基于共四阶矩的燃烧数据集降维方法
A co-kurtosis based dimensionality reduction method for combustion datasets
AI总结：
本文提出基于共四阶矩的CoK-PCA方法，用于改进燃烧数据集的降维，提高热化学状态和化学反应的表示精度。
摘要：
主成分分析（PCA）是一种用于减少燃烧现象数值模拟计算成本的降维技术。然而，PCA通过协方差矩阵的特征向量来转换热化学状态空间，可能无法捕捉到重要的局部化学动力学信息，如点火核的形成，这些信息可能以极端值样本出现在数据集中。本文提出了一种替代的降维方法，即共四阶矩PCA（CoK-PCA），其中所需的主向量是从高阶联合统计矩，即共四阶矩张量中计算得出，这可能更好地识别状态空间中代表刚性动力学的方向。我们首先通过合成生成的数据集验证所提出的CoK-PCA方法的潜力，该数据集具有典型的燃烧模拟特征。随后，我们对代表预混乙烷-空气在简单均质反应器中自发点火和乙醇燃料均质压燃（HCCI）发动机的的数据集进行表征和对比，分析CoK-PCA与PCA的准确性。具体而言，我们比较了低维流形在原始热化学状态、物种生成速率和热量释放率重构误差方面的表现。后者——物种生成速率和热量释放率的比较——是更严谨的降维准确性评估。我们发现，即使使用简单的线性重构，基于共四阶矩的降维流形在原始热化学状态的表示上也比PCA更准确，尤其是在化学反应重要的区域。
英文摘要：
Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermo-chemical state space based on eigenvectors of co-variance of the data, could fail to capture information regarding important localized chemical dynamics, such as the formation of ignition kernels, appearing as \rev{extreme-valued} samples in a dataset. In this paper, we propose an alternate dimensionality reduction procedure, co-kurtosis PCA (CoK-PCA), wherein the required principal vectors are computed from a high-order joint statistical moment, namely the co-kurtosis tensor, which may better identify directions in the state space that represent stiff dynamics. We first demonstrate the potential of the proposed CoK-PCA method using a synthetically generated dataset that is representative of typical combustion simulations. Thereafter, we characterize and contrast the accuracy of CoK-PCA against PCA for datasets representing spontaneous ignition of premixed ethylene-air in a simple homogeneous reactor and ethanol-fueled homogeneous charged compression ignition (HCCI) engine. Specifically, we compare the low-dimensional manifolds in terms of reconstruction errors of the original thermo-chemical state, and species production and heat release rates computed from the reconstructed state. \rev{The latter -- a comparison of species production and heat release rates -- is a more rigorous assessment of the accuracy of dimensionality reduction.} We find that, even using a simplistic linear reconstruction, the co-kurtosis based reduced manifold represents the original thermo-chemical state more accurately than PCA, especially in the regions where chemical reactions are important.
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