# Test signal design for failure detection: A linear programming approach

Héctor Scola; Ramine Nikoukhah; François Delebecque

International Journal of Applied Mathematics and Computer Science (2003)

- Volume: 13, Issue: 4, page 515-526
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topScola, Héctor, Nikoukhah, Ramine, and Delebecque, François. "Test signal design for failure detection: A linear programming approach." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 515-526. <http://eudml.org/doc/207664>.

@article{Scola2003,

abstract = {A new methodology for the design of filters that permits failure detection and isolation of dynamic systems is presented. Assuming that the normal and the faulty behavior of a process can be modeled by two linear systems subject to inequality bounded perturbations, a method for the on-line implementation of a test signal, guaranteeing failure detection, is proposed. To improve the fault detectability of the dynamic process, appropriate test signals are injected into the system. All the computations required by the proposed method are implemented as the solution of large sparse linear optimization problems. A simple numerical example is given to illustrate the proposed procedure.},

author = {Scola, Héctor, Nikoukhah, Ramine, Delebecque, François},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {failure detection; large scale programming; failure isolation; active detection; bounded perturbations; test signal design; large-scale linear programming; bounded perturbation; fault detection and isolation; linear discrete-time systems; detection filter; separating hyperplane test},

language = {eng},

number = {4},

pages = {515-526},

title = {Test signal design for failure detection: A linear programming approach},

url = {http://eudml.org/doc/207664},

volume = {13},

year = {2003},

}

TY - JOUR

AU - Scola, Héctor

AU - Nikoukhah, Ramine

AU - Delebecque, François

TI - Test signal design for failure detection: A linear programming approach

JO - International Journal of Applied Mathematics and Computer Science

PY - 2003

VL - 13

IS - 4

SP - 515

EP - 526

AB - A new methodology for the design of filters that permits failure detection and isolation of dynamic systems is presented. Assuming that the normal and the faulty behavior of a process can be modeled by two linear systems subject to inequality bounded perturbations, a method for the on-line implementation of a test signal, guaranteeing failure detection, is proposed. To improve the fault detectability of the dynamic process, appropriate test signals are injected into the system. All the computations required by the proposed method are implemented as the solution of large sparse linear optimization problems. A simple numerical example is given to illustrate the proposed procedure.

LA - eng

KW - failure detection; large scale programming; failure isolation; active detection; bounded perturbations; test signal design; large-scale linear programming; bounded perturbation; fault detection and isolation; linear discrete-time systems; detection filter; separating hyperplane test

UR - http://eudml.org/doc/207664

ER -

## References

top- Basseville M. and Benveniste A., (Eds.) (1985): Detection of Abrupt Changes in Signals and Dynamical Systems. -Berlin: Sprinter. Zbl0554.62070
- Basseville M., Benveniste A., Moustakids G. and Rougee A. (1987): Detection and diagnosis of changes in the eigenstructure of nonstationary multivariable system. -Automatica, Vol. 23, No. 4, pp. 479-489. Zbl0625.93060
- Clark R.N. (1978): Instrument fault detection. -IEEE Trans. Aerospace Electron. Syst., Vol. AES-14, pp. 456-465.
- Clark R.N. and Setzer W. (1980): Sensor fault detection in a system with random disturbances. -IEEE Trans. Aerospace Electron. Syst., Vol. AES-16, pp. 468-473.
- Clark R.N. and Walton V.M. (1975): Detecting instrument mal functions in control systems. - IEEE Trans. Aerospace Electron. Syst., Vol. AES-11, pp. 465-473.
- Gertler J. (1998): Fault Detection and Diagnosis in Engineering Systems. -New York: Marcel Dekker.
- Gondzio J. (1996): Multiple centrality corrections in a primal-dual method for linear programming. -Comput. Optim. Appl., Vol. 6, No. 2, pp. 137-156. Zbl0860.90084
- Isermann R. (1984): Process fault detection based on modeling and estimation methods. A survey. -Automatica, Vol. 20, No. 4, pp. 387-404. Zbl0539.90037
- Keresteciovglu F. (1993): Change Detection and Input Design in Dynamical Systems. -Taunton: Research Studies Press.
- Mangoubi R.S. (1998): Robust Estimation and Failure Detection, A Concise Treatment. -Berlin: Springer.
- Mehrotra S. (1992): On the implementation of a primal-dual interior point method. - SIAM J. Optim., Vol. 2, No. 4, pp. 575-601. Zbl0773.90047
- Mironovski L.A. (1980): Functional diagnosis of dynamic systems: A survey. - Autom. Remote Contr., Vol. 41, pp. 1122-1143.
- Nikoukhah R. (1998): Guaranteed active failure detection and isolation for linear dynamical systems. -Automatica, Vol. 34, No. 11, pp. 1345-1358. Zbl0961.93006
- Rockafellar R.T. (1972): Convex Analysis. -Princeton: Princeton University Press. Zbl0224.49003
- Rubio Scola H. (1999): Solving large linear optimization problems with Scilab: Application to multicommodity problems. -Techn. Rep. No. 0227, INRIA, Rocquencourt.
- Rubio Scola H. (2000a): Detection signal design for failure detection and isolation for linear dynamic systems. -Techn. Rep. No. 3935, INRIA, Rocquencourt.
- Rubio Scola H. (2000b): Toolbox Scilab: Detection signal design for failure detection and isolation for linear dynamic systems. User's guide. -Techn. Rep. No. 0241, INRIA, Rocquencourt.
- Rubio Scola H., Nikoukhah R. and Delebecque F. (2000): Detection signal design for failure detection: A linear linear programming approach. -Proc. 4th Symp. Fault Detection, Supervision and Safety for Technical Processes, Safeprocess'2000, Budapest, Hungary, Vol. 1, pp. 593-598. Zbl1049.93032
- Uosaki K., Tanaka I. and Sugiyama H. (1984): Optimal input design for autoregressive model discrimination with constrained output variance. -IEEE Trans. Automat. Contr., Vol.AC-29, No. 4, pp. 384-350. Zbl0536.93065
- Willsky A.S. (1976): A survey of design methods for failure detection in dynamic systems. -Automatica, Vol. 12, No. 4, pp. 601-611. Zbl0345.93067
- Zhang X.J. (1989): Auxiliary Signal Design in Fault Detection and Diagnosis. - Heidelberg: Springer. Zbl0679.68207
- Zhang Y. (1995): User's guide to LIPSOL. - Dept. Mathematics and Statistics, University of Maryland, Baltimore County, USA.