CN103926919A - Industrial process fault detection method based on wavelet transform and Lasso function - Google Patents

Abstract

The invention relates to an industrial process fault detection method based on wavelet transform and a Lasso function. The industrial process fault detection method comprises the steps of (1) obtaining normal data and fault data from a Tennessee and Eastman industrial process model, carrying out standardization processing on the obtained data, (2) carrying out wavelet transform on the normal data, compressing the normal data, carrying out Lasso regression between each set of training data processed through wavelet transform and a training data matrix in the mode that each set of training data is used as a pivot element column vector, obtaining different minimum estimated values (please see the symbol in the specification), (3) obtaining the optimal minimum estimated value (please see the symbol in the specification) through a probability density estimation method, using the optimal minimum estimated value as a threshold, and (4) sequentially carrying out wavelet transform and Lasso regression on test data, comparing the minimum estimated value (please see the symbol in the specification) obtained from each set of test data with the threshold, and judging whether each set of test data has a fault or not. Compared with the prior art, the industrial process fault detection method based on wavelet transform and the Lasso function has the advantages that all the eigenvalues are taken into consideration, and detection accuracy is improved.

Description

Industrial process fault detection method based on wavelet transformation and Lasso function

Technical field

The present invention relates to a kind of industrial process fault detection method based on wavelet transformation and Lasso function, belong to Intelligent Information Processing field.

Background technology

In processing industry and manufacturing industry, people are making great efforts to produce high-quality product, reduce the disqualification rate of product, to meet safety continuous enhancing, strict and environmental protection regulations.In order to pursue higher standard, modern industry process comprises a large amount of closed-loop control variablees, and deviser is design standards process controller often, by the interference that produces in compensation process or the impact of variation, maintains satisfied operation.Yet these controllers, if change in process is dealt with improperly, will produce fault just.Four steps of process monitoring are that fault detect, Fault Identification, fault diagnosis and process are recovered.Method by pattern-recognition, lays 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 has: principle component analysis (PCA), Fei Sheer discriminatory analysis (FDA), and partial least square (PLS) and canonical variate analysis (CVA), these methods are all the course monitoring methods based on data-driven.But diverse ways, emphasis is different.PCA, FDA and CVA are two kinds of dimensionality reduction technologies that grow up in pattern classification field, and wherein PCA is being widely used in the detection of chemical industry procedure fault continuously.And PLS technology is developed by field of statistics, be applied in continuous chemical industry procedure fault detection, be the method for data decomposition, it maximizes the fallout predictor of each parts (independently) data block to the covariance between predicted (relevant) data block.For different fault types, every kind of method has relative merits.

Summary of the invention

Object of the present invention is exactly to provide a kind of industrial process fault detection method based on wavelet transformation and Lasso function in order to overcome the defect of above-mentioned prior art existence, whole features of data, all as the whether normal feature of judgement data, have been improved to the precision of fault detect.

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

An industrial process fault detection method based on wavelet transformation and Lasso function, step comprises:

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 data that obtain are carried out to standardization;

2) normal data is carried out to wavelet transformation, packed data,, is Lasso with training data matrix and returns respectively using each group data as pivot column vector the training data after wavelet transformation, obtains respectively different least estimated value;

3), by probability density method of estimation, try to achieve best value is as threshold value;

4) test data is carried out to wavelet transformation and Lasso recurrence successively, each group data is tried to achieve value and threshold, judge whether every group of data exist fault:

If try to achieve value is greater than threshold value, and corresponding one group of data exist fault; If try to achieve value is less than threshold value, and 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, and X* represents the data matrix after standardization, the average that μ is data, and the standard deviation that σ is 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 Lasso returns and is specially:

The data of acquisition are expressed as to a sample matrix X (p * n), the hits that wherein n is sample, the number that p is observation data, chooses arbitrarily a row X in sample matrix _jas pivot column vector, be defined as Y:

Y＝(y ₁，y ₂，…y _n) ^T

Set up the Lasso linear regression constraint function that X is relevant with Y, its least estimated formula is as follows:

${\widehat{\mathrm{\β}}}_{\mathrm{lasso}}=\arg \underset{\mathrm{\β}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{X}_j{\mathrm{\β}}_j|}^2+\mathrm{\λ}\underset{j=1}{\overset{p}{\mathrm{\Σ}}}\left|{\mathrm{\β}}_j\right|$

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

Step 3), 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, dimensionality reduction thinking conventional in fault detect is converted into optimization problem, considered the feature of all data, can make the feature of each group data all be utilized, thereby have more the accuracy of detection, avoid some the non-principal character reducing because of dimensionality reduction technology, and affected the situation of industrial process fault detect.

2) the present invention is applied in continuous chemical industry procedure fault detection, can improve the accuracy of detection.By relatively traditional PCA method, carry out data analysis, analysis result shows that the present invention has improved the loss of fault detect.

3) the present invention uses small echo change process data, has compressed and has needed data volume to be processed, has reduced sample data amount, has improved operation efficiency.

4) the inventive method is to utilize statistical thinking, dimensionality reduction thinking conventional in fault detect is converted into optimization problem, although dimensionality reduction technology can extract main characteristic component, but very important is, this technology is bound to lack some feature, although these features are not main, can affect industrial process fault detect yet, and we adopt, based on the continuous chemical industry procedure failure testing method of wavelet transformation and Lasso constraint function, avoided the generation of this type of situation.

Accompanying drawing explanation

Fig. 1 is TEP process process flow diagram;

Fig. 2 is disposal route the general frame of the present invention;

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

Fig. 4 is for adopting 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 be take technical solution of the present invention and is implemented as prerequisite, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

In carrying out the process of fault detect, the data of utilizing are the data that gather in Tennessee-Yi Siman (TEP) process model.TEP process model Shi You Yisiman Chemical Company creates, and its object is exactly to provide a real industrial process for evaluation procedure control and method for supervising.Test process is that composition wherein, dynamics, service condition etc. are because Patent right problem has all been done modification based on a true chemical industry industrial process continuously.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 industrial process fault detection method based on wavelet transformation and Lasso function, step comprises:

Step S1: obtain normal data and fault data from Tennessee-Yi Siman industrial process model, using normal data as training data, using fault data as test data.

Step S2: the data that obtain are carried out to standardization, and the method for employing is Z-score standardization, and also referred to as standard deviation standardization, computing formula is:

$X*=\frac{X-\mathrm{\μ}}{\mathrm{\σ}}---\left(1\right)$

In formula, X represents data matrix, and X* represents the data matrix after standardized method is processed, and μ is the average of taking from data, and σ is the standard deviation of taking from data, and μ and σ computing formula are:

$\mathrm{\μ}=\frac{1}{n}{\mathrm{\Σ}}_{i=1}^n{x}_i---\left(2\right)$

$\mathrm{\σ}={\left[\frac{1}{n-1}{\mathrm{\Σ}}_{i=1}^n{(x_i-\mathrm{\μ})}^2\right]}^{\frac{1}{2}}---\left(3\right)$

In formula, x _ifor data.Data after Z-score standardization, data fit standardized normal distribution, average is 0, standard deviation is 1.

Step S3: normal data is carried out to wavelet transformation, packed data.The wavelet transformation here adopts haar wavelet transformation.

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

And corresponding convergent-divergent equation can be expressed as:

Its wave filter h[n] be defined as:

Step S4: the training data after wavelet transformation, respectively using each group data as pivot column vector, is Lasso with training data matrix and is returned, obtain respectively different least estimated value.

Introduce Lasso constraint function, build vectorial X _jlinear regression model (LRM) with Y.From Tennessee-Yi Siman industry (TEP) process model, obtain continuous chemical industry process data, obtain a sample matrix X (p * n), the hits that wherein n is sample, the number that p is observation data, chooses arbitrarily X _jas pivot column vector, be defined as Y:

Y＝(y ₁，y ₂，…y _n) ^T (7)

P different observed readings:

X _j＝(x _1j,x _2j，…，x _nj) ^T,j＝1,2，…p (8)

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

${\widehat{\mathrm{\β}}}_{\mathrm{lasso}}=\arg {\min }_{\mathrm{\β}}{|Y-{\mathrm{\Σ}}_{j=1}^p{X}_j{\mathrm{\β}}_j|}^2+\mathrm{\λ}{\mathrm{\Σ}}_{j=1}^p\left|{\mathrm{\β}}_j\right|---\left(9\right)$

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

Step S5: by probability density method of estimation, try to achieve best value is as threshold value.

The method that probability density is estimated adopts Parzen window method, i.e. kernel probability density estimation method; 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 guarantee P _n(x) can converge to P (x).In addition also has Kn nearest neighbour method.To different value is done probability density estimation, finally obtains one value is as the standard value of normal data, i.e. threshold value.

Step S6: test data is carried out to wavelet transformation and Lasso successively and return, try to achieve each group data according to formula (9) value.

Step S7: each group data is tried to achieve value and threshold, judge whether every group of data exist fault:

If try to achieve value is greater than threshold value, and corresponding one group of data exist fault; If try to achieve value is less than threshold value, and 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 the continuous chemical industry procedure failure testing method superiority based on wavelet transformation and Lasso constraint function, 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.T wherein ²statistic is used for multivariable process data to carry out fault detect.A given observation vector x also supposes ∧=∑ ^r∑ is reversible, T ²statistic can directly calculate by PCA expression formula:

T ²=X ^rv (∑ ^t∑) ^-1v ^rx (10) and T ²statistic threshold value can be expressed as:

$T_a^2=\frac{a(n-1)(n+1)}{n(n-a)}{F}_a(a,n-a)---\left(11\right)$

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 ^r)x] ^T(1-PP ^r)x (12)

Wherein, P is matrix of loadings, and SPE statistic threshold value can be expressed as:

$Q_a={\mathrm{\θ}}_1{[\frac{h_o{c}_a\sqrt{2{\mathrm{\θ}}_2}}{{\mathrm{\θ}}_1}+1+\frac{{\mathrm{\θ}}_2{h}_o(h_o-1)}{{\mathrm{\θ}}_1^2}]}^{1/h_o}---\left(13\right)$

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

With the basic thought that PCA method detects fault, be exactly in present normal data, to try to achieve respectively T ²the threshold value of statistic and SPE statistic, then asks respectively T to test data ²statistic and SPE statistic, be judged to normally lower than the data of threshold line, and the data that surpass threshold line are judged to fault data.Whole process is all studied based on TEP process model, and the step of process monitoring is as follows:

1) from TEP process data, concentrate and obtain sampled 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;

2) normal data is carried out to the conversion of PCA dimensionality reduction, obtains matrix of loadings:

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

4) calculate the T of test data ²statistic and SPE statistic;

5) the whether paranormal threshold line of the T2 statistic of monitor test data and SPE statistic.

We choose the result that fault type 13 provides fault detect, utilize respectively the method for PCA and Lasso constraint function to detect, respectively as shown in Figure 3,4, as shown in table 2 be PCA method and the method testing result comparison based on wavelet transformation and Lasso algorithm to analysis result data figure:

Table 2: the error rate and the loss that detect for continuous chemical industry procedure fault Class1 3 distinct methods

By the data results of example, can find out the accuracy that can improve detection based on the continuous chemical industry procedure failure testing method of wavelet transformation and Lasso constraint function.

Claims (5)

1. the industrial process fault detection method based on wavelet transformation and Lasso function, is characterized in that, step comprises:

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 data that obtain are carried out to standardization;

2) normal data is carried out to wavelet transformation, packed data,, is Lasso with training data matrix and returns respectively using each group data as pivot column vector the training data after wavelet transformation, obtains respectively different least estimated value;

3), by probability density method of estimation, try to achieve best value is as threshold value;

4) test data is carried out to wavelet transformation and Lasso recurrence successively, each group data is tried to achieve value and threshold, judge whether every group of data exist fault:

If try to achieve value is greater than threshold value, and corresponding one group of data exist fault; If try to achieve value is less than threshold value, and corresponding one group of data are normal.

2. a kind of industrial process fault detection method based on wavelet transformation and Lasso function according to claim 1, is characterized in that step 1) in, described standardization adopts Z-score standardized method, and computing formula is:

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

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

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

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

3. a kind of industrial process fault detection method based on wavelet transformation and Lasso function according to claim 1, is characterized in that step 2) in, described wavelet transformation is haar wavelet transformation.

4. a kind of industrial process fault detection method based on wavelet transformation and Lasso function according to claim 1, is characterized in that, described Lasso returns and is specially:

The data of acquisition are expressed as to a sample matrix X (p * n), the hits that wherein n is sample, the number that p is observation data, chooses arbitrarily a row X in sample matrix _jas pivot column vector, be defined as Y:

Y＝(y ₁，y ₂，…y _n) ^T

Set up the Lasso linear regression constraint function that X is relevant with Y, its least estimated formula is as follows:

${\widehat{\mathrm{\β}}}_{\mathrm{lasso}}=\arg \underset{\mathrm{\β}}{\min }{|Y-\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{X}_j{\mathrm{\β}}_j|}^2+\mathrm{\λ}\underset{j=1}{\overset{p}{\mathrm{\Σ}}}\left|{\mathrm{\β}}_j\right|$

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

5. a kind of industrial process fault detection method based on wavelet transformation and Lasso function according to claim 1, is characterized in that step 3) in, described probability density method of estimation adopts Parzen window method, i.e. kernel probability density estimation method.