Evolutionary Polynomial Regression Algorithm Enhanced with a Robust Formulation: Application to Shear Strength Prediction of RC Beams without Stirrups

Abstract

Many classes of engineering problems focus on the process of calibrating mathematical models using observed data. The enormous progress of scientific computation and data-mining techniques has allowed the search for accurate mathematical models from experimental data using algorithms. Among them, the evolutionary polynomial regression (EPR) is an artificial intelligence (AI) technique that merges genetic algorithms (GAs) and regression techniques such as ordinary least square (OLS). This paper presents a robust and well-conditioned EPR technique to remove potential outliers and leverage points included in any biased data set. This hybrid approach combines bisquare, Huber, and Cauchy robust multivariate techniques with GAs and the Akaike weight-based method to assess the optimal polynomial model while limiting the impact of the data bias. The robust techniques will define the parameters, the GAs will determine the exponents, and the Akaike weight-based method will evaluate the relative importance of each observed variable of the proposed model. As a case study, a shear strength data set of RC beams without stirrups is used to compare the standard EPR algorithm with the new proposed hybrid methodology. Furthermore, the optimal robust model is compared with different benchmark formulations to highlight its accuracy and consistency. The proposed hybrid technique can be adopted as a mathematical tool for many engineering problems, providing an unbiased prediction of the observed variable. Furthermore, the shear strength equation that provides the best compromise between accuracy and complexity allows its potential use in many engineering practices and building codes.