An efficient Bayesian inversion method for seepage parameters using a data-driven error model and an ensemble of surrogates considering the interactions between prediction performance indicators

Abstract The Bayesian method has been increasingly applied to the inversion of seepage parameters owing to its superiority of considering the uncertainty in the inversion process. However, most of the current Bayesian inversion studies only focus on parameter uncertainty, ignoring the model structure error. In addition, existing research has mostly adopted a single machine learning algorithm or an ensemble of surrogates based on a single prediction performance indicator as a substitute for the seepage forward model and has not considered the interactions between multiple prediction performance indicators, thereby leading to poor accuracy. To address these issues, this study proposed an efficient Bayesian inversion method for seepage parameters using a data-driven error model and an ensemble of surrogates considering the interactions between prediction performance indicators. A data-driven error model based on Gaussian process regression was integrated into the Bayesian inversion model to modify the likelihood function for dealing with the model structure error. For determining the weight coefficients of the ensemble surrogates, the improved Dempster-Shafer (D-S) evidence theory based on the Hellinger distance and Deng entropy was proposed to fuse multiple prediction performance indicators and consider their interactions. Further, an ensemble of surrogates in conjunction with support vector regression, Kriging, and multivariate adaptive regression splines was constructed through weighted summation. The validity and accuracy of the proposed method were verified by applying it to a real hydropower station in China. The results showed that the proposed method can significantly improve the accuracy and efficiency of Bayesian inversion of seepage parameters. The proposed method therefore serves as a new basis for the inversion of seepage parameters and can be applied to parameter inversion in other related fields.