基于因果推断和机器学习的农田玉米产量预测模型

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Smart Agriculture ›› 2026, Vol. 8 ›› Issue (2): 175-187.doi: 10.12133/j.smartag.SA202506027

• 信息处理与决策 •上一篇

基于因果推断和机器学习的农田玉米产量预测模型

王毅 1,6, 崔茜彤 1, 王晨 1, 熊宝伟 1, 邵国敏 2, 王琬莹 1, 曹培 3(), 韩文霆 4,5()

1. 1. 西安财经大学信息学院，陕西 西安 710100，中国

2. 西安理工大学西北旱区生态水利国家重点实验室，陕西 西安 710048，中国

3. 西北农林科技大学机械与电子工程学院，陕西杨凌 712100，中国

4. 西北农林科技大学旱区农业节水研究院，陕西杨凌 712100，中国

5. 国家作物高效用水工程实验室，陕西杨凌 712100，中国

6. 智财协同可信计算陕西省高等学校重点实验室，陕西 西安 710100，中国

• 收稿日期:2025-06-17 出版日期:2026-03-30
• 基金项目:国家社会科学基金(23BGL252); 陕西省自然科学基础研究计划项目(2022JQ-363); 陕西省重点产业创新链项目(2024NC-ZDCYL-05-01); 陕西省重点产业创新链项目(2023-ZDLNY-58); 西安市科技计划项目(25NJSYB00014)
• 作者简介:王 毅，博士，讲师，研究方向为农情信息空天地一体化智能感知与精准作业技术。E-mail：[email protected]
• 通信作者:曹 培，博士，副教授，研究方向为农业水信息天空地一体化智能感知与精准灌溉技术及装备。E-mail：[email protected] 韩文霆，博士，研究员，研究方向为农业水信息天空地一体化智能感知与精准灌溉技术及装备。E-mail：[email protected]

Field Maize Yield Prediction Model Based on Causal Inference and Machine Learningin Agricultural Fields

WANG Yi 1,6, CUI Xitong 1, WANG Chen 1, XIONG Baowei 1, SHAO Guomin 2, WANG Wanying 1, CAO Pei 3(), HAN Wenting 4,5()

1. 1. School of Information Science and Engineering, Xi'an University of Finance and Economics, Xi'an 710100, China

2. State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi'an University of Technology, Xi'an 710048, China

3. College of Mechanical and Electronic Engineering, Northwest A&F University, Yangling 712100, China

4. Institute of Water-saving Agriculture in Arid Areas (IWSA), Northwest A&F University, Yangling 712100, China

5. National Engineering Laboratory for Crop High-efficiency Water Use, Yangling 712100, China

6. Intelligent Financial Collaborative Trusted Computing Key Laboratory of Shaanxi Province for Higher Education Institutions, Xi'an 710100, China

• Received:2025-06-17 Online:2026-03-30
• Foundation items:National Social Science Fund Project(23BGL252); Basic Research Plan Project for Natural Sciences of Shaanxi Province(2022JQ-363); Key Innovation Chain Projects of Shaanxi Province(2024NC-ZDCYL-05-01); Key Innovation Chain Projects of Shaanxi Province(2023-ZDLNY-58); Xi'an Municipal Science and Technology Plan Project(25NJSYB00014)
• About author:WANG Yi, E-mail: [email protected]
• Corresponding author:CAO Pei, E-mail: [email protected] HAN Wenting, E-mail: [email protected]

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摘要/Abstract

摘要：

【目的/意义】 玉米作为中国主要粮食作物，其产量的精准预测在维护国家粮食供给体系稳定方面具有重要意义。针对传统预测方法难以揭示变量间因果关系的问题，提出了一种融合因果推断与机器学习的预测方法。 【方法】 首先，基于遥感指数、气象数据、土壤剖面湿度和阶段性作物观测数据等多源异构信息，采用偏相关与瞬时条件独立算法系统分析玉米产量与各影响因子之间的因果关系。其次，构建了移动平均-卷积神经网络-长短期记忆网络混合模型，先通过移动平均模块平滑数据噪声，进而利用卷积神经网络提取变量间的空间关联特征。最后，通过长短期记忆网络捕捉产量随时间变化的动态特征。 【结果和讨论】 10 cm和50 cm深度的土壤湿度对产量具有显著的正向影响（P<0.01），其中深层湿度具有更强的时滞效应；反射率中的改进叶绿素吸收指数与归一化植被指数等植被指数则在玉米生长中期呈现出短期因果关系。与其他模型的对比实验结果表明，所提出的模型在多个指标上表现突出，其中决定系数（R ²）达到0.955，平均绝对误差和均方根误差分别为1.201 kg/亩和1.474 kg/亩（1 hm 2=15亩）。 【结论】 因果分析可为模型提供关键变量筛选依据，显著提升产量预测性能。

关键词:偏相关与瞬时条件独立算法,移动平均,卷积神经网络,长短期记忆网络,产量预测,机器学习,因果推断

Abstract:

[Objective] Maize is one of the most important staple crops in the world and serves as a cornerstone of food security and agricultural sustainability. Accurate and timely prediction of maize yield is essential for optimizing agricultural management practices, supporting market regulation, and guiding policy decisions related to food supply and climate adaptation. In recent years, data-driven yield prediction methods based on machine learning and deep learning have achieved notable improvements in predictive accuracy. However, most existing approaches primarily rely on statistical correlations among variables and often treat influencing factors as independent predictors, without explicitly addressing the complex causal mechanisms and time-lagged interactions that govern crop growth processes. This limitation may lead to reduced model interpretability and compromised robustness under changing environmental conditions. To address these challenges, a novel maize yield prediction framework that integrates causal inference with a hybrid deep learning model was proposed, aiming to improve both predictive performance and mechanistic understanding. [Methods] Multi-source heterogeneous datasets collected across the maize growing season were utilized, including remote sensing-derived vegetation indices, meteorological variables (such as temperature and precipitation), soil profile moisture measurements at multiple depths, and crop observation data corresponding to key phenological stages. First, the Peter-Clark and momentary conditional independence (PCMCI) causal discovery algorithm was applied to systematically identify causal relationships between maize yield and its potential driving factors. The PCMCI method enables the detection of both contemporaneous and time-lagged causal links while effectively controlling for confounding effects in high-dimensional time series data. Through this process, the causal structure of yield formation was explicitly characterized, and key variables with statistically significant causal impacts were selected as inputs for the prediction model. Subsequently, a hybrid moving average, convolutional neural network-long short-term memory (MA-CNN-LSTM) model was constructed to capture the complex spatiotemporal patterns in the causally screened input variables. Specifically, a moving average module was employed as a preprocessing step to suppress high-frequency noise and enhance signal stability. A CNN was then used to extract latent correlation features among multiple variables, reflecting their joint influence on yield formation. Finally, an LSTM network was adopted to model temporal dependencies and cumulative effects across the growing season, enabling effective representation of dynamic yield responses. [Results and Discussions] The causal analysis revealed that soil moisture at depths of 10 cm and 50 cm exerted a significant positive influence on maize yield (P< 0.01), with deeper soil moisture showing a stronger and more persistent time-lagged effect. This finding highlighted the critical role of subsurface water availability in sustaining crop growth during later developmental stages. In addition, vegetation indiced such as the modified chlorophyll absorption ratio index and the normalized difference vegetation index exhibited significant short-term causal relationships with yield during the mid-growth stage of maize, indicating their sensitivity to canopy structure and photosynthetic activity during this period. Comparative experiments conducted against traditional statistical models and conventional machine learning approaches demonstrated that the proposed PCMCI-MA-CNN-LSTM framework consistently achieved superior predictive performance. On the test dataset, the coefficient of determination (R 2) reached 0.955, while the mean absolute error (MAE) and root mean square error (RMSE) were reduced to 1.201 kg/mu and 1.474 kg/mu (1 hm 2=15 mu). These results indicated that incorporating causal variable selection effectively enhances model accuracy and stability by reducing redundant and spurious correlations. [Conclusions] The results confirm that incorporating causal analysis into yield modeling provides a robust basis for identifying key driving variables and effectively enhances the accuracy and interpretability of maize yield prediction. The proposed framework offers a promising approach for precision agriculture and decision support in crop yield forecasting, particularly under complex and dynamic agro-environmental conditions.

Key words:peter-clark and momentary conditional independence (PCMCI),moving average,convolutional neural network,long short-term memory,yield prediction,machine learning,causal inference

中图分类号:

• S513.01

• TP181

• O212.1

引用本文

王毅, 崔茜彤, 王晨, 熊宝伟, 邵国敏, 王琬莹, 曹培, 韩文霆. 基于因果推断和机器学习的农田玉米产量预测模型[J]. 智慧农业(中英文), 2026, 8(2): 175-187.

WANG Yi, CUI Xitong, WANG Chen, XIONG Baowei, SHAO Guomin, WANG Wanying, CAO Pei, HAN Wenting. Field Maize Yield Prediction Model Based on Causal Inference and Machine Learningin Agricultural Fields[J]. Smart Agriculture, 2026, 8(2): 175-187.

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链接本文:https://www.smartag.net.cn/CN/10.12133/j.smartag.SA202506027

https://www.smartag.net.cn/CN/Y2026/V8/I2/175

[图/表 14](javascript:;)

图1

分期播种试验场不同播期样地分布图

图1

表1

玉米产量影响因子

数据类型	观测指标
作物数据	株高/cm、叶面积指数
气象数据	地面气压/hPa、平均气温/（℃）、降水量/mm、露点温度/（℃）、相对湿度/%、经向风速（U， m/s）、纬向风速（V， m/s）、太阳辐射净强度（net， J/（m 2/d））、太阳辐射总强度（down， J/（m 2/d））
土壤数据	土壤湿度（深度：10、20、30、40、50 cm）
遥感数据	增强植被指数（Enhanced Vegetation Index, EVI）、绿光归一化植被指数（Green Normalized Difference Vegetation Index, GNDVI）、归一化植被指数（Normalized Difference Vegetation Index, NDVI）、土壤调整植被指数（Soil-Adjusted Vegetation Index, SAVI）、转换叶绿素吸收比率指数（Transformed Chlorophyll Absorption in Reflectance Index, TCARI）、视觉大气阻力指数（Visible Atmospherically Resistant Index, VARI）、土壤饱和度（Simple Ratio, SR）、归一化差值红边（Normalized Difference Red Edge Index, NDRE）、归一化差分红边指数（Normalized Difference Red Edge Index, NDREI）、反射率中的改进叶绿素吸收指数（Modified Chlorophyll Absorption in Reflectance Index, MCARI）

表1

表2

植被指数及其计算公式

植被指数	公式	引用文献
EVI	E V I=2.5×(R N I R−R R)/(R N I R+6×R R−7.5×R B+1)$E V I = 2.5 \times \left(\right. R_{N I R} - R_{R} \left.\right) / \left(\right. R_{N I R} + 6 \times R_{R} - 7.5 \times R_{B} + 1 \left.\right)$ （1）	［14］
GNDVI	G N D V I=(R G−R R)/(R G+R R)$G N D V I = \left(\right. R_{G} - R_{R} \left.\right) / \left(\right. R_{G} + R_{R} \left.\right)$ （2）	［15］
NDVI	N D V I=(R N I R−R R)/(R N I R+R R)$N D V I = \left(\right. R_{N I R} - R_{R} \left.\right) / \left(\right. R_{N I R} + R_{R} \left.\right)$ （3）	［16］
SAVI	S A V I=(1+L)×(R N I R−R R)/(R N I R+R R+L)$S A V I = \left(\right. 1 + L \left.\right) \times \left(\right. R_{N I R} - R_{R} \left.\right) / \left(\right. R_{N I R} + R_{R} + L \left.\right)$ （4）	［17］
TCARI	T C A R I=3×[(R R E−R R)−0.2×(R R E−R G)×(R R E/R R)]$T C A R I = 3 \times \left[\left(\right. R_{R E} - R_{R} \left.\right) - 0.2 \times \left(\right. R_{R E} - R_{G} \left.\right) \times \left(\right. R_{R E} / R_{R} \left.\right)\right]$ （5）	［18］
VARI	V A R I=(R G−R R)/(R G+R R−R B)$V A R I = \left(\right. R_{G} - R_{R} \left.\right) / \left(\right. R_{G} + R_{R} - R_{B} \left.\right)$ （6）	［19］
SR	S R=R N I R/R R$S R = R_{N I R} / R_{R}$ （7）	［20］
NDRE	N D R E=(R N I R−R R E)/(R N I R+R R E)$N D R E = \left(\right. R_{N I R} - R_{R E} \left.\right) / \left(\right. R_{N I R} + R_{R E} \left.\right)$ （8）	［21］
MCARI	M C A R I=[(R R E−R R)−0.2×(R R E−R G)]×(R R E/R R)$M C A R I = \left[\left(\right. R_{R E} - R_{R} \left.\right) - 0.2 \times \left(\right. R_{R E} - R_{G} \left.\right)\right] \times \left(\right. R_{R E} / R_{R} \left.\right)$ （9）	［22］

表2

表3

不同研究区域玉米的关键生育期

名称	七叶期	拔节期	抽雄期	乳熟期
A区	6月25日	7月3日	7月28日	8月22日
B区	7月4日	7月10日	8月4日	8月27日
C区	7月13日	7月21日	8月13日	9月5日
D区	7月23日	7月30日	8月22日	9月18日

表3

图2

CNN-LSTM模型结构图

图2

图3

MA-CNN-LSTM模型预测流程图

图3

图4

基于因果推断和机器学习的农田玉米产量预测模型研究技术路线图

图4

图5

不同气象、作物、土壤、遥感因子与产量之间的P值 注： P<0.05表示关系显著，P<0.01表示高度显著，Lag表示变量在不同时间滞后下的因果关系显著性差异。

图5

表4

玉米产量预测模型输入特征筛选

数据类型	时间滞后
Lag 0	Lag 0—Lag 1
地面气压/hPa	▲
平均气温/°C	▲
降水量/mm
露点温度/°C
相对湿度/%
经向风速/（m/s）	▲
纬向风速/（m/s）	▲
太阳辐射净强度/（W/m 2）
太阳辐射总强度/（W/m 2）
土壤湿度10 cm	●
土壤湿度20 cm
土壤湿度30 cm
土壤湿度40 cm	●
土壤湿度50 cm	▲
株高/cm
叶面积指数/cm 2
EVI	▲
GNDVI
NDVI
SAVI	●
TCARI
VARI
SR
NDRE
MCARI	▲

表4

表5

MA窗口大小的梯度实验设计

模型配置	MAE/（kg/亩）	RMSE/（kg/亩）	R 2	核心变化分析
无MA （窗口=1）	1.798	2.105	0.908	原始数据含较多噪声，预测曲线波动明显
MA窗口=5	1.564	1.924	0.923	平衡噪声过滤与特征保留，性能最优
MA窗口=7	1.627	1.983	0.915	过度平滑导致关键时序特征（如抽雄期突增）被弱化

表5

图6

不同模型预测玉米产量结果

图6

表6

不同玉米产量预测模型评估结果

Model	MAE/（kg/亩）	RMSE/（kg/亩）	R 2
SVR	2.363	2.943	0.821
CNN	2.007	2.564	0.864
LASSO	3.473	3.947	0.679
LSTM	1.833	2.217	0.898
MA-CNN-LSTM	1.201	1.474	0.955

表6

[![Image 27](https://www.smartag.net.cn/fileup/2096-8094/FIGURE/2026-8-2/Images/2096-8094-2026-8-2-175/thumbnail/58730818-D102-41e5-A208-B2A22B2A852A-F0