Nguyen Quang Hung, Ly Hai-Bang, Le Tien-Thinh, Nguyen Thuy-Anh, Phan Viet-Hung, Tran Van Quan, Pham Binh Thai
Thuyloi University, Hanoi 100000, Vietnam.
University of Transport Technology, Hanoi 100000, Vietnam.
Materials (Basel). 2020 May 12;13(10):2210. doi: 10.3390/ma13102210.
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), population size (n), initial weight (w), personal learning coefficient (c), global learning coefficient (c), and velocity limits (f), 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 = 10, n = 50, w = 0.1 to 0.4, c = [1, 1.4], c = [1.8, 2], f = 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.
在本文中，主要目标是研究并选择粒子群优化算法（PSO）中最适合的参数，即规则数量（n）、种群规模（n）、初始权重（w）、个体学习系数（c）、全局学习系数（c）和速度限制（f），以提高自适应神经模糊推理系统在确定圆形开孔钢梁屈曲承载力方面的性能。就承受荷载作用下结构的安全性而言，这是一项重要的力学性能。利用一个包含3645个数据样本的可用数据库生成训练数据集（70%）和测试数据集（30%）。在算法的训练阶段使用了作为自然变异性生成器的蒙特卡罗模拟。采用各种统计测量方法，如均方根误差（RMSE）、平均绝对误差（MAE）、威尔莫特一致性指数（IA）和皮尔逊相关系数（R）来评估模型的性能。研究结果表明，通过粒子群优化算法优化的自适应神经模糊推理系统（ANFIS - PSO）的性能适用于确定圆形开孔钢梁的屈曲承载力，但在不同的粒子群优化算法研究和选择参数下非常敏感。本研究结果表明，n = 10，n = 50，w = 0.1至0.4，c = [1, 1.4]，c = [1.8, 2]，f = 0.1，这些是确保ANFIS - PSO最佳性能的最合适选择值。简而言之，本研究可能有助于为自适应神经模糊推理系统模型的优化选择合适的粒子群优化算法参数。
