Bayesian back analysis considering constraints

Soil parameters significantly affect the prediction performance of geotechnical models. In the field of parameter identification, the MCMC-based Bayesian method is an effective way to infer the probability distribution of soil parameters. However, this method only considers the prior distribution of soil parameters and the difference between predictions and observations, without considering other additional information such as empirical correlations between soil parameters. In addition, the MCMC method leads to high computational cost if the numerical methods are used as the model, which limits its application. In this study, a new approximate Bayesian method considering the additional constraints is proposed, named REnKF-MDA. The proposed method is compared with the MCMC-based Bayesian method, MCMC-based Bayesian method with constraints, and REnKF. The effectiveness of the proposed REnKF-MDA method is illustrated by a simple polynomial case and a foundation settlement project. The results indicate that assimilating the additional constraint informations is helpful to improve the rationality and confidence of the inferred parameters. The confidence of the constraint is determined by the covariance of the constraint information. Taking the MCMC-based Bayesian method with constraints as a reference, the REnKF provides an accurate evaluation of the mean value, but significantly underestimates the uncertainty of the posterior distributions. In contrast, the REnKF-MDA estimates both the mean and uncertainty well.