Nonlinear set-membership identification and fault detection using a Bayesian framework: Application to the wind turbine benchmark

This paper deals with the problem of nonlinear set-membership identification and fault detection using a Bayesian framework. The paper presents how the set-membership model estimation can be reformulated from a Bayesian viewpoint in order to determine the feasible parameter set and, in a posterior fault detection stage, to check the consistency between the model and the data. The paper shows that the Bayesian approach, assuming uniform distributed measurement noise and flat model prior probability distribution, leads to the same feasible parameter set as the set-membership technique. To illustrate this point a comparison with the subpavings approach is included. Finally, by means of the application to the wind turbine benchmark problem, it is shown how the Bayesian fault detection test works successfully.

[1]  J. Norton,et al.  Bounding Approaches to System Identification , 1996 .

[2]  Mario Milanese,et al.  Optimality, approximation, and complexity in set membership H∞ identification , 2002, IEEE Trans. Autom. Control..

[3]  Brett Ninness,et al.  Bayesian system identification via Markov chain Monte Carlo techniques , 2010, Autom..

[4]  Jordi Saludes,et al.  Robust fault detection using polytope-based set-membership consistency test , 2009, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[5]  Eric Walter,et al.  Set inversion via interval analysis for nonlinear bounded-error estimation , 1993, Autom..

[6]  Alex M. Andrew,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2002 .

[7]  Andrea Garulli,et al.  On Model Error Modeling in Set Membership Identification , 2000 .

[8]  Thomas B. Schön,et al.  System identification of nonlinear state-space models , 2011, Autom..

[9]  Graham C. Goodwin,et al.  Non-stationary stochastic embedding for transfer function estimation , 1999, Autom..

[10]  Vasso Reppa,et al.  Fault detection and diagnosis based on parameter set estimation , 2011 .

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

[12]  Luc Jaulin,et al.  Probabilistic Set-membership Approach for Robust Regression , 2010 .

[13]  Eduardo F. Camacho,et al.  Guaranteed state estimation by zonotopes , 2005, Autom..

[14]  Xiang Li,et al.  Probabilistically Constrained Linear Programs and Risk-Adjusted Controller Design , 2005, SIAM J. Optim..

[15]  Václav Peterka,et al.  Bayesian system identification , 1979, Autom..

[16]  P. Eykhoff.  System Identification Parameter and State Estimation , 1974 .

[17]  G. Goodwin,et al.  Rapprochement between bounded‐error and stochastic estimation theory , 1995 .

[18]  B. Ninness,et al.  Rapproachment Between Bounded Error and StochasticEstimation Theory , 1994 .

[19]  A. Vicino,et al.  Sequential approximation of feasible parameter sets for identification with set membership uncertainty , 1996, IEEE Trans. Autom. Control..

[20]  Vicenç Puig,et al.  Identification for passive robust fault detection using zonotope‐based set‐membership approaches , 2011 .

[21]  Lennart Ljung,et al.  Comparing different approaches to model error modeling in robust identification , 2002, Autom..

[22]  Mario Sznaier,et al.  Robust Systems Theory and Applications , 1998 .

[23]  Carlo Novara,et al.  Set Membership identification of nonlinear systems , 2004, Autom..

[24]  M. Milanese,et al.  Set membership identification of nonlinear systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[25]  Hüseyin Akçay.  The size of the membership-set in a probabilistic framework , 2004, Autom..