CAJ | 학술논문

分数阶微积分将整数阶微积分的概念推广到分数阶。以准东煤田五彩湾矿区为研究区，测定土壤样本的砷含量及光谱反射率。对土壤光谱、均方根、倒数、对数变换进行对应的0～2阶（间隔0．2阶）微分处理，利用偏最小二乘回归进行建模，并比较不同模型的反演效果。结果表明：均方根变换1．8阶微分数据所建立的模型，RMSEC＝1．996，R2C＝0．821，RMSEP＝1．973，R2P＝0．890，RPD＝2．367为最优模型，能较好的预测土壤砷含量。该结果可为分数阶微分在高光谱遥感监测土壤重金属污染中的应用提供参考。
분수계미적분장정수계미적분적개념추엄도분수계。이준동매전오채만광구위연구구，측정토양양본적신함량급광보반사솔。대토양광보、균방근、도수、대수변환진행대응적0～2계（간격0．2계）미분처리，이용편최소이승회귀진행건모，병비교불동모형적반연효과。결과표명：균방근변환1．8계미분수거소건립적모형，RMSEC＝1．996，R2C＝0．821，RMSEP＝1．973，R2P＝0．890，RPD＝2．367위최우모형，능교호적예측토양신함량。해결과가위분수계미분재고광보요감감측토양중금속오염중적응용제공삼고。
Fractional calculus extends the conception of integer calculus to the fractional order .This study set Wucaiwan open coalmine area in the Eastern Junggar Basin in Xinjiang Uygur Autonomous Region as the study area ,the arsenic (As) element content and spectral reflectance of the soil samples were measured .The paper treated the hyperspectral reflectance data ( R ) with 3 mathematical transforms such as R ,1/R ,ln(R) ,then the formula of Grünwald‐Letnikov fractional derivative was used to calculate their 0~2 order derivative(interval 0 .2 order) ,and the inversion effects were compared after the models between different transforms and the As content in soil were set up by PLSR .Results show that the model based on R 1 .8 order derivative transform (RMSEC= 1 .996 ,R2C = 0 .821 ,RMSEP= 1 .973 ,R2P = 0 .890 ,RPD=2.367) is much better than others ,and has a better capability to predict As content in soil .The results of this research would provide a reference basis for the application of fractional order derivative in monitoring heavy metal contamination by using hyperspectral data .