On the uniqueness of modal parameter estimation

We examine the question of uniqueness of solution to the modal parameter problem by applying a least-squares output error estimator to a six-degree-of-freedom shear building using both a two-and a six-parameter model. Multiple solutions are located by initiating the iterative parameter estimation algorithm from random starting points. The case study provides tangible illustrations of the phenomena latent in modal parameter estimators and demonstrates several counter-intuitive results. The study of the two-parameter model allows us to show the connection between multiple solutions for noise-free data and solution clustering for noisy data. The results suggest a new definition of the best measurement set as being the one most likely to lead to the correct solution with the least sensitivity to noise. We conclude that modal parameter estimation from sparse measurements, albeit fraught with difficulties, can yield valuable results.