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Abstract: Accurate wave forecasting with a couple of hours of warning time offers improvements in safety for maritime operation-related activities. autoregressive (AR) model is an efficient and highly adaptive approach for wave forecasting. However, it is based on linear and stationary theory and hence has limitations in forecasting nonlinear and non-stationary waves. Inspired by the capability of empirical mode decomposition (EMD) technique in handling nonlinear and non-stationary signals, this paper describes the development of a hybrid EMD-AR model for nonlinear and non-stationary wave forecasting. The EMD-AR model was developed by coupling an AR model with the EMD technique. Nonlinearity and non-stationarity were overcome by decomposing the wave time series into several simple components for which the AR model is suitable. The EMD-AR model was implemented using measured significant wave height data from the National Data Buoy Center, USA. Prediction results from various locations consistently show that the hybrid EMD-AR model is superior to the AR model. This demonstrates that the EMD technique is effective in processing nonlinear and non-stationary waves.

The authors compared capabilities of two time series forecasting models, the autoregressive model (AR) and the hybrid (EMD-AR) of the empirical mode decomposition (EMD) and AR, through prediction of long term significant wave height based on three NDBC buoy datasets. It is demonstrated by three indices including root mean square error (RMSE), correlation coefficient, and scatter diagram that the EMD-AR performs better than the AR for wave forecast especially in dealing with phase shifting.

一种用于非线性非平稳波浪极短期预报的复合经验模态分解自回归模型

[1]Agrawal, J.D., Deo, M.C., 2002. On-line wave prediction. Marine Structures, 15(1):57-74.

[2]Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6):716-723.

[3]Akaike, H., 1979. A Bayesian extension of the minimum AIC procedure of autoregressive model fitting. Biometrika, 66(2):237-242.

[4]Cannas, B., Fanni, A., See, L., et al., 2006. Data preprocessing for river flow forecasting using neural networks: wavelet transforms and data partitioning. Physics and Chemistry of the Earth, Parts A/B/C, 31(18):1164-1171.

[5]Chau, K.W., 2007. Application of a PSO-based neural network in analysis of outcomes of construction claims. Automation in Construction, 16(5):642-646.

[6]Deka, P.C., Prahlada, R., 2012. Discrete wavelet neural network approach in significant wave height forecasting for multistep lead time. Ocean Engineering, 43:32-42.

[7]Deo, M.C., Sridhar, N.C., 1998. Real time wave forecasting using neural networks. Ocean Engineering, 26(3):191-203.

[8]Deo, M.C., Jha, A., Chaphekar, A.S., et al., 2001. Neural network for wave forecasting. Ocean Engineering, 28(7):889-898.

[9]Douglas, S.C., 1996. Efficient approximate implementations of the fast affine projection algorithm using orthogonal transforms. IEEE International Conference on Acoustics, Speech, and Signal Processing, Atlanta, USA, 3:1656-1659.

[10]Duan, W.Y., Huang, L.M., Han, Y., et al., 2015. A hybrid AR-EMD-SVR model for the short-term forecast of nonlinear and non-stationary ship motion. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 16(7):562-576.

[11]Engle, R.F., 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation. Econometrica, 50(4):987-1008.

[12]Flandrin, P., Rilling, G., Gonçalvés, P., 2004. Empirical mode decomposition as a filter bank. IEEE Signal Processing Letters, 11(2):112-114.

[13]Gaur, S., Deo, M.C., 2008. Real-time wave forecasting using genetic programming. Ocean Engineering, 35(11-12):1166-1172.

[14]Hannan, E.J., 1982. A note on bilinear time series models. Stochastic Processes and Their Applications, 12(2):221-224

[15]Huang, L.M., Duan, W.Y., Han, Y., et al., 2015. Extending the scope of AR model in forecasting non-stationary ship motion by using AR-EMD technique. Journal of Ship Mechanics, 19(9):1033-1049 (in Chinese).

[16]Huang, N.E., Wu, Z.H., 2008. A review on Hilbert-Huang transform: method and its applications to geophysical studies. Reviews of Geophysics, 46(2):2007RG000228.

[17]Huang, N.E., Shen, Z., Long, S.R., et al., 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454(1971):903-995.

[18]Jain, P., Deo, M.C., 2007. Real-time wave forecasts off the western Indian coast. Applied Ocean Research, 29(1-2):72-79.

[19]Janssen, P.A.E.M., 2008. Progress in ocean wave forecasting. Journal of Computational Physics, 227(7):3572-3594.

[20]Kalra, R., Deo, M.C., Kumar, R., et al., 2005. RBF network for spatial mapping of wave heights. Marine Structures, 18(3):289-300.

[21]Kamranzad, B., Etemad-Shahidi, A., Kazeminezhad, M.H., 2011. Wave height forecasting in Dayyer, the Persian Gulf. Ocean Engineering, 38(1):248-255.

[22]Kim, D., Kim, K.O., Oh, H.S., 2012. Extending the scope of empirical mode decomposition by smoothing. EURASIP Journal on Advances in Signal Processing, 2012(1):168.

[23]Komen, G.J., Cavaleri, L., Donelan, M., et al., 1994. Dynamics and Modelling of Ocean Waves. Cambridge University Press, Cambridge.

[24]Li, G., Weiss, G., Mueller, M., et al., 2012. Wave energy converter control by wave prediction and dynamic programming. Renewable Energy, 48:392-403.

[25]Londhe, S.N., Panchang, V., 2006. One-day wave forecasts based on artificial neural networks. Journal of Atmospheric and Oceanic Technology, 23(11):1593-1603.

[26]Mandal, S., Prabaharan, N., 2010. Ocean wave prediction using numerical and neural network models. The Open Ocean Engineering Journal, 3(1):12-17.

[27]Özger, M., 2010. Significant wave height forecasting using wavelet fuzzy logic approach. Ocean Engineering, 37(16):1443-1451.

[28]Sandhya, K.G., Balakrishnan Nair, T.M., Bhaskaran, P.K., et al., 2014. Wave forecasting system for operational use and its validation at coastal Puducherry, east coast of India. Ocean Engineering, 80:64-72.

[29]Taormina, R., Chau, K.W., 2015. Neural network river forecasting with multi-objective fully informed particle swarm optimization. Journal of Hydroinformatics, 17(1):99-113.

[30]The Wamdi Group, 1988. The WAM model—a third generation ocean wave prediction model. Journal of Physical Oceanography, 18(12):1775-1810.

[31]Tolman, H.L., 2014. User Manual and System Documentation of WAVEWATCH III® Version 4.18. Tech. Note 316, NOAA/NWS/NCEP/MMAB, College Park, MD, USA, p.282.

[32]Tong, H., Lim, K.S., 1980. Threshold autoregressive, limit cycles and cyclical data. Journal of the Royal Statistical Society Series B, 42(3):245-292.

[33]Wang, W.C., Chau, K.W., Xu, D.M., et al., 2015. Improving forecasting accuracy of annual runoff time series using ARIMA based on EEMD decomposition. Water Resources Management, 29(8):2655-2675.

[34]Wu, C.L., Chau, K.W., 2013. Prediction of rainfall time series using modular soft computing methods. Engineering Applications of Artificial Intelligence, 26(3):997-1007.

[35]Wu, Q., Riemenschneider, S.D., 2010. Boundary extension and stop criteria for empirical mode decomposition. Advances in Adaptive Data Analysis, 02(02):157-169.

[36]Xiong, T., Bao, Y.K., Hu, Z.Y., 2014. Does restraining end effect matter in EMD-based modeling framework for time series prediction Some experimental evidences. Neurocomputing, 123:174-184.

[37]Zhang, G.Q., Patuwo, B.E., Hu, M.Y., 1998. Forecasting with artificial neural networks: the state of art. International Journal of Forecasting, 14(1):35-62.

[38]Zhang, J., Chu, F., 2005. Real-time modeling and prediction of physiological hand tremor. IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, USA, 5:v/645-v/648.

[39]Zhao, J.P., Huang, D.J., 2001. Mirror extending and circular spline function for empirical mode decomposition method. Journal of Zhejiang University-SCIENCE, 2(3):247-252.