Comparison of numerical methods for identification of viscoelastic line spectra from static test data

Abstract

Viscoelastic line spectra are identified from creep or relaxation data of static experiments with different numerical methods, which may or may not depend on additional informations, to be provided by the user, about the unknown parameters. If the least square method is applied, a non-linear optimization problem with non-negative constraints on the parameters has to be solved. Its solution can be achieved directly by using a gradient-based optimization algorithm like the projected Newton method of Bertsekas. However, appropriate starting values for the unknown parameters must be chosen. The problem can be alleviated by dividing the identification task into three successive steps, based on the Tschebyscheff approximation and the quadratic optimization method by Wolfe. Alternatively, the identification task can be reduced to a quadratic optimization problem, if the user provides additional informations about the distribution of the respondance times of the spectra. The windowing-method of Emri and Tschoegl is based on this assumption. If the line spectrum is assumed to have equally distributed spectrum lines on the logarithmic axis, the identification problem can also be solved by standard regularization techniques, like the truncated singular value decomposition or the Tikhonov regularization. The choice of qualified r espondance times as additional information requires some experience with the identification task at hand. Its results may be improved after several reruns of the algorithms. Various applications of the methods to test and experimental data are given and a comparison of their performance is discussed. Copyright © 2005 John Wiley & Sons, Ltd.