Ground Motion Prediction Equation Development by Heterogeneous Bayesian Learning

In ground motion prediction, the key is to develop a suitable and reliable GMPE (ground motion prediction equation) characterizing the ground motion pattern of the target seismic region. There are two critical goals encountered in GMPE development. Proposing a suitable predictive formula applicable to target seismic region has attracted much of the attention in previous studies. On the other hand, dependence between prediction–error variance and ground motion data has been observed and the study on this kind of heterogeneous relation becomes an important task yet to be explored. In this article, a novel HEteRogeneous BAyesian Learning (HERBAL) approach is proposed for achieving these two goals simultaneously. The homogeneity assumption on error in the traditional learning approach is relaxed, so the proposed approach is applicable for more general heterogeneous cases. With the generalization made on the traditional Bayesian learning by embedding the derived closed form expression for error variance parameter optimization component into the hyperparameter optimization of ARD (automatic relevance determination) prior, the proposed learning approach is capable of performing continuous model training on a prescribed predictive formula with unknown error pattern. A database of strong ground motion records in the Tangshan region of China is obtained for the analysis. It is shown that the trained optimal model class by the proposed approach is promising as that, the trained optimal model class retains model simplicity of the predictive formula with capability on both robustness enhancement ground motion prediction and precise determination of the error pattern.