Identification of structural systems using naturally induced vibration data in the presence of measurement noise

The identification of structural systems using naturally induced vibration data in the presence of measurement noise by the method of instrumental variables is studied. It is well known that when measurement noise is present least squares methods will yield an inconsistent estimator. This leads us to consider methods which will yield a consistent estimator in the presence of noise. The maximum likelihood method provides a solution to the method, but is difficult to implement in the case of large systems because of the amount of computation required. In this paper we present the application of the method of instrument variables for the identification of the parameters of structural systems excited by white noise in the presence of white measurement noise. The equations required for the application of the method to a structural system and the resulting consistent estimator are derived. Although the concept of instrumental variables is not new, the application of this method to problems of structural systems is sufficiently attractive to justify its presentation. The results of simulation experiments which verify the theoretical development are presented.