Parametric Investigation of Particle Swarm Optimization to Improve the Performance of the Adaptive Neuro-Fuzzy Inference System in Determining the Buckling Capacity of Circular Opening Steel Beams

Quang Hung Nguyen; Hai-Bang Ly; Tien-Thinh Le; Thuy-Anh Nguyen; Viet-Hung Phan; Van Quan Tran; Binh Thai Pham

doi:10.3390/ma13102210

Parametric Investigation of Particle Swarm Optimization to Improve the Performance of the Adaptive Neuro-Fuzzy Inference System in Determining the Buckling Capacity of Circular Opening Steel Beams

Materials (Basel). 2020 May 12;13(10):2210. doi: 10.3390/ma13102210.

Authors

Quang Hung Nguyen¹, Hai-Bang Ly², Tien-Thinh Le³, Thuy-Anh Nguyen², Viet-Hung Phan⁴, Van Quan Tran², Binh Thai Pham²

Affiliations

¹ Thuyloi University, Hanoi 100000, Vietnam.
² University of Transport Technology, Hanoi 100000, Vietnam.
³ Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam.
⁴ University of Transport and Communications, Ha Noi 100000, Vietnam.

Abstract

In this paper, the main objectives are to investigate and select the most suitable parameters used in particle swarm optimization (PSO), namely the number of rules (n_rule), population size (n_pop), initial weight (w_ini), personal learning coefficient (c₁), global learning coefficient (c₂), and velocity limits (f_v), in order to improve the performance of the adaptive neuro-fuzzy inference system in determining the buckling capacity of circular opening steel beams. This is an important mechanical property in terms of the safety of structures under subjected loads. An available database of 3645 data samples was used for generation of training (70%) and testing (30%) datasets. Monte Carlo simulations, which are natural variability generators, were used in the training phase of the algorithm. Various statistical measurements, such as root mean square error (RMSE), mean absolute error (MAE), Willmott's index of agreement (IA), and Pearson's coefficient of correlation (R), were used to evaluate the performance of the models. The results of the study show that the performance of ANFIS optimized by PSO (ANFIS-PSO) is suitable for determining the buckling capacity of circular opening steel beams, but is very sensitive under different PSO investigation and selection parameters. The findings of this study show that n_rule = 10, n_pop = 50, w_ini = 0.1 to 0.4, c₁ = [1, 1.4], c₂ = [1.8, 2], f_v = 0.1, which are the most suitable selection values to ensure the best performance for ANFIS-PSO. In short, this study might help in selection of suitable PSO parameters for optimization of the ANFIS model.

Keywords: adaptive neuro-fuzzy inference system; buckling capacity; circular opening steel beams; particle swarm parameters.