HIERARCHICAL BAYESIAN INFERENCE FOR QUANTIFICATION OF UNCERTAINTY IN MULTI LEVEL MODELS OF DYNAMICAL SYSTEMS

Abstract

Calibration of model parameters is increasingly playing a key role in the process of accurately predicting the responses of full-scale dynamical systems. Such systems often exhibit complexities arising from the assembling process and nonlinearities manifested at various modelling levels, from material to component to sub-system to system level, during operation under harsh environments. Recent advances [1-3] have enabled to calibrate the model parameters, quantify the uncertainties and predict uncertainties to output quantities of interest using data obtained from the system level. However, data at the system level may be lacking or be expensive to obtain or, usually, are not adequate to reliably calibrate material, component or sub-system parameters. In this context, we extend the framework in [2, 3] and present a systematic approach to calibrate the system model parameters using information and data from lower system levels which share common parameters with higher system level. The proposed approach can properly take into account the uncertainty in the component model parameters due to variabilities in experimental data, environmental conditions, material properties, manufacturing process, assembling process, as well as nonlinear mechanisms activated under different loading conditions. For this, the uncertainty is embedded within the structural model parameters by postulating a probability model for these parameters that depend on hyperparameters. Sampling techniques as well as asymptotic approximations are used to carry out the computation or reduce the computational burden in the proposed Bayesian multi-level modeling framework. Selected applications in structural dynamics are used to demonstrate the effectiveness of the proposed framework. © ESREL 2021. Published by Research Publishing, Singapore.