In this work, we introduce a new acquisition function for sequential sampling to efficiently quantify rare-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. Our acquisition is a generalization of the likelihood-weighted (LW) acquisition that was initially designed for the same purpose and then extended to many other applications. The improvement in our acquisition comes from the generalized form with two additional parameters, by varying which one can target and address two weaknesses of the original LW acquisition: (1) that the input space associated with rare-event responses is not sufficiently stressed in sampling; (2) that the surrogate model (generated from samples) may have significant deviation from the true ItR function, especially for cases with complex ItR function and limited number of samples. In addition, we develop a critical procedure in Monte-Carlo discrete optimization of the acquisition function, which achieves orders of magnitude acceleration compared to existing approaches for such type of problems. The superior performance of our new acquisition to the original LW acquisition is demonstrated in a number of test cases, including some cases that were designed to show the effectiveness of the original LW acquisition. We finally apply our method to an engineering example to quantify the rare-event roll-motion statistics of a ship in a random sea.

翻译：本文提出一种用于序列采样的新采集函数，以高效量化给定输入概率且函数评估代价高昂的输入-响应系统的稀有事件统计量。该采集函数是对最初为相同目的设计并随后拓展至多项应用的似然加权采集函数的推广。我们的采集函数改进源于其广义形式引入了两个额外参数，通过调整这些参数可针对并解决原始LW采集的两个缺陷：（1）与稀有事件响应相关的输入空间在采样过程中未被充分强调；（2）由样本生成的代理模型可能与真实输入-响应函数存在显著偏差，尤其针对输入-响应函数复杂且样本数量有限的情况。此外，我们开发了采集函数蒙特卡洛离散优化的关键流程，相较现有方法在该类问题上的处理速度实现了数量级提升。通过多个测试案例（包括若干旨在验证原始LW采集有效性的案例），我们证明了新采集函数相较原始LW采集的优越性能。最后将方法应用于工程实例，量化随机海浪中船舶稀有事件横摇运动统计量。