Identification of Correlated Damage Parameters under Noise and Bias Using Bayesian Inference



Published Sep 25, 2011
Dawn An Joo-Ho Choi Nam H. Kim


This paper present a statistical model parameter identification using Bayesian inference when parameters are correlated and observed data have noise and bias. The method is explained using the Paris model that describes crack growth in a plate under mode I loading. It is assumed the observed data are obtained through structural health monitoring systems, which may have random noise and deterministic bias. It was found that strong correlation exists (a) between two model parameters of the Paris model, and (b) between initially measured crack size and bias. As the level of noise increases, the Bayesian inference was not able to identify the correlated parameters. However, the remaining useful life was predicted accurately because the identification errors in correlated parameters were compensated by each other.

How to Cite

An, D., Choi, J.-H. ., & H. Kim, N. . (2011). Identification of Correlated Damage Parameters under Noise and Bias Using Bayesian Inference. Annual Conference of the PHM Society, 3(1).
Abstract 165 | PDF Downloads 163



parameters identification, damage growth parameters, correlated parameters, Bayesian inference, structural health monitoring (SHM), remaining useful life (RUL)

Andrieu, C., Freitas, de N., Doucet, A., & Jordan, M. (2003). An introduction to MCMC for Machine Learning. Machine Learning, vol. 50(1), pp. 5-43.

Bayes, T. (1763). An Essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, vol. 53, pp. 370-418.

Bechhoefer, E. (2008). A Method for Generalized Prognostics of a Component Using Paris Law. Proceedings of the American Helicopter Society 64th Annual Forum, Montreal, CA.

Carpinteri, A., & Paggi, M. (2007). Are the Paris' law parameters dependent on each other?. Frattura ed Integrità Strutturale, vol. 2, pp. 10-16.

Coppe, A., Haftka, R. T., & Kim, N. H. (2010). Least Squares-Filtered Bayesian Updating for Remaining Useful Life Estimation. 12th AIAA Non-Deterministic Approaches Conference, Orlando, FL.

Coppe, A. Haftka, R. T., Kim, N. H., & Yuan, F. G. (2010). Uncertainty reduction of damage growth properties using structural health monitoring. Journal of Aircraft, in press.

Giurgiutiu, V. (2008). Structural Health Monitoring: with Piezoelectric Wafer Active Sensors, Academic Press (an Imprint of Elsevier), Burlington, MA.

Jaw, L. C., Inc, S. M., & Tempe, A. Z. (1999). Neural networks for model-based prognostics. IEEE Aerospace Conference.

Jerome P. L., & Kenneth J. L. (2006). A Summary Review of Wireless Sensors and Sensor Networks for Structural Health Monitoring. The Shock and vibration digest, vol. 38(2), pp. 91-128.

Ling, Y., Shantz, C., Sankararaman, S., & Mahadevan, S. (2010). Stochastic Characterization and Update of Fatigue Loading for Mechanical Damage Prognosis. Annual Conference of the Prognostics and Health Management Society.

Liu, Y., & Mahadevan, S. (2009). Probabilistic fatigue life prediction using an equivalent initial flaw size distribution. International Journal of Fatigue. vol. 31(3), pp. 476-487.

Luo, J., Pattipati, K. R., Qiao, L., & Chigusa, S. (2008). Model-based Prognostic Techniques Applied to a Suspension System. IEEE Transactions on System, Man and Cybernetics, vol.
38(5), pp. 1156-1168.

Mohanty, S., Chattopadhyay, A., Peralta, P., & Das, S. (2011). Bayesian Statistic Based Multivariate Gaussian Process Approach for Offline/Online Fatigue Crack Growth Prediction. Experimental Mechanics, vol. 51, pp. 833-843.

Newman Jr, J. C., Phillips, E. P., & Swain, M. H. (1999). Fatigue-life prediction methodology using small-crack theory. International Journal of Fatigue, vol. 21, pp. 109-119.

Orchard, M., & Vachtsevanos, G. (2007). A Particle Filtering Approach for On-Line Failure Prognosis in a Planetary Carrier Plate. International Journal of Fuzzy Logic and Intelligent
Systems, vol. 7(4), pp. 221-227.

Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & V achtsevanos, G. (2008). Advances in Uncertainty Representation and Management for Particle Filtering Applied to Prognostics. International Conference on Prognostics and Health Management, Denver, CO.

Paris, P.C., & Erdogan, F. (1963). A Critical Analysis of Crack Propagation Laws. ASME Journal of Basic Engineerin , vol. 85, pp. 528-534.

Paris, P. C., Lados D., & Tada, H. (2008). Reflections on identifying the real ΔKeffective in the threshold region and beyond. International Journal of fatigue, vol.75, pp. 299-305.

Saha, B., & Goebel, K. (2008) Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques. IEEE Aerospace Conference.

Sankararaman, S., Ling, Y., & Mahadevan, S. (2010). Confidence Assessment in Fatigue Damage Prognosis. Annual Conference of the Prognostics and Health Management Society.
Schwabacher, M. A. (2005). A survey of data-driven prognostics, in AIAA Infotech@Aerospace Conference. Reston,V A.

Sheppard, J. W., Kaufman, M. A., Inc, A., & Annapolis, M. D. (2005). Bayesian diagnosis and prognosis using instrument uncertainty. IEEE Autotestcon, pp. 417-423.

Sinclair, G. B., & Pierie, R. V. (1990). On obtaining fatigue crack growth parameters from the literature. International Journal of Fatigue, vol. 12(1), pp. 57-62.

Virkler, D. A., Hillberry, B. M., & Goel, P. K. (1979). The statistical nature of fatigue crack propagation. ASME Journal of Engineering Materials and Technology, vol. 101, pp.148-153.

Yan, J., & Lee, J. (2007) A Hybrid Method for On-line Performance Assessment and Life Prediction in Drilling Operations. IEEE International Conference on Automation and Logistics.

Yu, W. K., & Harris, T. A. (2001). A new stress-based fatigue life model for ball bearings. Tribology Transactions, vol. 44, pp. 11–18. doi: 10.1080/ 10402000108982420.

Zio, E., & Peloni, G. (2011). Particle filtering prognostic estimation of the remaining useful life of nonlinear components. Reliability Engineering & System Safety, vol. 96(3), pp. 403-409.
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