An efficient simulation framework for prognostics of asymptotic processes- a case study in composite materials



Manuel Chiachío Juan Chiachío Abhinav Saxena Guillermo Rus Kai Goebel


This work presents an efficient computational framework for estimating the end of life (EOL) and remaining useful life (RUL) by combining the particle filter (PF)-based prognostics with the technique of Subset simulation. It has been named PFP-SubSim on behalf of the full denomination of the computational framework, namely, PF-based prognostics based on Subset Simulation. This scheme is especially useful when dealing with the prognostics of evolving processes with asymptotic behaviors, as observed in practice for many degradation processes. The effectiveness and accuracy of the proposed algorithm is demonstrated through an example for predicting the probability density function of EOL for a carbon-fibre composite coupon subjected to an asymptotic fatigue degradation process. It is shown that PFP-SubSim algorithm is efficient, and at the same time, fairly accurate in obtaining the probability density function of EOL and RUL as compared to the traditional PF-based prognostic approach reported in the PHM literature.

How to Cite

Chiachío, M., Chiachío, J., Saxena, A., Rus, G., & Goebel, K. (2014). An efficient simulation framework for prognostics of asymptotic processes- a case study in composite materials. PHM Society European Conference, 2(1).
Abstract 125 | PDF Downloads 19



Fatigue Prognosis, Subset Simulation, physics based prognostics, remaining useful life

Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. Signal Processing, IEEE Transactions on, 50(2), 174–188.
Au, S., & Beck, J. (2001). Estimation of small failure probabilities in high dimensions by Subset Simulation. Probabilistic Engineering Mechanics, 16(4), 263–277.
Au, S., & Beck, J. (2003). Subset Simulation and its application to seismic risk based on dynamic analysis. Journal of Engineering Mechanics, 129(8), 901-917.
Beck, J. (2010). Bayesian system identification based on probability logic. Structural Control and Health Monitoring, 17(7), 825–847.
Cappe, O., Guillin, A., Marin, J., & Robert, C. (2004). Population Monte Carlo. Journal of Computational and Graphical Statistics, 13(4), 907-927.
Chiachío, M., Chiachío, J., Saxena, A., Rus, G., & Goebel, K. (2013). Fatigue damage prognosis in FRP composites by combining multi-scale degradation fault modes in an uncertainty Bayesian framework. In Proceedings of Structural Health Monitoring, 2013 (Vol. 1).
Chiachío, J., Chiachío, M., Saxena, A., Rus, G., & Goebel, K. (2013). An energy-based prognostics framework to predict fatigue damage evolution in composites. In Proceedings of the Annual Conference of the Prognostics and Health Management Society, 2013 (Vol. 1, pp. 363–371).
Ching, J., Au, S., & Beck, J. (2005). Reliability estimation of dynamical systems subject to stochastic excitation using Subset Simulation with splitting. Computer Methods in Applied Mechanics and Engineering, 194(12-16), 1557–1579.
Daigle, M., & Goebel, K. (2011). Multiple damage progression paths in model-based prognostics. In Aerospace conference, 2011 IEEE (pp. 1–10).
Garrett, K., & Bailey, J. (1977). Multiple transverse fracture in 90 cross-ply laminates of a glass fibre-reinforced polyester. Journal of Materials Science, 12(1), 157–168.
Gordon, N., Salmond, D., & Smith, A. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEEE-Proceedings-F, 140, 107–113.
Gudmundson, P., &Weilin, Z. (1993). An analytic model for thermoelastic properties of composite laminates containing transverse matrix cracks. International Journal of Solids and Structures, 30(23), 3211–3231.
Hashin, Z. (1985). Analysis of cracked laminates: a variational approach. Mechanics of Materials, 4(2), 121–136.
Highsmith, A., & Reifsnider, K. (1982). Stiffness-reduction mechanisms in composite laminates. Damage in composite materials, ASTM STP, 775, 103–117.
Joffe, R., & Varna, J. (1999). Analytical modeling of stiffness reduction in symmetric and balanced laminates due to cracks in 90 layers. Composites Science and Technology, 59(11), 1641–1652.
Larrosa, C., & Chang, F. (2012). Real time in-situ damage classification, quantification and diagnosis for composite structures. In Proceedings of the 19th International Congress on Sound and Vibration (Vol. 15).
Lundmark, P., & Varna, J. (2005). Constitutive relationships for laminates with ply cracks in in-plane loading. International Journal of Damage Mechanics, 14(3), 235–259.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., & Teller, E. (1953). Equation of state calculations by fast computing machines. The journal of chemical physics, 21, 1087–1092.
Nairn, J., & Hu, S. (1992). The initiation and growth of delaminations induced by matrix microcracks in laminated composites. International Journal of Fracture, 57(1), 1–24.
Nairn, J. A. (1989). The strain energy release rate of composite microcracking: a variational approach. Journal of Composite Materials, 23(11), 1106–1129.
Nairn, J. A. (1995). Some new variational mechanics results on composite microcracking. In Proc. 10th international conference on composite materials (iccm-10) whistler bc, canada.
Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & Vachtsevanos, G. (2008). Advances in uncertainty representation and management for particle filtering applied to prognostics. In International conference on prognostics and health management.
Rubin, D. (1987). A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when the fraction of missing information is modest: the SIR algorithm (discussion of tanner and wong). Journal of American Statistical Association, 82, 543–546.
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., . . . Tarantola, S. (2008). Global sensitivity analysis: The primer. Wiley-Interscience.
Sankararaman, S., & Goebel, K. (2013). Uncertainty quantification in remaining useful life of aerospace components using state space models and inverse FORM. In AIAA, ASME, ASCE, AHS, ASC, Structures, Structural Dynamics, and materials conference (pp. 1–10). AIAA.
Saxena, A., Goebel, K., Larrosa, C., & Chang, F. (2008). CFRP Composites dataset. (NASA Ames Prognostics Data Repository, [], NASA Ames, Moffett Field, CA)
Saxena, A., Goebel, K., Larrosa, C., Janapati, V., Roy, S., & Chang, F. (2011). Accelerated aging experiments for prognostics of damage growth in composites materials. In The 8th International Workshop on Structural Health Monitoring, F.-K. Chang, editor. (Vol. 15).
Zuev, K., Beck, J., Au, S., & Katafygiotis, L. (2011). Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions. Computers & Structures, 93, 283-296.
Technical Papers

Similar Articles

1 2 3 4 5 6 7 > >> 

You may also start an advanced similarity search for this article.