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

Abstract

SUMMARYViscoelastic 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 respondance 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.

A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

“…To this end, a recursive computer algorithm proposed by Tschoegl and Emri [13] was employed in this study. The method was termed as the windowing method (WM) by Gerlach and Matzenmiller [41] in view of its computing characteristics. The WM is able to identify the discrete relaxation spectra from the storage or loss modulus data, since the two quantities contain the same spectral information.…”

Revisiting the identification of generalized Maxwell models from experimental results

“…Different identification methods for the material parameters of the generalized Maxwell model have been proposed in the past, see for example the general discussion in Gerlach and Matzenmiller (2005).…”

“…The third section presents the standard identification technique of parameters from DMA experiments as presented by Honerkamp (1989), Honerkamp and Weese (1990) and the theoretical results of Krein and Nudelman (1998) as well as the proposed identification algorithm. The discussion continues with the identification method of parameters from relaxation test as proposed in Baumgaertel and Winter (1992), Gerlach and Matzenmiller (2005) and the proposed optimal identification of relaxation times. The two methods are illustrated in the last chapter by a series of examples: first using artificial data, which also permits to investigate the influence of the noise and second using experimental data from literature and measurements.…”

“…A recent application example is given in Diani et al (2012), where a generalized Maxwell model is identified to describe the viscoelastic behavior of shape memory polymers. For the relaxation experiment a dual method is proposed in Baumgaertel and Winter (1992), Gerlach and Matzenmiller (2005) where the relaxation modulus is identified. Other techniques are based on different numerical schemes to tackle this problem, as for example the combination of Laplace transform and Padé approximants reported in Carrot and Verney (1996), or the cumulative relaxation spectrum proposed in Xiao et al (2013).…”

On parameter identification for material and microstructural properties

“…(5). The authors investigated four different numerical solution methods and presented the results in [30]. The main features of these methods are shortly repeated in the next subsections and their application to the creep data, found from the experiments of Sarabi in [42], is shown exemplarily.…”