Over the past decade, several acquisition functions have been proposed for kriging-based reliability analysis. Each of these acquisition functions can be used to identify an optimal sequence of samples to be included in the kriging model. However, no single acquisition function provides better performance over the others in all cases. Further, the best-performing acquisition function can change at different iterations over the sequential sampling process. To address this problem, this paper proposes a new acquisition function, namely expected uncertainty reduction (EUR), that serves as a meta-criterion to select the best sample from a set of optimal samples, each identified from a large number of candidate samples according to the criterion of an acquisition function. EUR does not rely on the local utility measure derived based on the kriging posterior of a performance function as most existing acquisition functions do. Instead, EUR directly quantifies the expected reduction of the uncertainty in the prediction of limit-state function by adding an optimal sample. The uncertainty reduction is quantified by sampling over the kriging posterior. In the proposed EUR-based sequential sampling process, a portfolio that consists of four acquisition functions is first employed to suggest four optimal samples at each iteration of sequential sampling. Each of these samples is optimal with respect to the selection criterion of the corresponding acquisition function. Then, EUR is employed as the meta-criterion to identify the best sample among those optimal samples. The results from two mathematical and one practical case studies show that (1) EUR-based sequential sampling can perform as well as or outperform the single use of any acquisition function in the portfolio, and (2) the best-performing acquisition function may change from one problem to another or even from one iteration to the next within a problem.

在过去的十年中，为基于克里金法的可靠性分析提出了几种采集功能。这些获取功能中的每一个都可以用于识别要包含在克里金模型中的最佳样本序列。但是，在所有情况下，没有一个单独的采集功能会比其他功能提供更好的性能。此外，性能最佳的采集功能可以在顺序采样过程中以不同的迭代次数进行更改。为了解决这个问题，本文提出了一种新的采集函数，即期望不确定度降低（EUR），该函数用作从一组最佳样本中选择最佳样本的元准则，每个样本均根据大量候选样本进行识别。以获取功能为标准。欧元不像大多数现有的收购职能那样依赖于基于绩效职能的克里金后验得出的当地效用度量。相反，EUR通过添加最佳样本直接量化了极限状态函数预测中不确定性的预期降低。通过对克里金后验进行采样来量化不确定性的降低。在建议的基于欧元的顺序抽样过程中，首先采用由四个采集函数组成的投资组合，以在顺序抽样的每次迭代中建议四个最佳样本。就相应的采集功能的选择标准而言，这些样本中的每个样本都是最佳的。然后，将EUR用作元标准，以从那些最佳样本中识别出最佳样本。