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.