CN112348358A - PLS analysis-based process industrial fault detection and prediction method - Google Patents
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Abstract
The invention provides a PLS analysis-based process industrial fault detection and prediction method, and relates to the technical field of fault detection and prediction. The flow industrial fault detection and prediction method based on PLS analysis comprises the following steps: and S1, determining the number of PLS main elements. S2, PLS multivariate statistical process detection diagram. S3, analyzing step based on PLS process. According to the PLS analysis-based process industrial fault detection and prediction method, the PLS method utilizes orthogonal projection to convert a multiple regression problem into a unitary regression problem, so that the problem of collinearity is effectively solved, high-dimensional data is mapped into low-dimensional data, feature vectors with mutually orthogonal measured variables are obtained, then a linear regression relation among the vectors is established to characterize the process, the accuracy of a model can be improved, the nonlinear action characteristics of independent variables on dependent variables can be extracted from the established model, and the analysis accuracy is greatly improved.
Description
Technical Field
The invention relates to the technical field of fault detection and prediction, in particular to a flow industrial fault detection and prediction method based on PLS analysis.
Background
The complex industrial process results are too huge, and along with the development of the process of the complex industry, the data analysis method corresponding to the complex industrial process is relatively lagged behind, so that two aspects of conditions occur, on one hand, along with the rapid development of the advanced sensor and the industrial measurement technology thereof, a large amount of data are accumulated in the continuous industrial production process, and the data inevitably contain unexplored swimming information and present an industrial big data phenomenon; on the other hand, a complex industrial production process has a complex redundant mechanism, and data generated in operation is subjected to various noises, errors, data loss and the like in an acquisition process, so that the acquired data is disordered and even wrong, and a reasonable model capable of effectively expressing a poke-in rule is difficult to find.
Disclosure of Invention
The invention aims to provide a flow industrial fault detection and prediction method based on PLS analysis, which can use historical data to perform real-time monitoring, fault detection and diagnosis and product quality prediction on a corresponding online process based on data-driven multivariate model analysis, and is beneficial to effect evaluation, safety production, fault problem diagnosis and analysis and process flow optimization on a production process of the flow industry.
In order to achieve the purpose, the invention is realized by the following technical scheme: a process industry fault detection and prediction method based on PLS analysis comprises the following steps:
s1, determining the number of PLS pivot elements, selecting the first pivot elements to represent the whole model, determining the number of the pivot elements by adopting a cross-validation method, reserving one sample as a test sample each time, circulating the rest samples once,
for each dependent variable, define:
for all dependent variables Y, the cross-validation of the composition is defined as:
s2 PLS multivariate statistical Process detection map
S201, when a fault occurs, one or more measured variables will be affected, thereby affecting the relationship between the variables.
S202, the model decomposes the monitoring variable into two subspaces, T, which are related to and unrelated to the quality variable2For monitoring faults occurring in a subspace associated with a quality variable, and SPE statistics for monitoring faults occurring in a subspace associated with a quality variableFailure of quantum-independent subspaces.
S203, if T2And SPE is in the control limit of calculation, the result is indicated to run normally, and if T is reached2If the SPE exceeds the control limit, a fault unrelated to the parameter matrix occurs.
Setting the sampling batch number as I, and obtaining a score matrix at the time k:
TR,K＝[tI1,K,tI2,K,...,tIR,K]。
the covariance matrix is:
s3, based on the PLS process analysis step, adopting batch data under normal working conditions to establish a model database, and calculating T2And limiting the control of the SPE statistic, and then performing an off-line model building process and an on-line model building process.
Further, according to the operation procedure in S1, Q is measured2 h≥(1-0.95)2The marginal contribution of the ingredient is significant when 0.00975, with at least one k for k 1,2,3hk0.00975, the composition is increased by at least one dependent variable ykThe prediction model of (2) is significantly improved.
Further, according to the operation steps in S203, the method includes the following steps:
s2031, passing T2And judging the abnormal condition of the system by the statistic and the SPE statistic.
S2032, making each process variable pair SPE statistic and T2And calculating the scores of the statistics to construct a score matrix, drawing the score matrix into a histogram, and judging the fault source of the system according to the numerical value and the trend of the histogram.
Further, according to the operation step in S2031: t is2The statistic is the standard sum of squares of the score vectors, representing the trend and magnitude of the change for each sample dataDegree of departure from the model, T, for the k-th sampling instant2The statistics are represented as:
T2the statistic obeys F distribution, so by setting control limits:
±S(r,r)F(R,I-R)r＝1,2,...,R。
wherein S (r, r) is SKDiagonal elements of (a).
The value of the SPE statistic at time k is a scalar quantity representing the deviation of the measured value xk from the statistical model built at that moment, and is a measure of the change of the data outside the model, and for the kth sampling time, the value is calculated by:
SPEK＝enem,keT new,k。
enew,k＝xnew,k(I-PPT)；
wherein x isnew,k(k 1, 2.., k) measurement data for the new batch time k.
Further, it is convenient to write the program inside the computer of the automobile according to the operation step in S8.
Further, according to the operation step in S2032: the contribution of each variable of the SPE score map to the SPE statistics is:
CSPE,ijk＝e2 ijkgX2 h。
expressed as: for the kth time, the contribution of variable j of the ith batch to SPE
T2Score chart variable pairs T2The contribution of the statistics is:
expressed as: for the kth time, the variable j of the ith batch is paired with T2The contribution of (c).
Further, according to the operation step in S3, the offline model building process:
1) and preprocessing data required by modeling to obtain a corresponding process variable X and a corresponding quality variable Y.
2) And establishing a PLS model and calculating T, P, W, U, Q.
3) And calculating a regression coefficient according to the model solution.
4) And calculating a corresponding covariance matrix and a residual error matrix.
5) Calculating T2And SPE statistics and determining control limits thereof.
Further, according to the operation step in S3, the online model building process:
1) obtaining new batch data and comparing variable data xnew,k(I x J) is normalized using the mean of the time instants of the off-line module k and their shore offsets.
2) Using the mean and variance of the training data for x according to the model establishednew,kA time k score vector is calculated.
3) Calculating xnew,kAnd residual enew,k。
4) Calculating T at time k2And SPE statistics.
5) And examination T2And whether the SPE statistics exceed respective control limits, if so, indicating that the fault exists, and determining a fault source according to the score map.
6) And repeating the steps 1) to 5) until the technological process of the new batch is finished.
The invention provides a process industrial fault detection and prediction method based on PLS analysis. The method has the following beneficial effects:
the PLS method converts a multiple regression problem into a unitary regression problem by orthogonal projection, effectively solves the problem of collinearity, and the PLS method not only can improve the accuracy of the model, but also can extract the nonlinear action characteristics of independent variables on dependent variables from the established model by mapping high-dimensional data into low-dimensional data to obtain characteristic vectors of mutually orthogonal measured variables and then establishing a linear regression relationship among the vectors to characterize the process, thereby greatly improving the accuracy of analysis compared with the traditional analysis means.
Drawings
FIG. 1 is a flow chart of the offline model building and online modeling of the present invention.
Detailed Description
The invention provides a technical scheme that: a process industry fault detection and prediction method based on PLS analysis comprises the following specific implementation steps:
the method comprises the following steps: determining the PLS pivot number, wherein the pivot number is relatively small according to actual conditions, the first pivot numbers represent the whole model, the pivot number determination effect is best by adopting a cross-validation method because the pivot number determination is carried out through both detection and prediction and experiments, wherein the number of grouped samples and the combination sequence of the samples can influence the test result of the model, one sample is reserved as a test sample each time, the rest samples are circulated once, and each dependent variable y is subjected to cyclekDefining:
for all dependent variables Y, the component thThe cross validity of (c) is defined as:
when Q is2 h≥(1-0.95)2The marginal contribution of the ingredient is significant when 0.00975, with at least one k for k 1,2,3hk0.00975, the composition is increased by at least one dependent variable ykThe prediction model of (2) is significantly improved.
Step two: a PLS multivariate statistical process detection graph,
s201, when a fault occurs, one or more measured variables will be affected, thereby affecting the relationship between the variables.
S202, the model decomposes the monitoring variable into two subspaces, T, which are related to and unrelated to the quality variable2For monitoring faults occurring in subspaces associated with the quality variable, and SPE statistics for monitoring faults occurring in subspaces not associated with the quality variable.
S203, if T2And SPE is in the control limit of calculation, the result is indicated to run normally, and if T is reached2If the SPE exceeds the control limit, a fault unrelated to the parameter matrix occurs.
Setting the sampling batch number as I, and obtaining a score matrix at the time k:
TR,K＝[tI1,K,tI2,K,...,tIR,K]。
the covariance matrix is:
s2031, passing T2Judging the abnormal condition of the system by statistic and SPE statistic, T2The statistic is the standard sum of squares of the score vectors, representing the degree to which each sample data deviates from the model in both trend and magnitude, T, for the kth sampling instant2The statistics are represented as:
T2the statistic obeys F distribution, so by setting control limits:
±S(r,r)F(R,I-R)r＝1,2,...,R。
wherein S (r, r) is SKDiagonal elements of (a).
The value of the SPE statistic at time k is a scalar quantity representing the measured value x at that momentkThe degree of deviation from the statistical model created is a measure of the variation of the data outside the model. For the k-th sampling instant, the value is calculated by:
SPEK＝enem,keT new,k。
enew,k＝xnew,k(I-PPT)；
wherein x isnew,k(k 1, 2.., k) measurement data for the new batch time k.
S2032, making each process variable pair SPE statistic and T2Calculating the score of the statistic to construct a score matrix, drawing the score matrix into a histogram, judging the fault source of the system according to the numerical value and the trend of the histogram, wherein the contribution of each variable of the SPE score map to the SPE statistic is as follows:
CSPE,ijk＝e2 ijkgX2 h。
expressed as: for the kth time, the contribution of variable j of the ith batch to SPE
T2Score chart variable pairs T2The contribution of the statistics is:
expressed as: for the kth time, the variable j of the ith batch is paired with T2The contribution of (c).
Step three: based on the PLS process analysis steps, adopting batch data under normal working conditions to establish a model database, and calculating T2And limiting the control of SPE statistic, then performing an offline model building process and an online model building process, wherein the offline model building process comprises the following steps: 1) preprocessing data required by modeling to obtain corresponding process variable X and quality variable Y, 2), establishing a PLS model, calculating T, P, W, U, Q, 3), calculating regression coefficients according to model solutions, 4), calculating corresponding covariance matrix and residual matrix, 5), and calculating T2SPE statistics and control limit determination, online model construction flow: 1) obtaining new batch data and comparing variable data xnew,k(I J) using the mean value of the off-line module at time k and its shore tolerance for normalization, 2) using the mean value and variance of the training data for x according to the model builtnew,kCalculate k time score vector, 3), calculate xnew,kAnd residual enew,k4), calculating time kT2SPE statistics, 5), check T2And judging whether the SPE statistics exceed respective control limits, if so, determining a fault, and determining a fault source according to a score map, 6), and repeating the steps 1) to 5) until the technological process of the new batch is finished.
The PLS method converts a multiple regression problem into a unitary regression problem by orthogonal projection, effectively solves the problem of collinearity, and the PLS method not only can improve the accuracy of the model, but also can extract the nonlinear action characteristics of independent variables on dependent variables from the established model by mapping high-dimensional data into low-dimensional data to obtain characteristic vectors of mutually orthogonal measured variables and then establishing a linear regression relationship among the vectors to characterize the process, thereby greatly improving the accuracy of analysis compared with the traditional analysis means.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the inventive concept of the present invention, and these changes and modifications are all within the scope of the present invention.
Claims (7)
1. A process industry fault detection and prediction method based on PLS analysis is characterized by comprising the following steps:
s1, determining the number of PLS pivot elements, selecting the first pivot elements to represent the whole model, determining the number of the pivot elements by adopting a cross-validation method, reserving one sample as a test sample each time, circulating the rest samples once,
for each dependent variable ykDefining:
for all dependent variables Y, the component thThe cross validity of (c) is defined as:
s2 PLS multivariate statistical Process detection map
S201, when a fault occurs, one or more measured variables are influenced, and therefore the relation among the variables is influenced;
s202, the model decomposes a monitoring variable into two subspaces which are related to and unrelated to the quality variable, T2 is used for monitoring faults occurring in the subspaces related to the quality variable, and SPE statistics are used for monitoring faults occurring in the subspaces unrelated to the quality variable;
s203, if T2The SPE and the SPE are both in the calculated control limit, the result is indicated to be normal operation, if T2 exceeds the control limit, a fault related to the parameter matrix occurs, and if the SPE exceeds the control limit, a fault unrelated to the parameter matrix occurs;
setting the sampling batch number as I, and obtaining a score matrix at the time k:
TR,K＝[tI1,K,tI2,K,...,tIR,K]；
the covariance matrix is:
s3, based on the PLS process analysis step, adopting batch data under normal working conditions to establish a model database, and calculating T2And limiting the control of the SPE statistic, and then performing an off-line model building process and an on-line model building process.
2. The method for flow industrial fault detection and prediction based on PLS analysis of claim 1, comprising the steps of: will be according to the operation procedure in S1 when Q is2 h≥(1-0.95)2The marginal contribution of the ingredient is significant when 0.00975, with at least one k for k 1,2,3hk0.00975, the composition is increased by at least one dependent variable ykThe prediction model of (2) is significantly improved.
3. The method for flow industrial fault detection and prediction based on PLS analysis of claim 1, wherein the steps according to S203 comprise the following steps:
s2031, judging the abnormal condition of the system through the T2 statistic and the SPE statistic;
s2032, calculating the scores of the SPE statistic and the T2 statistic by each process variable, thereby constructing a score matrix, drawing a histogram, and judging the fault source of the system according to the value and the trend of the histogram.
4. The method for flow industrial fault detection and prediction based on PLS analysis of claim 3, comprising the steps of: will follow the operation in S2031: the T2 statistic is the standard sum of squares of the score vectors, representing the degree to which each sample data deviates from the model in both trend and magnitude, and for the kth sampling instant, the T2 statistic is expressed as:
the T2 statistic follows the F distribution, so by setting control limits:
±S(r,r)F(R,I-R)r＝1,2,...,R；
wherein S (r, r) is SKA diagonal element of (a);
the value of the SPE statistic at time k is a scalar quantity representing the measured value x at that momentkThe degree of deviation of the statistical model created is a measure of the change in the data outside the model, and for the kth sampling instant, the value is calculated as:
enew,k＝xnew,k(I-PPT)；
wherein x isnew,k(k 1, 2.., k) measurement data for the new batch time k.
5. The method for flow industrial fault detection and prediction based on PLS analysis of claim 2, comprising the steps of: will follow the operation in S2032: the contribution of each variable of the SPE score map to the SPE statistics is:
CSPE,ijk＝e2 ijkgX2 h；
expressed as: for the kth moment, the contribution of the variable j of the ith batch to the SPE;
T2score chart variable pairs T2The contribution of the statistics is:
expressed as: for the kth time, the variable j of the ith batch is paired with T2The contribution of (c).
6. The method for flow industrial fault detection and prediction based on PLS analysis of claim 1, comprising the steps of: the offline model building process will be according to the operation steps in S3:
1) preprocessing data required by modeling to obtain a corresponding process variable X and a corresponding quality variable Y;
2) establishing a PLS model, and calculating T, P, W, U, Q;
3) calculating a regression coefficient according to the model solution;
4) calculating a corresponding covariance matrix and a residual error matrix;
5) calculating T2And SPE statistics and determining control limits thereof.
7. The method for flow industrial fault detection and prediction based on PLS analysis of claim 1, comprising the steps of: the online model building process will be according to the operation steps in S3:
1) obtaining new batch data and comparing variable data xnew,k(I x J) using the average of time k of the off-line module and its shore tolerance for normalization;
2) using the mean and variance of the training data for x according to the model establishednew,kCalculating a score vector at the k moment;
3) calculating xnew,kAnd residual enew,k；
4) Calculating T at time k2SPE statistics;
5) and examination T2Whether the SPE statistics exceed respective control limits or not, if yes, indicating that the fault exists, and determining a fault source according to the score map;
6) and repeating the steps 1) to 5) until the technological process of the new batch is finished.
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