基于随机须丛逐步分解模型的纤维长度分布计算方法

Method for calculating fiber length distribution based on hierarchical model of random-beard

为解决新的纤维长度测量方法随机须丛影像法分析纤维长度分布的瓶颈技术,建立了从随机须丛中分离出一定长度界限以下纤维的逐步分解模型,推导出通过须丛线密度曲线的离散点运算获得纤维长度一次累积分布和频率分布的计算公式,避免了以往对须丛线密度曲线二次微分求取长度频率分布时,测量噪声被微分运算放大导致结果失真的问题。将运用逐步分解模型的随机须丛影像法与单纤维测量法测得的纤维长度频率分布直方图进行了对比。结果显示:2种方法测得的棉、毛试样各个长度组质量分数的平均差异分别为0.31%和0.26%,最大差异均小于1%,证明逐步分解模型计算公式具有实际应用价值,可用于纤维长度测量仪器的数据处理。

A special hierarchical model was proposed to overcome the bottleneck on the fiber length distribution analysis by a random-beard image method, which is a new method for fiber length determination. Based on the two-end characteristic of random-beard, the model could figure out the proportion of fibers shorter than certain thresholds, and derive out a series of formulas for converting fibrogram to cumulative diagram and length frequency histogram via discontinuous point operations, avoiding the previous differential operations which magnified the measurement noise and led to serious measurement errors. Both cotton and wool were tested, respectively with the gauge of 2 mm and 6 mm, using these formulae and a single fiber measurement method. The histograms show that the mean differences of the weight frequencies of the length groups from the two methods, are 0. 31% and 0. 26% , respectively, and the differences are all less than 1% , which means the measurements from the two methods have a good agreement. The new calculation method in this paper is highly precise and valuable for the data processing of fiber length measuring instruments.