Optimal Excitation for Nonparametric Identification of Viscoelastic Materials

The problem of optimal excitation in nonparametric identification of the complex modulus of a viscoelastic material is considered. The goal is to design the input spectrum in an optimal way, so that the covariance matrix of the estimates is minimized in some sense. It is shown how the covariance matrix of the estimates can be expressed in terms of the input spectrum. This theory can also be used in order to identify the (unknown) excitation, used in a particular experiment, from measured strain data. Two scalar criteria connected to the trace and to the determinant of the covariance matrix, implying A- and D-optimal experiment design, are considered. The results indicate that the accuracy of the estimates can be greatly improved by applying an optimal input signal. Issues concerning the implementation of the achieved optimal input spectrum in an experiment are discussed briefly.