CN111983994B - V-PCA fault diagnosis method based on complex industrial chemical process - Google Patents

Abstract

The invention discloses a V-PCA fault diagnosis method based on a complex industrial chemical process. Due to inaccurate feature extraction of the traditional Principal Component Analysis (PCA), the phenomena of high false alarm rate and high false missing report rate frequently exist when the method is used for fault diagnosis. To this end, the present invention employs a new data preprocessing method to improve the performance index of PCA in fault diagnosis. Compared with the Euclidean distance preprocessing method of the traditional PCA method, the method cannot accurately reflect the correlation between data. Therefore, a change rate-based preprocessing method is provided, and the conditions of high false alarm rate and high missing report rate of PCA in fault diagnosis are effectively improved. Finally, the traditional PCA method and the PCA method based on the change rate preprocessing are verified through a simulation example. Experimental simulation results show that the method has better detection performance.

Description

V-PCA fault diagnosis method based on complex industrial chemical process

Technical Field

The invention belongs to the field of industrial and chemical engineering fault diagnosis, and particularly relates to a V-PCA (principal component analysis based on change rate preprocessing) fault diagnosis method based on a complex industrial and chemical process.

Background

In the complex industrial chemical process, the failure of equipment and system can produce adverse effect on production safety, product quality or efficiency, and even cause personal casualty or pollution to the environment in serious cases. With the improvement of the integration level of the equipment, the industrial environment is increasingly complex and the requirements on the quality of products are continuously improved, and the requirements on the safety and the reliability of the equipment are increasingly high, so that the fault diagnosis technology is more and more emphasized.

The core of fault diagnosis is a diagnosis method, and the existing fault diagnosis methods can be mainly divided into two types: the fault diagnosis method based on the analytical model and the fault diagnosis method based on the data driving. The data-driven method is to transform process data from a measurement space to a feature space and then analyze the process data under the condition that an accurate mathematical model is difficult to establish by a target, so as to realize fault diagnosis of a system, and a multivariate statistical method is a representative of the method, wherein the most common method is a Principal Component Analysis (PCA) method. Although the PCA method is widely applied in the field of fault detection and fault diagnosis, the conventional PCA data preprocessing generally adopts normalization to make data dimensionless, and neglects the influence of dimension on the correlation between variables, thereby resulting in the loss of information after normalization. In an actual system, because the dimensions of the component variables are different, some variables playing an important role in the system cannot detect a fault with a smaller absolute value because the absolute value of the variables is smaller. Minor faults of these important variables play a key role in the stability and safety of system operation, and if the faults cannot be eliminated, the faults can affect the normal operation of the system, and even cause accidents.

Disclosure of Invention

In order to overcome the defects and shortcomings of the prior art, the invention designs a V-PCA method based on a complex industrial chemical process. Compared with the traditional PCA method, the fault diagnosis method based on the V-PCA has better effect on process system detection from the relative change of the samples.

In order to achieve the purpose, the invention is realized by the following technical scheme: the method comprises a data preprocessing stage, a V-PCA model establishing stage, an online fault detection and fault diagnosis stage and a simulation test stage.

Wherein the data preprocessing stage comprises the steps of:

step X1, constructing the collected original complex industrial chemical engineering TE data set into a multi-dimensional variable system matrix X_n∈R^m×n,X_nAs follows:

wherein, the column vector x_i(j)＝[x₁(j),x₂(j),...x_m(j)]^TI 1,2, m, j 1,2, n represents a system variable, the data matrix is preprocessed, X_nHas a mean vector of b_n

Step X2, calculating the mean vector b of each variable sample_n

Wherein l_m＝[1,1,...1]∈R^1×mThe original data is transformed to obtain a matrix X^*。

Wherein the transformation method is as follows

The physical significance of this equation is centered on the sample mean of each variable, and the rate of change represents the degree to which the raw data deviates from the center. Then, whether the test sample data collected in real time falls in a normal range is checked through the change rate obtained after the normal sample data is preprocessed, and if the projection is outside the normal region, a fault occurs.

Wherein the stage of establishing the V-PCA model comprises the following steps:

y1, for the data matrix X^*Covariance decomposition is performed, and the number of principal elements is selected to obtain the following formula

Wherein Λ ═ diag { λ ═ λ₁,λ₂,…,λ_mIs a matrix of eigenvalues of S, and the elements on its diagonal satisfy λ₁>λ₂>…>λ_m，V∈R^m×mIs the eigenvector matrix of S, P ∈ R^m×rThe first r column of V contains all pivot information,

is the remaining m-r columns of V, containing residual information.

Y2, converting the original data matrix X^*Decomposing to obtain principal component subspace and residual subspace

In the above formula, T ∈ R^n×rTo score the matrix, P ∈ R^m×rIn the form of a load matrix, the load matrix,

is a main element space, and is characterized in that,

is the residual space.

The online fault detection and fault diagnosis phase comprises the following steps:

step Z1, compute SPE statistics. SPE statistics for measuring changes in sample vector projections in residual space

Here, the first and second liquid crystal display panels are,

for the control limit with a confidence level of α, it is calculated from the following equation

Wherein the content of the first and second substances,

λ_jeigenvalues of a covariance matrix of X, c_αIs a threshold value of a standard normal distribution at a confidence level alpha.

Step Z2, calculating Hotelling T²Statistics are obtained. It is used to measure the variation of sample vector in principal component space

In the above formula, Λ ═ diag { λ₁,λ₂,…,λ_A}，

For the control limit with confidence α, it is calculated by the following formula

Here, F_r,n-A；rIs the value of the F distribution with r and n-r degrees of freedom with a confidence level of alpha.

And step Z3, fault isolation based on SPE contribution rate. The contribution graph of the SPE is defined as follows:

wherein the content of the first and second substances,

for each variable contribution to the statistic SPE, where

ξ_iIs in identity matrix I_mColumn i.

Step Z4, based on T²Fault isolation of the contribution rate. T is²The contribution ratio of (c) is defined as follows:

whereinD＝P^TΛ^-1P calculates the contribution rate of each variable of the system to the fault according to the formula, and the larger is regarded as the cause variable of the fault, thereby carrying out fault isolation.

Compared with the prior art, the invention has the following advantages and beneficial effects: compared with the traditional PCA method for preprocessing in the Euclidean space, the preprocessing method based on the change rate can better reflect the relevant information among all variables, can better reflect the tiny faults in the TE process through the change rate, and can accurately diagnose the faults of the variables which are smaller but play an important role. The simulation result shows that the method provided by the invention can well detect the abnormity, and the failure report-missing rate of the method is obviously reduced compared with the traditional PCA (principal component analysis) as can be seen from the SPE statistic.

Drawings

FIG. 1 is a graph of PCA statistic variation;

FIG. 2 is a graph of the variance of the V-PCA statistic.

Detailed Description

The invention is further described below with reference to the drawings.

The invention provides a V-PCA (principal component analysis based on change rate preprocessing) fault diagnosis method based on a complex industrial chemical process. The fault diagnosis method based on the change rate has better effect on process system detection from the relative change of the sample compared with the traditional PCA method. Through the conversion rate thought, the conversion rate conversion is carried out on the complex industrial and chemical data set TE, then the fault diagnosis is carried out by applying the PCA method, the provided method is verified to be capable of effectively detecting the fault and reducing the occurrence of fault false alarm.

The invention is realized by the following technical scheme: a V-PCA fault diagnosis method based on a complex industrial chemical process. The method mainly comprises four stages, namely a data preprocessing stage and a V-PCA model establishing stage; online fault detection and fault diagnosis; and (5) a simulation test stage.

Wherein the data preprocessing stage comprises the steps of:

step X1, collecting original complex industrial chemical TE numberThe data set is constructed into a multi-dimensional variable system matrix X_n∈R^{m ×n},X_nAs follows.

Wherein, the column vector x_i(j)＝[x₁(j),x₂(j),...x_m(j)]^TI 1,2, m, j 1,2, n represents a system variable, the data matrix is preprocessed, X_nIs b as the mean vector of each variable sample_n

Step X2, calculating X_nMean vector of samples of variables of

Wherein l_m＝[1,1,...1]∈R^1×mThe original data is transformed to obtain a matrix X^*。

Wherein the transformation method is as follows

The physical meaning of the formula is that the mean value of each variable sample is taken as the center, and the change rate represents the degree of deviation of the original data from the center. And then, checking whether the test sample data acquired in real time falls in a normal range or not by the change rate obtained after preprocessing the normal data sample, and if the projection is outside the normal region, determining that a fault occurs. Wherein the stage of establishing the V-PCA model comprises the following steps:

y1, for the data matrix X^*Covariance decomposition is performed, and the number of principal elements is selected to obtain the following formula

Wherein Λ ═ diag { λ ═ λ₁,λ₂,…,λ_mIs a matrix of eigenvalues of S, and the elements on its diagonal satisfy λ₁>λ₂>…>λ_m，V∈R^m×mIs the eigenvector matrix of S, P ∈ R^m×rThe first r column of V contains all pivot information,

is the remaining m-r columns of V, containing residual information.

Y2, converting the original data matrix X^*Decomposing to obtain principal component subspace and residual subspace

In the above formula, T ∈ R^n×rTo score the matrix, P ∈ R^m×rIn the form of a load matrix, the load matrix,

is a main element space, and is characterized in that,

is the residual space.

The online fault detection and fault diagnosis phase comprises the following steps:

step Z1, compute SPE statistics. SPE statistics for measuring changes in sample vector projections in residual space

Here, the first and second liquid crystal display panels are,

for the control limit with a confidence level of α, it is calculated from the following equation

Wherein the content of the first and second substances,

λ_jis X^*Characteristic value of the covariance matrix of (c)_αIs a threshold value of a standard normal distribution at a confidence level alpha.

Step Z2, calculating HotellingT²Statistics are obtained. It is used to measure the variation of sample vector in principal component space

In the above formula, Λ ═ diag { λ₁,λ₂,…,λ_A}，

For the control limit with confidence α, it is calculated by the following formula

Here, F_r,n-A；rIs the value of the F distribution with r and n-r degrees of freedom with a confidence level of alpha.

And step Z3, fault isolation based on SPE contribution rate. The contribution graph of the SPE is defined as follows:

wherein the content of the first and second substances,

for each variable's contribution to the statistics SPE,

ξ_iis in identity matrix I_mColumn i.

Step Z4, based on T²Fault isolation of the contribution rate. T is²The contribution ratio of (c) is defined as follows:

wherein D ═ P^TΛ^-1P calculates the contribution rate of each variable of the system to the fault according to the formula, and the larger is regarded as the cause variable of the fault, thereby carrying out fault isolation.

A simulation test stage:

to verify the effectiveness of the above method and compare it with the conventional PCA method. Simulation tests are performed by TE processes, which are models established from actual chemical processes, and have been widely used as reference processes for control and monitoring research. Acquiring a test data set from the samples by acquiring data on line, and calculating T for the processed data by a V-PCA method²And the statistic and the SPE statistic are used for monitoring whether the data exceed the control limit of the normal state. For samples that exceed the control limit, each process variable pair T is calculated²And the contribution rate of the statistic and the SPE statistic, wherein the variable with the largest contribution rate is the variable which can cause the fault.

The TE process simulates 21-medium failure modes common in real industrial processes, and a detailed description of these 21 failure modes is shown in table 1. This example collected 22 simulation data sets (1 normal data set, 21 fault data sets, one for each fault mode) each including 960 sample points. In these 21 failure modes, the process initially runs in normal mode, and at the 160 th sampling point, a failure occurs, which persists until the end of the process.

Table 1 the 21 failure modes in the TE process are described below

For fault (5) condenser cooling water inlet temperature step change, fault detection of the conventional PCA method is shown in fig. 1, and fault detection of V-PCA is shown in fig. 2. Because the control loop configuration can compensate for the condenser cooling water inlet temperature step change and compensate most of the variables to near their steady state values, the conventional PCA method only detects a system fault between the 160 th sample point to the 340 th sample point, and then the statistics can hardly detect the fault, however, the fault is always present and affects the process system. T of conventional PCA method²The failure false-positive rates of the statistic and the SPE statistic are 0.7388 and 0.57 respectively, compared with the T of the V-PCA method based on the change rate²And the failure and false-positive rates of the SPE statistics are 0.7 and 0.0038 respectively, and the comparison results of the two methods are shown in the following table 2.

Claims (1)

1. A V-PCA fault diagnosis method based on a complex industrial chemical process is characterized by comprising the following steps:

a data preprocessing stage:

step X1, constructing the collected original complex industrial chemical engineering TE data set into a multi-dimensional variable system matrix X_n∈R^m×n,X_nAs follows;

wherein, the column vector x_i(j)＝[x₁(j),x₂(j),...x_m(j)]^TI 1,2, m, j 1,2, n represents a system variable, the data matrix is preprocessed, X_nHas a mean vector of b_n

Step X2, calculating X_nMean vector of samples of variables of

Wherein l_m＝[1,1,...1]∈R^1×mThe original data is transformed to obtain a matrix X^*；

Wherein the transformation method is as follows

The physical significance of the formula is that the sample mean value of each variable is taken as the center, and the change rate represents the degree of deviation of original data from the center; then, whether the test sample data acquired in real time falls in a normal range is checked through the change rate obtained after the normal sample data is preprocessed, and if the projection is outside the normal region, a fault occurs;

establishing a V-PCA model stage:

y1, for the data matrix X^*Covariance decomposition is performed, and the number of principal elements is selected to obtain the following formula

Wherein Λ ═ diag { λ ═ λ₁,λ₂,…,λ_mIs a matrix of eigenvalues of S, and the elements on its diagonal satisfy λ₁>λ₂>…>λ_m，V∈R^m×mIs the eigenvector matrix of S, P ∈ R^m×rThe first r column of V contains all pivot information,

is the remaining m-r columns of V, containing residual information;

y2 step, mixing X^*Decomposing to obtain principal component subspace and residual subspace

In the above formula, T ∈ R^n×rTo score the matrix, P ∈ R^m×rIn the form of a load matrix, the load matrix,

is a main element space, and is characterized in that,

is a residual space;

and (3) in an online fault detection and fault diagnosis stage:

step Z1, calculating SPE statistic; SPE statistics for measuring changes in sample vector projections in residual space

Here, the first and second liquid crystal display panels are,

for the control limit with a confidence level of alpha,calculated from the following equation

Wherein the content of the first and second substances,

λ_jeigenvalues of a covariance matrix of X, c_αA threshold value of a standard normal distribution at a confidence level α;

step Z2, calculating Hotelling T²Statistics; it is used to measure the variation of sample vector in principal component space

In the above formula, Λ ═ diag { λ₁,λ₂,…,λ_A}，

For the control limit with confidence α, it is calculated by the following formula

Here, F_r,n-A；rIs the F distribution value with r and n-r degrees of freedom and a confidence level of alpha;

step Z3, based on the fault isolation of SPE contribution rate, the contribution graph of SPE is defined as follows:

wherein the content of the first and second substances,

for each variable contribution to the statistic SPE, where

ξ_iIs in identity matrix I_mThe ith column;

step Z4, based on T²Fault isolation of contribution rate; t is²The contribution ratio of (c) is defined as follows:

wherein D ═ P^TΛ^-1P calculates the contribution rate of each variable of the system to the fault according to the formula, and the larger is regarded as the cause variable of the fault, thereby carrying out fault isolation.

Images