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 引用本文: 周锦, 李杰. 两相自适应训练策略与高效可靠度分析方法研究. 力学学报, 待出版.
Zhou Jin, Li Jie. The two-phase training strategy and highly-efficient reliability analysis method. Chinese Journal of Theoretical and Applied Mechanics, in press.
 Citation: Zhou Jin, Li Jie. The two-phase training strategy and highly-efficient reliability analysis method. Chinese Journal of Theoretical and Applied Mechanics, in press.

## THE TWO-PHASE TRAINING STRATEGY AND HIGHLY-EFFICIENT RELIABILITY ANALYSIS METHOD

• 摘要: 概率密度演化方法对于复杂工程结构的系统可靠度分析有良好的适用性, 但对于高维随机系统依然存在效率不高的问题. 近年来通过少量训练样本训练目标代理模型, 来替代目标随机系统提升可靠度分析效率的做法受到众多研究者的青睐. 为提升构建自适应代理模型的精度和效率, 本文提出了一种两相自适应训练策略, 通过对概率空间分层次剖分, 逐层次获得训练样本集. 在两相训练策略的基础上分两步训练Kriging模型, 不仅提升了Kriging模型对概率空间内失效边界的近似精度, 更进一步降低了训练过程对计算机物理内存的消耗需求. 随后通过结合概率密度演化理论, 提出了一种基于等价极值理论的高效可靠度分析方法. 为验证本文建议方法的有效性, 分析了不同类型功能函数为目标的代理模型构建效率, 并进行了一幢钢筋混凝土框架结构的抗震可靠度分析. 结果表明: 两相自适应训练策略极大提升了目标代理模型的导出速率并保有较高的分析精度, 弥补了概率密度演化理论在处理罕遇失效事件时精度不足的缺陷. 值得说明地是, 两相训练策略不仅适用于基于Kriging模型的代理模型训练, 同时对其他类型的自适应代理模型的训练也有指导意义, 并不受代理模型基本类型限制.

Abstract: The probability density evolution method demonstrates good applicability for system reliability analysis of complex engineering structures. However, it still faces a lot of challenges, such as inefficiency, particularly when dealing the reliability issues with high-dimensional stochastic dynamic systems. In recent years, a promising approach to enhance the efficiency of reliability analysis involves training surrogate models using a small set of training samples instead of relying on the actual stochastic system is favored by researchers. To improve the accuracy and efficiency of constructing adaptive surrogate models in order to carry out the system reliability analysis, this paper proposes a two-phase adaptive training strategy based on the adaptive Kriging model. It involves hierarchical partitioning of the probability space to obtain training sample sets at different levels. Building on this two-phase training strategy, the Kriging model is trained step by step. This not only enhances the Kriging model's approximation accuracy of failure boundaries within the probability space but also reduces the computational memory requirements during the training process. Subsequently, by combining the probability density evolution theory, an efficient reliability analysis method based on equivalent extreme value event is introduced. To validate the effectiveness of the proposed method, the construction of surrogate models for different types of performance functions is analyzed, and seismic reliability analysis of a reinforced concrete frame structure is conducted. The results indicate that the two-phase adaptive training strategy greatly improves the derivation rate of the objective surrogate model while maintaining high analysis accuracy, addressing the shortcomings of the probability density evolution theory in dealing with rare failure events. It is worth mentioning that the two-phase training strategy is not only suitable for surrogate model training based on the Kriging model, but also has guiding significance for the training of other types of adaptive surrogate models, and is not limited by the basic type of surrogate model.

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