Optimized Design of Parity Relation-Based Residual Generator for Fault Detection: Data-Driven Approaches

Abstract

In the conventional approaches to the design of fault diagnosis systems, little effort is usually paid to the selection of the parity vectors. As a result, the systems' performance can be significantly affected. In this article, novel approaches are proposed to derive the parity vectors that construct optimized residual generators for linear and nonlinear systems. Based on the analysis on the parity space dimension, a novel parameterization of all parity relation-based residual generators is proposed. An iterative procedure that guarantees minimal regression error is then employed in the search for the optimal parameters. Considering that the traditional parity relation-based approaches are only suitable for linear systems, in this work, the proposed approach is also generalized to deal with strong nonlinearities, with the aid of data-driven Hammerstein function estimation. Furthermore, optimized residual generation algorithms are summarized for offline design and online implementation, the performance of which is evaluated thoroughly with a three-tank system, a numerical nonlinear example, as well as a case study on an industrial hot rolling mill process. Results show that residuals generated by the proposed approaches can significantly improve the sensitivity to small faults, and thus, the fault detection rate is improved compared with the traditional nonoptimized approach.