Inversion of particle size distribution based on improved Chahine algorithm
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摘要: 反演算法的速度、精度及稳定性一直是颗粒测量领域中的研究重点。针对传统的Chahine迭代算法在反演过程中出现毛刺、伪峰及震荡等不稳定现象,将正则化理论与Chahine迭代算法相结合的改进算法用于颗粒粒径分布的重建。通过引入正则化理论建立新的线性方程,采用L曲线法确定正则化参数,再利用Chahine迭代算法求解该线性方程。仿真及实验结果表明:改进的算法解决了Chahine迭代算法的缺点,提高了反演结果的稳定性和平滑性。利用改进的算法实现国家标准颗粒的测量,其迭代15 000次所得中值粒径D50的相对误差在2%以内,用于描述分布曲线展宽的D10、D90的相对误差均在5%以内,且反演时间小于1 min,可满足颗粒粒径在线测量的需求。
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关键词:
- 反演 /
- Chahine迭代算法 /
- 稳定性 /
- 正则化 /
- 粒径分布
Abstract: The speed, precision and stability of inversion algorithm are research emphasis in the field of particle measurement. To counter the problems such as burrs, false peaks and concussion etc. in the process of inversion with traditional Chahine algorithm, an improved algorithm that combines regularization theory with Chahine algorithm was used to reconstruct particle size distribution. A new linear equation was constructed by introducing the regularization theory, the regularization parameter was determined by using L-curve, and Chahine algorithm was used to solve the linear equations. Simulation and experiment results show that the improved algorithm overcomes the disadvantages of traditional Chahine algorithm and improves the stability and gliding property of inversion results. Measured results of standardized polystyrene microsphere is measured by using the improved algorithm, which shows that the relative errors for median diameter D50 is within 2%, and D10, D90(characterize broadening of distribution curve) are both within 5% when the number of inversion is 15 000. In addition, the inversion time is less than 1 minute, which meets online particle size measurement.-
Key words:
- inversion /
- Chahine algorithm /
- repeatability /
- regularization /
- particle size distribution
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[1] [2] Shao Hongfei, Chai Juan, Huang Hui. Research progress of particle size analysis and particle size standard reference material[J]. Chemical Analysis and Meterage, 2012, 21(2): 99-101. (in Chinese) 邵鸿飞, 柴娟, 黄辉. 粒度分析及粒度标准物质研究进展[J]. 化学分析计量, 2012, 21(2): 99-101. [3] [4] Wang Naining. Optic Measurement Technology of Particle Size and Its Application[M]. Beijing: Atomic Energy Press, 2002: 168-175. (in Chinese) 王乃宁.颗粒粒径的光学测量技术及应用[M].北京: 原子能出版社, 2000: 168-175. [5] [6] Kouzelis D, Candel S M, Esposito E, et al. Particle sizing by laser light diffraction: improvements in optics and algorithms[J]. Particle Particle Systems Characterization, 1987, 4(1-4): 151-156. [7] [8] Wang Li, Sun Xiaogang. Research on pattern search method for inversion of particle size distribution in spectral extinction technique[J]. Spectroscopy and Spectral Analysis, 2013, 33(3): 618-622. (in Chinese) 王丽, 孙晓刚. 基于模式搜索的光谱消光粒径分布反演算法的研究[J]. 光谱学与光谱分析, 2013, 33(3): 618-622. [9] Xu Lijun, Xin Lei, Cao Zhang. l(1)-Norm-Based reconstruction algorithm for particle sizing[J]. IEEE Transactions on Instrumention and Measurement, 2012, 61(5): 1395-1404. [10] [11] Wang Yanmin, Liang Guobiao, Pan Zhidong, Inversion of particle size distribution from light-scattering data using a modified regularization algorithm[J]. Particuology, 2010, 8(4): 365-371. [12] [13] [14] Tang Hong. Retrieval of spherical particle size distribution with an improved Tikhonov iteration method[J]. Thermal Science, 2012, 16(5): 1400-1404. [15] [16] Shao Yang, Wang Qinghua. Application of the smooth chahine algorithm in deducing the particle size distribution with light scattering[J]. Journal of Nanjing Xiaozhuang University, 2008, 11(6): 15-18. (in Chinese) 邵阳, 王清华. 平滑 Chahine 迭代算法在光散射法粒度分布反演中的应用[J]. 南京晓庄学院学报, 2008, 11(6): 15-18. [17] [18] Andreas Kirsch. An Introduction to the Mathematical Theory of Inverse Problems[M]. Berlin: Springer, 2011: 24-40. [19] [20] Li Gongsheng, Yuan Zhongxin. A new class of optimal regularization methods for solving ill-posed problems[J]. Journal of Zhengzhou University, 1999, 31(4): 21-23. (in Chinese) 李功胜, 袁忠信. 求解病态问题的一种新的优化正则化方法[J]. 郑州大学学报: 自然科学版, 1999, 31(4): 21-23. [21] [22] Hansen P C. The L-curve and its Use in the Numerical Treatment of Inverse Problems[M]. Copenhagen: IMM, Department of Mathematical Modelling, Technical University of Denmark, 1999: 10-12. [23] Wang Bingxian, Hu Kangxiu, Wang Zewen. Advances in research in Landweber iterate method for inverse problems and its application[J]. Journal of Shandong University of Technology, 2010, 24(4): 24-28. (in Chinese) 王兵贤, 胡康秀, 王泽文. 反问题的Landweber迭代法及其应用研究进展[J]. 计算机应用研究, 2013, 30(9): 2583-2586. -
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