A New Residual Evaluation Function Based Fault Diagnosis for a Kind of Nonlinear Systems

Abstract

In this paper, a new residual evaluation function (EF) is proposed for the H i ∕H ∞ fault detection filter (FDF). Residuals are projected into the direction of fault, then energy of this projection is adopted as the new EF. Compared with the traditional EF, improvement in FD ability of the new EF is demonstrated rigorously, and a recursive way to calculate it is also proposed under the assumption that fault is slowly time varying. Furthermore, application of this new EF for fault isolation (FI) is discussed, which finally leads to a systematic FDI scheme for a kind of nonlinear systems. Simulations with a nonlinear unmanned aerial vehicle (UAV) model validate the proposed method.new,i and J f new,i , the accumulated terms in J r new,i are not quadric forms and their signs may change from step to step, thus it is reasonable to assume that J r new,i is much smaller than J d new,i and J f new,i . That is, J new,i is roughly approximated asThen, since J f new, ≥ J f new,i holds true, it is expected to isolate the fault correctly by J new, when J d new,i ≈ J d new, ≪ J f new, . That is, J new,i and J new, in the fault free case are roughly equal. Compared with the assumption that residual is dominated by fault (r ≈ Ω f ), this conditional is milder and more realistic.However, undesirable situations still exist, that is, J new,i and J new, differs from each other significantly in the fault free case. Without loss of generality, it is assumed that the direction of r 0 is much closer to Ω i , i ≠ , which result in J new,i ≫ J new, in the fault free case. To deal with this situation, the following normalized EF is proposed.where (J 0 new,i ) is an empirical mean of J new,i obtained from historical normal data. Then we havēSince the direction of r 0 is close to Ω i but far from Ω , directions of Ω i and Ω are not close to each other, thus J f new,i is very small when f occurs. Therefore, it is expected thatJ new,i will not increase obviously after f occurs, whileJ new, increase significantly after f occurs. Finally, it is expected to haveJ new, >J new,i . When J new,i and J new, are close to each other in the fault free case, J new,i ≈ 1 + J f new,i (J 0 new,i ) ≤J new, ≈ 1 + J f new, ance instrument, Beihang University, Beijing, China. His research interests are model-based fault diagnosis and applications.Maiying Zhong received the Ph.D. degree in control theory and control engineering from Northeastern University,

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