Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world problems, particularly when failure is a rare event. To implement multifidelity modeling, estimators that efficiently combine information from multiple models/sources are necessary. In past works, the variance reduction techniques of Control Variates (CV) and Importance Sampling (IS) have been leveraged for this task. In this paper, we present the CVIS framework; a creative take on a coupled Control Variates and Importance Sampling estimator for bifidelity reliability analysis. The framework addresses some of the practical challenges of the CV method by using an estimator for the control variate mean and side-stepping the need to estimate the covariance between the original estimator and the control variate through a clever choice for the tuning constant. The task of selecting an efficient IS distribution is also considered, with a view towards maximally leveraging the bifidelity structure and maintaining expressivity. Additionally, a diagnostic is provided that indicates both the efficiency of the algorithm as well as the relative predictive quality of the models utilized. Finally, the behavior and performance of the framework is explored through analytical and numerical examples.

翻译：多保真建模作为解决模型评估成本过高问题的手段，正逐渐受到关注——这一问题使得失效概率的估计成为复杂现实问题（尤其是稀有失效事件）中的重大计算挑战。为实施多保真建模，需要能够高效整合多模型/多源信息的估计器。以往研究中，控制变量（CV）和重要性采样（IS）等方差缩减技术已被用于此任务。本文提出CVIS框架：一种融合控制变量与重要性采样的双保真度可靠性分析估计器的新颖设计。该框架通过使用控制变量均值的估计器，并借助巧妙的调优常数选择来规避原估计器与控制变量间协方差估计的需求，从而解决了CV方法的若干实际难题。同时，本文考虑了高效IS分布的选取问题，旨在充分挖掘双保真度结构潜力并保持表达力。此外，研究提供了诊断指标，既可指示算法效率，又能反映所用模型的相对预测质量。最后，通过解析与数值算例探讨了该框架的行为与性能。