TITLE:
Spectral BRDF Prediction of Solar Panels Using a Five-Parameter Model and ExtraTrees
AUTHORS:
Haibin Tian, Zhou Wang, Dan Li, Hongxing Cai, Ziwei Zhou, Xuguo Zhang, Zhenwen Liu
KEYWORDS:
Solar Panel, Spectral BRDF, Five-Parameter Model, ExtraTrees, Nested Validation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.10,
October
20,
2026
ABSTRACT: Sparse angular measurements limit the prediction of solar-panel spectral bidirectional reflectance distribution functions (BRDFs), particularly near localized high-reflectance features. This study combines a wavelength-wise five-parameter semi-empirical model with two ExtraTrees regressors that predict a log-ratio residual and a direct log-spectrum. Their predictions are fused in log space, with reconstruction scale and fusion weight selected exclusively within each outer training partition. Measurements of a small solar-panel model containing solar cells under a glass covering comprise 120 angular configurations and 342 wavelengths from 500.08 to 759.85 nm. All configurations, including the highest-reflectance configuration, enter the primary evaluation; physically equivalent normal-view geometries remain together during splitting. Across 100 grouped random splits, the nested fusion model achieves mean global R2 of 0.7932, RMSE of 0.002421 sr−1, cosine-weighted normalized squared error of 4.2545%, and spectral angle of 2.1984˚. Four incidence-angle holdouts yield mean R2 of 0.8378 and RMSE of 0.002176 sr−1. The high-reflectance configuration has mean held-out RMSE of 0.008614 sr−1 over its 15 test occurrences in the random protocol, indicating substantial local sensitivity despite improved aggregate amplitude prediction. These results support internal prediction over the sampled geometry and spectral range, while limited angular coverage, nominal white-reference calibration, and unavailable repeat measurements constrain physical interpretation and uncertainty assessment.