Piecewise Positivity Preserving Cubic Bezier Interpolation for Estimating Solar Radiation Missing Value in Penang, Malaysia
Azizan Saaban, Mohd Lutfi Zainudin and Mohd Nazari Abu Bakar
DOI : 10.3844/jmssp.2016.302.307
Journal of Mathematics and Statistics
Volume 12, Issue 4
Complete solar radiation data is important in variety of disciplines such as solar radiation development system or solar project which is strongly affected by hourly variation of the solar radiation. However, the available data may contain missing data for several days in the absence of measurement due to several factors such as instrument failure and human errors. In this study, the secondary data of solar radiation at Penang, Malaysia taken from Malaysian Meteorology Department was investigated. In order to fill the gap of the above missing values, the interpolation method based on positivity preserving Bezier curves to ensure that the solar radiation are always positive is proposed. This paper start with the derivation of positivity preserving condition for Bezier curves by imposing lower bound of the Bezier control points. The proposed method is tested using simulated missing value of solar radiation dataset. Result from RMSE and Coefficient of Determination (r2) for different set of missing value from 10, 30 and 50%, show that the proposed method produce a better result compared to existing interpolation method without implementing positivity preserving condition. Finally, the proposed method was used to fill the gap of missing values of solar radiation at Penang, Malaysia.
© 2016 Azizan Saaban, Mohd Lutfi Zainudin and Mohd Nazari Abu Bakar. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.