Cylindrical spatialization-based field block test design method

Abstract

A cylindrical spatialization-based field block test design method, relating to the field of agricultural engineering technologies and tests. The method comprises content such as planning of a test area sample plot, cylindrical spatialization processing of a test area, design of test area cylindrical rear surface sampling lines, plane unfolding of a test area cylinder, and determination of sampling points. After cylindrical spatialization of a test area, on the basis of geometry and kinematics, sampling lines and test repetition lines are planned for the test area after the cylinder spatialization, sampling points are formed, each sampling point and sampling line have the characteristics such as randomness, equiprobability, equivalence, and uniformity, and the method is suitable for test point positioning or sampling requirements of various agricultural surface related block tests.

Description

A field plot test design method through cylindrical spatialization TECHNICAL FIELD

[0001] The present application belongs to the field of agricultural engineering technology and test, in particular to a kind of field plot test design method through cylindrical spatialization. Through cylindrical spatialization test area, after planning test test line and test point, it is unfolded as plan, and test sampling scheme is formed. It is suitable for various plot tests on the ground plane in farmland, woodland, grassland and the like. BACKGROUND

[0002] The agricultural field plot test is an important part of field test, and the determination of soil physical and chemical properties, plant growth, crop yield and the like involves plot test. The design of sampling point in field plot test is various, but the sampling method that meets the randomness and equivalence simultaneously is missing. When determining the influence of single factor or single test treatment on test index, test planning is relatively simple, and the method of randomly determining points on diagonal line in test area is generally used, but whether these points are equivalent in theory and practice has not been deeply explored and researched. However, in the case of limited test area, it is difficult to plan reasonable sampling points or test points that meet the randomness and equivalence simultaneously for multi-factor test repetition (when test treatment number ≥2 and test repetition ≥2), which leads to the decrease of reliability of test results. The commonly used field plot test method requires more test area, and has the requirements of mutual independence for each test area, which increases the requirement for test area and test cost, and the test is difficult to complete in the case of limited test objects. In addition, the current common field sampling and test planning pay too much attention to randomness, and the regularity of test point distribution on test area is not strong, which brings difficulties to the marking of test point after test treatment and the later statistical test results, and is not conducive to classification comparison and identification. Therefore, it is of great significance to propose a sampling test method that can realize multi-factor test repetition under each test treatment in limited test area, which has a positive effect on reducing test area and test cost of plot test. TECHNICAL PROBLEM

[0003] In view of the above technical problems, in the case of limited test area, it is difficult to plan reasonable sampling points or test points that meet the randomness and equivalence simultaneously for multi-factor test repetition (when test treatment number ≥2 and test repetition ≥2), which leads to the decrease of reliability of test results. The existing field plot test method increases the requirement for test area, increases the test cost, and the test is difficult to complete in the case of limited test objects. The regularity of test point distribution on test area is not strong, which brings difficulties to the marking of test point after test treatment and the later statistical test results, and is not conducive to classification comparison and identification. TECHNICAL SOLUTION

[0004] The application provides a field plot test design method based on cylindrical space, which spatializes a test rectangular area, takes a test point trajectory on a cylindrical surface as a test treatment line, takes an upper and lower cross section line of a cylindrical volume as a test repetition line, plans an intersection line of the two as a test point, and then unfolds the cylindrical surface into a plan view to form a test scheme.

[0005] The application aims to achieve the above-mentioned purpose through the following technical scheme.

[0006] The application provides a field plot test design method based on cylindrical space, which spatializes a test rectangular area, takes a test point trajectory on a cylindrical surface as a test treatment line, takes an upper and lower cross section line of a cylindrical volume as a test repetition line, plans an intersection line of the two as a test point, and then unfolds the cylindrical surface into a plan view to form a test scheme; and the method specifically comprises the following steps.

[0007] Step one: on a test site, estimate a sampling area, i.e., a test area, according to a sample quantity and a minimum area required for each sample to carry out a test;

[0008] Step two: according to the test area, plan the test area into a rectangular test area according to the test area, and determine the length and width of the test area;

[0009] Step three: spatialize the planned rectangular test area into a cylindrical space, determine a cylindrical radius and height, and establish a spatial rectangular coordinate system with the spatialized cylindrical bottom surface as an XOY plane and with a cylindrical central axis as a Z axis;

[0010] Step four: equally divide the circumference of the cylindrical bottom surface according to the quantity of different test treatments, and correspond each test treatment to an equally divided point;

[0011] Step five: equally divide the cylindrical volume according to the repetition number of the test by using a plane parallel to the bottom surface XOY, mark the cylindrical cross section to form a cross section equally divided line, and represent one repetition test by the cross section line on the upper and lower surfaces of each equally divided cylindrical segment;

[0012] Step six: take the equally divided point on the length of the cylindrical bottom surface as a starting point, assume that the same mass point at each starting point moves along a spiral line on the cylindrical surface, and decompose the spiral line movement of the mass point on the cylindrical surface into two kinds of movements, one is uniform circular motion along the circumference of the bottom surface, and the other is uniform linear motion along the generatrix of the cylinder perpendicular to the bottom surface, limit the two kinds of movements to have the same time to reach the end point, i.e., the time for the mass point to rotate at a uniform speed along the circumference of the bottom surface for one circle is equal to the time for the mass point to reach the top surface of the cylinder along the generatrix of the cylinder perpendicular to the bottom surface.

[0013] Step seven, draw the spiral line formed by each particle on the surface of the cylinder, and unfold the three-dimensional cylinder into a plan view;

[0014] Step eight, find the intersection point of the spiral line and the volume equal section line on the unfolded plan view, and the intersection point is the test candidate point;

[0015] Step nine, analyze the test candidate point, exclude equivalent repeated points under the same condition, determine the final test point, and complete the test sampling design.

[0016] Further, in step one, the test area is estimated, first, the test area is planned, the land area occupied by the test object or the minimum test area S1 occupied by one test is determined, the number of different test treatment types N CL and the number of repetitions n cf of each test are determined S =N CL ×n cf , the minimum total area of the test area Ss=S1×N S =S1×N CL ×n cf .

[0017] Further, in step two, the length and width of the rectangular test area are W and L respectively, then the minimum total area of the test area Ss=S1×N CL ×n cf =W×L, and the length L and the width W are respectively established with the test treatment number N CL and the test repetition number n CL The relationship between the width W and the number of test treatment types N cf is W=2πr / (N cf -1)×d, the relationship between the length L and the number of test repetitions n CL is L=(n cf -1)×l.

[0018] Further, in step three, the planar cylinder of the sampling test area is spatialized, and the circumference of the base and the height of the cylinder are determined according to the rectangular test area determined in steps one and two.

[0019] Further, after the test area is spatialized, the determination of the test point includes drawing sampling lines of different experimental treatments on the surface of the cylinder and drawing repeated test lines on the sampling lines of the same test treatment.

[0020] Furthermore, when sampling different test treatments and repeated tests of the same test treatment, different test treatment points are used as particles. On the one hand, the particles perform uniform circular motion along the perimeter line of the bottom surface, and the probability of appearing at any position of the perimeter line of the bottom surface at any time is the same; at the same time, the particles perform uniform linear motion along the busbar perpendicular to the bottom surface of the cylinder, and the probability of appearing at any position of the busbar of the cylinder at any time is the same, so that the time for the particle to complete a uniform circular motion is equal to the time for a uniform linear motion along the busbar. The particle forms a sampling line and test repetition points on the sampling line on the surface of the cylinder. Beneficial effects

[0021] The present invention has the characteristic of planning the minimum test area, and all test treatments and repeated tests can be completed in one test area. First, plan the appropriate test area, determine the surface area occupied by the test object or the minimum test area S1 occupied by the test to carry out a test, and determine the number of different test treatment types N. CL and the number of repetitions n for each trial cf , determine the total number of trials N S =N CL ×n cf , we can get the minimum total area of ​​the test area Ss=S1×N S =S1×N CL ×n cf .

[0022] The present invention establishes a correlation between the processing and number of repetitions of the test and the length and width of the test area, and establishes a connection between the abstract test plan design and the geometric characteristic parameters of the test area, thereby realizing the correlation between the test plan and the test area, and the specific location of the test points in the test area. According to the minimum area of ​​the test area, the test area is planned as a rectangular AHKP with a width of W and a length of L, and Ss=W×L=S1×N CL ×n cf Since the minimum test area S1 occupied by a test point is a fixed value, the width W of the rectangle can be calculated by comparing it with the number of different treatment types N. CL (N CL =1,2,3...n) to establish the correlation between the length L and the number of repetitions n under each experimental treatment. cf (n cf =1,2,3...n) to establish correlation.

[0023] This method spatializes the planned test area into a cylindrical space, assigns kinematic laws based on the desired characteristics of the test points, and determines the sampling line. Considering the requirements for randomness, equal probability, and uniformity of the test points, the corresponding starting points of the test treatment are assigned two kinematic laws: uniform circular motion and uniform linear motion. The sampling line (or test line) under different treatment conditions is determined based on the curved trajectory formed by the motion on the cylindrical surface.

[0024] The present application establishes a relationship between the cylindrical volume of the spatialized test area and the repeated tests under the same processing test conditions, and realizes the equivalence and uniformity of the repeated tests. The test repeated lines are evenly distributed by equally dividing the plane parallel to the bottom surface, and each test repeated line is parallel, equal and equidistant, and the test points distributed on the repeated lines are equivalent and uniform.

[0025] The present application has the design feature of spatializing the test area plane and then unfolding it into a plane. Under the condition of determining the test area size and shape, according to the number of test treatments and the number of test repetitions, the test area plane is processed by cylindricalization, the sampling line is determined, and the test repeated line is determined, and then the spatial cylinder is unfolded along the edge line forming the cylinder to form the test design points.

[0026] The present application further analyzes the test points on the unfolded plane, excludes equivalent and repeated test points, and determines the final test points and test scheme. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a schematic diagram of the test area quadrat plane.

[0028] Figure 2 is a schematic diagram of the cylindrical spatial processing of the test area.

[0029] Figure 3 is a planar unfolding diagram of the test area cylinder along the A0A1 line when the number of test treatment types N cL =1 and the number of test repetitions n cf =4.

[0030] Figure 4 is a schematic diagram of the cylindrical spatial processing of the test area when the number of test treatment types N cL =6 and the number of test repetitions n cf =7.

[0031] Figure 5 is a planar unfolding diagram of the test area cylinder along the A0A1 line when the number of test treatment types N cL =6 and the number of test repetitions n cf =7. BEST MODE FOR CARRYING OUT THE INVENTION

[0032] The present application will be described in detail below in conjunction with the drawings and examples.

[0033] Example: As shown in Figures 1-5, the present application is a field plot test design method by cylindrical spatialization, which spatializes the test rectangular area, takes the test point on the cylindrical surface trajectory as the test treatment line, takes the upper and lower cross-sectional lines equally divided by the cylindrical volume as the test repeated line, plans the intersection line of the two as the test point, and then unfolds the cylindrical surface into a planar diagram to form a test scheme; specifically including the following steps:

[0034] Step one: in the land to be tested, estimate the sampling area according to the number of samples and the minimum area required for each sample to carry out the test, that is, the test area;

[0035] Step two: according to the test area, plan it as a rectangular test area, determine the length and width of the test area;

[0036] Step three: plan the rectangular test area as a cylindrical space, determine the radius and height of the cylinder, and establish a spatial rectangular coordinate system with the bottom surface of the space as the XOY plane and the central axis of the cylinder as the Z axis;

[0037] Step four: divide the circumference of the cylinder bottom surface equally according to the number of different treatments, and each treatment corresponds to an equally divided point. The distance between adjacent treatment points on the circumference of the bottom surface is d;

[0038] Step five: divide the cylinder volume equally by a plane parallel to the bottom surface XOY, and mark the cross section to form a cross section. The cross section line on the upper and lower surfaces of each equal volume cylinder represents a repeated test. The distance between adjacent cross sections is l;

[0039] Step six: take the equally divided points on the circumference of the cylinder bottom surface as the starting point, and assume that the same mass point moves along the spiral line on the surface of the cylinder. The spiral line motion of the mass point on the surface of the cylinder is decomposed into two kinds of motion, one is uniform circular motion along the circumference of the bottom surface, and the other is uniform linear motion along the generatrix perpendicular to the bottom surface of the cylinder. Limit the two kinds of motion to reach the end point at the same time, that is, the time for the mass point to rotate one circle along the circumference of the bottom surface and the time for the mass point to reach the top surface of the cylinder along the generatrix perpendicular to the bottom surface are equal;

[0040] Step seven, draw the spiral lines formed by each mass point on the surface of the cylinder, and unfold the three-dimensional cylinder according to the plan;

[0041] Step eight, find the intersection points of the spiral lines and the volume division cross section lines on the unfolded plan, and the intersection points are the test points to be selected;

[0042] Step nine, analyze the test points to be selected, exclude equivalent repeated points under the same conditions, determine the final test points, and complete the test sampling design.

[0043] In step one, the test area is estimated. First, plan the test area, determine the surface area occupied by the test object or the minimum test area S1 occupied by one test, determine the number of different test treatment types N CL And the number of repetitions of each test n cf , determine the total number of tests N S =N CL ×n cf, the minimum total area of the test area Ss = S1 x N S = S1 x N CL = S1 x N cf = S1 x N CL = S1 x N cf = S1 x N CL = S1 x N cf = S1 x N CL = S1 x N CL = S1 x N cf = S1 x N cf = S1 x N

[0044] In step three, the planar sampling test area is spatialized as a cylinder, as shown in FIG. 2, and the length and width of the rectangular test area determined in steps one and two are used to determine the circumference of the cylinder base and the height of the cylinder. The number of different test treatment types N CL = 1, and the number of test repetitions n cf = 4. 1, 2, 3, and 4 are the cross-sectional lines of the cylinder formed by equally dividing the cylinder volume in the plane parallel to the cylinder base XOY, representing the number of test repetitions. a1 represents an arbitrary point on the circumference of the cylinder base, ω1 represents the angular velocity of a1 along the circumference of the base, and v1 represents the forward velocity of a1 along the generatrix of the cylinder perpendicular to the base, with the time for a1 to complete one circular motion along the circumference of the cylinder base being the same as the time for a1 to reach the end point along the generatrix at a constant linear velocity (isochronous effect). The spiral curve AP formed on the surface of the cylinder by the combined motion of a1 represents the sampling line formed under the A test condition.

[0045] After spatializing the test area cylinder, the determination of the test points includes drawing the sampling lines of different test treatments and drawing the repeated test lines on the sampling lines of the same test treatment. When sampling, the different test treatment points are taken as the mass points, which move at a constant angular velocity along the circumference of the base, with the probability of appearing at any position on the circumference of the base being the same at any time. At the same time, the mass points move at a constant linear velocity along the generatrix perpendicular to the base, with the probability of appearing at any position on the generatrix being the same at any time. The time for the mass point to complete one circular motion is equal to the time for the mass point to complete one linear motion along the generatrix, and the mass point forms a sampling line on the surface of the cylinder and a repeated test point on the sampling line.

[0046] As shown in Figure 1 is a test area sample plot plane schematic diagram. Among them, A, H, P, K are the four vertices of the plane rectangular test area, W is the width of the rectangular test area, L is the length of the rectangular test area, the width of the bottom edge AH of the rectangle AHPK represents the number of different treatment types of the test, the number value is N cL ; the length of the side KH of the rectangle AHPK represents the number of repetitions of the test, the value of the number of repetitions is n cf ; the side AP and HK of the rectangle AHPK is the starting edge and the ending edge of the cylindrical space, and the cylindricalization makes the side AP and HK coincide.

[0047] As shown in Figure 2 is a cylindrical space treatment schematic diagram of the test area. Among them, AP (HK) is the coincident line after the cylindrical space of the test area, which is also the generatrix of the cylinder perpendicular to the bottom surface XOY; the center of the bottom surface of the cylinder is O, the radius of the bottom surface circle is r (W = 2πr), the height is h (h = L), the XOZ coordinate system is a space rectangular coordinate system established with the center of the cylinder bottom as the center and the central axis of the cylinder as the Z axis, 1, 2, 3, 4 are the cross-sectional lines of each section of the cylinder formed after the cylindrical volume is equally divided, which represent the number of repetitions of the test; a1 represents an arbitrary point on the circumference of the cylindrical bottom surface, ω1 represents the angular velocity of a1 along the circumference of the bottom surface, v1 represents the forward speed of a1 along the generatrix perpendicular to the bottom surface of the cylinder, and the time of a1 along the circumference of the cylindrical ground to make one revolution is the same as the time of a1 along the generatrix of the cylinder to reach the endpoint (isochronous effect); the spiral curve AP formed by the combined motion of a1 on the surface of the cylinder represents the sampling line formed under the A test condition.

[0048] Figure 3 is a test treatment type number N cL =1, the number of test repetitions n cf =4 when the test area cylinder is unfolded along the AP plane, the angle of KH from AP to the fully unfolded rotation is 360°. Among them, AK line is the sampling line under the test treatment condition, 1, 2, 3, 4 line is the repeated test line, AK and 1, 2, 3, 4 intersection a1, a2, a3, a4 is the test point.

[0049] Figure 4 is a test treatment type number N cL =6, the number of test repetitions n cf=7, A0, B0, C0, D0, E0, F0 are six equal points of the bottom circumference of the cylinder, representing six treatments, A1, B1, C1, D1, E1, F1 are the intersection points of the cylinder generatrix passing through A0, B0, C0, D0, E0, F0 and the top circumference of the cylinder. 1, 2, 3, 4, 5, 6, 7 are the cross-sectional lines of the cylinder formed by equally dividing the cylinder volume into seven parts along the XOY plane parallel to the bottom of the cylinder, representing that the number of repetitions of the test under each treatment condition is 7. ω1 represents the angular velocity of A0, B0, C0, D0, E0, F0 moving uniformly along the bottom circumference, and v1 represents the forward speed of A0, B0, C0, D0, E0, F0 moving uniformly along the generatrix perpendicular to the bottom of the cylinder. The time for A0, B0, C0, D0, E0, F0 to move one circle along the bottom circumference is the same as the time for them to move uniformly along the generatrix to the end point (isochronous effect). A0, B0, C0, D0, E0, F0 move along the surface of the cylinder to form a spiral line, and the end point of the spiral line is exactly A1, B1, C1, D1, E1, F1 according to the above movement law.

[0050] Figure 5 is the number N of test treatment types cL =6, the number of repetitions n of the test cf =7, the plan view of the test area after being cylindrically expanded along the A0A1 line. A0G1 and the inclined lines parallel to AG1 are the spiral lines on the expanded cylinder surface, representing the sampling lines under different test treatment conditions, and the same lowercase letters are used to mark the sampling lines of the same test. The lines 1, 2, 3, 4, 5, 6, 7 are the repeated test lines, and the intersection points a1, a2, a3... of each sampling line with 1, 2, 3, 4, b1, b2, b3..., c1, c2, c3..., d1, d2, d3..., e1, e2, e3..., f1, f2, f3... are the test points of the 7 repeated tests under 6 different test treatment conditions.

[0051] For tests with multiple treatment conditions and multiple repetitions, some equivalent test points need to be removed from the planar expansion diagram. For example, b6 on the A0A1 line and b6, c5, d4, e3, f2 on the G0G1 line are equivalent repeated points, and only one of the two points can be selected for the test.

[0052] It can be understood that the above specific description of the present application is only used to illustrate the present application and is not limited to the technical solutions described in the embodiments of the present application. Those skilled in the art should understand that the present application can still be modified or replaced equivalently to achieve the same technical effect, as long as it meets the use needs, which is within the protection scope of the present application. Industrial applicability

[0053] The present application has the characteristics of planning minimum test area, and all test treatments and repeated tests can be completed in one test area. First, a proper test area is planned, the surface area occupied by the test object or the minimum test area S1 occupied by one test is determined, the number N of different test treatment types is determined CL and the number n of repetitions of each test cf , the total number of tests N S =N CL ×n cf is determined, the minimum total area Ss of the test area is obtained as Ss=S1×N S =S1×N CL ×n cf . It is suitable for various field, forest land, grassland and the like which carry out block test on the ground surface.

Claims

1. A field block experiment design method using cylindrical space, characterized in that: The test rectangular area is spatialized, the motion trajectory of the test point on the cylindrical surface is used as the test processing line, the upper and lower cross-section lines that divide the cylindrical volume into equal parts are used as the test repetition line, and the intersection of the two is planned as the test point. The cylindrical surface is then unfolded into a plane diagram to form a test plan. The specific steps include: Step 1: At the site to be tested, estimate the sampling area, i.e. the area of ​​the test area, based on the number of samples and the minimum area required to conduct the test for each sample; Step 2: Plan the test area into a rectangular test area based on the area of ​​the test area and determine the length and width of the test area; Step 3: Spatialize the planned rectangular test area cylinder, determine the cylinder radius and height, and establish a spatial rectangular coordinate system with the bottom surface of the spatialized cylinder as the XOY plane and the central axis of the cylinder as the Z axis; Step 4: Divide the circumference of the cylinder base into equal parts according to the number of different treatments in the experiment, with each experimental treatment corresponding to an equal division point; Step 5: Divide the volume of the cylinder into equal parts using a plane parallel to the bottom surface XOY according to the number of repetitions of the test, and mark the cross sections of the cylinder to form a bisecting line. The cross-sectional lines on the upper and lower surfaces of each section of the cylinder with equal volume represent one repetition of the test. Step 6: Take the equally divided points on the side length of the cylinder base as the starting point, and assume that at each starting point there is the same particle making the same spiral motion along the cylinder surface; the spiral motion law of the particle on the cylinder surface is decomposed into two motions, one is uniform circular motion along the circumference of the base, and the other is uniform linear motion along the generatrix perpendicular to the base at the starting point of the particle. The two motions are required to arrive at the end point at the same time, that is, the time it takes for the particle to rotate uniformly along the circumference of the base once is equal to the time it takes for the particle to reach the top of the cylinder from the base along the generatrix perpendicular to the base; Step 7: Draw the spiral lines formed by each particle on the surface of the cylinder, and unfold the three-dimensional cylinder according to the plane diagram; Step 8: Find the intersection of the spiral line and the volume-dividing cross-section line on the unfolded plane. The intersection is the point to be selected for the test; Step nine: Analyze the test points to be selected, exclude the equivalent effect repeated points under the same conditions, determine the final test points, and complete the test sampling design.

2. A field block experiment design method based on cylindrical space according to claim 1, characterized in that: In the first step of estimating the test area, the test area is first planned, the surface area occupied by the test object or the minimum test area S1 occupied by the test object is determined, and the number of different test treatment types N is determined. CL and the number of repetitions n for each trial cf , determine the total number of trials N S =N CL ×n cf , we can get the minimum total area of ​​the test area Ss=S1×N S =S1×N CL ×n cf .

3. The field block experiment design method based on cylindrical space according to claim 1, characterized in that: In step 2, the length and width of the rectangular test area are W and L respectively, so the minimum total area of ​​the test area is Ss = S1×N CL ×n cf =W×L, and the length L and width W are respectively CL and the number of test repetitions n cf Establish the following relationship: width W and the number of experimental treatment types N CL The relationship between them is W=2πr / (N CL -1) × d, length L and number of repetitions n of the test cf The relationship between them is L=(n cf -1)×l.

4. The method for designing a field block experiment using cylindrical space according to claim 1, wherein: In step three, the plane cylinder of the sampling test area is spatialized, and the bottom circumference and height of the cylinder are determined based on the rectangular test area determined in steps one and two.

5. The method for designing a field block experiment by cylindrical space according to claim 1, characterized in that: After the experimental area is spatialized into a cylindrical shape, the determination of the experimental points includes drawing sampling lines for different experimental treatments on the cylindrical surface and drawing repeated experimental lines on the sampling lines of the same experimental treatment.

6. The method for designing a field block experiment by cylindrical space according to claim 1, characterized in that: When sampling different test treatments and repeated tests of the same test treatment, different test treatment points are used as particles. On the one hand, the particles perform uniform circular motion along the perimeter line of the bottom surface, and the probability of appearing at any position of the perimeter line of the bottom surface at any time is the same; at the same time, the particles perform uniform linear motion along the generatrix perpendicular to the bottom surface of the cylinder, and the probability of appearing at any position of the generatrix of the cylinder at any time is the same, so that the time for the particles to complete one uniform circular motion is equal to the time for one uniform linear motion along the generatrix. The particles form a sampling line and test repeated points on the sampling line on the surface of the cylinder.

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