Zhao, Meng-Yun, Yan, Wang-Ji, Yuen, Ka-Veng and Beer, Michael 
ORCID: 0000-0002-0611-0345
(2021)
Non-probabilistic uncertainty quantification for dynamic characterization functions using complex ratio interval arithmetic operation of multidimensional parallelepiped model.
Mechanical Systems and Signal Processing, 156.
p. 107559.
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Abstract
Uncertainty quantification for the experimental estimations of dynamic characterization functions, including frequency response functions (FRFs) and transmissibility functions (TFs), is of practical importance in improving the robustness of the real applications of these functions for system identification and structural health monitoring. Interval analysis is an appealing tool for dealing with the uncertainties of engineering problems in which only the bounds of uncertain parameters are available. FRFs and TFs are complex-valued random variables. However, due to the negligence of the dependencies of complex-valued variables, the existing complex ratio interval arithmetic operation can be overly conservative. In this study, the polar representation of complex ratio numbers was extended to complex ratio polar intervals and a multidimensional parallelepiped (MP) interval model was introduced to accommodate the dependence between the numerator and the denominator. Based on the explicit expressions of the MP model through a dependence matrix, two new global extrema searching schemes with and without the regularization of the uncertainty domain of the MP model were proposed in order to derive the explicit formulas of the upper and lower bounds of the magnitudes and phases of the FRFs and TFs. The new schemes were then applied to the uncertainty propagation for a numerically simulated beam and a bridge subjected to a single excitation. The results showed that the interval overestimation problem could be significantly alleviated by using the new complex-valued ratio interval arithmetic operation of the parallelepiped model.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Frequency response function, Transmissibility, Interval analysis, Complex interval division, Parallelepiped model, Structural health monitoring |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 03 Mar 2021 09:04 |
| Last Modified: | 18 Jan 2023 22:57 |
| DOI: | 10.1016/j.ymssp.2020.107559 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3116433 |
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