A multi-agent formation recognition method based on interpolation and fuzzy recognition

Abstract

The present invention belongs to the field of artificial intelligence technology related to formation recognition, and specifically relates to a multi-agent formation recognition method based on interpolation and fuzzy recognition. The present invention includes a multi-agent formation entering a radar recognition area, the radar scanning and obtaining the coordinates of each agent in the recognition area to obtain a scattered point set; obtaining four vertices from the scattered point set; using a multi-point interpolation method, randomly adding interpolation points between the vertices and adding them to the scattered point set; constructing a formation based on the lines connecting the vertices; using a fuzzy recognition method to identify the constructed formation; multiple iterations, based on the last recognition result, predicting the next membership of each formation through a fitting function, and taking the formation corresponding to the maximum membership as the final recognition result. The present invention uses fuzzy recognition and uses membership functions as a measure of samples and templates, which can better reflect the overall characteristics of the pattern and has a strong ability to eliminate interference and noise in the sample.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence technology related to formation recognition, and in particular relates to a multi-agent formation recognition method based on interpolation and fuzzy recognition. Background Art

[0002] A multi-agent system is a collection of multiple agents. Its goal is to transform large and complex systems into smaller, more manageable systems that communicate and coordinate with each other. Its research involves the knowledge, goals, skills, and planning of the agents, as well as the formation recognition of the overall formation of the multi-agent system. Current developments in formation recognition technology include:

[0003] a) Rule-based multi-agent formation recognition. Current research on aerial multi-agent formations is often hampered by the resolution of detection equipment and measurement errors. Individual targets within an aerial formation are difficult to distinguish, and the intervals between targets in the formation vary widely and randomly, making formations difficult to capture. Rule-based multi-agent formation recognition establishes formation recognition rules. By building a rule-based operation platform and integrating aerial operation simulation data to drive rule execution, it identifies some typical aerial formations.

[0004] b) Formation recognition based on the Hough transform and K-means algorithm. In common formation recognition, the distance between targets directly affects the detector's capture accuracy. The smaller the distance between targets, the lower the detector's selectivity for a specific target. However, to improve the detector's target selection accuracy, the detector's search area must be narrowed, which reduces the probability of capturing the target. Using the Hough transform and K-means algorithm can accurately identify formations. This approach is easy to implement, produces accurate results, and is time-efficient, significantly improving formation recognition rates and reducing preparation time.

[0005] Through the above analysis, the problems and defects of the existing technology are as follows:

[0006] 1) Due to the significant influence of detection equipment resolution and measurement errors, individual targets in a formation are difficult to distinguish, and the intervals between targets in a formation vary widely and randomly, making it difficult to capture the formation. As the recognition range increases, recognition accuracy decreases, and increasing accuracy will correspondingly reduce recognition efficiency.

[0007] 2) When the formation detection is incomplete, the recognition accuracy is low.

[0008] 3) Since the current rules are mainly set by humans, they have great limitations.

[0009] The present invention expands upon the recognition method and proposes a formation recognition technology that can predict the result as early as possible when the formation is not fully presented. Summary of the Invention

[0010] The purpose of the present invention is to provide a multi-agent formation recognition method based on interpolation and fuzzy recognition.

[0011] A multi-agent formation recognition method based on interpolation and fuzzy recognition includes the following steps:

[0012] Step 1: The multi-agent formation enters the radar recognition area. The radar scans and obtains the coordinates of each agent in the recognition area to obtain a scattered point set A.

[0013] Step 2: Get four vertices from the scattered point set A;

[0014] For a set of scattered points A, define the distance between any two points as d; construct a set B, and take the first two sets of scattered points with the largest corresponding distance d; let the horizontal coordinates of each element in set B form vector X, and the vertical coordinates of each element form vector Y. However, when the elements in set B are very close, the vertex found in this way is meaningless. For this, a constraint condition needs to be added so that when the above situation occurs, the corresponding vertex will not be selected; the constraint condition is defined as:

[0015] Let the maximum value between vectors X and Y be greater than δ, that is, max|x i -y i |>δ

[0016] Among them, x i ,y i are the components of vector X, Y, i = 1, 2, 3, 4;

[0017] For the scattered point set A, get the distance between each scattered point and other scattered points, arrange all the distance results from large to small, and then calculate the distance according to the constraint max|x i -y i |>δSelect four scattered points as vertices;

[0018] Step 3: Using multi-point interpolation, randomly add a interpolation points between vertices and add them to the scattered point set A;

[0019] The formula for multi-point interpolation is:

[0020]

[0021] Step 4: Construct a formation based on the lines connecting the vertices in set B and obtain the four angular features A1, A2, A3, and A4 of the formation; where A1, A2, A3, and A4 represent the internal angles, and A1 ≥ A2 ≥ A3 ≥ A4;

[0022] Step 5: Use fuzzy recognition method to identify the constructed formation;

[0023] Assume that for a given quadrilateral (A1, A2, A3, A4), if A j It's A i The diagonal angle of D(A i ; A1, A2, A3) = A j , if A j It's A i adjacent angle, L(A i ; A1, A2, A3) = A j ;

[0024] Step 5.1: Calculate the V-shaped Va membership function;

[0025] According to the characteristics of the V-shape, its internal angles are three, which is different from the four angles of the rhombus and trapezoid. That is, when the number of angles is three, the formation is judged to be a V-shape;

[0026] When 180>A1>A2>A3>0, A4=0, Va(A1,A2,A3,A4)=1

[0027] When 180>A1>A2>A3>A4>0, Va(A1,A2,A3,A4)=0

[0028] Step 5.2: Calculate the diamond Pa membership function;

[0029] When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function Pa(A1, A2, A3, A4) of Pa is:

[0030]

[0031] When A2 is the adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function of Pa Pa(A1, A2, A3, A4) is:

[0032]

[0033] Step 5.3: Calculate the trapezoidal Tr membership function;

[0034] When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function Tr(A1, A2, A3, A4) of Tr is:

[0035]

[0036] When A2 is the adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function of Tr Tr(A1, A2, A3, A4) is:

[0037]

[0038] Step 5.4: Calculate the membership function Qu of other quadrilaterals; the other quadrilaterals do not have the characteristics of rhombus and trapezoid;

[0039] Qu(A1,A2,A3,A4)=Pa C ∧Tr C

[0040] =(1-Pa)∧(1-Tr)

[0041] Step 5.5: Calculate the membership of the four formations Va, Pa, Tr, and Qu respectively, and take the formation corresponding to the largest membership as the recognition result, R = max(Va, Pa, Ta, Qa);

[0042] Step 6: Repeat steps 2 and 5 until the set number of iterations b; based on the obtained b recognition results, predict the next formation membership Va through the fitting function δ ,Pa δ ,Ta δ ,Qa δ , take the formation corresponding to the largest membership as the final recognition result R δ =max(Va δ ,Pa, δ Ta δ ,Qa δ ).

[0043] The beneficial effects of the present invention are:

[0044] Compared with existing technologies, the present invention can quickly identify the target formation. The results of the present invention are fitted from the previous results, and the final formation can be predicted in a relatively short time. The present invention utilizes fuzzy recognition. In fuzzy pattern recognition, the membership function is used as a metric for samples and templates, which can better reflect the overall characteristics of the pattern and has a strong ability to eliminate interference and noise in the sample. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of a V-shaped multi-agent formation.

[0046] Figure 2 Schematic diagram of a diamond-shaped multi-agent formation.

[0047] Figure 3 Schematic diagram of a trapezoidal multi-agent formation.

[0048] Figure 4 Flowchart of the present invention.

[0049] Figure 5 A diagram showing the construction of a V-formation.

[0050] Figure 6 This is a diagram for constructing a diamond formation.

[0051] Figure 7 This is a diagram for the construction of a ladder formation. DETAILED DESCRIPTION

[0052] The present invention will be further described below with reference to the accompanying drawings.

[0053] This paper simulates the formation construction process by deeply analyzing the elements of multi-agent formation generation, including common formations, the addition of random points during formation generation, the formation angle that does not change the generated formation, and the gradual increase in the number of points in the formation from far to near. Starting from the initial state, the process of identifying vertices and then building formations is repeated. After a new formation is built, a new recognition result is generated for each newly constructed formation to ensure that the detection results can be obtained in the shortest possible time. This process is repeated until the formation is completed. Then, the results obtained in the previous several times are fitted to obtain the final result.

[0054] 1. Identify vertices

[0055] The design of the present invention adopts Manhattan distance. For a scattered point set A, the distance between any two points is defined as d, that is:

[0056] So d(m,n)=|x m -x n |+|y m -y n |

[0057] Further optimize the distance, let B = maxd(m,n), That is, set B is the subset of set A that maximizes the distance d(m,n).

[0058] Then let the horizontal coordinates of each element in set B form a vector X, and the vertical coordinates of each element form a vector Y. However, when the elements in set B are very close, the vertex found in this way is meaningless. For this, we need to add a constraint so that when the above situation occurs, the corresponding vertex will not be selected. The definition is as follows:

[0059] Let the maximum value between vectors X and Y be greater than δ, that is, max|x i -y i |>δ

[0060] where x i ,y i are the components of vectors X, Y, i = 1, 2, …, n, and n is the number of elements in set B.

[0061] For a bunch of scattered points, we can find the distance between each point and the farthest point from it, and then sort the results from large to small, and then calculate the distance according to max|x. i -y i |>δAfter eliminating some vertices, select the first four largest points.

[0062] 2. Formation Construction

[0063] To the original scanned point set A, we add some more points to create set A', adding a fixed number of points each time through the loop to simulate the process of increasing the number of targets as the distance increases. After the first step is completed, we obtain some vertices. We then use interpolation methods to calculate interpolation formulas based on these vertices. Using different interpolation methods, we can generate several interpolation formulas. Random points are then selected from these interpolation formulas and used as new points. Each additional point is added to the previous set.

[0064] The coefficients of the multi-point interpolation formula are:

[0065]

[0066] Substituting the y value of each point can obtain the interpolation formula.

[0067]

[0068] 3. Formation recognition

[0069] The present invention adopts a fuzzy recognition method to identify the constructed formation. First, some assumptions are given. According to the results after the formation is constructed, some features can be obtained. Four angles A1, A2, A3, and A4 are taken, where A1, A2, A3, and A4 represent the inner angles. For the convenience of calculation and discussion, it is assumed that A1≥A2≥A3≥A4.

[0070] We assume that for a given quadrilateral (A1, A2, A3, A4), if A j It's A i The diagonal angle, D(A i ; A1, A2, A3) = A j , if A j It's A i The adjacent angle of L(A i ; A1, A2, A3) = A j , i=1,2,3,4; j=1,2,3,4, i≠j.

[0071] Obviously, if A j It's A i The diagonal of i It's Aj The diagonal of j It's A i The adjacent angle of i It's A j Adjacent angles, i=1,2,3,4; j=1,2,3,4, i≠j.

[0072] The membership functions of the three formations are discussed below:

[0073] 1. Establishment of V-shaped Va membership function

[0074] According to the characteristics of the V-shape, its internal angles are three, which is different from the four angles of the rhombus and trapezoid. That is, when the number of angles is three, the formation is judged to be V-shaped.

[0075] (I) When 180>A1>A2>A3>0, A4=0, Va(A1,A2,A3,A4)=1;

[0076] (II) When 180>A1>A2>A3>A4>0, Va(A1,A2,A3,A4)=0

[0077] 2. Establishment of diamond Pa membership function

[0078] Among the four interior angles of a quadrilateral, the smaller angle A2 is either the opposite angle of A1 or the adjacent angle of A1. The following two cases are discussed:

[0079] (1) When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function Pa(A1, A2, A3, A4) of Pa should satisfy the following constraints:

[0080] (I) When A1=A2,A3=A4,Pa(A1,A2,A3,A4)=1;

[0081] (II) When A1=180, A2=A3=90, and A4=0, Pa(A1, A2, A3, A4)=0;

[0082] (III)0≤Pa(A1,A2,A3,A4)≤1.

[0083] The characteristic of rhombus Pa is that the closer the sum of an angle and its adjacent angle is to 180, and the smaller the difference with the opposite angle is, the more the quadrilateral resembles a rhombus. Therefore, combining the constraints (I), (II), and (III), we can define the membership function of Pa as

[0084]

[0085] The membership function Pa defined in this way obviously satisfies the constraints (I), (II), and (III).

[0086] (2) When A2 is an adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function Pa(A1, A2, A3, A4) of Pa should satisfy the following constraints:

[0087] (I) When D(A1;A3,A4)=A1, D(A2;A3,A4)=A2, Pa(A1,A2,A3,A4)=1;

[0088] (II) When A1 = 180, A2 = 180, A3 = 0, A4 = 0, Pa(A1, A2, A3, A4) = 0;

[0089] (III)0≤Pa(A1,A2,A3,A4)≤1.

[0090] The characteristic of rhombus Pa is that the closer the sum of an angle and any adjacent angle is to 180, and the smaller the difference with the opposite angle is, the more the quadrilateral resembles a rhombus. Therefore, combining constraints (I), (II), and (III), we can define the membership function of Pa as

[0091]

[0092] The membership function Pa defined in this way obviously satisfies the constraints (I), (II), and (III).

[0093] 3. Establishment of the membership function of trapezoidal Tr

[0094] As with the rhombus, the following two cases are discussed:

[0095] (1) When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function of Tr, that is, Tr(A1, A2, A3, A4), should satisfy the following constraints:

[0096] (I) When A1+A3=180, A1-A3=0, A1+A4=180, A1-A4=0, Tr(A1,A2,A3,A4)=1;

[0097] (II) When A1=180, A2=180, A3=0, A4=0, Tr(A1, A2, A3, A4)=0;

[0098] (III)0≤Tr(A1,A2,A3,A4)≤1.

[0099] The characteristic of trapezoid Tr is that the sum of an interior angle and any adjacent angle is close to 180. The closer the difference is to 0, the more the quadrilateral looks like a trapezoid. Therefore, combined with constraints (I), (II), and (III), we can define the membership function of Tr as

[0100]

[0101] The membership function Tr defined in this way obviously satisfies the constraints (I), (II), and (III).

[0102] (2) When A2 is an adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function of Tr, that is, Tr(A1, A2, A3, A4), should satisfy the following constraints:

[0103] (I) When A1+A2=180, A1-A2=0 or A1+L(A1;A3,A4)=180, A1-L(A1;A3,A4)=180, Tr(A1,A2,A3,A4)=1;

[0104] (II) When A1=180, A2=180, A3=0, A4=0, Tr(A1, A2, A3, A4)=0;

[0105] (III)0≤Tr(A1,A2,A3,A4)≤1.

[0106] The characteristic of trapezoid Tr is that the sum of an interior angle and any adjacent angle is close to 180. The closer the difference is to 0, the more the quadrilateral looks like a trapezoid. Therefore, combined with constraints (I), (II), and (III), we can define the membership function of Tr as

[0107]

[0108] The membership function Tr defined in this way obviously satisfies the constraints (I), (II), and (III).

[0109] 4. Establishment of membership functions of other quadrilaterals Qu

[0110] Other quadrilaterals do not have the characteristics of rhombus and trapezoid, so the membership function Qu of other quadrilaterals, that is, Qu(A1,A2,A3,A4) is

[0111] Qu(A1,A2,A3,A4)=Pa C ∧Tr C

[0112] =(1-Pa)∧(1-Tr)

[0113] Based on the above content, the present invention provides a multi-agent formation recognition method based on interpolation and fuzzy recognition, which includes the following steps:

[0114] Step 1: The multi-agent formation enters the radar recognition area. The radar scans and obtains the coordinates of each agent in the recognition area to obtain a scattered point set A.

[0115] Step 2: Get four vertices from the scattered point set A;

[0116] For a set of scattered points A, define the distance between any two points as d; construct a set B, and take the first two sets of scattered points with the largest corresponding distance d; let the horizontal coordinates of each element in set B form vector X, and the vertical coordinates of each element form vector Y. However, when the elements in set B are very close, the vertex found in this way is meaningless. For this, a constraint condition needs to be added so that when the above situation occurs, the corresponding vertex will not be selected; the constraint condition is defined as:

[0117] Let the maximum value between vectors X and Y be greater than δ, that is, max|x i -y i |>δ

[0118] Among them, x i ,y i are the components of vector X, Y, i = 1, 2, 3, 4;

[0119] For the scattered point set A, get the distance between each scattered point and other scattered points, arrange all the distance results from large to small, and then calculate the distance according to the constraint max|x i -y i |>δSelect four scattered points as vertices;

[0120] Step 3: Using multi-point interpolation, randomly add a interpolation points between vertices and add them to the scattered point set A;

[0121] The formula for multi-point interpolation is:

[0122]

[0123] Step 4: Construct a formation based on the lines connecting the vertices in set B and obtain the four angular features A1, A2, A3, and A4 of the formation; where A1, A2, A3, and A4 represent the internal angles, and A1 ≥ A2 ≥ A3 ≥ A4;

[0124] Step 5: Use fuzzy recognition method to identify the constructed formation;

[0125] Assume that for a given quadrilateral (A1, A2, A3, A4), if A j It's A i The diagonal angle of D(A i ; A1, A2, A3) = A j , if A j It's A i adjacent angle, L(A i ; A1, A2, A3) = A j ;

[0126] Step 5.1: Calculate the V-shaped Va membership function;

[0127] According to the characteristics of the V-shape, its internal angles are three, which is different from the four angles of the rhombus and trapezoid. That is, when the number of angles is three, the formation is judged to be a V-shape;

[0128] When 180>A1>A2>A3>0, A4=0, Va(A1,A2,A3,A4)=1

[0129] When 180>A1>A2>A3>A4>0, Va(A1,A2,A3,A4)=0

[0130] Step 5.2: Calculate the diamond Pa membership function;

[0131] When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function Pa(A1, A2, A3, A4) of Pa is:

[0132]

[0133] When A2 is the adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function of Pa Pa(A1, A2, A3, A4) is:

[0134]

[0135] Step 5.3: Calculate the trapezoidal Tr membership function;

[0136] When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function Tr(A1, A2, A3, A4) of Tr is:

[0137]

[0138] When A2 is the adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function of Tr Tr(A1, A2, A3, A4) is:

[0139]

[0140] Step 5.4: Calculate the membership function Qu of other quadrilaterals; the other quadrilaterals do not have the characteristics of rhombus and trapezoid;

[0141] Qu(A1,A2,A3,A4)=Pa C ∧Tr C

[0142] =(1-Pa)∧(1-Tr)

[0143] Step 5.5: Calculate the membership of the four formations Va, Pa, Tr, and Qu respectively, and take the formation corresponding to the largest membership as the recognition result, R = max(Va, Pa, Ta, Qa);

[0144] Step 6: Repeat steps 2 and 5 until the set number of iterations b; based on the obtained b recognition results, predict the next formation membership Va through the fitting function δ ,Pa δ ,Ta δ ,Qa δ , take the formation corresponding to the largest membership as the final recognition result R δ =max(Va δ ,Pa, δ Ta δ ,Qa δ ).

[0145] Example 1:

[0146] The present invention starts from three common formations, such as Figure 1 、 Figure 2 、 Figure 3 , respectively V-shaped, diamond-shaped, trapezoidal, and then the entire implementation process is divided into three steps, such as Figure 4 The present invention has built a formation simulation system that simulates and generates a multi-agent formation from a small number to a large number within a simulation cycle, gradually building up from an initial 20 targets to a maximum of 50 targets. Three typical multi-agent formations are designed: V-shaped, diamond-shaped, and trapezoidal.

[0147] Calculate the membership of the four formations Va, Pa, Tr, and Qu respectively, and take the formation corresponding to the largest membership as the recognition result, R = max(Va, Pa, Ta, Qa). Repeat this process five times to obtain five recognition results.

[0148] R1=max(Va1,Pa1,Ta1,Qa1)

[0149] R2=max(Va2,Pa2,Ta2,Qa2)

[0150] R3=max(Va3,Pa3,Ta3,Qa3)

[0151] R4=max(Va4,Pa4,Ta4,Qa4)

[0152] R5=max(Va5,Pa5,Ta5,Qa5)

[0153] Finally, in order to achieve the prediction effect, the present invention adopts the fitting method, assuming that the fitting function is δ, and obtains the new membership as the final recognition result. According to the formation obtained after the first 5 points are added, the corresponding membership is calculated, and then the membership calculated in the first 5 times is fitted to predict the next membership Va δ ,Pa δ ,Ta δ ,Qa δ .

[0154] Va δ =δ(Va1,Va2,Va3,Va4,Va5)

[0155] Pa δ =δ(Pa1,Pa2,Pa3,Pa4,Pa5)

[0156] Ta δ =δ(Ta1,Ta2,Ta3,Ta4,Ta5)

[0157] Q δ =δ(Qa1,Qa2,Qa3,Qa4,Qa5)

[0158] Take the formation corresponding to the largest membership as the final recognition result, R δ =max(Va δ ,Pa, δ Ta δ ,Qa δ ).

[0159] Compared with existing technologies, the present invention can quickly identify the target formation. The results of the present invention are fitted from the previous results, and the final formation can be predicted in a relatively short time. The present invention utilizes fuzzy recognition. In fuzzy pattern recognition, the membership function is used as a metric for samples and templates, which can better reflect the overall characteristics of the pattern and has a strong ability to eliminate interference and noise in the sample.

[0160] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A multi-agent formation recognition method based on interpolation and fuzzy recognition, characterized in that: The following steps are involved: Step 1: The multi-agent formation enters the radar recognition area. The radar scans and obtains the coordinates of each agent in the recognition area to obtain a scattered point set A; Step 2: Get four vertices from the scattered point set A; For a set of scattered points A, define the distance between any two points as d; construct a set B, and take the first two sets of scattered points with the largest corresponding distance d; let the horizontal coordinates of each element in set B form vector X, and the vertical coordinates of each element form vector Y. However, when the elements in set B are very close, the vertex found in this way is meaningless. For this, a constraint condition needs to be added so that when the above situation occurs, the corresponding vertex will not be selected; the constraint condition is defined as: Let the maximum value between vectors X and Y be greater than δ, that is, max|x i -y i |>δ Among them, x i ,y i are the components of vector X, Y, i = 1, 2, 3, 4; For the scattered point set A, get the distance between each scattered point and other scattered points, arrange all the distance results from large to small, and then calculate the distance according to the constraint max|x i -y i |>δSelect four scattered points as vertices; Step 3: Using multi-point interpolation, randomly add a interpolation points between vertices and add them to the scattered point set A; The formula for multi-point interpolation is: Step 4: Construct a formation based on the lines connecting the vertices in set B and obtain the four angular features A1, A2, A3, and A4 of the formation; where A1, A2, A3, and A4 represent the internal angles, and A1 ≥ A2 ≥ A3 ≥ A4; Step 5: Use fuzzy recognition method to identify the constructed formation; Assume that for a given quadrilateral (A1, A2, A3, A4), if A j It's A i The diagonal angle of D(A i ; A1, A2, A3) = A j , if A j It's A i adjacent angle, L(A i ; A1, A2, A3) = A j ; Step 5.1: Calculate the V-shaped Va membership function; According to the characteristics of the V-shape, its internal angles are three, which is different from the four angles of the rhombus and trapezoid. That is, when the number of angles is three, the formation is judged to be a V-shape; When 180>A1>A2>A3>0, A4=0, Va(A1,A2,A3,A4)=1 When 180>A1>A2>A3>A4>0, Va(A1,A2,A3,A4)=0 Step 5.2: Calculate the diamond Pa membership function; When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function Pa(A1, A2, A3, A4) of Pa is: When A2 is the adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function of Pa Pa(A1, A2, A3, A4) is: Step 5.3: Calculate the trapezoidal Tr membership function; When A2 is the diagonal of A1, that is, D(A1; A2, A3, A4) = A2, the membership function Tr(A1, A2, A3, A4) of Tr is: When A2 is the adjacent angle of A1, that is, L(A1; A2, A3, A4) = A2, the membership function of Tr Tr(A1, A2, A3, A4) is: Step 5.4: Calculate the membership function Qu of other quadrilaterals; the other quadrilaterals do not have the characteristics of rhombus and trapezoid; <h2 style=";text-align:left;direction:ltr">Qu(A1,A2,A3,A4)=Pa<h2 style=";text-align:left;direction:ltr"> C <h2 style=";text-align:left;direction:ltr"> ∧Tr<h2 style=";text-align:left;direction:ltr"> C =(1-Pa)∧(1-Tr) Step 5.5: Calculate the membership of the four formations Va, Pa, Tr, and Qu respectively, and take the formation corresponding to the largest membership as the recognition result, R = max(Va, Pa, Ta, Qa); Step 6: Repeat steps 2 and 5 until the set number of iterations b; based on the obtained b recognition results, predict the next formation membership Va through the fitting function δ ,Pa δ ,Ta δ ,Qa δ , take the formation corresponding to the largest membership as the final recognition result R δ =max(Va δ ,Pa, δ Ta δ ,Qa δ ).

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