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

Meggitt, JWR; Moorhouse, AT

Abstract

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 impactbased
FRF measurements) can lead to large errors in uncertainty estimates. E�cient 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.

Citation

Meggitt, J., & Moorhouse, A. (2020). A covariance based framework for the propagation of correlated uncertainty in frequency based dynamic sub-structuring. Mechanical Systems and Signal Processing, 136, 106505. https://doi.org/10.1016/j.ymssp.2019.106505

• Journal Article Type: Article
• Acceptance Date: Nov 6, 2019
• Online Publication Date: Dec 13, 2019
• Publication Date: Feb 1, 2020
• Deposit Date: Nov 20, 2019
• Publicly Available Date: Dec 13, 2020
• Journal: Mechanical Systems and Signal Processing
• Print ISSN: 0888-3270
• Publisher: Elsevier
• Volume: 136
• Pages: 106505
• DOI: https://doi.org/10.1016/j.ymssp.2019.106505
• Publisher URL: https://doi.org/10.1016/j.ymssp.2019.106505
• Related Public URLs: https://www.sciencedirect.com/journal/mechanical-systems-and-signal-processing
• Additional Information: Funders : Engineering and Physical Sciences Research Council (EPSRC); Projects : EMBED; Grant Number: EP/P005489/1