FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation. (January 2019) - Pourasghar, Masoud; Combastel, Christophe; Puig, Vicenç; Ocampo-Martinez, Carlos
Highlights: This paper proposes an zonotopic Kalman filter approach for enhancing the sensitivity to faults with respect to disturbances. A criterion combining set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system will be used for illustrating the proposed approach. The proposed approach is compared against the standard zonotopic Kalman filter approach that optimizes the precision of the state estimation as is usually done with Kalman Filters. Abstract: Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approach.