## 1 Introduction
By virtue of the excellent nonlinear learning ability, MLAs have already been employed to calculate the ultimate axial capacity of CFSTs. Artificial neural networks (ANN) have become the most commonly used MLA. [PERSON] et al. [15] utilized ANN to develop a model for predicting the ultimate strength of rectangular CFST beam-columns under eccentric axial loads. They used the same method to model and predict the ultimate strength of circular CFST beam-columns [16]. The predicted values were more accurate than the AISC and EC4 values in both cases. Similarly, ANN was applied in [17; 18; 19]. In addition, [PERSON] et al. [20] presented an alternative method to determine the confinement effect of the concrete infill and the axial load capacity of the stub CFST by using fuzzy logic. The focus was made on the accurate estimation of the confinement effect of the CFST using the fuzzy-based model. [PERSON] et al. [21; 22] respectively proposed a new formulation for the axial load carrying capacity of circular CFST short columns and concrete-filled double skin steel tubular composite columns based on gene expression programming (GEP). The GEP model was much better than the available formulae, yielding a higher correlation coefficient and lower error. MLAs were also used to estimate other properties of CFSTs. [PERSON] et al. [23] and [PERSON] et al. [24] each predicted the fire resistance and load-strain relationship of CFSTs with different dimensions and parameters using ANN. The prediction model for the ultimate pure bending moment of CFSTs via adaptive neuro-fuzzy inference system was raised by [PERSON] et al. [25]. The application of MLAs in CFST performance index calculation is still in its infancy. To the best of our knowledge, some advanced algorithms such as support vector machine (SVM) [26] have not been applied in this field until now. SVM is a new supervised learning method developed in statistical learning theory that performs well in solving small sample, nonlinear, and high dimensional problems [27]. To date, SVM has been widely used in various fields of structural engineering, including dam safety, scour monitoring, civil architecture, etc., due to its potential in nonlinear regression, function approximation, and pattern recognition [28; 29; 30; 31]. In brief, SVM can effectively deal with the data modeling problem under the condition of limited samples because of superior generalization ability and dimensionality insensitivity [32]. Nevertheless, the adjustment and optimization of SVMparameters is an essential problem, which greatly influences prediction effects. The metaheuristic algorithm does not depend too much on the organization structure information of the algorithm, which is suitable for parameter optimization and function calculation. Particle swarm optimization (PSO) is a global random search algorithm based on swarm intelligence [33]. PSO is easier to implement and produces more accurate results than other optimization algorithms, such as genetic algorithm (GA) [34]. In this paper, given enough experimental data of axial compression tests for square CFST short columns, a combined model termed PSVM (SVM optimized by PSO) is proposed to predict the ultimate axial capacity. The prediction performance of PSVM is verified by an independent test set and multi-model comparison. Performance assessment results are quantified by evaluation criteria. The simulation results show the feasibility and superiority of the proposed PSVM model. The rest of the paper is organized as follows. In Section 2, the axial pressure test procedure and dataset compilation are briefly described. The mathematical principles of SVM and PSO are presented in Section 3. Section 4 expatiates the complete implementation of PSVM. Section 5 illustrates and discusses the results of model validation and sensitivity analysis, and depicts a prediction error correction method. Conclusions and perspectives are finally provided in Section 6.