Structural Equation Modeling-Based Bayesian Method for Hierarchical Model Validation

Model validation involves quantitatively comparing model predictions with experimental observations, both of which contain uncertainty. A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system. This paper presents a structural equation modeling-based Bayesian approach to make use of the low-level data for system-level model validation under uncertainty. The model validation is dealt with as a hierarchical problem consisting of several parts: lowlevel data, system-level data, computational model, and latent variables. A structural equation modeling approach with latent variables is employed to model two sets of relationships, namely, the computational model to systemlevel data, and low-level data to system-level data. A hierarchical Bayesian network with Markov Chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level. The role of low-level data in the model validation assessment at the system level is identified by the Bayesian method and factor analysis. The proposed methodology is implemented for hierarchical assessment of two validation problems, using time series data.