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Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian ApproachThis work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.
Document ID
Document Type
Technical Publication (TP)
Warner, James E. (NASA Langley Research Center Hampton, VA, United States)
Hochhalter, Jacob D. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
May 6, 2016
Publication Date
March 1, 2016
Subject Category
Quality Assurance and Reliability
Structural Mechanics
Mathematical and Computer Sciences (General)
Report/Patent Number
Funding Number(s)
WBS: WBS 694478.
Distribution Limits
Work of the US Gov. Public Use Permitted.

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