Some Results on the Optimal Spacing of Measurements in the Identification of Structural Systems*

This paper deals with finding the optimal measurement locations for a structural system modelled by a single-degree-of-freedom oscillator, so that any one of the parameters to be identified can be estimated with a minimum variance. The measurements are assumed to be taken in a noisy environment, and the paper addresses both linear and nonlinear, nonhysteretic systems. Besides the analytical relations deduced for the optimal measurement locations, it is found that, in general, there may exist measurement locations at which no additional information on the parameter under consideration is generated. For the linear case, the optimal measurement locations are found to be independent of the system response and the actual values of the parameters to be identified. They solely depend on the nature of the excitation used in the identification procedure. Analytical results relating to the optimal measurement locations for minimizing the sum of the variances of the estimates of some of the parameters are also provided. Introduction. The identification of parameters in dynamic models for building structural systems is a field that is rapidly gaining importance [1-4], In this paper, we attempt to study the optimal spacing of measurements for a structural system modelled by a single-degree-of-freedom oscillator so that the variance of one of the parameters being identified is minimized. We start with a linear oscillator and, using Fourier transforms, derive a set a linear algebraic equations. The condition on the measurement frequencies so that the estimated variance (from noisy measurement data) of either the mass parameter, the stiffness parameter or the damping parameter is minimal is derived analytically. It is also found that there may exist a set of frequencies <o, at which no additional information on that parameter is available, yielding no reduction in its estimated variance. The determination of the optimal measurement frequencies depends solely on the nature of the forcing function used in the identification procedure and is invariant with respect to the actual values of the parameters being estimated. * Received January 10, 1984. ©1985 Brown University