Prediction of central deflection and slenderness limit for lateral stability of simply supported concrete beam using machine learning techniques

Abstract

In the field of mechanics, large deflection of simply supported beam (SSB) carrying a load intensity (w) is well-known topic that has been thoroughly studied by many researchers. Numerous methods have been used, such as the analytical precise solution and the finite element approach. A small number of researchers computed central deflection of SSB having uniformly distributed load and also checked the slenderness limit for lateral stability (L_s) of SSB using numerous machine learning (ML) techniques. This study compares the suitability and flexibility of the extreme gradient boosting (XGBoost), support vector regression (SVR) and polynomial regression (PR) model in the reliability investigation of SSB. It also provides an ML-based prediction method for δ and checks the slenderness limit for L_s of SSB. These three ML models apply to 400 datasets and predict the δ and as well as checks the slenderness limit for L_s of SSB by taking account five major input parameters such as beam width (b), beam depth (h), beam length (L), uniformly distributed load (w) and characteristics compressive strength of concrete (f_ck). Numerous performance indicators, including coefficient of determination (R²), variance account factor (VAF), a-20 index, root mean square error (RMSE), mean absolute error (MAE) and mean absolute deviation (MAD) are used to assess the efficacy of the well-established ML models. PR model achieved the best performance according to the performance metrics. This was attributed to its maximum R² = 0.999 and 1.000 and the lowest RMSE = 0.003 and 0 during the training phase, as well as R² = 0.994 and 1 and RMSE = 0.017 and 0 during the testing phase, while predicting central deflection (δ) and slenderness limit (Ls) of SSB respectively. The reliability index (β) was calculated using the first-order second moment (FOSM) method for all models. Rank analysis, reliability analysis, regression curve, William’s plot, Taylor diagram and error matrix plot are further tools used to assess the performance of the proposed model. First-order second moment (FOSM) approach is used to determine the reliability index (β) of the model and compared with the actual value. To check the influence of each input parameters, sensitivity analysis is performed for both the cases.