Bayesian structural equation modeling method for hierarchical model validation

A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A 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, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.