Sequential Monte Carlo sampling for crack growth prediction providing for several uncertainties



Matteo Corbetta Claudio Sbarufatti Andrea Manes Marco Giglio


The problem of fatigue crack growth monitoring and residual lifetime prediction is faced by means of sequential Monte Carlo methods commonly defined as sequential importance sampling/resampling or particle filtering techniques. The algorithm purpose is the estimation of the fatigue crack evolution in metallic structures, considering uncertainties coming from phenomenological aspects and material properties affecting the process. These multiple uncertainties become a series of unknown parameters within the framework of the dynamic state-space model describing the crack propagation. These parameters, if correctly estimated within the particle filtering algorithm, will cover the uncertainties coming from the real environment, improving the prognostic performances. The standard particle filter formulation needs additional methods to augment the state vector and to correctly estimate the parameters. The prognostic system composed by the sequential Monte Carlo algorithm able to account for different uncertainties is tested through several crack growth simulations. The applicability of the method to real structures and the employment in presence of real environmental conditions (i.e. variable loading conditions) is also discussed at the end of the paper.

How to Cite

Corbetta, M., Sbarufatti, C., Manes, A., & Giglio, M. (2014). Sequential Monte Carlo sampling for crack growth prediction providing for several uncertainties. PHM Society European Conference, 2(1).
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fatigue crack growth, Sequential Monte Carlo, damage prognosis, residual useful life prediction, parameter uncertainty

Arulampalam, M. S., Maskell, S., Gordon, N., Clapp, T. (2002). A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans on Signal Processing, 50(2), pp. 174-188.
Bourinet J.M., Lemaire, M. (2008). Form sensitivities to correlation: application to fatigue crack propagation based on Virkler’s data.4th International ASRANet colloquium, Athens.
Broek, D. (1988). The practical use of fracture mechanics. Netherlands: Kluwer Academic Publishers.
Cadini, F., Zio, E., Avram, D. (2009). Monte Carlo-based filtering for fatigue crack growth estimation. Probabilist Eng Mech, 24, pp. 367-373.
Chiachio, J., Chiachio, M., Saxena, A., Rus, G., Goebel, K. (2013). An Energy-Based Prognostics Framework to Predict Fatigue Damage Evolution in Composites. Annual Conference of the Prognostics and Health Management Society, October, 14-17, New Orleans, LA.
Corbetta, M., Sbarufatti, C., Manes, A., Giglio, M. (2013a). Stochastic definition of state-space equation for particle filtering algorithms. Chem Eng Trans, 33, pp. 1075-1080.
Corbetta, M., Sbarufatti, C., Manes, A., Giglio, M. (2013b). On-line updating of dynamic state-space model for Bayesian filtering through Markov chain Monte Carlo techniques. Chem Eng Trans, 33, pp. 133-138.
Corbetta, M., Sbarufatti, C., Manes, A., Giglio, M. (2014). On dynamic state-space models for fatigue induced structural degradation. Int J Fatigue, 61, pp. 202-219.
Cross, R., Makeev, A., Armanios, E. (2007). Simultaneous uncertainty quantification of fracture mechanics based life prediction model parameters. Int J Fatigue, 29, pp. 1510-1515.
Daigle, M., Goebel, K. (2011). Multiple damage progression paths in model-based prognostics. In Aerospace conference, 2011 IEEE, pp. 1-10.
Doucet, A., Godsill, S., Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, pp. 197-208.
Elber, W. (1970). Fatigue crack closure under cyclic tension. Eng Frac Mech, 2, pp.37-45.
Elber, W. (1971). The significance of crack closure. In ASTM STP 486, American Society for Testing and Materials, Damage Tolerance in Aircraft Structures (pp. 230-242). Philadelphia PA.
Haug, A.J. (2005). A tutorial on Bayesian estimation and tracking techniques applicable to nonlinear and non-Gaussian processes. MITRE technical report, MITRE McLean, Virginia.
Kantas, N., Doucet, A., Singh, S.S., Maciejowski, J.M. (2009). An overview of Sequential Monte Carlo Methods for Parameter Estimation in General State-Space Models. In 15th ifac symposium on system identification (Vol. 15).
Liu, J.S., West, M. (2001). Combined parameter and state estimation in simulation-based filtering, In Doucet, A., De Freitas, J.F.G., Gordon, N.J., (Eds.), Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag.
Gordon, N. J., Salmond, D. J., Smith, A. F. M. (1993). Novel approach to non-linear/non-Gaussian Bayesian state estimation, IEEE Proceedings F (Radar and Signal Processing), 140(2), pp. 107-113.
Mattrand, C., Bourinet, J. M. (2011). Random load sequences and stochastic crack growth based on measured load data. Eng Fract Mech, 78, pp. 3030-3048.
NASA J.S. Centre and Southwest Research Institute. (2002). NASGRO reference manual, Version 4.02.
Newman Jr., J. C. (1981). A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading. ASTM STP, 748, pp.53-84.
Newman Jr., J. C., (2005). Crack growth predictions in aluminum and titanium alloys under aircraft load spectra. In: Proceedings of the XIth international conference of fracture, Turin, Italy.
Newman Jr., J. C., Irving, P.E., Lin, J., Le, D., D. (2006). Crack growth predictions in a complex helicopter component under spectrum loading. Fatigue Fract Eng Mater Struct, 29, pp. 949-958.
Paris, P.C., Erdogan, F. (1963). A critical analysis of crack propagation laws. Trans ASME – J Basic Eng, 85, pp. 528-534.
Ray, A., Patankar, R. (1999). A stochastic model of fatigue crack propagation under variable-amplitude loading. Eng Fract Mech, 62, pp. 477-493.
Scafetta, N., Ray, A., West, B. J. (2006). Correlation regimes in fluctuations of fatigue crack growth. Physica A, 359, pp. 1-23.
Virkler, D.A., Hillberry, B.M., Goel, P.K. (1978). The statistical nature of fatigue crack propagation. Technical report, Air Force Flight Dynamics Laboratory, AFFDL-TR-78-43.
West, M. (1993). Mixture Models, Monte Carlo, Bayesian updating and dynamic models, In J. H. Newton (Ed.), Computing Science and Statistics: Proceedings of the 24th symposium of the Interface, pp. 325-333. Interface Foundation of North America, Fairfax Station, Virginia.
Willenborg, J., Engle, R. M., Wood, H.A. (1971). A Crack Growth Retardation Model Using an Effective Stress Concept. Technical Memorandum, Air Force Flight Dynamics Laboratory, AFFDL-TM-71-1-FBR.
Xu, X., Li, B. (2005). Rao-Blackwellised Particle Filter with Adaptive System Noise and its Evaluation for Tracking in Surveillance. In 2nd Joint IEEE International workshop on Visual Surveillance and Performance Evaluation of Tracking and Surveillance, Oct 15-16, Beijing, China.
Yang, J. N., Manning, S. D. (1996). A simple second order approximation for stochastic crack growth analysis. Eng Fract Mech, 53(5), pp. 677-686.
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