Calibration of empirical models considering model fidelity and model robustness — Focusing on predictions of liquefaction-induced settlements

Abstract Most data-driven empirical models adopted in the geotechnical design have various degrees of uncertainty. Consequently, it is important to properly calibrate this uncertainty prior to its application in the geotechnical analysis to ensure the integrity of the final design. The conventional probabilistic model calibration approaches, such as maximum likelihood estimate and Bayesian method, focus only on model fidelity (measured through, for example, likelihood). These approaches often yield models with a large model uncertainty, especially when the observed data are scattered. A large model uncertainty leads to a large variation in the model prediction, which poses a significant challenge in a geotechnical design. In this paper, we propose a new model calibration approach that can consider both model fidelity and model robustness. The new model calibration approach offers a way to balance the objectives of model fidelity and model robustness. Because model fidelity and model robustness are two conflicting objectives, the new approach involves a multi-objective optimization that leads to a Pareto front, which defines a tradeoff relationship between model fidelity and model robustness. By enforcing a certain level of robustness, the variation in the model prediction can be reduced, which overcomes the major weakness of the traditional probabilistic approaches that focus solely on model fidelity. The new approach is demonstrated through applications to the problems of liquefaction-induced settlement prediction.