纺织学报 ›› 2019, Vol. 40 ›› Issue (01): 32-39.doi: 10.13475/j.fzxb.20171206308

• 纺织工程 • 上一篇    下一篇

基于组合学的茧丝落绪分拆模拟与分析

黄继伟1,2, 宁晚娥1, 张锋2,3, 左保齐2,3()   

  1. 1.广西科技大学 生物与化学工程学院, 广西 柳州 545006
    2.苏州大学 纺织与服装工程学院,江苏 苏州 215006
    3.现代丝绸国家工程实验室(苏州), 江苏 苏州 215123
  • 收稿日期:2017-12-31 修回日期:2018-09-06 出版日期:2019-01-15 发布日期:2019-01-18
  • 通讯作者: 左保齐
  • 作者简介:黄继伟(1981—),男,副教授,博士生。主要研究方向为缫丝工程及丝绸新材料。
  • 基金资助:
    国家自然科学基金资助项目(51763001);广西自然科学基金资助项目(2016GXNSFBA380015);广西高校科研立项资助项目(KY2015LX174);广西科技大学科学基金资助项目(校科自1419203)

Simulation and analysis of bave partition produced by dropping end based on combinatorics

HUANG Jiwei1,2, NING Wan'e1, ZHANG Feng2,3, ZUO Baoqi2,3()   

  1. 1. College of Biological and Chemical Engineering, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, China
    2. College of Textile and Clothing Engineering, Soochow University, Suzhou, Jiangsu 215006, China
    3. National Engineering Laboratory for Modern Silk(Suzhou), Suzhou, Jiangsu 215123, China
  • Received:2017-12-31 Revised:2018-09-06 Online:2019-01-15 Published:2019-01-18
  • Contact: ZUO Baoqi

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摘要：

为模拟缫丝中1根完整茧丝分多段多次参与生丝并合的现象,以及为计算机模拟缫丝提供更合理的解舒丝段线密度序列数据,在离散化茧丝落绪点模型的基础上,利用组合学理论,先获取茧丝落绪节点集合的所有子集,并将1个子集与1种落绪分拆模式对应,进而计算出每种落绪分拆模式出现时的概率,构建出以落绪分拆模式为枚举型随机变量的概率质量函数,然后利用逆变换取样法对所有落绪分拆模式进行随机抽样,实现了对1根完整茧丝的落绪分拆模拟。结果表明:1根茧丝所有落绪模式的统计结果与该茧丝进行100万次落绪分拆模拟的统计结果验证了该方法的准确性;同时进一步地针对茧丝长为正态分布的2万根茧丝进行落绪分拆模拟和统计分析,确认其完全符合解舒丝长分布规律。

关键词: 茧丝落绪分拆, 组合学, 计算机模拟缫丝, 解舒丝长, 落绪次数, 茧丝线密度序列

Abstract:

In order to simulate the phenomenon that the merger of raw silk participated by bave in the forms of multiple segments and multiple times, and to provide reliable data about fineness sequence of filament for reeling simulation using a computer, based on the model of discrete dropping point of reeling and combinatorial theory, all subsets of bave dropping end point set were acquired, then a subset was corresponded to a bave dropping end partition modes, and the probability of artition model of dropping ends was calculated. The inverse transformation sampling method of an enumerated random variable distribution was employed to randomly sample partition models of dropping ends, making the simulation of partition dropping ends available. The simulation method is proved to be correct by means of statistical analysis for all dropping end patterns of bave and 100 million times partition simulation for dropping ends. Further, the dropping ends of 20 thousand of bave, with length in accordance with normal distribution, were simulated, confirming the accordance of the results with the distribution of the non-broken filament length of bave.

Key words: bave partition produced by dropping end, combinatorics, computer simulation of silk reeling, non-broken filament length, times of bave dropping end, size sequence of bave

中图分类号: 

  • TS143.2

图1

茧丝落绪节点及其落绪率"

图2

不同解舒率的茧丝落绪节点的落绪率曲线图"

图3

不同落绪均一度值的茧丝落绪节点的落绪率曲线图"

图4

不同落绪部位参数的茧丝落绪节点的落绪率曲线图"

表1

茧丝落绪分拆的简单实例"

茧丝长 落绪节
点数		 落绪节
点母集		 落绪模
式子集		 落绪模式
的概率		 概率和
1 0 { } { } 1 1
2 1 {1} { } q2,1 1
{1} p2,1
3 2 {1,2} { } q3,1q3,2 1
{1} p3,1q3,2
{2} q3,1p3,2
{1,2} p3,1p3,2
4 3 {1,2,3} { } q4,1q4,2q4,3 1
{1} p4,1q4,2q4,3
{2} q4,1p4,2q4,3
{3} q4,1q4,2p4,3
{1,2} p4,1p4,2q4,3
{1,3} p4,1q4,2p4,3
{2,3} q4,1p4,2p4,3
{1,2,3} p4,1p4,2p4,3

图5

不同解舒率参数时所有落绪模式的落绪次数和解舒丝长的统计情况"

图6

不同落绪均一度参数时所有落绪模式的落绪次数和解舒丝长的统计情况"

图7

不同落绪部位参数时所有落绪模式的落绪次数和解舒丝长的统计情况"

图8

茧丝长为一定值时的随机分拆模拟结果"

图9

茧丝长为正态分布时的随机分拆模拟结果"

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