A method for converting water distribution from a flat surface to a non-uniform sloped surface using a single sprinkler

Abstract

The present application relates to a kind of single nozzle from plane to non-uniform slope surface water distribution conversion method, its method includes: based on the radial irrigation intensity of single nozzle in plane, establish single nozzle plane water distribution model, based on the digital elevation model of non-uniform slope surface, fit single nozzle radial direction non-uniform slope surface topographic curve, based on the water droplet motion trajectory model of passing through non-uniform slope surface certain point and non-uniform slope surface topographic curve, obtain the intersection of water droplet motion trajectory and plane passing through non-uniform slope surface certain point, according to single nozzle radial direction water conservation and non-uniform slope surface topographic curve, the irrigation intensity of intersection position corresponding single nozzle plane water distribution model is converted to the irrigation intensity of non-uniform slope surface certain point, can solve the problem that existing non-uniform slope surface water distribution conversion method cannot meet the need of non-uniform slope surface water distribution conversion, improve applicability, to simplify non-uniform slope surface water distribution measurement and be applied to hilly and mountainous water-saving irrigation.

Description

Technical Field

[0001] This invention belongs to the field of water-saving irrigation technology, specifically relating to a method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head. Background Technology

[0002] China has numerous hilly and sloping areas. Of the country's 1.998 billion mu (approximately 129 million hectares) of arable land, about 40.39% has a slope of 2° to 25°. These hilly and sloping areas are important industrial bases for cash crops such as oilseeds, hemp, mulberry, fruit, medicinal herbs, and tea. Hilly and sloping areas typically suffer from low water levels, high soil depth, steep slopes, and thin soil layers. Traditional irrigation methods are not only labor-intensive but also prone to surface runoff and deep seepage, leading to soil compaction and hindering crop growth. Therefore, developing water-saving sprinkler irrigation technology in hilly and sloping areas can improve irrigation water utilization, eliminate the need for land leveling, and reduce surface runoff and deep seepage, making it an effective way to solve irrigation problems in these areas. Sprinkler head water distribution is the foundation of sprinkler irrigation system design and is crucial to the design of sprinkler irrigation systems. Due to the influence of terrain factors, it is more difficult to measure the water distribution of sprinklers on slopes, while it is easier to measure the water distribution of sprinklers on flat land. Research on the transformation of water distribution of sprinklers on flat land to water distribution on slopes is of great significance for evaluating the performance of sprinkler irrigation systems in hilly and mountainous areas and assessing the quality of crop irrigation.

[0003] In their research on the transformation of water distribution in planar sprinkler irrigation to that on slopes, scholars at home and abroad have made significant contributions. For example, Chen Xuemin, Soares, and others established the equation of water droplet flight motion based on dynamic principles and, based on the principle of water balance, established a model of water distribution in uniform slope sprinkler irrigation. Xiang Qingjiang, based on the jet trajectory calculation formula, applied the grid transformation method to establish the correspondence between water distribution data on flat land and uniform slopes, realizing the conversion of water distribution data between flat land and uniform slopes. Zhang Yisheng et al., based on ballistic theory and considering the evaporation of water droplets, established a calculation model of water distribution in uniform slope sprinkler irrigation. Mateos introduced the logarithmic relationship between wind speed and terrain into the droplet motion equation and established a model of water distribution in slope sprinkler irrigation under windy conditions.

[0004] The main drawback of the above methods is that they all assume a constant slope to obtain the conversion method from a plane to a uniform slope water distribution. The conversion principle is based on the measured water distribution data of the plane and, according to the principle of conservation of total water along the jet direction, introduces a water conversion factor: the ratio of the distance of the droplet landing point on the flat ground to the distance of the droplet landing point on the uniform slope in a certain rotation direction of the nozzle. By establishing the linear equation of the projection of the water droplet trajectory curve onto the uniform slope through the geometric relationship between the rotation angle of the nozzle, the slope angle, and the distance, the water volume actually measured on the flat ground is converted into the water volume on the slope: the water volume value of a certain point on the slope is the product of the water volume of the corresponding flat point measured at the actual measurement point and the conversion factor. However, hilly and mountainous areas contain a large number of non-uniform slopes. On non-uniform curved surfaces, the slope angle of the non-uniform slope changes with the distance from the sprinkler head. Moreover, the projection of the water droplet trajectory curve onto the non-uniform slope is a curve. The ratio of the distance of the droplet landing point on flat ground to the distance of the droplet landing point on the non-uniform slope in a certain rotation direction of the sprinkler head cannot describe the conversion relationship between them. Therefore, the conversion method of water distribution on uniform slopes cannot meet the needs of water distribution conversion on non-uniform slopes, and has certain limitations in evaluating the performance of sprinkler irrigation systems in hilly and mountainous areas and assessing crop irrigation quality.

[0005] Secondly, the following defects exist: (1) It only considers the transformation of slope water distribution under a certain fixed working pressure, without considering the influence of different working pressures on the transformation of slope water distribution, which restricts the applicability of the method. (2) Both the droplet motion model and the slope model are established in Cartesian coordinates. Under ideal windless conditions, the droplets ejected from the nozzle will move along a certain radial direction of the nozzle. It is difficult to model and solve in Cartesian coordinates. (3) The droplet size is different and the movement distance is also different. Usually, the droplet size is used as a variable, and the water volume at the corresponding landing point on the slope is calculated by changing the droplet size. Since the relationship between the slope distance and the droplet size is not established, this method cannot directly solve the water volume at a certain point on the slope. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the above-mentioned technical problems. The present invention provides a method for converting water distribution from a plane to a non-uniform slope using a single sprinkler, which can meet the needs of water distribution conversion on non-uniform slopes, improve applicability, simplify the measurement of water distribution on non-uniform slopes and be applied to water-saving irrigation in hilly and mountainous areas.

[0007] The technical solution adopted by this invention to solve its technical problem is:

[0008] A method for transforming water distribution from a plane to a non-uniform slope using a single sprinkler head, the method comprising:

[0009] A planar water distribution model for a single sprinkler head is established based on the radial irrigation intensity of a single sprinkler head in a plane.

[0010] A digital elevation model of a non-uniform slope is established, and a non-uniform slope terrain curve in the radial direction of a single nozzle is fitted based on the digital elevation model.

[0011] A water droplet trajectory model passing through a point on a non-uniform slope is established. Based on the water droplet trajectory model and the non-uniform slope topographic curve, the intersection point of the water droplet trajectory passing through a point on the non-uniform slope and the plane is obtained.

[0012] Based on the water conservation in the radial direction of a single sprinkler head and the non-uniform slope topography curve, the irrigation intensity of the single sprinkler head planar water distribution model corresponding to the intersection point is transformed into the irrigation intensity of a point on the non-uniform slope. By combining the irrigation intensities of any point on all the non-uniform slope topography curves, the water distribution of a single sprinkler head on the non-uniform slope is obtained.

[0013] Furthermore, considering the impact of different working pressures on the transformation of water distribution on slopes, a single-nozzle planar water distribution model is established based on the radial irrigation intensity of a single nozzle under different pressures, further improving the applicability of the method.

[0014] Furthermore, the method for obtaining the radial irrigation intensity by establishing single-nozzle water distribution tests under different pressures includes:

[0015] With the nozzle as the origin, measuring points are distributed radially at equal intervals. The number of measuring points is configured according to the range of the nozzle. Rain gauges are placed at each measuring point to collect the water droplets sprayed by the nozzle during operation.

[0016] Using the working pressure of the sprinkler head as the test factor, the number of test factor levels is determined according to the working pressure range of the sprinkler head. The sprinkler head is set to operate at the working pressure of each design level. The operating time and the precipitation depth data measured by the rain gauge at each measuring point are recorded, and the irrigation intensity at each measuring point is calculated to obtain the radial irrigation intensity.

[0017] Furthermore, based on the radial irrigation intensity of a single sprinkler head under different pressures, the method for establishing a planar water distribution model for a single sprinkler head using the Delaunay triangulation linear interpolation algorithm includes:

[0018] Based on the radial irrigation intensity, a Delaunay triangulation is constructed. The working pressure p and the distance r between the interpolation point and the sprinkler head are determined. The vertex information of the Delaunay triangle at the interpolation point (p,r) is found: q1(p1,r1), q2(p2,r2), q3(p3,r3), where p1 is the working pressure of vertex q1, r1 is the distance between vertex q1 and the sprinkler head, p2 is the working pressure of vertex q2, r2 is the distance between vertex q2 and the sprinkler head, p3 is the working pressure of vertex q3, and r3 is the distance between vertex q3 and the sprinkler head. The irrigation intensity value of the interpolation point (p,r) is calculated as: q(p,r)=ω1p+ω2r+ω3, where ω1, ω2, and ω3 are coefficients related to q1(p1,r1), q2(p2,r2), and q3(p3,r3), respectively.

[0019]

[0020]

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[0023] The results of Delaunay triangulation approximate equilateral triangles, which can further improve the accuracy of interpolation, thereby obtaining a high-precision single-nozzle planar water distribution model and further improving the conversion accuracy.

[0024] Furthermore, based on the set of elevation points (i.e., observation points) of the non-uniform slope, a digital elevation model of the non-uniform slope is established using the Kriging interpolation method. The Kriging interpolation method not only considers the positional relationship between the observation points and the estimated points, but also the relative positional relationship between the observation points. It also has a good interpolation effect when the observation points are sparse, which can further improve the accuracy of the digital elevation model and thus further improve the conversion accuracy.

[0025] Furthermore, with single nozzle position Loc(x) o ,y o ,z o With ) as the center, the furthest range r that a single nozzle can spray is... max To determine the local digital elevation map based on the radius, uniform interpolation is performed on the digital elevation model of the non-uniform slope in both the radial and axial directions of the local digital elevation map. The number of radial interpolation points is m, and the number of axial interpolation points is n, thus obtaining the coordinate system of the interpolation points in the local digital elevation map. The interpolation point s in the coordinate system is denoted as s. d (x k ,y k ,z k ),in With k≤m×n, the non-uniform slope terrain curve in the radial direction of a single nozzle is fitted based on the coordinate system. The water distribution of the non-uniform slope can be transformed within the local digital elevation map of the single nozzle location, which can further simplify the transformation method.

[0026] Furthermore, with single nozzle position Loc(x) o ,y o ,z o Using ) as the origin, uniform interpolation is performed on the digital elevation model to obtain a Cartesian coordinate system, and the interpolation point s in the Cartesian coordinate system is denoted as . d (x k ,y k ,z k The Cartesian coordinate system is then converted to a cylindrical coordinate system with the single nozzle position as the origin. The interpolation point in the cylindrical coordinate system is denoted as s. C (θ i ,r j ,z k ), θ i S represents c The rotation direction angle, r j S represents c radial coordinates, z k S represents c Given the vertical coordinates, the number of radial interpolation points is m, and the number of axial interpolation points is n, then: When i≤m and j≤n, fitting the non-uniform slope terrain curve in the cylindrical coordinate system can further reduce the difficulty of modeling and solving.

[0027] Furthermore, based on the radial direction θ of a single nozzle in the cylindrical coordinate system... i The set of interpolation points on the surface is used to fit the radial direction θ of a single nozzle using a polynomial curve. i Non-uniform slope topographic curves: z θi (r)=c1r n +c2r n-1 +…+c n r+c n+1 In the above formula, r represents the radial direction θ i The distance from the origin in the direction, c n This represents the coefficient of a polynomial of degree n.

[0028] The slope angle of a non-uniform slope varies with the distance from the nozzle, and the projection of the water droplet trajectory onto the non-uniform slope is a curve. Polynomial curve fitting can better describe this projected curve. The fitted curve z... θi Indicates the radial direction θ i The terrain above.

[0029] Furthermore, the curve z θiThe number of iterations n≥6 can further reduce the error and improve the accuracy of terrain curve fitting.

[0030] Furthermore, an equation for the trajectory of water droplets is established. Based on the location of a point on a non-uniform slope and the equation for the trajectory of water droplets, a model for the trajectory of water droplets passing through a point on a non-uniform slope is established. This allows for the establishment of the relationship between the distance from the slope and the droplet size. Compared with the existing method of calculating the amount of water at the corresponding landing point on the slope by changing the droplet size, the amount of water at a point on the slope can be directly solved.

[0031] Furthermore, based on the relationship between the forces acting on and the motion of the water droplet, methods for establishing a system of two-variable second-order partial differential equations for the motion of the water droplet include:

[0032]

[0033] In the above formula, r is the horizontal distance the water droplet travels, z is the vertical distance the water droplet travels, t is the travel time of the water droplet from the single nozzle, and v is the distance the droplet travels. r Let v be the horizontal component of the water droplet's velocity. z Let C be the vertical component of the water droplet's velocity v. D ρ is the air drag coefficient. a d is the density of air in the environment. w Let ρ be the diameter of the water droplet. w Let g be the density of the water droplet in the environment, and g be the acceleration due to gravity. To facilitate the solution, the equations of motion of the water droplet are transformed into a system of multivariate first-order partial differential equations to obtain the trajectory equation of the water droplet.

[0034] Furthermore, based on the location of a point on a non-uniform slope, the method of applying the bisection method to gradually approximate the trajectory of a water droplet passing through that point on the non-uniform slope, and establishing a model of the water droplet's trajectory passing through that point on the non-uniform slope, includes:

[0035] Initialization parameters include: initializing the radial coordinate r of the spatial position point through which the water droplet passes. p and vertical coordinate z p Initialize the nozzle structure parameters, initialize the parameters of the water droplet trajectory equation, initialize the water droplet start time t0, and initialize the minimum diameter d of the water droplet. wmin Initialize the maximum diameter d of the water droplet wmax Initialize the allowable error Δε and preliminarily determine the diameter d of the water droplet. w Let the iteration count n = 0;

[0036] Based on the initialization parameters, the equation of the water droplet's trajectory and the initial conditions at time t0 are obtained, calculated, and stored at time t0. n The horizontal coordinate value r(t) of the water droplet at time t n) and the vertical coordinates of the water droplet z(t) n );

[0037] Compare r(t) n ) and r p If r(t) n )<r p Let n = n + 1, and calculate r(t) at the next time step. n ) and z(t n If r(t) n )≥r p Then let ε = z(t) n )-z p Compare ε and Δε: If ε ≥ Δε, let d wmax =d w d w =(d wmax +d wmin ) / 2, n=0, clear r(t) n ) and z(t n The storage of ) is used to start a new round of operations; if ε≤-Δε, let d wmin =d w d w =(d wmax +d wmin ) / 2, n=0, clear r(t) n ) and z(t n The storage of ) is used to start a new round of calculations. If -Δε < ε < Δε, then output d. w .

[0038] Each droplet of different size corresponds to a unique trajectory. Solving for the trajectory of a droplet is equivalent to determining the size of the droplet. The above method can determine the trajectory and size of a droplet passing through a point on a non-uniform slope by using the spatial location point on that slope, thus providing basic data for solving the water volume at a point on a non-uniform slope.

[0039] Furthermore, the initialization parameters include: the initialization nozzle working pressure P, and the initialization nozzle structural parameters include: the nozzle flow coefficient C. p Given the nozzle elevation angle α0 and the nozzle riser height l, the initial conditions at time t0 include:

[0040] In the above formula, r(0) is the initial horizontal distance of the water droplet, z(0) is the initial vertical distance of the water droplet, and v r (0) represents the horizontal component of the initial droplet velocity, v z (0) represents the horizontal component of the initial droplet velocity, C p This is the flow coefficient of the nozzle.

[0041] Furthermore, initializing the unit time Δt of the water droplet's movement, and applying the fourth-order Runge-Kutta method, based on the relationship between the distance traveled by the water droplet in the horizontal and vertical directions and its velocity per unit time, r(t) is calculated. n ) and z(t n The methods include:

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[0050]

[0051]

[0052] r(t n )=r(t n-1 )+v r (t n )·Δt

[0053] z(t n )=z(t n-1 )+v z (t n )·Δt

[0054] In the above formula, t n-1 For t n At the previous time Δt, C D ρ is the air drag coefficient. a d is the density of air in the environment. w Let ρ be the diameter of the water droplet. w Let g be the density of the water droplet in the environment, g be the acceleration due to gravity, and v be the velocity of the droplet. r (t n-1 ) for t n-1 The horizontal component of the water droplet's velocity at time z r (t n-1 ) for t n-1 The vertical component of the water droplet's velocity at any given moment, v r (t n) for t n The horizontal component of the water droplet's velocity at time z r (t n ) for t n The vertical component of the water droplet's velocity at time t, r(t) n-1 ) for t n-1 The coordinates of the water droplet in the horizontal direction at time t, z(t) n-1 ) for t n-1 The accuracy of the water droplet trajectory model can be further improved by using the fourth-order Runge-Kutta method to determine the vertical coordinates of the water droplet at any given time.

[0055] Furthermore, the non-uniform slope topography curve along the radial direction θ0 of a single nozzle is fitted. Sprinkler intensity at a point on a non-uniform slope: In the above formula, This indicates the irrigation intensity of the single-nozzle planar water distribution model corresponding to the intersection point. express The tangent slope at a point on a non-uniform slope, k, represents the slope of the line at the intersection of the non-uniform slope and the point mentioned above. This slope can be established based on the conservation of water volume in the radial direction. The mathematical relationship between the sprinkler intensity at a point on a non-uniform slope and the intersection point is further simplified by the conversion method.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] (1) Establish a digital elevation model of the non-uniform slope to fit the non-uniform slope terrain curve in the radial direction of a single sprinkler. This can describe the projection curve of the water droplet trajectory curve on the non-uniform slope. Based on the water droplet trajectory model passing through a point on the non-uniform slope and the non-uniform slope terrain curve, the intersection point of the water droplet trajectory passing through a point on the non-uniform slope and the plane is obtained. Then, the irrigation intensity of the single sprinkler plane water distribution model corresponding to the intersection point is transformed into the irrigation intensity of a point on the non-uniform slope. This can realize the transformation of water distribution from a plane to a non-uniform slope by a single sprinkler. This solves the problem that the existing transformation method of water distribution on a uniform slope cannot meet the needs of water distribution transformation on a non-uniform slope. This simplifies the measurement of water distribution on a non-uniform slope and can be applied to water-saving irrigation in hilly and mountainous areas.

[0058] (2) Based on the radial irrigation intensity of a single sprinkler under different pressures, a planar water distribution model of a single sprinkler is established. The influence of pressure and distance between the sprinkler and the sprinkler on the transformation of water distribution on non-uniform slopes is considered. Compared with the existing water distribution transformation method under fixed working pressure, the applicability of the method can be further improved. The Delaunay triangulation linear interpolation algorithm can be used to further improve the transformation accuracy.

[0059] (3) After uniform interpolation of the digital elevation model, the Cartesian coordinate system is converted into a cylindrical coordinate system with the single nozzle position as the origin. Compared with the existing conversion method, this takes into account that the droplets ejected from the nozzle will move along a certain radial direction of the nozzle, which can further reduce the difficulty of modeling and solving.

[0060] (4) Based on the position of a point on a non-uniform slope and the equation of the water droplet trajectory, a water droplet trajectory model passing through a point on a non-uniform slope is established. The relationship between the slope distance and the droplet size can be established. Compared with the existing method of calculating the water volume at the corresponding landing point on the slope by changing the droplet size, it can be used to directly solve the water volume at a point on the slope. By applying the fourth-order Runge-Kutta method and the bisection method, the trajectory of the droplet passing through the point and the droplet size can be directly solved according to the position of a point on a non-uniform slope, which can further improve the applicability of the conversion method. Attached Figure Description

[0061] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0062] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0063] Figure 2 This is a flowchart illustrating the solution process for the diameter and trajectory of a water droplet according to one embodiment of the present invention.

[0064] Figure 3 This is a schematic diagram illustrating the conversion principle of non-uniform slope irrigation intensity according to an embodiment of the present invention.

[0065] Figure 4 This refers to the spraying intensity of the PY15 type sprinkler head according to one embodiment of the present invention.

[0066] Figure 5 This is a digital terrain elevation map according to one embodiment of the present invention.

[0067] Figure 6 This is a partial digital elevation map of the nozzle position according to an embodiment of the present invention.

[0068] Figure 7 This is a set of nozzle position interpolation points according to an embodiment of the present invention.

[0069] Figure 8 This is a radial direction interpolation point fitting curve according to an embodiment of the present invention.

[0070] Figure 9 This refers to the non-uniform slope spraying intensity according to one embodiment of the present invention.

[0071] Figure 10 This is a diagram showing the location of measurement points in a verification experiment according to one embodiment of the present invention.

[0072] Figure 11 yes Figure 10 Measured and predicted sprinkler intensity values ​​at measuring point 1 in the radial direction.

[0073] Figure 12 yes Figure 10 The measured and predicted sprinkler intensity values ​​at two measuring points in the radial direction. Detailed Implementation

[0074] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0075] A method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head includes: establishing a single sprinkler head plane water distribution model based on the radial irrigation intensity of the single sprinkler head in the plane; establishing a digital elevation model of the non-uniform slope; and fitting the non-uniform slope terrain curve in the radial direction of the single sprinkler head based on the digital elevation model. Compared with existing methods, this method can describe the projection curve of the water droplet trajectory curve on the non-uniform slope.

[0076] A water droplet trajectory model passing through a point on a non-uniform slope is established. Based on the water droplet trajectory model and the non-uniform slope topographic curve, the intersection point of the water droplet trajectory passing through the point on the non-uniform slope and the plane is obtained. According to the water conservation in the radial direction of a single sprinkler and the non-uniform slope topographic curve, based on the irrigation intensity of the single sprinkler plane water distribution model corresponding to the intersection point and the non-uniform slope topographic curve, the irrigation intensity relationship between the point on the non-uniform slope and the intersection point can be established. Based on the position coordinates of the point on the non-uniform slope to be determined, the established irrigation intensity relationship is applied to transform the irrigation intensity of the single sprinkler plane water distribution model corresponding to the intersection point, thereby obtaining the irrigation intensity of the point on the non-uniform slope. Then, the irrigation intensities of all points on the non-uniform slope topographic curve are aggregated to obtain the water distribution of a single sprinkler on the non-uniform slope. Specifically:

[0077] like Figure 1 As shown, this is a preferred embodiment of the water distribution transformation method of the present invention. Taking the PY115 sprinkler head as an example to establish a water distribution model from a plane to a non-uniform slope, the method includes the following steps:

[0078] Step 1: Establish a single-nozzle water distribution test under different pressures:

[0079] The PY115 type nozzle is used. The nozzle is characterized by a working pressure range of 150kPa-400kPa, a 45° circular nozzle structure, and a branch pipe height of 1.2m. Measuring points are distributed radially at equal intervals with the nozzle as the origin, and the distance between adjacent measuring points is 1m. The number of measuring points is 15 according to the range of the nozzle. Rain gauges are placed at each measuring point to collect water droplets sprayed by the nozzle during operation.

[0080] To improve the applicability of the method, the influence of different working pressures on the transformation of water distribution on slopes was considered: a single-factor experiment was conducted with the working pressure of the sprinkler head as the experimental factor. The number of levels of the experimental factor was determined to be 6 based on the working pressure range of the sprinkler head. The working pressure of the sprinkler head was observed by a pressure gauge. The opening of the ball valve on the branch pipe was adjusted to make the sprinkler head operate at the working pressure of each design level, namely, the working pressure states of the sprinkler head are 150 kPa, 200 kPa, 250 kPa, 300 kPa, 350 kPa, and 400 kPa. The operating time of the sprinkler head at each design level working pressure was set to 30 minutes. After the sprinkler head finished operating, the precipitation depth data measured by the rain gauge at each measuring point was read and recorded.

[0081] Step 2: Establish a single-nozzle planar water distribution model:

[0082] Using the measured precipitation depth data and precipitation time of the rain gauges arranged radially under different pressures in step one, the irrigation intensity at each measuring point in the radial direction under different pressures, i.e., the precipitation depth per unit time, is calculated, and the radial water distribution data are shown in Table 1 below:

[0083] Table 1. Radial water distribution data for PY115 nozzles.

[0084]

[0085] A planar water distribution model for a single sprinkler head is established using the Delaunay triangulation linear interpolation algorithm.

[0086] Based on the radial irrigation intensity described in Table 1, a Delaunay triangulation is constructed. The working pressure p and the distance r between the interpolation point and the sprinkler head are determined. The vertex information of the Delaunay triangle at the interpolation point (p,r) is found: q1(p1,r1), q2(p2,r2), q3(p3,r3), where p1 is the working pressure of vertex q1, r1 is the distance between vertex q1 and the sprinkler head, p2 is the working pressure of vertex q2, r2 is the distance between vertex q2 and the sprinkler head, p3 is the working pressure of vertex q3, and r3 is the distance between vertex q3 and the sprinkler head. The irrigation intensity value of the interpolation point (p,r) is calculated as follows: q(p,r)=ω1p+ω2r+ω3, where ω1, ω2, and ω3 are coefficients related to q1(p1,r1), q2(p2,r2), and q3(p3,r3), and are calculated as follows:

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[0090]

[0091] The error of traditional interpolation methods is related to the minimum angle of the triangulation. A "slender" triangulation will reduce the accuracy of interpolation, while the result of Delaunay triangulation is close to an equilateral triangle, which can further improve the accuracy of interpolation and thus obtain a high-precision single-nozzle planar water distribution model. Compared with previous studies, this model can calculate the irrigation intensity at any point in the irrigation area under any pressure, further improving the conversion accuracy.

[0092] To intuitively describe the relationship between the irrigation intensity of this sprinkler head and pressure and radial distance, a visualized three-dimensional surface diagram is established based on a single sprinkler head planar water distribution model, such as... Figure 4 As shown.

[0093] Step 3: Establish a digital elevation model for the non-uniform slope:

[0094] Based on the set of elevation points Q(x,y,z) of a non-uniform slope, i.e., the observation points, where x is the horizontal coordinate, y is the vertical coordinate, and z is the elevation, a digital elevation model of the non-uniform slope is established using the Kriging interpolation method:

[0095] Calculate the elevation data of any two data points (x,y,z) in the set Q(x,y,z). i ,y i ,z i ) and (x j ,y j ,z jThe distance d projected onto the ground ij and elevation semivariance r ij The formula is as follows:

[0096] Based on the Gaussian model, the least squares estimation method is applied to the data (d ij ,γ ij Find the optimal fitting function γ(d) in the equation, which describes the mapping relationship between d and γ, and its expression is: In the above formula, C0 is a function constant, C is the exponential coefficient, and a is the decay factor.

[0097] Given the optimal fitting function γ(d), calculate the corresponding elevation semivariance γ. i0 ;

[0098] The coordinates of the estimated interpolation point are (x0, y0), and the distance d between this estimated interpolation point and other observation points can be calculated. i0 ;

[0099] The weight w is calculated using the following formula. i :

[0100] The elevation value z0 of the interpolation point (x0, y0) is estimated using the following formula:

[0101] Based on the collected geographic information Q(x,y,z) of the non-uniform slope, a digital elevation model of the non-uniform slope is established, and a three-dimensional topographic map of the non-uniform slope is fitted, such as... Figure 5 As shown, the Kriging interpolation method not only considers the positional relationship between the observation point and the estimated point, but also the relative positional relationship between the observation points. It also has a good interpolation effect when the observation points are sparse, which can further improve the accuracy of the digital elevation model and thus further improve the conversion accuracy.

[0102] Step 4: Transform the coordinate system of the interpolation points on the local digital elevation map:

[0103] Based on the three-dimensional topographic map of the non-uniform slope described in step three, determine the location Loc(x) of the single nozzle. o ,y o ,z o ), where x o =1100m, y o =1000m; with the position of a single nozzle as the center, the furthest range r that a single nozzle can spray. max =A local digital elevation map is determined with a radius of 20m, such as Figure 6 As shown.

[0104] Uniform interpolation is performed on the digital elevation model of the non-uniform slope in the radial and axial directions of the local digital elevation map. The number of radial interpolation points is m=10, and the number of axial interpolation points is n=20. The Cartesian coordinate system of the interpolation points of the local digital elevation map is obtained, and the interpolation point s in the Cartesian coordinate system is denoted as s. d (x k ,y k ,z k ),in If k ≤ m × n, the set of interpolation points for the nozzle position is as follows: Figure 7 As shown.

[0105] The Cartesian coordinate system is converted to a cylindrical coordinate system with the single nozzle position as the origin. The interpolation point in the cylindrical coordinate system is denoted as s. C (θ i ,r j ,z k ), θ i S represents c The rotation direction angle, r j S represents c radial coordinates, z k S represents c Given the vertical coordinates, we have: When i≤m and j≤n, fitting the non-uniform slope terrain curve in the cylindrical coordinate system can further reduce the difficulty of modeling and solving.

[0106] Step 5: Fit the terrain curve in the radial direction:

[0107] Based on the radial direction θ of a single nozzle in the cylindrical coordinate system described in step four i = set of interpolation points on i·2π / n Where i = 1, 2, ..., n, the radial direction θ of a single nozzle is fitted using a polynomial curve. i Non-uniform slope terrain curves:

[0108] In the above formula, r represents the radial direction θ i The distance from the origin in the direction, c n This represents the coefficient of a polynomial of degree n.

[0109] Taking i=16 as an example, the interpolation points in the radial direction are transformed into interpolation points in cylindrical coordinates through step four. The set of interpolation points in cylindrical coordinates is shown in Table 2.

[0110] Table 2 Radial direction θ i =16·2π / 20 interpolation point

[0111]

[0112] In Table 2, r represents the radial direction θ. i The distance from the origin in the direction of the interpolation point, z represents the vertical coordinate, and the fitted curve of the interpolation point. The specific expression is as follows:

[0113]

[0114] The fitted non-uniform slope topography curve is as follows: Figure 8 As shown.

[0115] The slope angle of a non-uniform slope varies with the distance from the nozzle, and the projection of the water droplet trajectory onto the non-uniform slope is a curve. Polynomial curve fitting can better describe this projected curve. Indicates the radial direction θ i The terrain above.

[0116] Step 6: Establish the equation for the trajectory of the water droplet:

[0117] Water droplets flying through the air are affected by gravity and air resistance:

[0118] Gravity of water droplets: In the above formula, d w ρ is the diameter of the water droplet, in meters; w The density of a water droplet in the environment, kg / m³ 3 g is the acceleration due to gravity, 9.8 N / kg;

[0119] Air resistance: In the above formula, f represents inertial drag, which is opposite to the direction of velocity; ρ a ρ is the bulk density of air in the environment, kg / m³; v is the velocity of the water droplet, m / s; C D This refers to the air drag coefficient;

[0120] C D It is related to the Reynolds number Re, and its calculation formula is as follows:

[0121]

[0122] The Reynolds number Re is calculated as follows: Re = vd w / υ, where v is the velocity of the water droplet in the above formula, m / s; d w is the diameter of the water droplet, in meters; υ is the aerodynamic viscosity coefficient, in m / s.

[0123] υ is related to air temperature, and its calculation formula is as follows:

[0124] υ=1.3045×10 -5 +1.222×10 -7 T-9.6471×10 -7 T2 +7.2873×10 -12 T 3 In the above formula, T is the air temperature, in °C, which is taken as 30 °C;

[0125] Based on Newton's second law and the relationship between the forces acting on the water droplet and its motion, a system of two-variable second-order partial differential equations for the motion of the water droplet is established:

[0126]

[0127] In the above formula, r is the horizontal distance the water droplet travels (m); z is the vertical distance the water droplet travels (m); t is the travel time of the water droplet from the nozzle of a single spray head (s); v r Let v be the horizontal component of the water droplet's velocity, in m / s; v z Let v be the vertical component of the water droplet's velocity, in m / s; C D ρ is the air drag coefficient. a The bulk density of air in the environment is 1.293 kg / m³. 3 ;d w ρ is the diameter of the water droplet, in meters; w The density of the water droplet in the environment is 1×10⁻⁶. 3 kg / m 3 g is the acceleration due to gravity.

[0128] To facilitate the solution, the equations of motion of the water droplet are transformed into a system of multivariable first-order partial differential equations:

[0129]

[0130] Step 7: Establish a model of the trajectory of a water droplet passing through a point on a non-uniform slope:

[0131] To determine the sprinkler intensity at a point on a non-uniform slope, it is necessary to first know the trajectory of the water droplets passing through that point. Based on the location of the point on the non-uniform slope and the equation of the water droplet trajectory, a model of the water droplet trajectory passing through that point on the non-uniform slope can be established. This model can establish the relationship between the distance to the slope and the droplet size. Compared with the existing method of calculating the water volume at the corresponding landing point on the slope by changing the droplet size, this model can provide basic data for directly determining the water volume at a point on a non-uniform slope.

[0132] Different droplet sizes correspond to unique trajectories. Solving for the droplet trajectory is equivalent to determining the droplet size. Based on the location of a point on a non-uniform slope, the fourth-order Runge-Kutta method and the bisection method can be applied to gradually approximate the droplet trajectory to that point, thereby determining the droplet size d. w Therefore, this step can determine the trajectory and droplet size of a droplet passing through a point on a non-uniform slope by using that point as an example. Figure 2 The process shown is as follows:

[0133] Initialization parameters include: initializing the spatial position point (θ) of the water droplet. i ,r p ,z p ), θ i r is the rotation direction angle. p Z represents the radial coordinate. p Vertical coordinates; Initialize the nozzle's working pressure P; Initialize nozzle structural parameters: nozzle flow coefficient C p =0.98, nozzle elevation angle α0 = 30°, nozzle vertical pipe height l = 1.2m; Initialize the parameters of the water droplet trajectory equation: initial temperature T = 30℃, initial density ρ of the water droplet in the environment. w = 1×10³ kg / m 3 Initialize the bulk density ρ of air in the environment a =1.293kg / m 3 Initialize the inertial drag coefficient C D Initialize the droplet's start time t0 = 0, initialize the droplet's unit running time Δt = 0.001s, and initialize the droplet's minimum diameter d. wmin =0m, initialize the maximum diameter d of the water droplet. wmax =0.006m, initial allowable error Δε = 0.0001, initially determine the diameter d of the water droplet. w Let the iteration count n = 0.

[0134] Based on the above initialization parameter values, the water droplet motion equations are determined to be transformed into the multivariate first-order partial differential equation system described in step six. Therefore, the initial conditions at time t0 include:

[0135]

[0136] In the above formula, r(0) is the initial horizontal distance of the water droplet, z(0) is the initial vertical distance of the water droplet, and v r (0) represents the horizontal component of the initial droplet velocity, v z (0) represents the horizontal component of the initial droplet velocity, C p This represents the flow coefficient of the nozzle.

[0137] The fourth-order Runge-Kutta method is used to solve for the horizontal velocity v of the water droplet at the next time point t1 = t0 + Δt. r (t1) and the vertical velocity v z(t1); Based on the relationship between the distance traveled and the velocity of the water droplet in the horizontal and vertical directions per unit time, calculate the horizontal coordinate value r(t1) and the vertical coordinate value z(t1) of the water droplet at time t1; and so on, the values ​​can be calculated and stored in t1. n At time t, the horizontal coordinate value r(t) of the water droplet n ) and the vertical coordinates of the water droplet z(t) n The accuracy of the water droplet trajectory model can be further improved by applying the fourth-order Runge-Kutta method.

[0138] Using the initial spatial position of the water droplet (1.5π, 11.7823, -3.9511) and the initial working pressure of the nozzle P = 200 kPa, the diameter d of the water droplet is initially determined. w =0.001m, solve for the horizontal velocity v of the water droplet at time t1. r (t1) and the velocity v in the vertical direction z Taking (t1) as an example, the calculation process of the fourth-order Runge-Kutta method will be further explained:

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149] Taking the calculation of the water droplet's horizontal position r(t1) and vertical position z(t1) at time t1 as an example, the calculation process is explained:

[0150] Compare r(t) n ) and r p If r(t) n )<r p Let n = n + 1, and calculate r(t) at the next time step.n ) and z(t n If r(t) n )≥r p Then let ε = z(t) n )-z p Compare ε and Δε: If ε ≥ Δε, let d wmax =d w d w =(d wmax +d wmin ) / 2, n=0, clear r(t) n ) and z(t n The storage of ) is used to start a new round of operations; if ε≤-Δε, let d wmin =d w d w =(d wmax +d wmin ) / 2, n=0, clear r(t) n ) and z(t n The storage of ) is used to start a new round of calculations. If -Δε < ε < Δε, then output d. w After iterative calculation, when n = 2663, d w =0.0018.

[0151] Step 8: Convert surface irrigation intensity to slope irrigation intensity

[0152] To determine the sprinkler intensity at a point on a non-uniform slope, the trajectory of water droplets passing through that point must first be known. This allows us to determine the intersection of the water droplet trajectory with the plane, and then obtain the sprinkler intensity corresponding to the single-nozzle planar water distribution model at that intersection. This is then converted into the sprinkler intensity at the corresponding point on the non-uniform slope. The principle is as follows: Figure 3 As shown:

[0153] To determine the sprinkler intensity at a point p0(θ0,r0,z0) on a non-uniform slope in the cylindrical coordinate system described in step four, the non-uniform slope topography curve along the radial direction θ0 of a single sprinkler head is fitted with the sprinkler head's location as the origin. Establish a model of the water droplet's trajectory passing through point p0, solve for the water droplet's trajectory passing through point p0(r0,z0), and then calculate the trajectory based on the water droplet's trajectory and... Find the point where the water droplet's trajectory intersects the plane at point p1(r1,z1); the slope of the straight line passing through points p0 and p1 is k = (z1-z0) / (r1-r0), and the non-uniform slope curve. The slope of the tangent line at point p0 is... The tangent is Let the increment in the direction r be Δr = r2 - r0 > 0, and let p2(r2, z2) be a point on the tangent line passing through p0, where r2 = r0 + Δr. Then the length of p0p2 is Draw a line through point p2 parallel to p1p0, intersecting the plane at point p3; the length of p1p3 is...

[0154] Based on the conservation of water volume in the radial direction of a single nozzle, the water volume in line segment p0p2 should be equal to the water volume in line segment p1p3. Therefore: In the above formula, q f (p,r1) represents the sprinkler intensity on the plane when the pressure is p and the radial distance is r1; where q N (p, r0) represents the sprinkler intensity on a non-uniform slope when the pressure is p and the radial distance is r0; where

[0155] Therefore, the sprinkler intensity at a point (θ0, r0, z0) on a non-uniform slope under pressure p can be derived as follows:

[0156]

[0157] In the above formula, This indicates the irrigation intensity of the single-nozzle planar water distribution model at point p when the pressure is p.

[0158] Taking p0(θ0,r0,z0)=(1.6π,10,-3.365) as an example: As described in step five, based on the digital elevation model, fit the non-uniform slope terrain curve in the 1.6π radial direction; as described in step seven, solve for the trajectory of the water droplet passing through point p0(10,-3.365); based on the trajectory of the water droplet and the non-uniform slope terrain curve in the 1.6π radial direction, solve for the intersection of the water droplet trajectory and the plane at point p1(8.9315,0); the slope of the straight line passing through points p0 and p1 is k=(z1-z0) / (r1-r0)=-3.1508; based on the non-uniform slope curve, solve for the slope of the tangent at point p0. The sprinkler intensity at point p1(8.9315,0) is calculated according to step two. The value is 1.7805. Therefore, the sprinkler intensity on a non-uniform slope can be derived as follows:

[0159]

[0160] Similarly, based on the coordinates of points along the 1.6π radial direction, the irrigation intensities along the 1.6π radial direction can be calculated sequentially; similarly, the irrigation intensities in other radial directions can be calculated. By combining the irrigation intensities at any point on the non-uniform slope topography curve, the water distribution of a single sprinkler on a non-uniform slope can be obtained, as shown in the figure. Figure 9 As shown.

[0161] To verify the feasibility and accuracy of the above method, a single-nozzle irrigation experiment was conducted on a local terrain surface. The experiment used the location of the sprinkler head as the origin, and measuring points were arranged along two radial directions: radial direction 1 and radial direction 2. The distance between each measuring point in the radial direction was 1 meter. Figure 10 As shown, rain gauges were placed at each measuring point to measure the sprinkler intensity at each point, and the measured values ​​were used as the actual values.

[0162] The above-mentioned method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head is applied to predict the irrigation intensity at each measuring point, which is then used as the predicted value. The measured and predicted values ​​of the irrigation intensity at each measuring point in the two radial directions are compared as follows: Figure 11 and Figure 12 As shown. From Figure 11 and Figure 12 As can be seen, the predicted and measured values ​​are basically consistent in their trends. The root mean square error of the sprinkler irrigation intensity is 0.23–0.27 mm / h. Overall, the prediction results can reflect the distribution pattern of sprinkler irrigation water on non-uniform slopes.

[0163] The detailed descriptions listed above are merely specific illustrations of feasible embodiments of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head, characterized in that, The methods include: A planar water distribution model for a single sprinkler head is established based on the radial irrigation intensity of a single sprinkler head in a plane. A digital elevation model of a non-uniform slope is established, and a non-uniform slope terrain curve in the radial direction of a single nozzle is fitted based on the digital elevation model. An equation for the trajectory of a water droplet is established. Based on the location of a point on a non-uniform slope and the equation for the trajectory of the water droplet, a model for the trajectory of the water droplet passing through a point on a non-uniform slope is established. Based on the model for the trajectory of the water droplet and the topographic curve of the non-uniform slope, the intersection point of the trajectory of the water droplet passing through a point on a non-uniform slope and the plane is obtained. The methods for establishing a system of two-variable second-order partial differential equations for the motion of a water droplet based on the relationship between the forces acting on it and its motion include: In the above formula, The distance the water droplet travels in the horizontal direction. This represents the distance the water droplet travels in the vertical direction. The running time is the time from when the water droplets are ejected from a single nozzle. For the speed of water droplets The component of velocity in the horizontal direction, For the speed of water droplets The component of velocity in the vertical direction, The air drag coefficient, The density of air in the environment. The diameter of the water droplet. The density of the water droplet in the environment. The acceleration due to gravity is used; the equations of motion of the water droplet are transformed into a set of multivariate first-order partial differential equations to obtain the trajectory equation of the water droplet. Based on the location of a point on a non-uniform slope, the method of using the bisection method to make the trajectory of a water droplet gradually approach the location of that point on the non-uniform slope, and the method of establishing a model of the trajectory of a water droplet passing through a point on a non-uniform slope, also includes: Initialize the radial coordinates of the spatial position point through which the water droplet passes. and vertical coordinates Initialize the nozzle structure parameters, initialize the parameters of the water droplet trajectory equation, and initialize the water droplet start time. Initialize the minimum diameter of the water droplet. Initialize the maximum diameter of the water droplet Initialize allowable error The diameter of the water droplet was initially determined. Let the iteration count be... ; Based on the initialization parameters, the equation of the water droplet's trajectory and the time are obtained. The initial conditions at time are calculated and stored. The horizontal coordinates of the water droplet at a given moment The coordinates of the water droplet in the vertical direction ; Compare and :like Then let Calculate the next time step and ;like Then let ; Compare and :like ,make , , Clear and The storage initiates a new round of computation; if ,make , , Clear and The storage initiates a new round of computation, if Then output ; Based on the water conservation in the radial direction of a single sprinkler head and the non-uniform slope topography curve, the irrigation intensity of the single sprinkler head planar water distribution model corresponding to the intersection point is transformed into the irrigation intensity of a certain point on the non-uniform slope. By combining the irrigation intensities of any point on all the non-uniform slope topography curves, the water distribution of a single sprinkler head on the non-uniform slope is obtained.

2. The method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head according to claim 1, characterized in that, Based on the radial irrigation intensity of a single sprinkler head under different pressures, a planar water distribution model for a single sprinkler head is established using the Delaunay triangulation linear interpolation algorithm.

3. The method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head according to claim 1, characterized in that, Based on the set of elevation points of a non-uniform slope, a digital elevation model of the non-uniform slope is established using the Kriging interpolation method.

4. The method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head according to claim 1, characterized in that, A local digital elevation map is determined with the location of a single nozzle as the center and the maximum spray range that a single nozzle can spray as the radius. The digital elevation model of the non-uniform slope is uniformly interpolated in the radial and axial directions of the local digital elevation map to obtain the coordinate system of the interpolation points of the local digital elevation map. The non-uniform slope terrain curve in the radial direction of the single nozzle is fitted based on the coordinate system.

5. The method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head according to claim 1, characterized in that, The digital elevation model is uniformly interpolated to obtain a Cartesian coordinate system. This Cartesian coordinate system is then converted into a cylindrical coordinate system with the single nozzle position as the origin. The radial direction of the single nozzle in the cylindrical coordinate system is then considered. The set of interpolation points on the surface is used to fit the radial direction of a single nozzle using a polynomial curve. Non-uniform slope topographic curves: In the above formula, Indicates radial direction The distance from the origin in the direction. Indicates the number of times The coefficients of a polynomial.

6. The method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head according to claim 1, characterized in that, Initialize the water droplet's running time unit By applying the fourth-order Runge-Kutta method, and based on the relationship between the distance traveled by a water droplet in the horizontal and vertical directions and its velocity per unit time, the following calculations are performed. and The methods include: ; ; In the above formula, for Previous time, The air drag coefficient, The density of air in the environment. The diameter of the water droplet. The density of the water droplet in the environment. It is the acceleration due to gravity. for The horizontal component of the water droplet's velocity at any given moment. for The vertical component of the water droplet's velocity at any given moment. for The horizontal component of the water droplet's velocity at any given moment. for The vertical component of the water droplet's velocity at any given moment. for The coordinates of the water droplet in the horizontal direction at any given moment. for The coordinates of the water droplet in the vertical direction at any given moment.

7. A method for converting water distribution from a plane to a non-uniform slope using a single sprinkler head according to any one of claims 1 to 6, characterized in that, Fitting the radial direction of a single nozzle Non-uniform slope topography curves Sprinkler intensity at a point on a non-uniform slope: In the above formula, This indicates the irrigation intensity of the single-nozzle planar water distribution model corresponding to the intersection point. express The slope of the tangent at a point on a non-uniform slope. The slope of the line representing the intersection point of a point on a non-uniform slope with the given point is given.

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