Fault diagnosis by refining the parameter uncertainty space of nonlinear dynamic systems Esteban R. Gelso, Sandra M. Castillo, and Joaquim Armengol University of Girona, E17071 Girona, Spain. {esteban.gelso, sandra.castillo, joaquim.armengol}@udg.edu Abstract— This paper deals with fault detection and isolation problems for nonlinear dynamic systems. Both problems are stated as constraint satisfaction problems (CSP) and solved using consistency techniques. The main contribution is the iso- lation method based on consistency techniques and uncertainty space refining of interval parameters. The major advantage of this method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements, and model errors. Interval calculations bring independence from the assumption of monotony considered by several approaches for fault isolation which are based on observers. An application to a well known alcoholic fermentation process model is presented. I. I NTRODUCTION Early and accurate fault detection and diagnosis for indus- trial processes can minimize downtime, increase the safety of plant operations, and reduce costs. Different techniques have been developed in recent years that are intended to detect and diagnose faults. These tech- niques can be classified in different ways [1], [2]. For example, a distinction can be made between model-based techniques and techniques based on other kinds of knowl- edge, such as heuristic approaches, statistical approaches, learning systems, artificial neural networks, etc. Among others, all the fault detection and isolation tech- niques have to face the challenge of dealing with uncertainty. This can be achieved in several ways, e.g. by statistical data processing, averaging, or using intervals. This paper introduces a fault diagnosis approach based on a model that takes into account the uncertainties in the measured signals and in the model by means of intervals. These uncertainties are caused by, for example, non-modeled effects, electrical disturbances, model simplifications, and so on. Several engineering problems such as system and state estimation, fault detection, robustness analysis, robust control design, risk assessment, and worst case behavior analysis, can be solved when interval uncertainties are considered. As matters stand, some interval methods have been pro- posed in the context of fault detection and diagnosis, e.g. [3], [4] and [5]. A fault detection approach based on constraint propagation is proposed by Stancu et al. in [6]. In [7], the fault detection problem is solved using a tool known as E. R. Gelso, S. M. Castillo, and J. Armengol are with the Institut d’Inform` atica i Aplicacions (IIiA), University of Girona IntervalPeeler, based on constraint projection algorithms (2B- consistency) to reduce interval domains of variables without bisections. Consistency methods are used to perform results of this article. They are a combination of interval methods and con- straint satisfaction techniques. Constraint satisfaction tech- niques implement local reasoning on constraints to remove inconsistent values from variable domains. In practice, the set of inconsistent values is computed by means of interval reasoning. To introduce the results of this papers it is necessary to mention a method based on parameter partitioning and the monotony of an observer prediction error for fault isolation which is proposed in [8]. The method applies for fault isolation in non-linear dynamic systems and assumes that the fault is detected once it occurs, so the isolation procedure is triggered at this time. Its authors emphasize the approach speed, being quicker than other methods based on adaptive observers. Regarding the approach proposed in [8], the main contri- butions of this paper are: (i) the isolation problem is based on parameters uncertainty refining instead of partitioning, (ii) the isolation problem is stated as a Constraint Satisfac- tion Problem (CSP) and solved by means of consistency techniques. A sliding time window is used to reduce the computational effort. And (iii) interval calculations allow the proposed approach to be independent of the assumption (about the type of nonlinear systems) that the system dynam- ics is a monotonous function with respect to the considered parameters. The aim of this paper is to show the usefulness of the consistency methods to solve not only the fault detection problem, but also the isolation problem when a fault appears as a parameter deviation for non-linear dynamic systems. The method provides the estimation of the faulty parameter range, which is very useful information for the controller reconfiguration in the Fault Tolerant System (FTC). In section II the fault detection and isolation problems are shown to be constraint satisfaction problems and the resolution of them is achieved by the solver RealPaver [9]. An alternative, which is to use an efficient combination of Hull- and Box- consistency, is explored. The proposed approach effectiveness is illustrated by means of a well known alcoholic fermentation process pre- sented in [10], [11], [12], [8], [13] and [14], for instance. 2008 American Control Conference Westin Seattle Hotel, Seattle, Washington, USA June 11-13, 2008 FrBI01.9 978-1-4244-2079-7/08/$25.00 ©2008 AACC. 4304 Authorized licensed use limited to: UNIVERSITAT DE GIRONA. Downloaded on May 8, 2009 at 07:20 from IEEE Xplore. Restrictions apply.