CN115878987A - Fault positioning method based on contribution value and causal graph - Google Patents

Abstract

The invention discloses a fault positioning method based on contribution values and a causal graph, which comprises the steps of firstly inputting historical monitoring data of equipment, after a fault is found, firstly calculating the contribution value of each dimension of data characteristics, sequencing monitoring variables according to the contribution values, judging whether the variable corresponding to the maximum contribution value can be judged as a fault variable, if not, regarding the variable with the larger contribution value as a variable set to be selected, calculating a transfer entropy to draw the causal graph, thereby determining the fault variable, and finally outputting the fault variable; the method of the invention screens the variables through the characteristic sorting, thereby greatly reducing the complexity of analysis of the causal graph, and the accuracy of fault positioning is improved compared with the contribution value method because the causal graph is used for analyzing the mutual influence of the variables.

Description

Fault positioning method based on contribution value and causal graph

Technical Field

The invention relates to the technical field of fault diagnosis, in particular to a comprehensive T ² A fault location method for ordering contribution values and transferring entropy causal graphs.

Background

Along with the development of modern science and technology, the efficiency of manufacturing equipment has obtained very big promotion. Although the reliability of the equipment is also greatly improved, occasional failures are still unavoidable. The accidental faults not only influence the normal operation of the equipment, but also seriously even cause safety accidents. Therefore, the real-time sensing of the equipment state is realized, and the fault and the cause of the fault are found in time.

The fault location means that after a fault is detected, the data collected by the equipment are comprehensively analyzed, the sensor variable most relevant to the fault is determined, an operator can be helped to analyze the fault cause in time, and the normal operation of the equipment is recovered as soon as possible.

The traditional contribution value focuses on analyzing each variable and calculating the contribution degree of a single variable to a fault result. Although the method is simple, the internal coupling influence among system variables is not considered, and the accuracy needs to be improved. And analyzing the causal graph to determine the essential variables of fault. Due to the numerous variables, computational analysis is quite complex.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a comprehensive T ² A fault location method for ordering contribution values and transferring entropy causal graphs.

The technical scheme adopted by the invention for solving the technical problems is as follows: a fault positioning method based on contribution values and a causal graph comprises the following steps:

s1, inputting historical monitoring data of equipment for a period of time, judging whether a fault occurs, and if not, ending;

s2, after a fault is found, calculating the contribution value of each dimension of data feature (namely each monitoring variable), and sequencing the monitoring variables according to the contribution values;

s3, judging whether the variable corresponding to the maximum contribution value can be judged as a fault variable:

if the contribution value of the first feature in the sequence is far beyond the latter, the feature is a fault variable, and the fault variable is output and the process is finished; otherwise, putting the variable set F into a candidate variable set F: in the features from the first feature to the Nth feature, if the contribution value of the ith feature is far beyond the (i + 1) th feature, the candidate variable set F only contains the front i-dimensional feature, wherein the maximum capacity of the candidate variable set F is N, and the threshold is F;

otherwise, the candidate variable set F contains all the first N dimensional features, and then the transfer entropy between all the features in the candidate variable set F is calculated;

s4, drawing a causal graph according to the transfer entropy of the variable set F to be selected, and analyzing the causal graph to determine fault variables;

and S5, outputting fault variables.

Further, fault location is carried out by using a principal component analysis method in the step S1; calculating T of historical monitoring data ² Statistics, then analyzing each monitored variable pair T ² Comparing the contribution degrees of the statistics, and judging that the monitoring variable with larger contribution degree is more likely to be a cause of the fault;

the principal component analysis method realizes the dimensionality reduction of the original high-dimensional data by performing coordinate transformation on historical monitoring data and then only leaving the first few principal component directions with the largest variance, and similarly, the data after dimensionality reduction can be restored to the original high-dimensional data again through coordinate transformation.

Furthermore, the process of principal component analysis dimensionality reduction is as follows:

let X = (X) ₁ ,x ₂ ...x _n ) ^Τ Representing n m-dimensional monitored variables

A matrix of raw data samples, m representing the total number of sensors, nFor the number of samples, the monitoring variable in each dimension is normalized, i.e. all j sums are/are->

The standard deviation is 1;

use of

Represents the sample covariance matrix, { λ ₁ ,λ ₂ ...λ _a Is the first a (a ≦ m) largest eigenvalues of Y, then { p ≦ m ₁ ,p ₂ ...p _a Is its corresponding feature vector;

constructing a load matrix P = [ P ] ₁ ,p ₂ ...p _a ]If the monitoring data after the dimensionality reduction is obtained by calculation of a formula T = XP;

in the process of principal component analysis, a new sample coordinate T is obtained by forward a eigenvectors projection, the new sample can be restored to the original sample to a certain extent, and a formula is used

Calculating the recovered data, error (residual) or>

Using T ² And (3) carrying out fault positioning by using the statistics: assume that each sample point x = (x) ¹ ,x ² ...x ^m ) ^T Obeying a mixed Gaussian distribution of m dimensions; t is ² The statistic is the Mahalanobis distance from the new sample point t to the sample center

Wherein Λ = diag (λ) ₁ ,λ ₂ ...λ _a ) (ii) a Dividing a certain confidence interval according to chi-square distribution, and regarding sample points outside the interval as fault samples; when the fault positioning task is executed, analyzing each dimension of monitoring data x ⁱ For T ² The contribution degree of the statistic, and the variable with large contribution degree is considered as the cause of fault generation; wherein the ith dimension monitoring number is calculatedAccording to the contribution function of

Where (0,0.., x) _i ,...,0) ^T Meaning that only the ith element is x _i And the other elements are column vectors of 0.

Still further, the step of calculating the transition entropy in step S3 is:

recording the uncertainty of the random event X as entropy H (X), expressing the probability distribution of the discrete random variable X by p (X), and passing through a formula

The calculation is a measure of the degree of uncertainty of the information;

for two random processes X (t), Y (t) within time t, the transfer entropy of the sequence Y (t) to X (t) is calculated by the following formula:

wherein X (t-L: t-1) and Y (t-L: t-1) represent the X, Y sequence from t-L to t-1.

The invention has the beneficial effects that: the invention combines T ² Contribution value method and causal graph method, and T-based method ² Due to the fact that the causal graph is used for analyzing the mutual influence of the variables, the accuracy of fault location is improved compared with a method of the contribution value.

Drawings

FIG. 1 is a flow chart of the fault location of the present invention;

FIG. 2 is a graph of sample 8 contributions in experimental validation;

FIG. 3 sample 2 contribution plot in experimental validation;

fig. 4 is a sample 2 fault localization causal graph in experimental validation.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Referring to fig. 1, the method for fault location based on contribution values and a causal graph disclosed by the invention comprises the following steps.

S1, inputting historical monitoring data of the equipment for a period of time, judging whether a fault occurs, and if not, ending. The step uses Principal Component Analysis (PCA) method to locate the fault.

With respect to T ² Contribution value: the principal component analysis realizes the dimensionality reduction of the original high-dimensional data by performing coordinate transformation on the original data and then only leaving the first few principal component directions with the largest variance, and similarly, the data after dimensionality reduction can be restored to the original high-dimensional data again through coordinate transformation.

When PCA is used for fault location, T of monitoring data is calculated ² Statistics are obtained. The degree of contribution of each monitored variable to the statistics is then analyzed and compared. The more highly contributed monitoring variables are more likely to be the cause of the failure. The PCA dimension reduction process is as follows.

Let X = (X) ₁ ,x ₂ ...x _n ) ^Τ Representing n m-dimensional monitoring variables

A combined raw data sample matrix, m representing the total number of sensors and n representing the number of samples, is normalized for the monitored variable in each dimension, i.e. the sum of all j->

The standard deviation was 1.

Then use it

Represents the sample covariance matrix, { λ { ₁ ,λ ₂ ...λ _a Is the first a (a ≦ m) largest eigenvalues of Y, then { p ₁ ,p ₂ …p _a Is that it corresponds toA feature vector.

Constructing a load matrix P = [ P ] ₁ ,p ₂ ...p _a ]And calculating the data after the dimensionality reduction by using a formula T = XP.

In the PCA process, a new sample coordinate T is obtained by projecting a feature vectors forward. The new sample can be restored to the original sample to a certain extent

Represents the restored data and has a calculation formula of ≥ based on ≤>

Error (residual error)

Using T ² When fault location is carried out on the statistics, each sample point x = (x) is assumed ¹ ,x ² ...x ^m ) ^T Obeying a mixture gaussian distribution in m dimensions. According to the characteristics of Gaussian distribution, reducing the dimension by linear transformation to obtain a new sample point t = (t) ¹ ,t ² ...t ^a ) ^T Also, a mixed gaussian distribution is satisfied, and the new sample point corresponds to the covariance matrix cov = diag (λ) ₁ ,λ ₂ ...λ _a ) I.e. t ⁱ Also obey a Gaussian distribution, and t ⁱ And t ^j

Independently of each other, t ⁱ Is the corresponding eigenvalue lambda _i 。

T ² The statistic is the Mahalanobis distance from the new sample point t to the sample center

Wherein Λ = diag (λ) ₁ ,λ ₂ ...λ _a ). From mathematical analysis, T ² Obeying a chi-square distribution with a degree of freedom a. So for the data collected during normal operation of the equipment, T ² Should fall mainly within a certain range interval, T ² The probability of occurrence of particularly large values is low. />

During fault diagnosis, certain confidence intervals can be divided according to chi-square distribution, and sample points outside the intervals are regarded as fault samples. And when the fault positioning task is executed, analyzing each dimension of data x ⁱ For T ² The degree of contribution of the statistic, and a variable with a large degree of contribution is considered as a cause of the fault.

And S2, after the fault is found, calculating the contribution value of each monitoring variable (namely each dimension of data characteristic), and sequencing the monitoring variables according to the contribution values.

S3, judging whether the variable corresponding to the maximum contribution value can be judged as a fault variable: if the contribution value of the first feature in the sequence is far beyond the latter, the feature is a fault variable, and the fault variable is output and the process is finished; otherwise, putting the variable set F into a candidate variable set F: in the features from the first feature to the Nth feature, if the contribution value of the ith feature is far beyond the (i + 1) th feature, the candidate variable set F only contains the front i-dimensional features, otherwise, the candidate variable set F contains all the front N-dimensional features, and then the transfer entropy between every two features in the candidate variable set F is calculated; the maximum capacity of the variable set F to be selected is N, and the threshold value is F.

Regarding the transition entropy: for a real physical system, entropy is a physical quantity that quantitatively characterizes the degree of disorder of the system. For random event X, the uncertainty is usually measured using entropy, a physical quantity denoted as H (X).

Taking discrete random variables as an example, the probability distribution of X is represented by p (X), and the probability distribution is represented by a formula

In the calculation, H (X) is a measure of the degree of uncertainty of the information. Similar to the concept in thermodynamics, the larger H (X) indicates a higher degree of uncertainty and a higher chaos of the system.

The transfer entropy focuses on quantifying the amount of information transfer between random sequences in one direction. X (t) and Y (t) are two random processes, and t is time. The transition entropy of the sequence Y (t) to X (t) is then:

wherein X (t-L: t-1) and Y (t-L: t-1) represent the X, Y sequence from t-L to t-1. As can be seen in the formula, TE _Y→X The prediction method shows the degree of prediction uncertainty reduced by knowing the historical information of Y (t) when the X (t) sequence information in the past period is known and the value of X (t) in the next time is predicted. TE (TE) _Y→X The larger the future effect X (t) is, which indicates that the history of Y (t) is, the more X (t) may be affected by Y (t).

And S4, drawing a causal graph according to the transfer entropy of the variable set F to be selected, and analyzing the causal graph so as to determine the fault variable.

And S5, outputting a fault variable.

The contribution function of the ith dimension data is calculated as

Wherein (0,0,.., x) _i ,...,0) ^T Meaning that only the ith element is x _i And the other elements are column vectors of 0.

Specific algorithm (comprehensive T) ² The contribution ordering and fault location method of the transition entropy causal graph) are as follows.

In a specific experiment, the value of N is 5, and the threshold value f is 3. Because the variable is screened by the characteristic sequencing, the complexity of analysis of the causal graph is greatly reduced; because the influence of variables on each other is analyzed by using the causal graph, the accuracy of fault positioning is improved compared with a contribution value method.

The method of the present invention is verified by data from the aluminum stack etching process of a Lam9600 ion etching apparatus.

Three groups of ion etching experiments are carried out before and after the ion etching experiments, the total number of 129 experimental samples is obtained, wherein 21 experiments artificially introduce faults, and 19 experimental data are selected for fault analysis after data are cleaned. The introduced fault relates to BCl3 Flow, C12 Flow, RF Power, TCP Power, pressure and so on. During the etching process, the parameters are specially adjusted to be larger or smaller. The objective of this experiment is to detect these faults and accurately locate the fault variables.

After the fault is detected, the contribution value of each dimension feature is calculated and sorted, and the result is shown in the following table.

Serial number	Cause of failure	PCA(T 2 )	PCA(SPE)	KNN	AE
						1	TCP_pwr	○	○	○	○
2	RF_Pwr	○	×	×	×
						3	RF_Pwr	○	×	×	×
4	Pressure	○	○	√	○
						5	TCP_pwr	○	√	○	○
6	BCl3_Flow	√	×	×	○
						7	Pressure	√	√	√	√
8	Cl2_Flow	√	×	×	×
						9	TCP_pwr	○	○	○	×
10	Cl2_Flow	√	×	×	×
						11	BCl3_Flow	√	√	√	√
12	Pressure	√	√	√	√
						13	TCP_pwr	○	○	○	○
14	TCP_pwr	×	○	○	×
						15	Cl2_Flow	√	×	×	×
16	RF_Pwr	×	×	○	×
						17	BCl3_Flow	√	×	×	×
18	Pressure	√	○	√	√
						19	TCP_pwr	○	○	○	○

In table except for T ² Statistics, results of SPE statistics, KNN and AF fault location are also presented for comparison. Since both "Pressure" and "Vat _ Value" reflect the Pressure conditions within the cavity, it can be considered that locating "Vat _ Value" is also accurate for "Pressure" faults. The ". Smallcircle" in the table indicates that the fault variable is included in the set F to be selected; the symbol "represents that the fault variable is successfully positioned only by the contribution value; and the x represents a positioning error, and the to-be-selected set F has no fault variable or the positioned fault variable has an error. As can be seen from the above table, the T selected in this patent ² Statistics, the best results can be obtained. The accuracy of the preliminary positioning was 47.4%, the highest among the four methods. All the "Cl2_ Flow", "BCl3_ Flow" faults and part of the "pressure" faults are accurately located without the need for subsequent calculations, as shown in fig. 2.

For the "RF _ Pwr", "TCP _ Pwr" and the rest "Pressure" faults, the location is not so accurate, and taking sample 2 as an example, as shown in fig. 3 below, the feature "RF _ Pwr" belongs to the candidate set, and the fault variable range needs to be further narrowed. Furthermore, T ² The number of statistical positioning errors is also minimal, only two. Will be subsequently based on T ² And calculating the transfer entropy according to the result of the statistic characteristic value calculation, thereby drawing a causal graph and further carrying out fault positioning. Table 1 contribution value feature ranking results.

In the use of T ² And calculating a contribution value by statistics, calculating the transfer entropy among the variables after obtaining the set to be selected, and drawing a causal graph. Taking sample 2 as an example, the features in the candidate set are "RF _ Pwr", "TCP _ Load", and "Pressure", and the calculated transition entropy is shown in table 2 below. The values in the table measure the variables of the row to which they belongThe magnitude of the uncertainty reduction caused by the column variables. Because the transfer entropy among some variables is very low, the transfer entropy threshold set by the patent is 0.45, and when the value is lower than the threshold, the direct mutual influence relationship of the two variables is considered to be very small and can be ignored. According to the transfer entropy, a cause and effect graph is drawn as shown in fig. 4, and as can be seen in the graph, "RF _ Pwr" is a fault root variable, and the fault variable is accurately positioned. The following table is sample 2 candidate set feature transfer entropy.

	RF_Pwr	TCP_Load	Pressure
				RF_Pwr		0.200	0.466
TCP_Load	0.144		0.851
				Pressure	0.172	0.777

In combination with the above table, the fault positioning accuracy at this time is 78.9%, and the positioning accuracy is greatly improved.

The following table shows the results of the causal graph analysis.

Serial number	Cause of failure	Positioning result
			1	TCP_pwr	√
2	RF_Pwr	√
			3	RF_Pwr	×
4	Pressure	√
			5	TCP_pwr	√
9	TCP_pwr	√
			13	TCP_pwr	×
19	TCP_pwr	√

And analyzing a causal graph of the sample, and finally analyzing to obtain a positioning result. In the above table, √ denotes that the positioning result is accurate, and × denotes that the positioning result is erroneous. The results show that comprehensive T is used ² The method for sequencing the contribution values and positioning the faults of the transfer entropy causal graph not only obviously reduces misdiagnosis of the traditional contribution graph method, but also reduces the complexity of calculation and analysis of the traditional causal graph method, can help operators to timely eliminate the abnormity, recovers the production and improves the efficiency.

The above-described embodiments are merely illustrative of the principles and effects of the present invention, and some embodiments in use, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the inventive concept.

Claims (4)

1. A fault location method based on contribution values and a causal graph is characterized in that: the steps are as follows

S1, inputting historical monitoring data of equipment, judging whether a fault occurs, and if not, ending;

s2, after a fault is found, calculating the contribution value of each monitoring variable, and sequencing the monitoring variables according to the contribution values;

s3, judging whether the variable corresponding to the maximum contribution value can be judged as a fault variable: if the contribution value of the first sorted characteristic is far beyond the rear, the characteristic is a fault variable, and the fault variable is output and ended; otherwise, putting the variable set F into a candidate variable set F: in the features from the first feature to the Nth feature, if the contribution value of the ith feature is far beyond the (i + 1) th feature, the candidate variable set F only contains the front i-dimensional features, otherwise, the candidate variable set F contains all the front N-dimensional features, and the transfer entropy between every two features in the candidate variable set F is calculated;

s4, drawing a causal graph according to the transfer entropy of the variable set F to be selected, and analyzing the causal graph to determine fault variables;

and S5, outputting a fault variable.

2. The method for fault location based on contribution values and the causal graph according to claim 1, wherein in step S1, a principal component analysis method is used for fault location; calculating T of historical monitoring data ² Statistic, then analyzing each monitored variable pair T ² Comparing the contribution degrees of the statistics, and judging that the larger the contribution degree, the more possible the monitoring variable is to cause the fault;

the principal component analysis method carries out coordinate transformation on historical monitoring data, and leaves the first principal component directions with the largest variance, so that the dimensionality reduction of original high-dimensional data is realized.

3. The method according to claim 2, wherein the principal component analysis dimension reduction process comprises the following steps:

let X = (X) ₁ ,x ₂ ...x _n ) ^Τ Representing n m-dimensional monitored variables

Forming an original data sample matrix, wherein m represents the number of total sensors, n is the number of samples, and each dimension of monitoring variable is subjected to standardization processing;

use of

Represents the sample covariance matrix, { λ ₁ ,λ ₂ ...λ _a Is the first a largest eigenvalues of Y, a ≦ m, then { p ₁ ,p ₂ ...p _a IsIts corresponding feature vector;

constructing a load matrix P = [ P ] ₁ ,p ₂ ...p _a ]Calculating the monitoring data after dimensionality reduction by a formula T = XP;

in the process of principal component analysis, a forward eigenvector projection is carried out to obtain a new sample coordinate T, and a formula is used

Calculating the restored data, error>

Using T ² And (3) carrying out fault location by statistic: assume that each sample point x = (x) ¹ ,x ² ...x ^m ) ^T Obeying a mixed Gaussian distribution of m dimensions; t is ² The statistic is the Mahalanobis distance from the new sample point t to the sample center

Wherein Λ = diag (λ) ₁ ,λ ₂ ...λ _a ) (ii) a Dividing confidence intervals according to chi-square distribution, and regarding sample points outside the intervals as fault samples; when the fault positioning task is executed, analyzing each dimension of monitoring data x ⁱ For T ² The degree of contribution of the statistics; wherein a contribution function to i-th dimension of the monitored data is calculated as ^>

In the formula (0,0, x) _i ,...,0) ^T Meaning that only the ith element is x _i And the other elements are column vectors of 0.

4. A method for fault location based on contribution values and a cause and effect diagram according to claim 3, wherein the step of calculating the transition entropy in step S3 is:

recording the uncertainty of the random event X as entropy H (X), expressing the probability distribution of the discrete random variable X by p (X), and calculating the probability distribution of the discrete random variable X by formula

The calculation is a measure of the degree of uncertainty of the information;

for two random processes X (t), Y (t) within time t, the transfer entropy of the sequence Y (t) to X (t) is calculated by the following formula:

wherein X (t-L: t-1) and Y (t-L: t-1) represent the X, Y sequence from t-L to t-1.

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