Bayesian nonlinear structural equation modeling for hierarchical validation of dynamical systems

This paper presents a new Bayesian nonlinear structural equation modeling approach to hierarchical model assessment of dynamic systems, considering uncertainty in both predicted and measured time series data. A generalized structural equation modeling with nonlinear latent variables is presented to model two sets of relationships in multivariate hierarchical model assessment, namely, the computational model to system-level data, and low-level data to system-level data. A hierarchical Bayesian network with Markov Chain Monte Carlo simulation and Gibbs sampling is developed to represent the two relationships and estimate the influencing factors between them. A Bayesian interval hypothesis testing-based method is employed to quantify the confidence in the predictive model at various levels. The effect of low-level data on the model assessment at the system level is identified by Bayesian inference and factor analysis. The proposed methodology is implemented for hierarchical model validation of three dynamic system problems.