Uncertainty Assessment in Structural Damage Diagnosis
This paper develops methods for the quantification of uncertainty in each of the three steps of damage diagnosis (detection, localization and quantification), in the context of continuous online monitoring. A model-based approach is used for diagnosis. Sources of uncertainty include physical variability, measurement uncertainty and model errors. Damage detection is based on residuals between nominal and damaged system-level responses, using statistical hypothesis testing whose uncertainty can be captured easily. Localization is based on the comparison of damage signatures derived from the system model. Both classical statistics-based methods and Bayesian statistics-based methods are investigated to quantify the uncertainty in all the three steps of diagnosis, i.e. detection, localization, and quantification. While classical statistics-based methods use the concept of least squares-based optimization, Bayesian methods make use of likelihood function and Bayes theorem. The uncertainties in damage detection, isolation and quantification are combined to quantify the overall uncertainty in diagnosis. The proposed methods are illustrated using two types of example problems, a structural frame and a hydraulic actuation system.
KeywordsProbability Density Function Damage Detection Structural Health Monitoring Damage Parameter Uncertainty Quantification
Unable to display preview. Download preview PDF.
- 1.Achenbach, J.D. Quantitative nondestructive evaluation, International Journal of Solids and Structures, Volume 37, Issues 1-2, January 2000, Pages 13-27, ISSN 0020-7683, DOI: 10.1016/S0020-7683(99)00074-8.
- 2.Guratzsch, R. Sensor placement optimization under uncertainty for structural health monitoring systems of hot aerospace structures. Ph.D. Dissertation, Vanderbilt University, Nashville, TN. 2007.Google Scholar
- 3.Dalai, M., Weyer, E., and Campi M.C. Parametric Identification of Nonlinear Systems : Guaranteed Confidence Regions. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005.Google Scholar
- 4.Beck J.L, Au S.K, and Vanik M.V. Monitoring structural health using a probabilistic measure. Computer-Aided Civil and Infrastructure Engineering 2001; 16:1–11.Google Scholar
- 6.Sankararaman, S., and Mahadevan, S. Uncertainty Quantification in Structural Damage Diagnosis. doi: 10.1002/stc.400 Published Online May, 2010.
- 7.Migon H.S, and Gamerman D. Statistical Inference: An Integrated Approach. Arnold: London, 1999.Google Scholar
- 8.Moustafa, A., Mahadevan, S., Daigle, M., Biswas, G. Structural and Sensor Damage Identification using the Bond Graph Approach. J. International Association of Structural Control and Health Monitoring. Published Online Jul. 2008.Google Scholar
- 9.McKeeman, M.W. Algorithm 145: Adaptive numerical integration by Simpson's rule. Commun. ACM, Vol. 5, No. 12, Aug. 1962.Google Scholar
- 10.Sankararaman, S., Bartram, G., Biswas, G., and Mahadevan, S. 2009. Bond Graph Method for Hierarchical Multi-Domain Systems Diagnosis. In the Proceedings of 7th International Workshop on Structural Health Monitoring, Stanford, CA. Sept. 9-11, 2009.Google Scholar