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.
Highlights
Structural health monitoring (SHM) is the driving technology behind the transition from time-based to condition-based maintenance
Since an explicit quantification of damage is required for prognosis, model-based SHM is preferred to a data-based approach since the latter is generally limited to detection and localization in the absence of training data from damage states (Barthorpe, 2010)
While multimodal distributions may still pose a challenge, Equation 17 provides a simple and systematic way to generate an initial guess that will reside in a high probability region of the posterior distribution as a good starting point (Smith, 2013). It will be shown in this work that even the basic Metropolis Markov chain Monte Carlo (MCMC) method (Algorithm 1) can be effective and robust when starting the algorithm in this fashion
Summary
Structural health monitoring (SHM) is the driving technology behind the transition from time-based to condition-based maintenance. To alleviate this computational burden, advanced MCMC methods have been developed to reduce sampling time by improving sampling convergence (Haario, Laine, & Mira, 2006; Nichols et al, 2011) or through parallelization of the algorithms themselves (Vrugt et al, 2009; Neiswanger, Wang, & Xing, 2013; Prudencio & Cheung, 2012; Warner, Zubair, & Ranjan, 2017) Another common approach is to replace the original physics-based model with a computationally-efficient surrogate model using probabilistic spectral methods (Marzouk, Najm, & Rahn, 2006) or machine learning algorithms (Meeds & Welling, 2014). The findings of the study are summarized in the conclusion section
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