Prediction of the ultimate axial load of circular concrete‐filled stainless steel tubular columns using machine learning approaches

This paper investigates the accuracy of the existing empirical design models and different machine learning (ML) models, known as Decision Tree (DT), Random Forest (RF), K‐Nearest Neighbors (KNN), Adaptive Boosting (AdaBoost), Gradient Boosting Regression Tree (GBRT), and Extreme Gradient Boosting (XGBoost) in predicting the ultimate axial load of circular concrete‐filled stainless steel tubular (CFSST) columns under axial loading. A test database encompassing the test results of 142 CFSST columns is used to validate the accuracy of the existing empirical design and different ML models. It was demonstrated that all the ML models can provide a better estimation of the ultimate axial load than the existing empirical design models do, in which XGBoost can provide the best estimation of the ultimate axial load of CFSST columns. Finally, a simple equation is proposed based on the XGBoost model for the practical design of CFSST columns.


| INTRODUCTION
Concrete-filled steel tubular (CFST) columns are widely used in tall buildings, bridge piers, and other civil structures to carry large axial loads. [1][2][3][4] The composite action between the steel and concrete improves their ultimate axial load, ductility, fire, and cyclic performance compared to traditional reinforced concrete columns. In addition, the steel tube acts as formwork during the construction, thus, reducing the construction cost and increasing the construction pace. A circular CFST column provides an effective confinement to the core concrete compared to its square or rectangular counterparts, thus offering a better ultimate axial load and ductility compared to a square or rectangular cross-section. [5][6][7][8][9] Stainless steel, which has been used in the construction industry for many years, has excellent corrosion resistance and offers an aesthetic appearance. Owing to its distinguished strain-hardening characteristics, stainless steel has been proposed in the form of steel-concrete composite members known as concrete-filled stainless steel tubular (CFSST) columns, as illustrated in Figure 1. The structural performance in terms of strength and ductility of circular CFSST columns is much better than circular CFST columns composed of carbon steel owing to the distinguish strain-hardening characteristics of the stainless steel tube. 10 However, existing design codes have not provided specifications for the design of circular CFSST columns and limited studies have been conducted to investigate the accuracy of existing design models of CFST columns in designing CFSST columns. The existing design codes may underestimate the performance of circular CFSST columns. Considering the price of stainless steel, which is about 4-5 times that of carbon steel, accurate prediction of their structural performance is vital for the construction cost of projects.
Investigating the effects of various column parameters on the performance of composite columns through an experimental setup is very expensive and time-consuming. Although the numerical model is a cost-effective alternative to performing an inelastic analysis of composite columns, the development of such a numerical model is still very tedious and time-consuming. Recently, machine learning (ML) has been used in different fields including civil engineering. [54][55][56][57][58][59][60][61][62][63][64][65] The ML method is a cost-effective and time-efficient design tool as compared to the experimental and numerical schemes. In the ML method, a database is used to train the complex relationships of input and output variables of composite columns. The great advantage of the ML method is its excellent accuracy as well as its capability to derive mathematical expressions for practical use.
Although the ML method was previously employed to predict the ultimate axial load of CFST columns composed of carbon steel, 55

| RESEARCH SIGNIFICANCE
The behavior of the CFSST column is highly nonlinear and depends of the yield strength of the steel tube, the diameter of the column, the column tube thickness, the concrete compressive strength, the length of the column, and the confinement factor. As mentioned in the previous section, there is no design specifications specified by the existing design codes for predicting the ultimate strength of circular CFSST columns under concentric loading and no study has been performed to extensively investigate the accuracy of the existing design specifications of conventional CFST columns composed of carbon steel proposed by various design codes and other researchers in predicting the ultimate strength of CFSST columns. The classical computational techniques such as regression analysis can't predict the ultimate strength of CFSST columns due to the influence of a significant number of column parameters. Therefore, it is necessary to develop soft computing techniques to provide a more accurate estimation of their ultimate strength.

| DATABASE COLLECTION
To evaluate the accuracy of design prediction, an extensive literature review was performed to develop a test database of CFSST columns subjected to axial loading. The important column parameters that influence the ultimate axial load of CFSST columns (P exp ) were identified as the length of the columns (L), tube diameter (D), tube thickness (t), diameter-to-width ratio (D=t), concrete compressive strength (f 0 c ), steel yield strength taken as 0.2% proof stress of stainless steel tube (f y ), and confinement factor (ξ) calculated as ξ ¼ A s f y =A c f 0 c , where, A s and A s are the cross-sectional area of steel tube and core concrete, respectively. The concrete compressive strength of tested CFSST columns was determined either using cylindrical or concrete cube compression tests. For consistency, the database converted all the concrete cube strength to cylindrical strength using a reduction factor of 0.85, as proposed by Oehlers and Bradford. 75 In addition, considering the distinguish strain hardening behavior of stainless steel, some CFSST columns did not undergo strain softening and were tested for very large strain. In the development of this database, the ultimate axial load of CFSST columns was taken as the test ultimate axial load of the columns at 1% strain, as suggested by researchers earlier. [76][77][78][79] The developed database consisted of a total of 142 test data, covering a wide range of column parameters including: D ¼ 50 À 325 mm, t ¼ 0:9 À 12 mm, D=t ¼ 17 À 106, f 0 c ¼ 19 À 75 MPa, f y ¼ 225 À544 MPa, ξ ¼ 0:26 À 3:2, L ¼ 150 À 2940 mm, and P exp ¼ 112 À 13499 kN. Table 1 presents the test summary of the CFSST columns subjected to axial loading. Figure 2 shows the distributions of the column parameters of CFSST columns. Correlation values between the independent variables (L, D, t, f 0 c , f y , and CF) and dependent variable (P u ) are 0. 31 28 and AIJ 29 in predicting the ultimate axial load of CFSST columns is evaluated in this section. In addition, the accuracy of various empirical design formulas proposed by Giakoumelis and Lam, 13 Lin et al., 2 Wang et al. 30 and Patel et al. 50 in predicting their ultimate axial load under axial loading is also investigated. Eurocode 4 specified a local plate slenderness limit D t f y 235 ≤ 90 beyond which the local buckling of the steel tube needs to be considered. Wang et al. 80 modified the Eurocode 4 slenderness limit to D t f y 235 E s 210000 À Á ≤ 90 to account for the differences observed in yield strength (f y ) of steel and elastic modulus (E s ) of stainless steel and carbon steel. Chan and Gardner 81 proposed a formula to calculate the effective area for the unfilled steel tube exceeding the limit specified by Eurocode 4. This formula, which was modified by Wang et al. 80 for stainless steel tube, is used in the current study as stated in Equation (1): Eurocode 4 proposed a slenderness reduction factor (χ) which reflects the effect of column height slenderness ratio on calculating the ultimate loads of slender section as stated in Equation (2): where, χ can be calculated using Equations (3) and (4) proposed by Eurocode 3 82 : Slender/long column: Patel et al. 50 where, α is taken as 0.49 based on buckling curve "c" for CFSST columns. The relative slenderness ratio λ is expressed in Equation (5): where, N cr is the Euler buckling calculated using Equation (6): where, EI ð Þ eff is the effective flexural stiffness, which can be calculated using Equations (7) and (8): where, E s and I s elastic modulus and second moment of area of steel, respectively; E cm and I c elastic modulus and second moment of area of concrete, respectively. AISC 360-16 specified design recommendations of composite columns based on three different categories known as compact/noncompact (λ p ) and slender (λ r ) based on the local slenderness limit of the filled composite columns, calculated as D t f y E s ≤ 0:15 and D t f y E s ≤ 0:19, respectively. A compact/noncompact section can reach yield stress and obtain concrete compressive strength up to 0:95f 0 c , whereas a slender section neither reaches the yield strength nor achieve the concrete compressive strength beyond 0:70f 0 c . This is because infilled concrete has significant volumetric dilation when the compressive strength of concrete exceeds 0:70f 0 c . [83][84][85] The noncompact and slender section cannot provide sufficient confinement to the infilled concrete with significant volumetric dilation. [83][84][85] Furthermore, AISC 360-16 specified design formulae to calculate the ultimate axial load of slender/long composite columns under axial loading given in Table 2. ACI 318-19 specified the maximum local slenderness limit of the outer tube of the CFST column as D t ffiffiffi ffi beyond which the design of composite columns is not covered. For comparison purposes, the effective area of the CFSST columns that exceed this limit is calculated using the formula stated in Equation (1). AIJ considered the confinement effects of CFST columns but proposed a factor to increase the yield strength of the steel tube. Giakoumelis and Lam 13 recommended that the compressive strength of core concrete be increased using a factor of 1.3. Wang et al. 30 proposed formulas for the strength enhancement of steel and concrete in CFST columns based on extensive numerical data. Patel et al. 50 employed a similar confinement model of CFST columns encompassing carbon steel; however, recommended that the strain-hardening exponents for stainless steel be used based on the numerical data. Lin et al. 2 proposed a unified model to predict the ultimate axial load of CFST short columns with various cross-sections. A slenderness reduction factor proposed in an early study conducted by Lin et al. 19 can be used to calculate the ultimate axial load of CFSST slender columns, as given by Equation (9): Table 2 presents the empirical design formulas used to predict the ultimate axial load of CFSST columns using various design models. It should be noted that as the test database consists of the experimental test results of some CFSST long columns, the effect of column height slenderness ratio is considered for the design models specified by ACI 318-19, GB50936-2014, DBJ 13-51-2010, AIJ, Giakoumelis and Lam, 13 Wang et al. 30 and Patel et al. 50 using the slenderness reduction factor (χ) proposed by Eurocode 3, 82 given in Equation (3).

| EVALUATION OF THE ACCURACY OF THE EXISTING EMPIRICAL MODELS
The comparisons of the predicted ultimate axial load of CFSST columns using various design models are presented in Figure 3. It can be seen that those design models proposed by Eurocode 4 and Giakoumelis and Lam 13 obtained a mean prediction-to-test ultimate axial load close to unity. However, for some CFSST columns, there were significant differences between the experimental test results and the design predictions. The ultimate axial load of CFSST columns was overestimated by the design models of  30 Patel et al., 50 Giakoumelis and Lam, 13 and Lin et al. 2 were calculated as 0.122, 0.103, 0.089, 0.175, 0.103, 0.149, 0.106, 0.121, 0.116, and 0.121, respectively. It can be seen that there are significant deviations in the design prediction specified by the design models. Among all the design models, ACI 316-19 was found to be the most conservative which was due to the negligence of the confinement in design consideration. On the other hand, the design models proposed by DBJ 13-51-2010 and Lin et al. 2 were demonstrated to be the most unconservative ones. In addition, Figure 4 shows the effect of different parameters of CFSST columns on accurate design prediction of the ultimate axial load of CFSST columns. The following trends can be observed from the comparisons: • DBJ 13-51-2010 exhibited an ascending trend in predicting the ultimate axial load with the increase of the column length and concrete compressive strength. • GB50936-2014 and Giakoumelis and Lam 13 showed an ascending trend in predicting the ultimate axial load with the increase of the D/t ratio of the columns.
• DBJ 13-51-2010 and GB50936-2014 showed a descending trend in predicting the ultimate axial load with the increase of the steel-proof stress. • DBJ 13-51-2010, GB50936-2014, and Giakoumelis and Lam 13 showed a descending trend in predicting the ultimate axial load with the increase of confinement factor. • All the design models showed a descending trend in predicting the ultimate axial load with the increase of the column length slenderness ratio.

| OVERVIEW AND DEVELOPMENT OF ML MODELS
This section provides an overview and develops several ML algorithms, including DT, RF, KNN, AdaBoost, GBRT, and XGBoost to predict the ultimate axial load. A machine learning package developed in Python, Scikit-learn 86 is used to build the ML models. The following sections describe the overview of the ML methods used in this study.
Comparisons of the test and predicted ultimate strengths of circular CFSST columns.

| Decision tree (DT)
DT uses training data to generate a tree-like model. 87 The DT model has three nodes: the root node, the decision node (also known as the internal node), and the terminal node (also known as the leaf node). The algorithm starts at the root node with all training data followed by the root node splitting into decision nodes. This process continues for the subsequent levels until the tree meets a pre-defined maximum depth or when the nodes have only one sample of the training data. Figure 5 shows the DT structure with nodes.

| Random forest (RF)
RF is a combination of multiple decision trees that are constructed from the input features using the (a) L (mm)   tree classifiers using the bootstrap replacement method. 88 This algorithm encompasses two stages: First, the RF is developed, and in the second step, predictions are made based on the classifiers developed in the first stage. Figure 6 shows the typical flowchart for RF.

| K-nearest neighbors (KNN)
KNN algorithm is a non-parametric and lazy algorithm used for classification and regression purposes. 89 In KNN, the classifier selects k training samples approximate to the test sample point x and estimates based on these training samples. The most frequent outcome from the first k rows is considered as the final result. KNN encompasses three main hyper-parameters: the number of neighbors, the power parameter for the Minkowski metric, and the leaf size.

| Adaptive boosting (AdaBoost)
In AdaBoost, a base learner is trained using the training sets to update the weights. 90 The output of the AdaBoost model is the weighted combination. The main parameters of the AdaBoost algorithm are the learning rate and the number of estimators. It was first proposed by Freund and Schapire. 91

| Gradient boosting regression tree (GBRT)
GBRT first proposed by Friedman 92 combines multiple DT. The model starts with a first guess and for each step, a new DT is fitted to update the residual. GBRT prevents overfitting like some other models. 93 The main parameters of the GBRT algorithm are the learning rate, the maximum depth of the tree, and the number of estimators.

| Extreme gradient boosting (XGBoost)
XGBoost is a new boosting ML algorithm proposed by Chen and Guestrin. 94 The flowchart of the XGBoost model is shown in Figure 7. The main parameters of the XGBoost algorithm are the learning rate, the maximum depth of the tree, and the number of estimators.

| Machine learning-based ultimate axial load models
In the ML models, the input variables are considered as the length of the columns, the diameter and the thickness of the columns, the yield strength of the steel tube taken as 0.2% proof stress of the stainless steel tube, concrete compressive strength, and confinement factors whereas the output variable is considered the ultimate axial load of CFSST columns.
In order to speed up the convergence of the training process, each attribute in the data set was standardized based on the mean and SD using Equation (10): where, x 0 is the standardized value, x is the original value of the input parameter, μ is the mean of the original values, and σ is the SD of the input parameter. Evaluation of the ML learning models was based on the following standards: a coefficient of determination (R 2 ), a root mean squared error (RMSE), and a mean absolute error (MAE) which can be calculated using Equations (11)-(13), respectively: where N is the number of samples, t 1 , …,t N ½ T and o 1 ,…,o N ½ T are the actual and the predicted values, respectively, t is the average of actual values.
Generally, finding the optimal combination of hyper-parameter values can improve the performance of ML models. [95][96][97] Algorithms such as grid search (GS), random search (RS), and Bayesian optimization (BO) are commonly used to fine-tune hyper-parameters F I G U R E 7 Typical flowchart of XGBoost algorithm.
F I G U R E 8 Implementation of BO and 10-fold CV on the ML models.
F I G U R E 9 Performance of ML models with different training-testing ratios.
in ML models. 96 In GS, all hyper-parameters are combined to determine a suitable set of parameters. Therefore, the evaluation time of the model increases exponentially as more parameters are considered. However, it does not ensure that the optimal solution is found. 96 RS attempts to create an optimal set of hyperparameters by combining random hyper-parameter combinations. The weakness of this method lies in the unnecessarily high variance. 96 It is important to note that both the GS and RS methods require many trials, which can be time-consuming. Meanwhile, BO finds the value that minimizes the objective function by considering past evaluations more efficiently. 97,98,99 As a result, this method is more generalized on the testing set and requires fewer iterations than GS and RS methods. Furthermore, BO identifies the best parameters in significantly less time than the other methods. Therefore, the BO is used to find the optimal parameters of the ML models in this study.
It is necessary to divide the entire data set into a training set and a testing set to develop the ML models. ML models are constructed using the training set, and their performance is evaluated based on the testing set. In this study, the effect of the data splitting is investigated by investigating seven training-testing ratios of 60%, 65%, 70%, 75%, 80%, 8%5, and 90% of the database are used for the training phase, corresponding to 40%, 35%, 30%, 25%, 20%, 15%, and 10% of the database for the testing phase. Moreover, crossvalidation (CV) is implemented into the training data to ensure the generalization capacity of the model on the testing data to ensure that the ML model can perform well on unseen data (testing data) and avoid overfitting.
The flowchart for implementing the BOA and 10-fold CV to the ML models is shown in Figure 8. The fitness function is the average MAE value (MAE avg ) of 10 folds. Figure 9 shows the performance of ML models with different training-testing ratios. It can be seen that all ML models perform well with the training-testing ratio of 0.90-0.10. Therefore, this ratio is used for further investigations. Figure 10 shows the progress in fine-tuning the parameters using the BO algorithm of predictive models. It should be noted that the hyper-parameters that are not presented below have default values. The optimal hyperparameters associated with each ML model are as follows: • DT: the maximum depth of the tree (max_depth) is 6, the minimum number of samples required to split an internal node (min_samples_split) is 0.08459, and the minimum number of samples at a leaf node (min_ samples_leaf) is 0.01913. • RF: the number of trees in the forest (n_estimators) is 100, the maximum depth of the tree (max_depth) is 9, and the minimum number of samples required to split an internal node (min samples_split) is 0.01000. • KNN: the number of neighbors (n_neighbors) is 1, the power parameter for the Minkowski metric (p) is 1, and leaf size (leaf_size) is 1.  Figure 11 represents the scatter plots for the predicted ultimate axial load (P u,pred ) versus the experimental value (P u,exp ) using six ML models. There is a good correlation F I G U R E 1 0 Convergence plot of predictive models using the BO algorithm.

| COMPARISON OF THE ULTIMATE AXIAL LOAD PREDICTION USING THE MACHINE LEARNING MODELS
between the experimental and predicted ultimate axial load in all developed ML models with R 2 > 99% for the training set and R 2 > 98% for the testing set. A comparison of the performance metrics for the training and testing sets further demonstrate that the created ML models with the optimal hyper-parameters have a reasonable generalization performance. Table 3 shows the quantitative measures of the six ML models. It is widely accepted that the training phase is not sufficient for assessing the models. Therefore, choosing an appropriate F I G U R E 1 1 Scatter plot of the ML models for the ultimate strength of the CFSST columns.  Figure 11 and Table 3 Figure 12 reveals a good fit of the XGBoost model since the training loss plot decreases to a stable point and has a small gap with the validation loss plot. In addition, Table 4 and Figure 13 summarize each ML model's prediction-to-test ultimate axial load ratio with the testing set. A smaller SD and a mean value closer to 1 are considered as good conditions. A mean value greater than 1.0 indicates over-prediction, while a mean value of more than 1.0 indicates under-prediction. Among the ML models, the XGBoost model provides the most accurate predictions signified by the mean value of 1.039, and the corresponding values of SD and COV of 0.082 and 0.050, respectively followed by the GBRT model with the mean value of 1.049, the SD value of 0.067, and the COV value of 0.064. The RF model also shows a reliable result with a mean value of 1.030, the SD value of 0.089, and the COV value of 0.086. The performance of the DT and KNN models seems similar, with the mean values being 0.993 and 1.024, respectively; the SD values are 0.219 and 0.214, respectively; and the COV values are 0.220 and 0.209, respectively. The AdaBoost model shows the poorest performance as signified by the highest mean values (1.524) and also the highest values of SD (0.939) and COV (0.616). Furthermore, it was found that generally all ML models provide a better estimation of the ultimate axial load of CFSST columns that exceed the slenderness limit specified by AISC 360-16. For instance, the only tested columns reported by Guo et al. 48

| SHAP-BASED IMPORTANCE FACTOR IDENTIFICATION AND WEB APPLICATION
In this section, the SHAP method 100 is used to explain the outputs of the XGBoost model, as well as to illustrate the most significant factors that affect CFSST column strength. According to this approach, each input variable is assigned a SHAP value based on its average marginal contribution. The variable with the highest absolute SHAP value is considered the most significant. An example of a single prediction plot using the XGBoost model can be seen in Figure 14a, in which the base value represents the average of the observed response F I G U R E 1 2 Learning curves of the XGBoost model.  Figure 14b, the length and color of the bars represent the significance and direction (either positive or negative) of each input variable. As can be observed in Figure 14b, the yield strength of the steel tube showed the highest effect, followed by the diameter of the columns, the thickness of the columns, the concrete compressive strength, the length of the columns, and the confinement factor. It can be seen that the yield strength of the steel tube, the diameter of the column, the thickness of the columns, the concrete compressive strength, and the confinement factor contribute to the decrease in the base value due to their negative effects. Conversely, the column length contributes to the rise in the base value due to its positive impact.
F I G U R E 1 3 Relative frequency distribution of the prediction-to-test ultimate strength ratio. Figure 15 depicts the distribution of the Shapley values across all the input variables in the dataset. The points on Figure 15 represent the Shapley values for each feature and each observation in the dataset. Each point on the chart represents a Shapley value for each input variable, which illustrates how it influences CFSST column strength, whereas the y-axis provides the input variables ranked by importance. Colors indicate the feature value from low (blue) to high (red). For example, the high value of the diameter of the column, the yield strength of the steel tube, the thickness of the column, the concrete compressive strength, and the confinement factor increase the predicted ultimate axial load of CFSST columns. Whereas, the high value of the column length decreases the predicted ultimate axial load of CFSST columns. Figure 16 shows the global importance of the input features. It is apparent that the yield strength of the steel tube, the diameter of the column, the column thickness, and the concrete compressive strength are the most influential features. Column length and confinement factor are the least influential features. Figure 17 shows the SHAP dependency and interaction plots of variables. For each variable, the variation of another variable (the most dependent one) is illustrated by color in each figure. The red dot indicates a high value, and the blue one shows a low value of the most dependent variable. Based on the SHAP dependence plot for ultimate axial load, it can be seen that L interacts with f 0 c ; D and CF are the two features with the highest interaction with t; t, f y , and f 0 c are the two features with the highest interaction with D. For example, Figure 17 shows that increasing the values of D and t also leads to an increase in the corresponding SHAP values, which indicates an increasing effect on the model output. On the other hand, the column length and the model output are inversely proportional. Furthermore, increasing the CF does not significantly affect the model output.
Using the XGBoost model, a user-friendly web application is developed to predict the ultimate axial load of CFSST columns. 101 Using the sliders and radio buttons on the web application, the user specifies the following parameters: L,  D, t, f 0 c , f y , and CF. Datasets used during ML training correspond to parameter ranges in the application. A change in input variables will cause the code to run automatically. After setting the input values, only a few seconds are required for the prediction of the ultimate axial load of CFSST columns. All web browsers, including mobile devices, can open and run the application.
Although the XGBoost model can accurately predict the ultimate axial load of CFSST columns, it is considered a "black box" due to its inability to provide explicit equations between the input parameters and the design strength of CFSST columns. To overcome this limitation, the present study proposes a simple equation based on the SHAP summary plot in Figure 15, the global importance plot in Figure 16, and the feature dependence plots in Figure 17. The equation format consists of a single product term proposed in Equation (14).
where a, b, c, d, and e are the unknown coefficients; χ the slenderness reduction factor accounting for the effect of column height slenderness ratio calculated using the Equation (9) proposed by Lin et al. 19 The Teaching Learning Based Optimization (TLBO) algorithm developed by Rao et al. 102,103 is used to determine the unknown coefficients by minimizing the root mean square error (i.e., objective function) of the experimental and predicted results. The iteration number is set as 2000 to ensure the TLBO algorithm converges. Five population sizes (i.e., 100, 200, 300, 400, and 500) are tested on the TLBO algorithm. Seven trainingtesting ratios of the data set are also used to consider the effect of the data splitting. Figure 18 shows the converged curves of different TLBO models. It is found that the TLBO model with the training-testing ratio of 0.65-0.35 combined with a population size of 400 achieves the best results. Once the unknown coefficients are obtained, the final equation is expressed as given by Equation (15): F I G U R E 1 7 SHAP dependency and interaction plots. P u,eq ¼ 0:0012 Â χ Â D 1:4958 Â t 0:4939 Â f 0 c À Á 0:3342 Â f y 0:8020 The comparison of the design prediction and the test results given in Figure 19 shows that the formula proposed in Equation (15) can accurately predict the ultimate axial load of CFSST columns and can be used for practical design. The mean prediction-to-test ultimate axial load, SD, and coefficient of variance (COV) are calculated as 0.990, 0.132, and 0.133, respectively. The accuracy of the proposed design formula and the other design models given in Section 5 is also compared in Figure 20, where it can be seen that the proposed model provides better accuracy than other models. F I G U R E 1 8 Convergence curves of TLBO model with different training-testing ratios and population sizes.

| CONCLUSIONS
This study investigates the design performance of CFSST columns under axial loading. The accuracy of the existing design empirical models and various ML models was evaluated in predicting the ultimate axial load of CFSST columns under axial loading. A test database encompassing the experimental test results of 142 CFSST columns was used to validate their design accuracy. The following outcomes can be concluded from this study:  13 Wang et al., 30 and Patel et al., 50 respectively. However, there were significant differences observed between the test and design predictions of some CFSST columns predicted using these design models, which highlighted the need for a more robust design methodology. 4. The XGBoost model outperformed the other ML models whereas the GBRT model was demonstrated to have the second-best performance. The RF, DT, and KNN also demonstrated good performance. The AdaBoost model demonstrated to have the poorest prediction. 5. Based on SHAP dependency, it was found that the length (LÞ interacts with f 0 c À Á ; the diameter (DÞ and the confinement factor interact with the thickness (tÞ; the yield strength (f y Þ, the compressive strength of concrete f 0 c À Á , and the thickness (tÞ interacts with the diameter (DÞ. 6. This study developed a web application and a simple equation to predict the ultimate axial load of CFSST columns in order to leverage the XGBoost results with less effort.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.