An efficient procedure for prediction of the load-displacement curve of CFDST columns

Over the past few years, due to the advantages of high stiffness and strength, good ductility, fire resistance, low material cost, and convenient construction, concrete-filled double-skin steel tube (CFDST) columns have been extensively utilized in real-world structures, such as high-rise buildings, infrastructures, electricity transmission towers, etc. Compared with traditional concrete-filled steel tube (CFST) columns, it offers numerous advantages, including low self-weight, high fire resistance, high ductility and energy absorption, good strength and stiffness performances, and so on. Fig. 1 depicts the general design of CFDST columns, consisting of internal and external steel tubes and concrete infill.

Research related to CFDST columns has been extensively conducted in the literature, considering experimental, theoretical, and numerical investigations of its behavior under different loading conditions [[1], [2], [3], [4]]. It is known that the load-carrying capacity of the structure is one of the critical factors describing its actual strength behavior. Based on experimental and/or numerical investigations, some previous works proposed empirical formulae to predict the ultimate load of CFDST columns under axial compression [[5], [6], [7], [8]]. In addition, design standards including ACI [9], Eurocode 4 [10], and AISC 360–16 [11] offered equations for predicting the axial capacity of CFDST columns. While the empirical and design equations are relatively simple to apply, their accuracy is constrained by the limited number of parameters considered [12,13].

With the rapid development of artificial intelligence techniques, neural network and machine learning (ML) algorithms have been widely applied for the prediction of load-carrying capacity of structures [[14], [15], [16], [17], [18], [19], [20]]. For CFDST columns, some studies have been carried out to apply ML or hybrid ML models for the strength prediction of this column under uniaxial compression based on experimental and/or numerical databases. For instance, Ipek and Guneyisi [19] proposed a numerical model for axial strength prediction of the CFDST columns using an effective soft-computing technique, namely gene expression programming based on a database of 103 tests on the CFDST columns under compression. Tran and Kim [13] suggested three data-driven models for estimating the ultimate strength of the CFDST columns subjected to uniaxial compression. The work demonstrated the superior performance of an artificial neural network (ANN) model in predicting the axial compressive strength of the CFDST columns. Recently, Vu et al. [21] proposed hybrid ML methods for the strength prediction of the CFDST columns under compressive loading based on 125 experimental databases. Based on the proposed models, a user-friendly graphical interface (GUI), that can reliably and accurately predict the ultimate load of CFDST columns with various geometry and material parameters, was developed. Zhang and Xue [22] developed two hybrid ML models, including grey wolf optimizer (GWO) combined with group method of data handling (GMDH) and random forest (RF) optimized by particle swarm optimization (PSO), to predict the axial compression capacity of CFDST columns based on 139 experiments collected from the literature. The performance of developed hybrid models was verified by comparing their predictive results with those obtained from other ML models, empirical formulae, and design standards. In addition, a sensitivity analysis was implemented to investigate the effects of different input parameter combinations on the performance of proposed models. Nguyen and Ly [23] proposed hybrid ML models to estimate the axial compressive strength of CFDST columns using 153 experimental datasets. Three metaheuristic optimization algorithms were employed to fine-tune hyperparameters of the predictive models. It was reported that the finely tuned gradient-boosting regression model, optimized with the artificial rabbits optimization algorithm, outperformed other models and conventional benchmarks in predicting column strength. Furthermore, the developed model was applied to optimize the geometry and materials of CFDST columns, maximizing their capacity. Hong et al. [24] presented a data-driven framework adopting ML approaches to predict the axial compressive capacity of circular CFDST columns based on experimental and numerical databases. The results proved that the K-nearest neighbor (KNN) model presents superior performance compared to other ML models considered. More recently, Zarringol et al. [25] proposed an ANN-based equation and graphical user interfaces (GUIs) in MATLAB and Python to predict the axial compressive strength of CFDST short and slender columns with both normal- and high-strength materials. Two ML models were trained and tested on 1721 databases, consisting of 129 experimental results and 1592 finite element (FE) simulation results. The findings revealed that the ML models, along with the proposed ANN-based equation, outperformed other models and existing design methods in terms of accuracy.

As mentioned earlier, it is evident that ML or hybrid ML models can offer highly accurate predictions of the axial compression capacity of CFDST columns with a wide range of parameters involved. However, most ML applications related to CFDST columns solely focus on predicting axial compression capacity, rather than their load-displacement response. It is noted that the load-displacement curve of the structure reflects a better structural response than its axial compression capacity alone. In practical design, understanding the load-displacement curve of the structure helps engineers adjust input parameters to improve structural response of the selected design. Therefore, predicting the load-displacement curve provides better insight into the structural behavior rather than predicting only its ultimate load. However, research related to the prediction of this curve of the structure is limited. Zarringol and Thai [26] developed an ANN model mapping the load-shortening curves of CFST columns with rectangular and circular cross-sections. To predict this curve, the proposed method was used to predict some key parameters (i.e., ultimate load, corresponding displacement to the ultimate load, and factors describing ascending and descending strength responses) involved. Generally, this method can only provide an accurate prediction of the ascending response but not the descending part of the curve. Fan et al. [27] developed the (Long Short-Term Memory) LSTM model to estimate the load-strain curves of CFST columns subjected to axial compressive loading. In their study, the curve was divided into some key points, where the developed model was used to identify these points as output parameters. Strain values were fixed within a specified range, while the effects of CFST column properties on the load-strain curve, including geometric and material strength, were accounted for through a data configuration process that adjusted the length in strain increments. Although the predictive curves obtained from the developed model were generally good, each step of the curve is not accurately defined since the approach comes with some weaknesses in both data configuration process and the LSTM algorithm. On the other hand, research on the estimation of load-displacement responses for CFDST columns is very limited. Recently, Yeong and Li [28] applied six ML algorithms to estimate the yield, ultimate strength and failure points, allowing them to reconstruct the load-strain curve for CFDST columns. The predictive results were compared to experimental data. While the models showed a general trend that matched the load-strain curves of the test columns, they failed to accurately estimate the full load-strain curves. In addition, the experimental database used to train models was limited to only 143 test curves, which may restrict the model applicability to a broader range of cases. Furthermore, no sensitivity analysis was conducted to evaluate model accuracy across different parameter ranges. Lastly, ML models developed by the authors are black-box models. They did not provide any tools such as a graphical user interface (GUI) or web application to predict the load-strain curves of CFDST columns. There is a challenge for users to apply these models in practical design purposes, especially for those who are not familiar with computer programing or ML techniques. For this reason, it is necessary to apply a ML approach to develop an efficient framework for accurately estimating the entire load-shortening curves of CFDST columns for practical design purposes.

This paper therefore develops a CNN-based model to predict both the load-shortening response and load carrying capacity of CFDST columns subjected to uniaxial compression. The developed model is constructed on hybrid databases incorporating experimental databases collected from tests reported in literature with numerical databases obtained through FE simulations. The performance of the proposed CNN-based model is validated by comparing its predictions with testing databases. Following this, an efficient procedure is developed to improve the accuracy and efficiency of predicted results provided by the CNN-based model. Subsequently, a sensitivity analysis is conducted to evaluate how variations in input variables within stochastic environments affect the performance and stability of the developed model in predicting the load-displacement curves of CFDST columns. Finally, a cloud-based graphical user interface (GUI) is built under Hugging Face platform for a wide range of users to estimate the axial load-displacement curve of CFDST columns without special expertise in computer programing.