On non-invertibilities for Structural Analysis



Vincent de Flaugergues de Flaugergues Vincent Cocquempot Mireille Bayart Marco Pengov


This article deals with structural analysis, which is a simple but efficient method in the field of Fault Detection and Isolation (FDI), to determine systems properties, such as observability, fault detectability or diagnosability. Moreover, it allows to determine subsets of the model equations which may or may not yield fault indicators, namely residuals. Because some residuals are obtained by inverting parts of the model, the notion of constraint invertibility is used to assess the possibility of building a residual. Invertibilities are often considered a posteriori, after that the structural analysis has been performed, in order to keep the computable residuals. Taking into account these invertibility constraints in all steps of the structural method would allow, firstly, to provide directly computable residuals, and secondly, to reduce the complexity of structural analysis algorithms. Two types of non-invertibilities may be distinguished: those which are defined according to the nature of the functions, and those which are due to the structure of the model. Two algorithms are proposed for determining the latter ones. Integration of the two kinds of invertibilities from the first step of the structural analysis is the objective of this paper.

How to Cite

de Flaugergues , V. de F. ., Cocquempot, V. ., Bayart , M. ., & Pengov, M. . (2010). On non-invertibilities for Structural Analysis. Annual Conference of the PHM Society, 2(2). https://doi.org/10.36001/phmconf.2010.v2i1.1949
Abstract 1 | PDF Downloads 4



structural analysis, non-invertibilities

(Armengol et al., 2009) J. Armengol, A. Bregon, T. Escobet, E. Gelso, M. Krysander, M. Nyberg, X. Olive, B. Pulido, and L. Trave ́-Massuye`s. Minimal Structurally Overdetermined sets for residual generation: A comparison of alternative approaches. Proceedings of the IFAC-Safeprocess 2009, 2009.
(A ̊ slund and Frisk, 2006) J. A ̊ slund and E. Frisk. An observer for non-linear differential-algebraic systems. Automatica, 42(6):959–965, 2006.
(Blanke et al., 2006) M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki. Diagnosis and Fault-Tolerant Control. Springer Verlag, 2006.
(Caldero ́n-Espinoza et al., 2007) G. Caldero ́n- Espinoza, J. Armengol, J. Veh ́ı, and E.R. Gelso. Dynamic diagnosis based on interval analytical redundancy relations and signs of the symptoms. AI Communications, 20(1):39–47, 2007.
(Carpentieretal.,1997) T.Carpentier,R.Litwak,and J.P. Cassar. Criteria for the evaluation of FDI systems: Application to sensors location. Proc. IFAC SAFEPROCESS 97, 1083, 1088, 1997.
(Conrard et al., 2009) B. Conrard, V. Cocquempot, and M. Bayart. Sensor and Actuator Placement with Dependability Constraints and a Cost Criterion. Proceedings of the IFAC-Safeprocess 2009, 2009.
(de Flaugergues et al., 2009) V. de Flaugergues, V. Cocquempot, M. Bayart, and M. Pengov. A modified, invertibility-based canonical decomposi- tion. Proc. DX’09, 2009.
(Dressler and Freitag, 1994) O. Dressler and H. Fre- itag. Prediction Sharing Across Time and Contexts. 1994.
(Dulmage and Mendelsohn, 1958) AL Dulmage and NS Mendelsohn. Coverings of bipartite graphs. Canad. J. Math, 10:517–534, 1958.
(Dustegor et al., 2004) D. Dustegor, V. Cocquempot, and M. Staroswiecki. Structural analysis for fault detection and identification: an algorithmic study. Proceedings of the 2nd Symposium on System Structure and Control 2004 (SSSC’04), 2004.
(Frisk and Krysander, 2007) E. Frisk and M. Krysander. Sensor placement for maximum fault isolability. Proceedings DX-2007, Nashville, USA, 2007.
(Frisk, 2000) E. Frisk. Residual Generator Design For Non-Linear, Polynomial Systems – A Grobner Basis Approach. In Proc. IFAC Fault Detection, Supervision and Safety for Technical Processes, pages 979–984. Budapest, Hungary, 2000.
(Guernez et al., 1997) C. Guernez, J.P. Cassar, and M. Staroswiecki. Extension of parity space to non- linear polynomial dynamic systems. In Proc. Safe- process, volume 97, 1997.
(Krysander et al., 2008) M. Krysander, J. A ̊ slund, and M. Nyberg. An efficient algorithm for finding minimal overconstrained subsystems for model-based diagnosis. IEEE Transactions on Systems, Man and Cybernetics, Part A, 38(1):197–206, 2008.
(Krysander, 2006) M. Krysander. Design and analysis of diagnostic systems utilizing structural methods. Department of Electrical Engineering, Linko ̈pings universitet, 2006.
(Maquin et al., 1997) D. Maquin, V. Cocquempot, JP Cassar, M. Staroswiecki, and J. Ragot. Generation of Analytical Redundancy Relations for FDI purposes. IFAC Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives, SDEMPED’97, pages 86–93, 1997.
(Murota,1987) K.Murota.MatricesandMatroidsfor Systems Analysis. Springer, 1987.
(Pulido and Gonzalez, 2004) B. Pulido and CA Gonzalez. Possible conflicts: a compilation technique for consistency-based diagnosis. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 34(5):2192–2206, 2004.
(Pulido et al., 2008) B. Pulido, A. Brego ́n, and C. Alonso. Combining state estimation and simulation in consistency-based diagnosis using possible conflicts. In Proceedings of the 19th International Workshop on Principles of Diagnosis (DX- 08), pages 339–346, 2008.
(Rosich et al., 2007) A. Rosich, R. Sarrate, V. Puig, and T. Escobet. Efficient optimal sensor placement for model-based FDI using an incremental algorithm. In Proc. 46th IEEE Conference on Decision and Control, pages 2590–2595, 2007.
(Rosich et al., 2009) A. Rosich, E. Frisk, J. A ̊ slund, R. Sarrate, and F. Nejjari. Sensor placement for fault diagnosis based on causal computations. In Proceedings of IFAC Safeprocess, volume 9, pages 402–407, 2009.
(Shampine et al., 1999) L.F. Shampine, M.W. Re- ichelt, and J.A. Kierzenka. Solving index-I DAEs in MATLAB and Simulink. Siam Review, 41(3):538– 552, 1999.
(Sva ̈rd and Nyberg, 2008) C. Sva ̈rd and M. Nyberg. A Mixed Causality Approach to Residual Generation Utilizing Equation System Solvers and Differential-Algebraic Equation Theory. 19th International Workshop on Principles of Diagnosis, DX08, 2008.
(Sva ̈rd and Wasse ́n, 2006) C. Sva ̈rd and H. Wasse ́n.
Development of Methods for Automatic Design of Residual Generators. Linko ̈ ping University, Department of Electrical Engineering, 2006.
(Trave ́-Massuye`s et al., 2006) L. Trave ́-Massuye`s, T. Escobet, X. Olive, and T. CNRS. Diagnosability analysis based on component-supported analytical redundancy relations. IEEE Transactions on Systems, Man and Cybernetics, Part A, 36(6):1146–1160, 2006.
(Vidyasagar, 1980) M. Vidyasagar. On the well- posedness of large-scale interconnected systems. IEEE Transactions on Automatic Control, 25(3):413–421, 1980.
Technical Papers