Complex Coherence Constraint for the Definition of the Spectral Density Matrix
The cross spectral density (CSD) for a multiple-input/multiple-output (MIMO) random vibration is typically defined by the complex coherence consisting of the modulus and the phase. The purpose of this paper is to present a constraint for the complex coherence to allow the CSD to be defined more easily. The study of the complex coherence constraint is based on Cholesky decomposition of the spectral density matrix (SDM). The complex coherence must be bounded in the interior or on the boundary of a constraint circle to ensure a physically realizable random vibration. This paper proposes a new approach to define the complex coherences of the SDM by using recursive formulas based on the constraint circle.Abstract
Contributor Notes
ABOUT THE AUTHORS
Zhihua Liu holds a PhD from Tsinghua University, China. He is currently an Associate Research Fellow at the National Institute of Metrology in China. His research interests include vibration testing theory and method and the development of testing equipment design and control.
Chenguang Cai holds a PhD from Beijing University of Aeronautics and Astronautics, China. He is currently an Associate Research Fellow at the National Institute of Metrology in China. He is a member of ISO/TC 108/SC 3. His research interests include metrology standards and the theory and method of mechanical vibration and shock.
Yan Xia holds a B.Eng from Capital Normal University, China. His research interests include vibration measurement and sensitivity calibration.
Ming Yang holds a B.Eng from Beijing University of Chemical Technology, China, where he is currently pursuing a PhD. His research interests include machine vision for vibration measurement and sensor testing.