On Raw Silk Management Research

Based on the study of simulation of cocoon filament size curve and the distribution theory of length of the non-broken cocoon filament, depended on the methods of Monte Carlo simulation and analysis of time series, this paper mainly discusses the mathematical model making and application problem in the silk size management of the fixed cocoon number reeling process. The following are the main contents and results:1. Distribution of the Filament Number of Each Cocoon Layer in Raw Silk ThreadsDivide a cocoon filament into n layers from outside to inside according to a certain regulation, then cut these cocoon filaments into non-broken cocoon filaments according to the distribution of length of non-broken cocoon filaments, in the section of raw silk which is formed by the reeling with fixed number cocoons with these non-broken filaments, we discussed the probability of the filament number from different layer of cocoons, and the probability distribution and statistic characteristic were given in stable reeling state through the theoretical analysis, furthermore the theoretical results were verified by computer simulation of reeling process. The model of the stochastic process and analysis results obtained in this article provide the bases for theoretical study of cocoon matching in multi-end reeling process, and at the same time some of the results can be applied in the realm of systems engineering.2. Analysis of the periodic changing properties of the cocoon layers in the single cocoon reeling raw silk.In the multi-end reeling process the dropping end cocoons are classified into three types, which are the outer, the middle and the inner layer ones. Under the end-feeding rule of feeding whatdropped, different layer of cocoons presents periodic change in the raw silk by single cocoon reeling process. By discussing the properties of the periodic length distributing of the change, this article theoretically proves that the expected value of the one-period silk length of the cocoon layer is the average length of cocoon filament, and gives the computing method of the one-period silk length variance of the cocoon layer on the condition that the length of cocoon filament is a fixed value, and the rate of dropped end cocoon can be any random continuous curve.3. The analysis of the continuous property of single cocoon reeling raw silk sizeBy using an idealistic sine wave model, the time series of the single cocoon reeling raw silk size is made. In the model the change of the fluctuating extent and period have an effect on the decaying rate of the autocorrelation coefficient sequence. And by investigating the effects, the relational expression, based on the single cocoon reeling process, between the raw silk size autocorrelation coefficients decaying rateAand the characteristic value of the silk size time series is made. Thus enables us to make the time series of raw silk size with the required continuity, and also provides us new ways in further study of the raw silk size continuity.4. The analysis of the continuous property of raw silk sizeSetting the decaying rate^and the quasi-cycle value T in the model of the silk size autocorrelation coefficient, building the time series of a single cocoon reeling silk size with autoregressive model, then by combining k such time series according to different phrase, obtained time series of the raw silk size, and finally count up the silk size deviation of the time series. By this way, we discussed the effects of the decaying rate A and the quasi-cycle T on the silk size deviation, and mainly obtained the followingresults.Firstly, the silk size deviation obtained by the zero phase combing obviously greater than that obtained by stochastic changing phase combing, and the result don' t alter with the change of Aand T.Secondly, there is no evident difference in the deviation of silk size obtained by stochastic phase difference and that by same interval phase difference.Thirdly, as for the time series of raw silk size obtained by the zero phase co...