Study On Forecasting Size Curves Of Cocoon Filaments

The essential of modern management of engineering is computer simulation. To simulate the influences of the silk reeling conditions on the quality of raw silk, the size curves of cocoon filaments should be studied for simulating the size curves by computer. Theoretical description and size (or diameter) curves forecasting of the natural fiber are one of the basically studied projects in textiles in the past decades.Forecasting is a comprehensive subject including forgoing studies, and is the foundation to make scientific decisions. Forecast is to research and simulate unknown complicated mid-processes, deduces the results by some methods or technologies, according to the known conditions. For time series analysis, forecasting is to estimate the parameters of the system according to the preceding time series data.The length of the size curves of cocoon filaments within one lot varies at random. Although there is some trends in the mass, the trends of the size curves of the individual filaments are different from each other. Special methods and theories should be studied, in order to forecast size curves of cocoon filaments on the basis of investigated data of the size curves.Study on forecasting size curves of cocoon filaments is the foundation of computer simulation of silk reeling. Size curves of cocoon filaments have shape characters similar to life course. Mathematical model of non-stationary time series with finite length has to be studied for the theoretical studies. Correct foundation of this type of mathematical model will add important content to time series analysis and has influences on artificial intelligence, medical diagnosis, failure check. hydrometeorology and earthquake prediction etc.The purpose of the study is to found new mathematical model of size curves of cocoon filaments and to solve the problems about the methods, theories and demonstration in founding mathematical model. The important point of this project is to study some methods, models and theories, to simulate size curves of cocoon filaments by use of computer and size data of material cocoons.Size curves of cocoon filaments can be regarded as non-stationary time series with finite length varying at random. Generally, non-stationary time series may be very complicated and it is difficult to do any statistical analysis. Therefore the emphasis of this task is to study auto-regressive model of non-stationary time series with finite length.In this dissertation, two transform methods unifying the series lengths of the size curves of cocoon filaments are discussed. On the basis of transform experiments, transform error is analyzed. The method separating trend components and fluctuant components from size curves of cocoon filaments is put forward for analyzing mathematical model of size curves of cocoon filaments. The average at every time point of the fluctuant components separated by this method is zero.Fluctuant components of size curves of cocoon filaments are non-stationary time series with zero mean and different variance at every time point. After standardizing transform of fluctuant component series of size curves of cocoon filaments, the simulation method of the series is brought forward by means of auto-regressive model of stationary time series. The simulation and analysis are carried out.Time varying parameter auto-regressive model is founded for non-stationary time series. It is mathematically proved that the auto-covariances of original series are equal to that of series simulated by time varying parameter auto-regressive model. By means of time varying parameter auto-regressive model theory, size curves of cocoon filaments of 9 lots are simulated. The results show that size curves of cocoon filaments simulated by use of this model possess excellent statistical characters.Finally, pattern characteristic expression of size curves of cocoon filaments is put forward.