Abstract
This chapter uses the structure graph to describe the direct interactions among the signals. This graph is used to analyse the redundancies which can be exploited for fault diagnosis and control reconfiguration. Faults are interpreted as violation of constraints. The analysis shows how component faults, which imply the violation of single constraints, can be found by defining and utilising appropriate redundancy relations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
5.11 Bibliographical notes
C. Berge. Two Theorems in Graph Theory. Princeton University, 1957.
Blanke, M., Izadi-Zamanabadi, R., and Lootsma, T.F. (1998). Fault monitoring and reconfigurable control for a ship propulsion plant, Journal of Adaptive Control and Signal Processing, vol. 12, pp.671–688.
M. Blanke and M. Staroswiecki: Fault-tolerant control with safe behaviour under multiple actuator or sensor faults — Theory and application. 14th IFAC Safeprocess Symposium, Beijing 2006.
T. Carpentier, R. Litwak and J.-Ph. Cassar. Criteria for the evaluation of FDI systems — Application to sensors location. IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, pp. 1083–1088, Hull 1997.
G. Chartrand and O. R. Oellermann. Applied and algorithmic graph theory. Pure and applied mathematics. McGraw-Hill Inc., 1993.
M.-O. Cordier, P. Dague, F. Lévy, M. Dumas, J. Montmain, M. Staroswiecki, and L. Travé-Massuyès. AI and automatic control approaches of model-based diagnosis: links and underlying hypothesis. IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, pp. 274–279, Budapest 2000.
P. Declerck and M. Staroswiecki. Characterisation of the canonical components of a structural graph for fault detection in large scale industrial plants. Proc. European Control Conference, Grenoble 1991.
A. L. Dulmage and N. S. Mendelsohn. Covering of bi-partite graphs. Canada J. Math., 10:517–534, 1958.
A. L. Dulmage and N. S. Mendelsohn. A structure theory of bi-partite graphs of finite exterior dimension. Trans. of Royal Soc. Canada, Section III, 53: 1–13, 1959.
J. Edmonds. Paths, trees and flowers. Canad. J. of Math., 17: 449–467, 1965.
L. R. Ford and D. R. Fulkerson. Maximal flow through a network. Canad. J. Math., 8: 399–404, 1956.
L. R. Ford and D. R. Fulkerson. A simple algorithm for finding maximal network flows and an application to the hitchcock problem. Canad. J. Math., 9: 210–218, 1957.
A. L. Gehin, M. Assas and M. Staroswiecki. Structural analysis of system reconfigurability. IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, pp. 292–297, Budapest 2000.
A. Georgiou and C. A. Floudas. Structural analysis and synthesis of feasible control systems: Theory and applications. Chemical Engineering Research and Design, 67: 600–618, 1989.
J. Gertler and D. Singer. A new structural framework for parity space equation based failure detection and isolation. Automatica, 26: 381–388, 1990.
K. Golver and L. M. Silverman. Characterisation of structural controllability. IEEE Trans., AC-21,4: 534–537, 1976.
M. Gondran and M. Minoux. Graphes et algorithmes. Coll. Direction des Etudes et Recherches EDF, Eyrolles, (3d edition), 1995.
F. Harary. A graph theoretic approach to matrix inversion by partitioning. Numer. Math., 4: 128–135, 1962.
J. E. Hopcroft and R. M. Karp. An algorithm for maximum matchings in bipartite graphs. SIAM J. Comp., 2: 225–231, 1973.
Y. Iwasaki and H. A. Simon. Causality in device behaviour. Artificial Intelligence, 29: 3–32, 1986.
R. Izadi-Zamanabadi, P. Amann, M. Blanke, V. Cocquempot, G. L. Gissinger, E. C. Kerrigan, T. F. Lootsma, J. M. Perronne and G. Schreier. Ship propulsion control and reconfiguration. in [3], pp. 285–315.
H. W. Kuhn. The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2: 83–97, 1956.
A. Leitold and K. M. Hangos. Structural solvability analysis of dynamic process models. Computers and Chemical Engineering, 25: 1633–1646, 2001.
C. T. Lin. Structural controllability. IEEE Trans., AC-19: 201–208, 1974.
C. T. Lin. System structure and minimal structure controllability. IEEE Trans., AC-22: 855–862, 1977.
X. Lin, M. O. Tade and R. B. Newell. Output structural controllability condition for the synthesis of control systems for chemical processes. Int. J. Systems Sci., 22: 107–132, 1991.
M. Meyer, J.-M. Le Lann, B. Koehret and M. Enjalbert. Optimal selection of sensor location on a complex plant using a graph oriented approach. Computer Chemical Eng., 18: 535–540, 1994.
M. Morari and G. Stephanopoulos. Studies in the synthesis of control structures for chemical processes. Part ii: Structural aspects and the synthesis of alternative feasible control. AIChE Journal, 40: 232–246, 1980.
K. Murota. Systems analysis by graphs and matroïds. Structural solvability and controllability. Springer Verlag, 1987.
K. J. Reinschke. Multivariable Control: A Graph Theoretic Approach. Springer-Verlag, 1988.
C. Schizas and F. J. Evans. A graph theoretic approach to multivariables control system design. Automatica, 17: 371–377, 1981.
M. Staroswiecki, S. Attouche and M. L. Assas. A graphic approach for reconfigurability analysis. 10th Int. Workshop on Principles of Diagnosis, Loch Awe 1999.
M. Staroswiecki, J. P. Cassar and P. Declerck. A structural framework for the design of FDI in large scale industrial plants. In P. M. Frank and R. Clark (Eds.). Issues of Fault Diagnosis for Dynamical Systems. Springer-Verlag, London 1999 [195].
M. Staroswiecki and P. Declerck. Analytical redundancy in non-linear interconnected systems by means of structural analysis. IFAC/IMACS/IFORS Conf. AIPAC’ 89, Nancy, France, 1989.
D. V. Steward. On an approach to techniques for the analysis of the structure of large systems of equations. SIAM Review, 4: 321–342, 1962.
M. Tagina, J.-P. Cassar, G. Dauphin-Tanguy and M. Staroswiecki. Bond-graph models for direct generation of formal fault detection systems. Systems Analysis Modelling and Simulation J., 23: 1–17, 1996.
J. Unger, A. Kröner and W. Marquardt. Structural analysis of differential-algebraic equation systems — theory and applications. Computers and Chemical Engineering, 19: 867–882, 1995.
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2006). Structural analysis. In: Diagnosis and Fault-Tolerant Control. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-35653-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-35653-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35652-3
Online ISBN: 978-3-540-35653-0
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)