Efficient probabilistic back analysis of geotechnical engineering based on variational Bayesian Monte Carlo

Various inevitable uncertainties exist in geotechnical engineering, which may lead to inaccurate estimates of the geotechnical system performance. Bayesian updating offers a robust way to reduce such uncertainties by incorporating observation data, thereby improving the accuracy of system performance assessment. Conventional Bayesian updating methods often rely on Markov Chain Monte Carlo (MCMC) algorithms, which are computationally expensive, especially for time-consuming problems. In such a situation, this paper presents an efficient probabilistic back analysis framework based on the Variational Bayesian Monte Carlo (VBMC) algorithm. In comparison to MCMC-based methods, the proposed framework does not draw samples on the posterior distribution directly but employs a known distribution to approximate the posterior distribution. The time-consuming sampling is thus transformed into an optimisation problem. Further, Bayesian quadrature via Gaussian process is adopted to estimate the non-analytical integral associated with geotechnical prediction models. Three illustrative examples are applied to demonstrate the effectiveness of the proposed framework. The results of comparison with other methods demonstrate the high accuracy and efficiency of the proposed framework in addressing geotechnical problems.