Prediction of Ultimate Load of Rectangular CFST Columns Using Interpretable Machine Learning Method

Tien-Thinh Le,Hieu Chi Phan,Rizal Rashid

doi:10.1155/2020/8855069

Abstract

The ultimate compressive load of concrete-filled steel tubular (CFST) structural members is recognized as one of the most important engineering parameters for the design of such composite structures. Therefore, this paper deals with the prediction of ultimate load of rectangular CFST structural members using the adaptive neurofuzzy inference system (ANFIS) surrogate model. To this end, compression test data on CFST members were extracted from the available literature, including: (i) the mechanical properties of the constituent materials (i.e., steel’s yield strength and concrete’s compressive strength) and (ii) the geometric parameters (i.e., column length, width and height of cross section, and steel tube thickness). The ultimate load is the output response of the problem. The ANFIS model was trained using a hybrid of the least-squares and backpropagation gradient descent method. Quality assessment criteria such as coefficient of determination (R2), root mean square error (RMSE), and slope of linear regression were used for error measurements. A 11-fold cross-validation technique was employed to evaluate the performance of the model. Results showed that for the training process, the average performance was as follows: R2, RMSE, and slope were 0.9861, 89.83 kN, and 0.9861, respectively. For the validating process, the average performance was as follows: R2, RMSE, and slope were 0.9637, 140.242 kN, and 0.9806, respectively. Therefore, the ANFIS model may be considered valid because it performs well in predicting ultimate load using the validated data. Moreover, partial dependence (PD) analysis was employed to interpret the “black-box” ANFIS model. It is observed that PD enabled us to locally track the influence of each input variable on the output response. Besides reliable prediction of ultimate load, ANFIS can also provide maps of ultimate load. Finally, the ANFIS model developed in this study was compared with other works in the literature, showing that the ANFIS model could improve the accuracy of ultimate load prediction, in comparison to previously published results.

Highlights

Concrete-filled steel tubular (CFST) structural members exhibit very interesting properties, as they combine the advantages of the two constituent materials
Partial dependence (PD) analysis was applied in order to interpret the “black-box” adaptive neurofuzzy inference system (ANFIS) model, which elucidated the influence of each variable on the output response
An initial Sugeno-type fuzzy inference system (FIS) was generated, as illustrated in Figure 4. e parameters of this initial FIS are indicated in Table 3, showing the membership function type and the number of linear and nonlinear parameters

Summary

Introduction

Concrete-filled steel tubular (CFST) structural members exhibit very interesting properties, as they combine the advantages of the two constituent materials. Al-Khaleefi et al [60] introduced a neural network model for studying the fire resistance of CFST members, taking account of different structural, material factors, and loading conditions. Tran et al [21] developed a neural network-based model to predict the load-bearing capacity of square CFST columns. Erefore, more investigations are required to assess the potential applications of AI-based models for studying axial behavior of rectangular CFST columns, especially in the highly topical context of high-rise construction. Is work is devoted to the prediction and influence of variables on the ultimate load of rectangular CFST columns, using the adaptive neurofuzzy inference system (ANFIS) model. It should be noted that ANFIS has not yet been used, in the literature, for studying rectangular CFST members and highlighting the influence of variables on the macroscopic properties. Partial dependence (PD) analysis was applied in order to interpret the “black-box” ANFIS model, which elucidated the influence of each variable on the output response

Materials and Methods

Machine Learning Method

Interpretation of Machine Learning Method

Results and Discussion

Gaussian 2 4 Linear 48 28 76 1000 Root mean square error 11 folds

Conclusion and Outlook