The Determination of Modal Damping Ratios and Natural Frequencies from Bispectrum Modeling

Abstract

We present a new signal processing and testing technique by using higher statistical moment, the bispectrum, to determine the damping ratio and natural frequency of offshore structures excited by both unexpected Gaussian forces and known non-Gaussian driving forces. Due to the unexpected exciting forces, such as the turbulence, in the ocean environment, the transfer functions of the offshore structures are hardly determined through operating a known driving force and measuring its response. In order to overcome this problem, some of the existing techniques try to model the unexpected forces as white Gaussian forces or almost white Gaussian forces and determine the modal parameters from the response only. Some others are trying to average the input and output in certain effective way to suppress unexpected parts. Our method uses third order moment so as to keep the influence of the unexpected Gaussian forces away from the determination of the transfer function of the structure which has linear properties. We model the third order moment property of the response function with a bispectral model. And the modal parameters can be calculated from the estimated model's coefficients. Our method was proved by a considerable amount of simulations.