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

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 invention relates to an industrial process fault detection method based on wavelet transformation and a Lasso function, and belongs to the field of intelligent information processing.

Background

In the processing and manufacturing industries, efforts are being made to produce high quality products with reduced product reject rates to meet ever-increasing, stringent safety and environmental regulations. In pursuit of higher standards, modern industrial processes contain a large number of closed-loop control variables, and designers often design standard process controllers to maintain satisfactory operation by compensating for the effects of disturbances or variations in the process. However, it is these controllers that fail if the process changes are not properly handled. The four steps of process monitoring are fault detection, fault identification, fault diagnosis and process recovery. By means of pattern recognition, emphasis is placed on detecting faults. Fault detection, colloquially, is the determination of whether a fault has occurred. Timely detection can provide valuable alarm for problems to be generated, and by taking corresponding measures, serious process subversion is avoided.

The traditional fault detection method comprises the following steps: principal Component Analysis (PCA), Fisher Discriminant Analysis (FDA), Partial Least Squares (PLS) and Canonical Variate Analysis (CVA), which are all data-driven based process monitoring methods. However, different approaches have different emphasis. PCA, FDA and CVA are two dimension reduction technologies developed in the field of mode classification, wherein PCA is widely applied to fault detection of continuous chemical process. The PLS technique, developed in the field of statistics, is applied in continuous chemical process fault detection and is a data decomposition method that maximizes the covariance between the predictor (independent) data block and the predicted (correlated) data block of each component. Each method has advantages and disadvantages for different fault types.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide an industrial process fault detection method based on wavelet transformation and a Lasso function, all characteristics of data are used as the characteristics for judging whether the data are normal or not, and the fault detection precision is improved.

The purpose of the invention can be realized by the following technical scheme:

an industrial process fault detection method based on wavelet transformation and Lasso function comprises the following steps:

1) acquiring normal data and fault data from a Tiannaxi-Iseman industrial process model, taking the normal data as training data, taking the fault data as test data, and carrying out standardization processing on the acquired data;

2) wavelet transform is carried out on normal data, data is compressed, each group of data is used as principal element column vector of training data after wavelet transform, Lasso regression is carried out on each group of data and a training data matrix, and different results are obtained respectivelyMinimum estimate ofA value;

3) by means of probability density estimation, the best one is obtainedThe value is used as a threshold value;

4) wavelet transform and Lasso regression are carried out on the test data in sequence, and each group of data is obtainedComparing the value with a threshold value, and judging whether each group of data has faults:

if obtainedIf the value is larger than the threshold value, the corresponding group of data has a fault; if obtainedAnd if the value is smaller than the threshold value, the corresponding group of data is normal.

In the step 1), the standardization treatment adopts a Z-score standardization method, and the calculation formula is as follows:

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

wherein X is { X ═ X₁，x₂，…，x_nThe data matrix is represented by X, mu is the mean value of the data, sigma is the standard deviation of the data, and the calculation formula of mu and sigma is as follows:

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

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

in step 2), the wavelet transform is haar wavelet transform.

The Lasso regression is specifically as follows:

representing the obtained data as a sample matrix X (p × n), wherein n is the sampling number of samples, p is the number of observed data, and randomly selecting a column X in the sample matrix_jAs a principal element column vector, defined as Y:

Y＝(y₁，y₂，…y_n)^T

establishing Lasso linear regression constraint functions related to X and Y, wherein the minimum estimation 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 which λ is a non-negative parameter, β_jIs the corresponding regression coefficient vector.

In step 3), the probability density estimation method adopts a Parzen window method, namely a kernel probability density estimation method.

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

1) The invention converts the common dimensionality reduction thinking in the fault detection into an optimization problem by using statistical thinking, considers the characteristics of all data, and can utilize the characteristics of each group of data, thereby having more detection accuracy and avoiding the condition that the fault detection in the industrial process is influenced by some non-main characteristics reduced by the dimensionality reduction technology.

2) The invention is applied to the fault detection in the continuous chemical process, and can improve the detection accuracy. Compared with the traditional PCA method, the data analysis is carried out, and the analysis result shows that the missing rate of fault detection is improved.

3) The invention uses wavelet change to process data, compresses the data amount to be processed, reduces the sample data amount and improves the operation efficiency.

4) The method of the invention converts the commonly used thinking reduction in fault detection into an optimization problem by using statistical thinking, although the main characteristic components can be extracted by the technology of the invention, the technology can not neglect that certain characteristics are lacked, although the characteristics are not main, the fault detection of the industrial process can be influenced, and the continuous chemical process fault detection method based on wavelet transformation and Lasso constraint function avoids the situations.

Drawings

FIG. 1 is a process flow diagram of a TEP process;

FIG. 2 is a general block diagram of the process of the present invention;

FIG. 3 is a schematic diagram of a continuous chemical process fault type 13 based T using conventional PCA techniques²A detection result graph of the statistic detection and the SPE statistic;

fig. 4 is a diagram of the detection result based on the type of failure 13 in the continuous chemical process using the present invention.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.

In performing fault detection, the data utilized is data collected in a Tennessee-Iseman (TEP) process model. The TEP process model was created by eastman chemical company and is intended to provide a realistic industrial process for evaluating process control and monitoring methods. The testing process is based on a real continuous chemical industrial process, in which the composition, dynamics, operating conditions, etc. are modified due to patent rights. The process includes five main units: a reactor, a condenser, a compressor, a separator and a stripper; and comprises eight components: A. b, C, D, E, F, G and H. FIG. 1 is a process flow diagram of the industrial plant.

The process model for the Tennessee-Iseman problem includes 21 preset faults. Of these failures, 16 are known and 5 are unknown. Faults 1-7 are associated with step changes in process variables, such as changes in cold water inlet temperature or feed composition. Faults 8-12 are associated with increased variability of some process variables. Fault 13 is a slow drift in reaction kinetics and faults 14, 15, and 21 are associated with viscous valves. A process fault description for the tennessee-eastman process model is shown in table 1.

Table 1: process fault description

As shown in fig. 2, a method for detecting faults in an industrial process based on wavelet transform and Lasso function includes the steps of:

step S1: normal data and fault data are obtained from the Tiannaxi-Iseman industrial process model, the normal data are used as training data, and the fault data are used as test data.

Step S2: the data obtained are normalized by a method of Z-score normalization, also known as standard deviation normalization, using the formula:

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

wherein X represents a data matrix, X represents the data matrix after being processed by the normalization method, mu is the mean value taken from the data, sigma is the standard deviation taken from the data, and the calculation formula of mu and sigma is as follows:

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

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

in the formula, x_iIs the data. The data after the Z-score standardization meets the standard normal distribution, namely the mean value is 0 and the standard deviation is 1.

Step S3: and performing wavelet transformation on the normal data to compress the data. The wavelet transform here employs a haar wavelet transform.

The mother wavelet (heat wavelet) of a haar wavelet can be represented as:

and the corresponding scaling equation can be expressed as:

its filter h [ n ] is defined as:

step S4: respectively using each group of data as principal element column vector of the training data after wavelet transformation, performing Lasso regression with the training data matrix, and respectively calculating different minimum estimatesThe value is obtained.

Introducing a Lasso constraint function to construct a vector X_jObtaining continuous chemical process data from a Tennessee-Isemann Industrial (TEP) process model to obtain a sample matrix X (p × n), where n is the number of samples and p is the number of observed data, and optionally selecting X_jAs a principal element column vector, defined as Y:

Y＝(y₁，y₂，…y_n)^T(7)

p different observations, then:

X_j＝(x_1j,x_2j，…，x_nj)^T,j＝1,2，…p (8)

lasso is X_jAnd a linear regression constraint function associated with Y, the minimum estimate of which 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 which λ is a non-negative parameter, β_jIs the corresponding regression coefficient vector.

Step S5: passing probability densityEstimation method of finding the bestThe value is used as a threshold.

The probability density estimation method adopts a Parzen window method, namely a nuclear probability density estimation method; parzen window method: according to a certain determined volume function, e.g.To gradually shrink a given initial space, which requires a random variable k_nAndcan guarantee P_n(x) Can converge to p (x). Further, the Kn neighbor method is also available. For differentThe values are used for probability density estimation, and finally one is obtainedThe value is used as a standard value of normal data, i.e., a threshold value.

Step S6: wavelet transform and Lasso regression are carried out on the test data in sequence, and each group of data is obtained according to the formula (9)The value is obtained.

Step S7: from each set of dataComparing the value with a threshold value, and judging whether each group of data has faults:

if obtainedIf the value is larger than the threshold value, the corresponding group of data has a fault; if obtainedAnd if the value is smaller than the threshold value, the corresponding group of data is normal.

In the example, there are 500 sets of training data, each set of data having 52 observations. There are 960 sets of test data, each set of test data containing 52 observations, of which the first 160 sets of data are normal data and the last 800 sets of data are fault data.

In order to embody the superiority of the continuous chemical process fault detection method based on wavelet transformation and Lasso constraint function, the method is compared with the traditional detection technology utilizing PCA technology.

When fault detection is traditionally carried out by PCA, T is utilized²And SPE detect failures. Wherein T is²Given an observation vector x and assuming Λ ∑^r∑ is reversible, then T²The statistics can be calculated directly by the PCA expression:

T²＝X^rV(∑^T∑)^-1V^rx (10) and T²The statistic threshold may 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 the square prediction error, which is the square of the 2-norm, also known as Q statistic. To measure the deviation of the observed values from the low-dimensional PCA representation, the Q statistic can be expressed as:

Q＝[(I-PP^r)x]^T(1-PP^r)x (12)

where P is the load matrix and the SPE statistic threshold 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_ais the standard deviation corresponding to the (1- α) quantile.

The basic idea of using PCA method to detect the fault is to respectively calculate T on the current normal data²Threshold values of statistic and SPE statistic, and then respectively solving for T of test data²And the statistic and the SPE statistic, wherein the data below the threshold line is judged to be normal, and the data above the threshold line is judged to be fault data. The whole process is researched based on a TEP process model, and the process monitoring comprises the following steps:

1) acquiring sampling data from the TEP process data set, and standardizing according to the mean value and the variance of the models under normal conditions to obtain normal data and fault data of each fault type;

2) carrying out PCA dimension reduction transformation on the normal data to obtain a load matrix:

3) calculating T of normal data²Thresholds for the statistics and SPE statistics;

4) calculating T of test data²Statistics and SPE statistics;

5) the test data is monitored for T2 statistics and SPE statistics exceeding a normal threshold line.

We select the fault type 13 to give the fault detection result, and use the methods of PCA and Lasso constraint function to detect respectively, the analysis result data graphs are respectively shown in fig. 3 and 4, and as shown in table 2, the detection results of the PCA method and the method based on wavelet transform and Lasso algorithm are compared:

table 2: error rate and omission factor detected by different methods for fault types 13 of continuous chemical process

Through the data analysis result of the example, it can be seen that the continuous chemical process fault detection method based on the wavelet transformation and the Lasso constraint function can improve the detection accuracy.

Claims (3)

1. An industrial process fault detection method based on wavelet transformation and a Lasso function is characterized by comprising the following steps:

1) acquiring normal data and fault data from a Tiannaxi-Iseman industrial process model, taking the normal data as training data, taking the fault data as test data, and carrying out standardization processing on the acquired data;

2) performing wavelet transform on the normal data, compressing the data, and performing Lasso regression on the wavelet transformed training data by using each group of data as principal element column vector and training data matrixRespectively find different minimum estimatesA value;

3) by means of probability density estimation, the best one is obtainedThe value is used as a threshold value;

4) wavelet transform and Lasso regression are carried out on the test data in sequence, and each group of data is obtainedComparing the value with a threshold value, and judging whether each group of data has faults:

if obtainedIf the value is larger than the threshold value, the corresponding group of data has a fault; if obtainedIf the value is smaller than the threshold value, the corresponding group of data is normal;

the Lasso regression is specifically as follows:

representing the obtained data as a sample matrix X (p × n), wherein n is the sampling number of samples, p is the number of observed data, and randomly selecting a column X in the sample matrix_jAs a principal element column vector, defined as Y:

Y＝(y₁,y₂,…y_n)^T

establishing Lasso linear regression constraint functions related to X and Y, wherein the minimum estimation formula is as follows:

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

in which λ is a non-negative parameter, β_jIs the corresponding regression coefficient vector;

in step 3), the probability density estimation method adopts a Parzen window method, namely a kernel probability density estimation method.

2. The method for detecting the fault of the industrial process based on the wavelet transform and the Lasso function as claimed in claim 1, wherein in the step 1), the normalization processing adopts a Z-score normalization method, and the calculation formula is as follows:

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

wherein X is { X ═ X₁，x₂,…,x_nIs the data matrix, X^*And expressing a data matrix after normalization, wherein mu is a mean value of the data, sigma is a standard deviation of the data, and the calculation formula of mu and sigma is as follows:

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

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

3. the method for detecting the fault of the industrial process based on the wavelet transform and the Lasso function as claimed in claim 1, wherein in the step 2), the wavelet transform is haar wavelet transform.