Prediction of Ultimate Load of Rectangular CFST Columns Using Interpretable Machine Learning Method - Tien-Thinh Le; Hieu Chi Phan (Advances in Civil Engineering)
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.