Strategy for finding a near-optimal measurement set for parameter estimation from modal response

Algorithms that estimate structural parameters from modal response using least-squares minimization of force or displacement residuals generally do not have unique solutions when the data are spatially sparse. The number and character of the multiple solutions depend upon the physical features of the structure and the locations of the response measurements. It has been observed that both the number of solutions and the sensitivity of the parameter estimates to measurement noise is greatly influenced by the choice of measurement locations. In this paper, we present a heuristic method to select a near-optimal subset of measurement locations starting from a particular set of measurements, by minimizing the sensitivity of the parameter estimates with respect to observed response. The statistical properties of solution clusters generated from a Monte Carlo samples of noisy data are used to determine the best candidate measurement to be dropped from the current set. The process is repeated until solution sensitivity cannot be significantly reduced. We also show that the laborious Monte Carlo computations can be avoided in certain cases by using a direct computation of sensitivity estimates. A numerical example is provided to illustrate the method and to examine the performance of the proposed algorithm.