Observer based fault detection for two dimensional systems described by Roesser models

Fault detection and isolation for two dimensional (2-D) systems represent a great challenge in both theoretical development and applications. 2-D systems have been commonly represented by the Roesser Model and the Fornasini and Marchesini (F–M) model. Research on fault detection and isolation has been carried out using observer-based methods for the F–M model. In this paper, an observer based fault detection strategy is investigated for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique, a dead-beat observer is developed and the state estimate from the observer is then input to a residual generator to monitor occurrence of faults. An enhanced realization technique is combined to achieve efficient fault detection with reduced computations. Simulation results indicate that the proposed method is effective in detecting faults for systems without disturbances as well as those affected by unknown disturbances.

[1]  Ligang Wu,et al.  Mixed H2/H∞ approach to fault detection of discrete linear repetitive processes , 2011, J. Frankl. Inst..

[2]  Paul M. Frank,et al.  Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results , 1990, Autom..

[3]  JOHN w. WOODS,et al.  Kalman filtering in two dimensions , 1977, IEEE Trans. Inf. Theory.

[4]  Richard D. Braatz,et al.  Data-driven Methods for Fault Detection and Diagnosis in Chemical Processes , 2000 .

[5]  Wei Xing Zheng,et al.  Generalized H2 fault detection for two-dimensional Markovian jump systems , 2012, Autom..

[6]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[7]  Mark A. Kramer.  Malfunction diagnosis using quantitative models with non‐boolean reasoning in expert systems , 1987 .

[8]  J. Ramos,et al.  A subspace algorithm for identifying 2-D separable in denominator filters , 1994 .

[9]  Zhiping Lin,et al.  A direct-construction approach to multidimensional realization and LFR uncertainty modeling , 2008, Multidimens. Syst. Signal Process..

[10]  Sandro Zampieri.  2D residual generation and dead-beat observers , 1991 .

[11]  Zhiping Lin,et al.  The existence and design of functional observers for two-dimensional systems , 2012, Syst. Control. Lett..

[12]  Maria Elena Valcher,et al.  Dead-beat estimation problems for 2D behaviors , 2008, Multidimens. Syst. Signal Process..

[13]  Janos J. Gertler,et al.  Analytical Redundancy Methods in Fault Detection and Isolation , 1991 .

[14]  R. K. Mehra,et al.  Correspondence item: An innovations approach to fault detection and diagnosis in dynamic systems , 1971 .

[15]  Yun Zou,et al.  Robust H∞ filtering for uncertain two-dimensional discrete systems with state-varying delays , 2010 .

[16]  Yun Zou,et al.  Non-Fragile Robust Guaranteed Cost Control of 2-D Discrete Uncertain Systems Described by the General Models , 2011, Circuits Syst. Signal Process..

[17]  T. Çiftçibasi,et al.  Sufficient or necessary conditions for modal controllability and observability of Roesser's 2-D system model , 1983 .

[18]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[19]  Josiah C. Hoskins,et al.  Artificial neural network models for knowledge representation in chemical engineering , 1990 .

[20]  Yun Zou,et al.  H ∞ control for 2-D singular delayed systems , 2011, Int. J. Syst. Sci..

[21]  Maria Elena Valcher,et al.  Observer-based Fault Detection and Isolation for 2D State-space Models , 2006, Multidimens. Syst. Signal Process..

[22]  G. E. Antoniou,et al.  Minimal state-space realization of factorable 2-D transfer functions , 1988 .

[23]  Alf J. Isaksson,et al.  Analysis of identified 2-D noncausal models , 1993, IEEE Trans. Inf. Theory.

[24]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[25]  Huijun Gao,et al.  Robust finite frequency H∞ filtering for uncertain 2-D systems: The FM model case , 2013, Autom..

[26]  Lorenzo Ntogramatzidis,et al.  Detectability subspaces and observer synthesis for two-dimensional systems , 2012, Multidimens. Syst. Signal Process..

[27]  A. Willsky,et al.  A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems , 1976 .

[28]  Cishen Zhang,et al.  H2 and mixed H2/Hinfinity control of two-dimensional systems in Roesser model , 2006, Autom..

[29]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[30]  Daniel W. C. Ho,et al.  Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection , 2009, IEEE Transactions on Fuzzy Systems.

[31]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[32]  Eric Rogers,et al.  A Geometric Approach to 3D Fault Identification , 2013 .

[33]  T. Kaczorek.  Perfect Observers for Singular 2D Linear Systems , 2001 .

[34]  M. Ohki,et al.  Two-dimensional LMS adaptive filters , 1991 .

[35]  R. Eising.  Controllability and observability of 2-D systems , 1979 .

[36]  Ahmed Alenany,et al.  Subspace algorithms for identifying separable-in-denominator two-dimensional systems with deterministic inputs , 2011 .

[37]  Huijun Gao,et al.  Robust finite frequency Hinfinity filtering for uncertain 2-D Roesser systems , 2012, Autom..

[38]  Hans Zwart,et al.  A Review on Realization Theory for Infinite-Dimensional Systems , 2017 .

[39]  Ping-Ya Zhao,et al.  An unbiased and computationally efficient LS estimation method for identifying parameters of 2D noncausal SAR models , 1993, IEEE Trans. Signal Process..

[40]  Janos Gertler,et al.  Fault detection and diagnosis in engineering systems , 1998 .

[41]  Wei Xing Zheng,et al.  Fault Detection Filter Design for Markovian Jump Singular Systems With Intermittent Measurements , 2011, IEEE Transactions on Signal Processing.