Determination of influential factors and diagnostics using multivariate statistical relationships between variables and faults

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Abstract

This paper proposes a variable influence (VI) index-based on-line method for diagnosing discontinuous processes. The VI index is developed using the concept of contribution plots, and can be used to explain the influence of a process variable on a specific fault. The proposed method consists of two phases: off-line VI model-building and on-line diagnosis via VI index comparison. In the off-line VI model-building phase, the off-line VI model is constructed using off-line fault data and used as a reference model for the on-line diagnosis of a new batch. The on-line diagnosis phase is triggered by an out-of-control signal of a new batch. It calculates the VI index values for new process data available at that time, which are compared with the off-line VI index values of the off-line VI model stored in the data/model base. The proposed method has the advantage that it does not require any process knowledge of operators and can automatically select an assignable cause via the comparison of VI index values. A case study on a PVC batch process is conducted to demonstrate the diagnosis performance of the proposed method. The performance of the proposed method is also evaluated when an on-line mode is not considered in the proposed framework.

Introduction

A batch process is a finite duration process which has predetermined starting and stopping points. During a batch run, a reactor is charged with raw materials in specified amounts and the reaction takes place with raw materials processed under controlled conditions. Then, final products are discharged, and the same procedures are repeated for the production of next batch runs (Morris & Watson, 1997). Batch processes have played an important role in the production of high-value specialty products such as pharmaceuticals, bio-chemicals, and polymers.

The on-line monitoring and diagnosis of batch processes are an essential part of the operational tasks needed to run a process safely and to produce high quality products consistently (Boqué & Smilde, 1999). The early detection and reliable identification of a fault is crucial in an on-going batch run. For this purpose, one should build models that describe the nature or sources of variation for batch processes. One option is to adopt mathematical models (e.g., state estimator) or detailed knowledge-based models (e.g., expert system). Though they are potentially powerful methods, such models are time-consuming and practically difficult to develop (Raich & Cinar, 1997).

An alternative approach is to construct empirical models based on historical process data, which are readily available for most industrial processes. Recently, automation of modern industrial processes increases the potential of such a data-driven approach (Kourti & MacGregor, 1996). Multivariate statistical projection methods such as multiway principal component analysis (MPCA) and multiway partial least squares (MPLS) have been successfully applied for monitoring and diagnosing batch processes (Lennox et al., 2000, MacGregor et al., 1994, Wold et al., 1987). Due to the ability to overcome various problems of process data (e.g., dimensionality, collinearity, low signal-to-noise ratio, and missing data), they have proven to work well in practice.

For diagnosis purpose, many researchers have utilized contribution plots to identify the key process variable(s) responsible for a specific fault. The contribution plots show the contribution of each process variable to the statistics calculated from underlying monitoring model (Teppola, Mujunen, Minkkinen, Puijola, & Pursiheimo, 1998). Two types of contributions need to be calculated: contributions to T2 and squared prediction error (SPE) statistics. When a fault is detected in the T2 (and/or SPE) statistic, the contribution of each process variable to T2 (and/or SPE) statistic is investigated. Once the major contributing variable(s) are known, the diagnosis problem becomes much easier.

Boqué and Smilde (1999) adopted contribution plots as a diagnostic tool to identify the process variables that cause possible faults of industrial batch processes. Norvilas, Negiz, Decicco, and Cinar (2000) and Leung and Romagnoli (2002) developed a diagnosis method to combine contribution plots with knowledge-based systems. Moreover, Louwerse, Tates, Smilde, Koot, and Berndt (1999) utilized contribution plots to identify the operating conditions that are causing quality differences between PVC batch reactors implemented in parallel. For more information about the application of contribution plots, see Kourti et al., 1995, MacGregor et al., 1994, Neogi and Schlags, 1998, Nomikos, 1996 and Westerhuis, Gurden, and Smilde, 2000.

The use of contribution plots as a diagnostic tool, however, has some limitations. First of all, it does not directly identify an assignable cause of a fault. Rather, only key process variables (that are no longer consistent with past normal operating conditions) can be identified, based on the process knowledge of operators to deduce possible causes subjectively. Such a subjective interpretation of key process variables may yield unreliable or inconsistent diagnosis results depending on operators. In addition, it is difficult or sometimes impossible to interpret the conflicting patterns of process variables’ contributions obtained from different monitoring statistics of T2 and SPE.

This paper proposes an on-line diagnosis method for batch processes using a variable influence (VI) index. The VI index can be used to explain the influence of a process variable on a specific fault (in terms of T2 and SPE statistics) because it considers the contributions to T2 and SPE statistics simultaneously. Using off-line fault data (which consist of past unsuccessful batches with their assignable causes identified), the off-line VI model is constructed and used as a reference model for the on-line diagnosis of a new batch. These off-line VI index values for each of unsuccessful batches are compared with on-line VI index of a new batch to identify an assignable cause of a fault. The proposed method, unlike contribution plots, does not require any process knowledge of operators and can automatically select an assignable cause via the VI index.

The rest of the paper is organized as follows. First, characteristics of batch process data are described, and MPCA monitoring model and its statistics are reviewed along with contribution plots. Then, the proposed method is presented, and a case study on a PVC batch process is conducted to demonstrate the proposed diagnosis method. Finally, concluding remarks are given.

Section snippets

Batch process data and prediction of future observations

Analyzing batch process data is a typical three-way problem. A batch run has J variables measured at each of K time intervals throughout the batch. The same form of data exists for each of I batch runs stored in a historical database. Thus, a three-way array X is constructed as shown in Fig. 1. To analyze batch data of such a form, Wold et al. (1987) first proposed the multiway PCA (MPCA) to analyze the batch process data by unfolding X into a large two-dimensional matrix X.

When a new batch is

Proposed methodology

This section proposes an on-line diagnosis method for batch processes using variable influence index. Fig. 2 shows an overall framework of the proposed method. It consists of two phases, namely, off-line VI model-building and on-line diagnosis via VI comparison.

The off-line VI model-building phase has four major steps. Section 3.1.1 first receives off-line fault data Z (which refer to a collection of past unsuccessful batches with their assignable causes identified) from the data/model base and

Case study: PVC batch process

The performance of the proposed diagnosis method is tested using a real dataset from a PVC (polyvinyl chloride) batch process. The process consists of a reactor, condenser, agitator, and cooling jacket, and there are 11 process variables automatically measured on-line at 241 sampling times. PVC is one of the most popular products produced in batch processes. The PVC batch process has three major stages during a batch run. The first stage is the heating of feed materials from the room

Concluding remarks

This work has proposed a VI index-based method for diagnosing a batch process on-line. The VI index can be used to reveal the degree of a process variable’s “total” influence on a specific fault by combining VI index for T2 and SPE statistics simultaneously. Using off-line fault data, an off-line VI model is constructed and used as a reference model for the on-line diagnosis of a new batch. The proposed diagnosis method is the first work that attempts to develop a systematic method using the

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1

Present address: Division of Mechanical and Industrial Engineering, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, Republic of Korea. Tel.: +82 54 279 2208; fax: +82 54 279 2870.

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Tel.: +1 865 974 0234; fax: +1 865 974 0588.

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