Distribution-free stochastic model updating with copulas and staircase density functions

Abstract

In stochastic model updating, a probabilistic model is assumed for the model parameters and its hyperparameters (e.g., means and variances) are calibrated to minimize the stochastic discrepancy between model outputs and measurements. Thus, if the assumption about the probabilistic model is inappropriate, it may introduce a bias in the updating results. To avoid such inappropriate assumptions, we have recently developed a distribution-free approach that uses the staircase density function (SDF) to arbitrarily approximate a wide range of probability distributions. In this study, we aim to extend this approach to the calibration of dependent parameters. The dependence structure is represented by several types of copulas and the marginal distributions are modeled using the SDFs. An approximate Bayesian computation framework is then developed to calibrate the copula parameter as well as the SDF hyperparameters. Furthermore, in this framework, the most appropriate copula class is determined in the context of Bayesian model class selection.