Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos

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.