An application of the Fast Fourier Transform to the short-term prediction of sea wave behaviour J. Ross Halliday a , David G. Dorrell b, * , Alan R. Wood c a Natural Power Consultants Ltd., Dalry, Castle Douglas, Scotland, UK b University of Technology Sydney, School of Electrical, Mechanical and Mechatronic Systems, Sydney NSW 2007, Australia c University of Canterbury, Department of Electrical and Computer Engineering, Christchurch, New Zealand article info Article history: Received 3 February 2010 Accepted 29 November 2010 Available online 12 January 2011 Keywords: Fourier transform Wave prediction Dispersion relationship Non-harmonic modelling abstract This paper examines the appropriateness of the Fast Fourier Transform for decomposition and recon- struction of wave records taken at fixed locations and transposed to a different temporal and spatial point. In marine renewable energy, advanced control methods based on the future prediction of waves are being developed. These methods are based on the assumption that a forward looking prediction is available and over the years there has been a conjecture that the FFT may perform this role and that the prediction of wave behaviour at any point on the sea surface should be realizable. The validity of this statement is tested using numerical wave records. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction There are several aspects to the assessment of sea waves in terms of their spectral content and energy resource. Most studies are concerned with resource estimation, particularly in specific locations where the wave energy extraction potential is being considered [1e4]. Some studies address the impact of wave energy generation on the environment [5] and wave energy generation in nearshore locations where the wave spectrum is more chaotic [6]. Wave motion is often studied in relation to the operation of specific energy converters [7,8]. However one issue that is deemed to be useful in the deployment of sea wave energy generators is short term wave prediction using wave measurement devices or predictors at a distance from the generator. This would allow systems to foretell what wave conditions are oncoming so that a time-lag in system reaction can be removed. Essentially it can be tuned. There are many systems in development, examples are shown in Ref [9e11] and these may be aided in their operation by knowledge of the oncoming wave spectrum. A general misconception in early stage wave energy projects is that this prediction of surface elevation is a trivial problem. This perception is underpinned by observing shoreline waves, which appear to roll onshore with a semi-regular period, reinforcing the image of a theoretical wave of a single fixed frequency. This simplified model lends itself well to exploring the potential that the Fast Fourier Transform (FFT) holds in predicting wave behaviour. However, when taking visual observations to an offshore location it becomes very difficult to track a constant wave crest since the wave groups consist of waves with varying heights and wavelengths; hence, the ideal single-frequency wave model then breaks down. This is further complicated by presence of new and old sea states persisting from multiple directions. Over the past few decades there have been several studies into the use of the FFT for short term wave prediction. This paper, which expands an earlier paper [12], seeks to gather, implement and build upon outcomes from previous studies in order to develop and examine the point at which the FFT based prediction breaks down. We will go further and attempt to explain why this breakdown occurs. 1.1. Literature review Short term deterministic prediction of sea waves has been recently studied [13,14]. In the developing wave energy industry, a short term prediction would advantageous in advanced control strategies for various wave devices. These control techniques were briefly reviewed in Ref [15] and would allow economic system utilization. Belmont et al. [16] showed that a prediction of the order of 30 s ahead should be possible. In producing the prediction results it would appear that a limited number of widely spaced wave vectors were used in constructing the source records. The reduced complexity of the input data used should cast some doubt over the validity of the 30-seconds-ahead claim. Zhang et al. [17] went * Corresponding author. E-mail address: ddorrell@eng.uts.edu.au (D.G. Dorrell). Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.11.035 Renewable Energy 36 (2011) 1685e1692