基于分数阶微分的盐渍土电导率高光谱估算研究

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田安红^{1, 2,},
赵俊三²,
张顺吉¹,
付承彪^1,,,
熊黑钢^{3, 4}
1.曲靖师范学院信息工程学院曲靖 655011
2.昆明理工大学国土资源工程学院昆明 650093
3.北京联合大学应用文理学院北京 100083
4.新疆大学资源与环境科学学院乌鲁木齐 830046
基金项目: 国家自然科学基金项目41901065
国家自然科学基金项目41671198
国家自然科学基金项目41761081
教育部产学合作协同育人项目201802156014
曲靖师范学院教师教育研究专项项目2019JZ001

详细信息

作者简介:田安红, 主要研究方向为盐渍土的高光谱反演。E-mail:tianfucb@163.com

通讯作者:付承彪, 主要研究方向为高光谱遥感图像处理。E-mail:fucb305@163.com

中图分类号:S151.9

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出版历程

收稿日期:2019-12-10
录用日期:2020-02-04
刊出日期:2020-04-01

Hyperspectral estimation of saline soil electrical conductivity based on fractional derivative

TIAN Anhong^{1, 2,},
ZHAO Junsan²,
ZHANG Shunji¹,
FU Chengbiao^1,,,
XIONG Heigang^{3, 4}
1. College of Information Engineering, Qujing Normal University, Qujing 655011, China
2. Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China
3. College of Applied Arts and Science, Beijing Union University, Beijing 100083, China
4. College of Resource and Environment Sciences, Xinjiang University, Urumqi 830046, China
Funds: This study was supported by the National Natural Science Foundation of China41901065
This study was supported by the National Natural Science Foundation of China41671198
This study was supported by the National Natural Science Foundation of China41761081
the Industry-University Cooperation Collaborative Education Project of Ministry of Education of China201802156014
the Teacher Education Research Project of Qujing Normal University of China2019JZ001

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Corresponding author:FU Chengbiao, E-mail:fucb305@163.com

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摘要
摘要:传统电导率的反演模型采用整数阶微分（1阶或2阶）的预处理方法，忽略位于分数阶微分处的高光谱反射率信息。因此，本研究提出一种基于分数阶微分的盐渍土电导率高光谱估算方法，以新疆昌吉回族自治州境内的盐渍化土壤为研究靶区，于2017年5月采集0~20 cm的表层土壤样品，利用FieldSpec^?3 Hi-Res光谱仪测量盐渍土的野外高光谱，并在实验室化验土壤的电导率理化参数。在Matlab 2019a软件中编程实现0阶-2.0阶的Grünwald-Letnikov分数阶微分计算（阶数间隔为0.1）。分析土壤高光谱与电导率的相关系数曲线在21种微分处的变化规律，选择每阶微分的最大相关系数大于0.5时对应的波长为敏感波长，采用逐步多元线性回归模型对电导率进行预测。结果表明：分数阶微分预处理方法能够把相关系数曲线位于不同分数阶时的变化细节呈现出来，在全波段范围内出现更多的波峰和波谷信息。电导率的8个敏感波长为400 nm、418 nm、567 nm、1 667 nm、2 132 nm、2 193 nm、2 257 nm和2 258 nm。估算电导率的最佳模型位于分数阶1.5阶，其验证集的RPD值为1.99，R²为0.81，RMSE为1.08，该模型因RPD值大于1.8对电导率的估算能力好。本研究探索了电导率在不同分数阶微分处的差异信息，为电导率的估算提供一种新的研究思路，对新疆干旱区盐渍土的改良提供了科学可靠的依据。
关键词:盐渍土/
电导率/
Grünwald-Letnikov分数阶微分/
敏感波长/
野外高光谱
Abstract:The integer-order differential (first-order or second-order) preprocessing method is often used in traditional electrical conductivity inversion models, but it ignores the hyperspectral reflectance information at the fractional-order differential. In this paper, a hyperspectral method based on fractional differential to estimate the electrical conductivity of saline soil was proposed. The salinized soil in Changji, Xinjiang was used as the research subject. The surface soil samples of 0-20 cm were collected in May 2017, the field hyperspectral of the saline soil was measured by a FieldSpec^?3 Hi-Res spectrometer, and physical and chemical parameters of soil electrical conductivity were tested in the laboratory. Next, the Grünwald-Letnikov fractional derivative calculation between 0.0-order and 2.0-order was programmed in MATLAB 2019a software (order interval is 0.1). Then, the variation law of the correlation coefficient curves between soil hyperspectral and electrical conductivity under 21 kinds of differentials was analyzed. When the maximum correlation coefficient of each fractional derivative was greater than 0.5, the corresponding wavelength was selected as the sensitive wavelength. Finally, the stepwise multiple linear regression model was used to predict the electrical conductivity. The results showed that the fractional derivative preprocessing method could display the variation details of the correlation coefficient curve under different fractional orders, and more peaks and troughs appeared in the whole band. The eight sensitive wavelengths of electrical conductivity were 400 nm, 418 nm, 567 nm, 1 667 nm, 2 132 nm, 2 193 nm, 2 257 nm, and 2 258 nm. The best model for estimating electrical conductivity was located at the 0.5^th-order. The relative percent difference (RPD) value of the verification set was 1.99, the determination coefficient (R²) was 0.81, and the root mean square error (RMSE) was 1.08. This model had the ability to estimate the electrical conductivity because the RPD value was greater than 1.8. This study explored the difference in electrical conductivity estimates under different fractional derivatives and provided a new method for electrical conductivity estimation, which could be of considerable value for research into improvement of saline soils in the arid regions of Xinjiang.
Key words:Saline soil/
Electrical conductivity/
Grünwald-Letnikov fractional derivative/
Sensitive wavelength/
Field hyperspectral

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图1研究区土壤采样点示意图
Figure1.Schematic diagram of soil sampling points in the study area

下载: 全尺寸图片幻灯片

图2土壤高光谱与电导率在0阶-2.0阶之间的相关系数
< |P_0.01|表示极显著相关。
Figure2.Correlation coefficients between soil hyperspectral and electrical conductivity from 0 order to 2.0 order
< |P_0.01| shows extremely significant correlation.

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图3不同分数阶微分阶数对应的土壤高光谱和电导率最大相关系数和波长
Figure3.Maximum correlation coefficients between soil hyperspectral and electrical conductivity and wavelengths corresponding to different fractional differential orders

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图41.5阶(a)、1.0阶(b)和2.0阶(c)微分对应的土壤电导率实测值与预测值的散点图
Figure4.Scatter plots of measured and predicted soil electrical conductivities corresponding to different fractional differential orders of 1.5 order (a), 1.0 order (b), and 2.0 order (c)

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表1样本集土壤电导率的统计特征
Table1.Statistical characteristics of soil electrical conductivity of the sample sets

样本集 Samples set	样本数目 Number of samples	极小值 Min. value (mS·cm^-1)	极大值 Max. value (mS·cm^-1)	平均值 Mean (mS·cm^-1)	标准差 Standard deviation (mS·cm^-1)	变异系数 Variable coefficient (%)
全部样本?All samples	30	0.50	10.700	4.463	2.559	57.338
建模集样本?Samples of calibration set	18	0.50	9.700	4.328	2.699	62.361
验证集样本?Samples of validation set	12	1.70	10.700	4.667	2.435	52.175

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表28个敏感波长对应的土壤高光谱在不同分数阶微分阶次的电导率预测模型和预测精度
Table2.Soil electrical conductivity prediction models and prediction accuracies of the soil hyperspectral corresponding to the eight sensitive wavelengths at different fractional differential orders

阶数 Order	回归模型 Regression model	建模集 Calibration set		验证集 Validation set
阶数 Order	回归模型 Regression model	R²	RMSE	R²	RMSE	RPD
0	Y=12.6+1 298.3R₄₀₀–1 382.8R₄₁₈+244.6R₅₆₇–320.3R₁₆₆₇+250.9R₂₁₃₂–128.9R₂₁₉₃+75.9R₂₂₅₈	0.59	2.25	0.27	3.55	1.07
0.1	Y=13.8+915R₄₀₀–1 345.4R₄₁₈+365.1R₅₆₇–691R₁₆₆₇+675R₂₁₃₂–149.9R₂₁₉₃+17.2R₂₂₅₇–110.9R₂₂₅₈	0.65	2.18	0.29	3.91	1.13
0.2	Y=14.1+610.4R₄₀₀–1 259R₄₁₈+548.2R₅₆₇–1 239.9R₁₆₆₇+1 113.2R₂₁₃₂–208.3R₂₁₉₃+1.4R₂₂₅₇–147.8R₂₂₅₈	0.71	2.02	0.31	4.01	1.15
0.3	Y=10.2+441.2R₄₀₀–1 315R₄₁₈+663.2R₅₆₇–1 464.3R₁₆₆₇+1 125.8R₂₁₃₂–367.3R₂₁₉₃+472.9R₂₂₅₇–396.6R₂₂₅₈	0.71	1.99	0.45	2.77	1.29
0.4	Y=6.3+347.7R₄₀₀–1 448.1R₄₁₈+708.2R₅₆₇–1 378.3R₁₆₆₇+918.3R₂₁₃₂–537R₂₁₉₃+ 993.4R₂₂₅₇–800.9R₂₂₅₈	0.70	2.03	0.61	1.71	1.35
0.5	Y=5.3–20.6R₄₀₀–15 763R₄₁₈+12 194.1R₅₆₇+30 150.2R₁₆₆₇+2 181.1R₂₁₃₂+979R₂₁₉₃–333.5R₂₂₅₇–272R₂₂₅₈	0.92	1.05	0.49	1.86	1.39
0.6	Y=4+213.5R₄₀₀–2 434.8R₄₁₈+593.5R₅₆₇–877.3R₁₆₆₇+389.1R₂₁₃₂–772R₂₁₉₃+1 625.6R₂₂₅₇–1 133.9R₂₂₅₈	0.69	2.08	0.77	1.34	1.22
0.7	Y=4.4+161.5R₄₀₀–3 474.7R₄₁₈+190.1R₅₆₇+214.4R₁₆₆₇+482.3R₂₁₃₂–784.5R₂₁₉₃+1 675R₂₂₅₇–1 272.4R₂₂₅₈	0.68	2.09	0.84	1.23	1.27
0.8	Y=5.2+104.7R₄₀₀–5 205R₄₁₈–444.6R₅₆₇+3 652.2R₁₆₆₇+844.7R₂₁₃₂–555.2R₂₁₉₃+1 395.2R₂₂₅₇–1 348.1R₂₂₅₈	0.71	2.01	0.78	1.50	0.98
0.9	Y=5.3+45.3R₄₀₀–6 731.3R₄₁₈–312.7R₅₆₇+9 880.3R₁₆₆₇+1 477.9R₂₁₃₂–12.4R₂₁₉₃+847.7R₂₂₅₇–1 315.6R₂₂₅₈	0.77	1.79	0.70	1.63	1.03
1.0	Y=5+1 396.6R₄₀₀–16 527.4R₄₁₈+1 467R₅₆₇+19 953R₁₆₆₇+2 167.3R₂₁₃₂+1 075.9R₂₁₉₃+286.4R₂₂₅₇–1 425.5R₂₂₅₈	0.88	1.27	0.17	2.58	0.98
1.1	Y=3.8–3.6R₄₀₀–7 335.3R₄₁₈+3 375.6R₅₆₇+20 255.9R₁₆₆₇+2 172.4R₂₁₃₂+843.2R₂₁₉₃+21.4R₂₂₅₇–963.6R₂₂₅₈	0.88	1.26	0.65	1.68	1.41
1.2	Y=3.3–11.7R₄₀₀–8 254.8R₄₁₈+5 383R₅₆₇+23 314.2R₁₆₆₇+2 193.1R₂₁₃₂+898.4R₂₁₉₃–177R₂₂₅₇–748.2 R₂₂₅₈	0.91	1.10	0.59	1.69	1.48
1.3	Y=2.8–20.4R₄₀₀–10 339.6R₄₁₈+7 137.5R₅₆₇+25 870.9R₁₆₆₇+2 133.9R₂₁₃₂+859.3R₂₁₉₃–280.5R₂₂₅₇–556.6R₂₂₅₈	0.93	0.99	0.57	1.68	1.49
1.4	Y=2.1–25.3R₄₀₀–13 225.4R₄₁₈+9 108.4R₅₆₇+28 157.9R₁₆₆₇+2 112.5R₂₁₃₂+884.8R₂₁₉₃–324.9R₂₂₅₇–398.6R₂₂₅₈	0.93	0.98	0.55	1.71	1.47
1.5	Y=4.4+274.4R₄₀₀–1 893R₄₁₈+712.6R₅₆₇–1 196.5R₁₆₆₇+677.5R₂₁₃₂–674.2R₂₁₉₃+1 379R₂₂₅₇–947.6R₂₂₅₈	0.69	2.06	0.81	1.08	1.99
1.6	Y=0.5–8.8R₄₀₀–17 793R₄₁₈+16 131.7R₅₆₇+31 800.2R₁₆₆₇+2 319.6R₂₁₃₂+1 095.2R₂₁₉₃–327R₂₂₅₇–179.5R₂₂₅₈	0.95	1.17	0.49	1.95	1.39
1.7	Y=0.004+4.6R₄₀₀–20 746.5R₄₁₈+18 457.6R₅₆₇+33 334.4R₁₆₆₇+2 581.3R₂₁₃₂+1 304.8R₂₁₉₃–364.9R₂₂₅₇–109.6R₂₂₅₈	0.87	1.34	0.43	2.19	1.31
1.8	Y=–0.7+20.2R₄₀₀–24 526.6R₄₁₈+18 405.9R₅₆₇+34 954.1R₁₆₆₇+3 004R₂₁₃₂+1 615.2R₂₁₉₃–444.6R₂₂₅₇–43.7R₂₂₅₈	0.83	1.52	0.37	2.49	1.24
1.9	Y=–1.5+37.3R₄₀₀–28 236.7R₄₁₈+16 724.2R₅₆₇+36 771R₁₆₆₇+3 497R₂₁₃₂+1 932.5R₂₁₉₃–491.9R₂₂₅₇–17.4R₂₂₅₈	0.79	1.72	0.33	2.81	1.20
2.0	Y=5.3–6 516.4R₄₀₀+24 756.4R₄₁₈+22 634.9R₅₆₇–29 356.7R₁₆₆₇+1 859.7R₂₁₃₂–729.3R₂₁₉₃–3 933.7R₂₂₅₇–893.7R₂₂₅₈	0.59	2.38	0.01	3.45	0.80
R为高光谱反射率值, 下标数据为波长。R is hyperspectral reflectance, subscript data is the wavelength.

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