基于响应空间子域概率配点的重力坝分析代理模型与系统可靠度分析方法

COLLOCATION POINT SELECTION WITHIN SUBSETS OF RESPONSE PROBABILITY SPACE FOR SURROGATE MODELING IN GRAVITY DAM ANALYSIS AND SYSTEM RELIABILITY ANALYSIS

  • 摘要: 采用基于随机有限元的蒙特卡洛模拟方法估计重力坝失效概率计算效率低,代理模型方法可以有效提高计算效率,但其传统配点方法(如“3\sigma 原则”及拉丁超立方抽样)常会遇到维度问题。该文提出一种基于响应空间子域概率配点的重力坝分析代理模型与系统可靠度分析方法,采用广义子集模拟在响应空间配点,构建重力坝各失效模式代理模型,基于代理模型采用蒙特卡洛模拟估计失效概率。以一个“四边界系统”问题展示广义子集模拟的配点结果,以一个重力坝案例验证所提方法的有效性。结果表明:针对高维、非线性、小失效概率及多失效模式的重力坝失效概率计算问题,所提方法计算结果精度较高,且计算效率和方差缩减作用优于基于有限元模型的广义子集模拟方法。此外,在计算消耗相当的情况下,所提方法的方差缩减作用优于基于拉丁超立方抽样配点的代理模型方法。

     

    Abstract: Using Monte Carlo simulation (MCS) based on stochastic finite element model to estimate failure probability of gravity dams suffers from a lack of computational efficiency. Surrogate model methods can effectively improve the computational efficiency, however, the conventional collocation methods (e.g., the three-sigma rule, Latin hypercube sampling (LHS) etc.) may suffer from a curse of dimensionality. Thusly, this paper proposes a collocation point selection within subsets of response probability space for surrogate modeling in gravity dam analysis and system reliability analysis method. The proposed method collocates samples in the response space by generalized subset simulation (GSS), then establishes surrogate model of each failure mode of gravity dams, and estimates failure probability by surrogate models based on MCS. This paper exhibits the collocation point selection result based on GSS by the application of a simple two-dimensional “four-boundary system” problem. Subsequently, the paper proves the effectiveness of the proposed method by the application of a gravity dam engineering. For the reliability analysis with a high dimensionality, nonlinear structural performance function, small failure probability, and multiple failure modes, e.g., gravity dam reliability analysis, the proposed method achieves a high accuracy in estimating failure probability. Additionally, it improves the computational efficiency and outperforms the generalized subset simulation method based on finite element model in terms of variance reduction. With the same computational costs, the proposed approach also outperforms the LHS based surrogate model method.

     

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