A modeling method for identifying drought stress of kale seedlings

Abstract

This invention belongs to the field of plant physiological monitoring technology and provides a method for identifying and modeling drought stress in kale seedlings. The method includes: selecting seedlings with uniform growth and dividing them into a control group and mild / moderate / severe drought groups; collecting images of the leaves of each group labeled with nine fluorescence parameters; establishing five types of relationships and constraints based on these parameters, including PSII energy allocation conservation and quenching complementarity; transforming the first two types into hard constraints that are always true, and the latter two types into differentiable soft constraints, which together constitute photosynthetic physiological constraint loss; then combining the collaborative response patterns of parameters under normal and drought stress conditions to construct relevant prototype alignment and directional constraints, forming a collaborative constraint loss; and finally, based on the task loss, fusing the two types of constraint losses and assigning weights to obtain the total loss function, thereby constructing a drought stress identification model. This invention solves the technical problems of lack of interpretability, weak generalization ability, and poor stability in purely data-driven models.

Description

Technical Field

[0001] This invention belongs to the field of plant physiological monitoring technology and involves the cross-application of artificial intelligence in agricultural intelligent detection and agricultural water conservation, providing a method for identifying and modeling drought stress in kale seedlings. Background Technology

[0002] Kale, a cruciferous leafy vegetable, is widely considered an important nutritious food due to its excellent nutritional value. Against the backdrop of global climate change, drought and extreme heat events have caused global crop yield losses exceeding the combined losses from all biotic stresses, becoming the main abiotic stressors limiting crop productivity. Drought stress inhibits crop photosynthesis, causes stomatal closure, and leads to growth retardation and yield loss. For leafy vegetables, the seedling stage is a critical period for organ differentiation and root morphology establishment; drought during this period often causes irreversible damage or even death.

[0003] Therefore, establishing an early identification system for drought stress in kale seedlings and intervening in a timely manner is of great significance for ensuring the quality of vegetable production.

[0004] Currently, existing technologies for identifying and monitoring crop drought stress mainly rely on manual experience or threshold judgments based on single physiological parameters. This involves measuring leaf water content, stomatal conductance, or single chlorophyll fluorescence parameters (such as Fv / Fm, NPQ, etc.) and comparing them with empirical thresholds to determine the drought stress state. Deep learning methods based on chlorophyll fluorescence imaging, visible light imaging, or multispectral imaging data use models such as convolutional neural networks (CNNs) and Transformers to classify or regress stress states. These methods typically use fluorescence parameter images or their combinations as input features, employing an end-to-end data-driven approach to determine stress. Their core relies on the model's automatic learning of sample statistical features. However, the following problems exist:

[0005] 1. The network structure and parameter optimization process of the above model rely on one or more physiological parameters for judgment, making the model as a whole a pure data-driven black box modeling method.

[0006] 2. The high dependence of traditional deep learning models on large-scale labeled data significantly reduces their generalization ability in small sample scenarios. Existing deep learning models (such as CNN and Transformer) usually require a large number of labeled samples to achieve relatively stable practical recognition accuracy. However, it is difficult to obtain large-scale stress samples in kale seedling experiments, especially under complex conditions such as high noise and cross-environmental fluctuations commonly encountered in seedling detection. The stability and adaptability of the model are obviously insufficient.

[0007] 3. Purely data-driven black box models lack biological interpretability, which means that their predictions cannot provide reliable theoretical support for agricultural production decisions, thus limiting the interpretability and credibility of model predictions in agricultural production decisions. Summary of the Invention

[0008] To solve the above-mentioned technical problems, the technical solution of the present invention includes: Several seedling samples with uniform growth were taken and divided into a control group, a mild drought group, a moderate drought group, and a severe drought group for cultivation. After cultivation, images of each seedling leaf in each group were obtained, labeled with nine fluorescence parameters. The fluorescence parameters included actual fluorescence F, maximum fluorescence Fm' under illumination, and photochemical utilization. Quantum yield with non-regulated energy dissipation Quantum yield of regulated energy dissipation Non-photochemical quenching Photochemical quenching coefficient Non-photochemical quenching coefficient and lake-type photochemical quenching coefficient .

[0009] Based on various fluorescence parameters, the PSII energy distribution conservation relationship, quenching complementarity relationship, PSII energy conservation deviation, photochemical efficiency consistency, and physiological parameter value constraints are established. Then, after defining the vectors of nine fluorescence parameters, the PSII energy distribution conservation relationship and quenching complementarity relationship are transformed into hard constraints that always hold true through parameter mapping transformation. The photochemical efficiency consistency and physiological parameter value constraints are transformed into differentiable soft constraints through quantification of the degree of deviation. The hard constraints and soft constraints together constitute the photosynthetic physiological constraint loss.

[0010] Based on the coordinated response patterns of fluorescence parameters of seedling leaves under normal and drought stress conditions, relevant prototype alignment constraints and directional constraints are constructed, which constitute the coordinated constraint loss.

[0011] Using task loss as the basic loss term, the photosynthetic physiological constraint loss and collaborative constraint loss are fused together with weighting coefficients to obtain the total loss function, thereby constructing a drought stress identification model. The drought stress identification model judges the seedling status based on the nine fluorescence parameters obtained.

[0012] Furthermore, when collecting fluorescence parameters, the fluorescence parameters of abnormal samples with maximum photosynthetic efficiency Fv / Fm < 0.75 were removed. Fv is variable fluorescence, and Fm is maximum fluorescence.

[0013] Furthermore, the PSII energy distribution conservation relationship is as follows: ; The quenching complementarity relationship is as follows: ; The deviation of the PSII energy conservation rule is: ; The consistency of the photochemical efficiency is as follows: ; The physiological parameter values ​​are constrained as follows: .

[0014] Furthermore, the method for constructing photosynthetic physiological constraint loss is as follows: The nine fluorescence parameter vectors are defined as follows: ; The PSII energy allocation conservation relation is transformed into a hard constraint on energy allocation conservation as follows: ; make Heng was established.

[0015] The quenching cross relation is transformed into a quenching complementary hard constraint as follows: ; make Heng is established; in, This is the unconstrained logits vector output by the network. =[ ,…, ]∈ , d∈{3,5,9}, the standard k-dimensional simplex is: }, triples correspond to k=2, and binary complements correspond to k=1.

[0016] The aforementioned photochemical efficiency consistency is converted into a photochemical efficiency consistency loss as follows: ; Physiological parameter constraints are transformed into physiological boundary losses as follows: ; In the formula: ={ , , , } represents the set of constrained parameters, and the parameters are... for Physiologically feasible range , For boundary tolerance, The width of the center band.

[0017] Total loss of photosynthetic physiological constraints .

[0018] Furthermore, the method for constructing the collaborative constraint loss is as follows: Construct relevant prototype alignment constraints: For matrix Y∈ Each parameter in the equation is z-score normalized: In the formula, Let j be the mean of the j-th parameter. Let be the standard deviation of the j-th parameter, B be the sample size, and P be the number of parameters.

[0019] Define the standardized correlation matrix: Based on the class condition-related prototype matrix of normal and stress states and Establish a target-related prototype matrix: In the formula, This represents the proportion of samples subjected to stress in the overall sample. It is a positive semi-definite matrix.

[0020] Obtain relevant prototype alignment constraints : in, This is the normalization factor.

[0021] Constructing directional constraints: When the sample contains both states, a marginal hinge loss is applied to the population mean: Among them, tolerance parameter =0.02, =0.03, activated when π∈(0.05,0.95).

[0022] The collaborative constraint losses are summarized as follows: .

[0023] Furthermore, the method for constructing the total loss function is as follows: The mission loss is: Among them, the label smoothness coefficient =0.05.

[0024] The weighting coefficients of photosynthetic physiological constraint loss and cooperative constraint loss are combined. , Introducing the training objective function, we construct the total loss function: In the formula, Weights for photosynthetic physiological constraints loss. The weights for the collaborative constraint loss.

[0025] Furthermore, the weighting coefficients , The optimization method is as follows: Nine fluorescence parameters are convolved to extract a fused input feature map. A backbone network extracts high-level semantic features and low-level texture features from the fused input feature map. A feature pyramid network fuses the high-level semantic features and low-level texture features to obtain a cross-scale fused feature. A SE channel attention mechanism performs global average pooling on the cross-scale fused feature, followed by weight transformation through two fully connected layers. After ReLU and Sigmoid activation functions, a channel weight vector is generated, thus weighting the cross-scale fused feature. , The initial value.

[0026] Using nine fluorescence parameters from several seedling samples, the overall violation rate (VR) for each photosynthetic physiological constraint and the prototype alignment error for the collaborative constraint were calculated. ,in, In the formula, >0, where the conservation constraint is taken as =0.03, quenching relation taken =0.05, boundary constraints are taken as... =0.1, where S is the sample size. (ŷ) represents a given mechanism constraint. The residual function, where M is the number of statistical constraints; When the overall violation rate VR > 0.1, according to Upward .

[0027] when When >0.2, according to Upward .

[0028] ∈[0.4,0.8], ∈[0.03,0.1].

[0029] Furthermore, the method for obtaining the fused input feature map is as follows: For each of the nine fluorescence parameters, a parameter branch encoder with the same structure was built, and each branch encoder only processes the corresponding parameter.

[0030] A dual-path modeling structure is constructed within each parameter branch. Multiple images of each parameter are averaged or summarized across frames to obtain a spatial representative image that preserves the leaf morphology and spatial distribution characteristics. Global color or intensity statistical features are extracted from each image and summarized to obtain a cross-frame global statistical vector that characterizes the overall energy distribution of the parameter.

[0031] The cross-frame global statistical vector is expanded into a statistical feature map of the same size as the spatial representative map. The spatial representative map and the statistical feature map are then concatenated in the channel dimension to form a fused input feature map for each parameter branch.

[0032] Furthermore, the drought stress identification model includes a classification head for outputting a binary classification identification result of the drought stress status of seedlings.

[0033] Furthermore, the drought stress identification model includes a parameter prediction head for outputting an unconstrained logits vector. .

[0034] The technical solution provided by this invention has the following advantages compared with the prior art: This invention selects seedlings with uniform growth status and divides them into a control group and mild / moderate / severe drought groups. Nine fluorescence parameter images are collected. Based on photosynthetic physiological laws, five types of relationships, including the conservation of PSII energy distribution, are established and transformed into hard and soft constraints to construct photosynthetic physiological constraint loss. Combined with the collaborative response patterns of parameters under normal and drought stress, relevant prototype alignment and directional constraints are constructed to form collaborative constraint loss. Finally, task loss and weights are fused to obtain the total loss function to construct the model. Physiological constraints are based on the core mechanism of plant photosynthetic physiology, allowing the model to move beyond simple data statistical learning and providing logical support for modeling. This solves the problem of black-box modeling driven by pure data. Physiological constraints are inherent and universal laws of plants, while collaborative constraints capture fixed parameter response patterns. Both reduce dependence on large-scale labeled data and resist environmental noise and cross-environmental fluctuations, thus solving the problems of weak generalization ability and insufficient stability under small sample and complex conditions. All constraints originate from the core principles of photosynthetic physiology, and the prediction results can be directly correlated with the physiological changes of the leaf photosynthetic system under drought stress in kale seedlings, providing reliable theoretical support for agricultural production decisions. Ultimately, this achieves a simultaneous improvement in model interpretability, generalization ability, and stability.

[0035] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a schematic diagram of the drought stress identification model according to an embodiment of the present invention. Detailed Implementation

[0038] The following detailed description of a specific embodiment of the present invention is provided in conjunction with the accompanying drawings. However, it should be understood that the scope of protection of the present invention is not limited to the specific embodiment.

[0039] The term "small sample" as used in this invention refers to a training set with a total sample size of ≤100 plants and a single-class sample size of ≤30% of the original data size.

[0040] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the technical solution of this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0041] In the description of the embodiments of the present invention, unless otherwise stated, "a plurality of" means two or more.

[0042] In the description of the embodiments of the present invention, PSII is an abbreviation for Photosystem II, which is the core functional complex of the light reaction stage of plant photosynthesis.

[0043] like Figure 1 As shown, this invention provides a method for identifying and modeling drought stress in kale seedlings, comprising: Several seedling samples with uniform growth status were taken and divided into control group, mild drought group, moderate drought group and severe drought group. The mild / moderate / severe drought group was combined into a drought group and formed a binary label with the control group. Images of each seedling leaf labeled with nine fluorescence parameters were obtained in each group. Based on various fluorescence parameters, the PSII energy distribution conservation relationship, quenching complementarity relationship, PSII energy conservation deviation, photochemical efficiency consistency, and physiological parameter value constraints are established. Then, after defining the vectors of nine fluorescence parameters, the PSII energy distribution conservation relationship and quenching complementarity relationship are transformed into hard constraints that always hold true through parameter mapping transformation. The photochemical efficiency consistency and physiological parameter value constraints are transformed into differentiable soft constraints through quantification of the degree of deviation. The hard constraints and soft constraints together constitute the photosynthetic physiological constraint loss.

[0044] Based on the coordinated response patterns of fluorescence parameters of seedling leaves under normal and drought stress conditions, relevant prototype alignment constraints and directional constraints are constructed, which constitute the coordinated constraint loss.

[0045] Using task loss as the basic loss term, the photosynthetic physiological constraint loss and collaborative constraint loss are fused together with weighting coefficients to obtain the total loss function, thereby constructing a drought stress identification model. The drought stress identification model judges the seedling status based on the nine fluorescence parameters obtained.

[0046] Specifically, 96 uniformly growing kale seedlings were selected as experimental material and transplanted into plastic pots with a diameter of 15 cm and a height of 12 cm. General-purpose nursery potting soil was used as the soil substrate. The original root ball was preserved during transplanting to reduce transplant stress and promote rapid adaptation of the seedlings to the new environment. A one-week acclimatization period was administered after transplanting to ensure robust and uniform plant growth.

[0047] All experimental materials were cultured in an artificial climate chamber with the following environmental parameters set: 12h photoperiod / 12h darkness, day / night temperature of 25℃ / 18℃, photosynthetically active radiation of 600μmol·m⁻²·s⁻¹, relative humidity of 60%, and CO₂ concentration of 400μmol·mol⁻¹ to ensure a consistent crop growth environment.

[0048] Soil moisture content was used as the sole variable. Experimental seedlings were randomly divided into four treatment groups, with 24 seedlings in each group. Four moisture gradients were established based on soil moisture content: control group (60%-80%), mild drought (40%-60%), moderate drought (20%-40%), and severe drought (0%-20%). Each group was regularly irrigated to maintain the target soil moisture content range. Soil moisture status was monitored daily using a soil moisture sensor to ensure that the soil moisture content of each treatment group remained within the preset range.

[0049] Chlorophyll fluorescence images of kale leaves were acquired using the IMAGING-PAM-M series chlorophyll fluorescence imager (MAXI version). Before data acquisition, samples were placed in a dark environment for 30 minutes for dark adaptation to ensure complete opening of the PSII reaction centers. The 3rd to 4th uniformly developed functional leaves from the bottom of each plant were selected for measurement, and representative leaves from each group were randomly selected for fluorescence imaging. The acquired fluorescence images were 10cm × 13cm in size, in JPG format, with a resolution of 640px × 480px and a color depth of 24-bit pseudo-color.

[0050] The fluorescence parameters include actual fluorescence F, maximum fluorescence Fm' under illumination, and photochemical utilization. Quantum yield with non-regulated energy dissipation Quantum yield of regulated energy dissipation Non-photochemical quenching Photochemical quenching coefficient Non-photochemical quenching coefficient and lake-type photochemical quenching coefficient .

[0051] The three treatments—mild drought (LD), moderate drought (MD), and severe drought (SD)—were combined into an experimental group, resulting in two sample classes: an experimental group and a control group. The label distribution ratio was 1:3 for the control group and the experimental group. All sample image data were managed with a unique plant sample ID to prevent information leakage during the dataset partitioning process.

[0052] The dataset was strictly partitioned according to plant sample IDs to ensure that all images of the same plant were assigned to the same subset, preventing data leakage. Considering the small sample size, the dataset was divided into training, validation, and test sets in a ratio of 65%:15%:20%. A 5-fold cross-validation strategy was employed to fully evaluate the stability of the model's performance. The training set was used for model parameter optimization, the validation set for hyperparameter tuning, and the test set for evaluating the model's generalization ability.

[0053] To address the systematic errors present in the instrument, abnormal image data from the first few frames were manually removed. Simple image enhancement operations were performed on the training set data, including random horizontal flipping, random small-angle rotation, and other geometric transformations, to increase data diversity.

[0054] Furthermore, the Fv / Fm fluorescence parameter image was used as a sample quality screening indicator to assess the physiological health status of the leaves. The quality control criteria were as follows: if the parameter value of multiple pixel areas in the Fv / Fm image of a sample leaf was lower than 0.75, the sample was judged as abnormal and discarded. Fv is variable fluorescence, and Fm is maximum fluorescence.

[0055] Based on various fluorescence parameters, the following relationships were established: PSII energy distribution conservation relationship, quenching complementarity relationship, PSII energy conservation deviation, photochemical efficiency consistency, and physiological parameter value constraints. Under light-adaptive conditions, the excitation energy absorbed by PSII is distributed through three pathways: photochemical utilization... Adjustable non-photochemical dissipation Non-regulated dissipation Based on the principle of energy conservation, the three elements satisfy a mutually exclusive competition relationship on a unit time scale, that is, the PSII energy allocation conservation relationship is:

[0056] ; Photochemical quenching coefficient Indicates the open proportion of PSII reaction centers, and the non-photochemical quenching coefficient. This represents the proportion of non-photochemical quenching. Under the classic Puddle model and normalization conditions... and In a statistically significant sense, they exhibit a complementary relationship, i.e., the quenching of the complementary relationship is as follows:

[0057] ; The deviation of the PSII energy conservation rule is: ; Under photoadaptive steady-state conditions, applying a saturation pulse can "shut down" all PSII receptor sides, causing the fluorescence intensity to instantaneously increase from F to [value missing]. The difference between the two, ΔF = Fm' − F, reflects the excitation energy portion available for photochemical reactions. Normalizing this to Fm' yields the actual photochemical efficiency of PSII. That is, the consistency of photochemical efficiency is:

[0058] ; Based on the physical meaning of fluorescence parameters, all quantum yields and quenching coefficients are proportional and should be limited to a physiologically feasible range. NPQ, as a Stern-Volmer type heat dissipation index, is inherently non-negative; therefore, the physiological parameter values ​​are constrained as follows:

[0059] .

[0060] The method for constructing photosynthetic physiological constraint loss is as follows: The nine fluorescence parameter vectors are defined as follows: ; The PSII energy allocation conservation relation is transformed into a hard constraint on energy allocation conservation as follows: ; make Heng was established.

[0061] The quenching cross relation is transformed into a quenching complementary hard constraint as follows: ; make Heng is established; in, This is the unconstrained logits vector output by the network. =[ ,…, ]∈ , d∈{3,5,9}, the standard k-dimensional simplex is: }, triples correspond to k=2, and binary complements correspond to k=1.

[0062] The aforementioned photochemical efficiency consistency is converted into a photochemical efficiency consistency loss as follows: ; Physiological parameter constraints are transformed into physiological boundary losses as follows: ; In the formula: ={ , , , } represents the set of constrained parameters, and the parameters are... for Physiologically feasible range , For boundary tolerance, The width of the center band.

[0063] Relax the hard constraints into a differentiable penalty term, where ={ , , , } represents the set of constrained parameters. ,definition This is the physiologically feasible range. , For boundary tolerance and center band width.

[0064] NPQ, as a non-negative, unbounded parameter, is only constrained by the first term. Based on the penalty function method in constrained optimization theory, the total loss due to photosynthetic physiological constraints is defined. .

[0065] The solution to the optimization problem will approximate the feasible region that satisfies the hard constraints.

[0066] The method for constructing the collaborative constraint loss is as follows: Construct relevant prototype alignment constraints: Multiple chlorophyll fluorescence parameters exhibited significantly different synergistic response patterns under both normal and drought stress physiological states. To introduce prior knowledge at the feature relationship level, the batch data matrix Y∈ Process it.

[0067] For matrix Y∈ Each parameter in the equation is z-score normalized: In the formula, Let be the mean of the j-th parameter, and . Let be the standard deviation of the j-th parameter, B be the sample size, and P be the number of parameters.

[0068] Define the standardized correlation matrix: Based on the class condition-related prototype matrix of normal and stress states and Establish a target-related prototype matrix: In the formula, This represents the proportion of samples subjected to stress in the overall sample. It is a positive semi-definite matrix that adaptively adjusts when classes are unbalanced.

[0069] The relevant prototype alignment constraints are obtained by using the Frobenius norm metric. : in, As a normalization factor, it eliminates the influence of the number of parameters, making different configurations comparable.

[0070] Constructing directional constraints prompts the model prediction to approximate the "cooperative response fingerprint" of class conditions: To introduce macroscopic directional constraints, a marginal hinge loss is applied to the population mean when a batch contains both states simultaneously, preventing violations of the "..." constraint. The anomaly of a population pattern of "decreasing NPQ and increasing NPQ": Among them, tolerance parameter =0.02, =0.03, activated when π∈(0.05,0.95).

[0071] It is important to note that It means The vector, It means The vectors in the first case are similar to those in the second case.

[0072] The collaborative constraint losses are summarized as follows: .

[0073] The total loss function is constructed as follows: The mission loss is: Among them, the label smoothness coefficient =0.05.

[0074] The weighting coefficients of photosynthetic physiological constraint loss and cooperative constraint loss are combined. , Introducing the training objective function, we construct the total loss function: In the formula, Weights for photosynthetic physiological constraints loss. The weights for the collaborative constraint loss.

[0075] The weighting coefficient , The optimization method is as follows: The drought stress identification model also includes nine parameter branch encoders, each processing one parameter separately. This allows for convolution of the nine fluorescence parameters to extract a fused input feature map. The backbone network extracts high-level semantic features and low-level texture features from the fused input feature map. A feature pyramid network fuses the high-level semantic features and low-level texture features to obtain cross-scale fused features. An SE channel attention mechanism performs global average pooling on the cross-scale fused features, followed by weight transformation through two fully connected layers. After ReLU and Sigmoid activation functions, a channel weight vector is generated, thus calibrating the weights of the cross-scale fused features. , The initial value.

[0076] Using nine fluorescence parameters from several seedling samples, the overall violation rate (VR) for each photosynthetic physiological constraint and the prototype alignment error for the collaborative constraint were calculated. ,in, In the formula, >0, where the conservation constraint is taken as =0.03, quenching relation taken =0.05, boundary constraints are taken as... =0.1, where S is the sample size. (ŷ) represents a given mechanism constraint. The residual function, where M is the number of statistical constraints; When the overall violation rate VR > 0.1, according to Upward .

[0077] when When >0.2, according to Upward .

[0078] ∈[0.4,0.8], ∈[0.03,0.1].

[0079] Specifically, by mapping the satisfaction of multiple mechanistic constraints to the [0,1] interval, a quantitative assessment of the physiological rationality of the model's output is achieved. This indicator, combined with conventional performance indicators, constitutes a multi-dimensional comprehensive evaluation system for the model.

[0080] Each mechanism constraint Formalize as a residual function (ŷ), the violation rate is used as an indicator in the evaluation of the consistency between constraint optimization and prior knowledge. In this study, it is applied to the chlorophyll fluorescence mechanism constraint system to quantify the degree to which the model output follows the photosynthetic physiological mechanism.

[0081] Given mechanism constraints residual function (ŷ), Sample set S and tolerance threshold >0 indicates whether the sample violates constraints. "Define the characteristic event and calculate the sample mean to obtain the constraint." At the threshold Frequency of violations of experience values ​​greater than 0: threshold Based on the instrument accuracy (σ≈0.01-0.03) and the constraint type, the conservation constraint is determined as follows: =0.03, quenching relation taken =0.05, boundary constraints are taken as... =0.10. This statistic represents the overall probability of violation. The unbiased consistent estimator.

[0082] For each constraint Setting tolerance band >0 and weighting coefficient >0, defining single-sample satisfaction. Furthermore, the weighted overall satisfaction level is defined as follows: In summary, VR uses frequency to answer the question of "the proportion of samples that violate mechanistic constraints". The magnitude is used to answer the question of "the severity of the overall deviation". Both follow the standard photosynthetic physiology basis and measurement specifications to ensure the verifiability and repeatability of the "mechanistic consistency" assessment.

[0083] Table 1 summarizes the main mathematical symbols and their meanings in the mechanism consistency assessment system.

[0084] Table 1: Definition of Mathematical Symbols for Mechanism Consistency Assessment Specifically, the backbone network of the drought stress identification model was validated using three lightweight convolutional neural network architectures: ResNet18, MobileNet-V2, and EfficientNet-B0, to adapt to the needs of different application scenarios. A feature pyramid network was used to fuse high-level semantic features with low-level texture features. Feature maps of different scales were upsampled and laterally connected before being combined, thus unifying the overall trend of leaf changes while also taking into account the response differences in local heterogeneous regions such as leaf veins and leaf margins.

[0085] The drought stress identification model integrates an SE channel attention module to adaptively recalibrate the fused multi-channel features. This module first performs a global average pooling (GAP) operation on the feature map, then performs weight transformation through two fully connected layers, and generates channel weight vectors after passing through ReLU and Sigmoid activation functions, thereby achieving weighted calibration of features in each branch.

[0086] The model employs a dual-output head architecture: 1) a classification output head generates the drought state probability p∈[0,1]; 2) a head is used to output the unconstrained logits vector. This output header is only used for mechanistic constraint calculation and gradient backpropagation, and does not perform explicit regression tasks.

[0087] Furthermore, the method for obtaining the fused input feature map is as follows: For each of the nine fluorescence parameters, a parameter branch encoder with the same structure was built, and each branch encoder only processes the corresponding parameter.

[0088] A dual-path modeling structure is constructed within each parameter branch. Multiple images of each parameter are averaged or summarized across frames to obtain a spatial representative image that preserves the leaf morphology and spatial distribution characteristics. Global color or intensity statistical features are extracted from each image and summarized to obtain a cross-frame global statistical vector that characterizes the overall energy distribution of the parameter.

[0089] The cross-frame global statistical vector is expanded into a statistical feature map of the same size as the spatial representative map. The spatial representative map and the statistical feature map are then concatenated in the channel dimension to form a fused input feature map for each parameter branch.

[0090] The training strategy and hyperparameter configuration are as follows: A 5-fold cross-validation strategy was employed, with stratified partitioning based on plant sample ID to ensure that images of different fluorescence parameters from the same plant do not appear simultaneously in both the training and validation sets, thus preventing data leakage. The training set used a simple data augmentation strategy, while the validation and test sets underwent no data augmentation. All input channels were standardized channel-by-channel based on training set statistics; the input image size was uniformly adjusted to 224×224 pixels, and the batch size was set to 16.

[0091] Model optimization uses the AdamW optimizer with a weight decay factor of 1×10⁻⁴. The baseline learning rate is set to 3×10⁻⁴, and the output head uses the baseline learning rate. Cosine annealing is used for learning rate scheduling, and the total training epochs are set to 100. A gradient pruning mechanism is introduced to stabilize the training process, with a Dropout rate of 0.3 set before the classification output head; mixed-precision training is disabled by default.

[0092] Model retention is based on the validation set F1 score, retaining the model weights with the optimal F1 score, with a patience period of 20 epochs. The final classification threshold is determined using the optimal F1 score on the validation set. The three aforementioned network backbones are compared; the features fused from the feature pyramids are then globally pooled to obtain a discriminative feature vector, which is simultaneously used to train a traditional machine learning classifier.

[0093] The F1 score was used as the primary monitoring metric during training. Performance comparisons between models were performed using the paired Wilcoxon signed-rank test. All model training and testing were completed on an NVIDIA RTX A5000 GPU. A fixed random seed of 42 was used to ensure the reproducibility of model training.

[0094] To avoid data leakage, Grad-CAM visualization analysis is performed only on the test set, with a fixed number of representative samples sampled for each fold. The visualization layer selects the last convolutional feature map of the backbone network, and the generated class activation heatmap is normalized and then superimposed onto the original input image.

[0095] It should be noted that any parts not disclosed or specifically described in this invention are existing technology or conventional configurations, and their specific structures and working principles will not be elaborated further. In this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0096] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily implemented by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A method for identifying and modeling drought stress in kale seedlings, characterized in that, include: Several seedling samples with uniform growth were taken and divided into a control group, a mild drought group, a moderate drought group, and a severe drought group for cultivation. After cultivation, images of each seedling leaf in each group were obtained, labeled with nine fluorescence parameters. The fluorescence parameters included actual fluorescence F, maximum fluorescence Fm' under illumination, and photochemical utilization. Quantum yield with non-regulated energy dissipation Quantum yield of regulated energy dissipation Non-photochemical quenching Photochemical quenching coefficient Non-photochemical quenching coefficient and lake-type photochemical quenching coefficient ; Based on nine fluorescence parameters, the PSII energy distribution conservation relationship, quenching complementarity relationship, PSII energy conservation deviation, photochemical efficiency consistency, and physiological parameter value constraints are established. Then, after defining the vectors of the nine fluorescence parameters, the PSII energy distribution conservation relationship and quenching complementarity relationship are transformed into hard constraints that always hold true through parameter mapping transformation. The photochemical efficiency consistency and physiological parameter value constraints are transformed into differentiable soft constraints through quantification of the degree of deviation. The hard constraints and soft constraints together constitute the photosynthetic physiological constraint loss. Based on the coordinated response pattern of fluorescence parameters of seedling leaves under normal and drought stress conditions, relevant prototype alignment constraints and directional constraints are constructed, and the relevant prototype alignment constraints and directional constraints constitute the coordinated constraint loss. Using task loss as the basic loss term, and combining weighting coefficients, the photosynthetic physiological constraint loss and collaborative constraint loss are fused to obtain the total loss function, thereby constructing a drought stress identification model.

2. The method for identifying and modeling drought stress in kale seedlings as described in claim 1, characterized in that, When collecting fluorescence parameters, the fluorescence parameters of abnormal samples with maximum photosynthetic efficiency Fv / Fm < 0.75 were removed. Fv is variable fluorescence and Fm is maximum fluorescence.

3. The method for identifying and modeling drought stress in kale seedlings as described in claim 1, characterized in that, The energy distribution conservation relationship of the PSII is as follows: ； The quenching complementarity relationship is as follows: ； The deviation of the PSII energy conservation rule is: ； The consistency of the photochemical efficiency is as follows: ； The physiological parameter values ​​are constrained as follows: 。 4. The method for identifying and modeling drought stress in kale seedlings as described in claim 3, characterized in that, The method for constructing photosynthetic physiological constraint loss is as follows: The nine fluorescence parameter vectors are defined as follows: ； The PSII energy allocation conservation relation is transformed into a hard constraint on energy allocation conservation as follows: ； make Hengcheng was established; The quenching cross relation is transformed into a quenching complementary hard constraint as follows: ； make Hengcheng was established; in, This is the unconstrained logits vector output by the network. =[ ,…, ]∈ , d∈{3,5,9}, the standard k-dimensional simplex is: }, triples correspond to k=2, and complementary pairs correspond to k=1; The aforementioned photochemical efficiency consistency is converted into a photochemical efficiency consistency loss as follows: ； Physiological parameter constraints are transformed into physiological boundary losses as follows: ； In the formula: ={ , , , } represents the set of constrained parameters, and the parameters are... for Physiologically feasible range , For boundary tolerance, The width of the center band; Total loss of photosynthetic physiological constraints .

5. The method for identifying and modeling drought stress in kale seedlings as described in claim 4, characterized in that, The method for constructing the collaborative constraint loss is as follows: Construct relevant prototype alignment constraints: For matrix Y∈ Each parameter in the equation is z-score normalized: ， In the formula, Let j be the mean of the j-th parameter. Let be the standard deviation of the j-th parameter, B be the sample size, and P be the number of parameters; Define the standardized correlation matrix: ， Based on the class condition-related prototype matrix of normal and stress states and Establish a target-related prototype matrix: In the formula, This represents the proportion of samples subjected to stress in the overall sample. It is a positive semi-definite matrix; Obtain relevant prototype alignment constraints : ， in, Normalization factor; Constructing directional constraints: When the sample contains both states, a marginal hinge loss is applied to the population mean: ， Among them, tolerance parameter =0.02, =0.03, activated when π∈(0.05,0.95); The collaborative constraint losses are summarized as follows: .

6. The method for identifying and modeling drought stress in kale seedlings as described in claim 5, characterized in that, The total loss function is constructed as follows: The mission loss is: ， Among them, the label smoothness coefficient =0.05; The weighting coefficients of photosynthetic physiological constraint loss and cooperative constraint loss are combined. , Introducing the training objective function, we construct the total loss function: In the formula, Weights for photosynthetic physiological constraints loss. The weights for the collaborative constraint loss.

7. The method for identifying and modeling drought stress in kale seedlings as described in claim 6, characterized in that, The weighting coefficient , The optimization method is as follows: Nine fluorescence parameters are convolved to extract a fused input feature map. A backbone network extracts high-level semantic features and low-level texture features from the fused input feature map. A feature pyramid network fuses the high-level semantic features and low-level texture features to obtain a cross-scale fused feature. A SE channel attention mechanism performs global average pooling on the cross-scale fused feature, followed by weight transformation through two fully connected layers. After ReLU and Sigmoid activation functions, a channel weight vector is generated, thus weighting the cross-scale fused feature. , The initial value; Using nine fluorescence parameters from several seedling samples, the overall violation rate (VR) for each photosynthetic physiological constraint and the prototype alignment error for the collaborative constraint were calculated. ,in, ， ， In the formula, >0, where the conservation constraint is taken as =0.03, quenching relation taken =0.05, boundary constraints are taken as... =0.1, S is the sample size. (ŷ) represents a given mechanism constraint. The residual function, where M is the number of statistical constraints; When the overall violation rate VR > 0.1, according to Upward ; when When >0.2, according to Upward ; ∈[0.4,0.8]， ∈[0.03,0.1]。 8. The method for identifying and modeling drought stress in kale seedlings as described in claim 7, characterized in that, The method for obtaining the fused input feature map is as follows: For each of the nine fluorescence parameters, a parameter branch encoder with the same structure was built, and each branch encoder only processed the corresponding parameter. A dual-path modeling structure is constructed within each parameter branch. Multiple images of each parameter are averaged or summarized across frames to obtain a spatial representative image that preserves the leaf morphology and spatial distribution characteristics. Global color or intensity statistical features are extracted from each image and summarized to obtain a cross-frame global statistical vector that characterizes the overall energy distribution of the parameter. The cross-frame global statistical vector is expanded into a statistical feature map of the same size as the spatial representative map. The spatial representative map and the statistical feature map are then concatenated in the channel dimension to form a fused input feature map for each parameter branch.

9. The method for identifying and modeling drought stress in kale seedlings as described in claim 8, characterized in that, The drought stress identification model includes a classification head, which outputs a binary classification identification result of the drought stress status of seedlings.

10. The method for identifying and modeling drought stress in kale seedlings as described in claim 8, characterized in that, The drought stress identification model includes a parameter prediction head for outputting an unconstrained logits vector. .

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