Abstract The present study describes an improved inversion method for determining the two-dimensional mass distribution of non-refractory materials on refractory black carbon using a centrifugal particle mass analyzer (CPMA) and single-particle soot photometer (SP2) system. The novel approach is tested with several well-established regularization methods to determine which method works best in the new method. Contrary to other two-dimensional inversion applications in the literature, in the CPMA-SP2 inversion, there is a physical constraint that the refractory black carbon mass () cannot exceed the total particle mass (). This constraint has to be considered in the inversion to accommodate the sharp edge where equals which causes established regularization methods to underperform and potentially smooth the distribution over this boundary. This study introduces a novel deconvolution scheme which accommodates the physical constraint and can be solved with various inversion techniques including: least-squares, Twomey, Twomey–Markowski, multiplicative algebraic reconstruction technique (MART), Tikhonov, and exponential distance methods. The new method also accounts for the problem that the mobility of the black carbon particles is unknown but is required for kernel construction, by using an innovative approach based on constraining the inversion so that the marginal distribution from the CPMA-SP2 inversion matches the distribution of measured directly by SP2 while the CPMA is bypassed. The inversion technique is tested with synthetic data or “phantoms” – representing uncoated soot, soot coated with non-refactory material, and a mixture of coated and uncoated soot. The results reveal that the exponential distance method outperforms the other regularization methods tested. Copyright © 2020 American Association for Aerosol Research

中文翻译：

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一种确定非耐火材料在耐火黑碳上二维质量分布的改进反演方法

摘要 本研究描述了一种改进的反演方法，用于使用离心粒子质量分析仪 (CPMA) 和单粒子烟尘光度计 (SP2) 系统确定耐火黑碳上非耐火材料的二维质量分布。这种新方法用几种成熟的正则化方法进行了测试，以确定哪种方法在新方法中效果最好。与文献中的其他二维反演应用相反，在CPMA-SP2反演中，存在难熔黑碳质量()不能超过总颗粒质量()的物理约束。必须在反演中考虑此约束以适应锐边，其中 equals 导致已建立的正则化方法表现不佳并可能使该边界上的分布平滑。本研究引入了一种新的解卷积方案，该方案适应物理约束，可以使用各种反演技术解决，包括：最小二乘法、Twomey、Twomey-Markowski、乘法代数重建技术 (MART)、Tikhonov 和指数距离方法。新方法还解决了黑碳粒子的迁移率未知但内核构建需要的问题，通过使用基于约束反演的创新方法，使 CPMA-SP2 反演的边际分布与在绕过 CPMA 时由 SP2 直接测量。反演技术是用合成数据或“幻影”进行测试的——代表未涂层的烟灰、涂有非重构材料的烟灰以及涂层和未涂层​​烟灰的混合物。结果表明，指数距离方法优于测试的其他正则化方法。版权所有 © 2020 美国气溶胶研究协会