悬浮颗粒质量测量的双参数统计分形特征及其应用

The project aims at the signal's strong random, the serious overlap phenomenon, and so on problems of aerosol in the measurement process.First of all, a two-parameter statistical model of the random signals is established by introducing two basic conceptions---the amplitude and the width. Based on these, the experimental results show that, the random signals' parameter counting distributions all match well with the form of lognormal distribution with the natural number as the independent variable. And then, the reason and mechanism, which can be used to explain the above experimental result, are proposed. Besides, the statistical fractal characteristic of the random pulse signals are also studied in this project. The results indicate that the there is the internal relations between the counting distributions' statistical characteristic parameters and the corresponding signal's characteristic parameters. In essence, these relations are the representations of random signals' fractal character. In a word, two characteristic parameters' statistical distributions of the random signals have non-integral dimensional fractal character, while the fractal dimension is defined as the ratio of the lognormal dispersion for the two characteristic parameters' counting distribution. Based on these, the physical meaning and calculation method of the fractal dimension are given. According to the above researches, the various factors which could affect the measurement results are analyzed. These can be used to guide the improvement of the function of the sensors. Meanwhile, these results will have important theoretical significance and practical value on choosing correct calculating method and decreasing the dispersive degree of the measuring results.

本项目针对悬浮颗粒测量过程中信号随机性强、重叠现象严重等问题展开研究。首先以信号脉冲幅度、宽度为基本概念，建立一种随机信号的双参数统计模型。以此模型为基础，从实验上验证悬浮颗粒质量测量随机信号特征参数计数分布均服从以序列自然数为自变量的对数正态分布；并进一步从理论上探索随机信号特征参数计数分布服从对数正态分布的原因及机理。此外，项目还对随机脉冲信号群具有的统计分形特征进行了进一步研究。结果表明悬浮颗粒计数分布的统计特征量与信号的特征参数之间存在内在联系。这种联系的形式即随机信号分形特性的表现，表明随机信号特征参数的统计分布之间具有非整数维分形特征，且分形维数为两个分布离散度参数的比值，给出了分形维数的物理意义及计算方法。基于此，分析测量系统中各因素对测量结果的影响程度，指导仪器性能的改进；给出测量数据集合数学期望的正确计算方法，减小测量结果的离散度，具有重要的理论意义和实用价值。

本项目针对悬浮颗粒测量过程中信号随机性强、重叠现象严重等问题展开研究。首先以信号脉冲幅度、宽度为基本概念，建立一种随机信号的双参数统计模型。以此模型为基础，从实验上验证悬浮颗粒质量测量随机信号特征参数计数分布均服从以序列自然数为自变量的对数正态分布；并进一步从理论上探索随机信号特征参数计数分布服从对数正态分布的原因及机理。此外，项目还对随机脉冲信号群具有的统计分形特征进行了进一步研究。结果表明悬浮颗粒计数分布的统计特征量与信号的特征参数之间存在内在联系。这种联系的形式即随机信号分形特性的表现，表明随机信号特征参数的统计分布之间具有非整数维分形特征，且分形维数为两个分布离散度参数的比值，给出了分形维数的物理意义及计算方法。最终，将研究成果应用于颗粒的测量过程及其他随机信号的测量过程中。在颗粒大小的测量过程中，同时提取颗粒散射光信号幅度和宽度值，根据信号幅度值区分小粒径范围内的颗粒粒度信息，而根据信号宽度值区分大颗粒的颗粒粒度信息，扩大仪器的量程，提高粒径的分辨率。同时，将双参数质量模型作为理论基础，应用于颗粒浓度的测量过程中。此外，尝试给出了统计模型在其他随机信号的测量过程的应用。