Stochastic Model Updating Using The Jenson-Shannon Divergence For Calibration and Validation Under Limited Data

Abstract

The paper presents an investigation into the use of the Jenson-Shannon, along with an adaptive-binning algorithm, within the distance-based Approximate Bayesian computation framework. Under such framework, the distance function serves to quantify the difference between the observed data and the model predictions and from there, assigns higher statistical importance to model parameter samples which yields high degree of agreement between the model predictions and the observed model and lower statistical models to model parameter samples which achieve otherwise. The objective is to study the performance of the Jenson-Shannon divergence towards stochastic model updating for the subsequent model calibration and validation under limited data. To achieve this objective, the paper is divided into two parts: the first part of the paper reviews the mathematical formalism of the Jenson-Shannon divergence along with a review of the adaptive-binning algorithm from the literature; and the second part of the paper presents a case study in the form of the 2014 NASA-LaRC Uncertainty Quantification challenge problem involving a black-box model with uncertain model input parameters to demonstrate the feasibility of the proposed framework in stochastic model updating towards model calibration and validation under limited data.