Shared low-dimensional subspaces for propagating kinetic uncertainty to multiple outputs
Shared low-dimensional subspaces for propagating kinetic uncertainty to multiple outputs
复制标题
用于将动力学不确定性传播到多个输出的共享低维子空间
DOI：
10.1016/j.combustflame.2017.11.021
复制
发表时间：
2018-04-01
影响因子：
4.4
通讯作者：
Law, Chung K.
中科院分区：
文献类型：
--
作者：
Ji, Weiqi;Wang, Jiaxing;Law, Chung K.
燃烧模拟中动力学不确定性的前向传播通常采用响应面技术来加速蒙特卡罗采样。然而，为高维输入参数和昂贵的燃烧模型建立响应面在计算上具有挑战性。本研究采用主动子空间方法识别输入空间的低维子空间，在低维子空间内构建响应面。然而，以前只针对单个（标量）模型输出开发了主动子空间方法。本文介绍了一种利用单个低维共享子空间同时逼近多个输出的边际概率密度函数的新方法。我们通过求解最小二乘系统来确定共享子空间，从而计算出单输出活动子空间的适当组合。因为每个单独输出的有效子空间的识别可能需要大量的样本，这个过程对于昂贵的模型（如湍流燃烧模拟）可能在计算上难以处理。相反，我们提出了一种启发式方法，从更便宜的燃烧模型中学习相关的子空间。首先用氢/空气、甲烷/空气和二甲醚(DME)/空气混合物的点火延迟时间和层流火焰速度证明了单输出的主动子空间和多输出的共享子空间的性能。然后，我们展示了共享子空间的外推性能：使用在恒定体积下的点火延迟训练的共享子空间，我们通过零维HCCI模拟，特别是天然气/空气混合物的单级点火和二甲醚/空气混合物的两级点火，进行了动力学不确定性的前向传播。结果表明，在给定动力学不确定性的情况下，共享子空间可以准确地再现点火失败概率和点火曲柄角成功条件下的点火概率密度。(C) 2017燃烧研究所。Elsevier Inc.出版。版权所有。
Forward propagation of kinetic uncertainty in combustion simulations usually adopts response surface techniques to accelerate Monte Carlo sampling. Yet it is computationally challenging to build response surfaces for high-dimensional input parameters and expensive combustion models. This study uses the active subspace method to identify low-dimensional subspace of the input space, within which response surfaces can be built. Active subspace methods have previously been developed only for single (scalar) model outputs, however. This paper introduces a new method that can simultaneously approximate the marginal probability density functions of multiple outputs using a single low-dimensional shared subspace. We identify the shared subspace by solving a least-squares system to compute an appropriate combination of single-output active subspaces. Because the identification of the active subspace for each individual output may require a significant number of samples, this process may be computationally intractable for expensive models such as turbulent combustion simulations. Instead, we propose a heuristic approach that learns the relevant subspaces from cheaper combustion models. The performance of the active subspace for a single output, and of the shared subspace for multiple outputs, is first demonstrated with the ignition delay times and laminar flame speeds of hydrogen/air, methane/air, and dimethyl ether (DME)/air mixtures. Then we demonstrate extrapolatory performance of the shared subspace: using a shared subspace trained on the ignition delays at constant volume, we perform forward propagation of kinetic uncertainties through zero-dimensional HCCI simulations in particular, single-stage ignition of a natural gas/air mixture and two-stage ignition of a DME/air mixture. We show that the shared subspace can accurately reproduce the probability of ignition failure and the probability density of ignition crank angle conditioned on successful ignition, given uncertainty in the kinetics. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.