| The viscoelastic behavior expressed by the discrete linear relaxation spectrum [ g_i ,λ_i ] is one of the most important properties for molten polymers. This spectrum is commonly obtained from experimental data with the dynamic moduli [ G′( w ) ,G′′( w)]. The determination of the relaxation time spectrum has been recognized as an ill posed problem with degree of ill-posedness increasing as the number of relaxation times increases. One of the drawbacks of linear regression methods, apart from the obvious ill-posedness, is that the relaxation times are specified a priori. Unfortunately, we will show in this situation, the discrete Picard condition which is a necessary condition for obtaining good regularized solutions is often not satisfied in practical use. At present, a number of numerical packages (e.g., NLREG and GENEREG) have been developed to relieve the difficulties associated with the general linear regression methods by setting the integral kernel to be nonlinear. Nonlinear regression methods like IRIS allow the relaxation time to be freely adjustable. With these methods one can treat the problems properly for a sufficient wide range of experimental frequency. However there has no exhaustive study for the case of incomplete data sets.In this thesis, the emphasis is placed on cases of incomplete experimental data. effects of the time-scale truncation and errors of experimental data on the discrete relaxation spectrum are presented. How to represent the relaxation spectrum of a material by using the fewest possible Maxwell-modes (such a representation is called a'Parsimonious'model) is discussed. A method based on program GENEREG with Parsimonious model is proposed. Numerical results show that the modified method is efficient and reliable to compute a discrete spectrum from a given set of experimental data. Based on the analysis on the standard'Gaussian spectrum', it is found that .the data density is crucial for obtaining a more accurate spectrum. It also turns out that the experimental errors influence the range of relaxation time, and adding one or two more modes in spectrum calculation enhances accuracy of the solution. For a set of incomplete data, reliable results may be achieved if a prior information is given with the modified method. Finally through the analysis of the relaxation spectrum of Polycarbosilane (PCS), it is observed that the modified method is robust. |
