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Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos |
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| Affiliation: | 1. Department of Applied Statistics, Yonsei University, Shinchon Dong 134, Seoul, Republic of Korea;2. Department of Mathematics, Arak University, Arak 38156-8-8349, Iran;1. Université de Lyon, INSA-Lyon, LaMCoS, CNRS UMR 5259, 18-20 Rue des Sciences, bâtiment d’Alembert, F-69621 Villeurbanne, France;2. Laboratoire de Mécanique et Génie Civil, LMGC, Université Montpellier, CNRS, CC048, Place E. Bataillon, F-34095 Montpellier, France;3. School of Mechanical and Manufacturing Engineering, UNSW Australia, Sydney, NSW 2052, Australia;1. Chemical & Materials Engineering Department, University of Alberta, Edmonton, Alberta T6G 2V4, Canada;2. Department of Instrumentation Engineering, MIT Campus, Anna University, Chennai 600 044, India;1. State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China;2. School of Automation and Electrical Engineering, Zhejiang University of Science and Technology, Hangzhou 310023, Zhejiang, China |
| Abstract: | This paper presents a new methodology to identify and diagnose intermittent stochastic faults occurring in a process. A generalized polynomial chaos (gPC) expansion representing the stochastic inputs is employed in combination with the nonlinear mechanistic model of the process to calculate the resulting statistical distribution of measured variables that are used for fault detection and classification. A Galerkin projection based stochastic finite difference analysis is utilized to transform the stochastic mechanistic equation into a coupled deterministic system of equations which is solved numerically to obtain the gPC expansion coefficients. To detect and recognize faults, the probability density functions (PDFs) and joint confidence regions (JCRs) of the measured variables to be used for fault detection are obtained by substituting samples from a random space into the gPC expansions. The method is applied to a two dimensional heat transfer problem with faults consisting of stochastic changes combined with step change variations in the thermal diffusivity and in a boundary condition. The proposed methodology is compared with a Monte Carlo (MC) simulations based approach to illustrate its advantages in terms of computational efficiency as well as accuracy. |
| Keywords: | Stochastic faults Fault isolation Diagnosability Uncertainty analysis Computational efficiency |
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