Method for dynamic inversion of net photosynthetic rate of plant leaves based on transmission spectrum

Abstract

The application discloses a method for dynamically inverting a net photosynthetic rate of a plant leaf based on a transmission spectrum, and relates to the technical field of testing and analysis. Different from the reflection spectrum, the transmission spectrum directly penetrates the leaf tissue, contains absorption and scattering information of the light by the internal substances (chlorophyll, water and structure) of the leaf, the distance between the spectrum detector and the leaf is close to 0, is not affected by environmental conditions, and can more directly reflect the optical characteristics related to the core process of photosynthesis. The method aims at overcoming the shortcomings of the prior art, providing a fast, non-destructive, efficient and accurate Pn dynamic monitoring technical means for crops of different photosynthetic types, and serving the needs of precision agricultural management.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of agricultural product testing and analysis technology, and particularly relates to a method for dynamically inverting plant leaf net photosynthetic rate based on visible-near infrared (400-1100 nm) transmission spectrum. BACKGROUND

[0002] Plant leaf net photosynthetic rate (Pn) is a core physiological index for measuring its photosynthetic carbon assimilation efficiency, and directly affects the growth and development, yield formation and quality improvement of crops. Real-time and dynamic monitoring of the change of the net photosynthetic rate has great guiding significance for precise regulation of water and fertilizer, optimization of environmental factors, diagnosis of stress state and realization of fine management of crop production.

[0003] At present, the most reliable method for obtaining the net photosynthetic rate is to use a portable photosynthetic instrument (such as LI-6800, CIRAS-3) to indirectly calculate by measuring leaf gas exchange (Pn) and other parameters. Although this method has high precision and wide applicability, it is complicated and inefficient, needs to clamp the leaf, disturbs the normal microenvironment and physiological state of the leaf, and cannot realize real in-situ and continuous dynamic monitoring, so it is not practical in high-throughput screening or large-area field application.

[0004] In recent years, spectral technology (mainly reflection spectrum) has also been widely studied for the inversion of leaf physiological parameters. Lei Qian et al. (Lei Qian, Li Qian, Tang Liping, et al. Monitoring model of photosynthetic characteristics of winter rape based on canopy spectrum [J]. Crop Research, 2021, 35(04): 318-329) established a monitoring model of spectral and photosynthetic characteristics of rape under different fertilization amounts and density conditions; Liu Cong et al. (Liu Cong, Peng Yi, Fang Shenghui. Inversion of rice leaf net photosynthetic rate based on hyperspectral data [J]. Journal of China Agricultural University, 2020, 25(01): 56-65) found that the model based on chlorophyll vegetation index CI can be applied to the unified inversion of leaf net photosynthetic rate of different varieties; Wang Jianfeng et al. (Wang Jianfeng, Han Qingyan, Cui Hongbo, et al. Estimation method for inversion of onion leaf net photosynthetic rate based on hyperspectral reflectance [P]. China: CN119290820A, 2025-01-10) invented an estimation method for inversion of onion leaf net photosynthetic rate based on hyperspectral reflectance, which provides an effective means for non-destructive estimation of onion cylindrical leaf net photosynthetic rate. As a non-destructive means, spectral technology has the potential for rapid and large-area application. However, traditional reflection spectrum mainly reflects the surface and shallow information of the leaf. For C3 and C4 plant leaves with thin mesophyll and strong light transmission, the internal key photosynthesis information (especially the light absorption characteristics of deep mesophyll cells) may be difficult to fully capture in the reflection spectrum. At the same time, reflection spectrum is easily disturbed by factors such as leaf surface characteristics (such as wax and fluff), detection angle, detection distance, etc.

[0005] In summary, the prior art is difficult to dynamically and accurately estimate plant leaves, and there is a lack of a dynamic monitoring method for net photosynthetic rate that can take into account non-destructive, rapid, accurate and suitable for different plant types and photosynthetic types. SUMMARY

[0006] The present application is directed to the problems existing in the prior art, and provides a method for dynamically inverting the net photosynthetic rate of plant (C3 and C4 plant) leaves based on visible-near infrared (400-1100 nm) transmission spectrum. Unlike reflection spectrum, transmission spectrum directly penetrates leaf tissue, contains information on light absorption and scattering of internal substances (chlorophyll, water, structure) of the leaf, and the distance between the spectral detector and the leaf is close to 0, which is not affected by environmental conditions, and can more directly reflect the optical characteristics related to the core process of photosynthesis. The method aims to overcome the shortcomings of the prior art and provide a fast, non-destructive, efficient and accurate dynamic monitoring technical means for crops of different photosynthetic types, serving the needs of precision agriculture management.

[0007] In order to achieve the above purpose, the present application provides the following technical scheme:

[0008] The application provides a method for dynamically inverting a net photosynthetic rate of a plant leaf based on a transmission spectrum, comprising the following steps:

[0009] S1, selecting a healthy plant leaf as a sample, accurately measuring a net photosynthetic rate of the target leaf by using a gas exchange method, and synchronously measuring a transmission spectrum of the plant leaf by using a spectrometer to obtain a data pair of the plant leaf sample; the plant leaf comprises C3 plant and C4 plant leaves;

[0010] S2, performing spectral data preprocessing on the original transmission spectrum by using Savitzky-Golay smoothing;

[0011] S3, removing abnormal values by using a 3σ criterion;

[0012] S4, eliminating the influence of the physical structure of the plant leaf on the spectrum by using multiple scattering correction (MSC);

[0013] S5, eliminating baseline drift by using standard normal variable transformation (SNV);

[0014] S6, selecting characteristic wavelengths by using a successive projections algorithm (SPA);

[0015] S7, establishing a plant leaf net photosynthetic rate inversion model based on the transmission spectrum by using a random forest method (RF);

[0016] S8, evaluating the prediction performance of the established estimation model by using a training set determination coefficient , a training set root mean square error , a test set determination coefficient and a test set root mean square error .

[0017] Further, in step S1, when the plant leaf is measured, the left and right leaf blades of the same leaf blade of the same plant are selected, and the net photosynthetic rate is measured on one side, and the transmission spectrum is synchronously measured on the other side.

[0018] Further, in step S1, the transmission spectrum of the plant leaf is measured by using a spectrometer, and the process comprises:

[0019] First, the receiving end of the optical fiber is connected to the cosine corrector, then the cosine corrector is fixed below the leaf blade, and the distance between the leaf blade and the cosine corrector is kept unchanged during measurement; after the machine noise is deducted, the transmission spectrum data of the leaf sample is collected, the measurement wavelength range is 400-1100 nm, and the step interval is 1 nm; 180 samples are randomly collected as test samples.

[0020] Further, in step S2, the original transmission spectrum is preprocessed by using Savitzky-Golay smoothing, and the process comprises:

[0021] First, the parameter initialization is carried out, the window width is set to 21 nm, the polynomial fitting order is determined to be 2 orders, and the formula is:

[0022] ,

[0023] wherein, is the wavelength, is the wavelength smooth value, is the window radius, , is the Savitzky-Golay convolution coefficient; is the index value in the window, ; is the original transmission spectrum value at the wavelength point ;

[0024] Then, along the 400-1100 nm spectral range, the window is moved with a step of 1 nm, and 21 original transmission spectra in the window are extracted for each wavelength , and the Vandermonde matrix is constructed:

[0025] ,

[0026] Then, the polynomial coefficients are solved by the least square method:

[0027] ,

[0028] wherein, is the transpose matrix of the Vandermonde matrix , and is a vector composed of all original transmission spectrum values in the window;

[0029] Then, the center point convolution coefficient is calculated, when , , the smooth value is output;

[0030] Finally, the asymmetric window is adopted at the starting / ending wavelength point, the right extension window is used for the first 10 points in the wavelength 400-409 nm, and the left extension window is used for the last 10 points in the wavelength 1091-1100 nm, and the fitting consistency is maintained by dynamically adjusting the Vandermonde matrix dimension.

[0031] Further, the process of removing outliers by the 3 times standard deviation method in step S3 includes:

[0032] Let the spectral data matrix be wherein is the number of samples, is the value of the th sample at the th wavelength, for each wavelength , the mean and standard deviation are first calculated:

[0033] ,

[0034] Then, it is determined whether it is an outlier, which is defined as deviating from the mean more than 3 times the standard deviation:

[0035] If is an outlier,

[0036] Finally, the outlier is replaced by the median of the remaining non-outlier values at that wavelength :

[0037] ,

[0038] wherein is the value of the th sample at the th wavelength, is the value of the th sample at the th wavelength, wherein refers to all samples.

[0039] Further, the process of step S4 employing multivariate scatter correction comprises:

[0040] For the original spectrum vector of the th sample , taking the mean spectrum of all samples as the reference spectrum , linear regression is performed:

[0041] ,

[0042] wherein is the intercept term, is the slope term, is the residual;

[0043] The least squares method is used to solve:

[0044] ,

[0045] The corrected spectrum is:

[0046] .

[0047] Further, the process of step S5 using standard normal variable transformation includes:

[0048] For each sample spectrum Independent processing:

[0049] ,

[0050] wherein, is the mean value of the i-th sample at all wavelengths, is the standard deviation of the i-th sample, is the value of the i-th sample at the j-th wavelength after SNV processing.

[0051] Further, the process of step S6 using continuous projection algorithm to select characteristic wavelengths includes:

[0052] First, select the wavelength with the strongest correlation with leaf net photosynthetic rate y:

[0053] ,

[0054] Then, calculate the projection information amount for the remaining wavelengths

[0055] ,

[0056] wherein, is the vector composed of spectral data of all samples at the same wavelength point is the spectral matrix composed of selected wavelengths; Then, calculate the information amount of the projection vector:

[0057]

[0058] ,

[0059] Then, select the wavelength that maximizes the information amount:

[0060] ,

[0061] wherein, is the candidate wavelength set, ={1,2,…,p};

[0062] The termination condition is to reach the preset maximum number of wavelengths, , the information amount tends to be saturated, .

[0063] ​​​​​​Further, step S7 uses the random forest method to establish an inversion model of the net photosynthetic rate of plant leaves based on the transmission spectrum. The process includes:

[0064] First, input the data, the feature matrix. The wavelength subset selected for SPA, where d is the number of features, n is the number of samples, and the target vector is... This is the measured value of net photosynthetic rate. This is the measured net photosynthetic rate of the first sample. This is the measured net photosynthetic rate of the nth (i.e., the last) sample;

[0065] Then, the Kennard-Stone algorithm is used to divide the training and test sets for the sample set. Calculate the distance matrix:

[0066] ,

[0067] in, For balance coefficient, For the first The feature vector of the i-th sample represents the i-th... Each sample was screened by SPA. Spectral measurements at each characteristic wavelength For the first Measured net photosynthetic rate of each sample;

[0068] Then, initial points are selected, choosing the two samples that are furthest apart in the full sample space as the starting point for the training set:

[0069] ,

[0070] Sample and Add to training set Then iteratively expand:

[0071] ,

[0072] in, Selected for inclusion in the training set in the current round The index of the samples, For the sample With sample The mixed distance between them For those not yet selected into the training set The index of the candidate samples. For those already existing in the training set The index of a sample in the database. , For the entire sample set, For the already constructed training set, Exclude the training set from the total sample set, i.e., the remaining samples;

[0073] Then, the test set is constructed:

[0074] ,

[0075] The node splitting criterion for the SPA-RF model is as follows:

[0076] ,

[0077] in, It is a characteristic of splitting. For optimal splitting characteristics, The splitting threshold, To determine the optimal splitting threshold, For the sample set of the current node, The net photosynthetic rate of the current node sample ( The variance of ) left child node The variance of the measured net photosynthetic rate for all samples. right child node The variance of the measured net photosynthetic rate for all samples. and Node samples by features and threshold Divided into left and right subsets;

[0078] The ensemble prediction output formula is:

[0079] ,

[0080] The random forest consists of 500 decision trees, each tree supporting a sample. There is a predicted value , This refers to the index of the decision tree in the random forest, and the final predicted value. It is the average of the predicted values ​​for 500 trees.

[0081] Furthermore, in step S8, the formula for calculating the coefficient of determination of the training set is:

[0082] ,

[0083] in, The measured net photosynthetic rate of sample i in the training set. For the model to train samples The predicted value, This is the average net photosynthetic rate of all samples in the training set;

[0084] The test set determination coefficient calculation formula is:

[0085] ,

[0086] Wherein, represents the test set, is the net photosynthetic rate true value of the sample in the test set, is the predicted value of the sample in the test set, is the average value of all sample true values in the test set;

[0087] The root mean square error calculation formula of the training set is:

[0088] ,

[0089] The root mean square error calculation formula of the test set is:

[0090] .

[0091] Compared with the prior art, the beneficial effects of the present application are:

[0092] The method for dynamically inverting the net photosynthetic rate of plant leaves based on transmission spectrum provided by the present application overcomes the type limitations that may exist in traditional methods or single reflection spectrum models, and can effectively adapt to the physiological and biochemical differences of plants with different photosynthetic pathways (C3 / C4); The operation of clamping leaves and interfering with the physiological state required by the traditional gas exchange method is abandoned, and completely non-destructive detection is realized through transmission spectrum measurement below the leaves. The single measurement time is shortened to seconds, and the in-situ, continuous and dynamic monitoring of the leaf photosynthetic physiological process is truly realized. At the same time, for crops with thin leaves and strong light transmission (such as strawberries), the internal light absorption characteristics are directly captured by transmission light, and the problem of large error of traditional methods on soft leaves is overcome. High-frequency noise is suppressed by Savitzky-Golay smoothing (window 21nm, polynomial order 2); The spectral outliers are automatically removed by using 3σ criterion, and the data robustness is improved; Combined with multiple scattering correction (MSC) and standard normal variable transformation (SNV) double-path correction, the interference of leaf physical structure difference and baseline drift is eliminated; The continuous projection algorithm (SPA) is used to select the characteristic wavelengths strongly related to Pn, and the spectral dimension is compressed to ≤50 key wavelengths to avoid overfitting; A regression model is constructed based on random forest (RF), and the Kennard-Stone algorithm is used to divide the training / test set to ensure the model generalization ability. The method provided by the present application provides a real-time and accurate plant net photosynthetic rate monitoring tool, and the hardware cost is significantly lower than that of a portable photosynthetic instrument, and an ordinary spectrometer can be deployed, which is suitable for large-area promotion. BRIEF DESCRIPTION OF DRAWINGS

[0093] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments described in the present application, and other drawings can also be obtained by those skilled in the art based on these drawings.

[0094] Figure 1 The strawberry leaf detection method provided by the embodiment of the present application is shown in the schematic diagram.

[0095] Figure 2 The corn leaf detection method provided by the embodiment of the present application is shown in the schematic diagram.

[0096] Figure 3 The original transmission spectrum of the strawberry leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0097] Figure 4 The original transmission spectrum of the corn leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0098] Figure 5 The Savitzky-Golay smoothed transmission spectrum of the strawberry leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0099] Figure 6 The Savitzky-Golay smoothed transmission spectrum of the corn leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0100] Figure 7 The MSC-based transmission spectrum of the strawberry leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0101] Figure 8 The MSC-based transmission spectrum of the corn leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0102] Figure 9 The SNV-based transmission spectrum of the strawberry leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0103] Figure 10 The SNV-based transmission spectrum of the corn leaf provided by the embodiment of the present application is shown in the schematic diagram.

[0104] Figure 11 The feature wavelength and its distribution of the strawberry leaf selected by the SPA algorithm provided by the embodiment of the present application are shown in the schematic diagram.

[0105] Figure 12 The feature wavelength and its distribution of the corn leaf selected by the SPA algorithm provided by the embodiment of the present application are shown in the schematic diagram.

[0106] Figure 13The strawberry leaf provided by the embodiment of the present application is based on a SPA-RF model performance evaluation diagram.

[0107] Figure 14 The corn leaf provided by the embodiment of the present application is based on a SPA-RF model performance evaluation diagram. DETAILED DESCRIPTION

[0108] In order for those skilled in the art to better understand the technical solutions of the present application, the present application will be further described in detail below in combination with the drawings. The following embodiments are only specific embodiments of the present application, which are used to illustrate the technical solutions of the present application, but not to limit the protection scope of the present application. In the description of the present application, it should be noted that the directions or position relationships indicated by the terms "inner", "outer" and the like are based on the directions or position relationships shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as limiting the present application in that the devices or elements referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, it cannot be understood as a limitation of the present application.

[0109] The present application provides a method for dynamically inverting the net photosynthetic rate of plant leaves based on transmission spectrum, comprising the following steps:

[0110] S1, select healthy leaves of representative strawberries and corn plants of different varieties and different growth stages as samples, representing C3 plants and C4 plants respectively. The net photosynthetic rate of the target leaves is accurately measured by gas exchange method. The transmittance spectrum of the leaves is measured simultaneously using a spectrometer and its matching transmission measurement device. When measuring the strawberry leaves, the left and right leaves of the same compound leaf of the same plant are selected, one side measures the net photosynthetic rate, and the other side measures the transmittance spectrum simultaneously. When measuring the corn leaves, the veins of the same leaf of the same plant are selected, one side measures the net photosynthetic rate, and the other side measures the transmittance spectrum simultaneously. Respectively obtain sufficient number (180 groups each) of data pairs of strawberry and corn leaf samples.

[0111] Figure 1 and Figure 2The schematic diagram of the detection method for estimating the net photosynthetic rate of strawberry and corn leaves based on transmission spectrum inversion, respectively. The left part of the dashed line is the net photosynthetic rate measurement device. The instrument used is the LI-6800 photosynthesis-fluorescence automatic measurement system produced by the American LI-COR company, which can accurately measure the gas exchange parameters of plant leaves. The left side of the same compound leaf of strawberry leaf is clamped, and the left side of the same leaf vein of corn leaf is clamped for measurement. The right part of the dashed line is the spectral measurement device. The instrument used is the AvaSpec-ULS2048XL-EVO fiber optic spectrometer produced by the Netherlands Avantes company, which is used to measure the transmission spectrum of the leaf. First, the fiber receiving end is connected with the cosine corrector, then the cosine corrector is fixed under the leaf, the right side of the same compound leaf of strawberry leaf is clamped, and the right side of the same leaf vein of corn leaf is clamped for measurement. The distance between the leaf and the cosine corrector is kept constant during measurement to minimize the probability of human error. After deducting the machine noise, the leaf sample transmission spectrum data is collected. The measurement wavelength range is 400-1100 nm, and the step interval is 1 nm; 180 samples of strawberry and corn are randomly collected as test samples.

[0112] Figure 3 The original spectrum diagram of the estimation method for estimating the net photosynthetic rate of strawberry leaves based on transmission spectrum inversion. It can be observed from the diagram that in the visible light wavelength range of 400-700 nm, the spectral characteristics of plant leaves are the key characteristics of their photosynthetic efficiency and physiological activity. This method reveals the composition, structure and state information of the leaf interior by analyzing the transmission spectrum of the strawberry leaf, which is of great significance for optimizing photosynthesis.

[0113] The blue region (400-500 nm) has a very low photon flux density, indicating that chlorophyll a / b and carotenoids have strong absorption in this region (especially around 430-450 nm). Most of the blue light is captured by the leaf tissue for photosynthesis, and very little is transmitted. The green region (500-600 nm) has a relatively high photon flux density (forming a distinct "peak" in the graph), indicating that chlorophyll a / b have relatively weak absorption in the green region (they mainly absorb blue and red light). Although some of the green light is absorbed for photosynthesis (less efficiently than blue and red light), a large portion of the green light is reflected or transmitted by the leaf. The red region (600-700 nm) has a low photon flux density again, indicating that chlorophyll a / b have another very strong absorption peak in the red region (especially around 660 nm) for photosynthesis. Most of the red light is captured by the leaf tissue for use. The red edge region (680-750 nm) has a sharp rise in photon flux density from the low value in the red region (forming a steep rising slope). This indicates that the absorption of chlorophyll in the red region saturates at 680 nm, and beyond this wavelength the absorption capacity rapidly decreases. At the same time, the scattering effect of the internal structure of the leaf (cell wall, air cavity) on near-infrared light begins to dominate. The near-infrared region (750-1100 nm) has a very high photon flux density, indicating that plant pigments (chlorophyll, carotenoids) have little absorption in this region. Light mainly interacts with the internal structure of the leaf (cell wall, intercellular space / air cavity), resulting in strong scattering (including reflection and transmission). The healthier and more complex the structure of the leaf (such as multiple layers of mesophyll cells and a large number of air cavities), the stronger the scattering (transmission + reflection) of near-infrared light.

[0114] Figure 4 The original spectrum of the net photosynthetic rate of maize leaves based on transmittance spectrum. From the figure, it can be observed that the spectral characteristics of maize leaves in the visible-near-infrared band are closely related to the efficient physiological mechanism of their C4 photosynthetic pathway. By analyzing the transmittance spectrum, the unique structure and biochemical composition of the maize leaf can be revealed.

[0115] The blue region (400-500 nm) has a very low photon flux density, indicating that chlorophyll a / b and carotenoids have strong absorption in this region (especially around 430-450 nm). Most of the blue light is captured by the leaf tissue for photosynthesis, and very little is transmitted. The green region (500-600 nm) has a relatively high photon flux density (forming a distinct "peak" in the graph), indicating that chlorophyll a / b have relatively weak absorption in the green region (they mainly absorb blue and red light). Although some of the green light is absorbed for photosynthesis (less efficiently than blue and red light), a large portion of the green light is reflected or transmitted by the leaf. The red region (600-700 nm) has a low photon flux density again, indicating that chlorophyll a / b have another very strong absorption peak in the red region (especially around 660 nm) for photosynthesis. Most of the red light is captured by the leaf tissue for use. The red edge region (680-750 nm) has a sharp rise in photon flux density from the low value in the red region (forming a steep rising slope). This indicates that the absorption of chlorophyll in the red region saturates at 680 nm, and beyond this wavelength the absorption capacity rapidly decreases. At the same time, the scattering effect of the internal structure of the leaf (cell wall, air cavity) on near-infrared light begins to dominate. The near-infrared region (750-1100 nm) has a very high photon flux density, indicating that plant pigments (chlorophyll, carotenoids) have little absorption in this region. Light mainly interacts with the internal structure of the leaf (cell wall, intercellular space / air cavity), resulting in strong scattering (including reflection and transmission). The healthier and more complex the structure of the leaf (such as multiple layers of mesophyll cells and a large number of air cavities), the stronger the scattering (transmission + reflection) of near-infrared light.

[0116] The green region (500-600 nm) shows a significant increase in the light quantum flux density, forming a clear "green peak". This is due to the more developed mesophyll sheath cell structure of the corn leaf, which enhances the transmission ability of non-photosynthetically active bands (green light). However, the peak is relatively flat, reflecting its higher chlorophyll density.

[0117] The red region (600-700 nm) shows a decrease in the light quantum flux density again, especially at 660 nm, where a steep depression occurs. This is related to the high-efficiency photosystem II reaction center of corn - C4 plants maintain the energy balance of the Calvin cycle and C4 pathway through stronger red light capture. The light quantum flux density in the red region of corn is slightly higher than that in the blue region, but significantly lower than that in the green region.

[0118] The red edge region (680-750 nm) shows a sharp increase in the light quantum flux density, forming a steep slope. After the chlorophyll absorption saturates at 680 nm, it quickly weakens, and near-infrared scattering effects dominate. Figure 1 It can be seen that the red edge slope of corn is steeper than that of strawberry, which may reflect its higher chlorophyll density or more compact cell arrangement. At the same time, the red edge position (≈720 nm) is red-shifted compared to strawberry (≈700 nm). This feature is due to the thicker palisade tissue and higher chlorophyll a / b ratio of corn leaves, causing the absorption saturation point to shift towards the long wave direction.

[0119] The near-infrared region (750-1100 nm) maintains a high light quantum flux density with gentle fluctuations. Plant pigments have weak absorption in this waveband, and light is scattered by the internal structure of the leaf (cell wall, air cavity). In the 900-980 nm water-sensitive waveband, transmission decreases. This is because corn, as a monocotyledonous plant, has a parallel vein structure and a large number of silicified cells, which increase the light scattering path, making near-infrared light more fully contact the internal water of the leaf.

[0120] S2, the original transmission spectrum is preprocessed by Savitzky-Golay smoothing, the specific process includes:

[0121] First, the parameters are initialized, the window width is set to 21 nm, and the polynomial fitting order is determined to be 2 order, the formula is:

[0122] ,

[0123] where, is the wavelength, is the smoothed value of the wavelength , the window radius is , , is the Savitzky-Golay convolution coefficient; is the index value within the window, ; The original transmittance spectrum values at the wavelength points ;

[0124] Then move the window along the 400-1100 nm spectral range with a step of 1 nm, extract the 21 original transmittance spectrum values within the window, and construct the Vandermonde matrix :

[0125] ,

[0126] Then, solve the polynomial coefficients by least squares method:

[0127] ,

[0128] wherein is the transpose matrix of the Vandermonde matrix , and is a vector composed of all the original transmittance spectrum values within the window;

[0129] Then, calculate the center point convolution coefficient when , , and output the smoothed value ;

[0130] Finally, use an asymmetric window at the start / end wavelength points, use a right-extended window for the first 10 points within the wavelength range of 400-409 nm, and use a left-extended window for the last 10 points within the wavelength range of 1091-1100 nm, and keep the fitting consistency by dynamically adjusting the Vandermonde matrix dimension.

[0131] Figure 5 and Figure 6 are the Savitzky-Golay smoothed strawberry and corn transmittance spectrum graphs. The purpose of Savitzky-Golay smoothing is to remove random noise in the original spectrum data caused by measuring instruments, environmental interference or small differences in samples, while removing noise, the original shape and characteristics of the spectrum (such as absorption valleys, reflection peaks, and red edge steep slopes) are preserved as much as possible, especially important biological characteristics (such as chlorophyll absorption bands and red edge positions), making subsequent spectral analysis (such as feature extraction, modeling, and classification) more reliable and accurate. The smoothed spectrum curve is smoother than the original data, but the key features are more clear and identifiable.

[0132] S3, remove outliers using the 3σ criterion. The core is to identify and replace outliers in the spectral data, and the specific process includes:

[0133] Let the spectral data matrix be​ ,in For the sample size, For the first The value of a sample at the q-th wavelength, for each wavelength First, calculate the mean. with standard deviation :

[0134] ,

[0135] Then, determine whether it is an outlier. An outlier is defined as a deviation from the mean by more than 3 standard deviations.

[0136] like This is an outlier.

[0137] Finally, the outlier was replaced with the median of the remaining non-outlier values ​​for that wavelength. :

[0138] ,

[0139] in, Indicates the first The sample at the th Values ​​at each wavelength Indicates the first The sample at the th The values ​​at each wavelength, among which Refers to all samples in general.

[0140] S4. Employ multivariate scattering correction (MSC) to eliminate the influence of blade physical structure on the spectrum. The specific process includes:

[0141] For the The original spectral vector of each sample The mean spectrum of all samples is used as the reference spectrum. Perform linear regression:

[0142] ,

[0143] in For the intercept term, For the slope term, For residuals;

[0144] Solving using the least squares method yields:

[0145] ,

[0146] The corrected spectrum is:

[0147] .

[0148] Figure 7 and Figure 8 The transmittance spectra of strawberry and corn leaves after multiplicative scatter correction (MSC). The core goal of MSC is to eliminate the light scattering interference caused by the differences in leaf physical structure (such as thickness, surface roughness, cell arrangement), so as to extract purer chemical component information (such as chlorophyll, water content). The negative values on the vertical axis are due to the fact that the values after MSC correction no longer have the physical meaning of the original transmittance light (i.e. the actual number of photons penetrating the leaf). It is a relative value after mathematical transformation, mainly used to highlight the chemical absorption characteristics and for inter-sample comparison, representing that the absorption of this sample at this wavelength point is relatively stronger than the average level.

[0149] S5, adopt standard normal variable transformation (SNV) to eliminate baseline drift, the specific process includes: for each sample spectrum X i independent processing:

[0150] ,

[0151] wherein, is the mean value of the i-th sample at all wavelengths, is the standard deviation of the i-th sample, is the SNV processed value of the i-th sample at the j-th wavelength.

[0152] Figure 9 and Figure 10 The transmittance spectra of strawberry and corn leaves after standard normal variable transformation (SNV) processing. The core goal of SNV is to eliminate the baseline drift and amplitude variation caused by the differences in leaf physical structure (such as thickness, surface scattering), so that the spectral data is more focused on the chemical absorption characteristics. As can be seen, the "baseline" of all sample spectra is flattened to around 0, eliminating the overall transmittance level difference caused by thickness and scattering; the "amplitude of fluctuation" of all sample spectra is normalized, eliminating the spectral intensity scaling caused by the difference in scattering efficiency; the shapes of absorption valleys (such as chlorophyll in the blue / red light region, water in the near-infrared region) and reflection peaks (such as the green light region) are clearer and more comparable. The positive value on the vertical axis indicates that the absorption at this wavelength point is relatively weak (the transmittance is relatively high) compared to its own mean value, and the negative value indicates that the absorption is relatively strong (the transmittance is relatively low).

[0153] S6, select characteristic wavelengths using the successive projections algorithm (SPA). SPA algorithm is a method for selecting characteristic wavelengths of high-dimensional data, the core idea of which is to select wavelengths with large information content and low collinearity through iteration to optimize the performance of the prediction model. The specific process includes:

[0154] First, select the wavelength with the strongest correlation with leaf net photosynthetic rate y:​​​

[0155] ,

[0156] Then, the remaining wavelengths The information amount of the projection is calculated:

[0157] ,

[0158] where, is the vector composed of the spectral data of all samples at the same wavelength point , and is the spectral matrix composed of the selected wavelengths;

[0159] Then, the information amount of the projection vector is calculated:

[0160] ,

[0161] Then, the wavelength that maximizes the information amount is selected:

[0162] ,

[0163] where, is the candidate wavelength set, ;

[0164] The termination condition is that the maximum number of wavelengths is reached, , and the information amount tends to be saturated, .

[0165] Figure 11 and Figure 12 are the feature wavelengths and their distribution selected by the SPA algorithm. The two figures show that 50 wavelengths with the most information amount are selected from high-dimensional spectral data based on the successive projections algorithm (SPA) for strawberry leaves and corn leaves. The blue curve is the average spectral curve, representing the average transmittance spectral characteristics of all 180 samples; the red dots are the selected wavelength markers, a total of 50 markers, distributed in the key spectral region. Each point represents a feature wavelength selected by the SPA algorithm, and the dense area represents the key wavelength band with large information amount, and the sparse area represents the wavelength band with large information redundancy or noise.

[0166] S7, using the random forest method (RF), a plant leaf net photosynthetic rate inversion model is established based on the transmittance spectrum, and the specific process includes:

[0167] First, input the data, the feature matrix is the wavelength subset selected by the SPA, d is the number of features, n is the number of samples, the target vector is the measured value of the net photosynthetic rate, is the measured value of the net photosynthetic rate of the first sample, This is the measured net photosynthetic rate of the nth (i.e., the last) sample;

[0168] Then, the Kennard-Stone algorithm is used to divide the training and test sets for the sample set. Calculate the distance matrix:

[0169] ,

[0170] in, For balance coefficient, For the first The feature vector of the i-th sample represents the i-th... Each sample was screened by SPA. Spectral measurements at each characteristic wavelength For the first Measured net photosynthetic rate of each sample;

[0171] Then, initial points are selected, choosing the two samples that are furthest apart in the full sample space as the starting point for the training set:

[0172] ,

[0173] Sample and Add to training set Then iteratively expand:

[0174] ,

[0175] in, Selected for inclusion in the training set in the current round The index of the samples, For the sample With sample The mixed distance between them For those not yet selected into the training set The index of the candidate samples. For those already existing in the training set The index of a sample in the database. , For the entire sample set, For the already constructed training set, Exclude the training set from the total sample set, i.e., the remaining samples;

[0176] Then, the test set is constructed:

[0177] ,

[0178] The node splitting criterion for the SPA-RF model is as follows:

[0179] ,

[0180] in, It is a characteristic of splitting. The optimal splitting feature is... The splitting threshold, To determine the optimal splitting threshold, The sample set for the current node. The net photosynthetic rate of the current node sample ( The variance of ) left child node The variance of the measured net photosynthetic rate for all samples. right child node The variance of the measured net photosynthetic rate for all samples. and Node samples by features and threshold Divided into left and right subsets;

[0181] The ensemble prediction output formula is:

[0182] ,

[0183] The random forest consists of 500 decision trees, each tree supporting a sample. There is a predicted value , This refers to the index of the decision tree in the random forest, and the final predicted value. It is the average of the predicted values ​​for 500 trees.

[0184] S8. Use the training set coefficient of determination. Root mean square error (RMSEC) of the training set, and coefficient of determination of the test set. The root mean square error (RMSEP) of the test set is used to evaluate the predictive performance of the established estimation model. Wherein:

[0185] The formula for calculating the coefficient of determination of the training set is:

[0186] ,

[0187] in, For training set samples The measured net photosynthetic rate, For the model to train samples The predicted value, This is the average net photosynthetic rate of all samples in the training set;

[0188] The formula for calculating the coefficient of determination for the test set is:

[0189] ,

[0190] wherein, represents the test set, is the true value of the net photosynthetic rate of the sample in the test set, is the predicted value of the sample in the test set, is the average value of the true values of all samples in the test set;

[0191] The root mean square error calculation formula of the training set is:

[0192] ,

[0193] The root mean square error calculation formula of the test set is:

[0194] ,

[0195] Figure 13 and Figure 14 The SPA-RF model (a combination model based on the successive projection algorithm and random forest) shows the prediction performance evaluation results of the photosynthetic rate of strawberry and corn leaves. The horizontal axis represents the actual value, and the vertical axis represents the predicted value. The distribution of data points shows the correspondence between the predicted value and the true value of the model. The data points on the scatter plot are closely distributed near the ideal prediction line (diagonal line), indicating that the predicted value of the model is highly consistent with the actual value. After calculation, the determination coefficient of the training set is 0.9254 and 0.9856, respectively, which is close to 1, indicating that the fitting degree of the model to the training data is excellent. The model can explain 92.54% and 98.56% of the photosynthetic rate variation in the training data. The root mean square error of the training set is 1.0038 and 1.7593, respectively, representing the average error between the predicted value and the true value of the model on the training data. The determination coefficient of the test set is 0.8781 and 0.976, indicating that the model still has very good prediction ability and generalization ability on new data (test set) that has not been seen before. The model can explain 87.81% and 97.6% of the photosynthetic rate variation in the test data. The root mean square error of the test set is 0.7212 and 1.3123, representing the average error between the predicted value and the true value of the model on the test data. It is worth noting that the RMSEP (0.7212) of the strawberry model is lower than the RMSEC (1.0038), and the RMSEP (1.3123) of the corn model is also lower than the RMSEC (1.7936). This means that the prediction error of the model on unknown data is even slightly smaller than on training data, indicating that the model has not overfit the training data and has excellent generalization performance.

[0196] The above-described embodiments are merely specific implementations of the present application, and are used to illustrate the technical solutions of the present application, rather than limit the same. The protection scope of the present application is not limited thereto. Although the present application is described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any person skilled in the art can make modifications or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to part of the technical solutions within the technical scope disclosed by the present application. The modifications, changes or replacements do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application. All should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for dynamic inversion of leaf net photosynthetic rate based on transmittance spectra, characterized in that, The method comprises the following steps: S1, selecting healthy plant leaves as samples, using gas exchange method to accurately measure the net photosynthetic rate of the target leaves, and simultaneously using a spectrometer to measure the transmission spectrum of the plant leaves, so as to obtain a data pair of the plant leaf sample; the plant leaves include C3 plant leaves and C4 plant leaves; S2, performing spectral data preprocessing on the original transmission spectrum by using Savitzky-Golay smoothing; S3, removing abnormal values by using a 3-standard-deviation method; S4, eliminating the influence of the physical structure of the plant leaves on the spectrum by using multivariate scatter correction; S5, eliminating baseline drift by using a standard normal variable transformation; S6, selecting characteristic wavelengths by using a continuous projection algorithm; S7, establishing a plant leaf net photosynthetic rate inversion model based on the transmission spectrum by using a random forest method; S8, coefficient of determination for training set , root mean square error for training set , coefficient of determination for test set and root mean square error for test set Evaluate the predictive performance of the established estimation model.

2. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, characterized in that, In step S1, when measuring the plant leaves, the left and right leaves of the same leaf of the same plant are selected, and the net photosynthetic rate is measured on one side and the transmission spectrum is measured on the other side.

3. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S1, the transmission spectrum of the plant leaves is measured by using a spectrometer, and the process comprises the following steps: First, the receiving end of the optical fiber is connected to the cosine corrector, then the cosine corrector is fixed below the leaf, and the distance between the leaf and the cosine corrector is kept unchanged during measurement; after deducting the machine noise, the transmission spectrum data of the leaf sample is collected, the measurement wavelength range is 400-1100 nm, and the step interval is 1 nm; 180 samples are randomly collected as test samples.

4. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S2, the original transmission spectrum is preprocessed by using Savitzky-Golay smoothing, and the process comprises the following steps: First, the parameters are initialized, the window width is set to 21 nm, and the polynomial fitting order is determined to be 2, and the formula is: ， wherein, is the wavelength, is the wavelength is the smoothed value, is the window radius, , is the Savitzky-Golay convolution coefficient; is the index value within the window, ; is the original transmission spectrum value at the wavelength point . The window is then moved in steps of 1 nm along the 400-1100 nm spectral range, and for each wavelength The 21 original transmission spectra within the extraction window are extracted A Van der Monde matrix is constructed : ， Then, the polynomial coefficients are solved by using the least square method: ， wherein is the Vandermonde matrix is the transpose matrix of the Vandermonde matrix, is a vector composed of all original transmission spectrum values within the window; Then, the center point convolution coefficient is calculated When , , the output smoothing value ; Finally, an asymmetric window is used at the starting / ending wavelength points, the first 10 points in the wavelength range of 400-409 nm use a right extension window, the last 10 points in the wavelength range of 1091-1100 nm use a left extension window, and the fitting consistency is maintained by dynamically adjusting the dimension of the Vandermonde matrix.

5. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S3, the process of removing abnormal values by using a 3-standard-deviation method comprises the following steps: Let the spectral data matrix be where is the number of samples, is the value of the th sample at the th wavelength, for each wavelength First, compute the mean and the standard deviation : ， Then, it is judged whether it is an abnormal value, and the abnormal value is defined as deviating from the mean value by more than 3 times the standard deviation: If Outlier Finally, the outliers are replaced by the median of the remaining non-outliers in that wavelength : ， wherein, denotes the value of the th sample at the th wavelength, denotes the value of the th sample at the th wavelength, wherein refers to all samples.

6. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S4, the process of using multivariate scatter correction comprises the following steps: For the first original spectrum vector of the sample, the mean spectrum of all samples as the reference spectrum , linear regression: ， wherein is an intercept term, is a slope term, is a residual; The least square method is used to solve: ， The corrected spectrum is: 。 7. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S5, the process of using a standard normal variable transformation comprises the following steps: For each sample spectrum Independent processing: ， wherein, is the mean value of the first sample over all wavelengths, is the standard deviation of the first sample, is the value of the first sample at the first wavelength after SNV.

8. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S6, the process of selecting characteristic wavelengths by using a continuous projection algorithm comprises the following steps: First, the wavelength with the strongest correlation with the leaf net photosynthetic rate y is selected: ， Then, the remaining wavelengths Calculate the amount of projection information: ， wherein, is a vector of spectral data for all samples at the same wavelength point, is a spectral matrix of selected wavelengths;​ Then, the information amount of the projection vector is calculated: ， Then, the wavelength with the maximum information amount is selected: ， wherein is a set of candidate wavelengths, ; The termination condition is that a preset maximum number of wavelengths is reached, , the information amount tends to be saturated, .

9. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S7, the plant leaf net photosynthetic rate inversion model is established based on the transmission spectrum by using a random forest method, and the process comprises the following steps: First input data, feature matrix for the wavelength subset of the SPA screening, for the number of features, for the number of samples, target vector for the measured value of net photosynthetic rate, for the measured value of net photosynthetic rate of the first sample, for the measured value of net photosynthetic rate of the n-th sample; Then Kennard-Stone algorithm is used to divide the training set and the test set. For the sample set , the distance matrix is calculated: ， in, For balance coefficient, For the first The feature vector of the i-th sample represents the i-th... Each sample was screened by SPA. Spectral measurements at each characteristic wavelength For the first Measured net photosynthetic rate of each sample; Then, the initial point selection is performed, and the two samples farthest from each other in the whole sample space are selected as the starting points of the training set: ， The samples are combined and The training set is augmented and then iteratively expanded: ， wherein, is the index of the sample selected into the training set in the current round, is the sample is the mixing distance between the sample is the index of the candidate sample not yet selected into the training set, is the index of a certain sample already existing in the training set, is the entire sample set, is the constructed training set, is the remaining sample excluding the training set, i.e. the total sample set.​​​​​ Then, the test set is constructed: ， The node splitting criterion of the SPA-RF model is: ， wherein, is a split feature, is an optimal split feature, is a split threshold, is an optimal split threshold, is a set of samples of a current node, is a variance of net photosynthetic rate (Pn) of all samples of a left child node of all samples of a right child node and is a variance of net photosynthetic rate (Pn) of all samples of a left child node of all samples of a right child node is a left subset of node samples split by feature​​ The integrated prediction output formula is: ， where the random forest consists of 500 decision trees, each tree is trained on a sample of 1000 patients There is a predicted value , is the index of the decision tree in the random forest, the final predicted value is the average of the 500 tree predicted values.

10. The method for estimating the net photosynthetic rate of a plant leaf based on dynamic inversion of transmittance spectra according to claim 1, wherein, In step S8, the calculation formula of the determination coefficient of the training set is: ， wherein, is the measured value of net photosynthetic rate for a sample in the training set, is the predicted value of net photosynthetic rate for a sample in the training set by the model, is the average value of net photosynthetic rate for all samples in the training set.​​ The calculation formula of the determination coefficient of the test set is: ， wherein, represents the test set, is the true value of the net photosynthetic rate of the sample in the test set, is the predicted value of the sample in the test set, is the average value of the true values of all samples in the test set; The calculation formula of the root mean square error of the training set is: ， The root mean square error (RMSE) of the test set is calculated as follows: 。

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