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The New Solar Radiation Estimation Models Using Different Weight Functions in the Moving Least Squares Approach

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Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

In this study, moving least squares approach (MLSA) is used for solar radiation (SR) estimation in the selected region. While develo** new models with the MLSA, three different weight functions which are Gaussian, cubic spline and Wendland are used. The compatibility of some modified Angström-type equations were tested to estimate of monthly average daily global SR at selected region. The most suitable equation was found by comparing with the values measured and obtained from the equation. In this paper, six different statistical error analysis tests are used in order to compare the performance of new proposed models. According to the results obtained in the selected region, the weight function for which the best performance values are obtained is the cubic spline weight function.

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References

  1. Kaplan AG, Kaplan YA (2020) Develo** of the new models in solar radiation estimation with curve fitting based on moving least-squares approximation. Renew Energy 146:2462–2471

    Article  Google Scholar 

  2. Kaplan YA (2018) A new model for predicting the global solar radiation. Environ Prog Sustain Energy 37(2):870–880

    Article  Google Scholar 

  3. Togrul INT, Onat E (2000) A comparison of estimated and measured values of solar radiation in Elazig Turkey. Renew Energy 20(2):243–252

    Article  Google Scholar 

  4. ** Z, Yezheng W, Gang Y (2005) General formula for estimation of monthly average daily global solar radiation in China. Energy Convers Manage 46(2):257–268

    Article  Google Scholar 

  5. Menges HO, Ertekin C, Sonmete MH (2006) Evaluation of global solar radiation models for Konya Turkey. Energy Convers Manage 47(18):3149–3173

    Article  Google Scholar 

  6. Zang H, Jiang X, Cheng L, Zhang F, Wei Z, Sun G (2022) Combined empirical and machine learning modeling method for estimation of daily global solar radiation for general meteorological observation stations. Renew Energy 195:795–808

    Article  Google Scholar 

  7. Kaplan YA, Sarac MS, Unaldi GG (2022) Develo** a new model in solar radiation estimation with genetic algorithm method. Environ Prog Sustain Energy 41(6):e13912

    Article  Google Scholar 

  8. Demir V, Citakoglu H (2023) Forecasting of solar radiation using different machine learning approaches. Neural Comput Appl 35(1):887–906

    Article  Google Scholar 

  9. Tey WY, Che Sidik NA, Asako YW, Muhieldeen M, Afshar O (2021) Moving least squares method and its improvement: a concise review. J Appl Comput Mech 7(2):883–889

    Google Scholar 

  10. Degel JP, Hähnlein S, Klöffer C, Doppelbauer M (2020) A moving least-square approach for current slope estimation in an inverter fed IPMSM using field programmable gateway arrays. In: 2020 ınternational conference on electrical machines (ICEM) (vol 1, pp 1033–1039). IEEE

  11. Huang Z, Lei D, Han Z, Lin J (2020) Boundary moving least squares method for 3D elasticity problems. Eng Anal Boundary Elem 121:255–266

    Article  MathSciNet  Google Scholar 

  12. Zeng QH, Lu DT (2004) Curve and Surface fitting based on moving least-squares methods. J Eng Graph 1:84–89

    Google Scholar 

  13. Zuo CW, Nie YF, Zhao ML (2005) The selection about the radius of influence in MLS. Chin J Eng Math 21:833–838

    Google Scholar 

  14. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37(155):141–158

    Article  MathSciNet  Google Scholar 

  15. Zhang H, Guo C, Su X, Zhu C (2015) Measurement data fitting based on moving least squares method. Math Probl Eng 2015:195023

    Google Scholar 

  16. Kaplan AG, Dereli Y (2017) Numerical solutions of the GEW equation using MLS collocation method. Int J Mod Phys C 28(1):1750011

    Article  ADS  MathSciNet  Google Scholar 

  17. Wang JF, Bai FN, Cheng YM (2011) A meshless method for the nonlinear generalized regularized long wave equation. Chin Phys B 20(3):030206

    Article  ADS  Google Scholar 

  18. Kaplan AG, Dereli Y (2017) A meshless method and stability analysis for the nonlinear Schrödinger equation. Waves Random Complex Media 27(4):602–614

    Article  ADS  MathSciNet  Google Scholar 

  19. Duffie JA, Beckman WA (2013) Solar engineering of thermal processes. Wiley, New York

    Book  Google Scholar 

  20. Kallioglu MA (2014) Improving a model for calculating daily global diffuse and direct solar radiation on horizontal surfaces for Nigde. Master's thesis, Nigde University Graduate School of Natural and Applied Sciences Department of Mechanical Engineering

  21. Aras H, Balli O, Hepbasli A (2006) Global solar radiation potential, part 2: statistical analysis. Energy Sources Part B-Econ Plann Policy 1(3):317–326

    Article  Google Scholar 

  22. Ulgen K, Hepbasli A (2004) Solar radiation models, part 2: Comparison and develo** new models. Energy Sources 26(5):521–530

    Article  Google Scholar 

  23. Skeiker K (2006) Correlation of global solar radiation with common geographical and meteorological parameters for Damascus province Syria. Energy Convers Manage 47(4):331–345

    Article  Google Scholar 

  24. Oztürk M, Ozek N, Berkama B (2012) Comparison of some existing models for estimating monthly average daily global solar radiation for Isparta. Pamukkale University. J Eng Sci 18(1):13–27

    Google Scholar 

  25. Khorasanizadeh H, Mohammadi K, Mostafaeipour A (2014) Establishing a diffuse solar radiation model for determining the optimum tilt angle of solar surfaces in Tabass Iran. Energy Convers Manage 78:805–814

    Article  Google Scholar 

  26. Sabzpooshani M, Mohammadi K (2014) Establishing new empirical models for predicting monthly mean horizontal diffuse solar radiation in city of Isfahan Iran. Energy 69:571–577

    Article  Google Scholar 

  27. Agbulut U, Gürel AE, Bicen Y (2021) Prediction of daily global solar radiation using different machine learning algorithms: evaluation and comparison. Renew Sustain Energy Rev 135:110114

    Article  Google Scholar 

  28. Fan J, Wu L, Zhang F, Cai H, Ma X, Bai H (2019) Evaluation and development of empirical models for estimating daily and monthly mean daily diffuse horizontal solar radiation for different climatic regions of China. Renew Sustain Energy Rev 105:168–186

    Article  Google Scholar 

  29. Emang D, Shitan M, Abd Ghani AN, Noor KM (2010) Forecasting with univariate time series models: a case of export demand for peninsular Malaysia’s moulding and chipboard. J Sustain Dev 3(3):157

    Article  Google Scholar 

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  1. Department of Mathematics, Osmaniye Korkut Ata University, Osmaniye, Turkey

    Ayse Gul Kaplan

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  1. Ayse Gul Kaplan
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Kaplan, A.G. The New Solar Radiation Estimation Models Using Different Weight Functions in the Moving Least Squares Approach. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (2024). https://doi.org/10.1007/s40010-024-00880-0

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