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作物学报 ›› 2026, Vol. 52 ›› Issue (10): 3054-3068.doi: 10.3724/SP.J.1006.2026.61026

• 耕作栽培·生理生化 • 上一篇    下一篇

基于改进连续投影算法和CWT的冬小麦叶片氮浓度估算

付元元1,2(), 李帅锋1, 陈珂1, 夏天1, 冯海宽3, 束美艳1,2, 郭伟1,2, 乔红波1, 岳继博1,2,*()   

  1. 1 河南农业大学人工智能学院, 河南郑州 450046
    2 河南省农业大数据与人工智能国际联合实验室, 河南郑州 450046
    3 北京市农林科学院信息技术研究中心, 北京 100097
  • 收稿日期:2026-03-25 接受日期:2026-07-21 出版日期:2026-10-12 网络出版日期:2026-07-22
  • 通讯作者: * 岳继博, E-mail: yuejibo@henau.edu.cn
  • 作者简介:付元元, E-mail: yuanyuanfu@henau.edu.cn
  • 基金资助:
    河南省自然科学基金面上项目(252300421853)

Estimation of leaf nitrogen concentration in winter wheat based on an improved successive projections algorithm and continuous wavelet transform

Fu Yuan-Yuan1,2(), Li Shuai-Feng1, Chen Ke1, Xia Tian1, Feng Hai-Kuan3, Shu Mei-Yan1,2, Guo Wei1,2, Qiao Hong-Bo1, Yue Ji-Bo1,2,*()   

  1. 1 College of Artificial Intelligence, Henan Agricultural University, Zhengzhou 450046, Henan, China
    2 Henan International Joint Laboratory of Agricultural Big Data and Artificial Intelligence, Zhengzhou 450046, Henan, China
    3 Information Technology Research Center, Beijing Academy of Agriculture and Forestry Sciences, Beijing 100097, China
  • Received:2026-03-25 Accepted:2026-07-21 Published:2026-10-12 Published online:2026-07-22
  • Contact: * Yue Ji-Bo, E-mail: yuejibo@henau.edu.cn
  • Supported by:
    General Program of the Natural Science Foundation of Henan Province(252300421853)

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摘要：

作物叶片氮浓度(LNC)的遥感诊断对指导作物精准施氮、提升氮素利用效率和增加产量具有重要意义。本研究针对传统连续投影算法(SPA)难以处理特征间非线性关系的问题, 提出了一种改进的连续投影算法, 即核化连续投影算法(KSPA)。本研究采用连续小波变换(CWT)对光谱进行多尺度分解, 结合KSPA提取与LNC相关的关键特征。同时, 以植被指数、SPA和偏最小二乘-变量投影重要性(PLS-VIP)作为对比方法, 分别构建偏最小二乘回归(PLSR)、随机森林(RF)和类别提升算法(CatBoost)模型估算冬小麦LNC, 并采用沙普利加性解释(SHAP)方法进行模型可解释性分析。结果表明, CWT中等分解尺度(第5至第7尺度)在估算冬小麦LNC中表现优异, KSPA筛选的特征能有效提升模型性能。CatBoost在CWT第7尺度上结合KSPA的表现最优(R2 = 0.829, RMSE = 0.322%, RPD = 2.425), 相较于PLS-VIP (RF模型: R2 = 0.729, RMSE = 0.405%)和SPA (CatBoost: R2 = 0.731, RMSE = 0.403%)的最优模型, R2分别提升了0.100和0.098, RMSE分别降低了0.083%和0.081%。跨年留一验证进一步证实了该方法的稳健性与泛化能力。改进后的算法能克服传统SPA特征筛选的线性局限性, 可为冬小麦氮营养精准监测提供参考。

关键词: 冬小麦叶片氮浓度, 连续小波变换, 核化连续投影算法, 类别提升算法, SHAP分析

Abstract:

Remote sensing-based diagnosis of crop leaf nitrogen concentration (LNC) is of great importance for guiding precise nitrogen application, improving nitrogen use efficiency, and increasing crop yield. To address the limitations of the traditional successive projections algorithm (SPA) in handling nonlinear relationships among spectral features, this study proposes an improved successive projections algorithm, namely the kernel successive projections algorithm (KSPA). Continuous wavelet transform (CWT) was used for multi-scale spectral decomposition, and KSPA was subsequently applied to extract key features associated with LNC. For comparison, vegetation indices, SPA, and partial least squares-variable importance in projection (PLS-VIP) were also used for feature selection. Models based on partial least squares regression (PLSR), random forest (RF), and categorical boosting (CatBoost) were constructed to estimate winter wheat LNC, and Shapley additive explanations (SHAP) were used for model interpretability analysis. The results showed that intermediate CWT decomposition scales performed well in estimating winter wheat LNC, and the features selected by KSPA significantly improved model performance. The CatBoost model combined with KSPA at the seventh CWT scale achieved the best performance (R2 = 0.829, RMSE = 0.322%, RPD = 2.425). Compared with the best models based on PLS-VIP (RF: R2 = 0.729, RMSE = 0.405%) and SPA (CatBoost: R2 = 0.731, RMSE = 0.403%), this model increased R2 by 0.100 and 0.098 and reduced RMSE by 0.083% and 0.081%, respectively. Leave-one-year-out cross-validation further confirmed the robustness and generalization ability of the proposed method. Overall, the improved algorithm effectively overcomes the linear limitations of traditional SPA in feature selection and provides a useful reference for precision monitoring of nitrogen nutrition in winter wheat.

Key words: winter wheat leaf nitrogen concentration, continuous wavelet transform, kernel successive projections algorithm, categorical boosting, SHAP analysis

表1

冬小麦叶片氮浓度的描述性统计"

指标Index 所有数据All data 建模集Calibration set 验证集Validation set
样本数Sample 533 408 125
最大值Maximum value (%) 5.07 5.07 4.84
最小值Minimum value (%) 1.09 1.09 1.59
平均值 Mean (%) 3.11 3.08 3.18
标准差Standard deviation (%) 0.87 0.89 0.78
变异系数Coefficient of variation (%) 27.97 28.90 24.53
峰值Kurtosis (%) 2.13 2.09 2.14

表2

植被指数及其计算公式"

植被指数Vegetation index 计算公式Calculation formula
三角植被指数Triangular vegetation index (TVI) [17] R705/(R717+R491)
角度不敏感植被指数Angle insensitive vegetation index (AIVI) [18] [R445× (R720+R735)-R573× (R720-R735)]/[R720× (R573+R445)]
LIC指数Lightness index for chlorophyll (LIC) [19] R440/R690
改进型归一化差分705指数
Modified normalized difference 705 index (mND705) [20]		 (R750-R705)/(R750+R705-2×R445)
归一化色素叶绿素指数
Normalized pigment chlorophyll index (NPCI) [21]		 (R680-R430)/(R680+R430)
卡特指数Carter index (CTR) [18] R695/R420
归一化差分植被指数
Normalized difference vegetation index (NDVI) [22]		 (R731-R709)/(R731+R709)
比值指数Ratio index (RI) [21] R735/R720
归一化差分705指数Normalized difference 705 index (ND705) [21] (R750-R705)/(R750+R705)
光化学反射指数Photochemical reflectance index (PRI) [21] (R570-R531)/(R570+R531)
陆地叶绿素指数MERIS terrestrial chlorophyll index (MTCI) [23] (R754-R709)/(R709-R681)
沃格尔曼红边指数Vogelmann red edge index (VOG) [21] R740/R720
简单比值色素指数Simple ratio pigment index (SRPI) [21] R430/R680
改进型红边简单比值指数
Modified simple ratio 705 index (mSR705) [23]		 (R750-R445)/(R705-R445)
简单比值指数Simple ratio index (SR) [24] R712/R758

表3

基于原始光谱与植被指数的冬小麦LNC预测模型精度"

特征
Feature		 模型
Model		 建模集Calibration set 验证集Validation set
R2 RMSE (%) RPD R2 RMSE (%) RPD
原始光谱Original spectrum PLSR 0.712 0.477 1.864 0.600 0.491 1.588
RF 0.799 0.399 2.231 0.504 0.547 1.425
CatBoost 0.730 0.462 1.926 0.592 0.496 1.573
植被指数Vegetation index PLSR 0.624 0.545 1.633 0.627 0.475 1.643
RF 0.735 0.457 1.946 0.661 0.453 1.723
CatBoost 0.777 0.419 2.120 0.695 0.429 1.817

图1

CWT不同分解尺度下小波系数与LNC的相关系数矩阵 LNC: 叶片氮浓度; CWT: 连续小波变换。"

图2

CWT不同分解尺度的小波系数曲线 CWT: 连续小波变换。"

表4

CWT不同分解尺度下PLS-VIP、SPA和KSPA筛选小波系数的个数"

方法
Method		 尺度4
Scale 4		 尺度5
Scale 5		 尺度6
Scale 6		 尺度7
Scale 7		 尺度8
Scale 8
原始光谱Original spectrum 951 951 951 951 951
偏最小二乘-变量投影重要性PLS-VIP 32 34 32 26 44
连续投影算法SPA 40 37 26 39 32
核化连续投影算法KSPA 52 49 63 68 56

图3

CWT不同分解尺度与PLS-VIP结合的冬小麦LNC估算模型精度 A-C为建模集R2、RMSE和RPD变化曲线, D-F为验证集R2、RMSE和RPD变化曲线。缩写同表3和表4。"

图4

CWT不同分解尺度与SPA结合的冬小麦LNC估算模型精度 A-C为建模集R2、RMSE和RPD变化曲线, D-F为验证集R2、RMSE和RPD变化曲线。缩写同表3和表4。"

图5

基于最优尺度CWT与SPA的3种机器学习方法的冬小麦LNC估算模型性能 缩写同表3和表4。"

图6

CWT不同分解尺度与KSPA结合的冬小麦LNC估算模型精度 A-C为建模集R2、RMSE和RPD变化曲线, D-F为验证集R2、RMSE和RPD变化曲线。缩写同表3和表4。"

图7

基于最优尺度CWT与KSPA的3种机器学习方法的冬小麦LNC估算模型性能 缩写同表3和表4。"

表5

CWT与KSPA消融试验结果"

特征
Feature		 最佳尺度
Optimal scale		 最佳模型
Optimal model		 建模集Calibration set 验证集Validation set
R2 RMSE (%) RPD R2 RMSE (%) RPD
CWT 5 CatBoost 0.817 0.380 2.341 0.740 0.396 1.968
KSPA CatBoost 0.758 0.437 2.036 0.655 0.456 1.710

图8

基于CWT尺度7与KSPA特征筛选的CatBoost模型SHAP分析 缩写同表3和表4。SHAP: 沙普利加性解释。"

表6

各年冬小麦LNC的描述性统计"

指标
Index		 试验1
Trial 1		 试验2
Trial 2		 试验3
Trial 3		 试验4
Trial 4
样本数Sample 128 128 125 152
最大值Maximum value (%) 4.48 5.07 4.84 4.46
最小值Minimum value (%) 1.66 1.20 1.59 1.09
平均值Mean (%) 3.30 3.40 3.18 2.64
标准差Standard deviation (%) 0.71 0.98 0.78 0.75
变异系数Coefficient of variation (%) 21.52 28.82 24.53 28.41
峰值Kurtosis (%) 2.11 2.37 2.14 2.13

表7

以试验2、3、4为建模集, 试验1为验证集的冬小麦LNC跨年留一验证最优模型性能"

特征
Feature		 最佳尺度
Optimal scale		 最佳模型
Optimal model		 建模集Calibration set 验证集Validation set
R2 RMSE (%) RPD R2 RMSE (%) RPD
原始光谱Original spectrum PLSR 0.641 0.538 1.672 0.457 0.523 1.363
KSPA CatBoost 0.685 0.504 1.784 0.511 0.497 1.435
CWT 7 CatBoost 0.669 0.517 1.742 0.560 0.471 1.514
CWT+PLS-VIP 5 RF 0.742 0.456 1.971 0.602 0.448 1.591
CWT+SPA 6 CatBoost 0.752 0.448 2.009 0.624 0.467 1.527
CWT+KSPA 6 CatBoost 0.758 0.442 2.036 0.675 0.405 1.761

表8

以试验1、3、4为建模集, 试验2为验证集的冬小麦LNC跨年留一验证最优模型性能"

特征
Feature		 最佳尺度
Optimal scale		 最佳模型
Optimal model		 建模集Calibration set 验证集Validation set
R2 RMSE (%) RPD R2 RMSE (%) RPD
原始光谱Original spectrum PLSR 0.577 0.522 1.540 0.467 0.714 1.375
KSPA PLSR 0.693 0.445 1.807 0.529 0.671 1.464
CWT 7 CatBoost 0.776 0.380 2.114 0.544 0.660 1.487
CWT+PLS-VIP 7 CatBoost 0.675 0.458 1.756 0.523 0.675 1.454
CWT+SPA 7 CatBoost 0.750 0.402 2.001 0.582 0.632 1.553
CWT+KSPA 7 CatBoost 0.785 0.372 2.162 0.611 0.610 1.609

表9

以试验1、2、3为建模集, 试验4为验证集的冬小麦LNC跨年留一验证最优模型性能"

特征
Feature		 最佳尺度
Optimal scale		 最佳模型
Optimal model		 建模集Calibration set 验证集Validation set
R2 RMSE (%) RPD R2 RMSE (%) RPD
原始光谱Original spectrum CatBoost 0.699 0.458 1.826 0.437 0.562 1.338
KSPA RF 0.680 0.472 1.770 0.466 0.548 1.373
CWT 7 CatBoost 0.687 0.467 1.789 0.471 0.546 1.379
CWT+PLS-VIP 7 CatBoost 0.672 0.478 1.749 0.483 0.539 1.396
CWT+SPA 8 RF 0.661 0.486 1.719 0.478 0.542 1.389
CWT+KSPA 7 CatBoost 0.701 0.456 1.833 0.521 0.502 1.498
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