A Computationally-Efficient Probabilistic Approach to Model-Based Damage Diagnosis
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Published
Nov 16, 2020
James E. Warner
Geoffrey F. Bomarito
Jacob D. Hochhalter
William P. Leser
Patrick E. Leser
John A. Newman
Abstract
This work presents a computationally-efficient, probabilistic approach to model-based damage diagnosis. Given measurement data, probability distributions of unknown damage parameters are estimated using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. While the formulation is general for arbitrary component geometry, damage type, and sensor data, it is applied to the problem of strain-based crack characterization and experimentally validated using full-field strain data from digital image correlation (DIC). Access to full-field DIC data facilitates the study of the effectiveness of strain-based diagnosis as the distance between the location of damage and strain measurements is varied. The ability of the framework to accurately estimate the crack parameters and effectively capture the uncertainty due to measurement proximity and experimental error is demonstrated. Furthermore, surrogate modeling is shown to enable diagnoses on the order of seconds and minutes rather than several days required with the FE model.
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Keywords
Uncertainty Quantification, surrogate modeling, damage diagnosis
References
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using finite element analysis for structural health management.
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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.
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Open source scientific tools for Python.
Kaipio, J., & Somersalo, E. (2004). Statistical and computational
inverse problems. Springer.
Katsikeros, C., & Labeas, G. (2009). Development and validation
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Damage characterization using the extended finite element
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Dynamics, and Materials Conference 13th AIAA
Non-Deterministic Approaches Conference. Denver,
CO.
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conference, aiaa scitech forum. Grapevine,
TX.
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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.
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.
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Saltelli, A., Chan, K., & Scott, E. M. (2000). Sensitivity analysis (Vol. 1). Wiley New York.
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.
Smith, R. C. (2013). Uncertainty quantification: Theory, implementation, and applications. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.
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, J., & Zabaras, N. (2014). A bayesian approach to the inverse heat conduction problem. International Journal of Heat and Mass Transfer, 47, 3927-3941.
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.
Warner, J. E., Hochhalter, J. D., Leser, W. P., Leser, P. E., & Newman, J. A. (2016, October). A computationallyefficient inverse approach to probabilistic strain-based damage diagnosis. In Annual conference of the prognostics and health management society. Denver, CO.
Warner, J. E., Zubair, M., & Ranjan, D. (2017, January). Near real time damage diagnosis using surrogate modeling and high performance computing. In 19th AIAA nondeterministic
approaches conference, AIAA scitech forum. Grapevine, TX.
Wilde, D. J., & Beightler, C. S. (1967). Foundations of optimization. Prentice-Hall Englewood Cliffs, N.J.
Yan, G. (2012). A bayesian approach for identification of structural crack using strain measurements. In Sixth European Workshop on Structural Health Monitoring. Dresden, Germany.
to structural health monitoring (Unpublished
doctoral dissertation). University of Sheffield.
Bishop, C. M. (2006). Pattern recognition and machine
learning. New York, NY: Springer.
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.
Global sensitivity analysis: the primer. (n.d.).
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.
Kaipio, J., & Somersalo, E. (2004). Statistical and computational
inverse problems. Springer.
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.
Kennedy, M. C., & O’Hagan, A. (2001). Bayesian calibration
of computer models. Journal of the Royal Statistical
Society: Series B (Statistical Methodology), 63(3),
425–464.
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.
Leser, P. E., & Warner, J. E. (2017, January). A diagnosisprognosis
feedback loop for improved performance under
uncertainties. In 19th aiaa non-deterministic approaches
conference, aiaa scitech forum. Grapevine,
TX.
Li, H.-N., Li, D.-S., & Song, G.-B. (2004). Recent applications of fiber optic sensors to health monitoring in civil engineering. Engineering Structures, 26(11), 1647 - 1657.
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
http://arxiv.org/abs/1401.2838
Meltz, G., & Snitzer, E. (1981, October 20). Fiber optic strain sensor. Google Patents. (US Patent 4,295,738)
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.
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
Roy, C. J., & Oberkampf, W. L. (2011). A comprehensive framework forxfa verification, validation, and uncertainty quantification in scientific computing. Computer Methods in Applied Mechanics and Engineering, 200(2528), 2131 - 2144.
Saltelli, A., Chan, K., & Scott, E. M. (2000). Sensitivity analysis (Vol. 1). Wiley New York.
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.
Smith, R. C. (2013). Uncertainty quantification: Theory, implementation, and applications. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.
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, J., & Zabaras, N. (2014). A bayesian approach to the inverse heat conduction problem. International Journal of Heat and Mass Transfer, 47, 3927-3941.
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.
Warner, J. E., Hochhalter, J. D., Leser, W. P., Leser, P. E., & Newman, J. A. (2016, October). A computationallyefficient inverse approach to probabilistic strain-based damage diagnosis. In Annual conference of the prognostics and health management society. Denver, CO.
Warner, J. E., Zubair, M., & Ranjan, D. (2017, January). Near real time damage diagnosis using surrogate modeling and high performance computing. In 19th AIAA nondeterministic
approaches conference, AIAA scitech forum. Grapevine, TX.
Wilde, D. J., & Beightler, C. S. (1967). Foundations of optimization. Prentice-Hall Englewood Cliffs, N.J.
Yan, G. (2012). A bayesian approach for identification of structural crack using strain measurements. In Sixth European Workshop on Structural Health Monitoring. Dresden, Germany.
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