Estimation of Response Transfer Functions of Offshore Structures Using the Time-Varying ARX Model

ABSTRACT
The purpose of this paper is to propose and investigate a new approach
for estimating response transfer function of offshore structures with
wave as excitation input. The approach is based on time-varying
autoregressive with exogenous input (TVARX) model. This method is
virtually unexplored in offshore engineering field, as a number of
works have shown that transfer functions such as response amplitude
operator are estimated based on discrete Fourier transform (DFT).
Here, we outline a practical algorithm for TVARX model which uses
expectation-maximization (EM) algorithm based on Kalman smoother
to generate the transfer function. The method is then applied to sampled
discrete wave as excitation input and the motion responses of offshore
structures as output data, generated from simulated field measurements.
The proposed approach outlined here has shown the tremendous
potential in the estimation of transfer function. The results indicate that
TVARX model produces accurate, smooth and less noise TF estimates
over DFT method. TVARX model also allows for the creation of time
varying transfer function (TVTF).
KEY WORDS: Motion responses; Kalman smoother; Time-varying
ARX model; Transfer function.