Keywords: back-propagation neural network, time series, data complement, significant wave height.

The determination of the design wave for marine structures commonly requires a very long term consecutive wave recording data. However, it might encounter the difficulties that the data records are incomplete or there is even no available long term data. This is a crucial issue in coastal, harbor and ocean engineering. There were several models proposed to complete the incomplete time series, such as the interpolation method for small gaps, the autoregressive moving average (ARMA) models for longer gaps [1,2,3,4], and the use of transfer functions between two measuring stations based on ARMA processes [1,5] etc. Due to the seasonality of the time series of waves, the deseasonalized procedure was required a priori as the ARMA model was applied. Besides, it usually requires a very long term data base.

Alternative to stochastic models, this paper reports the application of artificial neural networks (ANN) to the complement of the time series of waves between two recording stations. The back-propagation procedures were adopted in the present model, from which the interconnection weights were obtained for the simulation of a time series based on the neighbouring measuring site. The field data of 1985 at two stations, approximately 20 km apart, in the northeast of Taiwan were used in the model testing. Because of the seasonality of waves, three types of waves were separately trained in the neural networks: winter waves, summer waves and typhoon waves. The interconnection weights between the two stations are obtained based on short-term data, from which the time series of waves of them can complement each other. The performance of the neural network model was discussed by using two indices: the root-mean-square error and the correlation coefficient. It is found that the ANN model performs well for the wave complementary when a short term record, for example a 45-day records, was used in the training process for the seasonal wind waves. For the season of typhoon, the ANN model could also be applied well in the complementary of the significant wave heights. This study showed that neural networks are a useful technique for the wave complementary between two wave stations if they have similar meteorological conditions.

1

O.S. Hidalgo, J.C.N., Borge, C. Cunha and C. Guedes Soares, "Filling missing observations in time series of significant wave height", Proceedings of 14th International Conference on Offshore Mechanics and Artic Engineering, 2, 9-17, 1995.

2

C. Guedes Soares, A.M. Ferreira and C. Cunha, "Linear models of the time series of significant wave height in the southwest coast of Portugal", Coastal Engineering, 29, 149-167, 1996. doi:10.1016/S0378-3839(96)00022-1

3

C. Cunha and C. Guedes Soares, "On the choice of data transformation for modelling time series of significant wave height", Ocean Engineering, 26, 489-506, 1999. doi:10.1016/S0029-8018(98)00014-6

4

C.N. Stefanakos and G.A. Athanassoulis, "A unified methodology for the analysis, completion and simulation of nonstationary time series with missing values, with application to wave data", Applied Ocean Research, 23, 207-220, 2001. doi:10.1016/S0141-1187(01)00017-7

5

P.C. Ho and J.Z. Yim, "A study of the data transferability between two wave-measuring stations", Coastal Engineering, 52, 313-329, 2005. doi:10.1016/j.coastaleng.2004.12.003

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