Graphically Oriented System for Textile Processes Models Building

摘要

Multiple linear and nonlinear models building in textile branch belongs to the most complex problems solved in practice. Interactive approach to model building can be divided into the following steps (Meloun, Militky and Forma 1998): 1) Selection of provisional models, 2) Analysis of assumptions about model, data and used regression methods (regression diagnostic), 3) Extension and modification of model, data and regression method, 4) Testing of model validity, their prediction capability, etc. Some interactive strategy of multiple regression model building based on the above steps is described in book (Meloun, Militky and Forina 1998). Many problems in realization of step i) are caused by strong multicollinearity. Multicollinearity in multiple linear regression analyses is defined as approximate linear dependencies among the explanatory variables (columns of design matrix X). It is well known that under strong multicollinearity the individual scatter plots between response y and explanatory variables x_j cannot be used for model building. Models of textile processes are usually created by the classical methods of experimental design. This approach enabling the optimization of experimental conditions is formally very general but in practice often leads to the incorrect models containing often too parameters. In this contribution, the graphically oriented method of textile type models building will be presented. This method is based on the special projection enabling the investigation of partial dependence of response on the selected exploratory variable. The aim of graphical analysis is to evaluate the type of nonlinearities due to function of predictors describing well the experimental data. For selection of suitable model the characteristics based on the cross validation principle will be proposed. The program MULTIREG in MATLAB is mentioned. This methodology is demonstrated on the example of PET/cotton type yarns tenacity prediction.