基于RBF神经网络的结构可靠度分析方法

Structural Reliability Analysis Based on RBF Neural Network

蒙特卡罗模拟是目前结构可靠度分析中最准确有效的方法,但因其计算量太大、效率低而受到很大的限制,特别是对于大型复杂结构的功能函数不能被明确表达的情况.鉴于此,在蒙特卡罗重要抽样方法的基础上,提出了利用RBF神经网络替代原结构功能函数的RBF-蒙特卡罗方法,以提高工作效率.RBF神经网络训练样本的选取则由均匀试验设计确定,以提高样本的代表性并大幅减少样本数量,从而加快网络的训练过程,加强网络的逼近能力.算例分析表明,该方法不但能最大限度地减少结构有限元分析次数,而且有满意的计算精度,具有实际应用价值.

Monte - Carlo simulation is the most exact and effective method for structural reliability analysis at present. Due to huge computation expenditure and low efficiency, however, this way is strongly subject to large-scale and sophisticated structures, especially which performance functions can not be expressed explicitly. In order to improve computational efficiency, this paper introduces RBF Neural Network to substitute structural performance function evaluations in Importance Sampling Monte - Carlo simulations and proposes RBF - Monte - Carlo approach for reducing structural analyses. The training samples of RBF Neural Network are determined by Uniform Experiment Design to accelerate training process and enhance approximate capacity of the neural network. Two case studies are presented to demonstrate efficiency, applicability and meaning of the methodology.