CN107272655B - Batch process fault monitoring method based on multi-stage ICA-SVDD - Google Patents

Abstract

The invention discloses a multi-stage ICA-SVDD-based intermittent process fault monitoring method. For batch processes with complex process mechanisms and multiple operating stages. Aiming at the multi-stage and non-Gaussian data distribution problems of some batch processes, an improved stage division and fault monitoring method is adopted. First, divide the stages according to the similarity of each time slice and the K-means algorithm, then use the independent component analysis method to extract the non-Gaussian feature information for each stage, and finally introduce the support vector data description algorithm to analyze the independent components and the remaining Gaussian residuals Statistical analysis models are established separately in each space to realize the fault monitoring of the whole process. Applied to the fault monitoring of an actual semiconductor etching process, the results show that the method has a better monitoring effect on the multi-stage batch process.

Description

Batch process fault monitoring method based on multi-stage ICA-SVDD

technical field

The invention relates to a multi-stage ICA-SVDD-based intermittent process fault monitoring method, which belongs to the field of industrial process fault diagnosis and soft measurement.

Background technique

Batch process is an important industrial production mode, its process mechanism is complicated and there are multiple operation stages, and the product quality is easily affected by uncertain factors. In order to ensure the safe and reliable operation of the batch production process and the pursuit of high-quality products, it is necessary to establish an effective process monitoring system to monitor the faults of the batch production process. Multivariate statistical process control methods have been widely used in batch process monitoring, such as multiway principal component analysis (MPCA) and multiway partial least squares analysis (multiway partial least squares, MPLS). But most of the data description methods related to principal component analysis and partial least squares analysis have the limitation that the data conform to Gaussian distribution and the relationship between different variables is linear.

In view of the non-Gaussian nature of batch process data, independent component analysis (ICA) was introduced into the field of process monitoring. In order to adapt to the fault monitoring of batch processes, some scholars extended the ICA method to multiway independent component analysis (multiway ICA, MICA) method. Although non-Gaussian data can be processed, when determining the confidence limits of process monitoring statistics, the calculation process based on the kernel density estimation method is complicated and the parameters cannot be obtained accurately. When the variable dimension is large, the "dimensionality" brought by kernel density estimation cannot be avoided disasters” and so on. In addition, for the monitoring of nonlinear batch processes, traditional MPCA/MPLS methods are also extended to their nonlinear forms, such as multi-kernel PCA and multi-kernel PLS, however, process monitoring methods based on these nonlinear methods also need to obey Gaussian distributed.

Multiple operating stages are an inherent characteristic of many batch processes. If a single modeling approach is used to monitor the entire batch process, the model will not perform well in monitoring different stages. Aiming at this characteristic, scholars at home and abroad have done a lot of research, by dividing the batch process into reasonable stages and establishing a process monitoring model in sub-stages, so as to improve the monitoring performance.

Process monitoring can be considered as a single-valued classification problem because the task of monitoring is to separate normal data from faulty data. Support vector data description (Support vector data description, SVDD) algorithm is a single value classification method originally proposed by Tax and Duin. The normal data sample space is mapped to the high-dimensional feature space through nonlinear transformation and a model is established to separate the normal data from the fault data and achieve the purpose of process fault monitoring. Using the SVDD algorithm for fault monitoring can simultaneously process data that does not conform to Gaussian distribution and non-linear relationship between variables. SVDD has been used in damage detection, image classification, pattern recognition and other fields, and its application in the field of process monitoring has also begun to receive attention.

A multi-stage batch process fault monitoring method based on independent component analysis and support vector data description can effectively improve the fault monitoring performance of batch process. Since most of the data description methods related to principal component analysis and partial least squares analysis have the limitation that the data conform to Gaussian distribution and the relationship between different variables is linear. This method can solve the non-Gaussian and nonlinear monitoring problems of process data at the same time, and has better fault monitoring effect.

Contents of the invention

In view of the multi-stage, non-Gaussian and non-linear nature of the batch process, the process mechanism is complex, and the product quality is easily affected by uncertain factors. In order to improve the fault monitoring performance of the multi-stage batch process, the present invention provides a method based on A Multi-Stage ICA-SVDD Approach to Batch Process Fault Monitoring.

First, the three-dimensional data is expanded along the batch direction, and the fuzzy stage division is carried out according to the similarity of each time slice, and the initial number of clusters can be obtained, so as to carry out accurate stage division through the K-means algorithm; when the stage is determined, the three-dimensional The data is expanded along the variable direction, and then the ICA method is used for feature extraction at each stage, and the corresponding non-Gaussian feature information and residual information are extracted; finally, the non-Gaussian space of the independent components and the remaining residual space are established by the SVDD algorithm The statistical analysis model realizes the online fault monitoring of the whole process.

The purpose of the present invention is achieved through the following technical solutions:

A batch process fault monitoring method based on multi-stage ICA-SVDD, the method includes the following process: for the multi-operation stage characteristics of the batch process, it is necessary to divide the production process into reasonable stages in order to establish multiple sub-models for fault monitoring. Firstly, according to the similarity of the mean value vectors of each time slice, the production process is divided into fuzzy stages, and the preliminary stage number is obtained. Then through the K-means algorithm, the moments with similar data characteristics are classified into one category, so as to obtain more accurate stage division.

Use the independent component analysis method to extract non-Gaussian feature information for each stage. After using the ICA algorithm to extract all independent components, rearrange them according to the degree of non-Gaussian, and select the first d independent components with strong independence to obtain the corresponding matrix. Since the batch process has been divided into multiple stages, it is necessary to perform ICA analysis on each stage for feature extraction. Furthermore, the non-Gaussian feature information and residual information corresponding to each stage can be extracted in order to establish a monitoring statistical model for fault monitoring.

Finally, the support vector data description algorithm is introduced to establish statistical analysis models for the independent components and the remaining Gaussian residual space, so as to realize the fault monitoring of the whole process. Through nonlinear transformation, the normal data sample space is mapped to the high-dimensional feature space and a model is established, so as to separate the normal data from the fault data and achieve the purpose of process fault monitoring. Using the SVDD algorithm for fault monitoring can simultaneously process data that does not conform to the Gaussian distribution and the non-linear relationship between variables.

Description of drawings

Fig. 1 is the flow chart of the batch process monitoring method based on multi-stage ICA-SVDD;

Figure 2 Batch process data expansion;

Figure 3 Multi-stage division results;

Figure 4 normal batch monitoring results;

Figure 5 fault TCP+50 batch monitoring results;

Detailed ways

Below in conjunction with shown in Fig. 1, the present invention is described in further detail:

The research data used is collected from an actual semiconductor etching process, and the fault monitoring is carried out on the normal data and fault data of semiconductor etching respectively.

Step 1: Two-dimensional expansion of the three-dimensional data set X (I×J×K) of the batch process, where I represents the number of batches, J represents the number of variables, and K represents the number of sampling points. Using the data processing method that combines the batch direction and the variable direction, the three-dimensional data X (I×J×K) is first transformed into a two-dimensional matrix X(I×KJ) along the batch direction, and then the two-dimensional matrix; and then recombine according to the variable direction to form a new two-dimensional matrix X(KI×J). The two-step data expansion method is shown in Figure 2.

Step 2: Carry out reasonable stage division for the production process in order to establish multiple sub-models for fault monitoring. First, according to the similarity of the mean value vector of each time slice, the production process is divided into fuzzy stages, and the preliminary stage number is obtained. Then through the K-means algorithm, the moments with similar data characteristics are classified into one category, so as to obtain more accurate stage division.

Step1: Expand the three-dimensional process data X (I×J×K) according to the batch direction to obtain a two-dimensional matrix X(I×KJ), and then cut it into a two-dimensional data time slice matrix composed of batches and variables according to the time axis direction X _k (I×J), k=1, 2, . . . , K.

Step2: Obtain the mean value vector of each time slice matrix X _k (I×J), denoted as These mean value vectors represent the feature information of each time slice, use these feature information to divide the time slice into initial stages, and identify each stage, take the first time slice X ₁ as the benchmark X _base of the first stage, Then follow the similarity calculation formula:

Calculate the time slice behind X _base and its similarity in turn, and set the similarity threshold α. If the similarity between X ₂ and X _base is greater than the threshold α, consider that X ₂ also belongs to the current period, and then continue to calculate the next time slice similarity with X _base ; otherwise, consider X ₂ to belong to the next stage, set X _base =X ₂ , and proceed according to the above steps.

According to the similarity, similar time slices are connected to form a time period, and a preliminary fuzzy division is obtained. The corresponding number of stages P can be obtained, which provides a basis for selecting the number of clusters with the clustering algorithm later. However, some points or very few continuous points cannot be accurately divided into a certain stage in this fuzzy division method. .

Step3: Cluster the mean vector of the time slice through the K-means clustering algorithm, and the input of the algorithm is a set of mean vectors And the number of clusters P, choose P cluster centers arbitrarily, and perform multiple iterative calculations. When the algorithm meets the convergence conditions, you can get the cluster centers of P sub-clusters, and calculate each mean vector The distance to all cluster centers can be obtained For the affiliation relationship of P sub-categories, since the input of the clustering algorithm is the time slice mean vector arranged in chronological order, according to the chronological order, the points in the fuzzy division that cannot be determined to belong to the stage can be divided into a corresponding stage. A more precise stage division can be obtained. The multi-stage division results of the semiconductor etching process are shown in Figure 3.

Step 3: Use independent component analysis (ICA) to extract feature information. ICA makes full use of the high-order statistical information of the data, and can further extract mutually independent latent variables from the observed data. These latent variables can be More essential extraction of reaction process features.

The ICA model is defined as

X=AS+E (2)

Where X=[x(1),x(2),...,x(n)]∈R ^m×n is the observation data matrix, A=[a ₁ ,a ₂ ,...,a _d ]∈ R ^m×d is an unknown mixing matrix, S=[s(1),s(2),...,s(n)]∈R ^d×n is a hidden independent component matrix, E∈R ^m×n is the residual matrix. n is the number of samples collected. It can be seen from d≤m that ICA is actually a data compression technique similar to PCA, which describes as much information as possible with as little data as possible.

The purpose of ICA is to estimate the mixing matrix W and independent components S from the observed data X, therefore, the goal of ICA: to find an unmixing matrix W that can separate the source signal from the observed signal, namely

When d=m, that is, when the unmixing matrix W is the inverse of the mixing matrix A, is the best estimate of the independent component S.

After using the ICA algorithm to extract all independent components, rearrange them according to the degree of non-Gaussian, and select the first d independent components with strong independence to obtain the corresponding matrix Since the batch process has been divided into multiple stages, it is necessary to perform ICA analysis on the X _p (K _p I×J) of each stage for feature extraction, where p represents the corresponding p-th stage, and X _p represents the p-th stage The stage is a two-dimensional matrix expanded along the variable direction, and K _p represents the number of samples corresponding to the p-th stage, and then the non-Gaussian feature information and residual information corresponding to each stage can be extracted in order to establish a monitoring statistical model for fault monitoring.

Step 4: Use Support vector data description (Support vector data description, SVDD) for online monitoring of intermittent processes. SVDD is a single-valued classification algorithm. The basic idea is to target the training data set X={ _xi ,i=1, …,N}, project the original space data to the feature space {Φ(x _i ),i=1,…,N} through nonlinear transformation Φ:X→F, then you can find in the feature space that can contain all data samples The hypersphere with the smallest volume, SVDD maps the input space to a high-dimensional space through the kernel function to learn a flexible and accurate data description model, and the obtained hypersphere data description boundary is represented by a small number of support vectors.

To construct such a minimal hypersphere, SVDD needs to solve the following optimization problem:

In formula (4), a is the center of the hypersphere, R is the radius of the hypersphere, and the penalty coefficient C weighs the volume of the hypersphere and the misclassification rate of the training samples. The introduction of the slack variable _ξi represents The sample produces a penalty term for misclassification, and the above optimization problem can be transformed into solving the corresponding dual problem:

Here, the kernel function K( _xi , x _j ) is introduced to replace the inner product function ( _xi , x _j ). Using quadratic programming, a _i can be obtained. If x ₀ represents any support vector, then the hypersphere The center and radius of the sphere can be expressed as:

For a new sample x _new , the distance to the center of the hypersphere can be obtained:

If Dist _new ≤ R, the sample is normal; otherwise, the sample is abnormal.

After using ICA to extract the features of each stage of the batch process, the data of the non-Gaussian space of the independent components and the remaining residual space can be obtained respectively, and the extracted independent components can be analyzed by the SVDD method and the residual matrix E to establish a statistical analysis model, first for the independent components Establish the SVDD model as follows:

In the formula: Indicates the kth sample, α _k is the Lagrangian multiplier of the corresponding sample, K(·) represents the Gaussian kernel function, and the independent components can be obtained The center and radius of the formed SVDD hypersphere are shown in formula (9):

Similarly, the SVDD model is established for the residual matrix E as follows:

Then, the center and radius of the SVDD hypersphere formed by the residual matrix E are shown in formula (11):

For each stage of the batch process, the hypersphere radius R of the corresponding stage can be obtained respectively. During online process monitoring, when the sampling data x _new at the current moment is obtained, after data preprocessing and ICA feature extraction, the independent components are obtained respectively and the distance from the residual matrix E _new to the center of the corresponding sphere and Dist _{E_new} , so when Dist≤R, it can be considered that the sample at the current moment is normal, and when Dist>R, it means that the sample at the current moment is faulty data.

After the stage division and preprocessing of the process data, in order to compare the fault monitoring effect of single modeling and multi-stage modeling, the single-stage and multi-stage statistical monitoring models of PCA, ICA, and ICA-SVDD were respectively established. All statistics The statistical control limits were set at 99%. Figure 4 shows the monitoring results of the six methods for normal batches. It can be seen that the six methods can obtain good monitoring results for normal batches. Among them, (a), (b), (c) are fault monitoring diagrams of normal batches with single modeling method, and (d), (e), (f) are fault monitoring diagrams of normal batches with multi-stage modeling method. Figure 5 shows the fault monitoring graph of TCP+50 faults, where (a), (b), (c) are the monitoring graphs of faulty batches with a single modeling method, and (d), (e), (f) are Monitoring plot of a faulty batch for a multi-stage modeling approach. It can be seen from Figure 5 that for TCP+50 faults, whether it is a single model or a multi-stage model for fault monitoring, ICA-SVDD is significantly better than the other two methods.

Claims (2)

1. the method for the intermittent process fault monitoring based on multistage ICA-SVDD, it is characterized in that, the method step is: Step 1: The three-dimensional data set X (I×J×K) of the batch process is expanded two-dimensionally, where I represents the number of batches, J represents the number of variables, and K represents the number of sampling points; using the combination of batch direction and variable direction According to the data processing method, the three-dimensional data X (I×J×K) is converted into a two-dimensional matrix X (I×KJ) along the batch direction first, and then the two-dimensional matrix is standardized; and then recombined according to the variable direction to form a new The two-dimensional matrix X(KI×J); Step 2: Divide the production process into reasonable stages in order to establish multiple sub-models for fault monitoring; first, divide the production process into fuzzy stages according to the similarity of the mean vectors of each time slice, and obtain the preliminary number of stages; then use K-means The algorithm classifies the moments with similar data characteristics into one category, so as to obtain more accurate stage division; Step1: Expand the three-dimensional process data X (I×J×K) according to the batch direction to obtain a two-dimensional matrix X(I×KJ), and then cut it into a two-dimensional data time slice matrix composed of batches and variables according to the time axis direction X _k (I×J), k=1,2,...,K; Step2: Obtain the mean value vector of each time slice matrix X _k (I×J), denoted as These mean value vectors represent the feature information of each time slice, use these feature information to divide the time slice into initial stages, and identify each stage, take the first time slice X ₁ as the benchmark X _base of the first stage, Then follow the similarity calculation formula: Calculate the time slice behind X _base and its similarity in turn, and set the similarity threshold α. If the similarity between X ₂ and X _base is greater than the threshold α, consider that X ₂ also belongs to the current period, and then continue to calculate the next time slice and the similarity of X _base ; otherwise, think that X ₂ belongs to the next stage, and make X _base =X ₂ , proceed according to the above steps; According to the similarity, similar time slices are connected to form a time period, and a preliminary fuzzy division can be obtained; the corresponding number of stages P can be obtained, which provides a basis for selecting the number of clusters with a clustering algorithm later, but this fuzzy division There will be some points or very few continuous points that cannot be accurately divided into a certain stage; Step3: Cluster the mean vector of the time slice through the K-means clustering algorithm, and the input of the algorithm is a set of mean vectors And the number of clusters P, choose P cluster centers arbitrarily, and perform multiple iterative calculations. When the algorithm meets the convergence conditions, you can get the cluster centers of P sub-clusters, and calculate each mean vector The distance to all cluster centers can be obtained For the affiliation relationship of P sub-categories, since the input of the clustering algorithm is the time slice mean vector arranged in chronological order, according to the chronological order, the points in the fuzzy division that cannot be determined to belong to the stage can be divided into a corresponding stage. A more precise stage division can be obtained; Step 3: Use independent component analysis (ICA) to extract feature information. ICA makes full use of the high-order statistical information of the data, and can further extract mutually independent latent variables from the observed data. These latent variables can be Extract the characteristics of the reaction process more essentially; The ICA model is defined as X=AS+E (2) Where X=[x(1),x(2),...,x(n)]∈R ^m × ⁿ is the observation data matrix, A=[a ₁ ,a ₂ ,...,a _d ]∈ R ^m × ^d is the unknown mixing matrix, S=[s(1),s(2),...,s(n)]∈R ^d×n is the hidden independent component matrix, E∈R ^m×n is the residual matrix; n is the number of samples collected, and it can be seen from d≤m that ICA is actually a data compression technique similar to PCA, which describes as much information as possible with as little data as possible; The purpose of ICA is to estimate the mixing matrix A and independent components S from the observed data X, therefore, the goal of ICA: to find an unmixing matrix W that can separate the source signal from the observed signal, that is When d=m, that is, when the unmixing matrix W is the inverse of the mixing matrix A, is the best estimate of the independent component S; After using the ICA algorithm to extract all independent components, rearrange them according to the degree of non-Gaussian, and select the first d independent components with strong independence to obtain the corresponding matrix Since the batch process has been divided into multiple stages, it is necessary to perform ICA analysis on the X _p (K _p I×J) of each stage for feature extraction, where p represents the corresponding p-th stage, and X _p represents the p-th stage The stage is a two-dimensional matrix expanded along the variable direction, and K _p represents the number of samples corresponding to the p-th stage, and then the non-Gaussian feature information and residual information corresponding to each stage can be extracted in order to establish a monitoring statistical model for fault monitoring; Step 4: Use Support vector data description (Support vector data description, SVDD) for online monitoring of intermittent processes. SVDD is a single-value classification algorithm. The basic idea is to target the training data set X={ _xi ,i=1, …,N}, project the original space data to the feature space {Φ( _xi ),i=1,…,N} through the nonlinear transformation Φ:X→F, and then find in the feature space that can contain all data samples The hypersphere with the smallest volume, SVDD maps the input space to a high-dimensional space through the kernel function to learn a flexible and accurate data description model. The obtained hypersphere data description boundary is represented by a small part of the support vector, in order To construct such a minimal hypersphere, SVDD needs to solve the following optimization problem: In formula (4), a is the center of the hypersphere, R is the radius of the hypersphere, the penalty coefficient C weighs the volume of the hypersphere and the misclassification rate of the training samples, and the introduction of the slack variable _ξi represents the The sample produces a penalty term for misclassification, and the above optimization problem can be transformed into solving the corresponding dual problem: Among them, α _i represents the Lagrange multiplier corresponding to the i-th training sample, and α _j represents the Lagrange multiplier corresponding to the j-th training sample; Here, the kernel function K( _xi , x _j ) is introduced to replace the inner product function ( _xi , x _j ). Using quadratic programming, a _i can be obtained. If x ₀ represents any support vector, then the hypersphere The center and radius of the sphere can be expressed as: For a new sample x _new , the distance to the center of the hypersphere can be obtained: If Dist _new ≤ R, the sample is normal; otherwise, the sample is an abnormal sample; After using ICA to extract the features of each stage of the batch process, the data of the non-Gaussian space of the independent components and the remaining residual space can be obtained respectively, and the extracted independent components can be analyzed by the SVDD method and the residual matrix E to establish a statistical analysis model, first for the independent components Establish the SVDD model as follows: In the formula: Indicates the kth sample, α _k is the Lagrangian multiplier of the corresponding sample, K(·) represents the Gaussian kernel function, and the independent components can be obtained The center and radius of the formed SVDD hypersphere are shown in formula (9): Similarly, the SVDD model is established for the residual matrix E as follows: Among them, β _k represents the Lagrangian multiplier corresponding to the kth training sample; Then, the center and radius of the SVDD hypersphere formed by the residual matrix E are shown in formula (11): For each stage of the batch process, the hypersphere radius R of the corresponding stage can be obtained respectively. During online process monitoring, when the sampling data x _new at the current moment is obtained, after data preprocessing and ICA feature extraction, the independent components are obtained respectively and the distance from the residual matrix E _new to the center of the corresponding sphere and Dist _{E_new} , so when Dist≤R, it can be considered that the sample at the current moment is normal, and when Dist>R, it means that the sample at the current moment is faulty data. 2. the method for the intermittent process failure monitoring based on multi-stage ICA-SVDD according to claim 1, is characterized in that, because intermittent process has the problem of multi-stage and data distribution non-Gaussian, based on independent component analysis and support vector The fault monitoring method of multi-stage batch process described by data can solve the monitoring problem of non-Gaussian and nonlinear process data at the same time.