# A Comparison of Ocean Wave Height Forecasting Methods for Ocean Wave Energy Conversion Systems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Denoising and Smoothing of Real Ocean Wave Height

## 3. Forecasting Methods of Ocean Wave Height

#### 3.1. ARMA Method

#### 3.2. BP Neural Network Method

#### 3.3. RBF Neural Network Method

## 4. Results and Comparison

## 5. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Khatri, P.; Wang, X. Comprehensive review of a linear electrical generator for ocean wave energy conversion. IET Renew. Power Gener.
**2020**, 14, 949–958. [Google Scholar] [CrossRef] - Jusoh, M.A.; Ibrahim, M.Z.; Daud, M.Z.; Albani, A.; Yusop, Z.M. Hydraulic power take-off concepts for wave energy conversion system: A review. Energies
**2019**, 12, 4510. [Google Scholar] [CrossRef] - Nabavi, S.F.; Farshidianfar, A.; Afsharfard, A. Novel piezoelectric-based ocean wave energy harvesting from offshore buoys. Appl. Ocean. Res.
**2018**, 76, 174–183. [Google Scholar] [CrossRef] - Deng, Z.; Wang, L.; Zhao, X.; Wang, P. Wave power extraction by a nearshore oscillating water column converter with a surging lip-wall. Renew. Energy
**2020**, 146, 662–674. [Google Scholar] [CrossRef] - Clemente, D.; Rosa-Santos, P.; Taveira-Pinto, F. On the potential synergies and applications of wave energy converters: A review. Renew. Sustain. Energy Rev.
**2021**, 135, 110162. [Google Scholar] [CrossRef] - Chen, Z.; Li, X.; Cui, Y.; Hong, L. Modeling, experimental analysis, and optimized control of an ocean wave energy conversion system in the Yellow Sea near Lianyungang port. Energies
**2022**, 15, 8788. [Google Scholar] [CrossRef] - Li, X.; Bian, Y. Modeling and prediction for the Buoy motion characteristics. Ocean. Eng.
**2021**, 239, 109880. [Google Scholar] [CrossRef] - Gao, J.-L.; Lyu, J.; Wang, J.-H.; Zhang, J.; Liu, Q.; Zang, J.; Zou, T. Study on transient gap resonance with consideration of the motion of floating body. China Ocean. Eng.
**2022**, 36, 994–1006. [Google Scholar] [CrossRef] - Li, D.-M.; Dong, X.-C.; Shi, H.-D.; Li, Y.-N. Theoretical and experimental study of a coaxial double-Buoy wave energy converter. China Ocean. Eng.
**2021**, 35, 454–464. [Google Scholar] [CrossRef] - Chen, Z.; Yu, H.; Liu, C.; Hong, L. Design, construction and ocean Testing of wave power generation system with permanent magnet tubular linear generator. Trans. Tianjin Univ.
**2016**, 12, 72–76. [Google Scholar] [CrossRef] - Giorgi, G.; Gomes, R.P.F.; Bracco, G.; Mattiazzo, G. The effect of mooring line parameters in inducing parametric resonance on the Spar-Buoy oscillating water column wave energy converter. J. Mar. Sci. Eng.
**2020**, 8, 29. [Google Scholar] [CrossRef] - Garcia-Rosa, P.B.; Ringwood, J.V. Ringwood. On the Sensitivity of optimal wave energy device geometry to the energy maximizing control system. IEEE Trans. Sustain. Energy
**2016**, 7, 419–426. [Google Scholar] [CrossRef] - Violini, D.G.; Pena-Sanchez, Y.; Faedo, N.; Ringwood, J.V. An energy-maximising linear time invariant controller (LiTe-Con) for wave energy devices. IEEE Trans. Sustain. Energy
**2020**, 11, 2713–2721. [Google Scholar] [CrossRef] - Zhang, W.; Li, S.; Liu, Y. Adaptive sliding mode back-stepping speed control of hydraulic motor for wave energy conversion device. IEEE Access
**2020**, 8, 89757–89767. [Google Scholar] [CrossRef] - Pei, Z.; Jing, H.; Tang, Z. Modeling and test results of an innovative gyroscope wave energy converter. Appl. Sci.
**2021**, 11, 4359. [Google Scholar] [CrossRef] - Gao, J.; Shi, H.; Zang, J.; Liu, Y. Mechanism analysis on the mitigation of harbor resonance by periodic undulating topography. Ocean. Eng.
**2023**, 281, 114923. [Google Scholar] [CrossRef] - Deshmukh, A.N.; Deo, M.C.; Bhaskaran, P.K.; Nair, T.M.B.; Sandhya, K.G. Neural-network-based data assimilation to improve numerical ocean wave forecast. IEEE J. Ocean. Eng.
**2016**, 41, 944–953. [Google Scholar] [CrossRef] - Rodríguez, C.A.; Taveira-Pinto, F.; Rosa-Santos, P. Experimental assessment of the performance of CECO wave energy converter in irregular waves. In Proceedings of the ASME 37th International Conference on Ocean, Offshore and Arctic Engineering, Madrid, Spain, 17–22 June 2018; p. V010T09A026. [Google Scholar]
- Falnes, J. Ocean Waves and Oscillating Systems; Cambridge University Press: Cambridge, MA, USA, 2002. [Google Scholar]
- Homayoun, E.; Ghassemi, H.; Ghafari, H. Power performance of the combined monopile wind turbine and floating buoy with heave-type wave energy converter. Pol. Marit. Res.
**2019**, 26, 107–114. [Google Scholar] [CrossRef] - Yang, C.; Zhang, Y.-L. Numerical study of hydrodynamic behavior and conversion efficiency of a two-buoy wave energy converter. J. Hydrodyn.
**2018**, 30, 235–248. [Google Scholar] [CrossRef] - Pinguet, R.; Benoit, M.; Molin, B.; Razende, F. CFD analysis of added mass, damping and induced flow of isolated and cylinder-mounted heave plates at various submergence depths using an overset mesh method. J. Fluids Struct.
**2022**, 109, 103442. [Google Scholar] [CrossRef] - Li, Y. Wave Theory and Wave Load; South China University of Technology Press: Guangzhou, China, 1994. [Google Scholar]
- Liu, Y. Butterworth Filter and Its Application in Single Phase PLL. Master’s Thesis, Huazhong University of Science and Technology, Wuhan, China, 2016. [Google Scholar]
- AAli, S.; Radwan, A.G.; Soliman, A.M. Fractional order butterworth filter: Active and passive realizations. IEEE J. Emerg. Sel. Top. Circuits Syst.
**2013**, 3, 346–354. [Google Scholar] [CrossRef] - Yun, H.W.; Choi, S.H.; Ryu, H.K. Study on the annual building load predicting method using a polynomial function. Trans. Korea Soc. Geotherm. Energy Eng.
**2017**, 13, 7–13. [Google Scholar] - Roy, S.; Chandra, A. On the order minimization of interpolated bandpass method based narrow transition band FIR filter design. IEEE Trans. Circuits Syst. I Regul. Pap.
**2019**, 66, 4287–4295. [Google Scholar] [CrossRef] - Cameron, R.J.; Kudsia, C.M.; Mansour, R.R. Microwave Filters for Communication Systems: Fundamentals, Design, and Applications; Wiley Press: Hoboken, NJ, USA, 2018. [Google Scholar]
- Zhou, Y.; Wang, H.; Lv, W. Time Series Analysis and Its Application; Higher Education Press: Beijing, China, 2021. [Google Scholar]
- Narkhede, P.; Raj, A.N.J.; Kumar, V.; Karar, V.; Poddar, S. Least square estimation-based adaptive complimentary filter for attitude estimation. Trans. Inst. Meas. Control
**2019**, 41, 235–245. [Google Scholar] [CrossRef] - Bańbura, M.; Modugno, M. Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data. J. Appl. Econom.
**2014**, 29, 133–160. [Google Scholar] [CrossRef] - Kirov, C.; Cotterell, R. Recurrent neural networks in linguistic theory: Revisiting pinker and prince (1988) and the past tense debate. Trans. Assoc. Comput. Linguist.
**2018**, 6, 651–665. [Google Scholar] [CrossRef] - Chang, C.; Huang, H. Automatic tuning of the RBF kernel parameter for batch-mode Active learning algorithms: A scalable framework. IEEE Trans. Cybern.
**2019**, 49, 4460–4472. [Google Scholar] [CrossRef] [PubMed] - Zhang, X.; Liu, X.; Tang, S.; Królczyk, G.; Li, Z. Solving scheduling problem in a distributed manufacturing system using a discrete fruit fly optimization algorithm. Energies
**2019**, 12, 3260. [Google Scholar] [CrossRef] - Gao, J.; Ma, X.; Zang, J.; Dong, G.; Ma, X.; Zhu, Y.; Zhou, L. Numerical investigation of harbor oscillations induced by focused transient wave groups. Coast. Eng.
**2020**, 158, 103670. [Google Scholar] [CrossRef] - Gao, J.; Ma, X.; Dong, G.; Chen, H.; Liu, Q.; Zang, J. Investigation on the effects of Bragg reflection on harbor oscillations. Coast. Eng.
**2021**, 170, 103977. [Google Scholar] [CrossRef]

**Figure 3.**The denoising result of real ocean wave height by the Butterworth filter. (

**a**) The nature frequency of Butterworth filter is 0.02 × 2. (

**b**) The nature frequency of Butterworth filter is 0.0085 × 2.

**Figure 7.**A 2 s-ahead forecast of future ocean wave height by ARMA method. (

**a**) Comparison of real ocean wave height and forecasted ocean wave height. (

**b**) Scatter of forecasted ocean wave height versus real ocean wave height.

**Figure 8.**A 2 s-ahead forecast of future ocean wave height by BP neural network method. (

**a**) Comparison of real ocean wave height and forecasted ocean wave height, (

**b**) scatter of forecasted ocean wave height versus real ocean wave height.

**Figure 9.**A 2 s-ahead forecast of future ocean wave height by RBF neural network method. (

**a**) Comparison of real ocean wave height and forecasted ocean wave height. (

**b**) Scatter of forecasted ocean wave height versus real ocean wave height.

**Figure 10.**The forecast errors comparison of ARMA method, BP neural network method and RBF neural network method. (

**a**) A 2 s-ahead forecast of future ocean wave height. (

**b**) A 3 s-ahead forecast of future ocean wave height.

**Table 1.**Error and calculation time consumption of different forecasting methods (2 s-ahead forecast).

Forecast Horizon | ARMA Method | BP Method | RBF Method |
---|---|---|---|

RMSE (m) | 0.013 | 0.0105 | 3.90 × 10^{−7} |

MAE (m) | 0.0087 | 0.0078 | 2.36 × 10^{−7} |

R | 0.9953 | 0.9929 | 1 |

Calculation time consumption (s) | 0.2578 | 0.2739 | 0.3704 |

**Table 2.**Error and calculation time consumption of different forecasting methods (3 s-ahead forecast).

Forecast Horizon | ARMA Method | BP Method | RBF Method |
---|---|---|---|

RMSE (m) | 0.0282 | 0.0148 | 5.16 × 10^{−7} |

MAE (m) | 0.019 | 0.0106 | 2.66 × 10^{−7} |

R | 0.9782 | 0.9868 | 1 |

Calculation time consumption (s) | 0.2726 | 0.2944 | 0.3945 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guodong, Q.; Zhongxian, C.
A Comparison of Ocean Wave Height Forecasting Methods for Ocean Wave Energy Conversion Systems. *Water* **2023**, *15*, 3256.
https://doi.org/10.3390/w15183256

**AMA Style**

Guodong Q, Zhongxian C.
A Comparison of Ocean Wave Height Forecasting Methods for Ocean Wave Energy Conversion Systems. *Water*. 2023; 15(18):3256.
https://doi.org/10.3390/w15183256

**Chicago/Turabian Style**

Guodong, Qin, and Chen Zhongxian.
2023. "A Comparison of Ocean Wave Height Forecasting Methods for Ocean Wave Energy Conversion Systems" *Water* 15, no. 18: 3256.
https://doi.org/10.3390/w15183256