# Use of the Gene-Expression Programming Equation and FEM for the High-Strength CFST Columns
###### Abstract  
The ultimate strength of composite columns is a significant factor for engineers and, therefore, finding a trustworthy and quick method to predict it with a good accuracy is very important. In the previous studies, the gene expression programming (GEP), as a new methodology, was trained and tested for a number of concrete-filled steel tube (CFST) samples and a GEP-based equation was proposed to estimate the ultimate bearing capacity of the CFST columns. In this study, however, the equation is considered to be validated for its results, and to ensure it is clearly capable of predicting the ultimate bearing capacity of the columns with high-strength concrete. Therefore, 32 samples with high-strength concrete were considered and they were modelled using the finite element method (FEM). The ultimate bearing capacity was obtained by FEM, and was compared with the results achieved from the GEP equation, and both were compared to the respective experimental results. It was evident from the results that the majority of values obtained from GEP were closer to the real experimental data than those obtained from FEM. This demonstrates the accuracy of the predictive equation obtained from GEP for these types of CFST column. on +
Footnote †: journal: Medical  
concrete core avoids inward buckling of the steel. Therefore, ductility and strength of these columns are usually high. Furthermore, the confinement of concrete in circular columns is more efficient compared to other types of sections which results in a better interaction and less slip between steel tube and concrete. It is consequently can lead to a higher axial strength and a better structural integrity [8; 9]. There is a few research which focused on the analysis of the CFST composite columns using artificial intelligence (AI) techniques. In the previous study [10] an extensive data collection was performed and they were analyzed by GEP. A valuable equation was generated to estimate the ultimate strength of the CFST columns and it was optimized afterwards [1]. Most studies in civil engineering are based on experimental work and numerical analysis using the finite element method (FEM). Normally, using an equation-based analysis is less time consuming and less costly than the laboratory tests and computational modelling and analysis. Therefore, this study tried to ensure that the proposed GEP-based equation could be reliable to be used in prediction of the bearing capacity of CFST composite columns. Furthermore, in order to show fidelity of the results from the GEP equation, in addition to comparison of them with the finite element analysis (FEA), the outcomes were also compared with the experimental ones in the literature. In previous research [10; 11], 303 samples of CFST columns were collected from literature and they were trained and tested using GEP. The assessment was performed five times and each time led to an equation. The equations were classified based on the coefficient of determination (R\({}^{2}\)) and the one with the closest R square to 1 was picked up for the further analysis. Then the GEP prediction equation has been optimized using AI optimization techniques. In this research, however, 32 different samples of those were collected in the previous research are considered with high-strength concrete but still within the range of the previous study. They are numerically modelled and analyzed to obtain their ultimate bearing capacity for the comparison purpose  
FEM is a tool for numerical analysis which can model different types of composite columns. It could be a useful method in many of such cases specifically in the prediction of ultimate bearing capacity. However, after applying AI techniques for the composite columns [11; 12; 13; 14], these novel methods were presented more promising results compared with the results of the FEA. Recently, AI techniques such as ANN and GEP are widely being used in the civil engineering to predict and optimize various criteria in this regard [15; 16; 17; 18; 19; 20; 21].