# Prediction of the Yield Strength of RC Columns Using a PSO-LSSVM Model
## 5 Conclusions  
A new ML-based method incorporating algorithms of the LSSVM and PSO is proposed for predicting the yield strength and displacement of RC columns. The present PSO-LSSVM model is capable of learning the nonlinear regression function that controls the mapping between the influencing factors and the yield strength and displacement with the PSO utilized for assisting to adaptively and quickly determine two optimal tuning parameters (\(\sigma\), \(\gamma\)). A test database of 382 pseudo-static cyclic test of RC columns is built, then the effects of the column featured parameters on the yield-related properties are investigated concerning the related research results. The proposed PSO-LSSVM model is then compared with the standard LSSVM and the LSSVM optimized by other metaheuristic algorithms, such as GA, ABC and DE algorithms, with the identical experimental database used for model training and testing. The comparative results show that the PSO empowers the LSSVM model to efficiently and accurately predict the target data with a self-optimized machine learning algorithm based on the collected data samples. Based on the analysis results about the prediction performance of the PSO-LSSVM for the yield strength and displacement of RC columns, the following conclusions are drawn:  
1. The determination coefficient \(R^{2}\) is 0.96, if 80% of the whole dataset is used for training the PSO-LSSVM model, which means a low prediction error. Meanwhile, the RMSE and MAE are 31.45 and 23.25, respectively, which indicates that the prediction model has a low prediction deviation.
2. The PSO adopted for parameter optimization of \(\sigma\) and \(\gamma\) that are embedded in the LSSVM model, can quickly find the optimal parameters to effectively assist the LSSVM model in prediction work.
3. The proposed PSO-LSSVM model can predict the yield strength and displacement of RC columns with high efficiency and accuracy by comparing them with the LSSVM models optimized by other metaheuristic algorithms.  
Hence, the developed PSO-LSSVM model can be a useful tool to provide effective guidance for the structural design of RC columns in practical engineering applications. Essentially, the proposed model based on the ML technique is a data-driven approach that focuses on correlations between research objects, different from the traditional research method that is more concerned with cause-effect relationships. Moreover, ML methods characterized by data-driven approaches are very powerful at solving regression and optimization problems, as long as sufficient data can be provided. In our future work, the model will be extended to study the deformation properties of other key component units of building structures, such as RC beams and shear walls, and, the data collection and processing of the relevant experimental database will be conducted.  
Conceptualization, B.W., W.G. and Z.L.; methodology, B.W. and W.G.; validation, B.W., W.G. and Y.W.; formal analysis, Y.W. and Z.L.; investigation, B.W. and H.L.; writing--review and editing, B.W and W.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (51808112, 51878160, 52078128), Natural Science Foundation of Jiangsu Province (BK20180155) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX21_1794).  
Not applicable.  
The authors declare no conflict of interest.