# Prediction of the Yield Strength of RC Columns Using a PSO-LSSVM Model
###### Abstract
The essence of the training process is to select the optimal solution for two key parameters that significantly affect the accuracy level of predicted results. The selection process of these two parameters can be regarded as an optimization problem [20]. Thus, an appropriate swarm intelligence (SI) algorithm is needed to solve the optimization problem. Several SI algorithms have been widely applied for solving various optimization problems owing to their powerful global search capability [29], typically genetic algorithm (GA) [30], differential evolution (DE) [31], artificial bee colony (ABC) [32] and particle swarm optimization (PSO) [33] algorithms. The PSO algorithm developed by [PERSON] and [PERSON] [33], is regarded as a reliable tool when combined with AI techniques due to its outstanding features of high calculation efficiency, high accuracy and powerful global optimization and search capability in searching for the optimal solution [34; 35; 36; 37]. The PSO has been used to enhance the training process of LSSVM or other models, and further improve the predictive \begin{table}
\begin{tabular}{c c l} \hline \hline
**Study** & **Model** & **Issues or Objectives** \\ \hline [PERSON] et al. [18] & LSSVM & Predict the strength of radiation-shielding concrete \\ [PERSON] and [PERSON] [19] & LSSVM & Predict the ultimate punching shear capacity of \\  & & FRP-RC slabs. \\ [PERSON] and [PERSON] [20] & ML-BCV & Predict backbone curves of RC columns \\ [PERSON] and [PERSON] [21] & MLs & Predict shear strength for RC beam-column joints \\ [PERSON] et al. [22] & DE-ANN & Predict the hysteresis loop of RC columns \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Application of machine learning in the study of RC structures. accuracy of forecasting models in the fields of engineering [38; 39; 40; 41; 42]. A detailed introduction to the PSO algorithm used in the present work can be found in Section 4.2. To the best of our knowledge, there are still few computational models that can rapidly calculate the strength-related properties of RC columns with high accuracy [7; 43; 44]. Moreover, the predictive models or formulae that enable the comprehensive covering of most of the influencing factors are still scarce due to the complexity of multi-factor issues. Based on the challenge, machine learning (ML) techniques are widely adopted by virtue of their data-driven nature and their expertise in dealing with nonlinear correlations between multiple factors. The present work focuses on developing a new prediction model based on machine learning techniques for achieving the goal of efficiently and accurately predicting yield strength and displacement of RC columns with more influence factors considered. In this model, the LSSVM is applied to establish a prediction model to estimate the nonlinear mapping between influence factors and yield properties. The PSO algorism is adopted to facilitate the training process of the LSSVM model for the purpose of improving the predictive accuracy of this model through selecting the optimal solution of key parameters i.e., regularization parameter (\(\gamma\)) and RBF kernel parameter (\(\sigma\)). For training and testing the performance of the present model, a test database of the proposed model is built up by an efficient program script compiled to collect and collate the existing experimental data obtained by pseudo-static cyclic testing of RC columns. The performance of the trained LSSVM model can be evaluated by the root mean square error (RMSE), mean absolute error (MAE), explained variance (EV) and coefficient of determination (\(R^{2}\)). Meanwhile, the effectiveness of the PSO in enhancing the prediction accuracy of the LSSVM model is evaluated compared to other metaheuristics.