Generalized robust H∞ fault diagnosis filtering based on conditional stochastic distributions of system outputs

Abstract The efficiency of fault detection and diagnosis by using output probability density functions (PDFs) for stochastic time-delayed systems has been shown in practical processes. Neural network modelling has been applied to characterize the output PDFs and to the dynamical weighting system. In this paper, the system perturbations and disturbance are considered and the robust fault diagnosis design is studied for the general stochastic system in the presence of time delays. The main objective is to design linear matrix inequality (LMI)-based fault diagnostic filtering (FDF) to estimate the fault and attenuate the disturbances. The modelling errors and system uncertainties resulting from both B-spline expansion and the weighting system are merged into system disturbance. It can be seen that the resulting weighting system comprises non-linearities, uncertainties, disturbances, and time delays, and includes the non-zero initial condition. The generalized H∞ optimization is presented and applied to the fault diagnosis problem of the weighting system with the non-zero initial condition and truncated norms. Simulations are given to demonstrate the efficiency of the proposed approach.

[1]  Jason L. Speyer,et al.  Optimal stochastic fault detection filter , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[2]  Hong Wang,et al.  Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions , 2000 .

[3]  Michèle Basseville,et al.  FAULT ISOLATION FOR DIAGNOSIS: NUISANCE REJECTION AND MULTIPLE HYPOTHESES TESTING , 2002 .

[4]  Marios M. Polycarpou,et al.  A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems , 2002, IEEE Trans. Autom. Control..

[5]  Hong Wang,et al.  Recent Developments in Stochastic Distribution Control/A Review , 2003 .

[6]  Ali Saberi,et al.  Optimal fault signal estimation , 2002 .

[7]  Michèle Basseville,et al.  Fault isolation for diagnosis: Nuisance rejection and multiple hypotheses testing , 2002, Annu. Rev. Control..

[8]  Hong Wang,et al.  Fault detection for non-linear non-Gaussian stochastic systems using entropy optimization principle , 2006 .

[9]  P. Frank,et al.  Survey of robust residual generation and evaluation methods in observer-based fault detection systems , 1997 .

[10]  Dominique Sauter,et al.  Robust Fault Diagnosis in an H∞ Setting , 1997 .

[11]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems , 2012 .

[12]  Rolf Isermann,et al.  Trends in the Application of Model Based Fault Detection and Diagnosis of Technical Processes , 1996 .

[13]  Hong Wang,et al.  Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.