Robust Fault Detection Based on l1 Regularization

Abstract

Herein, regularization‐based fault detection technique for stochastic discrete time systems in state space form is discussed. Compared with the deterministic nature of a fault which usually causes an abrupt change, the state of a system smoothly evolves in most cases and the disturbance in the process and the sensor measurement has a stochastic characteristic. The modeling uncertainty in the state space of a system can induce a bias in deterministic way and it can be combined to a fault. In the fault detection community, the modeling uncertainty is called a multiplicative fault and the abruptly‐changing fault is called an additive fault. Inspired by the fact that norm is useful for estimating smoothly evolving states and reducing a bias and norm for detecting abrupt change with spare structure, this research develops the technique for detecting fault which changes abruptly under stochastic disturbance and modeling uncertainty. The norm for bias compensation (due to modeling uncertainty and/or additive fault) is combined with norm for fault detection (especially abruptly changing fault) and the two norms are set up as a regularization problem. The regularization problem is convex thus, global solution can be found in efficient way.