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基于自适应集成Kriging的结构可靠性分析

Structural Reliability Analysis Based on Adaptive Ensemble Kriging

  • 摘要: 针对蒙特卡洛模拟计算成本高、AK-MCS方法在高维问题中收敛效率不足以及传统U学习函数局部搜索能力有限等相关问题,本文提出了一种基于自适应集成kriging的结构可靠性分析方法(AME-AK-MCS-L)。该方法首先采用基于空间再填充机制的高密度均匀初始采样方法,通过局部空洞检测与区域再填充机制,提高设计空间整体覆盖能力以及初始Kriging代理模型精度;其次,在传统U学习函数基础上引入预测错误概率、样本空间距离及动态探索因子,构建新的L学习函数,以增强全局探索和局部开发能力;同时建立自适应集成代理模型,通过动态权重融合多个子模型预测结果,提高可靠性分析精度与稳定性。通过采用低维算例四失效域串联系统和高维算例六维非线性振荡系统进行可靠性分析验证,并与AK-MCS-U、AK-MCS-L及AME-AK-MCS-U方法对比,验证所提方法的有效性,为高维复杂系统结构可靠性评估提供有效解决方法。

     

    Abstract: To address the high computational cost of Monte Carlo Simulation (MCS), the insufficient convergence efficiency of the Active Kriging–Monte Carlo Simulation (AK-MCS) method in high-dimensional problems, and the limited local search capability of the traditional U-learning function, this paper proposes a structural reliability analysis method based on an Adaptive Model Ensemble Kriging framework, termed AME-AK-MCS-L. First, a high-density uniform initial sampling strategy based on a space-refilling mechanism is employed. By incorporating local void detection and regional refilling procedures, the overall coverage of the design space and the accuracy of the initial Kriging surrogate model are significantly improved. Second, a novel L-learning function is developed by introducing the probability of prediction error, sample-space distance, and a dynamic exploration factor into the conventional U-learning function, thereby enhancing both global exploration and local exploitation capabilities. Furthermore, an adaptive ensemble surrogate model is established, in which the prediction results of multiple sub-models are integrated through dynamic weighting to improve the accuracy and robustness of reliability analysis. The proposed method is validated using two benchmark examples: a low-dimensional series system with four failure domains and a high-dimensional six-dimensional nonlinear oscillatory system. Comparative studies with AK-MCS-U, AK-MCS-L, and AME-AK-MCS-U demonstrate the effectiveness and superiority of the proposed approach. The method provides an efficient and reliable solution for structural reliability assessment of high-dimensional complex systems.

     

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