CN103926919B - Industrial process fault detection method based on wavelet transformation and Lasso function - Google Patents

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

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CN103926919B
CN103926919B CN201410177158.6A CN201410177158A CN103926919B CN 103926919 B CN103926919 B CN 103926919B CN 201410177158 A CN201410177158 A CN 201410177158A CN 103926919 B CN103926919 B CN 103926919B
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data
wavelet transformation
fault
lasso
industrial
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CN103926919A (en
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江晓栋
赵海涛
沙钰杰
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East China University of Science and Technology
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Abstract

The present invention relates to a kind of industrial process fault detection method based on wavelet transformation and Lasso function, step includes: 1) obtains normal data and fault data from Tennessee Yi Siman industrial process model, and is standardized processing to the data obtained;2) normal data is carried out wavelet transformation, compresses data, to the training data after wavelet transformation respectively using each group of data as pivot column vector, be Lasso with training data matrix and return, obtain different least estimated respectivelyValue;3) by Multilayer networks method, try to achieve optimalValue is as threshold value;4) test data are carried out wavelet transformation successively and Lasso returns, each group of data are tried to achieveValue is compared with threshold value, it is judged that often whether group data exist fault.Compared with prior art, the present invention has consideration All Eigenvalues, improves the advantages such as accuracy in detection.

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 intelligence Field of information processing.
Background technology
In processing industry and manufacturing industry, people make great efforts to produce high-quality product, reduce the disqualification rate of product, with full Continuous strengthen, the strict safety of foot and environmental protection regulations.In order to pursue higher standard, modern industry process comprises substantial amounts of closing Ring control variables, designer often designs standard process controller, by the interference produced in compensation process or the impact of change Maintain satisfied operation.But, these controllers just, if change in process is dealt with improperly, fault will be produced.Process Four steps of monitoring are that fault detect, Fault Identification, fault diagnosis and process are recovered.By the method for pattern-recognition, stress In by fault detect out.Fault detect, popular says, it is simply that determine whether fault there occurs.Carrying out detection in time can be right It would appear that problem propose valuable warning, by taking appropriate measures, it is to avoid serious process is overturned.
Traditional fault detection method has: principle component analysis (PCA), Fei Sheer discriminant analysis (FDA), partial least square (PLS) and canonical variate analysis (CVA), these methods are all based on the course monitoring method of data-driven.But different sides Method, emphasis is different.PCA, FDA and CVA are the two kinds of dimensionality reduction technologies grown up in pattern classification field, wherein PCA is widely used in continuous chemical industry procedure fault detects.And PLS technology is developed by field of statistics, application In continuous chemical industry procedure fault detects, being the method for data decomposition, it is by fallout predictor (independently) data block of each parts Maximize to the covariance between predicted (relevant) data block.For different fault types, every kind of method is all respectively arranged with excellent Shortcoming.
Summary of the invention
Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and provide a kind of based on wavelet transformation With the industrial process fault detection method of Lasso function, using whole features of data all as the spy judging that whether normal data are Levy, improve the precision of fault detect.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of industrial process fault detection method based on wavelet transformation and Lasso function, step includes:
1) from Tennessee-Yi Siman industrial process model, obtain normal data and fault data, using normal data as The data obtained using fault data as test data, and are standardized processing by training data;
2) normal data is carried out wavelet transformation, compress data, to the training data after wavelet transformation respectively by each group Data, as pivot column vector, are Lasso with training data matrix and are returned, obtain different least estimated respectivelyValue;
3) by Multilayer networks method, try to achieve optimalValue is as threshold value;
4) test data are carried out wavelet transformation successively and Lasso returns, each group of data are tried to achieveValue and threshold Value compares, it is judged that often whether group data exist fault:
If trying to achieveFault is there is in value more than threshold value, then one group of corresponding data;If trying to achieveIt is worth little In threshold value, then one group of corresponding data are normal.
Step 1) in, described standardization uses Z-score standardized method, and computing formula is:
X * = X - μ σ
In formula, X={x1, x2..., xnIt is data matrix, X* represents the data matrix after standardization, and μ is data Average, σ is the standard deviation of data, μ and σ computing formula is:
μ = 1 n Σ i = 1 n x i
σ = [ 1 n - 1 Σ i = 1 n ( x i - μ ) 2 ] 1 2
Step 2) in, described wavelet transformation is haar wavelet transformation.
Described Lasso return particularly as follows:
The tables of data of acquisition is shown as a sample matrix X (p × n), and wherein n is the hits of sample, and p is observation data Number, arbitrarily choose in sample matrix a row XjAs pivot column vector, it is defined as Y:
Y=(y1, y2... yn)T
Setting up Lasso linear regression constraint function relevant for X with Y, its least estimated formula is as follows:
β ^ lasso = arg min β | Y - Σ j = 1 p X j β j | 2 + λ Σ j = 1 p | β j |
In formula, λ is non-negative parameter, βjFor corresponding regression coefficient vector.
Step 3) in, described Multilayer networks method uses Parzen window method, i.e. kernel probability density estimation method.
Compared with prior art, the present invention has the following advantages.
1) present invention is to utilize statistical thinking, the dimensionality reduction thinking commonly used is converted into optimization asks in fault detect Topic, it is contemplated that the feature of all data, can make the feature of each group of data all be obtained by, thus have more the accurate of detection Degree, it is to avoid some the non-principal feature reduced because of dimensionality reduction technology, and affect the situation of industrial process fault detect.
2) present invention applies in continuous chemical industry procedure fault detects, and can improve the degree of accuracy of detection.By relatively passing The PCA method of system carries out data analysis, and analysis result shows that the present invention improves the loss of fault detect.
3) present invention uses Wavelet transformation to process data, have compressed and needs data volume to be processed, decreases sample data amount, Improve operation efficiency.
4) the inventive method is to utilize statistical thinking, and the dimensionality reduction thinking commonly used in fault detect is converted into optimization Problem, although dimensionality reduction technology can extract main characteristic component, but very important, this technology is bound to lack certain A little features, although these features are not main, but can affect industrial process fault detect yet, and we use based on little The continuous chemical industry procedure failure testing method of wave conversion and Lasso constraint function avoids the generation of this type of situation.
Accompanying drawing explanation
Fig. 1 is TEP process flow chart;
Fig. 2 is processing method the general frame of the present invention;
Fig. 3 is the T based on continuous chemical industry procedure fault Class1 3 using traditional PCA technology2Statistic detection and SPE The testing result figure of statistic;
Fig. 4 is the testing result figure based on continuous chemical industry procedure fault Class1 3 using the present invention.
Detailed description of the invention
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention Premised on implement, give detailed embodiment and concrete operating process, but protection scope of the present invention be not limited to Following embodiment.
During carrying out fault detect, the data utilized are to adopt in Tennessee-Yi Siman (TEP) process model The data of collection.TEP process model is created by Yisiman Chemical Company, and its purpose is contemplated to evaluation procedure control and monitoring Method provides a real industrial process.Test process is based on a true chemical industry industrial process continuously, composition therein, Dynamics, service condition etc. are because the problem of patent right is all modified.Process includes five formants: reactor, condensation Device, compressor, separator and stripper;And comprise eight kinds of compositions: A, B, C, D, E, F, G and H.Fig. 1 is this industrial equipment Process chart.
The process model of Tennessee-Yi Siman problem includes 21 presetting faults.In these faults, 16 is known , 5 is unknown.Fault 1-7 is relevant with the Spline smoothing of process variable, e.g., and cold water inlet temperature or feed constituents Change.Fault 8-12 is relevant with the changeability increase of some process variables.Fault 13 is the slow drift in kinetics, therefore Barrier 14,15 is relevant with sticking valve with 21.It is the procedure fault description of Tennessee-Yi Siman process model as shown in table 1.
Table 1: procedure fault describes
As in figure 2 it is shown, a kind of industrial process fault detection method based on wavelet transformation and Lasso function, step includes:
Step S1: obtain normal data and fault data, by normal data from Tennessee-Yi Siman industrial process model As training data, using fault data as test data.
Step S2: be standardized processing to the data obtained, the method for employing is Z-score standardization, also referred to as mark Quasi-difference standardization, computing formula is:
X * = X - μ σ - - - ( 1 )
In formula, X represent data matrix, X* represent standardized method process after data matrix, μ is take from data equal Value, σ is the standard deviation taking from data, μ and σ computing formula is:
μ = 1 n Σ i = 1 n x i - - - ( 2 )
σ = [ 1 n - 1 Σ i = 1 n ( x i - μ ) 2 ] 1 2 - - - ( 3 )
In formula, xiFor data.Data after Z-score standardization, data fit standardized normal distribution, the most all Value is 0, and standard deviation is 1.
Step S3: normal data carries out wavelet transformation, compresses data.Here wavelet transformation uses haar small echo to become Change.
The morther wavelet (mother wavelet) of haar small echo is represented by:
And the scaling equation of correspondence can be expressed as:
Its wave filter h [n] is defined as:
Step S4: to the training data after wavelet transformation respectively using each group of data as pivot column vector, with training number It is Lasso according to matrix to return, obtains different least estimated respectivelyValue.
Introduce Lasso constraint function, build vector XjLinear regression model (LRM) with Y.From Tennessee-Yi Siman industry (TEP) in process model, obtaining continuous chemical industry process data, i.e. obtain a sample matrix X (p × n), wherein n is sample Hits, p is the number of observation data, arbitrarily chooses XjAs pivot column vector, it is defined as Y:
Y=(y1, y2... yn)T (7)
P different observation, then:
Xj=(x1j,x2j..., xnj)T, j=1,2 ... p (8)
Lasso is XjThe linear regression constraint function relevant with Y, its least estimated formula is as follows:
β ^ lasso = arg min β | Y - Σ j = 1 p X j β j | 2 + λ Σ j = 1 p | β j | - - - ( 9 )
In formula, λ is the parameter of non-negative, βjFor corresponding regression coefficient vector.
Step S5: by Multilayer networks method, tries to achieve optimalValue is as threshold value.
The method of Multilayer networks uses Parzen window method, i.e. kernel probability density estimation method;Parzen window method: The volume function determined according to some, such asGradually tapering up a given initial space, this just requires at random Variable knWithEnsure that PnX () can converge to P (x).In addition with Kn nearest neighbour method.To differentIt is close that value makees probability Degree is estimated, finally obtains oneIt is worth the standard value as normal data, i.e. threshold value.
Step S6: test data are carried out wavelet transformation successively and Lasso returns, try to achieve each group of data according to formula (9) 'sValue.
Step S7: each group of data are tried to achieveValue is compared with threshold value, it is judged that often whether group data exist event Barrier:
If trying to achieveFault is there is in value more than threshold value, then one group of corresponding data;If trying to achieveIt is worth little In threshold value, then one group of corresponding data are normal.
In instances, training data has 500 groups of data, and often group data have 52 observations.Test data one have 960 groups Data, often group test data contain 52 observations, and the most 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, It is compared with traditional detection technique utilizing PCA technology.
When tradition utilizes PCA to carry out fault detect, it is all to utilize T2With SPE the two statistic, fault is detected. Wherein T2Statistic is used for multivariable process data are carried out fault detect.A given observation vector x also assumes ∧=∑r∑ Reversible, then T2Statistic can directly be calculated by PCA expression formula:
T2=XrV(∑T∑)-1VrX (10) and T2Statistic threshold value can be expressed as:
T a 2 = a ( n - 1 ) ( n + 1 ) n ( n - a ) F a ( a , n - a ) - - - ( 11 )
SPE is square prediction error, be 2-norm square, also known as Q statistical magnitude.It is used for measuring observation relative to low The deviation that dimension PCA represents, Q statistical magnitude can be expressed as:
Q=[(I-PPr)x]T(1-PPr)x (12)
Wherein, P is matrix of loadings, and SPE statistic threshold value can be expressed as:
Q a = θ 1 [ h o c a 2 θ 2 θ 1 + 1 + θ 2 h o ( h o - 1 ) θ 1 2 ] 1 / h o - - - ( 13 )
Wherein,caIt is and (1-α) standard deviation that quantile is corresponding.
The basic thought detected fault by PCA method is exactly to try to achieve T in present normal data respectively2Statistic and Then test data are sought T by the threshold value of SPE statistic respectively2Statistic and SPE statistic, be judged to less than the data of threshold line Normally, the data exceeding threshold line are judged to fault data.Whole process is all based on what TEP process model carried out studying, process The step of monitoring is as follows:
1) concentrate acquisition sampled data from TEP process data, and the average and variance by normal condition drag is marked Standardization, obtains normal data and the fault data of every kind of fault type;
2) normal data is carried out PCA dimensionality reduction conversion, obtains matrix of loadings:
3) T of normal data is calculated2Statistic and the threshold value of SPE statistic;
4) T of test data is calculated2Statistic and SPE statistic;
5) T2 statistic and the most paranormal threshold line of SPE statistic of test data are monitored.
We choose fault type 13 and provide the result of fault detect, the method being utilized respectively PCA and Lasso constraint function Detect, analysis result data figure respectively the most as shown in Figure 3,4, be as shown in table 2 PCA method and based on wavelet transformation with The method testing result of Lasso algorithm compares:
Table 2: for error rate and the loss of the detection of continuous chemical industry procedure fault Class1 3 distinct methods
By the data results of example, it can be seen that based on wavelet transformation and the continuous chemical industry of Lasso constraint function Procedure failure testing method can improve the degree of accuracy of detection.

Claims (3)

1. an industrial process fault detection method based on wavelet transformation and Lasso function, it is characterised in that step includes:
1) from Tennessee-Yi Siman industrial process model, normal data and fault data are obtained, using normal data as training The data obtained using fault data as test data, and are standardized processing by data;
2) normal data is carried out wavelet transformation, compress data, to the training data after wavelet transformation respectively by each group of data As pivot column vector, it is Lasso with training data matrix and returns, obtain different least estimated respectivelyValue;
3) by Multilayer networks method, try to achieve optimalValue is as threshold value;
4) test data are carried out wavelet transformation successively and Lasso returns, each group of data are tried to achieveIt is worth and threshold value phase Relatively, it is judged that often whether group data exist fault:
If trying to achieveFault is there is in value more than threshold value, then one group of corresponding data;If trying to achieveValue is less than threshold Value, then one group of corresponding data are normal;
Described Lasso return particularly as follows:
The tables of data of acquisition is shown as a sample matrix X (p × n), and wherein n is the hits of sample, and p is the individual of observation data Number, arbitrarily chooses a row X in sample matrixjAs pivot column vector, it is defined as Y:
Y=(y1,y2,…yn)T
Setting up Lasso linear regression constraint function relevant for X with Y, its least estimated formula is as follows:
β ^ l a s s o = arg min β | Y - Σ j = 1 p X j β j | 2 + λ Σ j = 1 p | β j |
In formula, λ is non-negative parameter, βjFor corresponding regression coefficient vector;
Step 3) in, described Multilayer networks method uses Parzen window method, i.e. kernel probability density estimation method.
A kind of industrial process fault detection method based on wavelet transformation and Lasso function the most according to claim 1, its It is characterised by, step 1) in, described standardization uses Z-score standardized method, and computing formula is:
X * = X - μ σ
In formula, X={x1, x2,…,xnIt is data matrix, X*Representing the data matrix after standardization, μ is the average of data, σ is the standard deviation of data, μ and σ computing formula is:
μ = 1 n Σ i = 1 n x i
σ = [ 1 n - 1 Σ i = 1 n ( x i - μ ) 2 ] 1 2 .
A kind of industrial process fault detection method based on wavelet transformation and Lasso function the most according to claim 1, its It is characterised by, step 2) in, described wavelet transformation is haar wavelet transformation.
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