Probabilistic calculation formula for the compressive strength of ultra-high-performance concrete with coarse aggregate based on feature engineering and genetic programming

Coarse aggregate ultra-high-performance concrete (UHPC-CA) has promising application prospects due to its superior properties. However, there is currently no well-established formula or model to guide its mix design from the perspective of compressive strength control. In this study, a dataset was established through standard compressive strength tests. Feature selection methods were employed to reduce data dimensionality and to select the key factors—chosen from coarse aggregate content, maximum particle size, minimum particle size, aggregate type, and steel fiber volume fraction—that govern the compressive strength. A deterministic prediction formula, controlled by selected factors, was developed using genetic programming. Bayesian parameter regression was then applied to construct a probabilistic model, using the deterministic formula as a prior. This modeling approach enables the prediction model to simultaneously achieve accuracy, simplicity, and interpretability, while also having the capability to handle uncertainty. In addition, it provides a modeling framework that can be reproducibly applied to other studies on similar materials. After validating the accuracy of both the deterministic and probabilistic calculation formulas, the study further analyzed the interaction effects among the key factors on UHPC-CA compressive strength and their influence on the uncertainty of prediction results. The effect of coarse aggregate content on compressive strength can be described by an exponential function or approximated as linear within the studied range. The influence of steel fiber volume fraction on compressive strength is more complex, showing a combination of linear and exponential trends, reflecting that compressive strength increases rapidly at first and then more gradually with higher steel fiber content. In addition, higher predicted compressive strength of UHPC-CA is associated with greater embedded uncertainty.