Elsevier

Automatica

Volume 47, Issue 7, July 2011, Pages 1349-1356
Automatica

Bayesian methods for control loop diagnosis in the presence of temporal dependent evidences

https://doi.org/10.1016/j.automatica.2011.02.015Get rights and content

Abstract

Conventional Bayesian methods commonly assume that the evidences are temporally independent. This condition, however, does not hold for most engineering problems. With the evidence transition information being considered, the temporal information can be synthesized within the Bayesian framework to improve diagnosis performance. In this paper, the important evidence dependency problem is solved by a data-driven Bayesian approach with consideration of evidence transition probability. The applications in a simulated distillation column and a pilot scale process are presented to demonstrate the data dependency handling ability of the proposed control loop performance diagnosis approach.

Introduction

Control loop performance assessment and diagnosis has been an active area of research in control engineering. Extensive research has been conducted on control performance assessment, and a large volume of papers can be found in the literature. A number of control performance assessment methods have been developed, including the ones based on minimum variance control (MVC), linear quadratic Gaussian control (LQG), historical data trajectories, and user-specified control benchmark, etc. (Harris et al., 1999, Huang and Shah, 1999, Jelali, 2006, Patwardhan and Shah, 2002, Qin, 1998, Schafer and Cinar, 2006). Several surveys on the control performance assessment research are available (Harris et al., 1999, Hoo et al., 2003, Hugo, 2006, Jelali, 2006, Qin, 1998). Besides performance assessment of control loops, significant progress has also been made in monitoring process and instruments, such as sensor monitors, valve stiction monitors, process model validation monitors (Ahmed et al., 2009, Choudhury et al., 2008, Mehranbod et al., 2005, Qin and Li, 2001). Despite significant progress, many problems remain. For example, one of the outstanding problems is that monitoring algorithms are often designed for detection of one specific abnormality. An implicit assumption that other unattended components are in good condition is made. Clearly this assumption does not always hold. It is therefore necessary to develop methods that not only monitor individual components, but also are capable of synthesizing information from different monitors to isolate the underlying source of problematic control performance.

Bayesian methods have a great potential to solve this problem by providing a probabilistic information synthesizing framework. Applications of the Bayesian method have been reported in medical science, image processing, target recognition, pattern matching, information retrieval, reliability analysis, and engineering diagnosis (Chien et al., 2002, Dey and Stori, 2005, Mehranbod et al., 2005, Steinder and Sethi, 2004). It is one of the most widely applied techniques in probabilistic inferencing. Built upon previous work in Bayesian fault diagnosis by Pernestal (2007) and a control performance diagnosis framework laid out in Huang (2008), a data-driven Bayesian algorithm for control loop diagnosis with consideration of missing data has been developed in Qi, Huang, and Tamayo (2010). The algorithm has been tested through simulation as well as an industrial application example, where the information synthesizing ability of the proposed approach was demonstrated. However, the developed algorithm, along with majority of other existing data-driven Bayesian methods, has not yet considered the temporal dependency problem. In this paper, a new algorithm is developed with consideration of evidence temporal dependency, so as to solve the important evidence dependency problem with Bayesian methods.

The remainder of this paper is organized as follows. In Section 2, the control loop diagnosis problem and related preliminaries are described, and the data-driven Bayesian approach for control loop diagnosis developed in Qi et al. (2010) is briefly revisited. The rationale to consider evidence dependency is detailed in Section 3. The estimation algorithm for the evidence transition probability is developed in Section 4. Section 5 proposes a dimension reduction solution for the high order evidence transition space. Section 6 presents applications of the proposed diagnosis approach to a simulated example as well as a pilot scale process. Section 7 concludes this paper.

Section snippets

Control loop diagnosis problem

Generally a control loop consists of the following basic components: controller, actuator, process, and sensor. These components may all be subject to malfunctions. Various monitors are designed to monitor some or all of these components. These monitors, however, are all subject to disturbances and thus can produce false alarms or missed alarms, and each monitor can be sensitive to abnormalities of other problem sources. Our target is to isolate the source of problematic control performance

Temporally dependent evidences

Note that in the approach developed in Qi et al. (2010), an assumption is made in that the current evidence only depends on the underlying mode, and is independent of the previous monitor readings. The assumptions regarding evidence independency, however, are restrictive in most of engineering applications; some important temporal information that is helpful for the diagnosis is neglected.

An evidence is a statistic estimated from a section (window) of process data. The independency among

Estimation of evidence transition probability

Our goal is to calculate the likelihood probability of an evidence Et given current underlying mode Mt and previous evidence Et1 to reflect the dependency with the Markov property, so every evidence transition sample, which is defined for evidence transition probability estimation purpose, should include these three elements, dEt1={Mt,Et1,Et}. The evidence transition data set DE, which is assembled from historical evidence data set D to estimate the evidence transition probability, is

Reduction of evidence transition space

A practical problem encountered in the evidence transition probability estimation is the large combinatorial number of evidence transitions. The total number of possible evidence transitions equals the square of the total number of single evidence values. The number of historical transition samples needs to increase dramatically in general to generate an accurate estimation of the evidence transition probability. Otherwise insufficient data will lead to degraded diagnosis performance. Obtaining

Case studies

A simulation example and a pilot scale experiment, are used to investigate the diagnosis performance of the Bayesian methods with different data dependency handling strategies.

Conclusion

In this work, a data-driven Bayesian approach with consideration of temporally dependent evidences is developed for control loop diagnosis. The temporal dependency problem is solved by introducing transition evidence. The evidence transition probabilities needed for the solution are estimated from the historical evidence data. The large evidence transition space problem is alleviated by using the test of correlation ratio of the evidence. The proposed method is applied to a simulated binary

Fei Qi was born in 1983 in Anhui, China. He received his B.E. degree in Automation in 2003, and his M.Sc. degree in Control Theory and Control Engineering in 2006, both at the University of Science and Technology of China. Since then he has been pursuing his Ph.D. degree in the Department of Chemical and Materials Engineering at the University of Alberta. Fei Qi’s main research interests are control loop diagnosis and Bayesian statistics.

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Fei Qi was born in 1983 in Anhui, China. He received his B.E. degree in Automation in 2003, and his M.Sc. degree in Control Theory and Control Engineering in 2006, both at the University of Science and Technology of China. Since then he has been pursuing his Ph.D. degree in the Department of Chemical and Materials Engineering at the University of Alberta. Fei Qi’s main research interests are control loop diagnosis and Bayesian statistics.

Biao Huang obtained his Ph.D. degree in Process Control from the University of Alberta, Canada, in 1997. He also had M.Sc. degree (1986) and B.Sc. degree (1983) in Automatic Control from the Beijing University of Aeronautics and Astronautics. Biao Huang joined the University of Alberta in 1997 as an Assistant Professor in the Department of Chemical and Materials Engineering, and is currently a Professor. He is a recipient of Germany’s Alexander von Humboldt Research Fellowship award, Canadian Chemical Engineer Society’s Syncrude Canada Innovation award, University of Alberta’s McCalla and Killam Professorship awards, Petro-Canada Young Innovator award, and a best paper award from Journal of Process Control. Biao Huang’s research interests include process control, system identification, control performance assessment and diagnosis, fault detection and isolation, fuel cell modeling and control. Biao Huang has applied his expertise extensively in industrial practice particularly in oil sands industry.

This work is supported in part by the Natural Sciences and Engineering Research Council of Canada and the Alberta Ingenuity Fund. The material in this paper was partially presented at the IFAC International Symposium on Advanced Control of Chemical Processes (ADCHEM 2009), July 12–15, 2009, Istanbul, Turkey. This paper was recommended for publication in revised form by Associate Editor Denis Dochain under the direction of Editor Frank Allgöwer.

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