Sains Malaysiana 52(8)(2023): 2419-2430

http://doi.org/10.17576/jsm-2023-5208-18

Modelling Wind Speed Data in Pulau Langkawi With Functional Relationship

(Memodelkan Data Kelajuan Angin di Pulau Langkawi dengan Perhubungan Fungsian)

NUR AIN AL-HAMEEFATUL JAMALIYATUL¹, BASRI BADYALINA¹, NURKHAIRANY AMYRA MOKHTAR^1,*, ADZHAR RAMBLI², YONG ZULINA ZUBAIRI ³ & ADILAH ABDUL GHAPOR⁴

¹Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM) Johor Branch, Segamat Campus, 85000 Segamat, Johor, Malaysia

²School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

³Institute of Advanced Studies, Universiti Malaya, 50603 Kuala Lumpur, Malaysia

⁴Department of Decision Science, Faculty of Business and Economics, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

Received: 16 December 2022/Accepted: 1 August 2023

Abstract

Wind speed influenced weather predictions, aerospace operations, and maritime operations, construction projects. This research aims to examine the relationship between Pulau Langkawi wind speed data during the southwest monsoons in 2019 and 2020. To model wind speed data that follows a normal distribution. An error-in-variables model (EIVM) is utilised, which is a linear functional relationship model (LFRM). The QQ-plots will be utilised to investigate the adequacy of the model’s fit. The maximum likelihood estimation (MLE) approach is employed to estimate the parameters of the model, while the covariance is calculated using the Fisher Information matrix. As a result, it is found that the estimated values demonstrate consistency and reduced dispersion. Thus, the findings could lead to a better knowledge of wind energy prediction.

Keywords: Linear functional relationship model; maximum likelihood estimation; wind speed

Abstrak

Kelajuan angin mempengaruhi ramalan cuaca, operasi aeroangkasa, operasi maritim dan projek pembinaan. Tujuan penyelidikan ini adalah untuk mengkaji hubungan antara data kelajuan angin Pulau Langkawi di Malaysia selama musim barat daya pada tahun 2019 dan 2020. Untuk memodelkan data kelajuan angin yang tertabur secara normal, model ralat dalam pemboleh ubah telah digunakan iaitu model hubungan kefungsian linear. Plot QQ digunakan untuk mengkaji kebolehupayaan penyuaian model terhadap data. Pendekatan anggaran maksimum digunakan untuk menganggar parameter model dan matriks Maklumat Fisher digunakan untuk menghitung kovarians. Keputusan menunjukkan bahawa nilai anggaran adalah konsisten dan kurang terserak. Hasil kajian ini boleh meningkatkan pengetahuan berkenaan ramalan tenaga angin.

Kata kunci: Anggaran kebolehjadian maksimum; kelajuan angin; model hubungan fungsi linear

REFERENCES

Amirinia, G., Kamranzad, B. & Mafi, S. 2017. Wind and wave energy potential in southern Caspian Sea using uncertainty analysis. Energy 120: 332-345. https://doi.org/10.1016/j.energy.2016.11.088

Arif, A.M., Zubairi, Y.Z. & Hussin, A.G. 2022. Outlier detection in balanced replicated linear functional relationship model. Sains Malaysiana 51(2): 599-607. https://doi.org/10.17576/jsm-2022-5102-23

Arif, A.M., Zubairi, Y.Z. & Hussin, A.G. 2021. Maximum likelihood estimation of replicated linear functional relationship model. Title of Journal 10(1): 301-308.

Arif, A.M., Zubairi, Y.Z. & Hussin, A.G. 2020. Parameter estimation in replicated linear functional relationship model in the presence of outliers. Malaysian Journal of Fundamental and Applied Sciences 16(2): 158-160. https://doi.org/10.11113/mjfas.v16n2.1633

Arif, A.M., Zubairi, Y.G. & Hussin, A.G. 2019. On robust estimation for slope in linear functional relationship model. Sains Malaysiana 48(1): 237-242. https://doi.org/10.17576/jsm-2019-4801-27

Buonaccorsi, J.P. 1996. A modified estimating equation approach to correcting for measurement error in regression. Biometrika 83(2): 433-440. https://doi.org/10.1093/biomet/83.2.433

Chen, Z., Wang, X. & Wang, H. 2018. Preliminary research on total nitrogen content prediction of sandalwood using the error-in-variable models based on digital image processing. PLoS ONE 13(8): 1-22. https://doi.org/10.1371/journal.pone.0202649

Doganaksoy, N. & van Meer, H. 2015. An application of the linear errors-in-variables assessment an application of the linear errors-in- variables model in semiconductor device performance assessment. Quality Engineering 27(4): 500-511. https://doi.org/10.1080/08982112.2015.1068330

Dookie, I., Rocke, S., Singh, A. & Ramlal, C. 2018. Evaluating wind speed probability distribution models with a novel goodness of fit metric: A Trinidad and Tobago case study. International Journal of Energy and Environmental Engineering 9(3): 323-339. https://doi.org/10.1007/s40095-018-0271-y

Fuller, W. 1987. Measurement Error Models. New York: John Wiley.

Ghapor, A.A., Zubairi, Y.Z., Mamun, A.S.M.A. & Imon, A.H.M.R. 2015a. A robust method to estimate the slope parameter in linear functional relationship model. Recent Advances in Renewable Energy Sources. pp. 42-49.

Ghapor, A.A., Zubairi, Y.Z., Mamun, A.S.M.A. & Imon, A.H.M.R. 2015b. A robust nonparametric slope estimation in linear functional relationship model. Pakistan Journal of Statistics 48(1): 339-350. https://doi.org/10.17576/jsm-2019-4801-27

Ghapor, A.A., Zubairi, Y.Z., Mamun, A.S.M.A. & Imon, A.H.M.R. 2014. On detecting outlier in simple linear functional relationship model using COVRATIO statistic. Pakistan Journal of Statistics 30(1): 129-142.

Hanoon, M.S., Ahmed, A.N., Kumar, P., Razzaq, A., Zaini, N., Huang, Y.F., Sherif, M., Sefelnasr, A., Chau, K.W. & El-Shafie, A. 2022. Wind speed prediction over Malaysia using various machine learning models: Potential renewable energy source. Engineering Applications of Computational Fluid Mechanics 16(1): 1673-1689. https://doi.org/10.1080/19942060.2022.2103588

Hassan, S.F., Hussin, A.G. & Zubairi, Y.Z. 2010. Estimation of functional relationship model for circular variables and its application in measurement problems. Chiang Mai Journal of Science 37(2): 195-205.

Hawkins, D.I. & Kanji, G.K. 1995. 100 statistical tests. Journal of Marketing Research 32(1): 112. https://doi.org/10.2307/3152117

Kwon, S.D. 2010. Uncertainty analysis of wind energy potential assessment. Applied Energy 87(3): 856-865. https://doi.org/10.1016/j.apenergy.2009.08.038

Lindley, D.V. 1947. Regression lines and the linear functional relationship. Supplement to the Journal of the Royal Statistical Society 9(2): 218-244.

Lo Brano, V., Orioli, A., Ciulla, G. & Culotta, S. 2011. Quality of wind speed fitting distributions for the urban area of Palermo, Italy. Renewable Energy 36(3): 1026-1039. https://doi.org/10.1016/j.renene.2010.09.009

Malaysian Meteorological Department. 2022. Northeast Monsoon Report Kuala Lumpur Monsoon Activity May 2022. MET Malaysia. pp. 1-2. https://www.met.gov.my/home

Malaysian Meteorology Department. 2019. Annual Report of Malaysian Meteorological Department 2019. Malaysian Meteorological Deparment. www.met.gov.my

Massey, F.J. 1951. The Kolmogorov-Smirnov test for goodness of fit. Journal of the American Statistical Association 46(253): 68. https://doi.org/10.2307/2280095

Mokhtar, N.A., Badyalina, B. & Zubairi, Y.Z. 2022. Functional model of wind direction data in Kuching, Sarawak, Malaysia. Applied Mathematical Sciences 16(7): 349-357.

Mokhtar, N.A., Badyalina, B., Chang, K.L., Ya’acob, F.F., Ghazali, A.F. & Shamala, P. 2021a. Error-in-variables model of Malacca wind direction data with the von Mises distribution in southwest monsoon. Applied Mathematical Sciences 15(9): 471-479. https://doi.org/10.12988/ams.2021.914521

Mokhtar, N.A., Zubairi, Y.Z., Hussin, A.G., Badyalina, B., Ghazali, A.F., Ya’Acob, F.F., Shamala, P. & Kerk, L.C. 2021b. Modelling wind direction data of Langkawi Island during Southwest monsoon in 2019 to 2020 using bivariate linear functional relationship model with von Mises distribution. Journal of Physics: Conference Series 1988(1): 012097. https://doi.org/10.1088/1742-6596/1988/1/012097

Nelder, J. 1977. Theory and application of the linear model. Journal of the Royal Statistical Society. Series A (General) 140(3): 384-385.

Rosenhead, J. 1963. The advanced theory of statistics: Volume 2: Inference and relationship. J Oper. Res. Soc. 14: 97-98. https://doi.org/10.2307/3006935

Zaharim, A., Najid, S.K., Razali, A.M. & Sopian, K. 2009. Analysing Malaysian wind speed data using statistical distribution. Proceedings of the 4th IASME / WSEAS International Conference on Energy & Environment (EE’09). pp. 363-370. http://www.wseas.us/e-library/conferences/2009/cambridge/EE/EE55.pdf

Zakaria, M. 2022. The limitation of widely used data normality tests in clinical research. Auditory and Vestibular Research 31(1): 1-3. https://doi.org/10.18502/avr.v31i1.8127

*Corresponding author; email: nurkhairany@uitm.edu.my