摘要
在随机结构分析中,蒙特卡洛方法作为随机数值模拟方法,为问题提供了最为直观和精确的解答,但计算量大、效率低下的缺点大大降低了方法的实用性。研究在蒙特卡洛方法中引入人工神经网络,仅进行少量确定性分析,训练后即可模拟确定性有限元求解器,用神经网络的快速泛化映射取代蒙特卡洛法中的大量确定性有限元分析。算例结果显示,提出的蒙特卡洛-神经网络法可将蒙特卡洛法的计算效率提高几十至一百倍,计算精度令人满意,是一种有潜力的随机结构实用分析方法。
Among all the methods for analysis of stochastic structures, Monte Carlo (MC) method, a digital simulation method, can provide the most intuitive and accurate solution. However, the disadvantages of vast computation and low computing efficiency block this method from wide use. In this paper, Artificial Neural Network (ANN) is used to replace the deterministic FEM solver in MC simulation. The idea is that FEM is only used to generate the input-output pairs needed for training ANN and that the trained ANN can map out instantly for the structural responses. Thus ANN is used to obtain all the samples for MC statistics. Two numerical examples for analysis of stochastic structures are given. The results show that the proposed MC-ANN method has much higher computing efficiency and better accuracy.
出处
《工程力学》
EI
CSCD
北大核心
2004年第3期49-54,共6页
Engineering Mechanics
基金
广东省自然科学基金资助项目(000387)
关键词
随机有限元
数值模拟
蒙特卡洛
神经网络
stochastic finite element
digital simulation
Monte Carlo
artificial neural network
