Fault Detection in Nonlinear Continuous-Time Systems with Uncertain Parameters

In model-based fault diagnosis for dynamic systems with uncertain parameters, an envelope of all fault-free behaviors can be determined from the model and used as a reference for detecting faults. We demonstrate here a method for generating an envelope that is rigorously guaranteed to be complete, but without significant overestimation. The method is based on an interval approach, but uses Taylor models to reduce the overestimation often associated with interval methods. To speed fault detection, a method that uses bounded-error measurement data and a constraint propagation procedure is proposed for shrinking the envelope. Several fault detection scenarios involving nonlinear, continuous-time systems are used to evaluate this approach. © 2008 American Institute of Chemical Engineers AIChE J, 2008

[1]  M. Mannan,et al.  A methodology for fault detection, isolation, and identification for nonlinear processes with parametric uncertainties , 2004 .

[2]  M. Stadtherr,et al.  Validated solutions of initial value problems for parametric ODEs , 2007 .

[3]  Nedialko S. Nedialkov,et al.  Validated solutions of initial value problems for ordinary differential equations , 1999, Appl. Math. Comput..

[4]  Nedialko S. Nedialkov,et al.  An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation , 1998, SCAN.

[5]  M. Stadtherr,et al.  Deterministic global optimization of nonlinear dynamic systems , 2007 .

[6]  M. Berz,et al.  TAYLOR MODELS AND OTHER VALIDATED FUNCTIONAL INCLUSION METHODS , 2003 .

[7]  R. B. Kearfott.  Rigorous Global Search: Continuous Problems , 1996 .

[8]  R. Martínez-Guerra,et al.  The fault detection problem in nonlinear systems using residual generators , 2005, IMA J. Math. Control. Inf..

[9]  Janos Gertler,et al.  A new structural framework for parity equation-based failure detection and isolation , 1990, Autom..

[10]  M. Stadtherr,et al.  Deterministic Global Optimization for Parameter Estimation of Dynamic Systems , 2006 .

[11]  N. Nedialkov,et al.  Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation , 1999 .

[12]  A. Neumaier.  Interval methods for systems of equations , 1990 .

[13]  Arnold Neumaier,et al.  Taylor Forms—Use and Limits , 2003, Reliab. Comput..

[14]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[15]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[16]  Josep Vehí,et al.  Fault detection and isolation of the three-tank system using the modal interval analysis , 2002 .

[17]  Youdong Lin,et al.  Guaranteed State and Parameter Estimation for Nonlinear Continuous-Time Systems with Bounded-Error Measurements , 2007 .

[18]  Martin Berz,et al.  Verified global optimization with Taylor model based range bounders , 2005 .

[19]  George F. Corliss,et al.  Validating an A Priori Enclosure Using High-Order Taylor Series , 2007 .

[20]  Nilay Shah,et al.  Quantitative framework for reliable safety analysis , 2002 .

[21]  John D. Pryce,et al.  An Effective High-Order Interval Method for Validating Existence and Uniqueness of the Solution of an IVP for an ODE , 2001, Reliab. Comput..

[22]  Richard D. Braatz,et al.  Fault Detection and Diagnosis in Industrial Systems , 2001 .

[23]  John D. Pryce,et al.  Interval Arithmetic with Containment Sets , 2006, Computing.

[24]  Raghunathan Rengaswamy,et al.  A review of process fault detection and diagnosis: Part II: Qualitative models and search strategies , 2003, Comput. Chem. Eng..

[25]  Janos Gertler,et al.  Generating directional residuals with dynamic parity relations , 1995, Autom..

[26]  Rolf Isermann,et al.  Model-based fault-detection and diagnosis - status and applications , 2004, Annu. Rev. Control..

[27]  Raghunathan Rengaswamy,et al.  A review of process fault detection and diagnosis: Part I: Quantitative model-based methods , 2003, Comput. Chem. Eng..

[28]  Rolf Isermann,et al.  Process fault detection based on modeling and estimation methods - A survey , 1984, Autom..

[29]  Paul I. Barton,et al.  Optimization of hybrid systems , 2006, Comput. Chem. Eng..

[30]  Martin Berz,et al.  5. Remainder Differential Algebras and Their Applications , 1996 .

[31]  Raghunathan Rengaswamy,et al.  A review of process fault detection and diagnosis: Part III: Process history based methods , 2003, Comput. Chem. Eng..

[32]  Nedialko S. Nedialkov,et al.  On Taylor Model Based Integration of ODEs , 2007, SIAM J. Numer. Anal..

[33]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[34]  Martin Berz,et al.  Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models , 1998, Reliab. Comput..

[35]  Josep Vehí,et al.  A Survey on Interval Model Simulators and their Properties Related to Fault Detection , 2000 .

[36]  Kewen Yin,et al.  Minimax methods for fault isolation in the directional residual approach , 1998 .

[37]  Martin Berz,et al.  Efficient Control of the Dependency Problem Based on Taylor Model Methods , 1999, Reliab. Comput..