Method, system and program product for estimating soybean aboveground biomass dynamics across the growing season

Abstract

The soybean aboveground biomass dynamic across growth period estimation method, system and program product relate to the crop yield technical field, fill the existing technology in the problem of combining research soybean AGB based on UAV remote sensing and machine learning relative blank. Through the unmanned aerial vehicle to soybean multiple growth stage data collection, and based on soybean growth stage data, respectively generate multispectral orthophoto and digital surface model; based on multispectral orthophoto and digital surface model, respectively extract the crown structure features, image texture features and multiple vegetation indexes related to aboveground biomass of crops; after improving the stacking model, using multiple data of soybean, crown structure features, image texture features and multiple vegetation indexes related to aboveground biomass of crops to train the improved stacking model, obtain the trained stacking model; based on the trained stacking model, complete the soybean aboveground biomass growth period estimation.

Description

Technical Field

[0001] This invention relates to the field of crop yield technology, specifically to a method, system, and program product for dynamically estimating soybean aboveground biomass across growth stages. Background Technology

[0002] Soybean is a core global oilseed and high-protein crop. Aboveground biomass (AGB) is a key agronomic parameter reflecting plant growth and ecological response, and is a crucial functional parameter determining final crop yield under the combined regulation of genetic background, ecological environment, and agronomic management. Within the framework of precision agriculture, achieving rapid, non-destructive, and accurate monitoring of soybean AGB during the growing season has significant practical value for selecting dominant plant types, optimizing fertilization decisions, pest and disease early warning, and yield prediction. Therefore, developing non-destructive, high spatiotemporal resolution estimation technologies for soybean AGB has become an urgent need to achieve a closed loop of dynamic crop growth monitoring and precision management.

[0003] The standard for crop biomass assessment is often based on destructive monitoring using field sampling. However, its extremely low spatiotemporal coverage flux makes it difficult to characterize the spatial heterogeneity in modern agricultural production. Compared with traditional destructive sampling methods, satellite remote sensing can monitor large areas in a cost-effective, real-time, and non-destructive manner, making it a favorable choice for obtaining AGB information in modern agriculture and ecological monitoring. However, it is often limited by fixed revisit cycles and atmospheric interference, often resulting in missing data during critical windows of crop phenotypic development, missing optimal field management opportunities, and limiting the real-time nature of dynamic field management. In contrast, the rapid development of UAV (Unmanned Aerial Vehicle) near-Earth remote sensing platforms has effectively bridged the scale difference between satellite and ground observations. Relying on its centimeter-level spatial resolution and the flexibility of on-demand observation, UAVs can traverse complex terrain and achieve high spatial consistency in acquiring growth information during critical growth periods. This high-frequency, ultra-high-resolution monitoring capability makes it possible to capture the transient biological responses of crops driven by the environment, and has become a core technological support for the transformation of precision agriculture from static assessment to dynamic feedback.

[0004] High-throughput, non-destructive phenotypic observation based on UAVs has become a key tool for accurately quantifying crop AGB (Advanced Genomic Growth Rate). UAVs equipped with multispectral sensors can acquire continuous spectral and structural information from the canopy level, providing high spatiotemporal resolution data support for crop growth status, nutrient accumulation, and yield prediction. A common method is to extract spectral features using VIs (vegetation indices) and correlate them with crop AGB. Various VI indices, such as NDVI (Normalized Differential Vegetation Index), SAVI (Soil-Adjusted Vegetation Index), and MCARI (Modified Chlorophyll Absorption Ratio Index), have shown high accuracy in AGB estimation for crops such as maize, rice, and wheat. However, for crops with dense canopies, and when crops enter the mid-to-late growth stages and the canopy structure becomes more complex, traditional spectral indices such as NDVI are prone to saturation, leading to decreased sensitivity to AGB changes. To address this issue, increasing research attempts to introduce additional image features to compensate for the information loss caused by spectral saturation. Among these, texture features, by quantifying the spatial distribution patterns of pixel grayscale in images, can reflect the spatial heterogeneity of the crop canopy. Combining texture and spectral features has proven effective in improving AGB estimation accuracy and has been successfully applied to crops such as rice, winter wheat, and potatoes. Furthermore, DSMs (Digital Surface Models) generated from UAV imagery can reflect crop height, serving as an important supplement to spectral information. [ Therefore, integrating multi-source features acquired by UAV has become a key direction for improving the accuracy and robustness of AGB estimation. However, compared with relatively simple gramineous crops such as rice and maize, research on legumes such as soybeans, which have complex branching patterns and compound leaf structures, is still relatively limited, and the evolution of their multi-feature sensitivity throughout their growth period still needs to be explored in depth.

[0005] As the dimensionality of UAV multi-source features increases, the nonlinear relationship between spectral, textural, and structural information and crop growth parameters becomes more complex, exhibiting high nonlinearity and spatiotemporal nonstationarity. Traditional single machine learning models are prone to getting stuck in local optima or facing a bias-variance tradeoff in multi-growth-stage generalization when processing such high-dimensional heterogeneous data. Ensemble learning methods have been introduced into crop phenotypic inversion research and have shown superior performance compared to single models. Among them, Stacking Ensemble Learning, as a high-order ensemble framework, integrates multiple Base Learners and MetaLearners to extract second-order features from the prediction preferences of multiple base learners, thus demonstrating higher adaptability in multi-source feature modeling. In the field of crop remote sensing estimation, stacking ensemble methods have been successfully applied to yield prediction, chlorophyll, and AGB inversion tasks, showing better fitting ability and generalization performance than single machine learning models. However, the applicability of this method to soybean AGB inversion performance under multi-growth-stage conditions still needs further verification.

[0006] While existing studies have validated the effectiveness of various imagery features and machine learning models in estimating crop aboveground biomass (AGB) using UAV imagery, most research focuses on modeling and analysis within a single growth stage, typically limited to either vegetative or reproductive growth. However, crop growth exhibits significant temporal dynamics, and single-stage models struggle to comprehensively reflect the cumulative changes in biomass across different growth stages. In contrast, inter-stage models integrating imagery features from multiple growth stages can utilize information from the entire crop growth process, supporting more stable and generalized AGB estimation. A systematic comparison of the applicability of single-stage and multi-stage strategies in soybean AGB retrieval is crucial for establishing a robust dynamic monitoring paradigm.

[0007] In recent years, although UAV remote sensing and machine learning technologies have achieved certain results in the field of biomass inversion for other crops such as maize and wheat, systematic research on soybean AGB is relatively limited. This is mainly due to the technical difficulties brought about by the biological characteristics and structural morphology of soybean itself. First, soybean is a low-growing, branching crop with a complex canopy structure and a high proportion of bare soil exposure between rows. In the early stages, spectral signals are severely interfered with by soil background, leading to decreased stability of vegetation indices. Second, soybean is prone to spectral index saturation in the middle and late stages, reducing the sensitivity of traditional vegetation indices to biomass changes and increasing the difficulty of inversion. Third, the leaf area index, branching structure, and pod ratio of soybean vary significantly at different growth stages, making the spectral response mechanism stage-dependent and difficult to establish a unified model. In addition, ground acquisition of soybean AGB usually relies on destructive sampling, resulting in a limited number of samples and uneven data distribution, increasing the difficulty of training and generalizing machine learning models.

[0008] Therefore, soybeans cannot be inverted simply by applying modeling methods to other crops. Instead, there are multiple technical obstacles, such as complex coupling of multi-source features, significant stage distribution drift, and limited sample size. This is also an important reason why there is a relative lack of research on soybean AGB using UAV remote sensing and machine learning. Summary of the Invention

[0009] This invention fills a gap in the existing technology for studying soybean AGB based on the combination of UAV remote sensing and machine learning.

[0010] The method for estimating soybean aboveground biomass dynamics across growth stages as described in this invention includes the following steps: Step S1: Collect various data on soybeans; Step S2: Collect data on multiple growth stages of soybeans using drones, and generate multispectral orthophotos and digital surface models based on the soybean growth stage data. Step S3: Based on multispectral orthophotos and digital surface models, extract crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass. Step S4: After improving the Stacking model, the improved Stacking model is trained using various soybean data, crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass to obtain the trained Stacking model. Step S5: Based on the trained Stacking model, complete the estimation of soybean aboveground biomass growth period.

[0011] Furthermore, in one embodiment of the present invention, in step S1, the various data of soybeans include plant height, fresh weight, and dry weight.

[0012] Furthermore, in one embodiment of the present invention, the data on multiple growth stages of soybeans in step S2 include flowering period, full pod stage, grain filling stage, and early maturity stage.

[0013] Furthermore, in one embodiment of the present invention, in step S3, the canopy structure features of the crop are obtained based on the difference between the digital surface model and the digital elevation model of the bare soil image taken after soybean sowing. The image texture features are obtained based on the gray-level co-occurrence matrix calculation; The various vegetation indices related to aboveground biomass are based on data obtained from multispectral orthophotos.

[0014] Furthermore, in one embodiment of the present invention, in step S4, the improved Stacking model adopts a two-layer stacked ensemble learning inversion framework. In the first base learner layer, partial least squares regression, long short-term memory network, random forest and extreme gradient boosting are selected; In the second-layer meta-learner, minimum absolute shrinkage and Lasso regression are selected to nonlinearly reconstruct the output of the first-layer base learner.

[0015] Furthermore, in one embodiment of the present invention, in step S4, the improved Stacking model is trained by performing five-fold cross-validation on various soybean data, crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass.

[0016] The soybean aboveground biomass dynamic cross-growth-stage estimation system of this invention is based on the high-precision dynamic cross-growth-stage estimation method for soybean aboveground biomass described above, and includes the following modules: Module S1 collects various data related to soybeans; Module S2 collects data on multiple growth stages of soybeans using drones, and generates multispectral orthophotos and digital surface models based on the soybean growth stage data. Module S3, based on multispectral orthophotos and digital surface models, extracts crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass. Module S4, after improving the Stacking model, uses various soybean data, crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass to train the improved Stacking model and obtain the trained Stacking model. Module S5, based on the trained Stacking model, completes the estimation of soybean aboveground biomass growth period.

[0017] The computer program product described in this invention includes a computer program or instructions that, when executed by a processor, implement the high-precision dynamic cross-growth-stage estimation method for soybean aboveground biomass described above.

[0018] This invention fills a gap in existing technologies for studying soybean AGB (Ambient Gas Gravity) based on a combination of UAV remote sensing and machine learning. Specific beneficial effects include: 1. The soybean aboveground biomass dynamic cross-growth stage estimation method described in this invention addresses the technical problems existing in the prior art by constructing an AGB inversion technology framework that integrates UAV multi-source features and an integrated learning model. This enables high-throughput, non-destructive dynamic monitoring of crop growth processes and provides a technical path with promotion potential for efficient monitoring and precise management of crop phenotypes in smart agriculture. 2. The soybean aboveground biomass dynamic cross-fertility estimation method described in this invention addresses the highly nonlinear and time-nonstationary mapping relationship between multi-source UAV features and AGB. It introduces stacked ensemble learning and constructs a cross-fertility modeling strategy, which significantly enhances the generalization ability and robustness of the model under different fertility stages. 3. The soybean aboveground biomass dynamic cross-growth stage estimation method described in this invention is based on the DSM of UAV imagery to achieve fine extraction of crop plant height structural features at the centimeter level. It uses structural information as the core to drive the fusion of multispectral and texture features to construct a multi-source feature collaborative modeling system, which effectively alleviates the spectral saturation effect in the high biomass stage and improves the physical consistency and model stability of AGB estimation. The soybean aboveground biomass dynamic estimation method across growth stages described in this invention is based on a multi-source, multi-temporal AGB inversion framework using UAV multispectral imagery and stacked ensemble learning. It provides a reliable technical path for high-throughput phenotypic monitoring and precision agricultural management of soybeans, and offers a methodological reference for remote sensing biomass estimation research across growth stages and crops. Attached Figure Description

[0019] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is the overall flowchart of the UAV-based soybean AGB inversion described in Implementation Method 1; Figure 2 This is a diagram of the Stacking model framework described in Implementation Method 1; Figure 3 The distribution map of soybeans at different growth stages as measured in the field in Implementation Method 1 is shown in (a) soybean plant height, (b) fresh weight of soybeans, and (c) dry weight of soybeans. Figure 4The above is a graph showing the estimation accuracy of soybean dry weight and fresh weight under different characteristic combinations and different models at four different time periods, as described in Implementation Method 1. (a) represents soybean fresh weight, and (b) represents soybean dry weight. Figure 5 The above are comparison charts of the performance of the improved Stacking model described in Implementation Method 1 in estimating the dry weight and fresh weight of soybeans at four key growth stages. (a) is a comparison chart of the coefficient of determination R² for dry weight and fresh weight at different growth stages. (b) is a comparison chart of the root mean square error RMSE for dry weight and fresh weight at different growth stages. (c) is a comparison chart of the mean absolute error MAE for dry weight and fresh weight at different growth stages. Detailed Implementation

[0020] Various embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. The embodiments described with reference to the drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0021] Implementation Method 1: In the prior art, UAV remote sensing and machine learning technologies have made significant progress in the inversion of biomass in other crops, but research on soybean AGB is still relatively lacking.

[0022] To address the technical problems existing in the prior art, this embodiment proposes a method for dynamically estimating soybean aboveground biomass across growth stages, including the following steps: Step S1, Select the study area: like Figure 1 As shown, this implementation method was implemented in 2025 through a field experiment at a teaching and research base (125°40′E, 43°81′N). This region plays an important role in soybean production, with an altitude of 222 meters and a temperate continental semi-humid monsoon climate, characterized by cold and dry winters, hot and rainy summers, sunny autumns, and significant snowfall in winter. The annual precipitation is approximately 600 mm, the average annual temperature is approximately 6.9℃, and the average annual sunshine duration is 2408 hours. A structured random block design was used, with two replicates. A total of 50 varieties suitable for cultivation in Northeast China were sown on May 5, 2025. Each plot had three rows of crops, each 2.5 meters long, with a plot spacing of 1 meter. Pesticide and fertilizer management followed local best practices. The flowering period was defined as S1, the pod-filling period as S2, the grain-filling period as S3, and the early maturity period as S4.

[0023] Step S2, Field Data Collection: After each UAV flight, field samples were collected simultaneously. Ground data collection included measurements of plant height, fresh weight, and dry weight in 100 experimental plots. Three representative plants were randomly selected from each plot, and pH (plant height) was measured using a measuring tape. The average of the three measurements was used as the pH of that plot. To measure AGB (Average Weight Gain), three representative plants were destructively sampled from each plot. All harvested soybean samples were immediately bagged, tagged, and transported to the laboratory. The roots were removed, and the fresh weight of the soybeans was measured. After blanching at 105°C, the samples were immediately dried in an 85°C oven to a constant weight to determine the dry weight of the collected plants. The total dry weight on the ground was then calculated.

[0024] To better illustrate the field data, the following examples are provided in detail: like Figure 3 As shown, this embodiment systematically monitored the pH, FW, and DW of 50 soybean varieties at four key growth stages to characterize the dynamic changes of crop agronomic parameters on a time-series scale. The results showed that as the growth process progressed, all three indicators exhibited a significant nonlinear evolution trend, accompanied by obvious population heterogeneity. Figure 3 As shown in (a), pH rises rapidly during the vigorous growth period, with the average value increasing from about 70 cm to 95 cm, but the growth slows down after entering the granulation stage dominated by reproductive growth; Figure 3 (b) and Figure 3 As shown in (c), in contrast, DW maintained continuous accumulation throughout the entire growth period and reached its peak at the early maturity stage, with an average of approximately 90 g / plant, while FW reached its peak at the grain-filling stage, with an average of approximately 330 g / plant, but declined at the early maturity stage, with the average dropping to approximately 290 g / plant. From the perspective of data dispersion, as the growth period progresses, the distribution range of each indicator gradually lengthens, especially at the grain-filling stage and the early maturity stage, where the biomass differences among different soybean genotypes gradually increase. The high CV (coefficient of variation) indicates that the sample in this embodiment covers diverse plant architectures, exhibiting both representativeness and complexity.

[0025] Step S3, UAV data acquisition and processing: During the soybean planting season, UAV multispectral data was collected through four aerial surveys, covering four key growth stages of soybeans: flowering, pod formation, grain filling, and early maturity. The DJI Mavic 3 Multispectral Edition drone platform was used, equipped with precise GPS / GNSS. This platform integrates a visible light and multispectral dual-camera module, featuring a 4 / 3-inch CMOS (Complementary Metal-Oxide-Semiconductor) visible light camera (20MP effective pixels) and a four-channel multispectral camera with center bands of Green (560±16nm), Red (650±16nm), Red Edge (730±16nm), and NIR (840±26nm). Data acquisition took place from 10:00 to 14:00 under clear, cloudless conditions and low wind speeds. The flight path was designed using DJI Pilot 2, with radiometric correction employing a 50% diffuse reflectance standard to ensure consistent spectral reflectance across images. Ground control points (GCPs) were set up for geometric correction of images at different growth stages to ensure accurate spatial alignment. The flight altitude was set to 30m, the UAV maintained a speed of 3m / s, and the forward overlap and lateral overlap were set to 80% and 70%, respectively. After the flight mission, the collected images were processed using Agisoft Metashape Professional software, including radiometric correction, geometric correction, and image stitching, generating RGB (red, green, and blue) images and multispectral orthophotos, and simultaneously generating a DSM (Distributed Image Model).

[0026] Step S4, Feature Extraction and Selection: Crop canopy SIs (Structure Indices) were obtained by comparing the DSM (Digital Elevation Model) with the DEM (Digital Elevation Model) of bare soil images taken after soybean planting. Spectral reflectance was extracted from multispectral orthophotos, as shown in Table 1, and nine VIs related to AGB (Ambient Geometric Scale) were calculated. Texture Indices (TIs) were calculated based on GLCM (Gray-Level Co-occurrence Matrix) to capture canopy spatial heterogeneity and geometric features. Eight typical texture indices were calculated in the green, red, red-edge, and near-infrared bands: Mean, Variance, Contrast, Homogeneity, Entropy, Dissimilarity, Correlation, and Angular Second Moment. To improve model computational efficiency and eliminate information redundancy among high-dimensional heterogeneous features, correlation analysis was used to perform multi-level screening of the initial feature pool. By extracting antecedent variables that are significantly correlated with AGB and combining autocorrelation analysis to remove highly collinear indicators, the optimal feature subsets for different fusion strategies were finally constructed. After completing the candidate feature screening, features of different stages were automatically classified according to the reproductive period identifier in the feature column names, and common basic features existing from the initial reproductive period to the target reproductive period were screened to construct a consistent input feature set suitable for cross-reproductive period time series modeling.

[0027] Table 1. Definitions of Features and Their Mathematical Formulas Used

[0028] in, For near-infrared reflectivity, Reflectivity in the red light band For red-edge band reflectivity, For green light band reflectivity, Gray levels in the gray-level co-occurrence matrix and The joint probability of simultaneous occurrence This represents the position of the gray level combination in the GLCM matrix. The grayscale value of a pixel. The average gray value of the gray-level co-occurrence matrix. For probability ( , The natural logarithm of ) The variance of the gray-level distribution in the gray-level co-occurrence matrix describes the degree of dispersion of gray-level values.

[0029] To better illustrate the correlation between VIs / TIs / SIs and AGB, the following examples are provided in detail: VIs, TIs, and SIs all showed significant correlations with soybean dry and fresh weight at different growth stages, but their response intensity and temporal variation characteristics differed significantly. Overall, most vegetation indices reached high correlations in the early or middle stages of growth, subsequently declining to varying degrees as growth progressed. In contrast, SIs maintained high and stable correlations throughout the entire growth period, while TIs gradually strengthened in the middle and later stages as canopy structure complexity increased, exhibiting better temporal stability.

[0030] Among the VIs, greenness-based indices, such as NDVI and GNDVI, showed high sensitivity to FW (fresh weight) in the early stages, with correlation coefficients reaching 0.72 and 0.77, respectively. As the growth period progressed, the correlation of NDVI decreased to approximately 0.64 and 0.54 at the pod-filling stage and early maturity, respectively. In contrast, red-edge and near-infrared band correlation indices, such as NDRE, RECI, and LCI, maintained high correlations at the full pod-filling stage. Between 0.65 and 0.75. EVI2 and MCARI reached a relatively high correlation level during the peak pod-bearing period, with fresh weight... The values ​​were 0.75 and 0.73 respectively, gradually decreasing during the grain-filling stage and early maturity. Both SIs and TIs exhibited strong temporal generalization ability. Specifically, PH remained highly correlated with DW (dry weight) and FW throughout the entire growth period. , Among the texture features, NIR Mean (near-infrared spectroscopy) showed the highest correlation between the granulation stage and the early maturity stage. , Meanwhile, Red Homogeneity and NIR Homogeneity maintained a moderate correlation in the mid-to-late stages. The correlation coefficients (TIs) ranged from 0.39 to 0.52, indicating that TIs can capture information on changes in canopy spatial heterogeneity during leaf senescence. From a temporal perspective, the correlation during peak flowering was generally slightly lower, with most indices showing lower correlations. The correlation between the pod-filling stage and the grain-filling stage generally reaches a high value; in the early stage of maturity, the correlation of some VIs decreases.

[0031] Step S5, Model Building: To achieve deep fusion of multi-source remote sensing features, which here originate from SIs, nine Vis and Tis related to AGB obtained in step S3, and field data obtained in step S2, this embodiment first uses an existing Stacking model to deeply fuse the multi-source remote sensing features. Chinese patent CN114818908A discloses a "Quantitative Assessment Method for Moisture State of Oil-Paper Insulation Based on Stacking Model Fusion." The Stacking model disclosed therein is mainly used for assessing the moisture state of oil-paper insulation. Its data source is single-frequency domain dielectric spectrum data, with relatively stable feature structure and small sample distribution variations. The modeling objective belongs to the parameter regression problem under the same physical system. This embodiment finds that if the two-layer architecture of this Stacking model is directly applied to this embodiment to achieve deep fusion of multi-source remote sensing features, significant technical incompatibility will occur. This is mainly because soybeans exhibit significant differences in spectral response mechanisms and canopy structure changes at different growth stages, and multi-source remote sensing features show significant statistical distribution drift between stages. However, the existing Stacking model architecture does not design any adaptive mechanism for cross-stage distribution changes.

[0032] To overcome the above-mentioned technical problems, such as Figure 2 As shown, this implementation makes a structural adjustment with a clear technical focus in Level 0 (the first base learner) of the Stacking model. In Level 0, four algorithms with significant heterogeneity—PLSR (Partial Least Squares Regression), SVR (Support Vector Regression), RF (Random Forest), and XGBoost (Extreme Gradient Boosting)—are selected, forming a heterogeneous combination structure of PLSR, SVR, RF, and XGBoost to comprehensively capture the potential linear and nonlinear mapping relationship between multi-source remote sensing features and AGB. This adjustment is not a simple algorithm replacement, but a targeted optimization based on the structural characteristics of multi-source remote sensing features and the needs of cross-fertility stage modeling. Specifically: This implementation introduces PLSR as a linear latent variable regression model. Its core advantage lies in its ability to simultaneously optimize feature dimensionality reduction and regression under conditions of high collinearity and multivariate coupling by constructing latent components. PLSR is particularly suitable for scenarios where variables are highly correlated in spectral and remote sensing data, effectively mitigating the impact of collinearity on model stability—a structural function that KNN (k-nearest neighbor algorithm) cannot achieve. Therefore, introducing PLSR at Level 0 can specifically establish a stable linear mapping foundation for the problem of collinearity in remote sensing features.

[0033] From the perspective of generalization across reproductive stages, PLSR is a global linear modeling method with low dependence on sample size and high stability, capable of building robust basic predictions under limited sample conditions; while tree models and kernel models are responsible for characterizing complex nonlinear relationships. This structure enables Level 0 output to have more balanced stability and expressive power across different reproductive stages, helping to provide more discriminative and selectable meta-features for Level 1 (the second-level meta-learner).

[0034] Based on this, this implementation improves upon the existing Stacking model's Level 0, employing kernel ridge regression from the existing Stacking model's Level 1 as the second-level meta-learner. Essentially an L2 regularized linear reconstruction model, it lacks sparsity filtering capabilities during implementation, failing to automatically remove base learners that perform poorly or overfit at specific reproductive stages. This easily introduces redundant model outputs and amplifies noise. Furthermore, significant collinearity and higher-order nonlinear interactions exist among multi-source remote sensing features. The original architecture emphasizes parallel model fusion rather than adaptive optimization and reconstruction based on model contributions, making it difficult to guarantee generalization stability across reproductive stages.

[0035] Similarly, to overcome the aforementioned technical challenges, this implementation employs minimum absolute shrinkage with L1 regularization and Lasso regression (selection operator regression, alpha = 0.01) to linearly reconstruct the output of Level 0. This enables Level 1 to automatically filter when combining Level 0 outputs. A sparse constraint mechanism compresses redundant or unstable base model weights, causing some weights to approach zero during optimization, thus achieving adaptive selection and dynamic optimization of the Stacking model's contribution. By introducing Lasso regression, Level 1 can automatically identify more stable and contributing Stacking model outputs under data conditions at different reproductive stages, suppressing the interference of stage-sensitive models and mitigating the instability caused by cross-reproductive stage distribution shifts. Simultaneously, the sparsity mechanism effectively alleviates the cumulative effect of multicollinearity in the meta-feature space, improving the overall structural interpretability and generalization ability of the model.

[0036] While the aforementioned Stacking model-based soybean aboveground biomass estimation method can integrate multiple machine learning models to improve the utilization efficiency and prediction accuracy of multi-source remote sensing features from UAVs, it is still primarily based on static feature input and traditional heterogeneous model integration. It lacks the ability to explicitly model temporal dependencies, growth continuity, and the dynamic accumulation process of biomass in observation data from different growth stages. Furthermore, remote sensing features at different growth stages may differ in dimensionality and completeness. The aforementioned method lacks a unified multi-stage feature organization and consistency constraint mechanism, resulting in insufficient expressive power, stability, and generalization ability in dynamic estimation across multiple growth stages. Therefore, it is necessary to propose an improved Stacking model estimation method that can uniformly construct multi-stage features and integrate the advantages of temporal modeling and static ensemble learning to improve the accuracy and robustness of soybean dry and fresh weight estimation.

[0037] To address the aforementioned technical issues, this implementation further improves the Stacking model. Based on the heterogeneous integration framework of the Stacking model described above, an LSTM temporal modeling channel based on a three-dimensional temporal feature tensor is introduced. This channel, along with RF, XGBoost, and PLSR static modeling channels based on a two-dimensional tiled feature matrix, forms a dual-channel heterogeneous Stacking model structure. The LSTM network consists of one LSTM layer, one Dropout layer (random deactivation layer), and two fully connected layers. The LSTM has 48 hidden units, the Dropout ratio is 0.25, the intermediate fully connected layers have 24 neurons, and the output layer is a single-neuron regression output. The model is trained using the Adam optimizer and mean squared error loss function, and overfitting is prevented through an Early Stopping mechanism.

[0038] Therefore, the Stacking model layer adopts a dual-channel heterogeneous learning structure. One channel is a temporal modeling channel, which uses LSTM (Long Short-Term Memory Network) to learn the three-dimensional temporal feature tensor in order to capture the dynamic dependencies and growth evolution patterns between different reproductive stages.

[0039] The other channel is a static modeling channel, which models the two-dimensional tiled feature matrix using Random Forest (RF), XGBoost, and PLSR respectively. Random Forest is used to capture robust nonlinear ensemble relationships; XGBoost is used to express complex nonlinear feature splitting relationships; and PLSR is used to mine latent linear structures in high-dimensional features. Before PLSR modeling, the features are standardized, and the number of principal components is dynamically determined based on the number of training samples and the feature dimension, with an upper limit of 10.

[0040] Specifically, features for each period (S1, S2, S3, and S4) are automatically identified, and a mapping relationship between basic feature names and reproductive periods is established. For the target reproductive period, common basic features present from the initial reproductive period to the target reproductive period are selected to ensure consistency of input dimensions across time steps. For example, when the target period is S3, basic features present in S1, S2, and S3 are retained; when the target period is S4, basic features present in S1, S2, S3, and S4 are retained. This avoids inconsistencies in input structure caused by missing features from different reproductive periods, providing a unified data foundation for subsequent time series modeling.

[0041] Based on this, this implementation constructs two input representations for the same set of multi-period features. The first is a three-dimensional temporal feature tensor, with dimensions of "number of samples × number of time steps × number of features," used to preserve the sequential information of feature changes with the reproductive period. The second is a two-dimensional tiled feature matrix, which expands the temporal tensor along the time dimension to form a tabular input of "number of samples × (number of time steps × number of features)," used to adapt to traditional machine learning models. Missing values ​​are handled using median imputation; for LSTM input data, standardization is performed according to the feature dimension during training; the target variable is also standardized in the LSTM branch and inversely transformed to restore its original dimensions after prediction.

[0042] To further enhance the model's generalization ability, this implementation employs a stacking model to fuse the aforementioned heterogeneous base models. Specifically, within the training set, 5-fold cross-validation is used to generate the OOF (Out-of-Flight) predictions of each base learner, including LSTM, RF, XGBoost, and PLSR. The OOF predictions of each base model are concatenated column-wise to form a meta-feature matrix, and the average of the fold predictions on the test set is used as the test meta-feature. Subsequently, Lasso regression with L1 regularization is used as the meta-learner to perform secondary learning on the meta-features to obtain the final biomass prediction value. The introduction of Lasso regression not only adaptively learns the combined weights of each base model but also suppresses redundant prediction information, improving the stability of the fused model.

[0043] In terms of model evaluation, the implementation method uses R², RMSE, and MAE to compare and analyze the predictive performance of each base model and the Stacking model. To reduce the impact of randomness caused by a single random partition, the training and test sets are repeatedly and randomly partitioned to evaluate model stability, and the mean and standard deviation of model performance are calculated.

[0044] In summary, this implementation constructs a dual-channel Stacking model that integrates temporal modeling and static heterogeneous ensemble learning. Level 0 consists of four types of heterogeneous base learners: LSTM, RF, XGBoost, and PLSR. These learners model the mapping relationship between UAV remote sensing features across multiple growth stages and soybean aboveground biomass from different perspectives, including temporal dynamic dependence, robust nonlinear ensemble relationships, complex nonlinear splitting rules, and latent linear structures. Level 1 employs Lasso regression with L1 regularization to sparsely and adaptively fuse the meta-features output by each base learner. An OOF mechanism ensures that the meta-features originate from samples not seen by the base learners, thus forming a collaborative estimation structure of "temporal dynamic modeling + static heterogeneous learning + sparse fusion optimization + generalization enhancement control." This structure not only uniformly addresses the issue of inconsistent feature dimensions across different growth stages but also simultaneously preserves the sequential information of features from multiple periods and the expressive advantages of traditional tabular features. This effectively improves the accuracy, stability, and cross-period generalization ability of soybean dry weight and fresh weight estimation at different growth stages, providing a more robust and widely applicable technical solution for dynamic cross-period inversion of soybean aboveground biomass.

[0045] To illustrate the impact of different feature combinations and different machine learning models on the accuracy of AGB estimation, the following examples provide a detailed description: like Figure 4 As shown, this embodiment systematically compares the estimation performance of soybean DW and FW at four growth stages, and comprehensively evaluates the inversion effects of five feature combinations (TIs+SIs, VIs+SIs, VIs+TIs, VIs+TIs+SIs, VIs) and five modeling methods (Stacking model, XGBoost, RF, PLSR, and Ridge regression). Overall results show that model performance exhibits significant differences between different growth stages and feature combinations.

[0046] From a model perspective, the Stacking model achieves the highest estimation accuracy across all reproductive stages and the vast majority of feature combinations, with its coefficient of determination... The accuracy is stably distributed in the range of 0.631–0.837, outperforming various single machine learning models. In contrast, while nonlinear models such as XGBoost and RF achieve good performance in some stages, their accuracy fluctuates significantly with changes in reproductive stage and feature input; while linear models such as PLSR and Ridge have relatively low overall explanatory power and low coefficient of determination. Most values ​​are below 0.5, making it difficult to characterize the complex nonlinear relationship between remote sensing features and AGB. The above results indicate that the Stacking model effectively integrates the advantages of different algorithms through multi-model collaborative learning, significantly improving the model's generalization ability and temporal stability while suppressing overfitting. At the feature combination level, the fusion of multi-source remote sensing features significantly promotes the improvement of estimation accuracy. Single features, such as using only VIs, exhibit relatively limited predictive ability across all periods. With the gradual introduction of TIs and SIs, the model accuracy increases stepwise, indicating significant complementarity among different information sources. Among these, the VIs+TIs+SIs combination shows the best or second-best performance across all growth stages and model types, clearly demonstrating that the synergistic effect of spectral information, canopy structure features, and spatial texture features can more comprehensively characterize the soybean AGB formation process.

[0047] Further comparison revealed that the VIs+SIs combination outperformed the VIs+TIs combination overall, indicating that structural features have a more direct and stable physical significance in explaining soybean AGB variations. However, TIs exhibited unique advantages under mid-to-late stage high biomass conditions, effectively compensating for the saturation of spectral information in the high-coverage stage and enhancing the model's ability to perceive canopy spatial heterogeneity. Therefore, when TIs are introduced as a complementary variable along with spectral and structural features, the model's ability to fit complex nonlinear relationships can be further improved.

[0048] To better illustrate the modeling and evaluation of dynamic biomass estimation throughout the entire reproductive period, the following examples provide a detailed explanation: To further improve the transferability of the model across different growth stages and the generalization ability of AGB inversion, and to verify the estimation ability of the improved Stacking model with the introduction of LSTM time-series modeling channels for soybean aboveground biomass at different growth stages, such as... Figure 5 As shown, this embodiment modeled and evaluated the dry weight and fresh weight of soybeans at four key growth stages: full bloom, initial pod formation, grain filling, and early maturity. R², RMSE, and MAE were used to comprehensively compare the model performance. Overall results show that the improved Stacking model can effectively estimate dry weight and fresh weight at different growth stages, but the prediction accuracy varies significantly between stages, exhibiting stage-specific characteristics consistent with crop growth progress and canopy phenotypic changes.

[0049] From the R² perspective, the model performed best in the early maturity stage, with high R² values ​​for both dry weight and fresh weight, at 0.855 and 0.859, respectively. At the pod-opening stage, the model showed better prediction for fresh weight, with an R² of 0.831, and for dry weight, approximately 0.776. During the grain-filling stage, the R² values ​​for both dry weight and fresh weight remained at 0.722 and 0.725, respectively. At full bloom, the model predicted dry weight better than fresh weight, with an R² of 0.693 for dry weight and 0.613 for fresh weight. These results indicate that the improved Stacking model has a stronger explanatory power for biomass in the middle and later stages of soybean growth, especially in the early maturity stage, where it can stably characterize changes in dry and fresh weight.

[0050] From the perspective of error indices, the trends of RMSE and MAE are basically consistent with R². The prediction errors for dry weight during the full bloom and early maturity stages are relatively small, with the RMSE at 24.68 g / m² and MAE at 18.51 g / m² during the early maturity stage, and both RMSE and MAE remaining at low levels during the full bloom stage. The error for dry weight during the initial pod stage increases slightly, but remains within an acceptable range. In contrast, the prediction error is most significant during the pod-filling stage, especially the fresh weight estimation error, which increases significantly, with an RMSE of approximately 459.6 g / m² and a MAE of approximately 319.6 g / m². The RMSE and MAE for dry weight during this period also reach the highest levels among the four stages. These results indicate that the rapid changes in canopy structure, accelerated pod filling, and increased fluctuations in plant water content during the pod-filling stage make the mapping relationship between fresh weight and dry weight and remote sensing features more complex, thus increasing the difficulty of model inversion.

[0051] Further comparison of the estimation results for dry weight and fresh weight reveals that the improved Stacking model generally outperforms fresh weight in predicting dry weight during most periods, especially during the full bloom, pod-filling, and early maturity stages, where the error in dry weight is significantly lower than that in fresh weight. However, at the initial pod stage, fresh weight exhibits a relatively higher coefficient of determination. This indicates that fresh weight is more sensitive to moisture status and short-term environmental changes, and its remote sensing response mechanism is more complex than that of dry weight. The improved model, by introducing an LSTM time-series modeling channel, can enhance its ability to utilize dynamic change information across multiple periods to a certain extent, thereby improving the adaptability and stability of biomass estimation at different growth stages.

[0052] In summary, the improved Stacking model with LSTM incorporated demonstrated good estimation capabilities for soybean aboveground biomass at all four key growth stages, achieving particularly high accuracy at the initial pod-filling stage and early maturity stage. Although the grain-filling stage remains the most challenging to estimate, the model as a whole can adapt well to the complex and dynamic relationship between multi-source remote sensing features and biomass at different growth stages, providing reliable technical support for the dynamic monitoring of soybean dry weight and fresh weight.

[0053] Implementation Method 2: The soybean aboveground biomass dynamic cross-growth-stage estimation system described in this implementation method is based on the high-precision dynamic cross-growth-stage estimation method for soybean aboveground biomass described in Implementation Method 1, and includes the following modules: Module S1 collects various data related to soybeans; Module S2 collects data on multiple growth stages of soybeans using drones, and generates multispectral orthophotos and digital surface models based on the soybean growth stage data. Module S3, based on multispectral orthophotos and digital surface models, extracts crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass. Module S4, after improving the Stacking model, uses various soybean data, crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass to train the improved Stacking model and obtain the trained Stacking model. Module S5, based on the trained Stacking model, completes the estimation of soybean aboveground biomass growth period.

[0054] Implementation Method 3: A computer program product described in this implementation method includes a computer program or instructions. When the computer program or instructions are executed by a processor, they implement the high-precision dynamic cross-growth-stage estimation method for soybean aboveground biomass described in Implementation Method 1.

[0055] The above provides a detailed description of the soybean aboveground biomass dynamic estimation method, system, and program product across growth stages proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for estimating the dynamic aboveground biomass of soybean across growth stages, characterized in that, Includes the following steps: Step S1: Collect various data on soybeans; Step S2: Collect data on multiple growth stages of soybeans using drones, and generate multispectral orthophotos and digital surface models based on the soybean growth stage data. Step S3: Based on multispectral orthophotos and digital surface models, extract crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass. Step S4: After improving the Stacking model, the improved Stacking model is trained using various soybean data, crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass to obtain the trained Stacking model. Step S5: Based on the trained Stacking model, complete the estimation of soybean aboveground biomass growth period.

2. The method for estimating soybean aboveground biomass dynamics across growth stages according to claim 1, characterized in that, In step S1, the various data of soybeans include plant height, fresh weight, and dry weight.

3. The method for estimating soybean aboveground biomass dynamics across growth stages according to claim 1, characterized in that, In step S2, the data on multiple soybean growth stages include flowering, full pod stage, grain filling stage, and early maturity.

4. The method for estimating soybean aboveground biomass dynamics across growth stages according to claim 1, characterized in that, In step S3, the canopy structure features of the crop are obtained based on the difference between the digital surface model and the digital elevation model of the bare soil image taken after soybean sowing. The image texture features are obtained based on the gray-level co-occurrence matrix calculation; The various vegetation indices related to aboveground biomass are based on data obtained from multispectral orthophotos.

5. The method for estimating soybean aboveground biomass dynamics across growth stages according to claim 1, characterized in that, In step S4, the improved Stacking model adopts a two-layer stacked ensemble learning inversion framework. In the first base learner layer, partial least squares regression, long short-term memory network, random forest and extreme gradient boosting are selected; In the second-layer meta-learner, minimum absolute shrinkage and Lasso regression are selected to nonlinearly reconstruct the output of the first-layer base learner.

6. The method for estimating soybean aboveground biomass dynamics across growth stages according to claim 1, characterized in that, In step S4, the improved Stacking model is trained using five-fold cross-validation on various soybean data, crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass.

7. A soybean aboveground biomass dynamic cross-growth-stage estimation system, wherein the system is based on the high-precision dynamic cross-growth-stage estimation method for soybean aboveground biomass as described in claim 1, characterized in that... Includes the following modules: Module S1 collects various data related to soybeans; Module S2 collects data on multiple growth stages of soybeans using drones, and generates multispectral orthophotos and digital surface models based on the soybean growth stage data. Module S3, based on multispectral orthophotos and digital surface models, extracts crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass. Module S4, after improving the Stacking model, uses various soybean data, crop canopy structure features, image texture features, and various vegetation indices related to aboveground biomass to train the improved Stacking model and obtain the trained Stacking model. Module S5, based on the trained Stacking model, completes the estimation of soybean aboveground biomass growth period.

8. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by the processor, they implement the high-precision dynamic cross-growth-period estimation method for soybean aboveground biomass as described in any one of claims 1 to 6.

Images