Explainable machine learning based efficient prediction tool for lateral cyclic response of post-tensioned base rocking steel bridge piers

This study presents a novel explainable machine learning (ML) based predictive model for the lateral cyclic response of post-tensioned (PT) base rocking steel bridge piers. The PT rocking steel bridge pier comprises a circular tube with welded circular base plate that is pre-compressed to its base by means of gravity loads and/or a PT tendon. The input factors were column diameter, column diameter-to-thickness ratio, column height-to -diameter ratio, cross-sectional area of tendon-to-column ratio, tendon initial post-tensioning ratio, dead load ratio, base plate thickness, and base plate extension. Response variables were column residual drift, column shortening, ratio of degraded stiffness to initial stiffness, maximum lateral strength to uplift force ratio, and lateral strength reduction ratio. Nine ML techniques that range from the simplest to advanced techniques were used to generate the predictive models. Several statistical performance indices are computed for the evaluation of the models. The results showed that the simplest white-box models are inadequate to capture the relationship between the input factors and the response variables. The comparative analysis of the examined models showed the superior prediction performance of the proposed xgBoost based model with a maximum coefficient of determination, agreement index, Kling-Gupta efficiency, and lowest error. The results also demonstrated that the optimized xgBoost model can be used to predict the lateral cyclic response of the rocking steel bridge piers efficiently and accurately. In addition, the unified model agnostic Shapley Additive exPlanation (SHAP) framework was employed to explain the outputs of xgBoost model and analyze the significance of the factors and their interaction on the predicted response quantities. Finally, the optimized best predictive model is used to develop a simple and user-friendly web-based prediction tool that facilitates the rapid and efficient lateral cyclic response prediction of post-tensioned base rocking steel bridge piers.