A Computationally-Efficient Inverse Approach to Probabilistic Strain-Based Damage Diagnosis



James E. Warner Jacob D. Hochhalter William P. Leser Patrick E. Leser John A. Newman


This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.

How to Cite

Warner, J. E., Hochhalter, J. D., Leser, W. P., Leser, P. E., & Newman, J. A. (2016). A Computationally-Efficient Inverse Approach to Probabilistic Strain-Based Damage Diagnosis. Annual Conference of the PHM Society, 8(1). https://doi.org/10.36001/phmconf.2016.v8i1.2509
Abstract 14 | PDF Downloads 10



Bayesian inference, surrogate modeling, damage diagnosis

Barthorpe, R. J. (2010). On model- and data-based approaches to structural health monitoring (Unpublished doctoral dissertation). University of Sheffield.
Buitinck, L., Louppe, G., Blondel, M., Pedregosa, F., Mueller, A., Grisel, O., . . . Varoquaux, G. (2013). API design for machine learning software: experiences from the scikit-learn project. In Ecml pkdd workshop: Languages for data mining and machine learning (pp. 108–122).
Correlated Solutions Inc. (2012). Vic-3d. Retrieved from www.correlatedsolutions.com
Farrar, C. R., & Worden, K. (2013). Structural health monitoring: A machine learning perspective. Wiley.
Gamerman, D., & Lopes, H. F. (2006). Markov chain monte carlo: Stochastic simulation for bayesian inference (Second ed.). Boca Raton, Florida: Chapman and Hall/CRC.
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (Third ed.). Boca Raton, Florida: Chapman and Hall/CRC.
Haario, H., Laine, M., & Mira, A. (2006). Dram: Efficient adaptive MCMC. Statistics and Computing, 16(4), 339-354.
Hochhalter, J. D., Krishnamurthy, T., Aguilo, M. A., & Gallegos, A. M. (2016). Strain-based damage determination using finite element analysis for structural health management. NASA/TM-2016-219186.
Huhtala, A., & Bossuyt, S. (2011). A bayesian approach to vibration based structural health monitoring with experimental verification. Journal of Structural Mechanics, 44(4), 330-344.
Isakov, V. (1998). Inverse problems for partial differential equations. New York: Springer.
Jones, E., Oliphant, T., Peterson, P., et al. (2001–). SciPy: Open source scientific tools for Python. Retrieved from http://www.scipy.org/.
Katsikeros, C., & Labeas, G. (2009). Development and validation of a strain-based structural health monitoring system. Mechanical Systems and Signal Processing, 23(2), 372 - 383.
Kehlenbach, M., & Hanselka, H. (2003, April). Automated structural integrity monitoring based on broadband lamb wave excitation and matched filtering. In Proceedings of the 44th AIAA, ASME, ASCE, AHS, ASC Structures, Structural Dynamics, and Materials Conference. Norfolk, VA.
Kim, J. T., & Stubbs, N. (2002). Improved damage identification method based on modal information. Journal of Sound and Vibration, 252, 223-238.
Krishnamurthy, T., & Gallegos, A. M. (2011, April). Damage characterization using the extended finite element method for structural health management. In 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 13th AIAA Non-Deterministic Approaches Conference. Denver, CO.
Mal, A. K., Ricci, F., Banerjee, S., & Shih, F. (2005). A conceptual structural health monitoring system based on vibration and wave propagation. Structural Health Monitoring, 4, 283-293.
Marzouk, Y. M., Najm, H. N., & Rahn, L. A. (2006). Stochastic spectral methods for efficient bayesian solution of inverse problems. Journal of Computational Physics, 224, 339-354.
Meeds, E., & Welling, M. (2014). GPS-ABC: gaussian process surrogate approximate bayesian computation. CoRR, abs/1401.2838. Retrieved from
Moore, E. Z., Murphy, K. D., & Nichols, J. M. (2011). Crack identification in a freely vibrating plate using bayesian parameter estimation. Mechanical Systems and Signal Processing, 25, 2125-2134.
Neiswanger, W., Wang, C., & Xing, E. (2013). Asymptotically exact, embarrassingly parallel mcmc. arXiv preprint arXiv:1311.4780.
Nichols, J. M., Link, W. A., Murphy, K. D., & Olson, C. C. (2010). A bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites. Journal of Sound and Vibration, 329, 2995-3007.
Nichols, J. M., Moore, E. Z., & Murphy, K. D. (2011). Bayesian identification of a cracked plate using a population-based markov chain monte carlo method. Computers and Structures, 89, 1323-1332.
Peng, T., Saxena, A., Goebel, K., Xiang, Y., & Liu, Y. (2014). Probabilistic damage diagnosis of composite laminates using bayesian inference. In 16th AIAA Non-Deterministic Approaches Conference.
Peters, W. H., & Ranson, W. F. (1982). Digital imaging techniques in experimental stress analysis. Optical Engineering, 21(3), 427-431.
Prudencio, E., Bauman, P. T., Faghihi, D., Ravi-Chandar, K., & Oden, J. T. (2015). A computational framework for dynamic data-driven material damage control, based on bayesian inference and model selection. International Journal for Numerical Methods in Engineering, 102(3-4), 379–403. Retrieved from http://dx.doi.org/10.1002/nme.4669 doi: 10.1002/nme.4669.
Prudencio, E., & Cheung, S. H. (2012). Parallel adaptive multilevel sampling algorithms for the bayesian analysis of mathematical models. International Journal for Uncertainty Quantification, 2(3), 215–237.
Python Software Foundation. (2016). Python language reference, version 2.7. Retrieved from www.python.org
Sbarufatti, C., Manes, A., & Giglio, M. (2013). Performance optimization of a diagnostic system based upon a simulated strain field for fatigue
damage characterization. Mechanical Systems and Signal Processing, 40(2), 667 - 690. doi: http://dx.doi.org/10.1016/j.ymssp.2013.06.003.
Sutton, M. A., Orteu, J.-J., & Schreier, H. (2009). Image correlation for shape, motion and deformation measurements: Basic concepts,theory and applications (1st ed.). Springer Publishing Company, Incorporated.
Vrugt, J. A., ter Braak, C. F., Diks, C. H., Higdon, D., Robinson, B. A., & Hyman, J. M. (2009). Accelerating markov chain monte carlo simulation by differential evolution with self-adaptive randomized subspace sampling. International Journal of Nonlinear Science and Numerical Simulation, 10(3), 273-290.
Wang, L., & Yuan, F. G. (2007). Active damage localization technique based on energy propagation of lamb waves. Smart Structures and Systems, 3, 201-217.
Warner, J. E., Bomarito, G. B., Heber, G., & Hochhalter, J. D. (2016). Scalable implementation of finite elements by NASA - implicit (ScIFEi). NASA/TM-2016-219180.
Warner, J. E., & Hochhalter, J. D. (2016). Probabilistic damage characterization using a computationally-efficient bayesian approach. NASA/TP-2016-219169.
Yan, G. (2012). A bayesian approach for identification of structural crack using strain measurements. In Sixth European Workshop on Structural Health Monitoring. Dresden, Germany.
Technical Papers