A Method for Determining the Optimal Temperature Control Range for the Entire Growth Stage of Greenhouse Peppers Based on Curvature Method

Abstract

This invention discloses a method for determining the optimal temperature control range for greenhouse peppers throughout their entire growth stage based on the curvature method. Through nested experiments, the photosynthetic rate of peppers at different growth stages under different environmental conditions is measured to construct a dataset. Environmental conditions include temperature, CO2 concentration, and photosynthetic photon flux density. Using growth stage, CO2 concentration, temperature, and photosynthetic photon flux density as input vectors, a backpropagation neural network optimized by a genetic algorithm is used to construct a photosynthetic rate prediction model, generating a corresponding photosynthetic rate response surface. The photosynthetic rate response surface is discretized into discrete points, and the Gaussian curvature at each point is calculated to construct a Gaussian curvature response surface. The Gaussian curvature response surface is then discretized into a temperature-Gaussian curvature response curve. Using the u-sine value as a metric, a random restart hill-climbing method is used to determine the critical boundary of the response curve, ultimately obtaining the optimal temperature control range.

Description

Technical Field

[0001] This invention belongs to the field of agricultural intelligent technology, and specifically relates to a method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method. Background Technology

[0002] In greenhouse production, extreme temperatures can damage crops, causing flower and fruit drop, and stunted growth. Traditional greenhouse temperature control primarily relies on fixed threshold methods or pursuing maximum photosynthetic rate (Pn) to ensure optimal yield. However, the former imposes strict temperature limits through thresholds, leading to delayed responses and a disconnect from the crop's physiological needs. The latter can temporarily increase productivity, but maintaining continuous peak Pn requires significant energy consumption, resulting in an imbalance between facility energy expenditure and growth benefits. This discrepancy underscores the urgent need to transition to dynamic range regulation strategies based on crop physiological feedback. Research indicates that dynamic changes in Pn, as a core metabolic process controlling crop growth stages, can accurately quantify the impact of temperature stress in real time, providing a feasible solution to the aforementioned challenges. Notably, recent studies have identified a resilient region for Pn regulation, where crop productivity remains stable when Pn decreases by approximately 20%. This finding provides a theoretical basis for the development of dynamic range control strategies.

[0003] Based on this elasticity theory, previous studies have confirmed its applicability in various regulatory scenarios, such as irrigation and supplemental lighting. Research results indicate that allowing Pn to vary within a moderate range not only ensures stable production but also significantly reduces the energy consumption of temperature regulation. Against this backdrop, a Pn prediction model is introduced as the basis for establishing dynamic temperature regulation standards. Accurately identifying the temperature inflection point in the photosynthesis model has become crucial for optimizing regulation efficiency and maximizing crop growth.

[0004] Recently, curvature theory has been widely used to find inflection points because it can describe the degree of curvature of a curve or surface at a specific point. Gao et al. constructed a Pn surface under the interaction of light and CO2 and used the u-string length algorithm to calculate the maximum curvature point of the discrete curve. This method can explore target inflection points synergistically controlled by light and CO2. However, although the u-string algorithm has robust anti-rotation and anti-noise properties, making it ideal for two-dimensional feature point calculation, it cannot fully capture three-dimensional morphology in space. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method, so as to more accurately divide the temperature control range for multiple growth stages of crops.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method includes the following steps:

[0008] Step 1: Through nested experiments, the photosynthetic rate of peppers at different growth stages under different environmental conditions is measured to construct a dataset; the environmental conditions include temperature, CO2 concentration, and photosynthetic photon flux density.

[0009] Step 2: Using the growth stage, CO2 concentration, temperature and photosynthetic photon flux density as input vectors, a backpropagation neural network optimized by a genetic algorithm is used to construct a photosynthetic rate prediction model and generate the corresponding photosynthetic rate response surface.

[0010] Step 3: Discretize the photosynthetic rate response surface into discrete points, calculate the Gaussian curvature at each point, and construct a Gaussian curvature response surface;

[0011] Step 4: Discretize the Gaussian curvature response surface into a temperature-Gaussian curvature response curve, use the u-sine value as a metric, and use the random restart hill-climbing method to determine the critical boundary of the response curve to obtain the optimal temperature control range.

[0012] In one embodiment, the growth stages include the seedling stage, flowering stage, pre-fruiting stage, mid-fruiting stage, and post-fruiting stage, and the different environmental conditions are set by setting several temperature gradients, several photosynthetic photon flux density gradients, and several CO2 concentration gradients.

[0013] In one embodiment, the data obtained through nested experiments is normalized using the following formula:

[0014]

[0015] Where, x i ′ represents normalized data, x i For the measured data under the i-th environmental condition, The minimum value of the measured data. This represents the maximum value of the measured data.

[0016] In one embodiment, the backpropagation neural network has a three-layer feedforward structure, including an input layer, a single hidden layer, and an output layer. The model is trained using the backpropagation method with mean squared error as the loss function. The calculation process is as follows:

[0017]

[0018] Where f(X) is the predicted photosynthetic rate, w ij w represents the weights between the hidden layer and the input layer. jkb represents the weights between the hidden layer and the output layer. j b is the threshold between the hidden layer and the input layer. k is the threshold between the hidden layer and the output layer, k is the number of input variables, n is the amount of data, h(·) is the Sigmoid activation function, which compresses the output to the [0,1] interval, and g(·) is the ReLU transfer function. It is the t-th feature under the i-th environmental condition, where t = 1, 2, 3, 4, representing the growth stage, CO2 concentration, temperature, and photosynthetic photon flux density, respectively.

[0019] In one embodiment, the input layer has 4 nodes, corresponding to four input variables: growth stage, CO2 concentration, temperature, and photosynthetic photon flux density, respectively; the hidden layer has 10 nodes; and the output layer has 1 node, outputting the predicted value of photosynthetic rate.

[0020] In one embodiment, step 2 involves constructing a photosynthetic rate response surface using photosynthetic photon flux density and temperature as x and y coordinates, respectively; step 3 involves normalizing the photosynthetic photon flux density, temperature, and photosynthetic rate to resolve significant amplitude differences between the parameters.

[0021] In one embodiment, in step 3, a discrete point of the photosynthetic rate response surface is arbitrarily selected as point P. Point P has four adjacent base points, corresponding to the positions of its adjacent surfaces. The geometric configuration approximates point P as infinitesimally close to the base surfaces, and point P and its four surrounding base points form adjacent triangles, as shown in the following formula:

[0022]

[0023]

[0024] In the formula, N is the number of triangles formed by point P and its adjacent base points, A is the sum of the areas of all triangles, and points P and V are used as the base points. i and point v i+1 Taking the triangle formed as an example, θ i Let l represent the vertex angle of the i-th triangle, and let l be the side length of the triangle. i l i+1 and k i , s = (l i +l i+1 +k i ) / 2 represents the semi-perimeter of the triangle intersecting point P; if the local surface area around point P is flat, that is, point P intersects point v i and point v i+1 If they are coplanar, the Gaussian curvature is 0. After obtaining the Gaussian curvature, the Gaussian curvature response surface is visualized with the photosynthetic photon flux density as the x-axis, the temperature as the y-axis, and the Gaussian curvature as the z-axis.

[0025] In one embodiment, step 4 involves introducing an incrementally instantiated Gaussian curvature response surface into the photosynthetic photon flux density to obtain temperature-Gaussian curvature response curves under different light intensities. The input of the temperature-Gaussian curvature response curve is temperature, and the output is curvature value. Subsequently, the input and output are normalized to eliminate magnitude differences, and any point on the temperature-Gaussian curvature response curve is set as M. i Calculate its u-chord value.

[0026] In one embodiment, by relative to point M i Two adjacent points M are generated by symmetrical and equidistant translation along the coordinate axes. j and M k The two adjacent points and M i While maintaining the Euclidean distance u, the following geometric constraints are satisfied:

[0027]

[0028] In the formula, u is the topological distance, 0 <u<1;

[0029] Calculate M i Support areas [M] j M k The cosine value related to the angle between the inner and outer arm vectors is used to measure the magnitude of the u-sine value. At this point, point M... i The chord value of u is calculated as follows:

[0030]

[0031] Among them, s i =sign[(x i -x k )(y j -y k )-(x j -x k )(y i -y k )] is used to determine the sign of the sine value, (x i ,y i ),(x j ,y j ),(x k ,y k ) represent points M respectively i M j M k The coordinates.

[0032] In one embodiment, a random restart hill-climbing method is used to obtain the upper and lower boundary points of a suitable temperature control target. These points are then mapped to the response surface of the photosynthetic rate prediction model to obtain the corresponding temperature control range. The formulas for obtaining the upper and lower boundary points are as follows:

[0033]

[0034] Among them, c i and c j Let u_sine values ​​be the upper and lower boundary points of the Gaussian response curve, respectively. and c i Any point on the left or right side of , and c j Any point on the left or right side of .

[0035] Compared with existing technologies, this invention, based on curvature theory, aims to determine the optimal temperature control range for different growth stages of greenhouse peppers. First, a four-factor nested experiment was conducted to study the effects of different temperatures, CO2 concentrations, and photosynthetic photon flux densities on the photosynthetic rate (Pn) of peppers at different growth stages. Subsequently, a photosynthetic rate prediction model was constructed using a backpropagation neural network optimized by a genetic algorithm. This model exhibits high accuracy and reliability, with R... 2 The value was 0.9812, and the MSE was 1.35 μmol·m⁻¹. -2 ·s -1 Then, the prediction model was discretized and applied to the calculation of the Gaussian curvature response surface of Pn. Finally, the boundary of the temperature regulation range was precisely defined using the u-chord length algorithm and the random restart hill-climbing method. Practical verification showed that the average dry weight of the pepper fruits in the experimental group was 96.83% higher than that of the no-regulation group and 243.65% higher than that of the fixed threshold group. This result fully demonstrates that the method not only promotes the growth of peppers but also exhibits good regulatory tolerance. The temperature regulation strategy of this invention provides key technical support and reliable decision-making basis for the precise environmental management of greenhouse crops in facility agriculture. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the measurement process of Pn in this invention.

[0037] Figure 2 This is the flowchart of the GA-optimized BPNN of the present invention.

[0038] Figure 3 This is a flowchart of the Gaussian curvature calculation process of the present invention.

[0039] Figure 4 This is a schematic diagram of the U-chord curvature calculation of the present invention.

[0040] Figure 5 The present invention simulates the temperature and PPFD change curves of a greenhouse, where (a) is the temperature change curve and (b) is the PPFD change curve.

[0041] Figure 6 This is the light response curve of the present invention, where (a) represents the CO2 concentration of 300 μmol·mol⁻¹. -1 (b) shows a CO2 concentration of 900 μmol·mol⁻¹ -1 .

[0042] Figure 7 This is the photosynthetic response surface of the present invention, wherein (a) represents a CO2 concentration of 600 μmol·mol⁻¹. -1 The flowering period, (b) is when the CO2 concentration is 900 μmol·mol⁻¹. -1 The early stage of fruit production.

[0043] Figure 8 This invention relates to the Gaussian curvature response surface and its thermogram.

[0044] Figure 9 This is the result of the greenhouse temperature control range of the present invention.

[0045] Figure 10 The results of the comparison and significance analysis of chili biomass under different control strategies of the present invention are shown, where (a) is plant height, (b) is stem diameter, (c) is fresh weight, (d) is dry weight, (e) is canopy leaf area, and (f) is seedling vigor index.

[0046] Figure 11 This invention compares the number of days from the two-leaf-one-cotyledon stage to flowering and fruiting of chili peppers under three control strategies, where (a) is the average daily flowering, (b) is the average daily fruiting, (c) is the average number of flowers, (d) is the average number of fruits, (e) is the average fresh weight of fruits, and (f) is the average dry weight of fruits. Detailed Implementation

[0047] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0048] In greenhouse agriculture, extreme temperatures can cause irreversible damage to crops, making temperature regulation a crucial component of greenhouse environmental management. Dynamic optimization of the temperature range is a core strategy for improving production stability. Therefore, determining the optimal temperature range is essential for maximizing greenhouse production efficiency.

[0049] To address this problem, this invention, using chili peppers as a sample, employs Gaussian curvature and u-chord length algorithms to provide a curvature-based method for determining the optimal temperature control range for the entire growth stage of greenhouse chili peppers. This method uses growth stage, CO2 concentration, temperature, and PPFD as input variables, employs a genetic algorithm-optimized backpropagation neural network (GA-BPNN) to construct a Pn prediction model and generate a corresponding Pn response surface. Subsequently, the Gaussian curvature of the Pn response surface is calculated to construct a Gaussian curvature response surface, comprehensively reflecting the changing trend of the Pn response surface. Finally, the Gaussian curvature response surface is discretized into temperature-Gaussian curvature (TG) response curves, using the u-chord length as a metric, and a random restart hill-climbing method is used to determine the critical boundaries of the response curves. This analysis process systematically identifies these boundary points and determines the optimal environmental regulation target range. This method comprehensively considers the interaction of multiple environmental factors, studies the suitable temperature ranges for multiple growth stages of chili peppers, and provides a reliable basis for temperature control in facility agriculture.

[0050] In an embodiment of this invention, the "Zhenyan" chili pepper was selected as a sample. A nested experiment was conducted from August 16th to October 4th, 2023, at the Key Laboratory of Agricultural Internet of Things, Ministry of Agriculture and Rural Affairs, Northwest A&F University, to measure the photosynthetic rate of the chili pepper at different growth stages under different environmental conditions and to construct a dataset. The experimental samples germinated and grew in 72-well seed trays. When they reached the stage of two leaves and one bud, they were transplanted into seedling cups with a diameter of 20cm and a height of 16cm, and continued to be cultivated in an RGL-P500D-CO2 climate chamber (Dascat, Hefei, China). The incubator was set with a 12-hour daytime period at 25℃ and a 12-hour nighttime period at 20℃. The humidity was 50% throughout the day, and the CO2 concentration was 400 μmol·mol⁻¹. -1 One week after the seedlings have established themselves, the phosphorus content (Pn) of peppers under various environmental factors throughout their entire growth period was measured using a Li-6800 portable plant photosynthesis meter (LI-COR, USA). During measurement, the pepper leaves were tightly clamped within the leaf chamber of the Li-6800 meter. Figure 1 As shown in Table 1, this invention measures light intensity using photosynthetic photon flux density. Data were collected from five stages: seedling stage, flowering stage, pre-fruiting stage, mid-fruiting stage, and post-fruiting stage. Five temperature gradients, ten photosynthetic photon flux density gradients, and four CO2 concentration gradients were set, resulting in a total of 1000 sets of data (5×5×10×4=1000).

[0051] By comprehensively controlling temperature, light intensity (PPFD), and CO2 concentration during consecutive key growth stages (seedling stage, flowering stage, pre-fruiting stage, mid-fruiting stage, and post-fruiting stage) of the same batch of plants, a multidimensional environmental physiological response dataset containing 1000 data points (5×5×10×4=1000) was generated through active construction, as detailed in Table 1. This continuous cross-cycle nested combination experiment of environmental factors improved data acquisition efficiency and effectively reproduced the complex and dynamic environmental interactions that crops may encounter throughout their entire life cycle. Therefore, it directly supports the engineering requirements for greenhouse environmental regulation.

[0052] Table 1 Environment Variable Settings

[0053] Environmental factors Variable value Temperature (°C) 20,24,28,32,36 <![CDATA[PPFD(μmol·m -2 ·s -1 )]]> 0,50,100,200,300,600,900,1200,1500,1800 <![CDATA[CO2 concentration (μmol·mol -1 )]]> 300,600,900,1200 <![CDATA[CO2 concentration(μmol·mol -1 )]]> 300,600,900,1200

[0054] Step 2, Model Building.

[0055] Using growth stage, CO2 concentration, temperature and photosynthetic photon flux density as input vectors and photosynthetic rate as output vector, a dataset is constructed as shown in formula (1).

[0056] {(X1,Y1),(X2,Y2)…,(X n ,Y n )}(1)

[0057] in, and Y represents the CO2 concentration, time period, temperature, and photosynthetic photon flux density of the i-th sample, respectively; i =[y i ] represents the measured photosynthetic rate of the i-th sample.

[0058] To avoid significant biases caused by differences in units and magnitudes among growth stages, CO2 concentration, temperature, photosynthetic photon flux density, and photosynthetic rate, and to improve the model's convergence speed and performance, this invention employs a normalized data preprocessing method to transform these environmental variables and photosynthetic rate to a uniform scale, mapping them to the interval [0.2, 0.8], as shown in Equation (2). Finally, the data is randomly divided into a training set and a test set in a 7:3 ratio. The training set is used to train the photosynthetic rate model, and the test set is used to evaluate the model's generalization ability.

[0059]

[0060] Where, x i ′ represents normalized data, x i For the measured data under the i-th environmental condition, The minimum value of the measured data. This represents the maximum value of the measured data.

[0061] Backpropagation Neural Networks (BPNNs) continuously refine the weights and thresholds of their network through a backpropagation mechanism, thereby achieving regression prediction of a dataset. Because of their intuitive structure and ability to effectively capture complex effects, this invention employs a genetic algorithm-optimized backpropagation neural network to construct a photosynthetic rate prediction model. To comprehensively evaluate the performance of BPNNs in Pn prediction, a comparative analysis was also conducted with Support Vector Regression (SVR) and Multinomial Regression (PR), both commonly used methods in Pn prediction.

[0062] The BPNN has a three-layer feedforward structure, including an input layer (4 nodes, corresponding to the four input variables: growth stage, CO2 concentration, temperature, and photosynthetic photon flux density), a single hidden layer (10 nodes), and an output layer (1 node, outputting the predicted photosynthetic rate). The model is trained using backpropagation with mean squared error (MSE) as the loss function. The learning rate is set to 0.01, and training continues for 1000 iterations or until convergence. The specific calculation process is shown in equation (3):

[0063]

[0064] Where f(X) is the predicted photosynthetic rate, w ij w represents the weights between the hidden layer and the input layer. jk b represents the weights between the hidden layer and the output layer. j b is the threshold between the hidden layer and the input layer. k is the threshold between the hidden layer and the output layer, k is the number of input variables, n is the amount of data, h(·) is the Sigmoid activation function, which compresses the output to the [0,1] interval, and g(·) is the ReLU transfer function. It is the t-th feature under the i-th environmental condition, where t = 1, 2, 3, 4, representing the growth stage, CO2 concentration, temperature, and photosynthetic photon flux density, respectively.

[0065] SVR and PR are used as comparison models with BPNN to evaluate the system's performance. SVR uses kernel functions to handle nonlinear relationships, transforming low-dimensional nonlinear problems into high-dimensional linear spaces. This model uses radial basis function (RBF) kernels for Pn prediction and optimizes hyperparameters using a grid search method. PR uses a four-variable fourth-order polynomial regression. This model simplifies complexity by treating the highest-order term of temperature as the primary influence and incorporating the interactions of temperature factors.

[0066] To enhance the robustness and convergence efficiency of the model, a genetic algorithm can be used for parameter tuning. The parameters to be optimized include the initial weights and threshold of the BPNN, the penalty parameter c and kernel function parameter g of the SVR, and the coefficient a of the PR. i Taking the optimization process of BPNN as an example, its flow is as follows: Figure 2 As shown. The genetic algorithm defines the population size S = 100, the number of generations G = 50, and the crossover probability P. x =0.5, mutation probability P c =0.2, M=3 mutated genes per chromosome.

[0067] To measure model performance and training effectiveness, root mean square error (RMSE), maximum absolute error (MAE), and coefficient of determination (R²) are used. 2 The performance of the model is evaluated using evaluation indicators such as (4)-(6):

[0068]

[0069] MAE = max{|Y i -f(X i )|},i=1,2,...,n (5)

[0070]

[0071] Where n is the number of data points, and f(·) is the photosynthetic rate predicted by the model.

[0072] Since photosynthesis plays a crucial role in crop biomass accumulation, excessively high or low temperatures can negatively impact crop yield. To determine the optimal growth temperature for chili peppers at different growth stages, a Gaussian curvature model was used to calculate the curvature changes of the corresponding Pn response surface. This method significantly enhances the fault tolerance and stability of dynamic environmental regulation, enabling a deeper identification of robust trends in the Pn response to environmental changes, thereby determining the optimal temperature range for crop growth.

[0073] Pn response surfaces were constructed using PPFD and temperature as the x and y coordinates, respectively. These surfaces integrate the effects of multiple factors such as temperature, PPFD, CO2 concentration, and growth stage on Pn, revealing the variation patterns of Pn and providing guidance for determining a suitable target temperature range. Gaussian curvature is mainly used to describe the degree of curvature or shape characteristics of a point on a surface. The higher the value, the greater the curvature of the surface; the lower the value, the flatter the surface. Therefore, this invention utilizes Gaussian curvature to explore the curvature changes of the Pn response surface, laying the foundation for determining the target temperature range.

[0074] Step 3: Construct the Gaussian curvature response surface.

[0075] The Gaussian curvature of the Pn response surface is determined by discretizing the Pn response surface into discrete points and calculating the Gaussian curvature at each point. Based on the experimental design range, the temperature discretization range is 20-36℃, the distance traveled is set to 0.1℃, and the discretization set is T={t i},t i=20+0.1i, i=0,1,2,…,160. Since the light compensation point of chili peppers is generally between 50-100 μmol·m⁻¹ -2 ·s -1 Therefore, the dispersion range of PPFD is set to 100-1800 μmol·m. -2 ·s -1 The step size is 10 μmol·m -2 ·s -1 The discrete set is P = {P} j}, where P j =100+10j, j=0,1,2,…,170. Through this discretization process, a total of 27,531 discrete points are generated for each Pn response surface.

[0076] The three-dimensional data of photosynthetic photon flux density, temperature, and photosynthetic rate are normalized to address significant amplitude differences between parameters. This preprocessing improves the stability of curvature calculations. Then, the Gaussian curvature at each point is calculated to construct a Gaussian curvature response surface. For computational analysis, a discrete point on the photosynthetic rate response surface is arbitrarily chosen as point P. Point P has four adjacent base points, corresponding to the positions of its adjacent surfaces. The geometric configuration approximates point P as infinitesimally close to the base surfaces, and point P and its four surrounding base points form adjacent triangles, as shown below. Figure 3 As shown. The Gaussian curvature K at point P is finally determined by the summation of angles and the calculation of triangular area using equations (7)-(9).

[0077]

[0078] In the formula, N is the number of triangles formed by point P and its adjacent base points, and A is the sum of the areas of all triangles. Let... Figure 3 The middle is composed of point P and point v i and point v i+1 The triangle formed, θ i Let l represent the vertex angle of the i-th triangle. The side length of this triangle is denoted as l. i l i+1 and k i , s = (l i +l i+1 +k i ) / 2 represents the semi-perimeter of the triangle intersecting point P; if the local surface area around point P is flat, that is, point P intersects point v i and point v i+1 If the surfaces are coplanar, then the Gaussian curvature is 0. When the Gaussian curvature is positive, the discrete surface resembles an ellipsoid. Conversely, if the Gaussian curvature is negative, the discrete surface is saddle-shaped.

[0079] After obtaining the Gaussian curvature, taking the photosynthetic photon flux density as the x-axis, the temperature as the y-axis, and the Gaussian curvature as the z-axis, visualization is carried out to obtain the Gaussian curvature response surface.

[0080] Step 4: Discretize the Gaussian curvature response surface into temperature-Gaussian curvature response curves. Taking the u chord value as the measure, use the random restart hill climbing method to determine the critical boundary of the response curve, and obtain the optimal temperature regulation interval.

[0081] The Gaussian curvature response surface can reveal the response law of Pn to temperature changes of chili peppers under different growth stages, CO2 concentrations and PPFD conditions. These general principles provide an important basis for determining the target regulation boundary. In order to accurately and intuitively identify the temperature regulation boundary, first, on the x-axis of the Gaussian curvature response surface, instantiate the Gaussian curvature response surface with a step size of 50 μmol·m -2 ·s -1 PPFD. Specifically, under different light intensity conditions (for example, when the PPFD is 50 μmol·m -2 ·s -1 , 100 μmol·m -2 ·s -1 , 150 μmol·m -2 ·s -1 etc.), obtain the curve relationship between temperature and Gaussian curvature, that is, the temperature-Gaussian curvature (T-G) response curve. The independent variable of the T-G response curve is temperature, and the dependent variable is the curvature value. Subsequently, use Equation (2) to normalize the independent variable and the dependent variable to eliminate the magnitude difference. According to the change law of the response curve, arbitrarily take a point on the T-G response curve and set it as M i . Based on point M i , generate two adjacent points M i and M j and M k by translating symmetrically along the coordinate axes relative to point M i . This translation operation is carried out in the two-dimensional coordinate system of the T-G response curve, ensuring that the Euclidean distances between points M j and M k and point M i remain u (topological distance, 0 < u < 1), and satisfy the geometric constraints of Equation (10) and Equation (11), as Figure 4 shown.

[0082] ||M j M i || = u (10)

[0083] ||M i M k || = u (11)

[0084] In the formula, u is the topological distance, 0 < u < 1.

[0085] Find M j and M k Two points are needed to obtain M. i Support areas [M] j M k ]. Calculate M i Support areas [M] j M k The cosine value related to the angle between the inner and outer arm vectors is used to measure the magnitude of the u-sine value. At point M... i The chord value of u is shown in equation (12):

[0086]

[0087] Among them, s i =sign[(x i -x k )(y j -y k )-(x j -x k )(y i -y k )] is used to determine the sign of the sine value, (x i ,y i ),(x j ,y j ),(x k ,y k ) represent points M respectively i M j M k The coordinates.

[0088] The u-sine value of the TG response curve quantifies the rate or extent of change of Gaussian curvature with temperature. It can serve as an important measure for obtaining boundary targets. A larger u-sine value indicates that the Gaussian curvature (i.e., the sensitivity of photosynthetic rate to temperature changes) changes more drastically near that temperature. Based on the u-sine value, reasonable upper and lower boundaries are selected on both sides of the peak of the TG response curve as the target range for temperature control. Figure 9 (a) illustrates the specific trend of the TG response curve. Due to the complex physiological phenomena of chili peppers, the curvature trends on both sides of the peak are different. To the left of the peak, the TG response curve shows a trend of first decreasing and then increasing. This reflects that during the temperature change process, the intensity of Pn's response to temperature changes increases significantly at a certain moment. Therefore, this point of drastic change is identified as the upper boundary. Corresponding to the u-sine value, its corresponding change is also first weakening and then increasing. Therefore, within this range, the minimum u-sine target value c is found. iThe upper boundary of the desired temperature range can then be obtained. To the right of the peak, the TG response curve gradually becomes stable, indicating that the trend of Pn with increasing temperature gradually weakens or even begins to decrease. Therefore, the critical point before the change of Pn with temperature weakens significantly is found as the lower boundary of the temperature. The corresponding change law of the u-sine value is that it first decreases, then increases, and then decreases again. The turning point of the u-sine value from increasing to decreasing can be found to determine the lower boundary of the temperature. Therefore, according to this law, the random restart hill climbing method is adopted, and the upper and lower boundary points of the suitable temperature control target are obtained according to the two strategies of equation (13) and (14). Finally, the obtained points are mapped to the response surface of the photosynthetic rate prediction model to obtain the corresponding temperature control range.

[0089]

[0090]

[0091] Among them, c i and c j Let u_sine values ​​be the upper and lower boundary points of the Gaussian response curve, respectively. and c i Any point on the left or right side of , and c j Any point on the left or right side of .

[0092] In this embodiment of the invention, from August 18 to October 18, 2024, a long-term cultivation verification experiment was completed using 'Zhenyan' pepper samples cultivated to the flowering stage as the research object, evaluating the effect of the optimal temperature range determined in this invention on pepper growth. Among the five growth stages of pepper, the seedling stage is a critical period for root development, leaf formation, and nutrient accumulation. It is highly sensitive to temperature, which directly affects their yield and quality. After entering the flowering stage, the focus of pepper growth shifts from vegetative growth to reproductive growth, resulting in a slower rate of branch and leaf expansion. Therefore, morphological and physiological phenotypes, including plant height, stem diameter, dry weight, fresh weight, leaf area, and seed vigor (Equation 15), were used to assess the growth of pepper seedlings. Furthermore, the number of flowers and fruits, the number of days required for flowering and fruiting, and the dry and fresh weight of the fruits were used as evaluation indicators for the flowering and fruiting stages.

[0093] The experiment consisted of one experimental group and two control groups. Using summer greenhouse data from the Jingyang Vegetable Experimental Demonstration Station of Northwest A&F University, an artificial climate chamber was used to simulate environmental changes. This simulated environment was designed based on real greenhouse data, ensuring the high representativeness of the scenarios in the validation experiment. Therefore, the results can directly provide information for the formulation of practical greenhouse control strategies. The control period was from 8:00 to 20:00. Temperature and PPFD were adjusted every 2 hours, while the average CO2 concentration of the first 15 minutes was used as the model input. This control frequency evaluated the model's ability to capture changes in the greenhouse environment while maintaining stability, representing a key method for addressing the inherent uncertainties in real-world environmental monitoring data. Figure 5 The environmental control conditions for the first 5 days are shown. The experimental group was conditioned towards the optimal temperature range as determined by the invention. A control group was cultured in a climate chamber, simulating... Figure 5 The greenhouse temperature fluctuations are shown in the diagram, while the control group was cultured at a fixed temperature of 25°C. All other environmental variables for all three groups remained consistent with those recorded at the time of data collection. Minitab 2022 software was used to analyze the above indicators.

[0094]

[0095] In the formula, S is the stem diameter, H is the plant height, RDW is the root dry weight, SDW is the stem dry weight, and TDW is the total dry weight.

[0096] Based on experimental data, the effects of temperature and environmental factors at different stages on Pn were explored and presented in the form of light response curves, such as... Figure 6 As shown in the figure. Comparative analysis reveals significant differences in the light response curves at different growth stages, with temperature being a key factor affecting photosynthetic characteristics. At low CO2 concentrations (300 μmol·mol⁻¹), the light response curves showed the best performance. -1 Under these conditions, the flowering period exhibited more aggregated light response curves than other flowering periods, and the Pn difference between adjacent temperature gradients (4℃) remained at 1 μmol·m⁻¹. -2 ·s -1 The following growth stages exhibit strong heat adaptability (20-32℃). However, during other growth stages, especially the seedling stage, the curve dispersion is 2.5 times higher than that during the flowering stage. When the temperature exceeds 32℃, PPFD ≥ 800 μmol·m -2 ·s -1 At that time, the average Pn during the seedling stage decreased by 83.24% compared to the condition at 28℃, indicating increased environmental sensitivity. When the CO2 concentration increased (900 μmol·mol⁻¹), the Pn concentration decreased further. -1 At this time, warming has a synergistic effect on photosynthetic capacity, manifested as an increase in Pn of 10-16 μmol·m -2 ·s -1The light response curve distribution widened. This CO2-temperature interaction significantly mitigated the co-inhibition of high temperature / intense light, especially during the seedling and mid-fruiting stages. Simultaneously, the plant's sensitivity to temperature increased, effectively buffering thermal fluctuations. These dynamically coordinated thermal responses establish a key framework for accurate modeling of photosynthetic mechanisms under climate change scenarios.

[0097] Pn at different growth stages was predicted using BPNN, SVR, and PR, along with their GA-optimized versions. The prediction performance of these models is based on RMSE, MAE, and R... 2 The evaluation was conducted, and the overall results are shown in Table 2. Among these methods, GA-BPNN demonstrated superior performance across all metrics, with R... 2 The highest value was 0.9812, while the lowest values ​​were 1.35 μmol·m⁻¹ and 1.35 μmol·m⁻¹, respectively. -2 ·s -1 and 0.89 μmol·m -2 ·s -1 GA-SVR performed second best, while PR performed the worst. Furthermore, the GA-BPNN model had a fitting slope of 0.9752, indicating that its predictions were closer to the ideal scenario (1:1 line). These results demonstrate that BPNN possesses robust nonlinear mapping capabilities and, after optimization using a genetic algorithm, can achieve high prediction accuracy. This provides a solid theoretical foundation for future research to determine the optimal growth temperature range.

[0098] Table 2 Comparison results of algorithm test set evaluation

[0099]

[0100] The above results demonstrate that, compared with other models, the BPNN model exhibits better performance in terms of prediction accuracy and applicability, making it more suitable for subsequent research on temperature regulation ranges. To visually illustrate the predictive performance of GA-BPNN, the Pn response surface is shown as follows: Figure 7 As shown. Figure 7 In (a) and (b), the CO2 concentration is 600 μmol·mol⁻¹, respectively. -1 And CO2 concentration of 900 μmol·mol -1 The prediction results of BPNN for flowering period and pre-fruiting period Pn.

[0101] Although the Pn trend varies across different stages and environmental conditions, it is noteworthy that Pn changes are often positively correlated with temperature changes. This indicates that within the maximum temperature (36°C) set in this invention, photosynthetic enzymes did not undergo denaturation or inactivation. However, as the temperature increases, the rate of increase in Pn gradually slows down, indicating that high temperatures inhibit photosynthesis in chili peppers. Therefore, in-depth exploration of the potential variation patterns of Pn at different growth stages of chili peppers is of great significance for rationally planning suitable temperature regulation ranges.

[0102] To comprehensively study the global response of chili pepper (Pn) to temperature changes, the Gaussian curvature of the Pn response surface was calculated, and a Gaussian curvature response surface model was constructed. The aim is to quantify and reflect the curvature characteristics of the Pn response surface, such as... Figure 8 As shown in the figure, this model can intuitively display the Gaussian response characteristics of the chili pepper Pn response surface under different conditions. Figure 8 The CO2 concentration is 600 μmol·mol -1 During the flowering period and with a CO2 concentration of 900 μmol·mol⁻¹ -1 Gaussian curvature response surface and its thermogram corresponding to the Pn response surface in the early real time period.

[0103] Figure 8 (a) shows the Gaussian response surfaces under different environments and periods. Both models show a high degree of similarity in shape in terms of temperature response. Figure 8 Quantitative analysis of the curvature parameters in (b) revealed that the interaction between temperature and PPFD significantly affects the morphology of the response surface. When PPFD is below approximately 800 μmol·m⁻¹, the morphology of the response surface is significantly affected. -2 ·s -1 At this point, the Gaussian curvature is negative (K<0), exhibiting a two-phase characteristic of first increasing and then decreasing with temperature, eventually stabilizing, and the response surface forms a concave surface. Combined with... Figure 8 Observational data show that within the PPFD range, in the temperature range of 20-36℃, temperature increase only leads to a slight increase in Pn, with an increase of no more than 5 μmol·m⁻¹. -2 ·s -1 However, the absolute value of curvature can reach over 0.20, indicating that temperature is not the main factor limiting Pn development at this point. The interaction between light intensity and temperature on Pn shows an antagonistic effect, making the chili pepper adaptable to a wider range of temperatures, which is consistent with the meaning of negative curvature.

[0104] Conversely, when PPFD is higher than 800 μmol·m -2 ·s -1As temperature increases, the Gaussian curvature gradually becomes positive (K>0), exhibiting the opposite trend to the aforementioned phenomenon, and the response surface becomes convex. Under these conditions, Pn grows faster with increasing temperature compared to low light intensity conditions. When light saturation is reached, temperature becomes the main limiting factor for Pn. The high-temperature inhibition effect aligns the light and temperature constraints, driving Pn growth in a convex acceleration mode. This change enhances the temperature sensitivity of peppers and narrows their adaptive temperature range. In greenhouse environments, high light intensity often occurs simultaneously with high temperature, making fixed threshold adjustment methods both inaccurate and costly. Balancing temperature regulation within the optimal range by slightly sacrificing Pn becomes a key priority in greenhouse management.

[0105] Notably, inflection points in pn temperature kinetics were observed in the ranges of 20–24 °C and 32–36 °C, which may be related to the phase transition temperature of photosynthetic enzyme kinetics. These inflection points elucidate the adaptation mechanism of pepper photosynthesis under different temperature conditions and are of great significance for understanding the temperature sensitivity of pepper growth. Therefore, determining the temperature regulation boundaries between 20–24 °C and 32–36 °C is crucial for optimizing temperature management in pepper cultivation greenhouses. This discovery lays a solid scientific foundation for advancing precision agriculture practices in controlled environments.

[0106] However, Gaussian curvature response surfaces have complex geometries, and points on the surface may exhibit different curvatures and orientations, making the identification and calculation of critical boundaries difficult and resource-intensive. Furthermore, while the Gaussian curvature method can effectively capture the global variation of Pn, noise present on this complex surface can interfere with the selection of feature points. This interference complicates the accurate depiction of temperature range boundaries, further affecting the precision of temperature regulation. Therefore, introducing the u-string algorithm, which excels in feature point selection, is particularly important. This integration reduces computational dimensionality, enabling a more accurate determination of the optimal temperature range for pepper growth, ultimately achieving more efficient and precise cultivation management.

[0107] To better reflect the prominent characteristics of the Gaussian curvature response surface and facilitate the exploration of critical boundaries, the Gaussian curvature response surface is transformed into multiple TG response curves. Then, based on actual planting conditions, the point with the largest rate of change to the left of the peak and the point with the smallest rate of change to the right are selected as the upper and lower boundaries of the optimal temperature regulation range, respectively. The peak value is the optimal regulation temperature. This method not only improves the accuracy of temperature management in solar greenhouses but also benefits crop growth and development. Based on this, the u-sine value is used as a metric to determine the upper and lower boundary points, and the results are as follows: Figure 9 As shown.

[0108] like Figure 9 As shown, at a CO2 concentration of 600 μmol·mol⁻¹ -1 The flowering period and CO2 concentration were 900 μmol·mol⁻¹-1 The optimal temperature range was obtained under 7 different PPFD levels in the early stage of fruit development. Figure 9 (a) shows the temperature range results of the TG response curves, indicating that the optimal growth temperature range for the crop varies at different growth stages and under different PPFD conditions. Generally, the optimal growth temperature range for peppers narrows with increasing PPFD. This is because strong light induces photoinhibition in the pepper's photosynthetic system, and the combined inhibitory effect of high temperature limits normal crop growth. Therefore, under strong light conditions, peppers exhibit greater sensitivity to temperature changes, resulting in a narrower optimal growth temperature range. Conversely, under weaker PPFD conditions, peppers show greater adaptability to temperature changes, leading to a wider optimal temperature range. Figure 9 Figure (b) shows a two-dimensional mapping of the temperature range corresponding to the Pn response surface. The two green lines represent the upper and lower boundaries of the adjustment range, and the black dashed line with an asterisk in the middle represents the optimal temperature. Figure 9 As shown in (b), the optimal temperature range for the pre-fruiting stage is significantly smaller than that for the flowering stage. This difference arises because the transition from vegetative to reproductive growth involves a more complex nutrient allocation, making pepper plants more sensitive to temperature requirements. Excessively high temperatures can lead to trunk elongation and fruit drop. This also confirms the necessity of managing greenhouse temperatures for peppers according to different stages. More detailed results are shown in Table 3. It can be seen that as PPFD increases from 300 μmol·m⁻¹, the optimal temperature range for the pre-fruiting stage is significantly smaller than that for the flowering stage. -2 ·s -1 Increased to 900 μmol·m -2 ·s -1 The optimal temperature range for each growth environment and growth stage generally shows a shrinking trend, compared with Figure 9 Consistent with the results. Furthermore, Table 3 clearly reflects the temperature requirements of chili plants: slightly lower temperatures during the seedling stage are beneficial for vegetative growth, while higher temperatures during the fruiting stage are beneficial for fruit development. In summary, the determined temperature range effectively avoids the high-temperature inhibition zone, providing a reasonable temperature management strategy for chili cultivation.

[0109] Table 3 Optimal temperature ranges under different environments and periods

[0110]

[0111] To verify the influence of different environmental conditions on the optimal temperature range for chili peppers, the method of this invention was theoretically compared with a fixed threshold adjustment method. The results are shown in Table 4. Table 4 shows the results for a CO2 concentration of 600 μmol·mol⁻¹. -1 Some results from that time. Figure 5 It is known that PPFD generally does not exceed 1000 μmol·m under summer greenhouse conditions. -2 ·s -1Therefore, Table 4 only shows PPFD results within this range. Compared to the fixed threshold method, the method proposed in this invention has an average Pn growth rate of 10.68%, indicating that temperature regulation can significantly improve photosynthetic efficiency. However, the seedling stage exhibits contradictory characteristics: although its Pn increment is the smallest (only 3.34%, significantly lower than other growth stages), its absolute Pn value is the highest among all growth stages. This phenomenon suggests that during seedling development, the response threshold of photosynthesis to temperature changes approaches saturation, at which point even slight thermal fluctuations can severely affect physiological performance. This behavior may stem from seedlings prioritizing organogenesis over stress response mechanisms, leading to reduced heat tolerance, resilience, and temperature adaptation range. These findings are consistent with the data in Table 3.

[0112] Table 4 Comparison of the optimal temperature range determined by the present invention and the fixed threshold method.

[0113]

[0114] Furthermore, analysis of the average temperature range for each growth stage of chili peppers in Table 4 reveals that the temperature requirements increase significantly at other growth stages compared to the optimal temperature of approximately 26.3℃ during the seedling stage, particularly reaching around 28.1℃ during the mid-fruiting stage. This indicates that the temperature adaptability of chili peppers varies throughout their growth process. This verifies the feasibility and necessity of adjusting greenhouse temperature according to physiological stages.

[0115] This invention, through systematic verification experiments, has demonstrated the significant advantages of dynamic range control strategies in chili pepper production. For example... Figure 10 As shown, compared with the control group under simulated summer greenhouse conditions (no-operation) and fixed threshold control, the control strategy proposed in this invention has stronger adaptability and better overall benefits. Specifically, the average fresh weight of the peppers in the experimental group was 63.37% higher than that of the no-operation control group and 16.13% higher than that of the fixed threshold control group. The average dry weight was 78.19% higher than that of the no-operation control group and 20.25% higher than that of the fixed threshold control group. In terms of stem diameter and seedling vigor index, the optimal amplitude control method is significantly better than the no-control strategy. Although there is no significant difference compared with fixed threshold control, the overall effect is better. Figure 10As shown in (e), under the optimal control range, the canopy leaf area of ​​pepper plants was the largest, increasing by 34.83% and 23.22% compared to no operation and fixed threshold control, respectively. These results further verify the multidimensional synergistic enhancement effect of this method, which is more conducive to pepper growth. Combined with the seedling data shown in Table 4, although the increase in Pn was not large, its growth-promoting effect on pepper plants was significant. This phenomenon can be attributed to the comprehensive consideration of other environmental factors and growth stages when selecting the optimal temperature range, thereby improving the overall photosynthetic efficiency and achieving cumulative growth benefits. These findings collectively confirm the rationality and applicability of the proposed temperature management strategy in guiding agricultural production practices.

[0116] The flowering and fruiting of peppers under three cultivation strategies are as follows: Figure 11 As shown in the figure, the flowering and fruiting performance of peppers grown within the optimal temperature range was significantly improved compared to the other two strategies. From... Figure 11 As shown in (a) and (b), compared to the fixed threshold and no-operation strategy, this group had an average flowering time that was 4-7 days earlier. The results indicate that the two treatments shortened the average fruiting period by 8.29 days and 14.15 days, respectively. In terms of the number of flowers and fruits, this group had a significant advantage over the other two groups, such as... Figure 11 As shown in (c) and (d), comparative analysis reveals that the fixed threshold strategy prolongs the plant's growth cycle, while the unmanaged environment disrupts the growth dynamics of peppers, leading to an imbalance of excessive vegetative growth at the expense of reproductive development. This imbalance results in delayed flowering and fruiting, as well as a high incidence of flower and fruit drop. Furthermore, Figure 11 (e)-(f) further demonstrate the superior fruit quality achieved by regulating the optimal temperature range. The average fresh fruit weight in the experimental group increased by 225.57% compared to the untreated group and by 91.53% compared to the fixed threshold group. Dry weight increased by 243.65% and 96.84% relative to these two baselines, respectively. These results confirm that maintaining the optimal temperature range not only accelerates pepper phenology (shortens the growth cycle) but also improves reproductive outcomes by increasing flower / fruit yield and fruit biomass.

Claims

1. A method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method, characterized in that, Includes the following steps: Step 1: Through nested experiments, the photosynthetic rate of peppers at different growth stages under different environmental conditions is measured to construct a dataset; the environmental conditions include temperature, CO2 concentration, and photosynthetic photon flux density. Step 2: Using the growth stage, CO2 concentration, temperature and photosynthetic photon flux density as input vectors, a backpropagation neural network optimized by a genetic algorithm is used to construct a photosynthetic rate prediction model and generate the corresponding photosynthetic rate response surface. Step 3: Discretize the photosynthetic rate response surface into discrete points, calculate the Gaussian curvature at each point, and construct a Gaussian curvature response surface; Step 4: Discretize the Gaussian curvature response surface into a temperature-Gaussian curvature response curve. Using the u-sine value as a metric, determine the critical boundary of the response curve using the random restart hill-climbing method to obtain the optimal temperature control range. In step 3, an arbitrary discrete point of the photosynthetic rate response surface is selected as a point. P ,point P There are four adjacent base points, corresponding to the positions of their adjacent faces. The geometric configuration will point... P Consider it as an infinitesimal point close to the base. P It forms an adjacent triangle with its four surrounding base points, as shown in the following formula: In the formula, N for P The number of triangles formed by a point and its adjacent base points. A The sum of the areas of all triangles, for point... P ,point v i and points v i+1 The triangle formed θ i Indicates the first i The vertex angle of a triangle, and the side length of the triangle is denoted as . l i , l i+1 and k i , s =( l i + l i+1 + k i ) / 2 represents the intersection with point P The semi-perimeter of the intersecting triangles; If point P The surrounding local surface area is flat, that is, point. P With point v i and points v i+1 If they are coplanar, then the Gaussian curvature is 0; after obtaining the Gaussian curvature, the photosynthetic photon flux density is used as... x Shaft, temperature is y axis, Gaussian curvature is z The axis is visualized to obtain the Gaussian curvature response surface.

2. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 1, characterized in that, The growth stages include the seedling stage, flowering stage, pre-fruiting stage, mid-fruiting stage, and post-fruiting stage. The different environmental conditions are set with several temperature gradients, several photosynthetic photon flux density gradients, and several CO2 concentration gradients.

3. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 1, characterized in that, The data obtained through nested experiments is normalized using the following formula: in, x i ′ To normalize the data, x i For the first i Measured data under various environmental conditions xi min The minimum value of the measured data. xi max This represents the maximum value of the measured data.

4. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 1, characterized in that, The backpropagation neural network has a three-layer feedforward structure, including an input layer, a single hidden layer, and an output layer. The model is trained using the backpropagation method with mean squared error as the loss function. The calculation process is as follows: in, This is a predicted value for photosynthetic rate. w ij The weights between the hidden layer and the input layer. w jk The weights between the hidden layer and the output layer. b j The threshold between the hidden layer and the input layer. b k The threshold between the hidden layer and the output layer. k For the number of input variables, n For data volume, h (·) is the Sigmoid activation function, which compresses the output to the [0,1] interval. g (·) is the ReLU transfer function. It is the first i The first environmental condition t One characteristic, t =1,2,3,4, representing the growth stage, CO2 concentration, temperature, and photosynthetic photon flux density, respectively.

5. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 4, characterized in that, The input layer has 4 nodes, corresponding to the four input variables: growth stage, CO2 concentration, temperature, and photosynthetic photon flux density. The hidden layer has 10 nodes, and the output layer has 1 node, which outputs the predicted value of photosynthetic rate.

6. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 1, characterized in that, Step 2, using photosynthetic photon flux density and temperature as... x coordinates and y The coordinates are used to construct the photosynthetic rate response surface; in step 3, the photosynthetic photon flux density, temperature and photosynthetic rate are normalized to resolve significant amplitude differences between parameters.

7. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 1, characterized in that, In step 4, an incrementally instantiated Gaussian curvature response surface is introduced into the photosynthetic photon flux density to obtain temperature-Gaussian curvature response curves under different light intensities. The input of the temperature-Gaussian curvature response curve is temperature, and the output is curvature value. Subsequently, the input and output are normalized to eliminate the magnitude difference, and any point on the temperature-Gaussian curvature response curve is set as... M i Calculate its u-chord value.

8. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 7, characterized in that, via a point M i Two adjacent points are generated by symmetrical and equidistant translation along the coordinate axes. M j and M k The two adjacent points and M i Maintain Euclidean distance u It satisfies the following geometric constraints: In the formula, u The topological distance is 0 < u <1; calculate M i Support areas [ M j , M k The cosine value related to the angle between the inner and outer arm vectors is used to measure the magnitude of the u-sine value. At this point, the point... M i The chord value of u is calculated as follows: in, s i = sign [( x i - x k ()( y j - y k )-( x j - x k ()( y i - y k ] is used to determine the sign of the sine value of u. x i , y i ),( x j , y j ), ( x k , y k ) represent points respectively M i , M j , M k The coordinates.

9. The method for determining the optimal temperature control range for the entire growth stage of greenhouse peppers based on the curvature method according to claim 7, characterized in that, The random restart hill-climbing method is used to obtain the upper and lower boundary points of the suitable temperature control target. By mapping the obtained points to the response surface of the photosynthetic rate prediction model, the corresponding temperature control range can be obtained. The formula for obtaining the upper and lower boundary points is as follows: in, c i and c j Let u_sine values ​​be the upper and lower boundary points of the Gaussian response curve, respectively. and They are respectively c i Any point on the left or right side of , and They are respectively c j Any point on the left or right side of .

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