TY - JOUR

T1 - Non-probabilistic uncertainty quantification for dynamic characterization functions using complex ratio interval arithmetic operation of multidimensional parallelepiped model

AU - Zhao, Meng-Yun

AU - Yan, Wang-Ji

AU - Yuen, Ka-Veng

AU - Beer, Michael

N1 - Funding Information: This research has been supported by the Natural Science Foundation of China under Award No. 51778203 , the Science and Technology Development Fund, Macau SAR (File no. FDCT/0017/2020/A1 and SKL-IOTSC-2018-2020), the Start-up Research Grant of University of Macau (File No. SRG2019-00194-IOTSC) and the Research Committee of University of Macau under Research Grant (File no.: MYRG2018-00048-AAO).

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Complex interval division

KW - Frequency response function

KW - Interval analysis

KW - Parallelepiped model

KW - Structural health monitoring

KW - Transmissibility

UR - http://www.scopus.com/inward/record.url?scp=85100398917&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2020.107559

DO - 10.1016/j.ymssp.2020.107559

M3 - Article

AN - SCOPUS:85100398917

VL - 156

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 107559

ER -