Rapid and automated seismic design of cable restrainer for simply supported bridges crossing fault rupture zones using explainable machine learning

Earthquakes in recent decades have demonstrated that fault-crossing simply supported bridges were susceptible to damage caused by the fault-induced permanent ground dislocation. Cable restrainer can potentially reduce the relative displacement of bridge spans, but the current seismic design method for restrainer is time-consuming and labor-intensive. This study aims to develop a rapid and automated seismic design method for cable restrainer using explainable machine learning (ML) models. To do this, a large database was first generated based on the current design approach. ML algorithms were utilized to develop classification models to determine the design classes and then regression models to estimate the restrainer stiffness for the fault-crossing bridges. Furthermore, SHapley Additive exPlanations (SHAP) analysis was utilized to provide interpretations for the best regression model. In particular, an empirical formula and two explainable prediction models by combining the empirical formula with simplified ML models were finally proposed to facilitate the design for engineers. Results show that the proposed design method can provide accurate and robust results of bridge restrainers. Within the method, artificial neural network was selected among nine ML models, because of its highest accuracy for both classification and regression. The SHAP analysis reveals that, the allowable displacement has a negative nonlinear effect, while permanent ground dislocation and initial relative displacement present positive nonlinear effects. The proposed empirical formula for restrainer design can provide conservative estimations with an accuracy of 79 %, whereas the proposed explainable prediction models have a high accuracy of 94 % and are significantly efficient and user-friendly.