Integration of fault diagnosis and control by finding a trade-off between the detectability of stochastic fault and economics

Abstract

This paper presents a first principle model based methodology for simultaneous optimal tuning of a fault detection algorithm and a feedback controller. The key idea is to calculate the effect of stochastic input disturbances on the variability of the output variables by using a generalized polynomial chaos (gPC) expansion and a mechanic model of the process. A two-level optimization is proposed for simultaneously tuning the fault detection and controller algorithms. The goal of the outer level optimization is to find a trade-off between the efficiency for detecting faults and the closed loop performance, while the inner optimization is designed to optimally calibrate the fault detection algorithm. The proposed method is illustrated for a continuous stirred tank reactor (CSTR). The results show that the computational cost of the gPC-based method is significantly lower than a Monte Carlo (MC) simulation-based approach, thus demonstrating the potential of the gPC method for dealing with large problems.