Prediction of Mechanical Properties of the Stirrup-Confined Rectangular CFST Stub Columns Using FEM and Machine Learning

Abstract

In this study, a machine learning method using gradient boost regression tree (GBRT) model was presented to predict the ultimate bearing capacity of stirrup-confined rectangular CFST stub columns (SCFST) by using a comprehensive data set and by adjusting the selected parameters indicated in the previous research (B, D, t, ρ_sa, f_cu, f_s). The advantage of GBRT is its strong predictive ability, which can naturally handle different types of data and very robust processing of outliers out of space. The comprehensive data set obtained from the FEM method which has been verified the accuracy and rationality by the existing literature. In order to make the data group closer to the engineering example, a large amount of experimental data collected in the literature was added to the data group to enhance the accuracy of the model. We compare a few regression models simply and the results show that the GBRT model has a good predictive effect on the mechanical properties of CFST columns. In summary, it can help pre-investigations for the CFST columns.

1. Introduction

After years of research, the concrete-filled steel tube (CFST) column has discovered many structural advantages. Among them, its superior seismic performance makes this structure widely used in super high-rise buildings in earthquake-prone areas [1]. However, the existed studies show that, the ductility of traditional thin-walled CFST columns may not satisfy strong earthquake demands [2]. However, in the engineering practice, thick-walled steel tube may cause problem of welding quality and undesirable cumbersome structures. For this reason, Ding et al. [3] carried out a series of experiments about a new structural form of thin-walled concrete-filled steel tubular column with stirrups. In the preliminary work, a lot of experiments were carried out to determine the optimal form of stirrups [3]. The influence of different stirrup forms on the ultimate bearing capacity and the final failure form of the CFST has been studied in depth. The results show that bidirectional stirrups are the most satisfactory for improving the overall performance of the CFST column, followed by loop stirrups.

The size and seismic performance of columns in super high-rise buildings have always been a problem that plagued structural engineers. The structural form of stirrup-confined CFST columns provides a new direction for solving this problem [4]. According to the above research results, the stirrup-confined CFST columns have the advantages of reducing the wall thickness of the steel tube while increasing the bearing capacity and rigidity. The working mechanism of the stirrups restraint is to provide a considerable restraint effect on the core concrete under the axial load. At the same time, the stirrups can support the steel tube walls on both sides to reduce local buckling deformation. The stirrups make the connection between the materials closer, and give full play to the advantages of the steel structure and the filled concrete. However, for promoting the stirrup-confined CFST columns, more deep research on its mechanical property and engineering application is needed. Due to the limitation of experimental conditions and experimental funds, it is impractical and arduous to analyze all mechanical properties and predict engineering values such as bearing capacity through experimental results.

Hence, the priority of this study is to use the finite element calculation software and programming software to accurately simulate the axial compression performance and predict the ultimate bearing capacity of concrete-filled rectangular steel tubular (RST) and stirrup-confined concrete-filled rectangular steel tubular (SST). In this way, the pre-research can be completed with lower material and time costs. The research results of machine learning in the civil engineering field [5,6,7,8,9,10] indicated that the powerful ability of aided design and prediction in the practical engineering applications. This enables civil engineers to predict the structural performance of concrete members rapidly using the trained machine learning model, which has been shown to capture the complicated non-linear relationship between concrete structures with its influencing parameters and providing highly accurate strength estimations. Therefore, these techniques are increasingly making their presence in the civil project. In brief, the machine learning is a modeling method that iteratively establishes the relationship between the input and output of a given data set through algorithm iteration. The advantage of this algorithm is that it can automatically generate a model based on the input historical data according to the iteration rules of the selected model. Once the model is built and tested, the output value of the newly generated input information can be predicted in a short time. Rafiei et al. [11] presented a novel deep restricted Boltzmann machine for estimating concrete properties based on mixture proportions. The effectiveness of the model is compared with two others widely used neural network/machine learning models: back propagation neural network and support vector machine. Masoud et al. [12] derived a new design equation for the assessment of shear resistance of steel fiber-reinforced concrete beams utilizing multi-expression programming (MEP). Vanessa et al. [13] demonstrate the application of random forest machine learning methods to predict the coefficient of thermal expansion of concrete and other properties from a database of Wisconsin concrete mixes. Prayogo et al. [14] presented a novel artificial intelligence technique based on two support vector machine models and symbiotic organisms search algorithm, called “optimized support vector machines with adaptive ensemble weighting”, to predict the shear capacity of reinforced-concrete deep beams.

In this study, the gradient boosting regression tree (GBRT) model is applied to establish the relationship between parameters and bearing capacity to achieve accurate and rapid prediction of the bearing capacity of components. First, based on the experimental data, ABAQUS software is used to establish the finite element model (FEM) for analysis to obtain corresponding data results for model training and testing. Then, in order to improve the generalization capability of the model, a simple feature selection is performed on the original data before the model training to achieve data dimensionality reduction. Finally, the GBRT model is established according to the target object, and the optimal prediction model is obtained by adjusting the factors. The workflow of this process is shown in Figure 1.

2. Experimental Data Set

In order to make the prediction results more convincing and closer to the engineering application, we collected the test data of the existing research as part of the data group to be added to the training and as the final verification. These data include: 48 experimental data from Ding [3,4,15], 8 experimental data from Chen [16], 9 experimental data from Rao [17], 9 experimental data from Qu [18], 10 experimental data from Jing [19], 6 experimental data from Hu [20]. Among these data, 10 groups of data from Ding [15] are taken as validation data groups, and the rest are training data groups. Figure 2 illustrates the details for the SCFST columns. The cross-sections of experimental specimens with four different aspect ratios (B/D) are shown in

Table 1. Sectional forms of specimens.

Aspect Ratio	B/D = 1	B/D = 1.5	B/D = 2	B/D = 3
RST
SST

.

After sorting out the conclusions of the literature, six essential factors affecting the ultimate bearing capacity of CFST columns are used as input variable sin the GBRT to estimate that. The factors are as follows and details data are given in

Table 2. The details for geometrical factors of specimens.

Variables	Unit	Min	Max	Mean
X1 = section length (B)	mm	121	601	266.3
X2 = section width (D)	mm	100	300	188.1
X3 = steel tube thickness (t)	mm	2	7.36	4.57
X4 = equivalent stirrup ratio(ρsa)	%	0	1.1	0.2
X5 = concrete compressive strength (fcu)	MPa	23.8	70.8	40.3
X6 = yield strength of steel tube(fs)	MPa	235	750	360.9
Y = ultimate bearing capacity of CFST columns (N)	KN	1000	8456	3477.8

: section length (B); section width (D); steel tube thickness (t); equivalent stirrup ratio defined as ρ_sa = ρ_sv × f_sv/f_s, where ρsv is the stirrup ratio; concrete compressive strength (f_cu); yield strength of steel tube (f_s). The remaining factor is the ultimate bearing capacity of CFST columns (N).

3. FEM Model

The accuracy of machine learning model prediction data depends on whether the amount of data used for model training and inspection is sufficient. Considering the burden of experimental cost and the investment of time cost, experimental methods alone cannot meet the requirements of data quantity and diversity.

Therefore, it is necessary to establish a large number of three-dimensional solid finite element models with different parameters by using ABAQUS finite element software to obtain bearing capacity data.

3.1. FEM Model

The element properties of the established model are as follows: the concrete, steel tube, and loading slab are all three-dimensional solid elements (C3D8R) with eight-node reduced integral format. The stirrups adopts three-dimensional truss element (T3D2). The structured meshing result is shown in Figure 3.

The contact mode between concrete and steel tube simulates the interaction between the two by setting the finite slip of the surface-to-surface contact in the horizontal direction and the hard contact in the normal direction. When setting the horizontal contact mode, it is necessary to set the corresponding friction coefficient to simulate and calculate the shear stress between the steel tube and the concrete. In the previous research, Baltay and Gjelsvik [21] determined the friction coefficient between the concrete and the steel tube through a large number of experiments, the result shows that the value should be between 0.3 and 0.6 and in this study, it was selected as 0.5. In the model, tie constraints were used between the loading plate and the concrete filled steel tube. The stirrups were merged with steel tube and embedded in concrete.

A concrete constitutive model of CFST columns under axial loading proposed in literature [22] was adopted in this finite element analysis, which is a modified model under triaxial compression presented by Ottosen [23]. The stress-strain relationship is described as:

$$y=\{\begin{array}{ll}\frac{kx+(m-1)x^2}{1+(k-2)x+m{x}^2}& x\le 1\\ \frac{x}{{\alpha }_1{(x-1)}^2+x}& x>1\end{array}$$

(1)

where y = σ/f_c and x = ε/ε_c is the stress and strain ratios of the core concrete to the uniaxial compressive concrete respectively. σ and ε are the stress and strain of the core concrete. f_c = 0.4f_cu^7/6 is the uniaxial compressive strength of concrete, where f_cu is the compressive cubic strength of concrete. ε_c is the strain corresponding with the peak compressive stress of concrete, where ε_c = 383f_cu^7/18 × 10⁻⁶. The parameter k is the ratio of the initial tangent modulus to the secant modulus at peak stress. M = 1.6(k − 1)² is a parameter that controls the increase in the axial stress-strain relationship and the decrease of the elastic modulus branch. For a CFST column, Parameter α₁ is taken as 0.15. More information of the concrete model could be found in reference [22].

The concrete damage plasticity model proposed by Ding [24] had been proven to be applicable to the finite element simulation analysis of various CFST columns with different cross-sections under axial compression. Poisson’s ratio (E_s) of the core concrete in elastic phase is 0.2; the eccentricity is 0.1; the ratio of initial iso-biaxial compressive yield stress to initial uniaxial compressive yield stress (f_b0/f_c0) is 1.225 [25]; the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian is taken as 2/3; the viscosity parameter is 0.005; and the dilatancy angle (θ) is 40°.The CFST column model established with the above parameters has been verified in the literature [24,25,26], and it can accurately simulate the axial compression performance of CFST columns with various cross-sections.

On the basis of a large number of experimental studies on the mechanical properties of steel, an isotropic strain hardening elasto-plastic constitutive model [24] considering the Prandtl–Reuss flow law and the Von Mises yielding criteria was used to describe the constitutive behavior of the steel in FEM models. The stress-strain relationship is described as:

$${\sigma }_{\mathrm{i}}=\{\begin{array}{cc}{E}_{\mathrm{s}}{\epsilon }_{\mathrm{i}}& {\epsilon }_{\mathrm{i}}\le {\epsilon }_y\\ f_s& {\epsilon }_{\mathrm{y}}<{\epsilon }_{\mathrm{i}}\le {\epsilon }_{\mathrm{st}}\\ f_s+\zeta E_{\mathrm{s}}({\epsilon }_{\mathrm{i}}-{\epsilon }_{\mathrm{st}})& {\epsilon }_{\mathrm{st}}<{\epsilon }_{\mathrm{i}}\le {\epsilon }_{\mathrm{u}}\\ f_{\mathrm{u}}& {\epsilon }_{\mathrm{i}}>{\epsilon }_{\mathrm{u}}\end{array}$$

(2)

where, σ_i and ε_i are the equivalent stress and strain of the steel tube; f_y, f_u (=1.5f_y) and E_s (=2.06 × 10⁵ MPa) is the yield strength, ultimate strength, and elastic modulus of steel, respectively; ε_y, ε_st and ε_u is the yield strain, hardening strain, and ultimate strain of steel, respectively, in which ε_st = 12ε_y and ε_u = ε_st+ 0.5f_s/(ζE_s) = 120ε_y. The parameter ζ is taken as 1/216.

3.2. Parameter Setting of Finite Element Analysis

According to statistics, the calculation results of the SCFST stub columns model established by the above constitutive relation are as follows:

In the study of square SCFST stub columns [3], the average ratio of the experimental results (N_u,o) to the results of load-bearing capacity modeled by FE (N_u,c) was 1.031 with a dispersion coefficient of 0.059. In the study of rectangular SCFST stub columns [15], N_u,o to N_u,c was 1.035 with a dispersion coefficient of 0.020. In the study of circular SCFST stub columns [26], N_u,o to N_u,c was 1.014 with a dispersion coefficient of 0.045. It can be seen that this modeling method can accurately predict the ultimate bearing capacity of the SCFST stub columns.

Therefore, 306 samples (90 experimental data and 216 FEM samples) were prepared for model training and checking. Some typical example factors are shown in

Table 3. Properties of specimens.

No	B × D × t/mm	B/D	ρsa	fcu/MPa	fs/MPa	Nu,fe/kN
1	500 × 500 × 5	1	0	60	345	16,241.7
2	500 × 500 × 5	1	0.005	40	235	12,006.1
3	750 × 500 × 6	1.5	0	60	420	25,516.3
4	750 × 500 × 6	1.5	0.015	60	235	26,049.7
5	1000 × 500 × 7	2	0	80	345	41,876
6	1000 × 500 × 7	2	0.01	40	345	28,674.6
7	1500 × 500 × 7.5	3	0	100	345	76,863.2
8	1500 × 500 × 7.5	3	0.007	40	235	35,168.5
9	500 × 250 × 4	2	0	38	323	6367.6
10	500 × 250 × 4	2	0.006	43	314	7637.58
11	375 × 250 × 3	1.5	0	48	354	5853.86
12	375 × 250 × 3	1.5	0.004	58	374	7268.44
13	400 × 200 × 4	2	0	63	382	6607.28
14	400 × 200 × 4	2	0.005	53	356	6220.35

. According to the research of the existing scholars, seven main factors affecting the bearing capacity of the specimen are selected as the eigenvalue, and the aspect ratio can be calculated by B/D, so it is not treated as an effective feature to delete it from the sample.

4. Property Prediction Based on Gradient Boosting Regression

4.1. The Model Selection

The dataset is divided into training set and testing set randomly with the proportion of about three to one, which the numbers of samples in each set are 231 and 75 respectively. Based on the data set, we compared a few regression models simply to find out which one is more suitable for our study, including linear regression (LR), K-neighbor regression (KNN), ridge regression (Ridge), lasso regression (Lasso), decision tree regression (DTR), extra tree regression (ETR), random tree regression (RTR), adaptive boosting regression (ABR), gradient boosting regression tree (GBRT) and bagging regression (BR). The Figure 4 presents the score and the average error of each model given in Equation (3) [27].

$$\begin{array}{c}{R}^2=(1-u/v)\\ u={\displaystyle \sum {(y_{true}-y_{pred})}^2}\\ v={\displaystyle \sum {(y_{true}-\frac{{\displaystyle \sum y_{pred}}}{N})}^2}\\ <error>=\frac{{\displaystyle \sum (|y_{true}-y_{pred}|/y_{true})}}{N}\end{array}$$

(3)

It can be seen from Figure 4 that GBRT has the best performance in all models. Therefore, we use the GBRT models for our prediction, which is proposed by the Friedman et al. [28,29,30]. GBRT is belonging to ensemble methods which fundamental concept is to get a better robustness by combining several base estimators using a given learning algorithm. For the boosting methods, base estimators are built in sequence and each estimator tries to reduce the bias of the model [31]. The motivation is to make an ensemble more powerful through combining several weak models. The GBRT model has advantages in handling of mixed type data and the predictive power. The algorithm (Algorithm 1) for GBRT is shown as follow:

Algorithm 1 Gradient Boost

1     ${\mathrm{F}}_0\left(\mathrm{x}\right)=\arg {\min }_{\mathsf{\rho }}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}\mathrm{L}\left({\mathrm{y}}_{\mathrm{i}},\mathsf{\rho }\right)$ 2     $\mathrm{For} \mathrm{m}=1 \mathrm{to} \mathrm{M}$ do: 3               ${\tilde{\mathrm{y}}}_{\mathrm{i}} =-{\left[\frac{\partial \mathrm{L}\left({\mathrm{y}}_{\mathrm{i}},\mathrm{F}\left({\mathrm{x}}_{\mathrm{i}}\right)\right)}{\partial \mathrm{F}\left({\mathrm{x}}_{\mathrm{i}}\right)}\right]}_{\mathrm{F}\left(\mathrm{x}\right)={\mathrm{F}}_{\mathrm{m}-1}\left(\mathrm{x}\right)},\mathrm{i}=1,\mathrm{N}$ 4               ${\mathrm{a}}_{\mathrm{m}}=\arg \underset{\mathrm{a},\mathsf{\beta }}{\min }{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\left[{\tilde{\mathrm{y}}}_{\mathrm{i}}-\mathsf{\beta }\mathrm{h}\left({\mathrm{x}}_{\mathrm{i}};\mathrm{a}\right)\right]}^2$ 5               ${\mathsf{\rho }}_{\mathrm{m}}=\arg {\min }_{\mathsf{\rho }}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}\mathrm{L}\left({\mathrm{y}}_{\mathrm{i}},{\mathrm{F}}_{\mathrm{m}-1}\left({\mathrm{x}}_{\mathrm{i}}\right)+\mathsf{\rho }\mathrm{h}\left({\mathrm{x}}_{\mathrm{i}};{\mathrm{a}}_{\mathrm{m}}\right)\right)$ 6               ${\mathrm{F}}_{\mathrm{m}}\left(\mathrm{x}\right)={\mathrm{F}}_{\mathrm{m}-1}\left(\mathrm{x}\right)+{\mathsf{\rho }}_{\mathrm{m}}\mathrm{h}\left(\mathrm{x};{\mathrm{a}}_{\mathrm{m}}\right)$ 7     End for

4.2. Discussion

The algorithm for the gradient boost algorithm is shown in Figure 5 [28]. $L\left(y_i,\rho \right)$ and $h\left(x_i;a\right)$ are the loss function and estimator (“base learner”) function, respectively. The arguments for the GBRT are divided into two kinds: the arguments for the boosting method and the ones for the regression tree. We first focus on the arguments for the boosting method. Based on the modeling process, the major factors that affect the performance are the loss function, the learning rate and number of the estimators. When the features and labels of the sample are fixed, the objective of the model is to minimize the loss function and determine all the GBRT factors. For the superior computational properties, the loss function $L\left(\mathbf{Y},F\left(x\right)\right)$ in the algorithm is adopted as the least squares [32] in this paper.

$$L(Y,F(X))={\displaystyle \sum _{i=1}^N{(y_i-F(x_i))}^2}$$

(4)

In the equation, $\mathbf{Y}$ is the vector of the actual values that are the ultimate strength $N$, while $F\left(X\right)$ is the predicted value. The subscript $i$ is the label of the $i$th sample. By keeping the remaining arguments default, the prediction errors of the different learning rates and numbers of estimators based on the selected learning rate are shown in Figure 5. In theory, a smaller rate and more estimators lead to a better accuracy. However, this may cause a higher risk of overfitting and deteriorate the performances of the model. Meanwhile, this leads to that the average error decreases with the increasing learning rate in Figure 5 in a certain range. Through integrating the results from Figure 5 and a variety of factors (such as the computation speed and overfitting), we obtain the learning rate is 0.1 and the number of estimators is 1000.

For the regression tree, the size of the base learner determines the degree of variable interactions captured by GBRT. The interactions of order can be captured by a tree with depth $\mathrm{h}$. There are two ways to control the size of the regression trees [27]: (a) as the depth of the tree is fixed, a tree with (at most) $2^{\mathrm{h}}$ leaf nodes and $2^{\mathrm{h}}-1$ internal nodes will be built. (b) Meanwhile, the size of the tree can be controlled by specifying the number of leaf nodes. For a better accuracy rate, we control the size by changing the depth of the tree. Figure 6 gives the average error for different depths of GBRT and the prediction results of the tree depths of 2, 4 and 8. It can be seen from the Figure 6a that the model shows the good ability of prediction as the tree depth reaches 3. Further, when the depth is 4, the average error meets a minimum level. Then the error increased gradually with the increasing tree depth. Figure 6b–d also indicate that the bias of the model with the tree depth of 8 is obviously larger than others. The reason for this is that the overfitting problem is more serious than the under fitting problem due to the relatively small data set. When the depth of the tree reaches a threshold value, the model captures a large number of sequential interactions from the training set, resulting in overfitting problems and performance degradation. Nonetheless, there is still the risk of under fitting. A significantly greater average error appeared as the tree depth of 1 in Figure 6a. This is a typical under fitting problem.

To facilitate modeling, the random seed for dividing the data set is fixed. Therefore, the error distributions for different random seeds are given in Figure 7 and the histogram of errors for the different random seeds is shown in Figure 8. In Figure 7a, the distribution of the errors focuses on the range 0 to 0.08. It is obviously seen from Figure 7 and Figure 8 that the relative errors are most distributed to the range 0 to 0.01. However, there exist a few samples with relative error that exceeds 0.05.

Table 4. Ultimate strengths of samples whose relative error exceeds 0.05.

Seed#1		Seed#2			Seed#3				Seed#4
${\mathit{N}}_{\mathit{t}\mathit{r}\mathit{u}\mathit{e}}$	${\mathit{N}}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$	$\mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$	${\mathit{N}}_{\mathit{t}\mathit{r}\mathit{u}\mathit{e}}$	${\mathit{N}}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$	$\mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$	${\mathit{N}}_{\mathit{t}\mathit{r}\mathit{u}\mathit{e}}$	${\mathit{N}}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$	$\mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$	${\mathit{N}}_{\mathit{t}\mathit{r}\mathit{u}\mathit{e}}$	${\mathit{N}}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$	$\mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$
4443	4721	0.063	5765	6425	0.103	3513	3513	0.104	3250	2852	0.122
2516	2651	0.053	9910	9041	0.096	3450	4027	0.167	6572	6190	0.058
3750	3944	0.051	2708	2345	0.064	2910	2284	0.215
3470	4045	0.166	9103	8236	0.105	2318	2193	0.054
2920	2687	0.080				1917	2236	0.166
						11,085	11,673	0.053

presents the detail of the ultimate strengths for corresponding samples with the larger error is shown. In Table 4, $N_{true}$ and $N_{pred}$ are true value of the ultimate bearing capacity and the predicted value, respectively. As shown in Table 4, all the ultimate strengths of those sample are less than 10,000 $\mathrm{Mpa}$. Meanwhile, most of the sample with a larger relative error has a smaller ultimate strength that is less than 10,000 $\mathrm{Mpa}$. The reason for this may be that the absolute error can lead to a larger relative error in the sample with small carrying capacity. Further, for the experiments with smaller samples, randomness can cause a more obvious difference. An obvious bias of model is caused by the above reasons in the small samples. However, the average error of the models with different random seeds almost is less than 0.02. Furthermore, the feature importance of the model with random seed #2 is shown in Figure 9. As is shown in Figure 9, the bearing capacity heavily depends on the size of the specimen and cubic compressive strength of concrete, which have been found in our previous research [15].

For the further understanding of the factor on the performance of the model [33], we illustrate the distribution of the Size $\mathrm{B}$ of the data set in the Figure 9 since Size $\mathrm{B}$ has the maximum effect. The Figure 10 shows that the samples distribute in range from 100 to 1500 and all experiment samples are in this range (the number of FEM and experimental samples is 216 and 90, respectively). Therefore, the performance more dependent on the FEM data and the accuracy of the prediction is affected by the accuracy of the FEM mode. Meanwhile, the experimental sample modified the prediction with certain extent. For those reasons, the prediction of the GBRT model has the high accuracy. In the experiments, the smaller size samples are more adopted due to the limit of the experimental facility and the expenditure. Therefore, the large size samples (72 samples which size is larger than 1000 mm) are added into the dataset to accord with the practical application.

5. Conclusions

In this research, a new method for predicting the bearing capacity of stirrup-confined rectangular CFST stub columns was proposed. This method combines the characteristics of FEM and machine learning to establish GBRT model to accurately predict the bearing capacity of stirrup-confined rectangular CFST stub columns. Furthermore, the GBRT prediction models efficiently satisfy different external validation phases. The final explanatory variables (B, D, t, ρ_sa, f_cu, f_s) were selected after developing different models with different combinations of the input factors. The results show that the GBRT model is suitable for data sets that have both binary and continuous features. For example, the ultimate bearing capacity of CFST data set in this article. The model does not need to scale the data, and by spending a certain amount of training time to fine-tune the factors, extremely accurate prediction results can be obtained, which is more in line with actual engineering applications. The errors are mostly from the accuracy of FEM model and the randomness of the experiments. However, the experimental data modified the prediction in a certain extent. Therefore, in summary, the model can be used for practical design purposes since it was derived from experiments on CFST columns with a wide range of geometrical and mechanical properties.