CN-115510940-B - Dynamic local sensitivity discriminant analysis fault diagnosis method based on mahalanobis distance

Abstract

The invention discloses a dynamic local sensitivity discriminant analysis fault diagnosis method based on a mahalanobis distance, which is used for establishing an accurate process fault diagnosis model in the field of complex chemical industry. The invention firstly uses a dynamic data expansion technology to expand the original data, and then adopts a local sensitivity discriminant analysis method combined with the mahalanobis distance to extract the characteristics of fault data, thereby accurately describing the behavior of the system. According to the invention, the weak classifier is trained by using the data after the feature extraction, and meanwhile, the weak classifier is integrated into the strong classifier by using the AdaBoost algorithm, so that the precision of the fault diagnosis model is improved. According to the method, a fault diagnosis model is built for the Tenn-Issmann process fault case, so that the precision of the model is remarkably improved, and the method has certain superiority and application prospect.

Inventors

• ZHU QUNXIONG
• SONG QI
• XU YUAN
• HE YANLIN

Assignees

• 北京化工大学

Dates

Publication Date

20260508

Application Date

20220515

Claims (3)

1. 1. A dynamic local sensitivity discriminant analysis fault diagnosis method based on a Markov distance is characterized by comprising the following steps: selecting and preprocessing data, selecting TEP data, wherein a training set comprises 6 faults, each training set fault comprises 480 fault training samples, a testing set comprises 6 faults, each testing set fault comprises 800 fault testing samples, and normalizing the training set and the data of the testing set; performing dynamic data expansion, adding time delay data of process variables into an original data matrix, taking each variable of sampling data at the first L moments as a new variable, and constructing an expansion matrix of the original data; Feature extraction is carried out by using LSDA-M algorithm, and intra-class diagram is constructed And class diagram Using the mahalanobis distance to replace the Euclidean distance as a measurement adjacent point to obtain the intra-class diagram And the inter-class diagram The method comprises the steps of (1) obtaining a projection vector A by using generalized eigenvalue decomposition, and extracting the characteristics of original data by using the projection vector A; Modeling by using an AdaBoost algorithm, training a weak classifier by using a training set after feature extraction, and integrating the weak classifier into a strong classifier by using the AdaBoost algorithm to form a fault diagnosis model; The step of extracting the characteristics by using the LSDA-M algorithm comprises the following steps: Constructing the intra-class diagram And the inter-class diagram Using mahalanobis distance As a method of measuring neighboring points; dividing k adjacent points into adjacent points in class And inter-class neighbor points The intra-class neighbor point Comprises and is connected with Similar neighbor points, the inter-class neighbor points Comprises and is connected with The neighboring points of the alien class are, Is a dot Category labels of the (1) to obtain the intra-category map And the inter-class diagram The expression of the weight of (c) is as follows: , , decomposing the following expression using the generalized eigenvalue: , wherein X is a data matrix; , Providing a natural measure; As a balance factor, the balance factor is, ; The expression for obtaining the projection vector a is as follows: , The projection vector a is used to perform feature extraction on the original data, Is expressed as The first d eigenvalues of (c) The corresponding feature vector.
2. 2. The mahalanobis distance based dynamic local sensitivity discriminant analysis fault diagnosis method of claim 1, wherein said normalizing process is expressed as follows: , Wherein eta and sigma are the mean and standard deviation of the sample set, respectively, and the raw data of the measurement space R n M points in total; the expression of the preprocessed data matrix is as follows: , wherein the preprocessed data M represents the number of samples, n represents the dimension of the samples; Front is put forward Each variable of the sampling data at each moment is taken as a variable of a new augmentation matrix, and the expression of the augmented data matrix is obtained as follows: , Wherein, the Is the n-dimensional observation variable obtained at time t, And L is the time lag order, which is an n-dimensional observation variable obtained at the time t-1.
3. 3. The mahalanobis distance based dynamic local sensitivity discriminant analysis fault diagnosis method of claim 2, wherein said modeling using an AdaBoost algorithm comprises: Setting training set Wherein Is a data set after feature extraction, , Is the number of samples that are to be taken, Is a sample label, N is a sample class number; Respectively initializing training sample weight and weight vector, and expressing as follows: , , average division of sample space into A portion; Calculation of The expression is as follows: , the output of the weak classifier is set, and the expression is as follows: , Wherein, the ; The normalization factor is calculated as follows: , selecting a weak classifier such that the normalization factor is minimized; The misclassification rate and the weight of each weak classifier are calculated respectively, and the expression is as follows: , , the weights of the weak classifiers are updated as follows: , Output of The strong classifier after the secondary cycle has the following expression: , A fault diagnosis model is formed.

Description

Dynamic local sensitivity discriminant analysis fault diagnosis method based on mahalanobis distance Technical Field The invention relates to the technical field of chemical industry, in particular to a dynamic local sensitivity discriminant analysis fault diagnosis method based on a mahalanobis distance. Background With the continuous progress of technology, the modern industry is changing over the sky and over the earth, and the complexity of factory operation is also dramatically increased. At the same time, the variables measured during operation are also more complex, nonlinear and massive. In the chemical process, the monitoring system generates a large amount of high-dimensional measured data, and real-time monitoring and fault diagnosis are realized by effectively utilizing the data, so that reliable assurance is provided for ensuring the safety of production equipment, reducing the maintenance cost and improving the profit margin. Extraction of important features from a large amount of information is important for improving the accuracy of fault diagnosis, and therefore this embodiment requires more attention to the dimension reduction algorithm. Currently, data-driven based methods are a popular research direction. The data-driven based approach does not require modeling of mechanisms nor relies on qualitative knowledge, but rather builds a corresponding model from historical data generated in the industrial process. Has the characteristics of simplicity and good universality. Common data-driven based approaches are PRINCIPAL COMPONENT ANALYSIS (PCA), FISHER DISCRIMINANT ANALYSIS (FDA), and INDEPENDENT COMPONENT ANALYSIS (ICA). These algorithms look at the global information of the mined data, looking for the best projection direction. Since these methods are all based on the assumption that the data set is a global linear structure, the assumption based on global linearity is no longer true when the structure of the high-dimensional data is highly nonlinear or its attributes are strongly correlated. Under the situation, the nonlinear structure of the high-dimensional data essence and the rule of the data internal distribution are difficult to reveal by the method based on global linearity, and finally the real structure of the data set cannot be reflected. Disclosure of Invention In order to solve the limitations and defects existing in the prior art, the invention provides a dynamic local sensitivity discriminant analysis fault diagnosis method based on a mahalanobis distance, which comprises the following steps: selecting and preprocessing data, selecting TEP data, wherein a training set comprises 6 faults, each training set fault comprises 480 fault training samples, a testing set comprises 6 faults, each testing set fault comprises 800 fault testing samples, and normalizing the training set and the data of the testing set; Performing dynamic data expansion, adding time delay data of process variables into an original data matrix, taking each variable of sampling data at the first L moments as a new variable, and constructing an augmentation matrix of the original data; Performing feature extraction by using an LSDA-M algorithm, constructing an intra-class graph G w and an inter-class graph G b, using a Markov distance to replace an Euclidean distance as a measurement adjacent point, acquiring weights of the intra-class graph G w and the inter-class graph G b, performing generalized feature value decomposition to obtain a projection vector A, and performing feature extraction on original data by using the projection vector A; Modeling is carried out by using an AdaBoost algorithm, a weak classifier is trained by using a training set after feature extraction, and the weak classifier is integrated into a strong classifier by using the AdaBoost algorithm, so that a fault diagnosis model is formed. Optionally, the expression of the normalization process is as follows: Wherein η and σ are the mean value and standard deviation of the sample set, respectively, and the original data x= (X 1,x2,...,xm) of the measurement space R n is m points in total; the expression of the preprocessed data matrix is as follows: Wherein, the preprocessed data X epsilon R m×n, m represents the number of samples, n represents the dimension of the samples; Taking each variable of the sampling data at the first L moments as a variable of a new augmentation matrix, and obtaining the expression of the augmented data matrix as follows: Wherein, the Is the n-dimensional observation variable obtained at time t,And L is the time lag order, which is an n-dimensional observation variable obtained at the time t-1. Optionally, the step of performing feature extraction using the LSDA-M algorithm includes: Constructing the intra-class graph G w and the inter-class graph G b using Mahalanobis distances As a method of measuring neighboring points; Dividing k neighbors into intra-class neighbor N w(xi) and inter-class neighbor N b(xi),