# Efficient Wind Speed Forecasting for Resource-Constrained Sensor Devices

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Forecasting Models

#### 3.1. Persistence Model

#### 3.2. ARIMA Model

#### 3.3. Pro-Energy Model

#### 3.4. D-WCMA Model

## 4. Forecasting Wind Speed Using an ARIMA Model

#### 4.1. Data Sets Description

#### 4.2. Model Identification

#### 4.3. Parameters Estimation

#### 4.4. Making Predictions

## 5. Adaptive ARIMA Implementation

#### 5.1. Parameters Estimation

- if $|{\widehat{\gamma}}_{1}|>|{\widehat{\gamma}}_{2}|$ then ARIMA ($1,1,1$)
- ${\widehat{\phi}}_{1}={\widehat{\gamma}}_{2}/{\widehat{\gamma}}_{1}$
- $-{\widehat{\theta}}_{1}={\widehat{\gamma}}_{1}/{\widehat{\gamma}}_{0}-{\widehat{\phi}}_{1}$

- else ARIMA ($0,1,2$)
- $-{\widehat{\theta}}_{1}={\widehat{\gamma}}_{1}/{\widehat{\gamma}}_{0}$
- $-{\widehat{\theta}}_{2}={\widehat{\gamma}}_{2}/{\widehat{\gamma}}_{0}$

#### 5.2. Making Predictions

- ${s}_{n}\leftarrow $ last observed wind speed value
- $\u25bd{s}_{n}={s}_{n}-{s}_{n-1}$
- ${\widehat{\u25bds}}_{n+1}=-{\widehat{\theta}}_{1}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}(\u25bd{s}_{n}-{\widehat{\u25bds}}_{n})-{\widehat{\theta}}_{2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}(\u25bd{s}_{n-1}-{\widehat{\u25bds}}_{n-1})$
- ${\widehat{s}}_{n+1}={s}_{n}+{\widehat{\u25bds}}_{n+1}$
- ${\widehat{\u25bds}}_{n-1}\leftarrow {\widehat{\u25bds}}_{n}$
- ${\widehat{\u25bds}}_{n}\leftarrow {\widehat{\u25bds}}_{n+1}$
- ${\widehat{\gamma}}_{0}$ +$=\u25bd{s}_{n}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\u25bd{s}_{n}$
- ${\widehat{\gamma}}_{1}$ +$=\u25bd{s}_{n}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\u25bd{s}_{n-1}$
- ${\widehat{\gamma}}_{2}$ +$=\u25bd{s}_{n}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\u25bd{s}_{n-2}$
- $\u25bd{s}_{n-2}\leftarrow \u25bd{s}_{n-1}$
- $\u25bd{s}_{n-1}\leftarrow \u25bd{s}_{n}$
- ${s}_{n-1}\leftarrow {s}_{n}$

- 3.
- ${\widehat{\u25bds}}_{n+1}={\widehat{\phi}}_{1}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\u25bd{s}_{n}-{\widehat{\theta}}_{1}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}(\u25bd{s}_{n}-{\widehat{\u25bds}}_{n})$

## 6. Evaluation

#### 6.1. Performance Comparison

#### 6.2. Optimistic Forecasting

#### 6.3. Computational and Memory Overhead

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

WSN | Wireless Sensor Network |

EH | Energy Harvesting |

NWP | Numerical Weather Prediction |

ARIMA | AutoRegressive Integrated Moving Average |

ACF | AutoCorrelation Function |

PACF | Partial AutoCorrelation Function |

MAE | Mean Absolute Error |

## References

- Shaikh, F.K.; Zeadally, S. Energy harvesting in wireless sensor networks: A comprehensive review. Renew. Sustain. Energy Rev.
**2016**, 55, 1041–1054. [Google Scholar] [CrossRef] - Gunduz, D.; Stamatiou, K.; Michelusi, N.; Zorzi, M. Designing intelligent energy harvesting communication systems. IEEE Commun. Mag.
**2014**, 52, 210–216. [Google Scholar] [CrossRef] - Zhou, H.; Jiang, T.; Gong, C.; Zhou, Y. Optimal Estimation in Wireless Sensor Networks with Energy Harvesting. IEEE Trans. Veh. Technol.
**2016**, 65, 9386–9396. [Google Scholar] [CrossRef] - Gupta, S.S.; Mehta, N.B. Revisiting Effectiveness of Energy Conserving Opportunistic Transmission Schemes in Energy Harvesting Wireless Sensor Networks. IEEE Trans. Commun.
**2019**, 67, 2968–2980. [Google Scholar] [CrossRef] - Li, J.; Yu, B. Model and Procedures for Reliable Near Term Wind Energy Production Forecast. Wind. Eng.
**2015**, 39, 595–608. [Google Scholar] [CrossRef] [Green Version] - Hernandez, W.; Méndez, A.; Maldonado-Correa, J.L.; Balleteros, F. Modeling of a Robust Confidence Band for the Power Curve of a Wind Turbine. Sensors
**2016**, 16, 2080. [Google Scholar] [CrossRef] [Green Version] - Kansal, A.; Hsu, J.; Zahedi, S.; Srivastava, M.B. Power Management in Energy Harvesting Sensor Networks. ACM Trans. Embed. Comput. Syst.
**2007**, 6. [Google Scholar] [CrossRef] - Liu, H.; Chen, C. Data processing strategies in wind energy forecasting models and applications: A comprehensive review. Appl. Energy
**2019**, 249, 392–408. [Google Scholar] [CrossRef] - Nazir, M.S.; Alturise, F.; Alshmrany, S.; Nazir, H.M.J.; Bilal, M.; Abdalla, A.N.; Sanjeevikumar, P.; Ali, Z.M. Wind Generation Forecasting Methods and Proliferation of Artificial Neural Network: A Review of Five Years Research Trend. Sustainability
**2020**, 12, 3778. [Google Scholar] [CrossRef] - Lazic, L.; Pejanovic, G.; Zivkovic, M. Wind forecasts for wind power generation using the Eta model. Renew. Energy
**2010**, 35, 1236–1243. [Google Scholar] [CrossRef] - Cheng, W.Y.Y.; Liu, Y.; Bourgeois, A.J.; Wu, Y.; Haupt, S.E. Short-term wind forecast of a data assimilation/weather forecasting system with wind turbine anemometer measurement assimilation. Renew. Energy
**2017**, 107, 340–351. [Google Scholar] [CrossRef] - Andrade, J.R.; Bessa, R.J. Improving Renewable Energy Forecasting with a Grid of Numerical Weather Predictions. IEEE Trans. Sustain. Energy
**2017**, 8, 1571–1580. [Google Scholar] [CrossRef] [Green Version] - Torres, J.L.; García, A.; de Blas, M.; de Francisco, A. Forecast of hourly average wind speed with ARMA models in Navarre (Spain). Sol. Energy
**2005**, 79, 65–77. [Google Scholar] [CrossRef] - Kavasseri, R.G.; Seetharaman, K. Day-ahead wind speed forecasting using f-ARIMA models. Renew. Energy
**2009**, 34, 1388–1393. [Google Scholar] [CrossRef] - Chen, P.; Pedersen, T.; Bak-Jensen, B.; Chen, Z. ARIMA-Based Time Series Model of Stochastic Wind Power Generation. IEEE Trans. Power Syst.
**2010**, 25, 667–676. [Google Scholar] [CrossRef] [Green Version] - Erdem, E.; Shi, J. ARMA based approaches for forecasting the tuple of wind speed and direction. Appl. Energy
**2011**, 88, 1405–1414. [Google Scholar] [CrossRef] - Wen, Y.; Song, M.; Wang, J. A Combined AR-kNN model for short-term wind speed forecasting. In Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, USA, 12–14 December 2016; pp. 6342–6346. [Google Scholar]
- Yunus, K.; Thiringer, T.; Chen, P. ARIMA-Based Frequency-Decomposed Modeling of Wind Speed Time Series. IEEE Trans. Power Syst.
**2016**, 31, 2546–2556. [Google Scholar] [CrossRef] - Xie, W.; Zhang, P.; Chen, R.; Zhou, Z. A Nonparametric Bayesian Framework for Short-Term Wind Power Probabilistic Forecast. IEEE Trans. Power Syst.
**2019**, 34, 371–379. [Google Scholar] [CrossRef] - Wang, Y.; Wang, H.; Srinivasan, D.; Hu, Q. Robust functional regression for wind speed forecasting based on Sparse Bayesian learning. Renew. Energy
**2019**, 132, 43–60. [Google Scholar] [CrossRef] - García, I.; Huo, S.; Prado, R.; Bravo, L. Dynamic Bayesian temporal modeling and forecasting of short-term wind measurements. Renew. Energy
**2020**, 161, 55–64. [Google Scholar] [CrossRef] - Liu, H.; Tian, H.Q.; Li, Y.F. Comparison of two new ARIMA-ANN and ARIMA-Kalman hybrid methods for wind speed prediction. Appl. Energy
**2012**, 98, 415–424. [Google Scholar] [CrossRef] - Zuluaga, C.D.; Álvarez, M.A.; Giraldo, E. Short-term wind speed prediction based on robust Kalman filtering: An experimental comparison. Appl. Energy
**2015**, 156, 321–330. [Google Scholar] [CrossRef] - Akçay, H.; Filik, T. Short-term wind speed forecasting by spectral analysis from long-term observations with missing values. Appl. Energy
**2017**, 191, 653–662. [Google Scholar] [CrossRef] - Wan, C.; Lin, J.; Wang, J.; Song, Y.; Dong, Z.Y. Direct Quantile Regression for Nonparametric Probabilistic Forecasting of Wind Power Generation. IEEE Trans. Power Syst.
**2017**, 32, 2767–2778. [Google Scholar] [CrossRef] - Wan, C.; Wang, J.; Lin, J.; Song, Y.; Dong, Z.Y. Nonparametric Prediction Intervals of Wind Power via Linear Programming. IEEE Trans. Power Syst.
**2018**, 33, 1074–1076. [Google Scholar] [CrossRef] - Shi, Z.; Liang, H.; Dinavahi, V. Direct Interval Forecast of Uncertain Wind Power Based on Recurrent Neural Networks. IEEE Trans. Sustain. Energy
**2018**, 9, 1177–1187. [Google Scholar] [CrossRef] - Khodayar, M.; Wang, J. Spatio-Temporal Graph Deep Neural Network for Short-Term Wind Speed Forecasting. IEEE Trans. Sustain. Energy
**2019**, 10, 670–681. [Google Scholar] [CrossRef] - Khodayar, M.; Wang, J.; Manthouri, M. Interval Deep Generative Neural Network for Wind Speed Forecasting. IEEE Trans. Smart Grid
**2019**, 10, 3974–3989. [Google Scholar] [CrossRef] - Zhang, Y.; Zhao, Y.; Pan, G.; Zhang, J. Wind Speed Interval Prediction Based on Lorenz Disturbance Distribution. IEEE Trans. Sustain. Energy
**2020**, 11, 807–816. [Google Scholar] [CrossRef] - Wang, J.; Hu, J. A robust combination approach for short-term wind speed forecasting and analysis. Energy
**2015**, 93, 41–56. [Google Scholar] [CrossRef] - Wu, J.L.; Ji, T.Y.; Li, M.S.; Wu, P.Z.; Wu, Q.H. Multistep Wind Power Forecast Using Mean Trend Detector and Mathematical Morphology-Based Local Predictor. IEEE Trans. Sustain. Energy
**2015**, 6, 1216–1223. [Google Scholar] [CrossRef] - Hu, Q.; Zhang, S.; Yu, M.; Xie, Z. Short-term wind speed or power forecasting with heteroscedastic support vector regression. IEEE Trans. Sustain. Energy
**2016**, 7, 241–249. [Google Scholar] [CrossRef] - Safari, N.; Chung, C.Y.; Price, G.C.D. Novel Multi-Step Short-Term Wind Power Prediction Framework Based on Chaotic Time Series Analysis and Singular Spectrum Analysis. IEEE Trans. Power Syst.
**2018**, 33, 590–601. [Google Scholar] [CrossRef] - Yang, M.; Chen, X.; Du, J.; Cui, Y. Ultra-Short-Term Multistep Wind Power Prediction Based on Improved EMD and Reconstruction Method Using Run-Length Analysis. IEEE Access
**2018**, 6, 31908–31917. [Google Scholar] [CrossRef] - Chen, N.; Qian, Z.; Nabney, I.T.; Meng, X. Wind Power Forecasts Using Gaussian Processes and Numerical Weather Prediction. IEEE Trans. Power Syst.
**2014**, 29, 656–665. [Google Scholar] [CrossRef] [Green Version] - Hoolohan, V.; Tomlin, A.S.; Cockerill, T. Improved near surface wind speed predictions using Gaussian process regression combined with numerical weather predictions and observed meteorological data. Renew. Energy
**2018**, 126, 1043–1054. [Google Scholar] [CrossRef] - Wu, Y.K.; Su, P.E.; Wu, T.Y.; Hong, J.S.; Hassan, M.Y. Probabilistic Wind-Power Forecasting Using Weather Ensemble Models. IEEE Trans. Ind. Appl.
**2018**, 54, 5609–5620. [Google Scholar] [CrossRef] - Qian, Z.; Pei, Y.; Zareipour, H.; Chen, N. A review and discussion of decomposition-based hybrid models for wind energy forecasting applications. Appl. Energy
**2019**, 235, 939–953. [Google Scholar] [CrossRef] - Alsheikh, M.A.; Lin, S.; Niyato, D.; Tan, H.P. Machine Learning in Wireless Sensor Networks: Algorithms, Strategies, and Applications. IEEE Commun. Surv. Tutor.
**2014**, 16, 1996–2018. [Google Scholar] [CrossRef] [Green Version] - Recas Piorno, J.; Bergonzini, C.; Atienza, D.; Simunic Rosing, T. Prediction and management in energy harvested wireless sensor nodes. In Proceedings of the 2009 1st International Conference on Wireless Communication, Vehicular Technology, Information Theory and Aerospace Electronic Systems Technology, Aalborg, Denmark, 17–20 May 2009; pp. 6–10. [Google Scholar]
- Kosunalp, S. A New Energy Prediction Algorithm for Energy-Harvesting Wireless Sensor Networks With Q-Learning. IEEE Access
**2016**, 4, 5755–5763. [Google Scholar] [CrossRef] - Ahmed, F.; Tamberg, G.; Le Moullec, Y.; Annus, P. Adaptive LINE-P: An Adaptive Linear Energy Prediction Model for Wireless Sensor Network Nodes. Sensors
**2018**, 18, 1105. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dehwah, A.H.; Elmetennani, S.; Claudel, C. UD-WCMA: An energy estimation and forecast scheme for solar powered wireless sensor networks. J. Netw. Comput. Appl.
**2017**, 90, 17–25. [Google Scholar] [CrossRef] [Green Version] - Cammarano, A.; Petrioli, C.; Spenza, D. Online Energy Harvesting Prediction in Environmentally Powered Wireless Sensor Networks. IEEE Sens. J.
**2016**, 16, 6793–6804. [Google Scholar] [CrossRef] - Box, G.E.P.; Jenkins, G.; Reinsel, G.C.; Ljung, G.M. Time Series Analysis: Forecasting and Control, 5th ed.; John Wiley & Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- Maxey, C.; Andreas, A. Oak Ridge National Laboratory (ORNL). Rotating Shadowband Radiometer (RSR); NREL Report No. DA-5500-56512; National Renewable Energy Lab. (NREL): Golden, CO, USA, 2007. [Google Scholar] [CrossRef]
- Jager, D.; Andreas, A. National Wind Technology Center (NWTC): M2 Tower; NREL Report No. DA-5500-56489; National Renewable Energy Lab. (NREL): Golden, CO, USA, 1996. [Google Scholar] [CrossRef]
- Andreas, A.; Stoffel, T. Solar Radiation Research Laboratory (SRRL): Baseline Measurement System (BMS); NREL Report No. DA-5500-56488; National Renewable Energy Lab. (NREL): Golden, CO, USA, 1981. [Google Scholar] [CrossRef]
- Jenkins, G.M.; Watts, D.G. Spectral Analysis and Its Applications; Holden-Day: San Francisco, CA, USA, 1968. [Google Scholar]
- Herrería-Alonso, S. EnergyPredictor. 2019. Available online: https://github.com/sherreria/EnergyPredictor (accessed on 31 January 2021).

**Figure 1.**Block diagram of a wind-powered energy harvesting (EH) node. Solid (dotted) lines represent energy (data) transfer.

Pro-Energy | D-WCMA | ||||
---|---|---|---|---|---|

Overhead | D | K | P | D | K |

Low | 30 | 2 | 1 | 10 | 2 |

Medium | 60 | 3 | 2 | 20 | 3 |

High | 90 | 5 | 5 | 40 | 5 |

ORNL | NWTC | SRRL | |||||
---|---|---|---|---|---|---|---|

Model | Horizon | Opt-MAE | Pes-MAE | Opt-MAE | Pes-MAE | Opt-MAE | Pes-MAE |

Persistent | 10 | $0.2308$ | $0.1907$ | $0.4813$ | $0.4966$ | $0.5053$ | $0.4876$ |

20 | $0.2722$ | $0.2309$ | $0.6531$ | $0.6671$ | $0.6926$ | $0.6697$ | |

30 | $0.2977$ | $0.2543$ | $0.7644$ | $0.7791$ | $0.8039$ | $0.7809$ | |

40 | $0.3185$ | $0.2714$ | $0.8496$ | $0.8620$ | $0.9001$ | $0.8599$ | |

50 | $0.3354$ | $0.2883$ | $0.9193$ | $0.9296$ | $0.9720$ | $0.9341$ | |

60 | $0.3515$ | $0.3009$ | $0.9802$ | $0.9852$ | $1.0358$ | $0.9917$ | |

Pro-Energy (High) | 10 | $0.1773$ | $0.2320$ | $0.4597$ | $0.5112$ | $0.4616$ | $0.5231$ |

20 | $0.2059$ | $0.2786$ | $0.5989$ | $0.6938$ | $0.6148$ | $0.7178$ | |

30 | $0.2246$ | $0.3050$ | $0.6865$ | $0.8068$ | $0.7093$ | $0.8275$ | |

40 | $0.2383$ | $0.3268$ | $0.7483$ | $0.8936$ | $0.7799$ | $0.9128$ | |

50 | $0.2495$ | $0.3447$ | $0.7939$ | $0.9621$ | $0.8343$ | $0.9859$ | |

60 | $0.2616$ | $0.3576$ | $0.8303$ | $1.0249$ | $0.8839$ | $1.0353$ | |

D-WCMA (High) | 10 | $0.1863$ | $0.2200$ | $0.5068$ | $0.5319$ | $0.5279$ | $0.5319$ |

20 | $0.2207$ | $0.2545$ | $0.6519$ | $0.6818$ | $0.6859$ | $0.6824$ | |

30 | $0.2433$ | $0.2765$ | $0.7501$ | $0.7821$ | $0.7876$ | $0.7819$ | |

40 | $0.2607$ | $0.2944$ | $0.8261$ | $0.8603$ | $0.8709$ | $0.8591$ | |

50 | $0.2763$ | $0.3089$ | $0.8932$ | $0.9225$ | $0.9403$ | $0.9228$ | |

60 | $0.2897$ | $0.3228$ | $0.9501$ | $0.9762$ | $0.9995$ | $0.9748$ | |

ARIMA | 10 | $0.1732$ | $0.2321$ | $0.4678$ | $0.4991$ | $0.4685$ | $0.5191$ |

20 | $0.2077$ | $0.2703$ | $0.6258$ | $0.6647$ | $0.6367$ | $0.7061$ | |

30 | $0.2296$ | $0.2956$ | $0.7266$ | $0.7727$ | $0.7430$ | $0.8174$ | |

40 | $0.2485$ | $0.3137$ | $0.8068$ | $0.8488$ | $0.8309$ | $0.9003$ | |

50 | $0.2646$ | $0.3312$ | $0.8708$ | $0.9134$ | $0.9012$ | $0.9742$ | |

60 | $0.2786$ | $0.3470$ | $0.9262$ | $0.9655$ | $0.9617$ | $1.0323$ |

Op. per Day | Op. per Prediction | ||||
---|---|---|---|---|---|

Model | Add/Sub | Mul/Div | Add/Sub | Mul/Div | Memory |

ARIMA ($1,1,1$) | 4 | 8 | 7 | 5 | 56 |

ARIMA ($0,1,2$) | 0 | 8 | 8 | 5 | 56 |

Pro-Low | Profiles Pool Update | 121 | 32 | 17,856 | |

Pro-Med | 367 | 67 | 35,136 | ||

Pro-High | 916 | 103 | 52,416 | ||

DWCMA-Low | Profiles Pool Update | 95 | 37 | 6336 | |

DWCMA-Med | 206 | 60 | 12,096 | ||

DWCMA-High | 488 | 106 | 23,616 |

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## Share and Cite

**MDPI and ACS Style**

Herrería-Alonso, S.; Suárez-González, A.; Rodríguez-Pérez, M.; Rodríguez-Rubio, R.F.; López-García, C.
Efficient Wind Speed Forecasting for Resource-Constrained Sensor Devices. *Sensors* **2021**, *21*, 983.
https://doi.org/10.3390/s21030983

**AMA Style**

Herrería-Alonso S, Suárez-González A, Rodríguez-Pérez M, Rodríguez-Rubio RF, López-García C.
Efficient Wind Speed Forecasting for Resource-Constrained Sensor Devices. *Sensors*. 2021; 21(3):983.
https://doi.org/10.3390/s21030983

**Chicago/Turabian Style**

Herrería-Alonso, Sergio, Andrés Suárez-González, Miguel Rodríguez-Pérez, Raúl F. Rodríguez-Rubio, and Cándido López-García.
2021. "Efficient Wind Speed Forecasting for Resource-Constrained Sensor Devices" *Sensors* 21, no. 3: 983.
https://doi.org/10.3390/s21030983