# Prediction of the Yield Strength of RC Columns Using a PSO-LSSVM Model
###### Abstract  
Accuracy prediction of the yield strength and displacement of reinforced concrete (RC) columns for evaluating the seismic performance of structure plays an important role in engineering the structural design of RC columns. A new hybrid machine learning technique based on the least squares support vector machine (LSSVM) and the particle swarm optimization (PSO) algorithm is proposed to predict the yield strength and displacement of RC columns. In this PSO-LSSVM model, the LSSVM is applied to discover the mapping between the influencing factors and the yield strength and displacement, and the PSO algorithm is utilized to select the optimal parameters of LSSVM to facilitate the prediction performance of the proposed model. A dataset covering the PEER database and the available experimental data in relevant literature is established for model training and testing. The PSO algorithm is then evaluated and compared with other metaheuristic algorithms based on the experiment's database. The results indicate the effectiveness of the PSO employed for improving the prediction performance of the LSSVM model according to the evaluation criteria such as the root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (\(R^{2}\)). Overall, the simulation demonstrates that the developed PSO-LSSVM model has ideal prediction accuracy in the yield properties of RC columns. R 2022 20  
Several numerical and experimental [8] methods have been extensively employed to investigate the nonlinear behaviors of RC structures. The numerical models, based on the finite element method, are usually used for nonlinear static or dynamic analyses. However, many FE-based models are incapable of capturing the hysteretic behaviors accurately, something which depends on the selection of model parameters and boundary conditions [4; 5; 6]. It is, therefore necessary to further improve the assessment accuracy of the behaviors of RC columns by the numerical simulation method. Additionally, the calculation of tedious iterative processes is time-consuming. In contrast, the experimental method is more effective and capable of identifying the real responses of a structure [9; 10], but it is quite costly, time-consuming and labor-intensive. Over the past few decades, artificial intelligence (AI) technologies, with the merits of their strong nonlinear learning capacities, have been widely utilized in the earthquake and civil engineering fields [11; 12; 13; 14; 15; 16]. The technologies have gradually developed into an effective research method to study the abovementioned problems [17; 18; 19; 20; 21; 22; 23; 24], one which enables civil engineers to predict the structural performance of concrete members. For instance, [PERSON] et al. [24] performed innovative work in which a machine-learning-aided approach was proposed to improve the accuracy of the mechanics-based shear capacity equation for RC beams and columns. On the other hand, many models based on hybrid machine learning (ML) techniques were developed to predict structural performance straightforwardly without explicit formulae. Typical of these predictive models, the support vector machine (SVM) proposed by [PERSON] [25] is a widely used machine learning technique. Thereafter, the least squares support vector machine (LSSVM) [26], as a modified version of SVM, is reported to be able to conduct a faster training process for tackling many complex and non-linear problems in engineering compared to the standard SVMs, i.e., with faster computational and generalized capacity [27; 28]. Some work on the application of machine learning (ML) to the study of RC structures is listed in Table 1, as follows:  
It is worth noting that [PERSON] and [PERSON] [20] developed a novel machine learning-based backbone curve (ML-BCV) model to predict backbone curves of RC columns subjected to three different failure modes. This model consists of a modified LSSVM to address the multioutput case, and a grid search algorithm (GSA) to facilitate the training process.