A projection-based method of fault detection for linear discrete time-varying systems

• Published in: International journal of systems science Vol. 44; no. 5; pp. 820 - 830
• Main Authors: Zhong, Maiying, Ding, Steven X.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.05.2013; Taylor & Francis
• Subjects: Adaptative systems; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Design engineering; Error analysis; Exact sciences and technology; Fault detection; Generators; Gramian matrix; linear discrete time-varying system; Mathematical models; Modelling and identification; Optimization; Projection; residual; Robustness; Unknown input; Error estimation; fault detection; L2 approximation; State space; residual; Optimal detection; Projection method; Time varying system; Innovation; linear discrete time-varying system; Linear combination; Observer; Robustness; System identification; projection; Measurement error; Estimation error; Output error; Probabilistic approach; Output signal; State space method; Gramian matrix; Orthogonal projection; Linear filter; Discrete time; Fault diagnostic; Defect detection
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2011.625481

This article is aimed at the development of a residual generator by making use of an arbitrary linear combination of measurement output estimation error sequence. First, Gramian matrix-based criteria are proposed to measure the influences of an unknown input and a fault on the residual. Then, the design of the residual generator is formulated into a sensitivity/robustness ratio maximisation problem. It is shown that the optimal solution is not unique and one of them can be derived by directly applying an orthogonal projection of the measurement output and, with the aid of an innovation analysis, a more generalised residual generator is also obtained. Furthermore, it is demonstrated that the obtained residual generators in state space description also provide optimal observer-based fault detection filters for the linear discrete time-varying systems subject to l 2 -norm bounded unknown inputs or stochastic noise sequences. To show the effectiveness of the proposed method, a numerical example is given.