Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Moving Point Prediction of Linear Irregular Water Waves Using
Numerical Impulse Response Function
Md Shahidullah Kaiser1 and Takahito Iida1
1

Department of Naval Architecture and Ocean Engineering, Osaka University, Osaka, Japan

ABSTRACTin expanding the sea states in which many crucial marine activities canbe safely performed (Giron-Sierra et al. 2010). Further, it can predict
the waves that a ﬂoating body will meet and the wave region surrounding
it, which may help predict and regulate the motion of a ship (Naaijenet al., 2018). Additionally, highly accurate real-time prediction of water
waves enables the experimental basin’s wave absorbers (Christensen andFrigaard 1994), as well as wave energy harvesters (Al Shami et al. 2019),
to operate correctly and to regulate wave energy device (Korde et al.
2017; Petranović et al. 2021), and to absorb wave energy (Naito andNakamura 1986).

Short-term prediction of ocean wave behavior is an eﬀective technology for operating ships and oﬀshore structures. It is possible to makemedium to long-term predictions up to one week in advance, thanks to
the development of the statistical approaches. On the other hand, using
short-term prediction, a precise forecast of the sea surface elevation at aspeciﬁc location can be provided in a comparable period (10s to 1minahead). However, most research on short-term deterministic predictionof waves has concentrated on a static point. So far, preliminary researchhas been conducted on the moving point, even though it is crucial forships in motion at forward speed. Consequently, it is one of the areasthat can be identiﬁed as needing improvement. The Fourier transformis widely used to examine and record time-series data. During the last
several decades, all prior eﬀorts for wave prediction appear to have been
based on the Fourier transform. Since the Fourier transform is not atime-developing process, the impulse response function may contributesigniﬁcantly to the accuracy of the water waves prediction. By deﬁning
an adequate causal region with the impulse response function, output atpresent can be predicted by inputs from the current and adjacent pasttimes. The impulse response function has previously been a viable technique for predicting ﬁnite depth water waves on a static point. This study
provides a numerical solution of an impulse response function for moving points while considering a ﬁnite-depth dispersion of water waves.
The numerical form of the response function is obtained using the inverse discrete Fourier transform. A towing tank experiment is carriedout at various train speeds, and predictions of irregular waves are compared with the experimental results. It is found that the impulse response
function can lead to the opportunity for more accurate short-term wave
prediction for moving points, which could be implemented for ships inmotion under head waves conditions at a certain point in the future.

Since its origins in the early 1990s, deterministic wave prediction havebecome one of the fastest-growing marine science disciplines (Al-Ani etal. 2020). Due to the advancement of statistical techniques, medium andlong-term forecasts may be achieved one week in advance. On the otherhand, the wave surface elevation may be accurately predicted using shortterm prediction at a speciﬁc location provided in a comparable period(10s to 1min ahead) (Halliday et al. 2005). Over the past few decades,
Fourier coeﬃcient estimation has been recognized as the most eﬀective
approach for deterministic wave prediction. Belmont et al. (2014) determined the Fourier coeﬃcients by using experimental wave proﬁling
radar and a fully two-dimensional approach in the form of the classic
discrete-time Fourier transform. As an additional measure of comparison, Al-Ani et al. (2019) utilized measurements taken at an up-wave
position to make predictions based on an estimation of Fourier coeﬃcients. However, as propagation distance increases, this approach loses
accuracy. The accuracy of the instantaneous predicted elevations at thedevice is enhanced by averaging the predictions based on Fourier coeﬃcient estimations closer to the device (Al-Ani et al. 2019). Furthermore,
to some extent, wave records obtained at a ﬁxed location have been decomposed and represented using the Fast Fourier transform (Halliday etal. 2006; Holphe et al. 2021).

KEY WORDS: Moving point prediction; Short-term prediction; Impulse response function; Inverse discrete Fourier transform; Convolution
integral.

Another method for deterministic linear water wave prediction is to employ the convolution integral of the input wave proﬁles and an impulse
response function. It can be considered one of the possibilities for water
wave prediction using a linear time-invariant system. Creating a suitablecausal region using the impulse response function makes it possible topredict output at present using inputs from the current and subsequent

INTRODUCTION
Short-term deterministic wave prediction is an eﬀective technique thatcan eﬃciently operate a wide range of marine services (Crossland et al.
2009) and oﬀshore operations (Klein et al. 2020). It can be beneﬁcial

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