Unveiling Nonlinear Synergistic Effects in Ultrahigh-Performance Concrete: A Data-Driven Framework for Optimized Mix Design and Accurate Strength Prediction

Abstract

Accurately predicting the compressive strength of ultrahigh performance concrete (UHPC) is challenging due to the nonlinear and coupled effects of its compositional variables. This study proposes a hybrid modeling framework that combines deep neural networks (DNNs) with traditional machine learning regressors (XGBoost, Random Forest, and SVR) to achieve both high prediction accuracy and interpretability. A data set comprising 810 UHPC mix designs was used, including 13 input variables such as cement, fiber, water–binder ratio, and curing age. The DNN was trained to extract deep nonlinear features, which were then fed into ensemble regressors. Among all models, DNN-XGBoost achieved the best performance with R 2 = 0.9872 , RMSE = 7.74    MPa , and an a20-index of 95.82%. External validation on 1,031 samples confirmed strong generalization ( R 2 = 0.8956 ). Model interpretability was explored using SHAP and partial dependence plots, revealing critical variables and nonlinear thresholds. For instance, fiber content improved strength up to 50    kg / m 3 , beyond which strength declined due to agglomeration. Neuron activation analysis further showed that the DNN learned physically meaningful patterns aligned with hydration and packing mechanisms. This hybrid framework provides a robust, interpretable, and scalable approach for UHPC strength prediction. It supports data-driven mix design optimization while maintaining alignment with engineering principles.