CN109376778B - Fault classification diagnosis method based on characteristic variable weighting - Google Patents

Fault classification diagnosis method based on characteristic variable weighting Download PDF

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CN109376778B
CN109376778B CN201811213324.8A CN201811213324A CN109376778B CN 109376778 B CN109376778 B CN 109376778B CN 201811213324 A CN201811213324 A CN 201811213324A CN 109376778 B CN109376778 B CN 109376778B
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皇甫皓宁
童楚东
俞海珍
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Ningbo University
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Abstract

The invention discloses a fault classification diagnosis method based on characteristic variable weighting, which aims to implement characteristic variable selection and weighting for each reference fault and establish a characteristic variable weighting principal component analysis model so as to implement online fault classification diagnosis. Specifically, the method of the invention distinguishes characteristic variables and abnormal degrees thereof for each reference fault type one by utilizing a neighbor component analysis algorithm. And then, establishing a single classification model for the weighted characteristic variables of each fault type by using a principal component analysis algorithm. And finally, diagnosing the fault type corresponding to the online fault data by using the single classification models. The method of the invention utilizes the characteristic variables of each fault to carry out fault classification diagnosis, which not only can eliminate the interference influence of non-characteristic variables, but also can highlight the difference of each characteristic variable through weighting processing when a single classification model is established. Therefore, the method of the present invention is a more preferable fault classification diagnosis method.

Description

Fault classification diagnosis method based on characteristic variable weighting
Technical Field
The invention relates to a data-driven fault diagnosis method, in particular to a fault classification diagnosis method based on characteristic variable weighting.
Background
The method has the advantages that faults occurring in the operation of production objects are accurately diagnosed, and the method is of great significance for ensuring safe production and maintaining stable product quality. For this reason, process monitoring has been the subject of extensive attention in both industry and academia. Throughout recent research results in the field of process monitoring, there are numerous studies on fault detection. In contrast, the results of research for fault diagnosis are exponential. Compared with available fault detection method technology, the available scientific research literature and patents have few fault diagnosis achievements. Generally, the task of fault detection is to tell us that an abnormal condition occurs in a production process object, and fault diagnosis is to find a problem, but the fault detection and the fault diagnosis cannot be realized. There are generally two ideas for fault diagnosis development up to now: one is to correctly locate the faulty measurement variable; and secondly, identifying the type of the currently detected fault by matching the known fault types in the historical database. The former depends on the contribution of the measured variables, while the latter relies on classification methods in the field of pattern recognition.
However, unlike the multi-classification problem, the data that can be used for fault classification is collected from the transient phase of the condition switch. The training data change situation of each fault type is very complex, and abnormal changes of different measurement variables can occur to different degrees after each fault occurs. In addition, after a fault occurs, field operators can restore the process to a normal operation state in the first time, and the data volume collected under various fault conditions is usually limited and mainly focuses on the transition process. If the fault classification diagnosis is carried out directly by adopting a classification algorithm commonly used in the mode classification field, the classification algorithm is as follows: the establishment of multi-classification models such as discriminant analysis, support vector machines, neural networks, etc. often fails to achieve satisfactory results. In addition, support vector machines and neural networks require a large amount of data to perform training to ensure model accuracy, and they are generally not suitable for fault classification diagnosis.
In consideration of the particularity of the fault classification diagnosis problem, not all measured variables are subjected to abnormal fluctuation after the fault occurs, and each fault type causes different measured variables to be subjected to abnormal changes in different degrees. Therefore, how to distinguish the characteristic variables of each reference fault and the corresponding abnormal change degree thereof is an effective way for solving the problem of fault classification diagnosis. Furthermore, due to the staggered relationship between the measured variables, the principle of discriminating between fault characteristic variables should be based on the overall level preference rather than considering the individual measured variables separately. Since different fault types correspond to different characteristic variables, a single multi-classification model cannot be uniformly and theoretically established. One feasible idea is to establish a single classification model of each fault type by using the feature variables only, so as to judge the attribution of the online fault data.
Disclosure of Invention
The invention aims to solve the main technical problems that: how to implement selection and weighting processing of fault characteristic variables for each fault type in a historical database, and a single classification model of each fault type is established by using the characteristic variables, so that fault classification diagnosis is implemented. Therefore, the method of the invention utilizes a novel characteristic selection method of Neighbor Component Analysis (NCA) to distinguish characteristic variables and abnormal degrees thereof for each reference fault type one by one. And then, establishing a single classification model for the weighted characteristic variables of each fault type by using a principal component analysis algorithm. And finally, diagnosing the fault type corresponding to the online fault data by using the single classification models.
The technical scheme adopted by the invention for solving the technical problems is as follows: a fault classification diagnosis method based on characteristic variable weighting comprises the following steps:
(1): collecting N under normal operation condition in production process0Forming a normal working condition training data matrix by using the sample data
Figure BSA0000172239650000021
Calculating a data matrix X0Mean value mu of each column vector1，μ2，…，μmAnd standard deviation delta1，δ2，…，δmWherein R represents a real number set,
Figure BSA0000172239650000022
represents N0X m dimensional real number matrix, N0Is the number of normal samples and m is the total number of process measurement variables.
(2): finding out sampling data under different fault working conditions from a production process duration database to form different reference fault data sets X1，X2，…，XCAnd initializing a subscript c ═ 1, where
Figure BSA0000172239650000023
NcFor the number of available samples of the C-th fault, the subscript C is 1, 2, …, C is the total number of categories of the reference fault.
(3): using the mean vector mu ═ mu1，μ2，…，μm]Diagonal matrix with standard deviation
Figure BSA0000172239650000024
Separately standardizing treatment X0，X1，X2…，XCTo obtain a normalized data matrix
Figure BSA0000172239650000025
The specific implementation mode is as follows:
Figure BSA0000172239650000026
wherein, diag { delta1，δ2，…，δmDenotes a will δ1，δ2，…，δmForming a diagonal matrix, X representing a matrix X0，X1，X2…，XCThe respective row vectors of (a) are,
Figure BSA0000172239650000027
is a normalized row vector.
(4): will matrix
Figure BSA0000172239650000028
And
Figure BSA0000172239650000029
are combined into a matrix
Figure BSA00001722396500000210
And construct class label vectors
Figure BSA00001722396500000211
Wherein the superscript T is the transpose of the matrix or vector, the vector ycMiddle front N0The numerical values of the elements are all 0 and then NcThe individual element values all equal 1.
(5): memory matrix YcIn each row vector is x1，x2，…，xnWherein N is N0+NcThen, the weight coefficient vector w is optimized and solved by using a Neighbor Component Analysis (NCA) algorithmcThe specific implementation procedure is as follows.
Initializing gradient step length alpha as 1 and initializing objective function value f0(wc)＝-106And initializing the weight coefficient vector wc＝[1，1，…，1]I.e. the weight coefficient of each variableThe initial value is set to 1 uniformly.
② calculating the current weight coefficient vector w according to the following formulacValue of objective function under the condition f (w)c)：
Figure BSA00001722396500000212
In the above formula, if and only if xiAnd xjCorresponding class numbers being the same, yijOther cases y 1ij0. Probability pijThe calculation of (c) is as follows:
Figure BSA0000172239650000031
in the above formula (3), j is 1, 2, …, n, Dw(xi，xj)＝||(xi-xj)diag(wc)||，diag(wc) Denotes a combination of wcThe elements in (1) are transformed into a diagonal matrix, and the symbol | | | | | represents the length of the calculated vector.
Thirdly, whether the convergence condition | f (w) is satisfied is judgedc)-f0(wc)|＜10-6Is there a If yes, outputting the weight coefficient vector wc(ii) a If not, continuing to implement the step (iv).
Fourthly, set up f0(wc)＝f(wc) Then, the gradient value Δ f is calculated according to the formula shown below, and the gradient value Δ f is calculated according to the formula wc＝wc+ α Δ f updates the weight coefficient vector:
Figure BSA0000172239650000032
according to updated wcCalculating the value of the objective function f (w)c) And judges whether or not the condition f (w) is satisfiedc)＞f0(wc) Is there a If yes, updating the gradient step length alpha according to the formula alpha which is 1.01 alpha; if not, updating the gradient step length alpha according to the formula alpha being 0.4 alpha.
And sixthly, returning to the step III to continue the next iteration optimization until the convergence condition in the step III is met.
(6): vector w of weighting coefficientscElements greater than 0.01 and their corresponding variables are respectively recorded as vectors
Figure BSA0000172239650000033
And set phicAnd according to phicSlave matrix
Figure BSA0000172239650000034
Selects corresponding column to form matrix FcThen according to the formula
Figure BSA0000172239650000035
Calculating to obtain a characteristic variable weighting matrix of the c-th type reference fault
Figure BSA0000172239650000036
(7): to be provided with
Figure BSA0000172239650000037
For training the data matrix, a Principal Component Analysis (PCA) algorithm is utilized to establish a characteristic variable weighting PCA model of the c-th type reference fault:
Figure BSA0000172239650000038
wherein
Figure BSA0000172239650000039
And PcScore matrix and load matrix, respectively, of the model, EcIs the residual matrix of the model, lcIs the number of model load vectors.
(8): will matrix Sc＝EcEc TElements on the diagonal are taken solely as column vectors QcThereafter, the upper control limit δ of the PCA model is determined according to the following formulac，limAnd ηc，lim：
Figure BSA00001722396500000310
In the above formula, the first and second carbon atoms are,
Figure BSA00001722396500000311
the confidence coefficient is alpha and the degree of freedom is lcAnd Nc-lcThe value corresponding to the F distribution of (a),
Figure BSA00001722396500000312
representing the degree of freedom as h and the confidence as alpha as the corresponding values of chi-square distribution, b and v are vectors QcMean and variance of.
(9): determine whether condition C < C? If yes, returning to the step (4) after c is set to c + 1; if not, obtaining a characteristic variable set phi of all the C-type reference faults1，φ2，…，φCWeight vector of feature variable
Figure BSA00001722396500000313
Feature variable weighted PCA model and control ceiling delta1，lim，δ2，lim，…，δC，limAnd η1，lim，η2，lim，…，ηC，lim。
The steps (1) to (9) complete the selection and weighting of the fault characteristic variables of each type, and a corresponding single classification model is established by utilizing a PCA algorithm. The steps (10) to (14) shown below are diagnostic procedures of the fault type to which the online fault data belongs.
(10): when the online monitored data z belongs to R1×mAfter being identified as fault sample data, according to formula
Figure BSA0000172239650000041
Normalizing z to obtain a vector
Figure BSA0000172239650000042
And initializes c to 1.
(11): utilizing the c-th type reference fault characteristic variable set phi in the step (6)cFrom
Figure BSA0000172239650000043
Selecting the corresponding component vector zcThen weighting the vector according to the characteristic variable
Figure BSA0000172239650000044
To zcPerforming weighting processing to obtain
Figure BSA0000172239650000045
(12): calling the c characteristic variable weighted PCA model established in the step (7), and calculating delta according to the formula shown in the specificationcAnd ηcThe specific numerical values of (A):
Figure BSA0000172239650000046
in the above formula, the matrix Λc＝Tc TTc/(Nc-1), the matrix I being an identity matrix.
(13): according to formula Dc＝δc/δc，lim+ηc/ηc，limCalculating the degree of matching DcAnd then judging whether the conditions are met: c < C? If yes, after c is set to c +1, returning to the step (11); if not, obtaining the matching degree D of all the C-type reference fault types to which the online fault data belongs1，D2，…，DC。
(14): according to D1，D2，…，DCThe minimum value in the process determines the online fault data z belongs to R1×mAnd (5) the attributed fault type is returned to the step (10) to continue to carry out fault diagnosis of the next fault sample.
Compared with the traditional method, the method has the advantages that:
firstly, the method of the invention screens characteristic variables for each fault type one by using a neighbor component analysis algorithm. In other words, the NCA algorithm itself optimizes the overall level to obtain the weight values of the measured variables, thereby realizing the selection and weighting of the characteristic variables. Secondly, the fault type matching is implemented by using the characteristic variables, so that not only can the interference influence of the non-characteristic variables be eliminated, but also the difference of the characteristic variables can be highlighted through weighting processing when a single classification model is established. In summary, the method of the present invention is an effective data-driven fault classification diagnosis method.
Drawings
FIG. 1 is a flow chart of an embodiment of the method for establishing a fault feature variable weighted PCA model.
Fig. 2 is a flow chart of an implementation of online fault type diagnosis in the method of the present invention.
Detailed Description
The following describes in detail a specific embodiment of the method of the present invention with reference to the accompanying drawings.
The invention discloses a fault classification diagnosis method based on characteristic variable weighting, an implementation process of establishing a fault characteristic variable weighting PCA model for each fault type by the method is shown in figure 1, and a specific implementation mode comprises the following steps (1) to (9).
Step (1): collecting N under normal operation condition in production process0Forming a normal working condition training data matrix by using the sample data
Figure BSA0000172239650000047
Calculating a data matrix X0Mean value mu of each column vector1，μ2，…，μmAnd standard deviation delta1，δ2，…，δmWherein R represents a real number set,
Figure BSA0000172239650000051
represents N0X m dimensional real number matrix, N0Is the number of normal samples and m is the total number of process measurement variables.
Step (2): finding out sampling data under different fault working conditions from a production process duration database to form different reference fault data matrixes X1，X2，…，XCAnd initializing a subscript c ═ 1, where
Figure BSA0000172239650000052
NcFor the number of samples available for the type C fault, the subscript C is 1, 2, …, C.
And (3): using the mean vector mu ═ mu1，μ2，…，μm]Diagonal matrix with standard deviation
Figure BSA0000172239650000053
Separately standardizing treatment X0，X1，X2…，XCTo obtain a normalized data matrix
Figure BSA0000172239650000054
The specific implementation mode is as follows:
Figure BSA0000172239650000055
wherein, diag { delta1，δ2，…，δmDenotes a will δ1，δ2，…，δmForming a diagonal matrix, X representing a matrix X0，X1，X2…，XCThe respective row vectors of (a) are,
Figure BSA0000172239650000056
is a normalized row vector.
And (4): will matrix
Figure BSA0000172239650000057
And
Figure BSA0000172239650000058
are combined into a matrix
Figure BSA0000172239650000059
And construct class label vectors
Figure BSA00001722396500000510
Wherein the superscript T is the transpose of the matrix or vector, the vector ycMiddle front N0The numerical values of the elements are all 0 and then NcThe individual element values all equal 1.
And (5): memory matrix YcIn each row vector is x1，x2，…，xnWherein N is N0+NcThen, the weight coefficient vector w is optimized and solved by using a Neighbor Component Analysis (NCA) algorithmc。
And (6): vector w of weighting coefficientscElements greater than 0.01 and their corresponding variables are respectively recorded as vectors
Figure BSA00001722396500000511
And set phicAnd according to phicSlave matrix
Figure BSA00001722396500000512
Selects corresponding column to form matrix FcThen according to the formula
Figure BSA00001722396500000513
Calculating to obtain a characteristic variable weighting matrix of the class c fault
Figure BSA00001722396500000514
And (7): to be provided with
Figure BSA00001722396500000515
For training the data matrix, a Principal Component Analysis (PCA) algorithm is used for establishing a characteristic variable weighted PCA model of the type c fault:
Figure BSA00001722396500000516
the specific implementation mode is shown in the steps (7.1) to (7.5).
Step (7.1): according to the formula
Figure BSA00001722396500000517
Calculating the covariance matrix phic；
Step (7.2): solving for phicAll non-zero eigenvalues
Figure BSA00001722396500000518
Corresponding feature vector
Figure BSA00001722396500000519
Here, it is required that all feature vectors are of unit length, where McThe number of non-zero eigenvalues;
step (7.3): setting the number l of load vectorscIs the minimum value that satisfies the conditions shown below:
Figure BSA00001722396500000520
step (7.4): feature vector
Figure BSA00001722396500000521
Forming a load matrix
Figure BSA00001722396500000522
And according to the formula
Figure BSA00001722396500000523
Calculating score matrix Tc；
Step (7.5): the corresponding feature variable weighted PCA model can be expressed as:
Figure BSA00001722396500000524
wherein the residual error
Figure BSA00001722396500000525
And (8): will matrix Sc＝EcEc TElements on the diagonal are taken solely as column vectors QcThereafter, the upper control limit δ of the PCA model is determined according to the following formulac，limAnd ηc，lim：
Figure BSA0000172239650000061
In the above formula, the first and second carbon atoms are,
Figure BSA0000172239650000062
the confidence coefficient is alpha and the degree of freedom is lcAnd Nc-lcThe value corresponding to the F distribution of (a),
Figure BSA0000172239650000063
representing the degree of freedom as h and the confidence as alpha as the corresponding values of chi-square distribution, b and v are vectors QcMean and variance of.
And (9): determine whether condition C < C? If yes, returning to the step (4) after c is set to c + 1; if not, obtaining a characteristic variable set phi of all the C-type reference faults1，φ2，…，φCWeight vector of feature variable
Figure BSA0000172239650000064
Feature variable weighted PCA model and control ceiling delta1，lim，δ2，lim，…，δC，limAnd η1，lim，η2，lim，…，ηC，lim。
When the fault sample data z belongs to R in the online detection1×mThen, an online fault type diagnosis is performed according to the implementation flow shown in fig. 2, and specific embodiments are as follows.
Step (10): when the online monitored data z belongs to R1×mAfter being identified as fault sample data, according to formula
Figure BSA0000172239650000065
Normalizing z to obtain a vector
Figure BSA00001722396500000610
And initializes c to 1.
Step (11): utilizing the c-th type reference fault characteristic variable set phi in the step (6)cFrom
Figure BSA0000172239650000066
Selecting the corresponding component vector zcThen weighting the vector according to the characteristic variable
Figure BSA0000172239650000067
To zcPerforming weighting processing to obtain
Figure BSA0000172239650000068
Step (12): calling the c characteristic variable weighted PCA model established in the step (7), and calculating delta according to the formula shown in the specificationcAnd ηcThe specific numerical values of (A):
Figure BSA0000172239650000069
in the above formula, the matrix Λc＝Tc TTc/(Nc-1), the matrix I being an identity matrix.
Step (13): according to formula Dc＝δc/δc，lim+ηc/ηc，limCalculating the degree of matching DcAnd then judging whether the conditions are met: c < C? If yes, after c is set to c +1, returning to the step (11); if not, obtaining the matching degree D of all the C-type reference fault types to which the online fault data belongs1，D2，…，DC。
Step (14): according to D1，D2，…，DCThe minimum value in the process determines the online fault data z belongs to R1×mAnd (5) the attributed fault type is returned to the step (10) to continue to carry out fault diagnosis of the next fault sample.

Claims (2)

1. A fault classification diagnosis method based on characteristic variable weighting is characterized by comprising the following steps:
step (1): collecting N under normal operation condition in production process0Sample data of each sample, compositionNormal condition training data matrix
Figure FSB0000190597240000011
Calculating a data matrix X0Mean value mu of each column vector1，μ2，…，μmAnd standard deviation delta1，δ2，…，δmWherein R represents a real number set,
Figure FSB0000190597240000012
represents N0X m dimensional real number matrix, N0The number of normal samples, m is the total number of process measurement variables;
step (2): finding out sampling data under different fault working conditions from a historical database in the production process to form a data matrix X of each reference fault1，X2，…，XCAnd initializing a subscript c ═ 1, where
Figure FSB0000190597240000013
NcThe number of available samples of the C-th fault is shown, wherein the subscript number C is 1, 2, …, and C is the total number of categories of the reference fault;
and (3): using the mean vector mu ═ mu1，μ2，…，μm]Diagonal matrix with standard deviation
Figure FSB0000190597240000014
Separately standardizing treatment X0，X1，X2…，XCTo obtain a normalized data matrix
Figure FSB0000190597240000015
The specific implementation mode is as follows:
Figure FSB0000190597240000016
wherein, diag { delta1，δ2，…，δmDenotes a will δ1，δ2，…，δmForming a diagonal matrix, X representing a matrix X0，X1，X2…，XCThe respective row vectors of (a) are,
Figure FSB0000190597240000017
the normalized row vector is obtained;
and (4): will matrix
Figure FSB0000190597240000018
And
Figure FSB0000190597240000019
are combined to obtain a matrix
Figure FSB00001905972400000110
And construct class label vectors
Figure FSB00001905972400000111
Wherein the superscript T is the transpose of the matrix or vector, the vector ycMiddle front N0The numerical values of the elements are all 0 and then NcThe individual element numbers all equal 1;
and (5): memory matrix YcIn each row vector is x1，x2，…，xnWherein N is N0+NcThen, the weight coefficient vector w is optimized and solved by using a Neighbor Component Analysis (NCA) algorithmcThe specific implementation process is shown as the steps (5.1) to (5.6):
step (5.1): initializing gradient step length alpha as 1, initializing objective function value f0(wc)＝-106And initializing the weight coefficient vector wc＝[1，1，…，1]Namely, the initial value of the weight coefficient of each variable is uniformly set to 1;
step (5.2): the current weight coefficient vector w is calculated according to the formula shown belowcValue of objective function under the condition f (w)c)：
Figure FSB00001905972400000112
In the above formula, if and only if xiAnd xjCorresponding class numbers being the same, yijOther cases y 1ij0, probability pijThe calculation of (c) is as follows:
Figure FSB00001905972400000113
in the above formula (3), j is 1, 2, …, n, Dw(xi，xj)＝||(xi-xj)diag(wc)||，diag(wc) Denotes a combination of wcThe element in (1) is converted into a diagonal matrix, and the symbol | | | | represents the length of a calculation vector;
step (5.3): judging whether a convergence condition | f (w) is satisfiedc)-f0(wc)|＜10-6(ii) a If yes, outputting the weight coefficient vector wc(ii) a If not, continuing to implement the step (5.4);
step (5.4): set up f0(wc)＝f(wc) Then, the gradient value Δ f is calculated according to the formula shown below, and the gradient value Δ f is calculated according to the formula wc＝wc+ α Δ f updates the weight coefficient vector:
Figure FSB0000190597240000021
step (5.5): according to the updated wcCalculating the value of the objective function f (w)c) And judges whether or not the condition f (w) is satisfiedc)＞f0(wc) (ii) a If yes, updating the gradient step length alpha according to the formula alpha which is 1.01 alpha; if not, updating the gradient step length alpha according to a formula alpha which is 0.4 alpha;
step (5.6): returning to the step (5.3) to continue the next iterative optimization until the convergence condition in the step (5.3) is met;
and (6): vector w of weighting coefficientscElements greater than 0.01 and their corresponding variables are respectively recorded as vectors
Figure FSB0000190597240000022
And set phicAnd according to phicSlave matrix
Figure FSB0000190597240000023
Selects corresponding column to form matrix FcThen according to the formula
Figure FSB0000190597240000024
Calculating to obtain a characteristic variable weighting matrix of the c-th type reference fault
Figure FSB0000190597240000025
And (7): to be provided with
Figure FSB0000190597240000026
For training the data matrix, a Principal Component Analysis (PCA) algorithm is utilized to establish a characteristic variable weighting PCA model of the c-th type reference fault:
Figure FSB0000190597240000027
wherein
Figure FSB0000190597240000028
And PcScore matrix and load matrix, respectively, of the model, EcIs the residual matrix of the model, lcIs the number of model load vectors;
and (8): will matrix Sc＝EcEc TElements on the diagonal are taken solely as column vectors QcThereafter, the upper control limit δ of the PCA model is determined according to the following formulac，limAnd ηc，lim：
Figure FSB0000190597240000029
In the above formula, the first and second carbon atoms are,
Figure FSB00001905972400000210
the confidence coefficient is alpha and the degree of freedom is lcAnd Nc-lcThe value corresponding to the F distribution of (a),
Figure FSB00001905972400000211
representing the degree of freedom as h and the confidence as alpha as the corresponding values of chi-square distribution, b and v are vectors QcMean and variance of;
and (9): judging whether the condition C is more than C; if yes, returning to the step (4) after c is set to c + 1; if not, obtaining a characteristic variable set phi of all the C-type reference faults1，φ2，…，φCWeight vector of feature variable
Figure FSB00001905972400000212
Feature variable weighted PCA model and control ceiling delta1，lim，δ2，lim，…，δC，limAnd η1，lim，η2，lim，…，ηC，lim；
Step (10): when the online monitored data z belongs to R1×mAfter being identified as fault sample data, according to formula
Figure FSB00001905972400000213
Normalizing z to obtain a vector
Figure FSB00001905972400000214
And initializing c to 1;
step (11): utilizing the c-th type reference fault characteristic variable set phi in the step (6)cFrom
Figure FSB00001905972400000215
Selecting the corresponding component vector zcThen weighting the vector according to the characteristic variable
Figure FSB00001905972400000216
To zcPerforming weighting processing to obtain
Figure FSB00001905972400000217
Step (12): calling the c characteristic variable weighted PCA model established in the step (7), and calculating delta according to the formula shown in the specificationcAnd ηcThe specific numerical values of (A):
Figure FSB00001905972400000218
in the above formula, the matrix Λc＝Tc TTc/(Nc-1), the matrix I being an identity matrix;
step (13): according to formula Dc＝δc/δc，lim+ηc/ηc，limCalculating the degree of matching DcAnd then judging whether the conditions are met: c is less than C; if yes, after c is set to c +1, returning to the step (11); if not, obtaining the matching degree D of all the C-type reference fault types to which the online fault data belongs1，D2，…，DC；
Step (14): according to D1，D2，…，DCThe minimum value in the process determines the online fault data z belongs to R1×mAnd (5) the attributed fault type is returned to the step (10) to continue to carry out fault diagnosis of the next fault sample.
2. The method for fault classification diagnosis based on feature variable weighting according to claim 1, wherein the implementation process of establishing a Principal Component Analysis (PCA) model by using a PCA algorithm in the step (7) is specifically as follows:
according to a formula
Figure FSB0000190597240000031
Calculating the covariance matrix phic；
② solving for phicAll non-zero eigenvalues
Figure FSB0000190597240000032
Corresponding feature vector
Figure FSB0000190597240000033
Here, it is required that all feature vectors are of unit length, where McThe number of non-zero eigenvalues;
setting the number l of load vectorscIs the minimum value that satisfies the conditions shown below:
Figure FSB0000190597240000034
fourthly, the characteristic vector
Figure FSB0000190597240000035
Forming a load matrix
Figure FSB0000190597240000036
And according to the formula
Figure FSB0000190597240000037
Calculating score matrix Tc；
The corresponding feature variable weighted PCA model can be expressed as:
Figure FSB0000190597240000038
wherein the residual error
Figure FSB0000190597240000039
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