Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. We propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential \emph{acquisition function}-based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest in the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set estimation and probability estimation on synthetic test functions as well as two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier--Stokes equations. We demonstrate that our method predicts the failure boundary and probability more accurately and computationally efficiently while using varying fidelity models compared with using just a single expensive high-fidelity model.
翻译:航空系统失灵的估计概率是飞行认证和资格认证的关键要求。失灵概率估计涉及解决概率分布的尾巴,而蒙特卡洛的取样方法在需要询问昂贵的高度忠诚模拟时是难以解决的。我们提出了一个方法来使用多种忠诚模式的模式,这种模式可以使计算效率达到贸易准确性。具体地说,我们提议使用多种忠诚高斯过程模型,在多种忠诚性条件下有效地将模型结合成一个高效的组合,从而提供一种廉价的代金模型,在所有忠诚性方面都效仿原始模型。此外,我们提议了一个基于新颖的顺序/emph{购置函数}基数的实验设计框架,可以自动从适当的忠诚模型中选择样本,对最高忠诚性的利益数量作出预测。我们在重要的取样中采用我们所建议的方法,在故障等级设定估计和对合成测试功能的概率估计以及两个真实世界应用上展示我们的方法,即使用一种有限的元素方法的可靠性分析,以及一个使用Reynolds-平均的纳菲尔-斯托克斯的立方试验案例,同时用一种更精确的概率和更高程度的公式来精确地预测我们的方法,同时用一种比较的概率和高的边界的概率计算。