Research article Special Issues

Smart irrigation system for environmental sustainability in Africa: An Internet of Everything (IoE) approach

  • Received: 21 December 2018 Accepted: 30 May 2019 Published: 13 June 2019
  • Water and food are two of the most important commodities in the world, which makes agriculture crucial to mankind as it utilizes water (irrigation) to provide us with food. Climate change and a rapid increase in population have put a lot of pressure on agriculture which has a snowball effect on the earth's water resource, which has been proven to be crucial for sustainable development. The need to do away with fossil fuel in powering irrigation systems cannot be over emphasized due to climate change. Smart Irrigation systems powered by renewable energy sources (RES) have been proven to substantially improve crop yield and the profitability of agriculture. Here we show how the control and monitoring of a solar powered smart irrigation system can be achieved using sensors and environmental data from an Internet of Everything (IoE). The collected data is used to predict environment conditions using the Radial Basis Function Network (RBFN). The predicted values of water level, weather forecast, humidity, temperature and irrigation data are used to control the irrigation system. A web platform was developed for monitoring and controlling the system remotely.

    Citation: Favour Adenugba, Sanjay Misra, Rytis Maskeliūnas, Robertas Damaševičius, Egidijus Kazanavičius. Smart irrigation system for environmental sustainability in Africa: An Internet of Everything (IoE) approach[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5490-5503. doi: 10.3934/mbe.2019273

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  • Water and food are two of the most important commodities in the world, which makes agriculture crucial to mankind as it utilizes water (irrigation) to provide us with food. Climate change and a rapid increase in population have put a lot of pressure on agriculture which has a snowball effect on the earth's water resource, which has been proven to be crucial for sustainable development. The need to do away with fossil fuel in powering irrigation systems cannot be over emphasized due to climate change. Smart Irrigation systems powered by renewable energy sources (RES) have been proven to substantially improve crop yield and the profitability of agriculture. Here we show how the control and monitoring of a solar powered smart irrigation system can be achieved using sensors and environmental data from an Internet of Everything (IoE). The collected data is used to predict environment conditions using the Radial Basis Function Network (RBFN). The predicted values of water level, weather forecast, humidity, temperature and irrigation data are used to control the irrigation system. A web platform was developed for monitoring and controlling the system remotely.




    [1] B. N. Fantu, B. Guush, M. Bart, et al., Agricultural Transformation in Africa? Assessing the Evidence in Ethopia, World Dev., 105 (2018), 286–298.
    [2] S. Trilles, J. Torres-Sospedra, Ó. Belmonte, et al., Development of an open sensorized platform in a smart agriculture context: A vineyard support system for monitoring mildew disease, Sustain. Comput. Infor., (2019), in press.
    [3] Intergovernmental Panel on Climate Change, Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Core Writing Team, R.K. Pachauri and L.A. Meyer (eds.)]. IPCC (2014), Geneva, Switzerland, 151 pp., [online] Available from: https://www.ipcc.ch/site/assets/uploads/2018/02/SYR_AR5_FINAL_full.pdf.
    [4] A. M. García, I. F. García, E. C. Poyato, et al., Coupling irrigation scheduling with solar energy production in a smart irrigation management system, J. Clean. Prod., 175 (2018), 670–682.
    [5] M. Kala, U. Sadrul and B. Steven, Solar photovoltaic water pumping-opportunities and challenges, Renew. Sust. Energ. Rev., 4 (2008), 1162–1175.
    [6] European Commission, Overview of CAP Reform 2014–2020, December 2013, [online] Available from: http://ec.europa.eu/agriculture/policy-perspectives/policy-briefs/05_en.pdf.
    [7] S. Biswajit, Green Computing, Int. J. Comput. Trends Technol., 14 (2014), 46–50.
    [8] S. Murugesan, Harnessing green IT: Principles and practices, IT Prof., 10 (2008), 24–33.
    [9] E. Okewu, S. Misra, R. Maskeliunas, et al., Optimizing green computing awareness for environmental sustainability and economic security as a stochastic optimization problem, Sustainability, 9 (2017), 1857.
    [10] E. Okewu, S. Misra, L. Fernandez-Sanz, et al., An e-environment system for socio-economic sustainability and national security, Probl. Ekorozw., 13 (2018), 121–132.
    [11] A. C. Orgerie, Green Computing and Sustainability, Journées scientifiques, 15, (2016), 23–27.
    [12] A. Al-Zamil and A. K. J. Saudagar, Drivers and challenges of applying green computing for sustainable agriculture: A case study, Sustain. Comput. Infor., (2018), in press.
    [13] A. Mansur, H. Ghassan, S. A. Syed, et al., A review of solar-powered water pumping systems, Renew. Sust. Energ. Rev., 87 (2018), 61–76.
    [14] N. Mehdi, M. Peyman, N. Mohammad, et al., Techno-economic feasibility of off-grid solar irrigation for a rice paddy in Guilan province in Iran: A case study, Sol. Energy, 150 (2017), 546–557.
    [15] P. E. Campana, H. L. Li and J. Y. Yan, Techno-economic feasibility of the irrigation system for the grassland and farmland conservation in China: Photovoltaic vs. wind power water pumping, Energ. Convers. Manage., 103 (2015), 311–320.
    [16] P. E. Campana, H. L. Li and J. Y. Yan, Dynamic modelling of a PV pumping system with special consideration on water demand, Appl. Energy, 112 (2013), 635–645.
    [17] Z. Gu, Z. Qi, L. Ma, et al., Development of an irrigation scheduling software based on model predicted crop water stress, Comput. Electron. Agric., 143 (2017), 208–221.
    [18] R. López-Luque, J. Reca and J. Martínez, Optimal design of a standalone direct pumping photovoltaic system for deficit irrigation of olive orchards, Appl. Energy, 149 (2015), 13–23.
    [19] G. Vellidis, M. Tucker, C. Perry, et al., A real-time wireless smart sensor array for scheduling irrigation, Comput. Electron. Agric., 61 (2008), 44–50.
    [20] T. Ojha, S. Misra and N.S. Raghuwanshi, Wireless sensor networks for agriculture: the state-of-the-art in practice and future challenges, Comput. Electron. Agric., 118 (2015), 66–84.
    [21] B. Keswani, A. G. Mohapatra, A. Mohanty, et al., Adapting weather conditions based IoT enabled smart irrigation technique in precision agriculture mechanisms, Neural Comput. Appl., 31(S1) (2018), 277–292.
    [22] S. T. Oliver, A. González-Pérez and J. H. Guijarro, An IoT proposal for monitoring vineyards called SEnviro for agriculture, Proceedings of 8th International Conference on the Internet of Things, (2018), 20. ACM.
    [23] S. A. M. Varman, A. R. Baskaran, S. Aravindh, et al., Deep learning and IoT for smart agriculture using WSN, IEEE International Conference on Computational Intelligence and Computing Research, ICCIC 2017, (2018).
    [24] A. Goap, D. Sharma, A. K. Shukla, et al., An IoT based smart irrigation management system using machine learning and open source technologies, Comput. Electron. Agric., 155 (2018), 41–49.
    [25] T. Kashiwao, K. Nakayama, S. Ando, et al., A neural network-based local rainfall prediction system using meteorological data on the Internet: A case study using data from the Japan Meteorological Agency, Appl. Soft Comput., 56 (2017), 317–330.
    [26] O. Adeyemi, I. Grove, S. Peets, et al., Dynamic neural network modelling of soil moisture content for predictive irrigation scheduling, Sensors, 18 (2018), 3408.
    [27] L. Huang, L. Chen, Q. Wang, et al., Regional short-term micro-climate air temperature prediction with CBPNN, E3S Web of Conferences, 53 (2018).
    [28] L. T. Yang, B. Di Martino and Q. Zhang, Internet of Everything, Mob. Inf. Syst., (2017).
    [29] S. R. Barkunan, V. Bhanumathi and J. Sethuram, Smart sensor for automatic drip irrigation system for paddy cultivation, Comput. Electr. Eng., 73 (2019), 180–193.
    [30] C. Chang and K. Lin, Smart agricultural machine with a computer vision-based weeding and variable-rate irrigation scheme, Robotics, 7 (2018), 38.
    [31] C. Corbari, R. Salerno, A. Ceppi, et al., Smart irrigation forecast using satellite LANDSAT data and meteo-hydrological modeling, Agric. Water Manag., 212 (2019), 283–294.
    [32] W. Difallah, K. Benahmed, B. Draoui, et al., Implementing wireless sensor networks for smart irrigation, Taiwan Water Conservancy, 65 (2017), 44–54.
    [33] S. Geetha and R. Sathya Priya, Smart agriculture irrigation control using wireless sensor networks, GSM and android phone, Asian J. Inf. Technol., 15 (2016), 3780–3786.
    [34] A. Goap, D. Sharma, A. K. Shukla, et al., An IoT based smart irrigation management system using machine learning and open source technologies, Comput. Electron. Agr., 155 (2018), 41–49.
    [35] N. Hema and K. Kant, Cost-effective smart irrigation controller using automatic weather stations, Int. J. Hydrol. Sci. Technol., 9 (2019), 1–27.
    [36] C. Kamienski, J. Soininen, M. Taumberger, et al., Smart water management platform: IoT-based precision irrigation for agriculture, Sensors, 19 (2019), 276.
    [37] S. Katyara, M. A. Shah, S. Zardari, et al., WSN based smart control and remote field monitoring of Pakistan's irrigation system using SCADA applications, Wireless Pers. Commun., 95 (2017), 491–504.
    [38] O. Abayomi-Alli, M. Odusami, D. Ojinaka, et al., Smart-Solar Irrigation System (SMIS) for Sustainable Agriculture, International Conference on Applied Informatics, ICAI 2018, (2018), 198–212.
    [39] A. G. Mohapatra, S. K. Lenka and B. Keswani, Neural network and fuzzy logic based smart DSS model for irrigation notification and control in precision agriculture, P. Natl. A. Sci. India A, 89 (2019), 67–76.
    [40] M. S. Munir, I. S. Bajwa, M. A. Naeem, et al., Design and implementation of an IoT system for smart energy consumption and smart irrigation in tunnel farming, Energies, 11 (2018), 3427.
    [41] X. Fan, W. Wei, M. Wozniak, et al., Low energy consumption and data redundancy approach of wireless sensor networks with bigdata, Inf. Technol. Control, 47 (2018), 406–418.
    [42] A. Venčkauskas, N. Jusas, E. Kazanavičius, et al., An energy efficient protocol for the internet of things, J. Electr. Eng., 66 (2015), 47–52.
    [43] W. Wei, Z. Sun, H. Song, et al., Energy balance-based steerable arguments coverage method in WSNs, IEEE Access, 6 (2018), 33766–33773.
    [44] C.M Bishop, Neural networks for pattern recognition, Oxford University Press, 1995.
    [45] Z. Boger and H. Guterman, Knowledge extraction from artificial neural network models, IEEE Systems, Man, and Cybernetics Conference, 4 (1997), 3030–3035.
    [46] N. Srivastava, G. Hinton, A. Krizhevsky, et al., Dropout: a simple way to prevent neural networks from overfitting, J. Mach. Learn. Res., 15 (2014), 1929–1958.
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    70. A note for the global stability of a delay differential equation of hepatitis B virus infection, 2011, 8, 1551-0018, 689, 10.3934/mbe.2011.8.689
    71. Jinliang Wang, Ran Zhang, Toshikazu Kuniya, The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes, 2015, 9, 1751-3758, 73, 10.1080/17513758.2015.1006696
    72. Michael Y. Li, Hongying Shu, Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response, 2012, 13, 14681218, 1080, 10.1016/j.nonrwa.2011.02.026
    73. Salih Djilali, Tarik Mohammed Touaoula, Sofiane El-Hadi Miri, A Heroin Epidemic Model: Very General Non Linear Incidence, Treat-Age, and Global Stability, 2017, 152, 0167-8019, 171, 10.1007/s10440-017-0117-2
    74. Shengqiang Liu, Shaokai Wang, Lin Wang, Global dynamics of delay epidemic models with nonlinear incidence rate and relapse, 2011, 12, 14681218, 119, 10.1016/j.nonrwa.2010.06.001
    75. Liming Cai, Bin Fang, Xuezhi Li, A note of a staged progression HIV model with imperfect vaccine, 2014, 234, 00963003, 412, 10.1016/j.amc.2014.01.179
    76. Yasin Ucakan, Seda Gulen, Kevser Koklu, Analysing of Tuberculosis in Turkey through SIR, SEIR and BSEIR Mathematical Models, 2021, 27, 1387-3954, 179, 10.1080/13873954.2021.1881560
    77. Soufiane Bentout, Salih Djilali, Sunil Kumar, Tarik Mohammed Touaoula, Threshold dynamics of difference equations for SEIR model with nonlinear incidence function and infinite delay, 2021, 136, 2190-5444, 10.1140/epjp/s13360-021-01466-0
    78. Chunyue Wang, Jinliang Wang, Ran Zhang, Global analysis on an age‐space structured vaccination model with Neumann boundary condition, 2022, 45, 0170-4214, 1640, 10.1002/mma.7879
    79. Vijay Pal Bajiya, Jai Prakash Tripathi, Vipul Kakkar, Jinshan Wang, Guiquan Sun, Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age, 2021, 42, 0252-9599, 833, 10.1007/s11401-021-0294-1
    80. Qianqian Cui, Jiabo Xu, Qiang Zhang, Kai Wang, An NSFD scheme for SIR epidemic models of childhood diseases with constant vaccination strategy, 2014, 2014, 1687-1847, 10.1186/1687-1847-2014-172
    81. S.Y. Tchoumi, H. Rwezaura, J.M. Tchuenche, A mathematical model with numerical simulations for malaria transmission dynamics with differential susceptibility and partial immunity, 2023, 3, 27724425, 100165, 10.1016/j.health.2023.100165
    82. Jiaxin Nan, Wanbiao Ma, Stability and persistence analysis of a microorganism flocculation model with infinite delay, 2023, 20, 1551-0018, 10815, 10.3934/mbe.2023480
    83. Aboudramane Guiro, Dramane Ouedraogo, Harouna Ouedraogo, 2023, Chapter 10, 978-3-031-27660-6, 259, 10.1007/978-3-031-27661-3_10
    84. Ying He, Junlong Tao, Bo Bi, Stationary distribution for a three-dimensional stochastic viral infection model with general distributed delay, 2023, 20, 1551-0018, 18018, 10.3934/mbe.2023800
    85. F. Najm, R. Yafia, M. A. Aziz Alaoui, A. Aghriche, A. Moussaoui, A survey on constructing Lyapunov functions for reaction-diffusion systems with delay and their application in biology, 2023, 10, 23129794, 965, 10.23939/mmc2023.03.965
    86. Abderrazak NABTi, Dynamical analysis of an age-structured SEIR model with relapse, 2024, 75, 0044-2275, 10.1007/s00033-024-02227-6
    87. Jinxiang Zhan, Yongchang Wei, Dynamical behavior of a stochastic non-autonomous distributed delay heroin epidemic model with regime-switching, 2024, 184, 09600779, 115024, 10.1016/j.chaos.2024.115024
    88. Narges M. Shahtori, S. Farokh Atashzar, Temporal Dynamics and Interplay of Transmission Rate, Vaccination, and Mutation in Epidemic Modeling: A Poisson Point Process Approach, 2024, 11, 2327-4697, 5023, 10.1109/TNSE.2024.3421308
    89. Isam Al‐Darabsah, Global Dynamics of a Within‐Host Model for Immune Response With a Generic Distributed Delay, 2025, 0170-4214, 10.1002/mma.11021
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