CN106444666A - Dynamic process monitoring method based on weighted dynamic distributed PCA model - Google Patents

Abstract

The invention discloses a dynamic process monitoring method based on a weighted dynamic distributed PCA model. The method is to solve a problem how to effectively describe the dynamic characteristics of each measured variable for the complex dynamic characteristics of modern industrial process data and to establish a dynamic distributed monitoring model on this basis. The method weights each variable in a augmented matrix by using a correlation coefficient between each measured variable and other different delayed measurement values so that the weighted training data can better reflect the dynamic relation of the corresponding measured variable. The PCA model established on this basis can better excavate the hidden information related to each measured variable, and the interpretability of the model can be further improved. Compared with a traditional method, despite establishing a PCA fault detection model by using all different delay variables, the method assigns larger weights to the variables with large correlation and assigns smaller weights to the variables with small correlation, which not only prevents information loss to the utmost extent, but also highlights the process variables with strong correlation because of different weight values while suppressing the interference of irrelevant variables. Therefore, the dynamic process monitoring method based on a weighted dynamic distributed PCA model can obtain a superior fault detection effect.

Description

Dynamic process monitoring method based on weighted dynamic distributed PCA model

Technical Field

The invention relates to an industrial process monitoring method, in particular to a dynamic process monitoring method based on a weighted dynamic distributed PCA model.

Background

The real-time monitoring of the running state of the production process is a necessary means for ensuring production safety and maintaining stable product quality, and a reliable and effective fault detection method is an essential component for achieving the goal. In recent decades, modern industrial processes have gradually completed the transition from a single production unit to a combination of multiple staggered production units. Physical models that accurately describe their mechanism of operation are difficult to obtain, and process monitoring methods based on mechanism models are no longer suitable for modern industrial processes. Instead, data-driven process monitoring methods that core production process sampling data. Generally, as an important branch of data-driven process monitoring methods, the core idea of multivariate statistical process monitoring is that: how to effectively mine the normal process data to establish a statistical model capable of describing the normal process running state, thereby realizing the purpose of monitoring whether the process fails. Considering that the modern industrial process widely adopts DCS and advanced detection instrument technology, the data sampling time interval is short and the system can store massive industrial data. Complex dynamic relationships exist among the industrial data and the measured variables, and challenges are raised to the practicability of the traditional dynamic process monitoring method.

In the existing dynamic process monitoring method, in order to deal with the autocorrelation among process data, the most common processing means is to introduce data of a plurality of previous sampling moments into each sample to form an augmented matrix, and then to establish a corresponding statistical process monitoring model by using the augmented data matrix. For example, the classical Dynamic Principal Component Analysis (DPCA) is a method of establishing a PCA-based fault detection model using an augmented matrix. The use of an augmented matrix is the simplest dynamic process data processing method, but it confuses the autocorrelation and cross correlation of data, and is not favorable for deep analysis of a process model. For this reason, Dynamic process monitoring methods based on Dynamic Latent Variables (DLV) models have attracted attention in both academic and industrial fields. The DLV model realizes effective monitoring of the dynamic process by separately extracting the dynamic latent components and the static latent components of the process. Meanwhile, due to the distinguishability of the model on the dynamic component and the static component, the interpretability of the DLV model is obviously superior to that of the classic DPCA model. Recently, in consideration of the complexity of the dynamic relationship between process data, that is, the interaction between different measurement variables will be reflected in different sampling moments, researchers propose to select dynamic characteristics for each measurement variable of the process, and establish a PCA monitoring model corresponding to the variable to realize distributed monitoring of the dynamic process. Although the fault detection effect obtained by the dynamic distributed monitoring method is obviously superior to that obtained by the DPCA and DLV methods, when the dynamic characteristic selection is implemented, a threshold value needs to be set so as to select other measurement values which are closely related to the current measurement variable at different sampling moments. Without sufficient a priori knowledge, the determination of the threshold value directly affects the fault detection performance of the subsequent monitoring model. Therefore, the wide application of the method is still in need of further improvement and perfection.

Although this approach of performing dynamic feature selection for each measured variable has its unique advantages, how to determine the threshold value is likely to be the biggest impediment to its further generalization. Generally, the larger the threshold setting, the smaller the number of variables selected. Although the interference influence of irrelevant variables on modeling can be greatly eliminated, certain information can be lost. On the contrary, if a smaller threshold is set, information loss is not a problem, but irrelevant variables introduce interference factors to the model building. Therefore, a better method for describing the dynamic characteristics of each measured variable needs to be designed, and various problems caused by the size of the threshold value are avoided.

Disclosure of Invention

The main technical problem to be solved by the invention is how to effectively describe the dynamic characteristics of each measured variable aiming at the dynamic data of the modern industrial process, and a dynamic distributed monitoring model is established on the basis. Therefore, the invention provides a dynamic process monitoring method based on a weighted dynamic distributed PCA model, which firstly uses an augmentation matrix to calculate the correlation coefficient between each measured variable and other different delay measured values. Then, weighting each variable in the augmentation matrix by using the correlation coefficients, and establishing a corresponding PCA fault detection model. Finally, the PCA models are utilized to perform distributed monitoring on whether the production process fails.

The technical scheme adopted by the invention for solving the technical problems is as follows: a dynamic process monitoring method based on a weighted dynamic distributed PCA model comprises the following steps:

(1) under the normal operation state of the production process, the collected data form a training data set X ∈ R^n×mAnd constructing the augmented matrix X as follows_a∈R^{(n-d)×m(d+1)}：

Wherein n is the number of training samples, m is the number of process measurement variables, R is the set of real numbers, R is the number of training samples^n×mA matrix of real numbers representing dimension n × m, d being the number of delay measurements introduced, x_k∈R^1×mThe sample data at the kth sampling instant has a subscript number k of 1, 2, …, n.

(2) For matrix X_aEach variable in the data matrix is standardized to obtain a new data matrix with a mean value of 0 and a standard deviation of 1Namely:

wherein, y^jRepresenting normalized augmented matricesIn the j-th column (or j-th variable) of (1), the reference number j is 1, 2, …, m (d +1), and i is initialized to 1.

(3) Calculating the ith measurement variable according to the formulaCorrelation coefficient C between different variables_i，j：

Wherein the upper label T represents the transpose of the matrix or vector, the symbol | | | | | represents the length of the calculation vector, and the obtained m (d +1) phase relation is combined into the weighting vector C_i＝[C_i，1，C_i，2，…，C_i，m(d+1)]。

(4) According to the formulaWeighting each variable to obtain a new matrix

In the above formula, the weighting matrix W_i＝diag(C_i) For diagonal matrices, the elements on the diagonal correspond to the vector C_iThe respective numerical values in (1).

(5) Is a matrixEstablishing corresponding PCA fault detection model and reserving model parametersReady to be called during on-line monitoring, wherein q_iThe number of principal components reserved for the ith PCA model,for the corresponding projective transformation matrix or matrices,for q in the ith PCA model_iThe covariance matrix of the individual principal components,andcontrol limits for two monitoring statistics in the ith PCA model, respectively.

(6) If i is equal to i +1 and i is less than or equal to m, returning to the step (3); otherwise, the obtained m weighting matrixes W are saved₁，W₂，…，W_mAnd m different sets of PCA fault detection model parameters theta₁，Θ₂，…，Θ_m。

(7) Collecting data samples x at new sampling instants_i∈R^1×mThe samples of the previous d sampling moments are introduced to obtain an augmented vector x_a＝[x_t，x_t-1，…，x_t-d]And subjecting it to the same normalization treatment

(8) Using m weighting matrices W₁，W₂，…，W_mRespectively to vectorWeighting to obtain m sumsWeighted vector

(9) Calling m different PCA fault detection model parameters theta₁，Θ₂，…，Θ_mRespectively calculating monitoring statistics corresponding to different PCA models according to the following formula:

where the subscript i is 1, 2, …, m until m sets of monitoring statistics are obtained.

(10) Deciding whether the data at the current sampling moment is normal or not, and if all the statistic numerical values meet the conditionAndthe current data is a normal sample; otherwise, the decision system fails.

The method of the invention accomplishes the dynamic feature description of each measured variable by weighting each variable in the augmentation matrix. Compared with the traditional method, the method can define the unique dynamic relation for each measured variable, the interpretability of the model is further enhanced, and the process monitoring method implemented on the basis should obtain more excellent fault detection effect. In addition, the method of the invention utilizes all different delay variables to establish a PCA fault detection model, and only endows a variable with large correlation with a larger weight and endows a variable with small correlation with a smaller weight, thereby not only avoiding the problem of information loss to the maximum extent, but also showing the process variable with strong correlation and simultaneously inhibiting the interference influence of irrelevant variables due to different weights. The method makes up the defects of the traditional dynamic process monitoring method in the aspect of dynamic description of the measured variable, and the specific implementation steps of the method are not limited by the threshold parameter any more. Therefore, the method of the present invention is more suitable for monitoring modern dynamic industrial processes.

Drawings

FIG. 1 is a flow chart of an embodiment of the method of the present invention.

Detailed Description

The method of the present invention will be described in detail below with reference to the accompanying drawings.

As shown in fig. 1, the present invention relates to a dynamic process monitoring method based on a weighted dynamic distributed PCA model, which comprises the following specific implementation steps:

step 1, collecting data to form a training data set X ∈ R under the normal operation state of the production process^n×mAnd constructing the augmented matrix X as follows_a∈R^{(n-d)×m(d+1)}：

Wherein n is the number of training samples, m is the number of process measurement variables, R is the set of real numbers, R is the number of training samples^n×mA matrix of real numbers representing dimension n × m, d being the number of delay measurements introduced, x_k∈R^1×mThe sample data at the kth sampling instant has a subscript number k of 1, 2, …, n.

Step 2: for matrix X_aEach variable is subjected to standardization processing to obtain new data with the mean value of 0 and the standard deviation of 1Matrix arrayNamely:

wherein, y^jRepresenting normalized augmented matricesIn the j-th column (or j-th variable) of (1), the reference number j is 1, 2, …, m (d +1), and i is initialized to 1.

And step 3: let i equal i +1, calculate the ith measurement variable andcorrelation coefficient C between different variables_i，j：

Wherein the upper label T represents the transpose of the matrix or vector, the symbol | | | | | represents the length of the calculation vector, and the obtained m (d +1) phase relation is combined into the weighting vector C_i＝[C_i，1，C_i，2，…，C_i，m(d+1)]。

And 4, step 4: according to the formulaWeighting each variable to obtain a new matrix

In the above formula, the weighting matrix W_i＝diag(C_i) For diagonal matrices, the elements on the diagonal correspond to the vector C_iThe respective numerical values in (1).

And 5: is a matrixEstablishing corresponding PCA fault detection model and reserving model parametersReady to be called during on-line monitoring, wherein q_iThe number of principal components reserved for the ith PCA model,for the corresponding projective transformation matrix or matrices,for q in the ith PCA model_iThe covariance matrix of the individual principal components,andthe specific steps for solving the PCA fault detection model are as follows:

first, calculateCovariance matrix of

Next, solve for S_iAll non-zero eigenvalues λ₁＞λ₂＞…＞λ_NCorresponding feature vector p₁，p₂…，p_NWherein N isThe number of non-zero eigenvalues;

thirdly, the number q of reserved principal components is set_iTo satisfy the conditionsAnd will correspond to q_iThe feature vectors form a projective transformation matrix

Then, the principal component is calculatedOf the covariance matrix Λ_i＝T_i ^TT_iV (n-d-1), and calculating a control limit according to the following formulaAnd

wherein,representing a confidence of α and a degree of freedom of q_iAnd n-d-q_iThe value corresponding to the F distribution of (a),representing the degree of freedom h and the confidence α as the corresponding values of chi-square distribution, M and V are Q_iThe estimated mean and the estimated variance of the statistics.

Finally, the model parameters are retainedTo be called.

Step 6: if i is equal to i +1 and i is less than or equal to m, returning to the step (3); otherwise, the obtained m weighting matrixes W are saved₁，W₂，…，W_mAnd m different sets of PCA fault detection model parameters theta₁，Θ₂，…，Θ_m。

And 7: collecting data samples x at new sampling instants_t∈R^1×mThe samples of the previous d sampling moments are introduced to obtain an augmented vector x_a＝[x_t，x_t-1，…，x_t-d]And subjecting it to the same normalization treatment

And 8: using m weighting matrices W₁，W₂，…，W_mRespectively to vectorPerforming weighting processing, namely:

where the subscript i is 1, 2, …, m, corresponding to m weighted vectors

And step 9: for the ith vectorCalling the corresponding ith PCA model parameter theta_iEstablished as shown belowTwo monitoring statistics:

to this end, m different sets of monitoring statistics can be obtained.

Step 10: deciding whether the data at the current sampling moment is normal or not, and if all the statistic numerical values meet the conditionAndthe current data is a normal sample; otherwise, the decision system fails.

Claims (1)

1. A dynamic process monitoring method based on a weighted dynamic distributed PCA model is characterized by comprising the following steps:

(1) under the normal operation state of the production process, collecting data to form a training data set X ∈ R^n×mAnd constructing the augmented matrix X as follows_a∈R^{(n-d)×m(d+1)}：

$X_a=\left[\begin{array}{cccc}{x}_{d+1}& x_d& \mathrm{...}& x_1\\ x_{d+2}& x_{d+1}& \mathrm{...}& x_2\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_n& x_{n-1}& \mathrm{...}& x_{n-d}\end{array}\right]---\left(1\right)$

Wherein n is the number of training samples, m is the number of process measurement variables, R is the set of real numbers, R is the number of training samples^n×mA matrix of real numbers representing dimension n × m, d being the number of delay measurements introduced, x_k∈R^1×mFor the sample data at the kth sampling instant, the subscript number k is 1, 2, …, n:

(2): for matrix X_aEach variable in the data matrix is standardized to obtain a new data matrix with a mean value of 0 and a standard deviation of 1Namely:

$\stackrel{\‾}{X}=\[y^1,y^2,\mathrm{...},y^{m(d+1)}\]---\left(2\right)$

wherein, y^jRepresenting normalized augmented matricesColumn j (or jth variable) in (a), the superscript j is 1, 2, …, m (d +1), and initializes i to 1;

(3): calculating the ith measurement variable according to the formulaCorrelation coefficient C between different variables_i，j：

$C_{i,j}=\left|\frac{y^{iT}{y}^j}{\left|\right|y^i\left|\right|\·\left|\right|y^j\left|\right|}\right|---\left(3\right)$

Wherein the upper label T represents the transpose of the matrix or vector, the symbol | | | | | represents the length of the calculation vector, and the obtained m (d +1) phase relation is combined into the weighting vector C_i＝[C_i，1，C_i，2，…，C_i，m(d+1)]；

(4): according to the formulaWeighting each variable to obtain a new matrix

${\stackrel{\‾}{X}}_i=\[y^1{C}_{i,1},y^2{C}_{i,2},\mathrm{...},y^{m(d+1)}{C}_{i,m(d+1)}\]=\stackrel{\‾}{X}{W}_i---\left(4\right)$

In the above formula, the weighting matrix W_i＝diag(C_i) For diagonal matrices, the elements on the diagonal correspond to the vector C_iThe numerical values in (1);

(5): is a matrixEstablishing corresponding PCA fault detection model and reserving model parametersReady to be called during on-line monitoring, wherein q_iThe number of principal components reserved for the ith PCA model,for the corresponding projective transformation matrix or matrices,for q in the ith PCA model_iThe covariance matrix of the individual principal components,andthe specific steps for solving the PCA fault detection model are as follows:

① calculationCovariance matrix of

② solving for S_iAll non-zero eigenvalues λ₁＞λ₂＞…＞λ_NCorresponding feature vector p₁，p₂…，p_NWherein N is the number of non-zero eigenvalues;

③ setting the number of principal components q reserved_iTo satisfy the conditionsAnd will correspond to q_iThe feature vectors form a projective transformation matrix

④ calculating principal componentsOf the covariance matrix Λ_i＝T_i ^TT_iV (n-d-1), and calculating a control limit according to the following formulaAnd

$D_i^{\lim }=\frac{q_i(n-d-1)}{n-d-q_i}{F}_{q_i,n-d-q_i,\mathrm{\α}}---\left(5\right)$

$Q_i^{\lim }={\mathrm{g\χ}}_{h,\mathrm{\α}}^2,g=\frac{V}{2M},h=\frac{2M^2}{V}---\left(6\right)$

wherein, F_{d，n-l-d，α}Representing a confidence of α and a degree of freedom of q_iAnd n-d-q_iThe value corresponding to the F distribution of (a),representing the degree of freedom h and the confidence α as the corresponding values of chi-square distribution, M and V are Q_iAn estimated mean and an estimated variance of the statistics;

⑤ preserving model parametersTo be called;

(6): if i is equal to i +1 and i is less than or equal to m, returning to the step (3); otherwise, the obtained m weighting matrixes W are saved₁，W₂，…，W_mAnd m different sets of PCA fault detection model parameters theta₁，Θ₂，…，Θ_m；

(7): collecting data samples x at new sampling instants_t∈R^1×mThe samples of the previous d sampling moments are introduced to obtain an augmented vector x_a＝[x_t，x_t-1，…，x_t-d]And subjecting it to the same normalization treatment

(8): using m weight vectors C₁，C₂，…，C_mRespectively to vectorPerforming weighting processing, namely:

${\stackrel{\‾}{x}}_i=\stackrel{\‾}{x}{W}_i---\left(7\right)$

where the subscript i is 1, 2, …, m, corresponding to m weighted vectors

(9): calling m different PCA fault detection model parameters theta₁，Θ₂，…，Θ_mRespectively calculating monitoring statistics corresponding to different PCA models according to the following formula:

$D_i={\stackrel{\‾}{x}}_i{P}_i{\mathrm{\Λ}}_i^{-1}{P}_i^T{\stackrel{\‾}{x}}_i^T---\left(8\right)$

$Q_i=\left|\right|{\stackrel{\‾}{x}}_i-{\stackrel{\‾}{x}}_i{P}_i{P}_i^T|{|}^2---\left(9\right)$

so far, m groups of different monitoring statistics can be obtained;

(10): deciding whether the data at the current sampling moment is normal or not, and if all the statistic numerical values meet the conditionAndthe current data is a normal sample; otherwise, the decision system fails.