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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方法在处理复杂问题时收敛效率不足,以及传统学习函数能力有限等问题,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。该方法采用空间填充机制的高密度初始采样,通过局部空洞检测与区域填充机制,提高设计空间整体覆盖能力和初始Kriging代理模型精度。此外,通过引入预测错误概率、样本空间距离及动态探索因子,构建新的学习函数。同时,建立集成代理模型,通过留一法交叉验证误差动态计算融合权重,集成多个子模型预测结果,提高可靠性分析精度与稳定性。本文利用四失效域串联系统和六维非线性振荡系统这两个算例,对本文提出方法进行可靠性分析验证,并与其他5种可靠性分析算法进行对比。结果表明,本文所提方法行之有效,为复杂系统的结构可靠性评估提供了有效解决方法。

     

    Abstract: To address the issues of high computational cost in Monte Carlo simulation, insufficient convergence efficiency of the AK-MCS method when dealing with complex problems, and the limited capability of traditional learning functions, this paper proposes a structural reliability analysis method based on adaptive ensemble Kriging. The proposed method first employs a high-density initial sampling strategy with space-filling mechanisms, incorporating local void detection and region-filling schemes to enhance the overall coverage of the design space and improve the accuracy of the initial Kriging surrogate model. Furthermore, a novel L-learning function is constructed by integrating the probability of prediction error, sample spatial distance, and a dynamic exploration factor. Meanwhile, an ensemble surrogate model is established, in which fusion weights are dynamically computed through leave-one-out cross-validation errors, integrating the prediction results of multiple sub-models to enhance the accuracy and stability of reliability analysis. The effectiveness of the proposed method is validated through reliability analysis of two case studies—a four-failure-domain series system and a six-dimensional nonlinear oscillatory system—and compared with five other reliability analysis algorithms. The results demonstrate the efficacy of the proposed method, providing an effective solution for structural reliability assessment of complex systems.

     

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