基于切比雪夫函数的正交多项式拟合模拟渤海石油浓度空间分布
Simulation of Hydrocarbon Concentration Spatial Distribution in the Bohai Sea Using Chebyshev-Based Orthogonal Polynomial Fitting
摘要: 本研究以中国浅海内海渤海为研究区域，针对石油污染物排入海洋生态系统造成的环境风险，开展污染物空间分布建模与影响评估研究。基于2018年石油浓度综合监测数据集，系统比较了空间插值方法的误差相关指标，成功重建了研究区全年各季节石油浓度的空间变化规律。研究发现，切比雪夫拟合法(CPF)在十折交叉验证中表现出优异的统计性能，其均方根误差(RMSE = 0.0160 mg/L)和平均绝对误差(MAE = 0.0094 mg/L)较传统方法降低约4%~37%。
Abstract: This study utilizes the Bohai Sea, a shallow inland sea in China, as the study area to conduct pollutant spatial distribution modeling and impact assessment studies for the environmental risks posed by petroleum hydrocarbon pollutants discharged into the marine ecosystem. Based on the 2018 comprehensive monitoring dataset of petroleum hydrocarbon concentrations, the study systematically compared error-related metrics of spatial interpolation methods and successfully reconstructed the spatial variation patterns of petroleum hydrocarbon concentrations throughout the year in the study area. The method reconstructed the spatial variation of petroleum hydrocarbon concentrations in the study area in all seasons. The findings of the study indicated that the Chebyshev fitting method (CPF) exhibited superior statistical performance in ten-fold cross-validation, with a mean absolute error (MAE = 0.0094 mg/L) and root mean square error (RMSE = 0.0160 mg/L) that were reduced by about 4%~37% compared with the traditional method.
文章引用：郭书苇. 基于切比雪夫函数的正交多项式拟合模拟渤海石油浓度空间分布[J]. 应用数学进展, 2026, 15(1): 198-209. https://doi.org/10.12677/aam.2026.151021

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