Element synergistic effect evaluation method applied to potash magnesium sulphate fertilizer

Abstract

The invention discloses an element synergy evaluation method applied to potash magnesium sulphate fertilizer, and relates to the field of intelligent fertilizer element evaluation.The element synergy evaluation method adopts a generalized additive model to model three elements of potassium, magnesium and sulfur and interaction of the elements, fully considers nonlinear effects and interaction of the elements, and improves the evaluation accuracy of the elements. And carefully fitting the influence of the B-spline primary function on the nutrient elements to obtain a smooth function so as to analyze the synergistic effect of different nutrient elements and environmental factors. The method can systematically reveal the relationship among the elements and effectively optimize the fertilization strategy.

Description

Technical Field

[0001] The invention relates to the field of intelligent fertilizer element evaluation, and specifically to an element synergistic effect evaluation method applied to potassium magnesium sulfate fertilizer. Background Art

[0002] In modern agriculture, it is common practice to apply fertilizers to improve crop yield and quality. With the advancement of agricultural technology, especially driven by precision agriculture and sustainable agriculture concepts, the use of fertilizers is no longer limited to traditional nitrogen, phosphorus and potassium (NPK) fertilizers. In recent years, potassium sulfate magnesium fertilizer has attracted more and more attention from farmers due to its unique advantages in providing the nutrients required by plants. Potassium sulfate magnesium fertilizer can not only provide three key nutrients, potassium (K), magnesium (Mg) and sulfur (S), but also play an important role in improving soil structure and enhancing crop resistance. Especially in some areas with poor soil, the application of this compound fertilizer can effectively improve crop growth, promote plant photosynthesis and energy metabolism, thereby improving crop yield and quality.

[0003] Although potassium sulfate magnesium fertilizer has many advantages in agricultural production, there are some obvious shortcomings in its actual application. Existing technologies usually lack systematic and scientific evaluation methods, and cannot comprehensively analyze the synergistic effects between the three elements of potassium, magnesium and sulfur. Most studies tend to focus on the role of a single nutrient element and ignore the mutual influence between them. For example, the interactions between potassium, magnesium and sulfur in plants are complex and may produce different effects under different concentrations and soil conditions, and existing technologies fail to effectively consider these factors. In addition, traditional fertilization methods mostly use empirical methods, lack of real-time monitoring and dynamic adjustment of nutrient content in the soil, resulting in poor fertilization effects and waste of resources. This limitation makes agricultural producers face greater uncertainty when applying potassium sulfate magnesium fertilizer, affecting the growth and yield of crops. Summary of the invention

[0004] In view of the defects of the above-mentioned prior art, the present application scheme provides a method for evaluating the synergistic effect of elements applied to potassium magnesium sulfate fertilizer, aiming to provide a scientific basis for precision fertilization through systematic feature extraction and modeling analysis.

[0005] Among them, a method for evaluating the synergistic effect of elements applied to potassium magnesium sulfate fertilizer comprises the following steps:

[0006] S1. Collect the potassium, magnesium and sulfur contents in the soil as input features;

[0007] S2. The nonlinear effects of each element and its combination were modeled by generalized additive model, and each element and its interaction terms were fitted by B-spline, and the smoothing function was calculated. The synergistic effects of different nutrients and environmental factors were analyzed by the smoothing function, and the established model was optimized by using the square loss function;

[0008] S3. Explain the synergistic effect between elements through the smooth function in the model;

[0009] Among them, in step S3, the explanation process is specifically as follows:

[0010] When the smooth functions of potassium and magnesium have positive effects on potassium and magnesium, it means that the increase of magnesium enhances the effect of potassium on plant growth;

[0011] When the smoothed functions of magnesium and sulfur have positive effects on magnesium and sulfur, it means that the increase of magnesium enhances the effect of sulfur on plant growth;

[0012] When the smooth functions of potassium and sulfur elements have a positive effect on potassium and sulfur, it means that the increase of potassium enhances the effect of sulfur on plant growth.

[0013] Furthermore, in step S2, the model expression for modeling by generalized additive model is:

[0014] y=β0+f1(K)+f2(Mg)+f3(S)+f4(K×Mg×S)+f5(K×Mg)+f6(K×S)+f7(Mg×S);

[0015] Among them, y represents the target variable, i.e., plant growth, β0 represents a bias term, f1, f2, f3 represent smoothing functions for potassium, magnesium and sulfur, respectively, f4, f5, f6 and f7 represent smoothing functions for the synergistic effect between potassium-magnesium-sulfur, potassium-magnesium, potassium-sulfur and magnesium-sulfur, respectively, K represents potassium, Mg represents magnesium, and S represents sulfur.

[0016] Furthermore, in step S2, fitting each element and its interaction term using B-spline to obtain a smooth function specifically includes the following sub-steps:

[0017] S201. Fitting a smooth function by B-spline;

[0018] S202. Segment each feature, define nodes, and recursively calculate the B-spline basis function according to the order of the spline;

[0019] S203. Perform linear combination on the B-spline basis functions calculated for each feature to obtain corresponding nonlinear fitting terms.

[0020] Furthermore, in step S202, each feature is segmented, and the nodes are defined as follows: t = [t0, t2, ..., t m+3 ], wherein t0, t2, ..., t m+3 Node, wherein t represents a node sequence.

[0021] Furthermore, in step S201, the fitting process is specifically expressed as follows:

[0022]

[0023] Wherein, f(x) represents a smoothing function, N represents the total number of B-spline basis functions, k represents the index of the B-spline basis function, x represents a feature, and β k represents the spline coefficient, the B k represents the kth B-spline basis function.

[0024] Furthermore, in step S202, recursive calculation of the B-spline basis function by the order of the spline is specifically to recursively construct a third-order basis function step by step from the 0th-order basis function, and the process includes the following sub-steps:

[0025] S2021. For the 0th order B-spline basis function, the calculation process is:

[0026]

[0027] Among them, the B i，0 (x) represents the 0th order B-spline basis function, x represents the feature, and t i represents the i-th node, the t i+1 represents the i+1th node, where i represents the index of the B-spline basis function;

[0028] S2022. For the 1st order B-spline basis function, the calculation process is:

[0029]

[0030] Among them, the B i，1 (x) represents the 1st order B-spline basis function, and the t i+2 represents the i+2th node;

[0031] S2023. For the 2nd order B-spline basis function, the calculation process is:

[0032]

[0033] Among them, the B i，2 (x) represents the 2nd order B-spline basis function, and the t i+3 represents the i+3th node;

[0034] S2024. For the third-order B-spline basis function, the calculation process is:

[0035]

[0036] Wherein, the third-order B-spline basis function represents that the t i+4 Represents the i+4th node.

[0037] Furthermore, in step S202, each feature is segmented and nodes are defined to segment the feature value range.

[0038] Furthermore, in step S203, the nonlinear fitting items obtained include:

[0039] Linear combination of cubic B-spline basis functions of potassium: Linear combination of cubic B-spline basis functions for magnesium: Linear combination of cubic B-spline basis functions for sulfur: Linear combination of cubic B-spline basis functions for the interaction of potassium, magnesium, and sulfur elements:

[0040] Linear combination of cubic B-spline basis functions of potassium and magnesium elements: Linear combination of cubic B-spline basis functions of potassium and sulfur elements: Linear combination of cubic B-spline basis functions of magnesium and sulfur elements:

[0041] Wherein, n1, n2, n3 represent the number of basis functions corresponding to potassium, magnesium, and sulfur elements, respectively; n4, n5, n6, and n7 represent the number of basis functions corresponding to the interaction of potassium-magnesium-sulfur, potassium-magnesium, potassium-sulfur, and magnesium-sulfur, respectively; and β f , γ j ,δ l , ε m ,θ p , μ q and They respectively represent the spline coefficients of the corresponding B-spline basis functions, and f, j, l, m, p, q and r respectively represent the indexes of the corresponding B-spline basis functions.

[0042] Furthermore, in step S2, the square loss function is expressed as:

[0043]

[0044] Among them, the represents the loss function, the y represents the actual observation value, the represents the model observation value, λ represents the regularization coefficient, and β f , γ j ,δ l , ε m ,θ p , μ q and They respectively represent the spline coefficients of the corresponding B-spline basis functions, and f, j, l, m, p, q and r respectively represent the indexes of the corresponding B-spline basis functions.

[0045] Furthermore, in step S3, the positive effect is specifically: when the smoothing function is greater than zero within a specified interval and the derivative is greater than zero, it indicates that the characteristic element has a positive impact on the yield.

[0046] The beneficial effects of the invention are:

[0047] The present invention uses a generalized additive model to model the three elements of potassium, magnesium and sulfur and their interactions, fully considering their nonlinear effects and interactions, and uses B-spline basis functions to carefully fit the effects of nutrient elements, thereby obtaining a smooth function to analyze the synergistic effects of different nutrient elements and environmental factors. This method can systematically reveal the relationship between the elements and effectively optimize the fertilization strategy.

[0048] The present invention reduces the waste of resources in the fertilization process and improves the accuracy of fertilization by optimizing the model. This method not only improves the growth potential of crops, but also provides scientific support for the sustainable development of agricultural production. Through the scheme proposed by the present invention, agricultural producers can scientifically manage and apply potassium magnesium sulfate fertilizer in a dynamically changing environment, thereby achieving higher yield and quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A method structure diagram of a method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0052] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative work are within the scope of protection of the present invention. It should be noted that relational terms such as the terms "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0053] Moreover, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a list of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of more restrictions, an element defined by the phrase "comprises a ..." does not exclude the presence of additional identical elements in the process, method, article or apparatus that includes the element.

[0054] The features and performance of the present invention are further described in detail below in conjunction with the embodiments.

[0055] like Figure 1 As shown, a method for evaluating the synergistic effect of elements applied to potassium magnesium sulfate fertilizer comprises the following steps:

[0056] S1. Collect the potassium, magnesium and sulfur contents in the soil as input features;

[0057] S2. The nonlinear effects of each element and its combination were modeled by generalized additive model, and each element and its interaction terms were fitted by B-spline, and the smoothing function was calculated. The synergistic effects of different nutrients and environmental factors were analyzed by the smoothing function, and the established model was optimized by using the square loss function;

[0058] S3. Explain the synergistic effect between elements through the smooth function in the model;

[0059] Among them, in step S3, the explanation process is specifically as follows:

[0060] When the smooth functions of potassium and magnesium have positive effects on potassium and magnesium, it means that the increase of magnesium enhances the effect of potassium on plant growth;

[0061] When the smoothed functions of magnesium and sulfur have positive effects on magnesium and sulfur, it means that the increase of magnesium enhances the effect of sulfur on plant growth;

[0062] When the smooth functions of potassium and sulfur elements have a positive effect on potassium and sulfur, it means that the increase of potassium enhances the effect of sulfur on plant growth.

[0063] Specifically, for potassium sulfate magnesium fertilizer, potassium can promote photosynthesis, enhance plant drought resistance, and increase yield; magnesium is the core element of chlorophyll, promoting plant photosynthesis and energy metabolism; sulfur is a component of proteins and enzymes, helping nitrogen metabolism and photosynthesis. The combination of these elements may produce a synergistic effect, that is, the presence of one element can enhance the absorption and utilization efficiency of other elements. For example, the presence of magnesium can enhance the absorption of potassium, while sulfur contributes to the metabolic process of magnesium. This implementation is aimed at the above principle, and an effective evaluation is conducted on the synergistic effect between potassium sulfate magnesium fertilizers.

[0064] Furthermore, in step S2, the model expression for modeling by generalized additive model is:

[0065] y=β0+f1(K)+f2(Mg)+f3(S)+f4(K×Mg×S)+f5(K×Mg)+f6(K×S)+f7(Mg×S);

[0066] Wherein, y represents the target variable, i.e., plant growth, β0 represents a bias term, f1, f2, f3 represent smoothing functions for potassium, magnesium, and sulfur, respectively, f4, f5, f6, and f7 represent smoothing functions for the synergy between potassium, magnesium, sulfur, potassium, magnesium, and sulfur, respectively, K represents potassium, Mg represents magnesium, and S represents sulfur. Specifically, y is determined according to actual calculation requirements. For example, crop yield or element absorption rate can be selected as the target variable.

[0067] Furthermore, the generalized additive model (GAM) allows different nonlinear terms to be introduced for different features and can handle complex interactions between features. This model can flexibly model statistical models of nonlinear relationships. Its basic form is to add nonlinear functions of multiple input features to predict the target variable. This model is particularly suitable for capturing the complex nonlinear effects of various elements and their interactions on plant growth in the synergistic effect of nutrients.

[0068] Furthermore, in step S2, fitting each element and its interaction term using B-spline to obtain a smooth function specifically includes the following sub-steps:

[0069] S201. Fitting a smooth function by B-spline;

[0070] S202. Segment each feature, define nodes, and recursively calculate the B-spline basis function according to the order of the spline;

[0071] S203. Perform linear combination on the B-spline basis functions calculated for each feature to obtain corresponding nonlinear fitting terms.

[0072] Furthermore, in step S202, each feature is segmented, and the nodes are defined as follows: t = [t0, t2, ..., t m+3 ], wherein t0, t2, ..., t m+3 Node, wherein t represents a node sequence.

[0073] Furthermore, in step S201, the fitting process is specifically expressed as follows:

[0074]

[0075] Wherein, f(x) represents a smoothing function, N represents the total number of B-spline basis functions, k represents the index of the B-spline basis function, x represents a feature, and β k represents the spline coefficient, the B k represents the kth B-spline basis function.

[0076] Furthermore, in step S202, recursive calculation of the B-spline basis function by the order of the spline is specifically to recursively construct a third-order basis function step by step from the 0th-order basis function, and the process includes the following sub-steps:

[0077] S2021. For the 0th order B-spline basis function, the calculation process is:

[0078]

[0079] Among them, the B i，0 (x) represents the v-order B-spline basis function, x represents the feature, and t i represents the i-th node, the t i+1 represents the i+1th node, where i represents the index of the B-spline basis function;

[0080] S2022. For the 1st order B-spline basis function, the calculation process is:

[0081]

[0082] Among them, the B i，1 (x) represents the 1st order B-spline basis function, and the t i+2 represents the i+2th node;

[0083] S2023. For the 2nd order B-spline basis function, the calculation process is:

[0084]

[0085] Among them, the B i，2 (x) represents the 2nd order B-spline basis function, and the t i+3 represents the i+3th node;

[0086] S2024. For the third-order B-spline basis function, the calculation process is:

[0087]

[0088] Wherein, the third-order B-spline basis function represents that the t i+4 Represents the i+4th node.

[0089] Specifically, in the generalized additive model (GAM), the order of B-spline refers to the polynomial order of the basis function, which is used to determine the smoothness of the fit, and the choice of the order is closely related to the complexity of the problem itself and the smoothness requirement of the fit. This embodiment selects the 3rd order B-spline basis function for calculation. The cubic B-spline is smooth enough to fit most nonlinear relationships while avoiding overfitting. Furthermore, too high an order will increase the computational complexity, while the cubic B-spline achieves a good balance between smoothness and computational efficiency. Furthermore, the cubic B-spline ensures the continuity of the function and its first-order and second-order derivatives, and is suitable for describing most smooth changes in actual systems.

[0090] Further, in step S202, each feature is segmented and nodes are defined to segment the feature range. Exemplarily, for a set of potassium content values, a node sequence needs to be determined to divide the feature range, and the nodes determine the flexibility of the B-spline. At the nodes, the shape of the spline changes, thereby better fitting the data.

[0091] Furthermore, in step S203, the nonlinear fitting items obtained include:

[0092] Linear combination of cubic B-spline basis functions of potassium: Linear combination of cubic B-spline basis functions for magnesium: Linear combination of cubic B-spline basis functions for sulfur: Linear combination of cubic B-spline basis functions for the interaction of potassium, magnesium, and sulfur elements:

[0093] Linear combination of cubic B-spline basis functions of potassium and magnesium elements: Linear combination of cubic B-spline basis functions of potassium and sulfur elements: Linear combination of cubic B-spline basis functions of magnesium and sulfur elements:

[0094] Wherein, n1, n2, n3 represent the number of basis functions corresponding to potassium, magnesium, and sulfur elements, respectively; n4, n5, n6, and n7 represent the number of basis functions corresponding to the interaction of potassium-magnesium-sulfur, potassium-magnesium, potassium-sulfur, and magnesium-sulfur, respectively; and β f , γ j ,δ l , ε m ,θ p , μ q and They respectively represent the spline coefficients of the corresponding B-spline basis functions, and f, j, l, m, p, q and r respectively represent the indexes of the corresponding B-spline basis functions.

[0095] Furthermore, in step S2, the square loss function is expressed as:

[0096]

[0097] Among them, the represents the loss function, the y represents the actual observation value, the represents the model observation value, λ represents the regularization coefficient, and β f , γ j ,δ l , ε m ,θ p , μ q and They respectively represent the spline coefficients of the corresponding B-spline basis functions, and f, j, l, m, p, q and r respectively represent the indexes of the corresponding B-spline basis functions.

[0098] Furthermore, in step S3, the positive effect is specifically: when the smoothing function is greater than zero within a specified interval and the derivative is greater than zero, it indicates that the characteristic element has a positive impact on the yield.

[0099] Specifically, the evaluation of the individual effects of potassium, magnesium, and sulfur is as follows:

[0100] Potassium, as one of the key nutrients in plant growth, can improve crop drought resistance, disease resistance and yield. The nonlinear smooth function of the model can be used to evaluate the impact of increased potassium content on plant yield. If the smooth function shows a significant positive effect on potassium content, it means that crop yield increases significantly with the increase in potassium content. If the increase in the smooth function decreases or tends to be flat within a higher potassium content range, it means that the effect of potassium has entered a saturated state, that is, after the potassium content increases to a certain level, its effect on increasing yield is no longer significant.

[0101] Magnesium is a core element of chlorophyll and is involved in photosynthesis and energy metabolism of plants. The smooth function in the model represents the effect of magnesium content on plant growth. If the smooth function shows a positive effect, it means that the increase in magnesium promotes photosynthesis and nutrient metabolism of plants, thereby increasing yield. If the smooth function shows a negative effect within a certain range, it means that too much magnesium may cause element imbalance, affect the absorption of other elements, and lead to a decrease in yield.

[0102] Sulfur is an essential element for plant metabolism, enzyme activity, and protein synthesis. A smooth function was used to explain the role of sulfur. The smooth function showed a positive effect, indicating that an increase in sulfur helps protein synthesis and nitrogen metabolism, improving plant health and yield. Similar to potassium, sulfur may show a saturation effect within a certain range, that is, too much sulfur will not further significantly increase yield.

[0103] The evaluation of the synergy between its elements is as follows:

[0104] The synergistic effect of potassium and magnesium reflects how these two elements affect each other in plant growth processes. The role of magnesium in chlorophyll can enhance the photosynthesis effect of potassium, and potassium also affects the metabolism of magnesium. If the smooth function shows a positive effect, it means that the interaction between potassium and magnesium can enhance each other's effectiveness within a specific concentration range. For example, increasing the content of magnesium can significantly improve the effect of potassium in photosynthesis, thereby increasing yield. If the smooth function shows a negative effect, it may indicate that there is a competition or inhibition relationship between potassium and magnesium. Too much potassium or magnesium may inhibit the absorption or utilization of the other, thereby reducing yield.

[0105] Sulfur helps plants absorb and utilize potassium by promoting protein synthesis. The smooth function in the model represents the synergistic effect of potassium and sulfur. If the smooth function shows a positive effect, it means that the increase in sulfur significantly enhances the absorption and utilization efficiency of potassium. Especially when the sulfur content in the soil is moderate, the absorption efficiency of potassium can be improved, thereby promoting plant growth. If the smooth function shows a negative effect, it may indicate that the excessive presence of sulfur inhibits the absorption of potassium, leading to an imbalance in plant nutrition, which in turn has a negative impact on yield.

[0106] Magnesium and sulfur are involved in plant energy metabolism and protein synthesis. The smooth function in the model reflects the synergistic effect between magnesium and sulfur. If the smooth function shows a positive effect, it means that magnesium and sulfur cooperate with each other within a certain range, which can effectively enhance the metabolic function of plants and thus increase yields. For example, magnesium contributes to photosynthesis, while sulfur can enhance the effect of magnesium in energy metabolism. If the smooth function shows a negative effect, it may be that the excessive presence of magnesium and sulfur at the same time triggers a negative effect, resulting in a decrease in plant metabolic efficiency and affecting plant growth.

[0107] Potassium, magnesium and sulfur participate in energy metabolism and protein synthesis during plant growth. The synergy between the three can be analyzed by the performance of the smooth function in the model. If the smooth function shows a positive effect, it indicates that potassium, magnesium and sulfur have good mutual cooperation within a certain range. This synergy can effectively enhance the metabolic function of plants, thereby increasing crop yields. For example, potassium can regulate the opening and closing of stomata and optimize photosynthesis; magnesium, as an important component of chlorophyll, enhances the absorption and utilization of light energy; sulfur plays a key role in amino acid synthesis and promotes protein synthesis. The benign interaction of the three helps to improve the overall growth and development of plants. If the smooth function shows a negative effect, it may indicate that the excessive presence of potassium, magnesium and sulfur at the same time has caused negative effects. This situation will lead to a decrease in the metabolic efficiency of plants, which in turn affects the normal growth of plants. For example, excessive potassium may inhibit the absorption of magnesium, causing magnesium deficiency; at the same time, excessive sulfur may interfere with the normal function of potassium, causing obstacles in plant energy metabolism.

[0108] Further, as a preferred specific implementation of the above embodiment, a system for evaluating the synergistic effect of elements applied to potassium magnesium sulfate fertilizer is proposed, which specifically includes:

[0109] The feature collection module is used to collect the potassium, magnesium and sulfur contents in the soil as input features;

[0110] The collaborative calculation module is used to model the nonlinear effects of each element and its combination through a generalized additive model, fit each element and its interaction terms using B-splines, calculate the smoothing function, analyze the synergistic effects of different nutrients and environmental factors through the smoothing function, and optimize the established model using the square loss function;

[0111] The synergy effect evaluation module is used to explain the synergy effect between elements through the smooth function in the model.

[0112] Furthermore, the collaborative computing module further includes the following units:

[0113] B-spline fitting unit, used for fitting a smooth function through B-spline;

[0114] A recursive calculation unit, used to segment each feature, define nodes, and recursively calculate the B-spline basis function through the order of the spline;

[0115] The linear combination unit is used to perform linear combination on the B-spline basis functions calculated for each feature to obtain the corresponding nonlinear fitting term.

[0116] Furthermore, the recursive calculation unit further includes the following subunits:

[0117] The 0th order basis function calculation subunit is used to calculate the 0th order B-spline basis function, and its calculation process is as follows:

[0118]

[0119] Among them, the B i,0 (x) represents the 0th order B-spline basis function, x represents the feature, and t i represents the i-th node, the t i+1 represents the i+1th node, where i represents the index of the B-spline basis function;

[0120] The first-order basis function calculation subunit is used to calculate the first-order B-spline basis function, and its calculation process is as follows:

[0121]

[0122] Among them, the B i,1 (x) represents the 1st order B-spline basis function, and the t i+2 represents the i+2th node;

[0123] The second-order basis function calculation subunit is used to calculate the second-order B-spline basis function, and its calculation process is as follows:

[0124]

[0125] Among them, the B i,2 (x) represents the 2nd order B-spline basis function, and the t i+3 represents the i+3th node;

[0126] The third-order basis function calculation subunit is used to calculate the third-order B-spline basis function, and its calculation process is as follows:

[0127]

[0128] Wherein, the third-order B-spline basis function represents that the t i+4 Represents the i+4th node.

[0129] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art shall not deviate from the spirit and scope of the present invention, and shall be within the scope of protection of the claims attached to the present invention.

Claims

1. A method for evaluating the synergistic effect of elements applied to potassium magnesium sulfate fertilizer, characterized in that: The following steps are involved: S1. Collect the potassium, magnesium and sulfur contents in the soil as input features; S2. The nonlinear effects of each element and its combination were modeled by generalized additive model, and each element and its interaction terms were fitted by B-spline, and the smoothing function was calculated. The synergistic effects of different nutrients and environmental factors were analyzed by the smoothing function, and the established model was optimized by using the square loss function. S3. Explain the synergistic effect between elements through the smooth function in the model; Among them, in step S3, the explanation process is specifically as follows: When the smooth functions of potassium and magnesium have positive effects on potassium and magnesium, it means that the increase of magnesium enhances the effect of potassium on plant growth; When the smoothed functions of magnesium and sulfur have positive effects on magnesium and sulfur, it means that the increase of magnesium enhances the effect of sulfur on plant growth; When the smooth functions of potassium and sulfur have positive effects on potassium and sulfur, it means that the increase of potassium enhances the effect of sulfur on plant growth; When the smooth functions of potassium, magnesium, and sulfur have a positive effect on potassium, magnesium, and sulfur, it means that the increase of potassium, magnesium, and sulfur is beneficial to the participation in energy metabolism and protein synthesis.

2. The method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer according to claim 1, characterized in that: In step S2, the model expression for modeling by generalized additive model is: y=β0+T1(K)+T2(Mg)+T3(S)+T4(K×Mg×S)+T5(K×Mg)+T6(K×S)+T7(Mg×S); Among them, y represents the target variable, i.e., plant growth, β0 represents a bias term, T1, T2, T3 represent smoothing functions for potassium, magnesium and sulfur, respectively, T4, T5, T6 and T7 represent smoothing functions for the synergistic effect between potassium-magnesium-sulfur, potassium-magnesium, potassium-sulfur and magnesium-sulfur, respectively, K represents potassium, Mg represents magnesium, and S represents sulfur.

3. The method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer according to claim 1, characterized in that: In step S2, fitting each element and its interaction term by using B-spline to obtain a smooth function specifically includes the following sub-steps: S201. Fitting a smooth function by B-spline; S202. Segment each feature, define nodes, and recursively calculate the B-spline basis function according to the order of the spline; S203. Perform linear combination on the B-spline basis functions calculated for each feature to obtain corresponding nonlinear fitting terms.

4. The method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer according to claim 3, characterized in that: In step S201, the fitting process is specifically expressed as follows: Wherein, T(x) represents a smoothing function, N represents the total number of B-spline basis functions, k represents the index of the B-spline basis function, x represents a feature, and β k represents the spline coefficient, the B k represents the kth B-spline basis function.

5. The method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer according to claim 3, characterized in that: In step S202, each feature is segmented, and the nodes are defined as follows: t = [t0, t2, ..., t m+3 ], wherein t0, t2, ..., t m+3 Node, wherein t represents a node sequence.

6. The method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer according to claim 3, characterized in that: In step S202, recursive calculation of the B-spline basis function by the order of the spline is specifically to recursively construct a third-order basis function step by step from the 0th-order basis function, and the process includes the following sub-steps: S2021. For the v-order B-spline basis function, the calculation process is: Among them, the B i，0 (x) represents the 0th order B-spline basis function, x represents the feature, and t i represents the i-th node, the t i+1 represents the i+1th node, where i represents the index of the B-spline basis function; S2022. For the 1st order B-spline basis function, the calculation process is: Among them, the B i，1 (x) represents the 1st order B-spline basis function, and the t i+2 represents the i+2th node; S2023. For the 2nd order B-spline basis function, the calculation process is: Among them, the B i，2 (x) represents the 2nd order B-spline basis function, and the t i+3 represents the i+3th node; S2024. For the third-order B-spline basis function, the calculation process is: Wherein, the third-order B-spline basis function represents that the t i+4 Represents the i+4th node.

7. The method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer according to claim 3, characterized in that: In the step S202, each feature is segmented and nodes are defined to segment the feature value range.

8. The method for evaluating the synergistic effect of elements applied to potassium-magnesium sulfate fertilizer according to claim 3, characterized in that: In step S203, the nonlinear fitting items obtained include: Linear combination of cubic B-spline basis functions of potassium: Linear combination of cubic B-spline basis functions for magnesium: Linear combination of cubic B-spline basis functions for sulfur: Linear combination of cubic B-spline basis functions for the interaction of potassium, magnesium, and sulfur elements: Linear combination of cubic B-spline basis functions of potassium and magnesium elements: Linear combination of cubic B-spline basis functions of potassium and sulfur elements: Linear combination of cubic B-spline basis functions of magnesium and sulfur elements: Wherein, n1, n2, n3 represent the number of basis functions corresponding to potassium, magnesium, and sulfur elements, respectively; n4, n5, n6, and n7 represent the number of basis functions corresponding to the interaction of potassium-magnesium-sulfur, potassium-magnesium, potassium-sulfur, and magnesium-sulfur, respectively; and β f , γ j , δ l , ε m ,θ p , μ q and They respectively represent the spline coefficients of the corresponding B-spline basis functions, and f, j, l, m, p, q and r respectively represent the indexes of the corresponding B-spline basis functions.

9. The method for evaluating the synergistic effect of elements applied to potassium magnesium sulfate fertilizer according to claim 1, characterized in that: In step S2, the square loss function is expressed as: Among them, the represents the loss function, the y represents the actual observation value, the represents the model observation value, λ represents the regularization coefficient, and β f , γ j , δ l , ε m ,θ p , μ q and They respectively represent the spline coefficients of the corresponding B-spline basis functions, and f, j, 1, m, p, q and r respectively represent the indexes of the corresponding B-spline basis functions.

10. The method for evaluating the synergistic effect of elements applied to potassium magnesium sulfate fertilizer according to claim 1, characterized in that: In step S3, the positive effect specifically means that when the smoothing function is greater than zero within a specified interval and the derivative is greater than zero, it indicates that the characteristic element has a positive impact on the yield.

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