Modal identification in presence of noise using an optimisation approach

This paper deals with the problem of modal parameter identification when the measurements are perturbed by unknown but bounded noise. It is well known that the classical Total Least Square (TLS) solution is the most accurate one, but that it is quite sensitive to data perturbations. This feature is a big drawback since it is desirable that the estimated modal parameters should not vary when perturbations on measurements change. An optimisation technique suited to so-called second-order cone programs [2] is proposed and tested. This method sets the identification problem in a MIN-MAX formulation [1] and uses an iterative interior-point primal-dual potential reduction algorithm [3, 4]. The residual error is first maximised over the set of possible perturbations leading thus to a worst-case residual error. Then, it is minimised over the set of identification variables. This procedure guarantees the robustness of the solution in the sense that no perturbation of the considered set could make the residual error bigger. This robustness is obtained to the detriment of an absolute accuracy. A good compromize between robustness and accuracy may be found through the prior resolution of the associate TLS problem. The optimisation program is tested in the case of a clamped-free beam for which closed-form solutions are available. A comparison with the TLS solution is also performed.