An Efficient Bayesian Updating Method and Its Application in the Structural Analysis of Underground Tunnels

Abstract

Model updating (i.e., inverse problems) involving high-dimension and nonlinearity plays an increasingly important role in various research fields, e.g., digital twin model updating. Bayesian updating has become a robust and rigorous probabilistic means for parameter uncertainty quantification. However, it remains a challenging task to simultaneously ensure theoretically rigorous and computationally efficient solving of inverse problems involving high-dimensionality and nonlinearity. To address the issue, by applying the basic idea of subset simulation (SuS) to the ensemble Kalman filter (EnKF) that is computationally efficient and applicable to high-dimensional inverse problems, we designed an efficient Monte Carlo method, termed ensemble Kalman filter with subset simulation (EnKF-SuS). In EnKF-SuS, SuS provides a rigorous theoretical basis for guiding EnKF to adaptively search and explore the true target space(s), while avoiding the disadvantages of Markov chain Monte Carlo (MCMC)-based sampling methods by utilizing EnKF to generate updated ensemble samples. The performance of EnKF-SuS was validated and analyzed through three case studies involving multimodal posterior, strongly nonlinear, or high-dimensional problems. Moreover, based on a simplified model for longitudinal response analysis of shield tunnels, we present the application of EnKF-SuS in model updating using centrifuge data and field data, respectively. Results indicate that EnKF-SuS can accurately and efficiently sample from general target posterior distributions, especially in the tested strongly nonlinear or high-dimensional problems, and it is computationally one to two orders of magnitude faster than tested with MCMC-sampling methods.