The problem of modelling and forecasting the sway motion response of a moored vessel to random sea waves is discussed. When the sea wave fluctuation is measured and recorded digitally with a proper sampling rate, the future response of the vessel can be actually predicted with relatively high accuracy by utilizing an (adaptive) quadratic filtering technique, which is summarized in this paper. Some experimental results based on a scaled model wave basin test are also presented to demonstrate the utility of the above technique.


It is well known that the relationship between random sea wave excitation and the corresponding response of a moored vessel is highly nonlinear. When moored in a random sea, ships and barges undergo large amplitude oscillations near the undamped natural frequency of the vessel-mooring system, which is far below the frequencies of the incident sea waves. This phenomenon, known as the low-frequency drift oscillation (LFDO), has been an important subject in offshore engineering and related applications. Recent works by Pinksterl, Remery and Hermans2 and others indicate that the mean and low-frequency wave drift forces are related to the amplitude of the incident sea wave by a quadratic nonlinearity.

In a previous paper, we proposed a new time domain approach, based on statistical estimation theory, to modelling the LFDO and presented some preliminary results demonstrating the performance of the proposed approach. This approach, called the quadratic filtering method, is computationally simple and seems to be potentially useful in related problems such as stabilizing the sway response of a moored vessel.

The purpose of this paper is to summarize some recent results on the quadratic filtering method and its application to the prediction of LFDO of a moored vessel. In addition to a formal solution to the optimum quadratic prediction filter, we present two practical procedures, batch-processing and adaptive, to synthesize the quadratic prediction filter (QPF). This paper also includes some results of experiments which were conducted using data collected from a scaled model wave basin test to investigate the utility of QPF methods, batch-processing and adaptive; in forecasting the sway response of a moored barge.


Investigation of statistical relationships between observed data and their application to constructing an optimum estimator are important aspects of estimation theory. When the behavior of a dynamic system is to be studied, the physical property of the system is implicitly used in terms of the statistical relationships between input and output of the system. In this regard, the linear filtering technique has been successfully used in many applications such as geophysics and seismic data analysis. However, if one is to study a nonlinear system such as the response of a moored vessel to random sea waves, the linear approach must be generalized to nonlinear systems.

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