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Inversion methods to determine two-dimensional aerosol mass-mobility distributions II: Existing and novel Bayesian methods
Journal of Aerosol Science ( IF 3.9 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.jaerosci.2020.105565
T.A. Sipkens , J.S. Olfert , S.N. Rogak

Abstract Moving towards two-dimensional distributions of particle properties is important to the study of aerosol formation, aerosol climate impacts, and aerosols in material science. This paper builds on existing work to examine Bayesian or statistical approaches to inverting tandem particle mass analyzer (PMA) and differential mobility analyzer (DMA) data to retrieve the two-dimensional mass-mobility distribution. We first consider the Bayesian representation of derivative-based Tikhonov regularization, focusing on the first-order case. We demonstrate a new Bayesian model selection scheme to choose the regularization parameter, which generally outperforms the L-curve approach for derivative-based Tikhonov regularization. We also perform a Bayesian-based uncertainty analysis to evaluate the quality of the reconstructions, noting that uncertainties are lowest in regions close to device setpoints. We then present a new exponential distance prior, a variant of generalized Tikhonov regularization that provides a natural approach to regularizing the two-dimensional aerosol size distribution problem by allowing smoothing preferentially along the length of the distribution. The exponential distance approach is observed to reduce errors in the reconstructions by up to 60%, with the benefit to using the exponential distance prior increasing as the distributions become increasingly narrow, i.e. more highly correlated. Finally, Bayesian model selection is shown to also be a good candidate to optimize the regularization parameters in the exponential distance prior.

中文翻译:

确定二维气溶胶质量迁移率分布的反演方法 II:现有的和新的贝叶斯方法

摘要 粒子性质的二维分布对于材料科学中气溶胶形成、气溶胶气候影响和气溶胶的研究非常重要。本文建立在现有工作的基础上,以检查贝叶斯或统计方法来反转串联粒子质量分析仪 (PMA) 和差分迁移率分析仪 (DMA) 数据以检索二维质量迁移率分布。我们首先考虑基于导数的 Tikhonov 正则化的贝叶斯表示,重点是一阶情况。我们展示了一种新的贝叶斯模型选择方案来选择正则化参数,它通常优于基于导数的 Tikhonov 正则化的 L 曲线方法。我们还执行基于贝叶斯的不确定性分析来评估重建的质量,注意到靠近设备设定点的区域的不确定性最低。然后,我们提出了一个新的指数距离先验,这是广义 Tikhonov 正则化的一种变体,它通过允许优先沿着分布的长度进行平滑,提供了一种自然的方法来正则化二维气溶胶尺寸分布问题。观察到指数距离方法可将重建中的错误减少多达 60%,使用指数距离先验的好处随着分布变得越来越窄,即更高度相关而增加。最后,贝叶斯模型选择也被证明是优化指数距离先验中正则化参数的良好候选者。广义 Tikhonov 正则化的一种变体,通过允许优先沿分布长度进行平滑,提供了一种自然的方法来正则化二维气溶胶尺寸分布问题。观察到指数距离方法可将重建中的错误减少多达 60%,使用指数距离先验的好处随着分布变得越来越窄,即更高度相关而增加。最后,贝叶斯模型选择也被证明是优化指数距离先验中正则化参数的良好候选者。广义 Tikhonov 正则化的一种变体,通过允许优先沿分布长度进行平滑,提供了一种自然的方法来正则化二维气溶胶尺寸分布问题。观察到指数距离方法可将重建中的错误减少多达 60%,使用指数距离先验的好处随着分布变得越来越窄,即更高度相关而增加。最后,贝叶斯模型选择也被证明是优化指数距离先验中正则化参数的良好候选者。观察到指数距离方法可将重建中的错误减少多达 60%,使用指数距离先验的好处随着分布变得越来越窄,即更高度相关而增加。最后,贝叶斯模型选择也被证明是优化指数距离先验中正则化参数的良好候选者。观察到指数距离方法可以将重建中的错误减少多达 60%,使用指数距离先验的好处随着分布变得越来越窄,即更高度相关而增加。最后,贝叶斯模型选择也被证明是优化指数距离先验中正则化参数的良好候选者。
更新日期:2020-08-01
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