Statistics-based Bayesian modeling framework for uncertainty quantification and propagation

A new Bayesian modeling framework is proposed to account for the uncertainty in model parameters arising from and measurements errors, as well experimental, operational, environmental manufacturing variabilities. Uncertainty embedded using a single level hierarchy where uncertainties are quantified by Normal distributions with mean covariance treated hyperparameters. Unlike existing hierarchical modelling frameworks, likelihood function each observed quantity built based on Kullback–Leibler divergence used quantify discrepancy between probability density functions (PDFs) of predictions measurements. The constructed assuming that this measured follows truncated normal distribution. For Gaussian PDFs response predictions, posterior PDF depends lower two moments respective PDFs. This representation also non-Gaussian approximate parameters. can tackle situation only or statistical characteristics available propagation accomplished through sampling. Two applications demonstrate use effectiveness framework. In first one, structural parameter inference considered simulated statistics modal frequencies mode shapes. second probabilistic S-N curves fatigue experimental data.