Design of experiments for static influences on harmonic processes

In mechanics it happens that some fixed influencing factors determine the nature of a harmonic process. This can be modelled by regression of the influencing factors on periodogram ordinates of the relevant frequencies. Thereby the time-domain is bypassed, and static models can be applied. Since it is known that periodogram ordinates are (non-central) chi-squared distributed, when the noise process is gaussian, it seems to be natural to tackle the problem with generalised linear models. But in the case of harmonic processes the ordinates at the relevant frequencies typically show large non-centrality parameters and therefore a normal approximation may be an alternative. Prior information about the error distribution, parameter estimates and the link function is needed to construct an optimal experimental design for a generalised linear model. Therefore it is of interest to assess the loss realised by using a normality assumption in the construction of the experimental design. This possible loss is investigated in a simulation study. The experimental design of the simulation study itself is chosen to span a wide range of possible situations.