A covariance based framework for the propagation of correlated uncertainty in frequency based dynamic sub-structuring

摘要

Dynamic sub-structuring (DS) is the procedure by which the passive properties (i.e. frequency response functions) of an assembled structure are predicted from those of its constituent sub-structures. In this paper we are concerned with the propagation of correlated uncertainty through such a prediction, in this work a first-order covariance based propagation framework is derived based on the primal and dual formulations of the sub-structuring problem and the complex bivariate description of FRF uncertainty. The proposed framework is valid also in the case of sub-structure decoupling, since the underlying equations are of an identical form. The present paper extends previous work into a more general framework by accounting for the presence of correlated uncertainty. This is important as recent work has demonstrated that the neglect inter-FRF correlation (i.e. the correlated uncertainty associated with impact-based FRF measurements) can lead to large errors in uncertainty estimates. Efficient algorithms are introduced for implementation of the proposed framework. Results are compared against Monte-Carlo simulations and shown to be in good agreement for both correlated, uncorrelated and mixed uncertainty. These results further illustrate that the neglect of inter-FRF correlation, when physically present, can lead to large over-estimations in the uncertainty of coupled structures. This result justifies use of the proposed framework.