Simultaneous inversion of fractal morphology and particle size distribution of soot aggregate based on light scattering intensity
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摘要:
利用散射光信号实现碳黑团聚体分形结构和粒径分布参数的同时反演，在火焰辐射换热模拟和污染物测定方面有着重要应用价值。反演的正问题基于瑞利-德拜-甘斯多分散分形团聚体（RDG-PFA）散射理论，研究了2种信号方案，包括多角度散射及多角度散射-准直透射率。反演前，对比2种信号方案的残余适应度值分布发现，散射与透射信号同时使用有效减弱了反问题的病态性。反演过程基于协方差矩阵自适应的演化策略（CMA-ES）算法，该算法具有很强的局部搜索能力，为快速且稳定地反演各个目标参数提供了保障。反演结果表明了CMA-ES算法较大搜索空间内的可行性和普适性，同时也证明了采用多角度散射-准直透射率的组合信号有效提高了目标参数的反演精度。
Abstract:The use of light scattering signals to achieve the simultaneous inversion of the fractal morphology and particle size distribution parameters of soot aggregates have important application value in flame radiation heat transfer simulation and pollution control. The direct model of inversion is based on the Rayleigh-Debye-Gans Polydisperse Fractal Approximation (RDG-PFA) light scattering theory. Two signal schemes were investigated: multi-angle scattering, multi-angle scattering and collimated transmittance. Before the inversion, by comparing the residual fitness value distributions of the two signal schemes, it is found that the simultaneous use of scattering and transmission signals effectively reduces the ill-posedness of the inverse problem. The inversion process is based on the Covariance Matrix Adaptive Evolutionary Strategy (CMA-ES) algorithm, which has a strong local search capability and provides a guarantee for fast and stable inversion of each target parameter. The final inversion results demonstrate the feasibility and universality of the method in a large search space. And it is also proved that the combination of multi-angle scattering and collimated transmittance effectively improves the inversion accuracy of the target parameters.
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Key words:
- light scattering /
- soot /
- aggregate /
- fractal dimension /
- inverse problems /
- optimization algorithm
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图 4 没有噪声与10%高斯噪声下的角度散射光强度对比
Figure 4. Comparison of angular light scattering intensity under no noise and 10% Gaussian noise
图 5 两种信号方案下的残余适应度分布
Figure 5. Residual fitness distribution contour under two signal schemes
图 6 不同高斯噪声下使用不同信号方案反演得到的粒径分布曲线
Figure 6. Particle size distribution profiles obtained by inversion results of different signal schemes under different Gaussian noise
图 7 不同高斯噪声下散射-透射组合信号的收敛过程
Figure 7. Convergence process of scattering-transmittance combined signal under different Gaussion noise
表 1 目标参数的真实值和搜索范围
Table 1. Original value and search range of target parameters
目标参数 真实值 搜索范围 C 0.8 [0, 10] Df 1.65 [1,3] μg/nm 90 [0, 500] σg 1.6 [0, 10] 
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表 2 CMA-ES算法的参数设定值
Table 2. Parameter value setting of CMA-ES algorithm
参数 设定值 maxgens 1000 eps 10-10
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表 3 不同高斯噪声下使用不同信号方案的目标参数反演结果
Table 3. Inversion results of target parameters obtained by different signal schemes under different Gaussian noise
目标参数 真实值 高斯噪声/% 散射 散射+透射 平均结果 εrel/% 标准差 平均结果 εrel/% 标准差 C 0.8 0 0.8000 0 6.05×10-5 0.8000 0 1.10×10-4 6 0.8563 7.03 1.73×10-1 0.7929 0.89 6.19×10-2 10 0.8323 4.04 1.37×10-1 0.8010 0.12 1.03×10-1 Df 1.65 0 1.650 0 9.57×10-5 1.600 0 1.58×10-5 6 1.600 3.06 1.39×10-1 1.654 0.24 5.67×10-2 10 1.615 2.12 1.49×10-1 1.645 0.29 9.02×10-2 μg/nm 90 0 90.00 0 2.25×10-2 90.00 0 1.33×10-5 6 108.81 20.90 2.99×101 90.25 0.28 9.35 10 109.17 21.30 3.75×101 93.38 3.75 1.77×101 σg 1.6 0 1.600 0 1.10×10-4 1.650 0 2.29×10-3 6 1.513 5.45 1.48×10-1 1.600 0 3.79×10-2 10 1.491 6.78 2.05×10-1 1.584 0.97 7.03×10-2
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