Entropy-based probabilistic fatigue damage prognosis and algorithmic performance comparison
In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an underlying physics-based crack growth model. Various uncertainties from measurements, modeling, and parameter estimations are considered to describe the stochastic process of fatigue damage accumulation. A probabilistic prognosis updating procedure based on the maximum relative entropy concept is proposed to incorporate measurement data. Markov Chain Monte Carlo (MCMC) technique is used to provide the posterior samples for model updating in the maximum entropy approach. Experimental data are used to demonstrate the operation of the proposed probabilistic prognosis methodology. A set of prognostics-based metrics are employed to quantitatively evaluate the prognosis performance and compare the proposed method with the classical Bayesian updating algorithm. In particular, model accuracy, precision and convergence are rigorously evaluated in* addition to the qualitative visual comparison.It is shown that the proposed maximum relative entropy methodology has narrower confidence bounds of the remaining life prediction than classical Bayesian updating algorithm.
How to Cite
crack detection, damage detection, damage modeling, damage propagation model, fatigue crack growth, materials damage prognostics, model based prognostics, performance metrics, physics of failure, prognostics, remaining useful life (RUL), structural health management, uncertainty management
(Metropolis et al., 1953) N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller (1953). Equations of state calculations by fast computing machine. Journal of Chemical Physics, vol. 21(6), pp.1087-1092.
(Paris and Erdogan, 1963) P. Paris and F. Erdogan (1963). A critical analysis of crack propagation laws. Trans. The ASME, J. Basic Eng. pp. 528-534.
(Hastings, 1970) W. K. Hastings (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, vol. 57(1), pp. 97-109.
(Virkler et al., 1979) D. A. Virkler, B. M. Hillberry, and P. K. Goel (1979). The statistical nature of fatigue crack propagation, ASME Journal of Engineering Materials and Technology, vol. 101, pp.148-153.
(Ostergaard and Hillberry, 1983) D. F. Ostergaard and B. M. Hillberry (1983). Characterization of the variablility in fatigue crack propagation data, In J. M. Bloom and J. C. Ekvall (Eds.), Probabilistic Fracture Mechanics and Fatigue Methods: Application for Structural Design and Maintenance, ASTM STP 798, pp. 97-115.
(Skilling, 1988) J. Skilling (1988). The axioms of maximum entropy. In G.J. Erickson and C.R. Smith (Eds.), Maximum Entropy and Bayesian Methods, in Science and Engineering, volume 1. pp 173-187,
Netherlands: Kluwer Academic Publishers. (Madsen, 1997) H. Madsen (1997). Stochastic modeling of fatigue crack growth and inspection. In C.G. Soares (Ed.), Probabilistic methods for structure design, collection Solid Mechanics and its applications, pp. 59-83. Netherlands: Kluwer
(Kotulski, 1998) Z. A. Kotulski (1998). On efficiency of identification of a stochastic crack propagation model based on Virkler experimental data. Archives of Mechanics, vol. 50(5), pp. 829-847.
(McMaster and Smith, 1999) F. J. McMaster and D. J. Smith (1999). Effect of load excursions and specimen thickness on crack closure measurements, Advances in Fatigue Crack Closure Measurements and Analysis: Second Volume, ASTM STP 1343, pp 246-264. R. C. McClung and J. C. Newman, Jr., Eds., West Conshohocken, Pennsylvania: American Society for Testing and Materials.
(Zhang and Mahadevan, 2000) R. Zhang and S. Mahadevan (2000). Model uncertainty and Bayesian updating in reliability-based inspection. Structure Safety, vol. 22(2), pp.145-160.
(Perrin et. al., 2007) F. Perrin, B. Sudret, and M. Pendola (2007). Bayesian updating of mechanical models – Application in fracture mechanics. In 18ème Congrès Français de Mécanique, CFM 2007, Grenoble.
(Caticha and Preuss, 2004) A. Caticha and R. Preuss (2004). Maximum entropy and Bayesian data analysis: Entropic prior distributions. Physical Review E. vol. 70(4), 046127.
(Caticha and Giffin, 2006) A. Caticha and A. Giffin (2006). Updating probabilities. In A.M. Djafari (Ed.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, 31: 872.
(Giffin and Caticha, 2007) A. Giffin and A. Caticha (2007). Updating probabilities with data and moments. In K. Knuth (Ed.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, 954:74
(Tseng and Caticha, 2008) C. Tseng and A. Caticha (2008). Using relative entropy to find optimal approximations: An application to simple fluids. Physica A, vol. 387, pp. 6759-6770.
(Bourdin et. al., 2008) B. Bourdin, G. A. Francfort and J. J. Marigo (2008). The Variational Approach to Fracture, Netherlands: Springer.
(Saxena et al., 2008) A. Saxena, J. Celaya, E. Balaban, K. Goebel, B. Saha, S. Saha, and M. Schwabacher (2008). Metrics for evaluating performance of prognostic techniques. International Conference on Prognostics and Health Management, PHM 2008. 6-9 Oct. 2008, pp: 1-17.
(Saxena et al., 2009) A. Saxena, J. Celaya, B. Saha, S.
Saha, and K. Goebel (2009). Evaluating algorithm performance metrics tailored for prognostics. IEEE Aerospace conference, 7-14 March 2009, pp. 1-13.
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
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.