhouette coefficient s(x i ) based on the silhouette coefficient calculation formula. The silhouette coefficient calculation formula is as follows: Among them, a(x i ) is the average distance between the sample feature x i and other sample features x within the same cluster j , and b(x i ) is the average distance between the sample feature x i and the sample features x in other clusters j .

7. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to any one of claims 1-4 or 6, characterized in that, The method for constructing the MSDAE offline model is as follows: Construct multiple stacked denoising autoencoders SDAE. Each stacked denoising autoencoder includes M stacked denoising autoencoders DAE. Train the encoding and decoding processes of each stacked denoising autoencoder SDAE. Among them, the training process of each denoising autoencoder DAE is as follows: h m h(x') = f(W m y m-1 h(x') + b m ) y m (x') = g(W' m h m (x') + b' m ) where \(f(\cdot)\) and \(g(\cdot)\) are the non-linear activation functions from the input layer to the hidden layer and from the hidden layer to the output layer respectively, and \(y m-1 (x') is the output feature of the output layer of the \((m - 1)\)-th layer, and \(y m (x') represents the output feature of the output layer of the \(m\)-th layer, and \(h m (x') represents the output feature of the hidden layer of the \(m\)-th layer. \(W m and \(b m are the weight parameter and bias parameter of the encoder of the denoising autoencoder DAE, and \(W' m and \(b' m are the weight parameter and bias parameter of the decoder of the denoising autoencoder DAE; After each round of training of each stacked denoising autoencoder (SDAE), the gradient descent algorithm is used to continuously correct the reconstruction error to obtain the optimal network parameters, thereby establishing the MSDAE fault detection model.

8. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to claim 7, characterized in that, The calculation formula for the reconstruction error is as follows: Among them, x represents the input features before noise reduction of each stacked denoising autoencoder, y represents the features finally output by each stacked denoising autoencoder, and W c = [W, W'], b c = [b, b'] respectively represent the weight parameters and bias parameters for reconstruction. W = [W1, W2,..., W m ,..., W M and b = [b1, b2,..., b m ,..., b M are the weight parameters and bias parameters of the encoder of the stacked denoising autoencoder SDAE. W' = [W'1, W'2,..., W' m ,..., W' M and b' = [b'1, b'2,..., b' m ,..., b' M are the weight parameters and bias parameters of the decoder of the stacked denoising autoencoder SDAE; The calculation method for the offline SPE is as follows: SPE = (x - y) T ∑ -1 (x - y) Among them, ∑ represents the covariance matrix of x and y; The method for determining each steady-state control limit based on the offline SPE using the KDE method is as follows: Calculate the kernel density estimation function. By performing numerical integration on the kernel density estimation results, obtain the cumulative distribution function. For a given confidence level of 98%, calculate the control limit based on the quantile of the cumulative distribution function.

9. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to claim 2, characterized in that, The method for calculating the posterior probability of the online sample features is as follows: where p(l|x test ) is the posterior probability that the online sample feature x test belongs to the l-th cluster center, and each cluster center corresponds to a modality, d test,l is the Euclidean distance between the online sample feature x test and the l-th cluster center of the historical sample features, L is the number of cluster centers of the historical sample features. If the posterior probability p(l|x test ) is close to 1, it means that the online sample feature x test belongs to the modality corresponding to the l-th cluster center of the historical sample features; The method for calculating the fault probability of the online SPE using each steady-state control limit UCL is as follows: where SPE(x test ) represents the SPE of the online sample, and (SPE UCL |l) represents the control limit of the SPE of the l-th mode. (SPE(x test )|l) represents the SPE statistic of the l-th mode, and Prob(·) represents the probability that the SPE value exceeds the control limit. Indicates the failure probability of the online sample belonging to the l-th modality.

10. The multi-modal process fault detection method based on SKDPC-RS-MSDAE according to claim 9, wherein The method for calculating the global Bayesian joint probability index is as follows: Among them, BIP is the local probability jointly formed by the posterior probability p(l|x test ) under each modality and the fault probability . The method for fault discrimination based on the BIP index is as follows: Set the confidence level 1-α as the control threshold. When the BIP index is higher than the control threshold, it is determined that a fault occurs in the process.

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