Orthogonal Projection-Based Fault Detection for Linear Discrete-Time Varying Systems

This article is devoted to one-class fault detection in linear discrete-time varying (LDTV) systems with uncertainties. Specifically, following the Hilbert Projection theorem, the residual generation problem is solved by means of an orthogonal projection of process data onto system subspaces in Hilbert space. The resulted Pythagorean equation enables establishing an adaptive threshold driven by the residual signal and using gap metric as the similarity measure. In this projection-based fault detection framework, the design and implementation of the residual generators and threshold setting can be uniformly addressed, which provides a systematic solution to the detection issues in linear discrete-time varying systems. Moreover, a comparison with the observer- and differential-algebraic equations-based fault detection schemes is studied, which highlights the improved fault detection capability of the projection-based method.