Nonlinear ARX (NARX) based identification and fault detection in a 2 DOF system with cubic stiffness

This paper addresses the problem of system identification and fault detection in a two DOF nonlinear system characterized by cubic stiffness. System identification is based upon Nonlinear ARX (NARX) models, while a novel Functional Model Based Method is employed, for the first time within the context of a nonlinear system, for tackling the combined problem of fault detection, identification (localization), and fault magnitude estimation. The Functional Model Based Method utilizes Functional NARX (FNARX) models, which are capable of accurately representing the system in a faulty state for the latter's continuum of fault magnitudes, as well as statistical decision theory tools. The results of the study indicate the effectiveness of both NARX based identification and the Functional Model Based Method in detecting, identifying, and estimating the magnitude of faults based upon only two measured signals.