Abstract
Almost all papers dealing with modeling problem focus their attentions in how to find optimum values of parameters of a system model, of which form is given a priori. In practical situations, however, it is not known in advance whether the given form of the model is valid as a mathematical expression of the system behaviour, so it is necessary to test goodness of fit of the model.
A method to test goodness of fit of a transfer function model of a dynamical system is proposed in this paper. The hypothesis that the model is valid is rewritten into the hypothesis that
E[I]=0
Where I is a random variable, a function of the system input and output, and has following properties;
1) I is normally distributed, and
2) every sample of I is independent.
The hypothesis is then able to be tested by the well-known method of Student. Two examples of simuation tests, discussion on the data length required to detect the invalidity of the model, and the method of test when model parameters have dispersion are described.
