论文标题
通过尺寸分解的广义多项式混沌kriginging多折叠条件价值估计
Multifidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos-Kriging
论文作者
论文摘要
我们提出了在高维依赖性随机输入下对非线性系统有条件值的风险（CVAR）估计的新方法。我们开发了一种新型的DD-GPCE抗体替代物，该替代物将尺寸分解的广义多项式膨胀和Kriging合并，以准确地近似于非线性和非平滑随机输出。我们将DD-GPCE-KRIGING（1）用于蒙特卡洛模拟（MCS）和（2）在多重性重要性采样（MFIS）中。来自DD-GPCE-KRIGING的基于MCS的方法样品，对于高维依赖性随机输入既有效且准确，却引入了偏差。因此，我们提出了一种基于MFIS的方法，其中DD-GPCE策略决定了偏置密度，从中我们从中绘制一些高保真样品来提供无偏见的CVAR估计。为了加速偏置密度构建，我们使用廉价的低保真模型来计算DD-GPCE策略。数学函数的数值结果表明，基于MFIS的方法比输出非滑动时基于MCS的方法更准确。提出的方法的可伸缩性及其在复杂工程问题上的适用性在具有28个（部分依赖）随机输入的二维复合层压板上，并具有三维复合T-关节，并具有20个（部分依赖）随机输入。在前者中，与使用高保真模型相比，提出的基于MFIS的方法可实现104倍的速度，同时准确地估算CVAR，误差为1.15％。
We propose novel methods for Conditional Value-at-Risk (CVaR) estimation for nonlinear systems under high-dimensional dependent random inputs. We develop a novel DD-GPCE-Kriging surrogate that merges dimensionally decomposed generalized polynomial chaos expansion and Kriging to accurately approximate nonlinear and nonsmooth random outputs. We use DD-GPCE-Kriging (1) for Monte Carlo simulation (MCS) and (2) within multifidelity importance sampling (MFIS). The MCS-based method samples from DD-GPCE-Kriging, which is efficient and accurate for high-dimensional dependent random inputs, yet introduces bias. Thus, we propose an MFIS-based method where DD-GPCE-Kriging determines the biasing density, from which we draw a few high-fidelity samples to provide an unbiased CVaR estimate. To accelerate the biasing density construction, we compute DD-GPCE-Kriging using a cheap-to-evaluate low-fidelity model. Numerical results for mathematical functions show that the MFIS-based method is more accurate than the MCS-based method when the output is nonsmooth. The scalability of the proposed methods and their applicability to complex engineering problems are demonstrated on a two-dimensional composite laminate with 28 (partly dependent) random inputs and a three-dimensional composite T-joint with 20 (partly dependent) random inputs. In the former, the proposed MFIS-based method achieves 104x speedup compared to standard MCS using the high-fidelity model, while accurately estimating CVaR with 1.15% error.
