Textile Surfaces Analysis and Modeling based on Statistical Methods: Variance Analysis and Autocorrelation Functions

Abstract

Statistical analysis using between-variance are usually used in various industries. In this paper we propose to apply these statistical analysis tools to textile surfaces. Based on early theories [1— 9] statistical tools have been developed to take into account periodic and random defects observed on linear textiles. Indeed, in the textile industry the raw material presents a strong random unevenness and moreover each processing step introduces its own periodic irregularity (e.g. faults due to an elliptic roller or defective gear). A method for determining these irregularities is developed whereby it is possible to define the function of the variance-mass per unit area of the fibrous web if the overall mass variance of the web produced during the industrial process is known. Indeed, with the help of the autocorrelation function, the between-area-density variance function B(S) of the fibrous web can be predicted and the shape of the B(S) curve is determined. The two types of irregularities have also been examined and analyzed. Random irregularities were developed based on the functions of the most common distributions (isoprobable, equiprobable, uniform distributions). Then, the periodic irregularities have been developed and generalized. Finally, we discussed the actual industrial case known as a superposition of periodic and random irregularities.