A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.
Katarzyna Czyż, Bożena Patkowska-Sokoła, Andrzej Filistowicz, Marzena Janczak and Robert Bodkowski
The aim of the study was to analyse the hair coat of the three dachshund varieties, i.e. shorthaired, longhaired, and wirehaired, with respect to its histological structure and content of selected chemical elements. The study was conducted on female dachshunds originating from individual breeders. The study included the assessment of the contribution of particular hair fractions, measurements of hair thickness and length, and also the analysis of histological structure of particular hair fractions. A great differentiation in the parameters and structure of particular kinds of hair from the examined dogs was demonstrated. Thickness and length of hair of particular varieties showed statistically significant differentiation, as well as percentage contribution of particular hair fractions. As regard the content of chemical elements in particular hair fractions and dachshund variety, it appeared that the elements forming hair keratin were the most abundant. The findings presented in the paper may be a useful tool for the recognition of dachshund varieties based on their hair coat structure. They may be also a valuable contribution to the expanding breed standards, which lack histological hair description.