基于分数阶微分的土壤重金属锌和镍的定量反演模型研究

doi:10.3964/j.issn.1000-0593(2024)10-2850-08

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摘要：传统的土壤重金属反演模型通常在预处理中使用整数阶微分方法（如1阶或2阶），其忽略了与目标变量相关的分数阶光谱反射率。分数阶微分（FOD）能通过灵活选定微分阶次，有效增强光谱信号。以云南省普洱市墨江哈尼族自治县的农田土壤为研究对象，测量了61个土壤高光谱反射率和土壤重金属含量数据（锌和镍），对高光谱反射率信息进行了0～2阶（间隔为0.05）分数阶微分预处理，将分数阶微分预处理后的各阶次的光谱反射率输入到连续投影算法（SPA）中进行特征波段筛选；分别建立了偏最小二乘回归（PLSR）、随机森林（RF）和袋装法（Bagging）三种土壤重金属反演模型。结果表明: 在经过0到2阶（以0.05为间隔，共41个阶次）的分数阶微分处理，整体光谱强度呈逐渐减弱的趋势，伴随着分数阶阶次的增加逐渐趋向于零。光谱吸收带逐渐收窄，不同光谱曲线之间的差异逐渐减小，随着微分阶次的提高，产生了更为丰富的波峰和波谷。基于分数阶微分的最好阶次模型均优于原始光谱模型和整数阶模型，模型较好阶次大部分集中在低阶分数阶。对于重金属锌，预测模型精度最好的是0.75阶次的RF模型（R²=0.675，RMSE=6.149，RPD=1.755），0.75阶次的Bagging模型次之（R²=0.633，RMSE=6.534，RPD=1.652），0.25阶次的PLSR模型最低（R²=0.551，RMSE=7.230，RPD=1.493）。对于重金属镍，预测模型精度最好的是0.80阶次的RF模型（R²=0.854，RMSE=127.823，RPD=2.618），0.80阶次的Bagging模型次之（R²=0.841，RMSE=133.304，RPD=2.510），0.40阶次的PLSR模型最低（R²=0.762，RMSE=163.162，RPD=2.051）。本研究基于FOD预处理和SPA降维后构建的非线性模型（RF和Bagging）在农田土壤重金属含量估测具有一定的适用性，可以为类似区域的土壤重金属含量反演提供参考依据。

关键词：分数阶微分；高光谱；土壤重金属锌和镍；随机森林；袋装法

Abstract：Integer-order derivative methods (such as 1st or 2nd order) are traditional preprocessing methods for soil heavy-metal inversion models, which ignore the fractional-order spectral reflectance information associated with the target variable. Fractional order derivative (FOD) can flexibly select the differential order to enhance the spectral signal effectively. This study focused on the farmland soil in Mojiang Hani Autonomous County, Pu'er City, Yunnan Province, China. Sixty-one soil hyperspectral reflectance information and soil heavy metal content data (zinc and nickel) were measured. The spectral reflectance information underwent 0 to 2 fractional-order derivative preprocessing with intervals of 0.05. The preprocessed spectral reflectance information at each order was input into the Successive Projections Algorithm (SPA) to select characteristic bands. Subsequently, three soil heavy metal prediction models were separately established using Partial Least Squares Regression (PLSR), Random Forest (RF), and Bagging methods. The results show that after the fractional order derivative processing from 0 to 2 orders (41 orders in total with an interval of 0.05), the overall spectral intensity gradually weakens and gradually approaches zero with the increase of fractional orders. The spectral absorption band gradually narrows, and the differences between different spectral curves gradually decrease. As the derivative order increases, more abundant peaks and valleys are produced. The best-order models based on fractional derivatives are better than the original spectral model and the integer order model, and most of the better orders of the model are concentrated in low-order fractional orders. For heavy metal zinc, the best prediction model accuracy was achieved by the RF model of 0.75 order (R²=0.675, RMSE=6.149, RPD=1.755), followed by the Bagging model of 0.75 order (R²=0.633, RMSE=6.534, RPD=1.652), and the lowest was achieved by the PLSR model of 0.25 order (R²=0.551, RMSE=7.230, RPD=1.493). For the heavy metal nickel, the best prediction model accuracy was the RF model of order 0.80 (R²=0.854, RMSE=127.823, RPD=2.618), the Bagging model of order 0.80 was the next best (R²=0.841, RMSE=133.304, RPD=2.510), the PLSR model of order 0.40 lowest (R²=0.762, RMSE=163.162, RPD=2.051). Visible, the nonlinear models (RF and Bagging) constructed based on FOD preprocessing and SPA dimensionality reduction in this study have certain applicability in estimating heavy metal content in farmland soil. They can be a reference for predicting heavy metal content in similar regions.

Key words：Fractionalorder derivative; Hyperspectral; Soil heavy metals Zn and Ni; Random forest; Bagging method

收稿日期: 2024-01-24 修订日期: 2024-05-31

中图分类号:

P237

基金资助: 国家自然科学基金项目（42067029），云南省科技厅项目（202205AC160005）, 云南省“兴滇英才支持计划”青年人才项目（KKXX202303001）资助

通讯作者: 付承彪 E-mail: fcb@kust.edu.cn

作者简介: 蒋宇恒，2001年生，昆明理工大学信息工程与自动化学院硕士研究生 e-mail: 20232204148@stu.kust.edu.cn

引用本文:

蒋宇恒，晏博，庄清源，王爱平，曹霜，田安红，付承彪. 基于分数阶微分的土壤重金属锌和镍的定量反演模型研究[J]. 光谱学与光谱分析, 2024, 44(10): 2850-2857.
JIANG Yu-heng, YAN Bo, ZHUANG Qing-yuan, WANG Ai-ping, CAO Shuang, TIAN An-hong, FU Cheng-biao. Quantitative Inversion Model of Soil Heavy Metals Zn and Ni Based on Fractional Order Derivative. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2024, 44(10): 2850-2857.

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