Abstract: Multi-source uncertainty often exists in engineering practice, which affects the safe operation of engineering structures. Structural reliability analysis considers the influence of uncertainty in the form of failure probability, which can provide an effective guidance for the structural safety design. However, the evaluation of failure probability often requires a large number of calls to the actual performance function, leading to unaffordable computational expense, especially for the time-consuming models. To solve this problem, Kriging-based reliability analysis methods have attracted a lot of attention in recent years. In these methods, a well-trained Kriging model is used to replace the actual performance function, thus improving the computational efficiency of failure probability. Note that the number of calls to the actual performance function is equal to the size of the design of experiment, and the estimation accuracy of failure probability depends on the approximation quality of Kriging. Therefore, how to reduce the number of training samples as much as possible while ensuring the accuracy of failure probability is the goal of Kriging-based reliability analysis methods.
In this paper, an efficient structural reliability analysis method based on a two-stage local sampling strategy is proposed under the framework of active learning Kriging to improve the estimation accuracy and computational efficiency of failure probability. In the process of active learning, an inaccurate Kriging model is first established based on a small initial design of experiment, and then the design of experiment is sequentially enriched and the Kriging model is gradually refined with the expected feasibility function and the two-stage local sampling strategy, until the stopping criterion is met. Since the new samples are designed based on the prediction information of Kriging during previous iterations, the sequential design is more efficient than the one-shot design. Moreover, the two-stage local sampling strategy is implemented to reduce the size of the candidate pool, which can improve the efficiency of searching the new samples. In the first stage, the new sample is selected from such a local region where the sampling center is assigned as the mean point of design variables and the sampling region is defined by the joint probability density of design variables. When the estimated failure probability reaches the threshold of stage division based on confidence interval, the second stage sampling will start. In the second stage of local sampling, the sampling center is located at the most likely failure point, and the sampling region is determined based on the target reliability and the nonlinearity of the performance function. In fact, both the first and second stage sampling methods have their disadvantages when used alone. For example, the selected samples of the first stage may contribute little to the accuracy of Kriging when the sampling center is far away from the limit state boundary; The estimated failure probability of the second stage may be inaccurate when the obtained most likely failure point deviates greatly from the actual value. However, our proposed local sampling strategy can overcome these shortcomings by switching adaptively between the first stage and second stage. Finally, the failure probability is estimated by combining the refined Kriging model and Monte Carlo simulation.
Three application examples with different dimensions and complexity are employed to verify the performance of the proposed method. Among the compared methods, Monte Carlo simulation has a high accuracy when generating enough samples, and thus its estimated value is regarded as a reference. For fairness, the other three methods of comparison are all based on the active learning Kriging model. Among these three Kriging-based reliability analysis methods, both global and local sampling strategies are involved. The comparison results show that the proposed method can balance the global exploration and local exploration in the effective sampling area, and achieve high accuracy and efficiency of failure probability estimation. Note that the number of Monte Carlo samples may be very large when involving a small failure probability, which decreases computational efficiency. To accelerate the convergence of failure probability estimation, some advanced simulation techniques, such as importance sampling, subset simulation and line sampling, will be combined in the future work.

Key words: structural reliability, Kriging model, two-stage local sampling, expected feasibility function

摘要： 工程实践中存在着各种不确定性因素,影响着工程结构的安全运行。结构可靠性分析以失效概率的形式考虑了不确定性的影响,可为结构的安全设计提供指导。然而,失效概率的评估往往涉及昂贵功能函数的调用,导致难以负担的计算成本。为解决该问题,基于Kriging模型的可靠性分析法在近年来受到了广泛的关注。该方法以训练良好的Kriging模型近似真实功能函数,从而在失效概率的计算中达到减少功能函数评价次数的目的。本文在主动学习Kriging模型的框架下,提出了基于两阶段局部抽样策略的结构可靠性分析法,以提高失效概率的估计精度和计算效率。在该方法中,Kriging模型的训练样本以两阶段局部抽样的方式从候选样本池中被逐渐添加。第一阶段以输入变量的均值点为抽样中心,利用概率密度函数确定抽样区域。当所估计失效概率满足基于置信区间的阶段划分阈值时,则开始第二阶段的局部抽样。第二阶段则以最可能失效点为抽样中心,以目标可靠度和功能函数的非线性度确定抽样区域。应用案例表明:所提方法能平衡有效抽样区域的全局探索和局部搜索,实现高精度失效概率估计的同时提高计算效率。

关键词: 结构可靠性, Kriging模型, 两阶段局部抽样, 期望可行性函数