From machine learning to semi-empirical formulas for estimating compressive strength of Ultra-High Performance Concrete

Although some machine learning (ML) models have successfully developed for ultra-high-performance concrete (UHPC), they do not provide insights and explicit relations between all input variables and its compressive strength. This paper will address these ambiguities and provide a tool to predict the compressive strength by explainable and interpretable equations and plots. Explicit semi-empirical formulas are derived from a multivariate polynomial regression (Lasso) and automated feature engineering and selection (Autofeat) using a 810 dataset of UHPC with 15 input variables, which are collected from literature. Coefficient of determination R2 = 0.8223 is the same for the first-order degree (linear regression) of both models, however, the Autofeat achieves a better result than Lasso for the third-order degree with R2 = 0.9616 vs. R2 = 0.9503. A comprehensive parametric study is carried out via relative feature importance and partial dependence plots to explain and gain profound insights into the effects of some important input variables on the compressive strength of UHPC. Some details discussions related to these effects with previous studies are also presented. The proposed models not only show better performance with those from reference in terms of R2, especially for Autofeat model but also have explicit relations of compressive strength with 15 input variables. Hence, they can be used as a reliable tool in mixture design optimization of the UHPC.