A new initial point search algorithm for bayesian calibration with insufficient statistical information: greedy stochastic section search

Abstract

Digital Twin (DTw) model is a numerical model in a virtual world that supports engineer decisions using observed data from a real system. However, uncertainty in the physical model parameters of DTw degrades the predictive performance of a DTw. Bayesian calibration utilizes both observed data and prior knowledge to estimate uncertain model parameters in a statistical manner using Bayes' theorem. Markov Chain Monte Carlo (MCMC) is an effective searching algorithm that can be used to estimate a complex posterior distribution. In the MCMC method, the point that is used to initiate the MCMC sampling significantly affects the burn-in period impacting the accuracy and efficiency of the estimation. However, a proper initial point is hard to select because of the computational cost of searching high-dimensional parameter space. Previous optimization algorithms or random sampling algorithms have focused on solution convergence for a local or global optimum solution. However, the initial points searching method for DTw required suggesting multiple feasible optimum points where a solution can be existed to make proper engineering decisions based on DTw analysis based on each optimum. This paper describes the development of a cost-effective, stochastic algorithm, called the Greedy Stochastic Section Search (GSSS) algorithm that can systematically explore high-dimensional parametric space to select proper initial points for DTw. We verified the new algorithm's performance by applying it to a numerical example with a Mixture of Gaussian (MoG) 6 and by calibrating an engineering example, specifically a digital twin approach for an on-load tap changer.