Integrated Diagnosis and Prognosis of Uncertain Systems: A Bond Graph Approach
Bond Graph (BG) methodology is used to model the dynamic uncertain systems. Uncertainty is considered on the system parameters in form of intervals. The uncertain parameters are allowed to deviate within their prescribed interval limits. Single fault hypothesis is considered in this work such that the parameter undergoing degradation is known a priori. A new method for generation of interval valued thresholds is briefly described in the framework of BG models in Linear Fractional Transformation form. The diagnostic module is formed using such thresholds which detect the beginning of degradation of a parameter in the real system. The new concept of Interval Extension of Analytical Redundancy Relations (IE-ARRs) is introduced which consider the parametric uncertainties and the evolution of degrading parameter in real time. Then, the Centre and Range method for fitting linear regression models to interval symbolic data is adapted to fit piece wise linear models to the interval valued times series data of IE-ARRs. Further, the new concept of generation of failure thresholds from a nominal system model is introduced and developed. Finally, the fitted linear model is used to estimate the remaining useful life of the parameter under degradation. Simulations are carried out on an example DC motor model. Linear and non-linear parametric degradations are considered. Results are presented in form of simulations.
How to Cite
Parameter interval, failure prognosis, integrated system health management, model uncertainty
Armengol, J. (1999). Application of Modal Interval Analysis to the simulation of the behavior of dynamic systems with uncertain parameters, Phd thesis, University of Girona, Girona, Catalonia, Spain.
Armengol, J., Vehi, J., Angel Sainz, M., & Herrero, P. (2003). ‘Fault detection in a pilot plant using interval models and multiple sliding time windows. Safeprocess, (pp. 729-734). Washington,USA.
Billard, L., & Diday, E. (2003). From the statistics of data to the statistics of knowledge: symbolic data analysis. Journal of American Statistics Association, 98 (462), 470-487.
Billard, L., & Diday, E. (2000). Regression analysis for interval-valued data. Proceedings of the Seventh Conference of the International Federation of Classification Societies (IFCS’00).Data Analysis, Classification and Related Methods, pp. 369-374. Belgium: Springer.
Billard, L., & Diday, E. (2002). Symbolic Regression Analysis. Proceedings of the Eighenth Conference of the International Federation of Classification Societies (IFCS’02),.In: Classification, Clustering and Data Analysis,, pp. 281-288. Poland: Springer.
Djeziri, M., Dauphin Tanguy, G., & Merzouki, R. (2007). Bond Graph Model Based For Robust Fault Diagnosis. Proceeding of the 2007 American Control Conference, (pp. 3017-3022). New York City.
Djeziri, M., Merzouki, R., & Ould Bouamama, B. (2006). Fault Detection of Backlash Phenomenon in Mechatronic System with Parameter Uncertainties using Bond Graph Approach. Proceeding of the 2006 IEEE International Conference on Mechatronics and Automation , (pp. 600-605). Luoyang, China.
Djeziri, M., Merzouki, R., & Ould Bouamama, B. (2007). Robust Fault Diagnosis Using Bond Graph Approach. Journal of IEEE/ASME Transactions on Mechatronics, 12 (6), pp. 599-611.
Fagarasan, I., Ploix, S., & Gentil, S. (2004). Causal fault detection and isolation based on a set-membership approach. Automatica, 40, 2099-2110.
Greitzer, F., & Pawlowski, A. (2002). Embedded Prognostics Health Monitoring. 48th Annual Instrumentations, Systems, and Automation Society International Instrumentation Symposium. San Diego,USA.
Hansen, E. (1992). Global Optimization Using Interval Analysis. New York: Marcel Dekker, Inc.
Hargreaves, G. (2002). Interval Analysis in MATLAB. University of Manchester: Master’s thesis, Department of Mathematics.
James, C., & Hyungdae, L. (2005). Gear fatigue crack prognosis using embedded model, gear dynamic model and fracture mechanics. Mechanical Systems and Signal processing, 19 (4), 836-846.
Jha, M., Dauphin-Tanguy, G., & Ould Bouamama, B. (2014). Robust FDI based on LFT BG and Relative Activity at Junction European Control Conference:Accepted. Starsbourg, France.
Kam, C. S., & Dauphin-Tanguy, G. (2005). Bond Graph models for structured parameter uncertainities. Journal of th Franklin Insititute .
Lima Neto, E., & De Carvalho, F. (2008). Centre and range Method for fitting a linear regression model to symbolic interval data,Computational Statistics and Data Analysis. Computational Statistics and Data Analysis, 52, 1500-1515.
Ming, Y. (2012). Fault diagnosis and prognosis of hybrid systems using Bond Graph model and Computational intelligence. Nanyang: PhD Thesis,School of Engineering and Electronic Engineering,Nanyang Techological Institute.
Mohanty, S., Teale, R., Chattopadhyay, A., Peralta, P., & Willhauck, C. (2007). Mixed Gaussian process and state-space approach for fatigue crack growth prediction. International Workshop on Stuctural Health Monitoring, (pp. Vol 2,pp.1108-1115).
Moore, R. (1996). Interval Analysis. Englewood Cliffs,NJ: Prentice Hall.
Ould Bouamama, B., Staroswiecki, M., & Samantaray, A. (2006). Software for Supervision System Design In Process Engineering Industry. 6th IFAC, SAFEPROCESS, (pp. 691-695). Beijing, China
Ragot, J., Alhaj Dibo, M., & Maquin, D. (2003). Validation of data by Bounding Approaches, Journées Doctorales d’Automatique, (pp. 347-352). Valencienne- France,.
Ragot, J. & Maquin, D. (2003). Validation of data from systems of measurement uncertainty. European Journal of Automated Systems RS special issue JESA Applications tools set-calculations, 37 (9).
Rump, S. (1998). INTLAB-INTerval LABoratory. Developments in Reliable Computing , 77-104.
Trana, V., Yanga, B., Oha, M., & Tanb, A. (2008). Machine condition prognosis based on regression trees and one-step-ahead Prediction. Mechanical Systems and Signal Processing, 22, 1179-1193.
Wu, W., Hu, J., & Zhang, J. (2007). Prognostics of machine health condition using an improved ARIMA-based prediction method. IEEE, (pp. 1062-1067). Harbin,China.
Yang, S. (2002). “An experiment of state estimation for predictive maintenance using Kalman filter on a DC motor. Realiablity Engineering & System Safety, 75 (1), 103-111.
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.