Quantifying the uncertainty in model parameters for the purpose of damage prognosis can be accomplished utilizing Bayesian inference and damage diagnosis techniques such as non-destructive evaluation or structural health monitoring. The number of samples required to solve the Bayesian inverse problem through common sampling techniques (e.g., Markov chain Monte Carlo) renders high-fidelity finite element-based
damage growth models unusable due to prohibitive computation times. However, these types of models are often the only option when attempting to model complex damage growth in real-world structures. Here, a recently developed highfidelity fatigue crack growth model is used which, when compared to finite element-based modeling, has demonstrated reductions in computation times of three orders of magnitude through the use of surrogate models and machine learning. A probabilistic prognosis framework incorporating this model is developed and demonstrated for non-planar crack growth in a modified edge-notched aluminum tensile specimen. Predictions of remaining useful life are made over time for five
updates of the damage diagnosis data, and prognostic metrics are utilized to evaluate the performance of the prognostic framework. Challenges specific to the probabilistic prognosis of non-planar fatigue crack growth are highlighted and discussed in the context of the experimental results.
How to Cite
fatigue crack growth, Uncertainty Quantification, Bayesian inference, Remaining useful Life, Markov Chain Monte Carlo (MCMC), surrogate modeling, finite element analysis, non-planar cracks
Carpinteri, A., & Paggi, M. (2007). Self-similarity and crack growth instability in the correlation between the paris constants. Engineering Fracture Mechanics, 74(7), 1041–1053.
Chiachıo, J., Chiachıo, M., Saxena, A., Rus, G., & Goebel, K. (2013). An energy-based prognostics framework to predict fatigue damage evolution in composites. In S. Sankararaman & I. Roychoudhury (Eds.), Proceedings of the Annual Conference of the Prognostics and Health Management Society (pp. 363–371). New York: Prognostics and Health Management Society.
Cortie, M. (1991). The irrepressible relationship between the paris law parameters. Engineering Fracture Mechanics, 40(3), 681–682.
Erdogan, F., & Sih, G. (1963). On the crack extension in plates under plane loading and transverse shear. Journal of Fluids Engineering, 85(4), 519–525.
Farrar, C. R., & Worden, K. (2012). Structural health monitoring: a machine learning perspective. John Wiley & Sons.
FRANC3D Reference Manual, Version 6 [Computer software manual]. (2011).
Geweke, J. (1992). Evaluating the accuracy of samplingbased approaches to the calculation of posterior moments.
In J. Bernardo & J. Berger (Eds.), Bayesian Statistics 4: Proceedings of the Fourth Valencia International Meeting (pp. 169–193). Oxford, UK: Oxford
Gobbato, M., Conte, J. P., Kosmatka, J. B., & Farrar, C. R. (2012). A reliability-based framework for fatigue damage prognosis of composite aircraft structures. Probabilistic Engineering Mechanics, 29, 176 - 188.
Gope, P. (1999). Determination of sample size for estimation of fatigue life by using Weibull or log-normal distribution. International Journal of Fatigue, 21(8), 745–752.
Hombal, V., Ling, Y., Wolfe, K., & Mahadevan, S. (2012). Two-stage planar approximation of non-planar crack growth. Engineering Fracture Mechanics, 96, 147–164.
Hombal, V., & Mahadevan, S. (2013). Surrogate modeling of 3D crack growth. International Journal of Fatigue, 47, 90–99.
Ingraffea, A., Grigoriu, M., & Swenson, D. (1991). Representation and probability issues in the simulation of multi-site damage. In S. Atluri, S. Sampath, & P. Tong (Eds.), Structural integrity of aging airplanes (pp. 183–197). Berlin: Springer-Verlag.
Johnston, G. (1983). Statistical scatter in fracture toughness and fatigue crack growth rate data. In J. Bloom & J. Ekvall (Eds.), Probabilistic fracture mechanics and fatigue methods: Applications for structural design and maintenance (pp. 42–66). Philadelphia: American Society for Testing and Materials.
Laloy, E., & Vrugt, J. A. (2012). High-dimensional posterior exploration of hydrologic models using multipletry DREAM (ZS) and high-performance computing. Water Resources Research, 48(1), 239–249.
Leser, P. E., Hochhalter, J. D., Warner, J. E., Newman, J. A., Leser, W. P., Wawrzynek, P. A., & Yuan, F.-G. (2016). IWSHM 2015: Probabilistic fatigue
damage prognosis using surrogate models trained via three-dimensional finite element analysis. Structural Health Monitoring (currently online only). doi: 10.1177/1475921716643298.
Li, C., & Mahadevan, S. (2016). An efficient modularized sample-based method to estimate the first-order Sobol´ index. Reliability Engineering & System Safety, 153, 110–121.
Ling, Y., & Mahadevan, S. (2012). Integration of structural health monitoring and fatigue damage prognosis. Mechanical Systems and Signal Processing, 28, 89–104.
Liu, Y., & Mahadevan, S. (2009). Probabilistic fatigue life prediction using an equivalent initial flaw size distribution. International Journal of Fatigue, 31(3), 476–487.
Neiswanger, W., Wang, C., & Xing, E. (2014). Asymptotically exact, embarrassingly parallel MCMC. In N. Zhang & J. Tian (Eds.), Proceedings of the 30th
Conference on Uncertainty in Artificial Intelligence (pp. 623–632). Oregon: AUAI Press Corvallis.
Parzen, E. (1961). Mathematical considerations in the estimation of spectra. Technometrics, 3(2), 167-190.
Patil, A., Huard, D., & Fonnesbeck, C. J. (2010). PyMC: Bayesian stochastic modelling in Python. Journal of Statistical Software, 35(4), 1–81.
Peng, T., He, J., Xiang, Y., Liu, Y., Saxena, A., Celaya, J., & Goebel, K. (2015). Probabilistic fatigue damage prognosis of lap joint using Bayesian updating. Journal of Intelligent Material Systems and Structures, 26(8), 965–979.
Peng, T., Liu, Y., Saxena, A., & Goebel, K. (2015). In-situ fatigue life prognosis for composite laminates based on stiffness degradation. Composite Structures, 132, 155–165.
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., . . . Tarantola, S. (2008). Global sensitivity analysis: the primer. Chichester, West Sussex, UK: John Wiley & Sons.
Sankararaman, S., Ling, Y., & Mahadevan, S. (2011). Uncertainty quantification and model validation of fatigue crack growth prediction. Engineering Fracture Mechanics, 78(7), 1487–1504.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2011). Uncertainty quantification in fatigue crack growth prognosis. International Journal of Prognostics and Health Management, 2(1), 1–15.
Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K. (2010). Metrics for offline evaluation of prognostic performance. International Journal of Prognostics and Health Management, 1(1), 4–23.
Smith, R. C. (2013). Uncertainty quantification: Theory, implementation, and applications. Philadelphia: SIAM.
Ter Braak, C. J. (2006). A Markov chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces. Statistics and Computing, 16(3), 239–249.
Van Rossum, G., & Drake, F. J. (2011). An introduction to Python. Godalming, Surrey, UK: Network Theory Ltd.
Vrugt, J. A., Ter Braak, C., Diks, C., Robinson, B. A., Hyman, J. M., & Higdon, D. (2009). Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling. International Journal of Nonlinear Sciences and Numerical Simulation, 10(3), 273–290.
Walker, K. (1970). The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum. In M. Rosenfield (Ed.), Effects of environment and complex load history on fatigue life (pp. 1–14). Philadelphia: American Society for Testing and Materials.
Xu, C., & Gertner, G. Z. (2008). Uncertainty and sensitivity analysis for models with correlated parameters. Reliability Engineering & System Safety, 93(10), 1563–1573.
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