Mathematical Problems in Engineering

Volume 2016, Article ID 9567967, 11 pages

http://dx.doi.org/10.1155/2016/9567967

## Monitoring of Distillation Column Based on Indiscernibility Dynamic Kernel PCA

Tianjin Key Laboratory for Control Theory & Applications in Complicated Systems, Tianjin University of Technology, Tianjin 300384, China

Received 31 August 2015; Accepted 10 January 2016

Academic Editor: Wen Chen

Copyright © 2016 Qiang Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Aiming at complicated faults detection of distillation column industrial process, it has faced a grave challenge. In this paper, a new indiscernibility dynamic kernel principal component analysis (I-DKPCA) method is presented and applied to distillation column. Compared with traditional statistical techniques, I-DKPCA not only can capture nonlinear property and dynamic characteristic of processes but also can extract relevant variables from all the variables. Applying this new method to distillation column process (a hardware-in-the-loop simulation system), the results prove the proposed method has great advantages, that is, lower missing rate and higher detection rate for the faults, compared with KPCA and DPCA.

#### 1. Introduction

With the emergence and development of industrial 4.0, modern industrial processes are more complicated in both structure and automatic degree. The safety and reliable issues about the industrial processes have become the most critical problems for system design [1–14]. To avoid abnormal accidents and losses, the process monitoring problem has become a severe topic in the area of process control. Among different process models, multivariate statistical process monitoring provides a data-driven framework for monitoring the industrial process. With the wide use of smart sensors, a large amount of data is collected in industrial processes; process information can be extracted directly from the huge amounts of the process data without considering complicated system models by data-driven methods, which lead to data-driven methods that have attracted much attention in the recent research works. Principal component analysis (PCA) is one of most widely used models in statistical process monitoring [15–20].

PCA is a basic multivariate statistical method which can extract useful information from large amount of process data by reducing dimensions. And the process data is divided into systematic part that reflects normal data change and noisy part that reflects the variation of noise. Hotelling’s statistic and statistic are used for chemical process monitoring to detect the changes of process variation in the principal component subspace and residual, respectively. And it is applied to petroleum and chemical industry widely. The conventional PCA has been well performed in only steady-state linear processes. However, dynamic and nonlinear characteristics are widespread in many industrial processes.

To handle nonlinearity, a lot of methods have been proposed [21, 22], such as neural network PCA and kernel PCA (KPCA) [23–29]. And neural network PCA needs training to determine the number of principal components; KPCA was developed to overcome this problem. The basic idea of KPCA is that the mapped data are analyzed by conventional PCA method in feature space. The traditional PCA is a static method. It is difficult to acquire the serial correlation of data [30]. But industrial processes are dynamic, which will lead to fault missing. To handle this problem, the dynamic characteristics should be taken into consideration when developing a monitoring model [31]. Ku et al. developed dynamic PCA which takes into account serial correlation in the data by augmenting each observation vector with the previous observations. After years of research, DPCA has been applied to many fields [30, 32, 33].

In this paper, to improve the PCA, we propose a new nonlinear dynamic process monitoring method based on indiscernibility dynamic kernel PCA (I-DKPCA). The proposed method can not only capture nonlinear property and dynamic characteristic of industrial processes but also simplify the process data by extracting valid data. We compare the results of DPCA, KPCA, and I-DKPCA for detecting various faults in distillation column industrial process.

The remaining sections of this paper are organized as follows. Section 2 explains the new I-DKPCA algorithm in detail. In Section 3, we applied the four methods to distillation column. At last conclusions are drawn in Section 4.

#### 2. Algorithm of New I-DKPCA

There are strong dynamic and nonlinear characteristics in the industrial processes; the I-DKPCA was a nonlinear dynamic method and proposed aiming at these two characteristics. For the I-DKPCA algorithm, some faults may not affect all the operating and process variables. To a given fault, some variables are not influenced. The proposed indiscernibility dynamic kernel PCA finds the variables which are affected by the faults severely, and these variables are extracted to form new sample matrix and test matrix. Therefore the proposed method has higher sensitivity and accuracy for process monitoring. The new method consists of three parts.

##### 2.1. Indiscernibility and the Cross-Degree ( and )

In process industry, for a complex system, there are a lot of process and operation variables; these variables are collected and stored; in the traditional multivariate statistical process monitoring, the selection of control variable often considered all the process variables, which caused a lot of inconvenience for process monitoring; for an actual fault, only a few variables are affected in the process. So a new dynamic kernel principal component analysis method is put forward in this paper. Two parameters are proposed, the indiscernibility degree and the degree of cross. The new method can get rid of irrelevant variables, reduce the data dimension, simplify the calculation algorithm, and improve the efficiency and accuracy of fault diagnosis.

The train samples are gotten from normal process; the average for each variable is as follows:

The test samples , are gotten from abnormal process; the average for each variable is as follows:where is the number of samples and is the number of variables.

To determine the threshold,where the threshold value is to distinguish the abnormal data of the train data and the abnormal data of the fault data; if there are data which are beyond (below) the threshold in the train data, those data would be considered the abnormal data. If there are data which are below (beyond) the threshold in the fault data, these data would also be considered the abnormal data. Take all the abnormal data of train data and fault data in a set of fault samples; the wrong points are called samples of fault point, shown as follows:where is the number of variables. is the number of wrong points; for different variable, is different.

The parameter of the indiscernibility degree which is proposed in this paper is represented by as follows:

Parameter of the degree of cross is the ratio of the number of wrong points and the number of all samples in each variable and is represented by as follows:For each known fault, we need to set a limit of and to choose the variables; in this paper, the author obtained the best value of and by many simulation results; in general, as the value of and is smaller, the effort is better, and get rid of irrelevant variables, and make the monitor data more concise. Because of reducing the irrelevant variables and simplifying the computation, according to the selected variables to monitor the production processes, the effect of diagnosis is better.

##### 2.2. Dynamic Characteristic Analysis

To consider the dynamic of the new data , , the PCA methods can be extended to take the serial correlations into account by augmenting each observation vector with the previous observations and stacking the data matrix in the following manner [3, 34]:where is the -dimensional observation vector in the training set at the time instance . As shown in Figure 1. The number of lags is selected by [32, 35, 36]. The DPCA can get rid of the correlation of the data in some degree and improve the accuracy of diagnosis.