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In view of the fact that the production process of Polyvinyl chloride (PVC) polymerization has more fault types and its type is complex, a fault diagnosis algorithm based on the hybrid Dynamic Kernel Principal Component Analysis-Fisher Discriminant Analysis (DKPCA-FDA) method is proposed in this paper. Kernel principal component analysis and Dynamic Kernel Principal Component Analysis are used for fault diagnosis of Polyvinyl chloride (PVC) polymerization process, while Fisher Discriminant Analysis (FDA) method was adopted to make failure data for further separation. The simulation results show that the Dynamic Kernel Principal Component Analyses to fault diagnosis of Polyvinyl chloride (PVC) polymerization process have better diagnostic accuracy, the Fisher Discriminant Analysis (FDA) can further realize the fault isolation, and the actual fault in the process of Polyvinyl chloride (PVC) polymerization production can be monitored by Dynamic Kernel Principal Component Analysis.

In today’s chemical industry, the polymer production has occupied a very important position. Polyvinyl chloride (PVC) is an important organic synthetic material, and it is also the chemical product which has a variety of uses. PVC resin is a kind of chemical products, the failure mechanism of the production process is complex, and there are serious dynamic and nonlinear problems in the production process; then there is an urgent need to improve the system reliability and safety production, in order to avoid generating fault system; otherwise it will lead to economic losses and even accidents. Therefore, the fault study in production of PVC resin has been an important issue research for experts [

After analyzing the characteristics of the data for the production of PVC resin, there are serious nonlinear and dynamic data, and this article adopts the method of a compound Dynamic Kernel Principal Component Analysis (DKPCA), using the nonlinear and dynamic process, and, after studying it, there is the defect of the traditional principal component. At the same time this paper also included the fisher discriminant method for further classification of failure data, to ensure that one quickly finds out the cause of the problem, then for further processing.

Taking a unit of the production process of PVC resin as the research object, polymerization process is shown in Figure

Polymerizer process diagram.

The monomer, initiator, dispersion agent, and other materials are fed into the polymerization reactor from inlets. After a series of reactions, the polymers are ultimately generated. In the polymerization process, the heat is ceaselessly released so that the temperature in the polymerization reactor is continuously increased, which will make the reaction more severe and causing material flow imbalances so as to affect the product quality. So the mixing system is added in the polymerization reactor, and the cooling water is timely injected in the jacket and the damper in order to balance the temperature in the polymerization reactor. After the reaction, join the terminators; then the polymerization reaction will be terminated.

From PVC polymerization process, there are many indicators affecting the quality of product and any one variable over its boundaries; it will lead the quality of the product to be out of control. Therefore, perform the real-time monitoring of quality index in the process of polymerization, and then ensure the product quality changed can be diagnosed timely and accurately. After a comprehensive comparative study, we ultimately selected 10 variables identified as the object of study; these 10 variables are as follows: the temperature within the reactor, the reactor pressure, stirring currents, injection into the water flow, seal water flow, jacket water flow, water flow baffles, cooling water inlet temperature, outlet temperature of the water jacket, and the water outlet temperature of the baffle. Monitor the 10 variables, respectively, and ensure the stable operation of the polymerization system.

PCA is based on data to establish the system statistical model and detect anomalies and failures based on the multivariate statistical techniques. First, take some normal conditions data set

It can be seen that each score vector is equal to the data matrix projection on its load vector, the size of

Generally adopt the principle of cumulative contribution rate, and determine the number of PCA.

The statistic index of control limits is calculated as follows:

When statistics are within the scope of the control limit, then the system is in a trouble-free state; if the statistics are beyond the control limit, then there is a fault in the system. The basic idea of KPCA is through nonlinear map

In the feature space

By determining the characteristics of the vector

There is a coefficient of

Therefore, combined with the type, it can be obtained that

At the same time,

Therefore, (

In the application of KPCA, first you have to get the mean centered on high dimensional space. It can be done by using the following formula instead of nuclear matrix

Therefore, the principal

We found that KPCA is by introducing

The kernel function used in this paper is radial basis kernel function.

The traditional PCA method to the diagnosis result of system process data with dynamic properties and the nonlinear characteristics is not very ideal, so for such a dynamic nonlinear system one should study a new method; this method must be able to capture the dynamic and nonlinear characteristics of the data at the same time. This is the following Dynamic Kernel Principal Component Analysis (DKPCA) method.

The fault detection principle of Dynamic Kernel Principal Component Analysis is as follows: analyze the system dynamic characteristics at first, the time-series data of the system at normal state were analyzed, and kernel principal component analysis mode of the system under the normal state is constructed. Then a new system data is mapped to the kernel principal component model and, respectively, by principal component scores and the residuals to determine the state of the system.

DKPCA fault diagnosis method is that each of the observation variables is expanded by

After the augmented matrix by extending the time sequence, the kernel principal component analysis is used for fault detection. DKPCA flow chart is shown in Figure

Dynamic flow chart of kernel principal component analysis.

The FDA’s basic idea is to maximize the dispersion between classes at the same time to minimize the dispersion in class, through the optimization objective function to determine the optimal FDA vector FDA, and the vector can represent the direction of the different fault class optimal separation [

To further classify the fault, the FDA method is adopted for further classification to the failure data detected by DKPCA to ensure that one finds out the cause of the problem quickly, which provides the theoretical basis to make failure countermeasures.

First of all, the characteristics of the polymerization process were analyzed, this analysis found that there are 10 process variables affecting the polymerization product quality indicators, 50 sets of data under normal polymerization process are collected and used as the training sample matrix

According to the above process, T2 and SPE are used for fault monitoring of PVC polymerization process by using the traditional principal component analysis, kernel principal component analysis, and the Dynamic Kernel Principal Component Analysis.

The traditional principal component analysis was adopted, 200 groups of data are to be collected, the sampling interval is 1 min, and the fault detection results are as shown in Figure

The kernel principal component analysis was adopted, 200 groups of data are to be collected, the sampling interval is 1 min, and the fault detection results are as shown in Figure

The Dynamic Kernel Principal Component Analysis was adopted, 200 groups of data are to be collected, the sampling interval is 1 min, and the fault detection results are as shown in Figure

Principal component analysis of fault detection results.

Kernel principal component analysis of fault detection results.

Dynamic Kernel Principal Component Analysis of fault detection results.

In order to more clearly identify which kind of diagnosis methods is more effective, the false positive rates are compared. The lower the false positive rate, the more appropriate this method to be applied in the polymerization kettle fault diagnosis system. Diagnostic results are as Table

Diagnostic results.

Diagnostic methods | PCA | KPCA | DKPCA |
---|---|---|---|

False alarm rate | 17% | 8% | 1% |

It can be clearly seen from the simulation results that there are many cases exceeding the control limits and the false positive rate is quite serious for the traditional principal component analysis method and the kernel principal component analysis method before the 50 sampled points, which will lead to the incorrect judgment of the operators. But, in the fault detection of Dynamic Kernel Principal Component Analysis, there are only two false alarms, and the introduction of fault phase, obvious beyond control limit, thus improves the efficiency of fault diagnosis.

In order to further find out the cause of the problem, we need to make further classification of failure data, to ensure rapid recovery production, and now we will extract 100 groups detected by DKPCA. There are two types of failures, respectively, one is resin transformation due to temperature and pressure, and the other failure is caused by the stirring electric current; in order to make better separation of two types of failure, we use the method of judging the FDA, and the results are shown in Figure

Fault classification results of FDA.

By the graph, we can see clearly that

Based on the traditional principal component analysis and kernel principal component analysis, the data of dynamic principle were introduced, introducing Dynamic Kernel Principal Component Analysis method, which is used for fault detection to the dynamic and nonlinear strong polymerizing process. At the same time, there are further references to the FDA methods for fault isolation. Simulation results show that the method can real time monitor the change of variables in the polymerization process; the fault of the polymerization process is more sensitive to reduce the probability of false alarm and can quickly find out the cause of the problem. Results indicate that this method can be applied to the fault handling of polymerization, at the same time, and, for the general nonlinear dynamic chemical process, also it has certain applicability.

The authors declare that there is no conflict of interests regarding the publication of this article.

This work is partially supported by the Project by National Natural Science Foundation of China (Grant no. 21576127), the Program for Liaoning Excellent Talents in University (Grant no. LR2014008), the Project by Liaoning Provincial Natural Science Foundation of China (Grant no. 2014020177), the Program for Research Special Foundation of University of Science and Technology of Liaoning (Grant no. 2015TD04), and the Opening Project of National Financial Security and System Equipment Engineering Research Center (Grant no. USTLKFGJ201502).