Dimensionless Machine Learning: Dimensional Analysis to Improve LSSVM and ANN models and predict bearing capacity of circular foundations

Abstract

This research focuses on developing hybrid intelligence techniques to predict the bearing capacity of circular foundations using the most effective parameters. In this regard, a database involving 968 test circular foundations involving different rock properties, soil characteristics, and foundation radius has been prepared by laboratory tests for training and testing the new model presented in this study. For adequately considering various factors, the several parameters of depth (D) in m, density of soil (DS) in gr/cm³, internal angle of friction (IAF) in degree, cohesion of soil (CS) in kg/cm², and foundation radius (FR) in m were considered as the input of the model and bearing capacity in kg/cm² was considered as the target parameter. Three main strategies were addressed in this study. First, four well-known machine learning algorithms, Artificial Neural Network (ANN), Bagging Regressor (BR), Least Squares Support Vector Machine (LSSVM), and Gradient Boosting Regressor (GBR), were adopted to predict bearing capacity. Second, a novel and robust mathematical computation named dimensional analysis (DA) theorem was integrated with machine learning techniques to improve the accuracy and performance of the models by decreasing the number of inputs. Third, based on DA implementation, a rational mathematical formula using gene expression programming (GEP) was structured to anticipate bearing capacity. Furthermore, the sensitivity analysis process specified the impact of the five effective factors. The results of this study demonstrate the effectiveness of integrating DA with machine learning models to predict the BC of circular foundations. Among the developed models, the DA-LSSVM model showed superior performance, achieving an R² of 0.998 and 0.996 for training and testing, respectively, indicating high prediction accuracy. The results indicated that the IAF was the most sensitive factor with r = 0.709, while CS was the least sensitive with r = -0.087. A graphical user interface (GUI) app has been designed to apply the proposed models in this study conveniently. In the last step of this process, the GUI and the DA-based machine learning models were implemented by analyzing two examples. According to the findings, the GUI may be employed to make a reliable and speedy projection of the bearing capacity of circular foundations by considering a variety of input parameters.