Fault diagnosis method based on dynamic local sensitive discriminant analysis of mahalanobis distance

Abstract

The application discloses a dynamic local sensitive discriminant analysis fault diagnosis method based on Mahalanobis distance, which is used to establish an accurate process fault diagnosis model in a complex chemical field. First, the original data is expanded by using a dynamic data expansion technology, and then a local sensitive discriminant analysis method combined with Mahalanobis distance is used to extract features of fault data, so that the behavior of the system is accurately described. The data after feature extraction is used to train a weak classifier, and the AdaBoost algorithm is used to integrate the weak classifier into a strong classifier, so as to improve the accuracy of the fault diagnosis model. The method is used to establish a fault diagnosis model for a Tennessee-Eastman process fault case, and the accuracy of the model is significantly improved, so that the method has certain superiority and application prospect.

Description

Technical Field

[0001] This invention relates to the field of chemical engineering technology, and in particular to a fault diagnosis method based on dynamic local sensitivity discriminant analysis using Mahalanobis distance. Background Technology

[0002] With the continuous advancement of technology, modern industry is undergoing tremendous changes, and the complexity of factory operations is increasing dramatically. At the same time, the variables measured during operations are becoming more complex, nonlinear, and massive. In chemical processes, monitoring systems generate a large amount of high-dimensional measured data. The effective utilization of this data for real-time monitoring and fault diagnosis provides a reliable guarantee for ensuring the safety of production equipment, reducing maintenance costs, and improving profit margins.

[0003] Extracting key features from large amounts of information is crucial for improving the accuracy of fault diagnosis; therefore, this embodiment focuses more on dimensionality reduction algorithms. Currently, data-driven methods are a popular research direction. These methods do not require mechanistic models or rely on qualitative knowledge; instead, they build models based on historical data generated during industrial processes. They are characterized by simplicity and versatility. Common data-driven methods include Principal Component Analysis (PCA), Fisher Discriminant Analysis (FDA), and Independent Component Analysis (ICA). These algorithms aim to mine global information from the data and find the optimal projection direction. However, since these methods are based on the assumption that the dataset has a globally linear structure, this assumption no longer holds when the structure of high-dimensional data is highly nonlinear or its properties are strongly correlated. In such cases, globally linear methods struggle to reveal the inherent nonlinear structure and distribution patterns of high-dimensional data, ultimately failing to reflect the true structure of the dataset. Summary of the Invention

[0004] To address the limitations and shortcomings of existing technologies, this invention provides a fault diagnosis method based on Mahalanobis distance dynamic local sensitivity discriminant analysis, comprising:

[0005] Data selection and preprocessing are performed. TEP data is selected, where the training set includes 6 types of faults, each of which includes 480 fault training samples, and the test set includes 6 types of faults, each of which includes 800 fault test samples. The data in the training set and the test set are normalized.

[0006] Dynamic data augmentation is performed by adding time-lag data of process variables to the original data matrix, treating each variable of the sampled data from the first L time steps as a new variable, and constructing an augmented matrix of the original data.

[0007] Feature extraction was performed using the LSDA-M algorithm to construct the intra-class graph G. w Inter-class graph G b The intra-class graph G is obtained by using Mahalanobis distance instead of Euclidean distance as the metric for nearest neighbors. w and the inter-class graph G b The weights are used to obtain the projection vector A by generalized eigenvalue decomposition, and the projection vector A is used to extract features from the original data.

[0008] The AdaBoost algorithm is used for modeling. Weak classifiers are trained using the training set after feature extraction, and then the AdaBoost algorithm is used to integrate the weak classifiers into a strong classifier to form a fault diagnosis model.

[0009] Optionally, the expression for the normalization process is as follows:

[0010]

[0011] Where η and σ are the mean and standard deviation of the sample set, respectively, and the measurement space R n The original data X = (x1, x2, ..., x m There are m points in total;

[0012] The expression for the preprocessed data matrix is ​​as follows:

[0013]

[0014] Wherein, the preprocessed data X∈R m×n m represents the number of samples, and n represents the dimension of the samples;

[0015] Treating each variable of the sampled data from the first L time steps as a variable in the new augmented matrix, the expression for the augmented data matrix is ​​as follows:

[0016]

[0017] in, It is the n-dimensional observation variable obtained at time t. Let L be the n-dimensional observation variable obtained at time t-1, and L be the time delay order.

[0018] Optionally, the step of feature extraction using the LSDA-M algorithm includes:

[0019] Construct the intra-class graph G w and the inter-class graph Gb Using Mahalanobis distance As a method for measuring nearest neighbors;

[0020] Divide the k nearest neighbors into N intra-class nearest neighbors. w (x i ) and inter-class nearest neighbor N b (x i The intra-class nearest neighbor points Includes x i Nearest neighbors of the same class, and nearest neighbors between classes Includes x i The nearest neighbor of the outlier, l(x) i () is point x i The category label is used to obtain the in-class graph G. w and the inter-class graph G b The expression for the weights is as follows:

[0021]

[0022]

[0023] The generalized eigenvalue decomposition is used as the following expression:

[0024] argmax A T X(αL b +(1-α)W w )X T A

[0025] stA T XD w X T A = 1

[0026] The expression for obtaining the projection vector A is as follows:

[0027] x i →y i =A T x i

[0028] A = (a1, a2, ..., a d )

[0029] The projection vector A is used to extract features from the original data.

[0030] Optionally, the step of modeling using the AdaBoost algorithm includes:

[0031] Setting up the training set in It is the dataset after feature extraction, i∈[1,n], where n is the number of samples, yi ∈[1,N] are the sample labels, and N is the number of sample categories;

[0032] Initialize the training sample weights and weight vectors respectively, as shown in the following expressions:

[0033]

[0034]

[0035] Divide the sample space into τ equal parts;

[0036] Calculate P(x) i ∈X j ,η i The weight of (j) is expressed as follows:

[0037]

[0038] The output of the weak classifier is set using the following expression:

[0039]

[0040] Where δ∈[1,d];

[0041] The normalization factor is calculated using the following expression:

[0042]

[0043] Select a weak classifier that minimizes the normalization factor;

[0044] The misclassification rate and the weight of each weak classifier are calculated separately, as shown in the following expressions:

[0045]

[0046]

[0047] Update the weights of the weak classifier using the following expression:

[0048]

[0049] The strong classifier after d iterations is expressed as follows:

[0050]

[0051] Develop a fault diagnosis model.

[0052] The present invention has the following beneficial effects:

[0053] This invention provides a novel fault diagnosis technique based on dynamic local sensitivity discriminant analysis using Mahalanobis distance. This technique considers the temporal correlation between observed variables in complex industrial process data, adds time-lag data of process variables to the monitoring matrix, constructs an augmented matrix of the original data, and thus accurately describes the dynamic behavior of the system.

[0054] This invention provides a novel fault diagnosis technique based on Mahalanobis distance-based Local Sensitivity Discriminant Analysis (LSDA-M). This technique uses LSDA-M to extract features from the original fault data. This algorithm not only preserves the local geometric structure of the original data and introduces discriminative information, but also retains the hidden local discriminative structure in the high-dimensional measurement space. Furthermore, it uses Mahalanobis distance, which can eliminate interference from correlations between variables, to measure nearest neighbors. Compared with traditional feature extraction algorithms, this algorithm significantly improves subsequent classification.

[0055] This invention takes a TEP (Transmission Electrode Flow) failure case as the research object. First, it performs a more effective feature extraction process on the failure data, and then uses the AdaBoost algorithm to build a failure diagnosis model. Using the same modeling algorithm, the algorithm provided by this invention can achieve higher failure diagnosis accuracy, offering valuable assistance for fault investigation and safe production in chemical enterprises. Attached Figure Description

[0056] Figure 1 This is a flowchart of a fault diagnosis method based on Mahalanobis distance for dynamic local sensitivity discrimination analysis provided in Embodiment 1 of the present invention.

[0057] Figure 2 This is a process flow diagram of TEP provided in Embodiment 1 of the present invention.

[0058] Figure 3 This is a schematic diagram of the average fault diagnosis accuracy of DLSDA-M, LSDA-M, LSDA, FDA, and PCA provided in Embodiment 1 of the present invention.

[0059] Figure 4 This is a schematic diagram of the confusion matrix of DLSDA-M provided in Embodiment 1 of the present invention.

[0060] Figure 5 This is a schematic diagram of the confusion matrix of LSDA-M provided in Embodiment 1 of the present invention.

[0061] Figure 6 This is a schematic diagram of the confusion matrix of LSDA provided in Embodiment 1 of the present invention.

[0062] Figure 7 This is a schematic diagram of the FDA's confusion matrix provided in Embodiment 1 of the present invention.

[0063] Figure 8 This is a schematic diagram of the confusion matrix of PCA provided in Embodiment 1 of the present invention. Detailed Implementation

[0064] To enable those skilled in the art to better understand the technical solution of the present invention, the following detailed description of the fault diagnosis method based on Mahalanobis distance for dynamic local sensitivity discrimination analysis provided by the present invention is given in conjunction with the accompanying drawings.

[0065] Example 1

[0066] Manifold learning algorithms can uncover nonlinear mappings between high-dimensional manifold structures embedded in low-dimensional spaces. The core idea of ​​manifold learning is to minimize local information loss. Points that are close together in high-dimensional space remain close after projection. They can reveal the inherent local geometry of the data. Preserving local structure ensures that samples that are close together in the measurement space remain close in the projection space. This idea of ​​preserving local data structure is highly beneficial for subsequent classification. Common manifold learning algorithms include Laplacian Eigenmaps (LE), locally linear embedding (LLE), and Locality Preserving Projections (LPP). However, these methods neglect discriminative information, which is crucial in classification problems. Therefore, Locality Sensitive Discriminant Analysis (LSDA) was proposed. LSDA analyzes the local manifold structure of high-dimensional data, making similar samples closer in the low-dimensional subspace and distancing dissimilar samples further apart. It not only preserves the local structure of the data but also introduces discriminative information. LSDA has been widely used in the field of image recognition.

[0067] Currently, in the field of fault diagnosis, other manifold learning algorithms such as LPP and NPE have been applied by scholars. However, there are fewer attempts to apply LSDA. Therefore, this embodiment introduces LSDA into fault diagnosis to discover hidden local discriminative structures in high-dimensional measurement spaces. When constructing a nearest neighbor graph using the LSDA algorithm, this embodiment chooses Mahalanobis distance instead of Euclidean distance to measure the distance between local points. This is because Mahalanobis distance is unaffected by dimensions and eliminates the interference of correlation between variables, thus compensating for the shortcomings of Euclidean distance. Furthermore, considering that complex industrial processes are generally dynamic processes with temporal correlations between observed variables, static multivariate methods have certain limitations. Based on the above, this embodiment proposes a dynamic local sensitivity discriminant analysis method based on Mahalanobis distance (DLSDA-M) for fault diagnosis. This method not only focuses on the local geometric structure of high-dimensional data but also introduces discriminative information, bringing similar data closer together and distancing different data further apart. Using Mahalanobis distance to measure the distance between nearest neighbors eliminates the interference of correlation between variables, enhancing the local discriminative information of the data. Finally, the extracted data was used to train a weak classifier, and the AdaBoost algorithm was employed to integrate the weak classifier into a strong classifier to improve the accuracy of the fault diagnosis model. The proposed method was then used to build a fault diagnosis model for Tennessee-Eastman process data, and experimental results show a significant improvement in accuracy.

[0068] Figure 1 This is a flowchart of the fault diagnosis method based on Mahalanobis distance for dynamic local sensitivity discrimination analysis provided in Embodiment 1 of the present invention. Figure 1 As shown, this embodiment includes data selection and preprocessing, dynamic data augmentation, feature extraction using the LSDA-M algorithm, and modeling using the AdaBoost algorithm. This embodiment utilizes Dynamic Local Sensitivity Discriminant Analysis (DLSDA-M) fault diagnosis technology based on Mahalanobis distance to establish accurate process fault diagnosis models in complex chemical engineering fields. First, dynamic data augmentation technology is used to augment the original data. Then, a local sensitivity discriminant analysis method combined with Mahalanobis distance is used to extract features from the fault data. Finally, the feature-extracted data is used to train a weak classifier, and the AdaBoost algorithm is used to integrate the weak classifier into a strong classifier to improve the accuracy of the fault diagnosis model.

[0069] The data selection and preprocessing process is as follows: The Tennessee-Eastman process created by Eastman Chemical Company was selected as the research object. Figure 2 This is a process flow diagram of the TEP provided in Embodiment 1 of the present invention. Figure 2As shown, the Tennessee-Eastman process involves 53 measurement variables, including 12 operational variables, mainly involving valves, speeds, and flow rates that are regulated by operation, and 41 process variables, mainly involving pressure, temperature, and liquid level of various components in the chemical process. The process includes 21 fault types, numbered IDV1-IDV21. This embodiment selects IDV2, 5, 8, 12, 13, and 14 to form the experimental data. The training set contains 480 faults for each of the six fault types, and the test set contains 800 faults for each of the six fault types. Subsequently, the data is used... The training set data is normalized.

[0070] The dynamic data augmentation process is as follows: the original data X is augmented according to the concept of dynamic time series, that is, all monitoring variables are augmented using the L monitoring data points preceding time t, and finally the augmented data matrix is ​​obtained, as shown below:

[0071]

[0072] in, It is the n-dimensional observation variable obtained at time t. This refers to the n-dimensional observed variable obtained at time t-1. The meanings of the other characters can be deduced similarly. L is called the time lag order. L is determined using the parallel analysis method, which assumes that each observed variable has the same time lag order. The specific steps for calculating L are as follows: First, calculate the number of linear relationships in the monitoring matrix when L=0; then, starting from 0, increment L by one order each time, checking if the number of linear relationships has increased. If it has, continue incrementing by one order; otherwise, the previous order is the final choice.

[0073] The feature extraction process using the LSDA-M algorithm is as follows: Constructing an intra-class graph G w Inter-class graph G b Mahalanobis distance is used. As a method for measuring nearest neighbors, this embodiment further divides the k nearest neighbors into intra-class nearest neighbors N. w (x i ) and inter-class nearest neighbor N b (x i ). Includes x i Nearest neighbors of the same type, Includes x i The nearest neighbor of the outlier. Where, l(x) i () is point x i The category labels. This embodiment uses the following formula to calculate the weights of the intra-class and inter-class graphs:

[0074]

[0075]

[0076] Finally, the following expression is decomposed using generalized eigenvalues:

[0077] argmax A T X(αL b +(1-α)W w )X T A

[0078] stA T XD w X T A = 1

[0079] The projection vector A is obtained as follows:

[0080] x i →y i =A T x i

[0081] A = (a1, a2, ..., a d )

[0082] The final step is to achieve the feature extraction process from the original data.

[0083] The process of modeling using the AdaBoost algorithm is as follows: Weak classifiers are trained using the feature-extracted training set, and then the AdaBoost algorithm is used to integrate the weak classifiers into a strong classifier. Finally, a fault diagnosis model was established.

[0084] In the field of fault diagnosis for complex chemical processes, industrial data often exhibits high dimensionality and nonlinearity, leading to unsatisfactory fault diagnosis accuracy. To address these issues, this embodiment proposes a fault diagnosis technique based on Dynamic Local Sensitivity Discriminant Analysis (DLSDA-M) using Mahalanobis distance. Figure 3 This is a schematic diagram illustrating the average fault diagnosis accuracy of DLSDA-M, LSDA-M, LSDA, FDA, and PCA provided in Embodiment 1 of the present invention. Figure 3 As shown, by preserving local geometric structure while extracting features from Tennessee-Eastman Process (TEP) data, and using the AdaBoost algorithm for modeling, the modeling accuracy of fault diagnosis is improved. This provides technical support for fault handling and safe operation of industrial processes.

[0085] The method described in this embodiment includes: data selection and preprocessing, dynamic data augmentation, feature extraction using the LSDA-M algorithm, and modeling using the AdaBoost algorithm.

[0086] The data selection and preprocessing process is as follows: The TEP data contains 21 types of faults. In this embodiment, IDV2, 5, 8, 12, 13, and 14 are selected as experimental cases. The training set contains 480 faults for each of the 6 types, and the test set contains 800 faults for each of the 6 types. Next, the training set data is normalized. To simulate the online diagnostic scenario, the mean and variance of the training set are used to normalize the test set data.

[0087] The dynamic data augmentation process is as follows: time-lag data of process variables are added to the original data matrix, that is, each variable of the sampling data at the previous L time steps is treated as a new variable, thereby constructing an augmented matrix of the original data.

[0088] The feature extraction process using the LSDA-M algorithm is as follows: constructing an intra-class graph G w Inter-class graph G b The method uses Mahalanobis distance instead of Euclidean distance as a measure of nearest neighbors, then calculates the weights of intra-class and inter-class graphs, and finally uses generalized eigenvalue decomposition to obtain the projection vector A, thus realizing the feature extraction process of the original data.

[0089] The process of modeling using the AdaBoost algorithm is as follows: a weak classifier is trained using the training set after feature extraction, and the AdaBoost algorithm is used to integrate the weak classifiers into a strong classifier, ultimately establishing a fault diagnosis model.

[0090] Figure 4 This is a schematic diagram of the confusion matrix of DLSDA-M provided in Embodiment 1 of the present invention. Figure 5 This is a schematic diagram of the confusion matrix of LSDA-M provided in Embodiment 1 of the present invention. Figure 6 This is a schematic diagram of the confusion matrix of LSDA provided in Embodiment 1 of the present invention. Figure 7 This is a schematic diagram of the FDA's confusion matrix provided in Embodiment 1 of the present invention. Figure 8 This is a schematic diagram of the confusion matrix of PCA provided in Embodiment 1 of the present invention. The Local Sensitivity Discriminant Analysis (LSDA) technique based on Mahalanobis distance provided in this embodiment is used to establish an AdaBoost fault diagnosis model for complex chemical process data. Dynamic augmentation technology is used to augment the original data, and the LSDA-M algorithm is used to extract features from the original fault data, preserving the hidden local discriminant structures in the high-dimensional measurement space. Subsequently, the feature-extracted data is used to train a weak classifier, and the AdaBoost algorithm is used to integrate the weak classifiers into a strong classifier to establish a fault diagnosis model, thereby improving the accuracy of fault diagnosis.

[0091] Data selection and preprocessing: The Tennessee-Eastman process (TE) created by Eastman Chemical Company was selected as the research object. The TE process involves 53 measurement variables, including 12 operational variables, mainly involving variables that are regulated by operation such as valves, speed and flow rate, and 41 process variables, mainly involving the pressure, temperature and liquid level of various components in the chemical process.

[0092] The process includes 21 fault types, numbered IDV1-IDV21. This embodiment selects IDV2, 5, 8, 12, 13, and 14 as experimental cases, detailed in Table 1. This case includes four fault types, covering most of all fault types: IDV2 and 5 are step faults, IDV8 and 12 are random variable faults, IDV13 is a slow drift, and IDV14 is valve sticking. The difficulties of this case are as follows: First, IDV5 is difficult to diagnose correctly, and the faults in IDV5 and 12 are both related to the condenser cooling water inlet temperature, showing a strong coupling between them. Second, IDV2 and IDV8 are related to component B, showing a certain correlation between them. During the simulation, each fault type contains two datasets. The training set is sampled for 25 hours, with samples taken every 3 minutes, and has 500 samples, including 480 fault training samples. The test set is sampled for 48 hours, with a total of 960 samples, including 800 fault test samples.

[0093] Table 1. Fault Case Selection and Fault Description

[0094]

[0095] Given a measurement space R n The original data in the dataset is X = (x1, x2, ..., x...). m There are m points in total. To eliminate the influence of different data units on the data, reduce distribution differences, and improve the effect of feature extraction, the training set data is normalized. Here, η and σ are the mean and standard deviation of the sample set, respectively, and their expressions are as follows:

[0096]

[0097] This embodiment provides a dynamic data augmentation process. Given preprocessed data X∈R m×n , where m represents the number of samples and n represents the dimension of the samples, i.e. the number of monitored variables.

[0098] The specific expression for X is as follows:

[0099]

[0100] The original data X was expanded according to the concept of dynamic time series, that is, all monitored variables were expanded using the first L monitoring data points. This can also be understood as treating each variable of the sampling data from the first L time points as a variable of the new augmented matrix, resulting in the expanded data matrix, as shown in the following expression:

[0101]

[0102] in, It is the n-dimensional observation variable obtained at time t. This refers to the n-dimensional observed variable obtained at time t-1. The meanings of the other characters can be deduced similarly. L is called the time lag order. The time lag order L is determined using the parallel analysis method. This method considers the correlation between the observed variable and the lagged variable and has the advantage of being simple to use. The parallel analysis method assumes that each observed variable has the same time lag order.

[0103] In this embodiment, the specific steps for obtaining L are as follows: Calculate the number of linear relationships in the monitoring matrix when L = 0; starting from 0, for each increment of L, determine whether the number of linear relationships has increased; if it has, continue to increment by one order; otherwise, the previous order is the final selection. The following expression is used for further explanation:

[0104]

[0105] This refers to the number of new relations added as the time lag order increases from L1 to L, where r(L) refers to the number of relations between variables with lag order L. In this case, L1 is chosen as the final order.

[0106] The method for calculating the number of linear relationships in the steps is as follows: perform eigenvalue decomposition on the covariance matrix, and the number of eigenvalues ​​that are approximately 0 is the number of linear relationships.

[0107] This embodiment utilizes the LSDA-M algorithm for feature extraction. First, a nearest neighbor graph G is constructed to simulate the local geometry of the original space. For each point x... i Find its k nearest neighbors. The measure of nearest neighbors is Mahalanobis distance, which can eliminate the interference of correlation between variables. The expression is as follows, which is expressed as N(x) in this embodiment. i )

[0108]

[0109]

[0110] To discover the discriminative structure of the data, discriminative information was introduced, and an intra-class graph G was further constructed. w Inter-class graph G bIn this embodiment, the k nearest neighbors are further divided into intra-class nearest neighbors N. w (x i ) and inter-class nearest neighbor N b (x i N w (x i ) contains x i Nearest neighbors of the same type, N b (x i ) contains x i The nearest neighbor of a different class is expressed as follows. Where, l(x i () is point x i Category tags.

[0111]

[0112]

[0113] This embodiment uses W respectively. w and W b Represents an intra-class graph G w Inter-class graph G b The weights can be considered as the original weight matrix W being split into W0 and W1. w and W b When x i and x j When W is a nearest neighbor belonging to the same class w The value is 1 when x i and x j When the nearest neighbors belong to different classes, the expression is as follows:

[0114]

[0115]

[0116] Finally, based on the idea of ​​clustering similar sample points and dispersing dissimilar sample points, the objective function of LSDA was constructed, and its expression is as follows:

[0117]

[0118]

[0119] In class graph G w In the middle, if the nearest neighbor x belongs to the same class i and x j If the mapped points are far apart, the objective function expression (11) will incur a severe penalty. Similarly, if the nearest neighbors x belong to different classes... i and x j After mapping, the distances are very close, and the inter-class graph G bThe expression for the objective function (12) will also incur severe penalties. Therefore, the purpose of constructing the above objective function is to ensure that the nearest neighbors of the same type in the measurement space remain close after dimensionality reduction, while the nearest neighbors of different types remain far apart after dimensionality reduction. This idea of ​​preserving the local structure of the data is very beneficial for subsequent classification.

[0120] The ultimate goal of the LSDA algorithm is to find a projection vector A that maps m points in the measurement space to a low-dimensional space R. l In the diagram, it is represented as Y = (y1, y2, ..., y...). m ), where y i =A T x i .

[0121] The expression for the objective function (11) is simplified to:

[0122]

[0123] in Here D w It provides a natural measure. (D) w,ii The larger the value, the more likely it is to include sample x. i The class in x i The density is higher at point D. w,ii The larger the value, the greater the value of x. i The more important it is, the better. Set the following constraints:

[0124]

[0125] The objective function expression (13) is rewritten as follows:

[0126]

[0127] The expression for the objective function (12) is simplified to:

[0128]

[0129] Ultimately, the two objective functions can be combined and expressed as follows:

[0130]

[0131] Here, α is the balance factor, 0 ≤ α ≤ 1. By changing the value of α, the ratio of the two objective functions is adjusted, which can also be considered as defining the importance of the intra-class and inter-class graphs.

[0132] Finally, using the Lagrange multiplier method, the expression (17) of the objective function is reduced to the problem of solving the generalized eigenvalues ​​of expression (18), and the projection vector A = (a1, a2, ..., a d(where a1, a2, ..., a) d For the first d eigenvalues ​​of expression (18), λ1≥λ2≥,...,≥λ d The corresponding feature vectors. Finally, the original data of the measurement space is projected into the low-dimensional feature space through expression (19).

[0133] X(αL b +(1-α)W w )X T A=λXD w X T A (18)

[0134] x i →y i =A T x i (19)

[0135] This embodiment utilizes the AdaBoost algorithm for modeling. The LSDA-M algorithm is used to extract features from the original fault data, resulting in new training and test sets. A weak classifier is trained using the new training set, and the AdaBoost algorithm is used to integrate the weak classifiers into a strong classifier, ultimately establishing the fault diagnosis model. The steps for establishing the fault diagnosis model are as follows:

[0136] First, given the training set in It is the dataset after feature extraction, i∈[1,n], where n is the number of samples, y i ∈[1,N] are the sample labels, and N is the number of sample categories.

[0137] This embodiment constructs an ensemble classifier through the following steps:

[0138] The following expressions (20) and (21) initialize the training sample weights and weight vectors respectively:

[0139]

[0140]

[0141] The following operation is iterated d times, where δ∈[1,d].

[0142] Using the CART classification tree described in the previous section as a weak classifier ψ, the following steps are performed: the sample space is divided into equal parts of τ, and the case P(x) is calculated. i ∈X j ,η i The weight of (j) is expressed as follows:

[0143]

[0144] Set the output of the weak classifier

[0145] The normalization factor is calculated using the following expression:

[0146]

[0147] Choose a suitable weak classifier and minimize the normalization factor Q. δ ;

[0148] The misclassification rate and the weight of each weak classifier are calculated using expressions (24) and (25), respectively, where X(x i ) represents x i The actual tag, expressed as follows:

[0149]

[0150]

[0151] Update the weights of the weak classifier using the following expression:

[0152]

[0153] The strong classifier after d iterations is expressed as follows:

[0154]

[0155] In summary, a fault diagnosis model for TEP fault cases was established through four processes: data selection and preprocessing, dynamic data augmentation, feature extraction using LSDA-M, and integrated modeling using the AdaBoost algorithm.

[0156] This embodiment proposes a fault diagnosis method based on Mahalanobis distance and dynamic local sensitivity discriminant analysis (LSDI) to establish accurate process fault diagnosis models in complex chemical engineering fields. First, dynamic data augmentation technology is used to expand the original data. Then, a local sensitivity discriminant analysis method combined with Mahalanobis distance is employed to extract features from the fault data, thereby accurately characterizing the system behavior. This embodiment uses the feature-extracted data to train a weak classifier, and simultaneously uses the AdaBoost algorithm to integrate the weak classifier into a strong classifier to improve the accuracy of the fault diagnosis model. This embodiment establishes a fault diagnosis model for a Tennessee-Eastman process fault case using the proposed method, significantly improving the model's accuracy and demonstrating certain advantages and application prospects.

[0157] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of the present invention, and the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A fault diagnosis method based on dynamic local sensitivity discriminant analysis using Mahalanobis distance, characterized in that, include: Data selection and preprocessing are performed. TEP data is selected, where the training set includes 6 types of faults, each of which includes 480 fault training samples, and the test set includes 6 types of faults, each of which includes 800 fault test samples. The data in the training set and the test set are normalized. Dynamic data augmentation is performed by adding time-lag data of process variables to the original data matrix, thus expanding the previous data matrix. L Treat each variable of the sampled data at each time point as a new variable, and construct the augmented matrix of the original data; Feature extraction was performed using the LSDA-M algorithm to construct the intra-class graph. Inter-class graph The intra-class graph is obtained by using Mahalanobis distance instead of Euclidean distance as the metric for nearest neighbors. and the inter-class graph The weights are used to obtain the projection vector A by generalized eigenvalue decomposition, and the projection vector A is used to extract features from the original data. The AdaBoost algorithm is used for modeling. Weak classifiers are trained using the training set after feature extraction. The AdaBoost algorithm is then used to integrate the weak classifiers into a strong classifier to form a fault diagnosis model. The steps for feature extraction using the LSDA-M algorithm include: Construct the class graph and the inter-class graph Using Mahalanobis distance As a method for measuring nearest neighbors; Classify the k nearest neighbors into intra-class nearest neighbors. Inter-class nearest neighbors The intra-class nearest neighbor Includes and Nearest neighbors of the same class, and nearest neighbors between classes Includes and The nearest neighbor of an outlier. It is a point The category label is used to obtain the in-class graph. and the inter-class graph The expression for the weights is as follows: , , The generalized eigenvalue decomposition is used as the following expression: , in, X For data matrices; , It provides a natural measure; As a balance factor, ; The expression for obtaining the projection vector A is as follows: , The projection vector A is used to extract features from the original data. For expression The former d eigenvalues The corresponding eigenvector.

2. The fault diagnosis method based on Mahalanobis distance for dynamic local sensitivity discriminant analysis according to claim 1, characterized in that, The expression for the normalization process is as follows: , in, η and σ These are the mean and standard deviation of the sample set, respectively, and the measurement space. R n raw data ,common m One point; The expression for the preprocessed data matrix is ​​as follows: , Among them, the preprocessed data , m Indicates the number of samples. n Indicates the dimension of the sample; Before Treating each variable of the sampled data at each time point as a variable of the new augmented matrix, the expression for the augmented data matrix is ​​as follows: , in, It is a moment t Received n Dimensional observed variables, for t -1 time obtained n Dimensional observed variables, L This refers to the time delay order.

3. The fault diagnosis method based on Mahalanobis distance for dynamic local sensitivity discrimination analysis according to claim 2, characterized in that, The steps for modeling using the AdaBoost algorithm include: Setting up the training set ,in It is the dataset after feature extraction. , It is the sample size. These are the sample labels, and N is the number of sample categories; Initialize the training sample weights and weight vectors respectively, as shown in the following expressions: , , Divide the sample space into equal parts part; calculate The weights are expressed as follows: , The output of the weak classifier is set using the following expression: , in, ; The normalization factor is calculated using the following expression: , Select a weak classifier that minimizes the normalization factor; The misclassification rate and the weight of each weak classifier are calculated separately, as shown in the following expressions: , , Update the weights of the weak classifier using the following expression: , Output The strong classifier after the second iteration is expressed as follows: , Develop a fault diagnosis model.

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