Evaluation of Errors in Reduced Order Modeling

Abstract

The purpose of this paper is to make a comparison between the equation errors and the output errors which are used as criteria for measuring modeling errors in system identification.
In many practical situations real systems have high system orders which are often unknown, and reduced order models are used for estimating the parameters of the systems. In such a case there inevitably exists a modeling error due to the reduction of orders. The modeling error is usually evaluated by the equation error and the output error.
This paper analyzes a relationship between these two errors in the case of ARX model to the system which has no zero, consequently derives that the variance of the output error is no less than that of the equation error. Furthermore it shows how the system's nature affects these two errors. To achive this purpose, the model parameters can be explicitly described by the system parameters. The result shows that when the system's poles are near the unit circle, which means a marginal stability of the system, the variance of the output error take the maximum value.