CN104062968A - Continuous chemical process fault detection method - Google Patents

Abstract

The invention relates to a continuous chemical process fault detection method. The continuous chemical process fault detection method comprises the following steps that (1) a linear regression model of a vector Xj and a vector Y is built, and a regression constraint function is introduced; (2) data compression is carried out through haar wavelet transformation to improve computational efficiency; (3) a regression constraint construction sparse pivot element model with the addition of 1-norm and 2-norm is built, and an optimal solution of a sparse pivot element is worked out through derivation of the SPCA algorithm; (4) the optimal threshold value of the T2 statistic and the optimal threshold value of the SPE statistic are estimated through the kernel density estimation (kde) method; (5) calculation of the T2 statistic and the SPE statistic is conducted on fault data, and the value of the T2 statistic and the value of the SPE statistic of the fault data are obtained in sequence; (6) whether a fault exists in the data is detected. According to the continuous chemical process fault detection method, the data size related to a pivot element after sparsity is reduced, so that the calculated quantity is reduced, the computation time is shortened, real-time performance of monitoring is improved, and accuracy and efficiency of fault detection can be improved.

Description

A kind of chemical industry procedure failure testing method continuously

Technical field

The present invention relates to Intelligent Information Processing field, especially relate to a kind of chemical industry procedure failure testing method continuously.

Background technology

Along with controlling the progress of the reach of science and industrial technology, productive capacity and the modernization level of industrial system improve day by day, also becoming increasingly complex thereupon of production technology, production equipment and production run.Meanwhile, the Potential feasibility that these complicated systems break down also improves accordingly, and the seriousness of fault also can be along with the complexity of system significantly increases, once there is fault, will cause very large personnel and property loss so.So how Real-Time Monitoring production run and fault is detected in advance and just seems particularly important.Only carry out effective process monitoring, just can guarantee the quality of production safety and raising product.

Four steps of process monitoring are that fault detect, Fault Identification, fault diagnosis and process are recovered.By the method for pattern-recognition, lay particular emphasis on by fault detect out.Fault detect, popular says, determines exactly whether fault has occurred.Detect in time and can, to the problem there will be is proposed to valuable warning, by taking appropriate measures, avoid serious process to overturn.

Traditional fault detection method mainly contains detection method, the method based on data-driven and the method based on priori based on model.Wherein the method based on data-driven is to utilize statistical thinking, to the data analysis producing in production run, first in normal data, tests, then is applied to the monitoring to production process data.In the method for data-driven, PCA detection method is a kind of detection method of classics, is widely used in production practices.But PCA detection method also has its limitation, PCA method has two Utopian results: the one, and the maximum that pivot can embody data changes, and information loss is minimum; The 2nd, between pivot, be independently, a pivot is uncorrelated with other pivots.Obtaining of the above results is because the detection method of PCA hypothesis process data is linear Gauss, in the case, chooses pivot can obtain good result according to variance contribution ratio.But in large-scale industrial processes, tend to exist various process variable in system, can not meet linear Gauss's hypothesis completely, often calculated amount is very large for traditional PCA detection method in addition, has affected the actual effect of counting yield and process monitoring.

Summary of the invention

The object of the invention is to the deficiency existing in existing method, a kind of chemical industry procedure failure testing method is continuously proposed, by introducing the thought of sparse pivot, traditional dimensionality reduction problem is converted into recurrence optimization problem, improve the precision of detection and the efficiency of detection with this.The method is detected for continuous chemical industry procedure fault, can improve the precision of detection.

Object of the present invention can be achieved through the following technical solutions:

A kind of chemical industry procedure failure testing method continuously, the method comprises the following steps:

1) from Tennessee-Yi Siman industrial process model, obtain normal data and fault data, using normal data as training data, using fault data as test data, and the test data obtaining is carried out to standardization;

2) training data is carried out to wavelet transformation, packed data;

3) introduce, with the recurrence constraint function of 1-norm and 2-norm, training data is returned to calculating, utilize rarefaction principle component analysis to calculate the load vector of rarefaction;

4) T of the training data of calculating after small echo changes ²statistic and SPE statistic;

5) method of utilizing probability density to estimate is tried to achieve T ²threshold value with SPE statistic;

6) according to step 3), 4) test data of carrying out after small echo variation is calculated to corresponding T ²with SPE statistic, judge whether test data exists fault:

When using T ²when statistic detects, if the T trying to achieve ²the value of statistic is greater than its corresponding threshold value, and corresponding one group of data exist fault; If the T trying to achieve ²the value of statistic is less than its corresponding threshold value, and corresponding one group of data are normal;

In the time using SPE statistic to detect, if the value of the SPE statistic of trying to achieve is greater than its corresponding threshold value, there is fault in corresponding one group of data; If the value of the SPE statistic of trying to achieve is less than its corresponding threshold value, corresponding one group of data are normal.

Step 1) in, described standardization adopts Z-score standardized method, and computing formula is:

$X^{*}=\frac{X-\mathrm{\μ}}{\mathrm{\σ}}$

In formula, X={x ₁, x ₂..., x _nbe data matrix, X ^*represent the data matrix after standardization, the average that μ is training data, the standard deviation that σ is training data, μ and σ computing formula are:

$\mathrm{\μ}=\frac{1}{n}{\mathrm{\Σ}}_{i=1}^n{x}_i$

$\mathrm{\σ}={\left[\frac{1}{n-1}{\mathrm{\Σ}}_{i=1}^n{(x_i-\mathrm{\μ})}^2\right]}^{\frac{1}{2}}$

Step 2) in, described wavelet transformation is haar wavelet transformation.

Described step 3) be specially:

301) establish current sample data and integrate as X, pivot load vector is α _k, sample data collection variance matrix is:

${\mathrm{\α}}_k^T\left(X^{T}X\right){\mathrm{\α}}_k$

It meets constraint condition:

${\mathrm{\&alpha;}}_k^T{\mathrm{\&alpha;}}_k=1(k\&GreaterEqual;2),{\mathrm{\&alpha;}}_h^T{\mathrm{\&alpha;}}_k=0(h<k)$

Definition t is that sparse property regulates parameter, has:

$\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&alpha;}}_{k,j}\right|\&le;t$

Suppose that Y is the pivot matrix of sample data, Y _jfor the column vector of Y, be j pivot, if there is parameter lambda > 0, return and be estimated as:

$\widehat{\mathrm{\&beta;}}=\arg \underset{\mathrm{\&beta;}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{X}_j{\mathrm{\&beta;}}_j|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&beta;}}_j\right|$

Wherein, parameter lambda is for returning constrained parameters, β _jfor corresponding regression coefficient vector;

302) introduce other non-negative parameter lambda ₁, above formula expansion is obtained to following optimization problem:

$\widehat{\mathrm{\&beta;}}=\arg \underset{\mathrm{\&beta;}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{X}_j{\mathrm{\&beta;}}_j|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2+{\mathrm{\&lambda;}}_1{\left|\right|{\mathrm{\&beta;}}_j\left|\right|}_1$

Wherein, ${\left|\right|{\mathrm{\&beta;}}_j\left|\right|}_1={\mathrm{\&Sigma;}}_{j=1}^p\left|{\mathrm{\&beta;}}_j\right|$ It is the 1-norm of β;

Try to achieve after, the related coefficient V of calculating constraint function _j:

$V_j=\frac{{\widehat{\mathrm{\&beta;}}}_j}{\left|{\widehat{\mathrm{\&beta;}}}_j\right|}$

XV _jbe j pivot;

303) choose front k pivot in pivot matrix, definition α and β are parameter matrix, and dimension is all p × k, X _ifor the row vector of X, β _jfor the column vector of β, if there is parameter lambda > 0, and α ^tα=I _k, consider elastic network(s) constraint simultaneously:

$(\widehat{\mathrm{\&alpha;}},\widehat{\mathrm{\&beta;}})=\arg \underset{\mathrm{\&alpha;},\mathrm{\&beta;}}{\min }\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{|X_i-\mathrm{\&alpha;}{\mathrm{\&beta;}}^T{X}_i|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2+\underset{k=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_{1,j}\left|{\mathrm{\&beta;}}_j\right|$

Wherein, λ _{1, j}the λ of corresponding j pivot ₁value, j=1,2..., k;

304) utilize the β after the convergence of finally trying to achieve to be normalized, and solve a final k pivot, obtain the load vector of rarefaction:

P _j≈XV _j＝Xβ _j/|β _j|(j＝1，2，…k)

Step 4) in, T ²the computing formula of statistic is:

T ²＝X ^TV(∑ ^T∑) ^-1V ^TX

Wherein, V is the covariance matrix ∑=X of sample ^tx carries out orthogonal vector after svd, and X is sample data collection;

The computing formula of SPE statistic is:

SPE＝[(I-PP ^T)X] ^T(I-PP ^T)X

The matrix of loadings of the load vector composition that wherein, P is rarefaction.

Step 5) in, described probability density method of estimation adopts Parzen window method, i.e. kernel probability density estimation method.

Compared with prior art, the present invention has the following advantages.

1) the present invention utilizes statistical thinking, a kind of continuous chemical industry procedure failure testing method has been proposed, on the basis of PCA detection technique, introduce the thought of sparse pivot, utilize a recurrence constraint function with 1-norm and 2-norm to build sparse principal component model, utilize statistical thinking, dimensionality reduction thinking conventional in fault detect is converted into recurrence optimization problem.By restriction load the nonzero coefficient in vector number so that try to achieve sparse load vector.Be different from according to variance contribution ratio and choose pivot, sparse pivot analysis is to obtain pivot by the load number of the nonzero element in vector of restriction.Sparse pivot analysis has better utilized the characteristic of process data itself, rarefaction representation by process data self is chosen pivot, break through original mode of choosing pivot by variance contribution ratio, be more applicable to continuous chemical process, and can obtain better fault detect effect.

2) the present invention is applied in continuous chemical industry procedure fault detection, can improve the accuracy of detection.Carry out data analysis by relatively traditional PCA method, analysis result shows that the present invention effectively reduces error rate and the loss of fault detect.

3) the present invention, in the time that process data is carried out to pre-service, carries out wavelet transformation by haar small echo to data, both can reach the effect of the denoising to data, also can amount of compressed data, and reduce the calculated amount detecting and then improve the efficiency detecting.

4) the inventive method has utilized the method for kernel probability density estimation to solve T ²with the threshold value of SPE statistic, the threshold value of obtaining can reflect the criterion of normal data more.

Brief description of the drawings

Fig. 1 is TEP process process flow diagram;

Fig. 2 is the overall procedure block diagram of the inventive method;

Fig. 3 is the T based on continuous chemical industry procedure fault Class1 3 that adopts traditional PCA technology ²the testing result figure of statistic detection and SPE statistic;

Fig. 4 adopts the testing result figure based on continuous chemical industry procedure fault Class1 3 of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment is implemented as prerequisite taking technical solution of the present invention, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Carrying out in the process of fault detect, the data of utilizing are the data that gather in Tennessee-Yi Siman (TEP) process model.TEP process model is created by Yisiman Chemical Company, and its object is exactly to provide a real industrial process for evaluation procedure control and method for supervising.Test process is based on a true chemical industry industrial process continuously, and composition wherein, dynamics, service condition etc. are because the problem of patent right has all been done amendment.Process comprises five formants: reactor, condenser, compressor, separation vessel and stripping tower; And comprise eight kinds of composition: A, B, C, D, E, F, G and H.Fig. 1 is the process chart of this commercial unit.

The process model of Tennessee-Yi Siman problem comprises 21 faults that preset.In these faults, 16 is known, and 5 is unknown.Fault 1-7 is relevant with the step variation of process variable, as, the variation of cold water inlet temperature or charging composition.Fault 8-12 increases relevant with the changeability of some process variable.Fault 13 is the slow drifts in reaction kinetics, and fault 14,15 is relevant with sticking valve with 21.As shown in table 1 is the procedure fault description of Tennessee-Yi Siman process model.

Table 1: procedure fault is described

As shown in Figure 2, a kind of chemical industry procedure failure testing method continuously, step comprises:

Step 1, build vectorial X _jwith the linear regression model (LRM) of Y, introduce and return constraint function.

Step 1.1, from Tennessee-Yi Siman (TEP) industrial process model, obtain continuous chemical industry procedure fault data.Obtain a sample matrix X (p × n), the hits that wherein n is sample, the number that p is observation data.Choose arbitrarily X _jrelevant pivot column vector, is defined as Y:

Y＝(y ₁，y ₂，…y _n) ^T

P different observed readings:

X _j＝(x _1j，x _2j，…，x _nj) ^T，j＝1，2，…P

X _jthe linear regression constraint function relevant with Y, its least estimated formula is as follows:

$\widehat{\mathrm{\&beta;}}=\arg \underset{\mathrm{\&beta;}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{X}_j{\mathrm{\&beta;}}_j|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&beta;}}_j\right|$

In formula, λ is non-negative parameter, β _jfor corresponding regression coefficient vector.

Step 1.2, from Tennessee-Yi Siman (TEP) process model, obtain normal data and fault data, wherein normal data is as training data, and fault data is as test data.

Step 2, test data is carried out to standardization, wherein in the time of standardization, all take from training set as the average of subtrahend with as the standard deviation of divisor.

The method of step 2.1, data normalization, adopts Z-score standardization, also referred to as standard deviation standardization.

$X^{*}=\frac{X-\mathrm{\&mu;}}{\mathrm{\&sigma;}}$

In formula, X represents test data matrix, and μ is the average of taking from training data.

$\mathrm{\&mu;}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i$

σ is the standard deviation of taking from training data;

$\mathrm{\&sigma;}={\left[\frac{1}{n-1}{\mathrm{\&Sigma;}}_{i=1}^n{(x_i-\mathrm{\&mu;})}^2\right]}^{\frac{1}{2}}$

Step 2.2, data after Z-score standardization, data fit standardized normal distribution, average is 0, standard deviation is 1.

Step 3, normal data is done to small echo change, it is for amount of compressed data that this method is used wavelet transform process data, raises the efficiency.Here select haar wavelet transformation.

Female small echo (mother wavelet) of step 3.1, haar small echo can be expressed as:

And corresponding convergent-divergent equation can be expressed as:

Its wave filter h[n] be defined as:

Step 4, will be applied in principal component model with the lasso constraint function of 1-norm and 2-norm, obtain the restrictive algorithm of sparse pivot.

Step 4.1, suppose that pivot now load vector is α _k, sample data integrates as X, and its variance matrix is:

${\mathrm{\&alpha;}}_k^T\left(X^{T}X\right){\mathrm{\&alpha;}}_k$

Meeting constraint condition is:

${\mathrm{\&alpha;}}_k^T{\mathrm{\&alpha;}}_k=1(k\&GreaterEqual;2),{\mathrm{\&alpha;}}_h^T{\mathrm{\&alpha;}}_k=0(h<k)$

Definition t is that sparse property regulates parameter, has:

$\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&alpha;}}_{k,j}\right|\&le;t$

In the time that t reduces, more load vector coefficient will converge to 0, so the size of t value has influence on the sparse degree of pivot.

SPCA is based upon on the basis of pivot analysis (PCA), supposes that Y is the pivot matrix of sample data, Y _jfor the column vector of Y, be j pivot, if there is parameter lambda > 0, return and be estimated as:

$\widehat{\mathrm{\&beta;}}=\arg \underset{\mathrm{\&beta;}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{X}_j{\mathrm{\&beta;}}_j|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&beta;}}_j\right|$

Wherein, parameter lambda is the constrained parameters in regretional analysis, and can be used for the reconstruct of pivot.

Step 4.2, on the basis of the recurrence constraint of step 4.1, introduce again other non-negative parameter lambda ₁, above formula expansion is obtained to following optimization problem:

$\widehat{\mathrm{\&beta;}}=\arg \underset{\mathrm{\&beta;}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{X}_j{\mathrm{\&beta;}}_j|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2+{\mathrm{\&lambda;}}_1{\left|\right|{\mathrm{\&beta;}}_j\left|\right|}_1$

Here ${\left|\right|{\mathrm{\&beta;}}_j\left|\right|}_1={\mathrm{\&Sigma;}}_{j=1}^p\left|{\mathrm{\&beta;}}_j\right|$ It is the 1-norm of β.

Try to achieve after, the related coefficient V of calculating constraint function _j:

$V_j=\frac{{\widehat{\mathrm{\&beta;}}}_j}{\left|{\widehat{\mathrm{\&beta;}}}_j\right|}$

XV _jbe exactly j pivot.The extraction algorithm of pivot that Here it is.

Step 4.3, choose front k pivot of sample, wherein α and β are parameter matrix, and dimension is all p × k, X _ifor the row vector of X, β _jfor the column vector of β, if there is parameter lambda > 0, and α ^tα=I _k:

$(\widehat{\mathrm{\&alpha;}},\widehat{\mathrm{\&beta;}})=\arg \underset{\mathrm{\&alpha;},\mathrm{\&beta;}}{\min }\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{|X_i-\mathrm{\&alpha;}{\mathrm{\&beta;}}^T{X}_i|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2$

The Solve problems of k pivot is converted into linear regression problem, sets the objective function returning as follows:

$x=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{|X_i-\mathrm{\&alpha;}{\mathrm{\&beta;}}^T{X}_i|}^2$

If make β=α, it is PCA method.

If in formula

$(\widehat{\mathrm{\&alpha;}},\widehat{\mathrm{\&beta;}})=\arg \underset{\mathrm{\&alpha;},\mathrm{\&beta;}}{\min }\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{|X_i-\mathrm{\&alpha;}{\mathrm{\&beta;}}^T{X}_i|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2$

Basis on consider elastic network(s) constrained procedure, can obtain:

Work as α ^tα=I _ktime

$(\widehat{\mathrm{\&alpha;}},\widehat{\mathrm{\&beta;}})=\arg \underset{\mathrm{\&alpha;},\mathrm{\&beta;}}{\min }\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{|X_i-\mathrm{\&alpha;}{\mathrm{\&beta;}}^T{X}_i|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2+\underset{k=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_{1,j}\left|{\mathrm{\&beta;}}_j\right|$

Wherein, λ _{1, j}corresponding k different λ ₁value.

The solution procedure of the optimum solution of rarefaction is as follows:

(1) solve k pivot of sample matrix, the initial value of parameter matrix α is V _i(i=1: k).

(2) for fixing α value, in parameter j=1,2 ... when k, another parameter beta of compute sparse constraint:

${\mathrm{\&beta;}}_j=\arg \underset{\mathrm{\&beta;}}{\min }{({\mathrm{\&alpha;}}_j-\mathrm{\&beta;})}^T{X}^{T}X({\mathrm{\&alpha;}}_j-\mathrm{\&beta;})+\mathrm{\&lambda;}{\left|\right|\mathrm{\&beta;}\left|\right|}^2+{\mathrm{\&lambda;}}_{1,j}{\left|\right|\mathrm{\&beta;}\left|\right|}_1$

(3) solve after parameter beta, solve now corresponding parameter alpha.β value is carried out to svd, has:

X ^TXβ＝UDV ^T

(4) repeat above two steps, undated parameter α and parameter beta repeatedly, until β convergence.

(5) utilize the final β after convergence to be normalized, and solve a final k pivot, obtain sparse optimum solution, i.e. the load vector of rarefaction:

P _j≈xV _j＝xβ _j/|β _j|(j＝1，2，…k)

Step 5, solve normal data (training data) each group data calculate T ²statistic or SPE statistic.

Wherein T ²the computing formula of statistic is:

T ²＝X ^TV(∑ ^T∑) ^-1V ^TX

Wherein V is sample covariance matrix ∑=X ^tx carries out orthogonal vector after svd.

The computing formula of SPE statistic is:

SPE＝[(I-PP ^T)X] ^T(I-PP ^T)X

The matrix of the load vector composition that wherein P is rarefaction.

Step 6, for each group data corresponding T of normal data ²statistic or SPE statistics value, the method for utilizing probability density to estimate is obtained the threshold line of normal data, using this as the standard that judges that whether normal data are.

The method that probability density is estimated: have " Parzen window method " and k _n-nearest neighbour method.This method is used Parzen window method, claims again kernel probability density estimation method (KDE).

Parzen window method: according to some definite volume functions, such as shrink gradually a given initial space.This just requires stochastic variable k _nwith can ensure P _n(x) can converge to P (x).

To different T ²statistic and SPE statistic are done probability density estimation, finally obtain respectively a T ²statistic and SPE statistic are as the standard value of normal data, i.e. threshold value.

Step 7, fault data is detected, according to the formula of step 6, obtain respectively every group of fault data T ²statistic and SPE statistic, then utilize threshold line to detect data:

When using T ²when statistic detects, if the T trying to achieve ²the value of statistic is greater than its corresponding threshold value, and corresponding one group of data exist fault; If the T trying to achieve ²the value of statistic is less than its corresponding threshold value, and corresponding one group of data are normal;

In the time using SPE statistic to detect, if the value of the SPE statistic of trying to achieve is greater than its corresponding threshold value, there is fault in corresponding one group of data; If the value of the SPE statistic of trying to achieve is less than its corresponding threshold value, corresponding one group of data are normal.

In example, training data has 500 groups of data, and every group of data have 52 observed readings.Test data one has 960 groups of data, and every group of test data contains 52 observed readings, and wherein front 160 groups of data are normal data, and then 800 groups of data are fault data.

In order to embody a kind of chemical industry procedure failure testing method superiority continuously, itself and the traditional detection technique of utilizing PCA technology are compared.

When tradition utilizes PCA to carry out fault detect, be all to utilize T ²with these two statistics of SPE, fault is detected.Wherein T ²statistic is used for multivariable process data to carry out fault detect.A given observation vector x also supposes ∧=∑ ^t∑ is reversible, T ²statistic can directly calculate by PCA expression formula:

T ²＝X ^TV(∑ ^T∑) ^-1V ^Tx

And T2 statistic threshold value can be expressed as:

$T_a^2=\frac{a(n-1)(n+1)}{n(n-a)}{F}_a(a,n-a)$

SPE is square prediction error, be 2-norm square, claim again Q statistic.Be used for measuring the deviation that observed reading represents with respect to low-dimensional PCA, Q statistic can be expressed as:

Q＝[(I-PP ^T)x] ^T(I-PP ^T)x

Here P is matrix of loadings.

And SPE statistic threshold value can be expressed as:

$Q_a={\mathrm{\&theta;}}_1{[\frac{h_0{c}_a\sqrt{2{\mathrm{\&theta;}}_2}}{{\mathrm{\&theta;}}_1}+1+\frac{{\mathrm{\&theta;}}_2{h}_0(h_0-1)}{{\mathrm{\&theta;}}_1^2}]}^{1/h_0}$

Here c _abe and (1-α) standard deviation that quantile is corresponding.

It is exactly the threshold value of trying to achieve respectively T2 statistic and SPE statistic in present normal data with the basic thought that PCA method detects fault, then fault data is asked respectively to T2 statistic and SPE statistic, be judged to normally lower than the data of threshold line, the data that exceed threshold line are judged to fault data.Whole process is all carried out simulation study based on TEP process, and the step of process monitoring is as follows:

Step 1, concentrate and obtain sampled data from TEP process data, and carry out standardization by the average of normal condition drag and variance, obtain normal data and the fault data of every kind of fault type;

Step 2, normal data is carried out to the conversion of PCA dimensionality reduction, obtain matrix of loadings;

Step 3, calculate the T of normal data ²the threshold value of statistic and SPE statistic;

The T of step 4, calculating fault data ²statistic and SPE statistic;

The T of step 5, supervision fault data ²the whether paranormal threshold line of statistic and SPE statistic;

We choose fault type 13 and provide the result of fault detect, utilize respectively the method for PCA and SPCA to detect, and respectively as shown in Figure 3,4, as shown in table 2 is PCA method testing result to analysis result data figure, the testing result that table 3 is the inventive method.

Table 2: error rate and loss that the PCA based on continuous chemical industry procedure fault Class1 3 detects

Table 3: error rate and loss that the SPCA based on continuous chemical industry procedure fault Class1 3 detects

By the data results of example, can find out that a kind of continuous chemical industry procedure failure testing method utilizes the method for dimensionality reduction, on different dimensions, testing result is different, and the testing result in some dimensions is better than the detection method of PCA.

Claims (6)

1. a continuous chemical industry procedure failure testing method, is characterized in that, the method comprises the following steps:

1) from Tennessee-Yi Siman industrial process model, obtain normal data and fault data, using normal data as training data, using fault data as test data, and the test data obtaining is carried out to standardization;

2) training data is carried out to wavelet transformation, packed data;

3) introduce, with the recurrence constraint function of 1-norm and 2-norm, training data is returned to calculating, utilize rarefaction principle component analysis to calculate the load vector of rarefaction;

4) T of the training data of calculating after small echo changes ²statistic and SPE statistic;

5) method of utilizing probability density to estimate is tried to achieve T ²threshold value with SPE statistic;

6) according to step 3), 4) test data of carrying out after small echo variation is calculated to corresponding T ²with SPE statistic, judge whether test data exists fault:

When using T ²when statistic detects, if the T trying to achieve ²the value of statistic is greater than its corresponding threshold value, and corresponding one group of data exist fault; If the T trying to achieve ²the value of statistic is less than its corresponding threshold value, and corresponding one group of data are normal;

In the time using SPE statistic to detect, if the value of the SPE statistic of trying to achieve is greater than its corresponding threshold value, there is fault in corresponding one group of data; If the value of the SPE statistic of trying to achieve is less than its corresponding threshold value, corresponding one group of data are normal.

2. the continuous chemical industry procedure failure testing method of one according to claim 1, is characterized in that step 1) in, described standardization adopts Z-score standardized method, and computing formula is:

$X^{*}=\frac{X-\mathrm{\&mu;}}{\mathrm{\&sigma;}}$

In formula, X={x ₁, x ₂..., x _nbe data matrix, X ^*represent the data matrix after standardization, the average that μ is training data, the standard deviation that σ is training data, μ and σ computing formula are:

$\mathrm{\&mu;}=\frac{1}{n}{\mathrm{\&Sigma;}}_{i=1}^n{x}_i$

$\mathrm{\&sigma;}={\left[\frac{1}{n-1}{\mathrm{\&Sigma;}}_{i=1}^n{(x_i-\mathrm{\&mu;})}^2\right]}^{\frac{1}{2}}$

。

3. the continuous chemical industry procedure failure testing method of one according to claim 1, is characterized in that step 2) in, described wavelet transformation is haar wavelet transformation.

4. the continuous chemical industry procedure failure testing method of one according to claim 1, is characterized in that described step 3) be specially:

301) establish current sample data and integrate as X, pivot load vector is α _k, sample data collection variance matrix is:

${\mathrm{\&alpha;}}_k^T\left(X^{T}X\right){\mathrm{\&alpha;}}_k$

It meets constraint condition:

${\mathrm{\&alpha;}}_k^T{\mathrm{\&alpha;}}_k=1(k\&GreaterEqual;2),{\mathrm{\&alpha;}}_h^T{\mathrm{\&alpha;}}_k=0(h<k)$

Definition t is that sparse property regulates parameter, has:

$\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&alpha;}}_{k,j}\right|\&le;t$

Suppose that Y is the pivot matrix of sample data, Y _jfor the column vector of Y, be j pivot, if there is parameter lambda > 0, return and be estimated as:

$\widehat{\mathrm{\&beta;}}=\arg \underset{\mathrm{\&beta;}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{X}_j{\mathrm{\&beta;}}_j|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&beta;}}_j\right|$

Wherein, parameter lambda is for returning constrained parameters, β _jfor corresponding regression coefficient vector;

302) introduce other non-negative parameter lambda ₁, above formula expansion is obtained to following optimization problem:

$\widehat{\mathrm{\&beta;}}=\arg \underset{\mathrm{\&beta;}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{X}_j{\mathrm{\&beta;}}_j|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2+{\mathrm{\&lambda;}}_1{\left|\right|{\mathrm{\&beta;}}_j\left|\right|}_1$

Wherein, ${\left|\right|{\mathrm{\&beta;}}_j\left|\right|}_1={\mathrm{\&Sigma;}}_{j=1}^p\left|{\mathrm{\&beta;}}_j\right|$ It is the 1-norm of β;

Try to achieve after, the related coefficient V of calculating constraint function _j:

$V_j=\frac{{\widehat{\mathrm{\&beta;}}}_j}{\left|{\widehat{\mathrm{\&beta;}}}_j\right|}$

XV _jbe j pivot;

303) choose front k pivot in pivot matrix, definition α and β are parameter matrix, and dimension is all p × k, X _ifor the row vector of X, β _jfor the column vector of β, if there is parameter lambda > 0, and α ^tα=I _k, consider elastic network(s) constraint simultaneously:

$(\widehat{\mathrm{\&alpha;}},\widehat{\mathrm{\&beta;}})=\arg \underset{\mathrm{\&alpha;},\mathrm{\&beta;}}{\min }\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{|X_i-\mathrm{\&alpha;}{\mathrm{\&beta;}}^T{X}_i|}^2+\mathrm{\&lambda;}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\left|{\mathrm{\&beta;}}_j\right|}^2+\underset{k=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_{1,j}\left|{\mathrm{\&beta;}}_j\right|$

Wherein, λ _{1, j}the λ of corresponding j pivot ₁value, j=1,2..., k;

304) utilize the β after the convergence of finally trying to achieve to be normalized, and solve a final k pivot, obtain the load vector of rarefaction:

P _j≈XV _j＝Xβ _j/|β _j|(j＝1，2，…k)

。

5. the continuous chemical industry procedure failure testing method of one according to claim 4, is characterized in that step 4) in, T ²the computing formula of statistic is:

T ²＝X ^TV(∑ ^T∑) ^-1V ^TX

Wherein, V is the covariance matrix ∑=X of sample ^tx carries out orthogonal vector after svd, and X is sample data collection;

The computing formula of SPE statistic is:

SPE＝[(I-PP ^T)X] ^T(I-PP ^T)X

The matrix of loadings of the load vector composition that wherein, P is rarefaction.

6. the continuous chemical industry procedure failure testing method of one according to claim 1, is characterized in that step 5) in, described probability density method of estimation adopts Parzen window method, i.e. kernel probability density estimation method.