A method for analyzing a radome structure based on fuzzy variables

Abstract

The application discloses a radar cover structure analysis method based on fuzzy variables, and belongs to the field of radar cover structure analysis. The method is based on the membership function of the fuzzy input variable of the radar cover model. Firstly, the unconditional limited membership function of the model output response is obtained by using the "alpha-cut" technology. Then, each fuzzy input variable is fixed as a specific value in its domain. The conditional limited membership function of the model output response is obtained again by using the "alpha-cut" technology. Then, the domain of the fuzzy input variable is traversed to obtain different specific values, and a polyhedron representing the fuzzy process is obtained. On this basis, an index is proposed, which can better reflect the influence degree of different fuzzy inputs on the model output, so as to screen out the key inputs which play an important role in the model output.

Description

Technical Field

[0001] This invention belongs to the field of reliability analysis technology for complex structures, specifically relating to a radome structure analysis method based on fuzzy variables. Background Technology

[0002] like Figure 1 The radome shown is an indispensable and important component of an aircraft. Its function is to protect the antenna or radar from harsh environmental conditions, such as external loads, lightning strikes, hail, and vibration, while maintaining a smooth aerodynamic shape. To meet the requirements of weight reduction and electromagnetic wave transmission, honeycomb sandwich composite materials are widely used as the material for radomes.

[0003] During the design, manufacturing, and assembly processes, uncertainties exist in the materials and geometric parameters of the radome, leading to a certain degree of uncertainty in its model response. Although there are many sources of uncertainty affecting the output response, each uncertainty source contributes to the output response to a different degree. Often, only a few uncertainty sources with high contributions to the output response play a crucial role in the structure's output response. Therefore, if the uncertainty sources are not distinguished when performing uncertainty analysis on the structure, the computational workload will be extremely large, consuming a great deal of human and material resources.

[0004] Meanwhile, probabilistic models are currently the primary tool for characterizing uncertainty when conducting reliability analysis on complex structures. However, as mentioned earlier, uncertainties exist in the materials and geometric parameters of the radome during the design, manufacturing, and assembly processes. Some parameters can only be estimated near certain values ​​based on existing experiments and expert assessments, providing only vague information. In such cases, the uncertainty of some materials and geometric parameters arises precisely from imprecision, ambiguity, or unclearness; that is, the variable is fuzzy, cannot be objectively quantified, or can be simply considered random. Therefore, probabilistic models cannot be used, and non-probabilistic models are required. Summary of the Invention

[0005] To address the problem that conventional probabilistic models cannot effectively characterize the uncertainties in radome materials and geometric parameters, and lack effective differentiation of uncertainty sources, resulting in a very high computational burden when performing uncertainty analysis on the structure, this invention proposes a radome structure analysis method based on fuzzy variables, based on fuzzy models.

[0006] Fuzzy models are non-probabilistic models widely used in engineering to analyze the geometric features and material properties of engineering objects, enabling analysis even with insufficient sample information. This invention focuses on radome structures, utilizing fuzzy models to study global sensitivity under fuzzy uncertainty. A new fuzzy sensitivity index is proposed, quantifying and ranking the influence of fuzzy inputs on the model output across the entire uncertainty range. This allows for the selection of inputs more critical to the model output, guiding the optimization of the fuzzy model.

[0007] To achieve the above-mentioned objectives, the technical solution of this invention is as follows:

[0008] A radome structure analysis method based on fuzzy variables is characterized by the following implementation steps:

[0009] Step 1: Using the maximum displacement of the radome structure as the output response Z, the materials and geometric parameters of each component of the radome are considered as n independent fuzzy input variables X. i Their set is the fuzzy variable set X = (X1, X2, ..., X...). n );

[0010] Based on the fuzzy input variable X i The characteristics define the membership function. To fuzzy variable X i The probability that each value x is mapped to a value in the interval [0, 1];

[0011] A three-dimensional model of the radome is constructed, and a stress analysis simulation is performed on the three-dimensional model of the radome to obtain the input and output relationship of the structure as Z = f(X);

[0012] Step 2: Using α-cut theory, realize the fuzzy input variable X i Different degrees of discretization:

[0013] Step 2.1: Define the cutoff value of the membership function as the membership degree α∈[0,1], and assign n membership functions... All variables are fixed under the same membership degree α, and fuzzy uncertainty is propagated to obtain n fuzzy input variables X. i boundary range (See Figure 7 );

[0014] in, For X i The minimum value, For X i The maximum value;

[0015] Step 2.2: As Figure 2As shown, the sampling parameter Q is set, and the n fuzzy input variables X obtained in step 2.1 are used. i boundary range Substitute the extracted values ​​into Z = f(X) to obtain Q Z(α). Then, select the maximum and minimum values ​​from the Q output responses Z(α) to form the boundary range [Z] of the output response Z(α). l (α), Z u (α)];

[0016] Among them, Z l Z(α) is the minimum value of the output response Z(α) under the membership degree α. u (α) is the maximum value of the output response Z(α) under the membership degree α;

[0017] Step 2.3: Repeat steps 2.1 to 2.2, iterating through the values ​​of α in [0, 1] to obtain the boundary [Z] of the output response Z(α) under different membership degrees α. l (α), Z u (α)];

[0018] Step 2.4: Define the unconditional membership function μ Z To determine the probability of each value in the output response Z;

[0019] The Z obtained in step 2.3 l (α) and Z u (α) is plotted with independent variable Z(α) and dependent variable μ. z value μ Z —See Figure Z (see) Figure 6 Connecting the points and fitting the data, we obtain the unconditional membership function μ for the model output response Z. z And at the same time, the range of the output response Z is obtained as [Z l Z u ];

[0020] Step 3: Construct fuzzy input variable X i The fuzzy process of membership function:

[0021] Step 3.1: Set the i-th fuzzy input variable X i Let X be a fixed value x′ within the domain. i =x′;

[0022] Iterate through the values ​​of α in [0, 1] to obtain the output response under different membership degrees α. boundary

[0023] Step 3.2: Define the conditionally restricted membership function For output response The degree of probability of each value point in the equation;

[0024] The result obtained in step 3.1 and After plotting, the model output response is fitted to obtain the result. Conditional membership function

[0025] Step 3.3: Repeat steps 3.1 and 3.2, setting the traversal span ΔX. i traverse X i The domain of definition takes the value x′, resulting in N fuzzy input variables X. i The corresponding output response Conditional membership function (See Figure 3 (Chinese map B);

[0026] Step 3.4: Calculate the N membership function curves obtained in Step 3.3. Drawing in In the figure, connecting the curves and fitting them together yields a polyhedron (see...). Figure 4 );

[0027] The polyhedron represents the fuzzy input variable X. i The fuzzy process in X i Slicing the polyhedron along the axis yields the X-axis slice. i The slice section on x′ is

[0028] The boundaries of this polyhedron in the three directions are, in order: X i The domain of the output response Z in step 2.4 [Z l Z u ] and conditionally restricted membership functions The range of Z is [0, 1]. The boundaries in the above three directions form a square envelope that encompasses all possibilities of the output response Z of the fuzzy process.

[0029] Step 4: Repeat steps 3.1 to 3.4, sequentially traversing the input fuzzy variable set X = (X1, X2, ..., X...). n Each X in ) i n fuzzy input variables X are obtained. i The fuzzy process (see) Figure 5 );

[0030] Step 5: Compare the n fuzzy processes obtained in Step 4. In the function graph, conduct a preliminary analysis on the shape features of the n polyhedra, the volume ratio of the polyhedra to the envelope, etc., and select one or more fuzzy input variables with prominent features.

[0031] Step 6: Introduce an index to the n fuzzy input variables X obtained in Step 4. i The fuzzy process is abstracted, and the fuzzy input variable X is defined. i The fuzzy sensitivity index is T i The calculation formula is as follows:

[0032]

[0033] Among them, X i，j (j = 1, 2, ..., N) represents the fuzzy input variable X. i The j-th fixed value x′; Indicates the model output response The k-th value in the middle; the For slice cross section The traversal span is set during traversal, where M is the traversal span. Traversal The number of values ​​that can be taken from the domain;

[0034] Step 7: Combining Steps 5 and 6, rank the influence of the n fuzzy processes based on both function graph features and index magnitude, and select one or more key fuzzy input variables X in the structural analysis. i ;

[0035] Among them, when T i When →1, input variable X i The more significant the impact on the model's output, the greater T. i When the input variable X is 1, the input variable X is 1. i This plays a key and dominant role in the model;

[0036] If the membership function The shape is triangular, T i When the value reaches 0.5, input variable X. i The smaller the impact on the model's output, the better T i Input variable X when = 0.5 i This has no effect on the model;

[0037] If the membership function The shape is trapezoidal, when T i When →0, input variable X i The smaller the impact on the model's output, the better T i Input variable X when = 0 iThis has no effect on the model.

[0038] Furthermore, the steps also include:

[0039] Step 3.5: Based on X in Step 1 i The corresponding membership function middle Size (see) Figure 9 ), respectively, for the N membership function curves in step 3.3 Uneven coloring and drawing in step 3.4 In the diagram, let X represent the variable X in the fuzzy input. i The darker the color of the selected x′ probability, the more significant the difference in the fuzzy input variable X. i The higher the probability of selecting x′.

[0040] The concept and principle of this invention:

[0041] like Figure 8 As shown:

[0042] First, based on the fuzzy input variable X of the model... i Membership function By utilizing the α-cut technique and the functional relationship Z = f(X) between the input variables and the output, the propagation of fuzzy uncertainty from the input variables to the output response is realized, and the output response Z of the fuzzy input variable set X is obtained.

[0043] Then, based on the output response Z obtained under different α-cuts, the unconditional membership function μ of the model output response Z is obtained. z ;

[0044] Then, a fuzzy input X is given. i The model output response is obtained by fixing a specific value x′ within its domain, while keeping other input variables as fuzzy variables. Again, the α-cut technique and the functional relationship Z = f(X) between the input variables and the output are used. Conditional membership function

[0045] Finally, by iterating through X... i The domain of the function is x′, which gives the corresponding conditionally restricted membership function. Then, through the membership function with conditional constraints... Add an X above i The axis represents X i Given different values ​​of x′, and all conditionally restricted membership functions... Connect and fit, in The diagram shows a polyhedron representing X. i The fuzzy process.

[0046] Similarly, traverse the fuzzy variable set X = (X1, X2, ..., X... n ), thus obtaining n fuzzy input variables X i The fuzzy process.

[0047] By comparing the shape characteristics of different polyhedra, the volume ratio of polyhedra to the envelope, and comparing the unoccupied volume of the envelope with the volume of the polyhedra, a new fuzzy sensitivity index T is defined. i Use this indicator for all fuzzy inputs X i By ranking and conducting comprehensive analysis, one or more fuzzy input variables X that are key in structural analysis and play a decisive role in influencing the output are identified. i .

[0048] The advantages of this invention are:

[0049] 1. The index proposed in this invention has a concise definition, a clear calculation approach, and a simple process. It also considers all possibilities of the structural model output, and can better reflect the degree of influence of fuzzy input on the model output, thereby screening out the key inputs that play an important role in the model output.

[0050] 2. This invention constructs a visualization model of fuzzy processes, which can intuitively represent the influence of input on output and provide more intuitive and interpretive information about the model output.

[0051] 3. Before calculating the indicators, this invention analyzes the cross-section of the polyhedron of the fuzzy process and pre-screens various model inputs, which speeds up the analysis process and makes it applicable to situations with a large number of fuzzy input variables, thereby improving analysis efficiency. Attached Figure Description

[0052] Figure 1 This is a schematic diagram showing the specific materials and layering of the radome.

[0053] Figure 2 This is a schematic diagram illustrating the transmission process of fuzzy uncertainty.

[0054] Figure 3 For X i When fixed on x′, the slice shape of the blurring process.

[0055] Figure 4 This is a schematic diagram of uneven coloring during the blurring process.

[0056] Figure 5 For fuzzy input X1~X 21 The fuzzy process.

[0057] Figure 6μ is the membership function of the unconditionally restricted output response Z. z Schematic diagram.

[0058] Figure 7 This is a schematic diagram illustrating the transmission of fuzzy uncertainty.

[0059] Figure 8 This is a flowchart of radome analysis based on fuzzy variables.

[0060] Figure 9 This diagram illustrates the membership function types and their distribution parameters for 21 types of fuzzy inputs. Detailed Implementation

[0061] The honeycomb sandwich radome studied in this embodiment is mainly composed of three parts: part I is the top of the radome, part II is the middle of the radome, and part III is the bottom of the radome.

[0062] These three parts differ in their constituent materials and layering methods, with three main constituent materials:

[0063] Material #1 is a composite laminate, material #2 is a flexible honeycomb core, and material #3 is a hexagonal honeycomb core.

[0064] Parts I and II are each composed of three layers of material, while part III consists of only two layers. Specific materials and layer configurations are as follows: Figure 1 As shown.

[0065] Step 1: The radome structure undergoes displacement due to external aerodynamic pressure. The maximum displacement of the radome structure is taken as the output response. The three types of inputs (i.e., elastic modulus, density, and thickness) of each part of the radome are considered as fuzzy inputs. The membership function type and distribution parameters of the fuzzy inputs are as follows: Figure 9 As shown;

[0066] Wherein, Mat1E11, Mat1E22, Mat1G12, Mat1G13, and Mat1G23 represent the elastic moduli E and G of material #1 in the 11, 22, 12, 13, and 23 directions, respectively;

[0067] Similarly, Mat2E11, Mat2E22, Mat2G12, Mat2G13, and Mat2G23 also represent the elastic moduli E and G of material #2 in these directions, respectively;

[0068] Similarly, Mat3E11, Mat3E22, Mat3G12, Mat3G13, and Mat3G23 also represent the elastic moduli E and G of material #3 in these directions, respectively;

[0069] Among them, Mat1Rho, Mat2Rho, and Mat3Rho represent the densities ρ of each material, respectively;

[0070] Where Th1 represents the thickness th of the first and third layers of part I and II; Th2 represents the thickness th of the second layer of part I and II; and Th3 represents the thickness th of the first and second layers of part III.

[0071] Unify the fuzzy input variable as X i (i = 1, 2, ..., 21), then its input fuzzy variable set is x = (X1, X2, ..., X...). 21 );

[0072] Based on the fuzzy input variable X i The characteristics define the membership function. To fuzzy variable X i The probability that each value x maps to a value in the interval [0, 1], for example Representing the fuzzy variable X i The probability of obtaining 'a' from the given information;

[0073] Define the output response of the fuzzy input set X as Z;

[0074] A three-dimensional model of the radome is constructed, and a stress analysis simulation is performed on the three-dimensional model of the radome to obtain the input and output relationship of the structure as Z = f(X);

[0075] Step 2: Using α-cut theory, realize the fuzzy input variable X i Different degrees of discretization:

[0076] Step 2.1: Define the cutoff value of the membership function as the membership degree α∈[0,1];

[0077] 21 membership functions All variables are fixed under the same membership degree α, and fuzzy uncertainty propagation is performed to obtain 21 fuzzy input variables X. i boundary range (See Figure 7 );

[0078] in, For X i The minimum value, For X i The maximum value;

[0079] Step 2.2: As Figure 2 As shown, the sampling parameter Q is set, and the 21 fuzzy input variables X obtained in step 2.1 are used. i boundary range Substitute the extracted values ​​into Z = f(X) to obtain Q Z(α). Then, select the maximum and minimum values ​​from the Q output responses Z(α) obtained from the formula to form the boundary range [Z]. l (α), Z u (α)];

[0080] Among them, Z l Z(α) is the minimum value of the output response Z(α) under the membership degree α. u (α) is the maximum value of the output response Z(α) under the membership degree α;

[0081] Step 2.3: Repeat steps 2.1 to 2.2, iterating through the values ​​of α in [0, 1] to obtain the boundary [Z] of the output response Z(α) under different membership degrees α. l (α), Z u (α)];

[0082] Step 2.4: Define the unconditional membership function μ Z To determine the probability of each value in the output response Z;

[0083] The Z obtained in step 2.3 l (α) and Z u (α) is plotted with independent variable Z(α) and dependent variable μ. z value μ Z —See Figure Z (see) Figure 6 Connecting the points and fitting the data, we obtain the unconditional membership function μ for the model output response Z. z ;

[0084] Step 3: Construct 21 fuzzy input variables X i The fuzzy process:

[0085] Step 3.1: Set the i-th fuzzy input variable X i Let X be a fixed value x′ within the domain, that is, let X... i =x′;

[0086] Similar to step 2.3, iterate through the values ​​of α in [0, 1] to obtain the output response under different membership degrees α. boundary

[0087] Step 3.2: Define the conditionally restricted membership function For output response The degree of probability of each value point in the equation;

[0088] Similar to step 2.4, the result obtained in step 3.1 is... and After plotting, the model output response is fitted to obtain the result. Conditional membership function

[0089] Step 3.3: Repeat steps 3.1 and 3.2, setting the traversal span ΔX. i traverse X i The domain of definition takes the value x′, resulting in N fuzzy input variables X. i The corresponding output response Conditional membership function (See Figure 3 (Figure B in the middle);

[0090] Step 3.4: Calculate the N membership function curves obtained in Step 3.3. Drawing in In the figure, connecting the curves and fitting them together yields a polyhedron (see...). Figure 4 );

[0091] The polyhedron represents the fuzzy input variable X. i The fuzzy process in X i Slicing along the axis yields the polyhedron in the X-axis. i The slice section on x′ is (See Figure 3 (Figure B in the middle);

[0092] The boundaries of this polyhedron in the three directions are, in order: X i The domain of the output response Z, and the boundary of Z[Z] l (α), Z u (α)] and conditionally restricted membership function

[0093] Step 3.5: Based on X in Step 1 i The corresponding membership function middle Size (see) Figure 9 ), respectively, for the N membership function curves in step 3.3 Uneven coloring and drawing in step 3.4 In the diagram, let X represent the variable X in the fuzzy input. i The darker the color of the selected x′ probability, the more significant the difference in the fuzzy input variable X. i The higher the probability of selecting x′;

[0094] Step 4: Repeat steps 3.1 to 3.5, sequentially traversing the input fuzzy variable set X = (X1, X2, ..., X...). n Each X in ) i 21 fuzzy input variables X were obtained. i The fuzzy process (see) Figure 5 );

[0095] Step 5: Compare the 21 fuzzy processes obtained in Step 4. Analyze the shape features and volume ratio of the 21 polyhedra to the envelope in the function graph, and select one or more fuzzy input variables with prominent features.

[0096] Through observation Figure 5 It becomes quite apparent that the blurring process corresponding to X2 stands out significantly compared to other blurring processes, with its slice shape being quite unique. Furthermore, during the blurring process of X2, V... blank In V total The spatial volume in the figure accounts for a much larger proportion than that of other fuzzy variables. Furthermore, observing the fuzzy inputs X1 and X2 in the figure... 21 In the corresponding fuzzy process, the proportion of blank volume within the cube is also slightly larger than that of other fuzzy variables.

[0097] In addition to the variables mentioned above (X2, X1, X...) 21 ), and variables X3 and X 19 In addition, the roots of the polyhedra corresponding to other fuzzy inputs are closely attached to the two sides of the boundary of the blank volume, and the shape of the slice cross section is similar to the shape of the membership function of the response Z of the unconditionally restricted output. This indicates that their influence on the fuzzy structure response is small and can be ignored.

[0098] In other words, there are only five key variables that can truly affect the maximum displacement of the honeycomb sandwich radome, with variable X2 having the greatest impact. Other inputs have virtually no effect on the output response.

[0099] Step 6: Introduce indices for the 21 fuzzy input variables X obtained in Step 4 i The fuzzy process is abstracted, and the fuzzy input variable X is defined. i The fuzzy sensitivity index is T i The calculation formula is as follows:

[0100]

[0101] Among them, V total The envelope obtained in step 3.4 (i.e. Figure 4 The volume of the square envelope in the figure is calculated using the following formula:

[0102]

[0103] V field The volume of the polyhedron obtained in step 3.4 is calculated using the following formula:

[0104]

[0105] V blank For envelope V total Besides the polyhedron V field The volume of space outside;

[0106] Substituting equations (2) and (3) into equation (1), the fuzzy sensitivity index is T. i The calculation formula is:

[0107]

[0108] The results are shown in Table 1;

[0109] Among them, X i，j (j = 1, 2, ..., N) represents the fuzzy input variable X. i The j-th fixed value x′; Indicates the model output response The k-th value in the middle; the For slice cross section The traversal span is set during traversal, where M is the traversal span. Traversal The number of values ​​that can be taken from the domain;

[0110] Calculate the 21 fuzzy sensitivity indices T obtained in step 4. i :

[0111] Table 1. 21 fuzzy input variables X i The fuzzy sensitivity index T i value

[0112]

[0113] Step 7: Combining Steps 5 and 6, rank the influence of the n fuzzy processes based on both function graph features and index magnitude, and select one or more key fuzzy input variables X in the structural analysis. i ;

[0114] Among them, when T i When →1, input variable X i The more significant the impact on the model output, i.e., T i When the input variable X is 1, the input variable X is 1. i This plays a key and dominant role in the model;

[0115] In this embodiment, the membership function The shape is triangular, T i When the value reaches 0.5, input variable X. i The smaller the impact on the model output, i.e., T i Input variable X when = 0.5i This has no effect on the model;

[0116] As can be seen from Table 1, the fuzzy input X2 is the variable that has the most significant impact on the maximum displacement of the honeycomb sandwich radome.

[0117] Secondly, use the sensitivity index T i The sensitivity of the five key variables obtained in step 5 was ranked as follows: X2 > X 21 >X1>X 19 >X3.

[0118] According to the results, the fuzzy input X2 (elastic modulus of material #1 in direction 22) plays a dominant role in the maximum displacement of the cellular sandwich radome, followed by X21 (thickness of the first and second layers of component III), X1 (elastic modulus of material #1 in direction 11), X19 (thickness of the first and third layers of components I and II) and X3 (elastic modulus of material #1 in direction 12).

[0119] Among the five key inputs that affect the maximum displacement of the honeycomb sandwich radome, analysis revealed that three of them are the elastic modulus of material #1 in different directions, and the other two are the thickness of different parts of the honeycomb sandwich radome.

[0120] The discovery that the materials in these two different locations are exactly material #1 means that all five inputs that play a crucial role in the output are related to material #1. This also indicates that the properties of material #1 have a significant impact on the mechanical response of the honeycomb sandwich radome structure, making it a primary focus for design improvements.

[0121] Meanwhile, it was also found that the elastic modulus of material #1 in the 22 direction plays a crucial role in the displacement response of the entire structure and is a material parameter that urgently needs to be focused on. Therefore, in the design and structural analysis of the cellular sandwich radome, the influence of the material parameters of material #1 on the structural response must be fully considered to ensure the safety and reliability of the structure.

[0122] For other embodiments, if the membership function in the embodiment... The shape is trapezoidal, when T i When →0, input variable X i The smaller the impact on the model output, i.e., T i Input variable X when = 0 i This has no effect on the model.

Claims

1. A radome structure analysis method based on fuzzy variables, characterized in that, The implementation steps are as follows: Step 1: Using the maximum displacement of the radome structure as the output response Z, the materials and geometric parameters of each component of the radome are considered as n independent fuzzy input variables X. i Their set is the fuzzy variable set X = (X1, X2, ..., X...). n ); Based on the fuzzy input variable X i The characteristics define the membership function. To fuzzy variable X i The probability that each value x is mapped to a value in the interval [0, 1]; A three-dimensional model of the radome is constructed, and a stress analysis simulation is performed on the three-dimensional model of the radome to obtain the input and output relationship of the structure as Z = f(X); Step 2: Using α-cut theory, realize the fuzzy input variable X i Different degrees of discretization: Step 2.1: Define the cutoff value of the membership function as the membership degree α∈[0,1], and assign n membership functions... All variables are fixed under the same membership degree α, and fuzzy uncertainty is propagated to obtain n fuzzy input variables X. i boundary range in, For X i The minimum value, For X i The maximum value; Step 2.2: Set the sampling parameter Q, and obtain the n fuzzy input variables X from Step 2.

1. i boundary range Substitute the extracted values ​​into Z = f(X) to obtain Q Z(α). Then, select the maximum and minimum values ​​from the Q output responses Z(α) to form the boundary range [Z] of the output response Z(α). l (α), Z u (α)]; Among them, Z l Z(α) is the minimum value of the output response Z(α) under the membership degree α. u (α) is the maximum value of the output response Z(α) under the membership degree α; Step 2.3: Repeat steps 2.1 to 2.2, iterating through the values ​​of α in [0, 1] to obtain the boundary [Z] of the output response Z(α) under different membership degrees α. l (α), Z u (α)]; Step 2.4: Define the unconditional membership function μ z To determine the probability of each value in the output response Z; The Z obtained in step 2.3 l (α) and Z u (α) is plotted with independent variable Z(α) and dependent variable μ. z value μ Z —In the Z-plot, connecting the points and fitting the graph yields the unconditional membership function μ for the model's output response Z. z And at the same time, the range of the output response Z is obtained as [Z l Z u ]; Step 3: Construct fuzzy input variable X i The fuzzy process of membership function: Step 3.1: Set the i-th fuzzy input variable X i Let X be a fixed value x′ within the domain. i =x′; Iterate through the values ​​of α in [0, 1] to obtain the output response under different membership degrees α. boundary Step 3.2: Define the conditionally restricted membership function For output response The degree of probability of each value point in the equation; The result obtained in step 3.1 and After plotting, the model output response is fitted to obtain the result. Conditional membership function Step 3.3: Repeat steps 3.1 and 3.2, setting the traversal span ΔX. i traverse X i The domain of definition takes the value x′, resulting in N fuzzy input variables X. i The corresponding output response Conditional membership function Step 3.4: Calculate the N membership function curves obtained in Step 3.

3. Drawing in In the figure, connecting the curves and fitting them together yields a polyhedron. The polyhedron represents the fuzzy input variable X. i The fuzzy process in X i Slicing the polyhedron along the axis yields the X-axis slice. i The slice section on x′ is The boundaries of this polyhedron in the three directions are, in order: X i The domain of the output response Z in step 2.4 [Z l Z u ] and conditionally restricted membership functions The range of Z is [0, 1]. The boundaries in the above three directions form a square envelope that encompasses all possibilities of the output response Z of the fuzzy process. Step 4: Repeat steps 3.1 to 3.4, sequentially traversing the input fuzzy variable set X = (X1, X2, ..., X...). n Each X in ) i n fuzzy input variables X are obtained. i The fuzzy process; Step 5: Compare the n fuzzy processes obtained in Step 4. Analyze the shape features and volume ratio of the polyhedra to the envelope in the function graph, and select one or more fuzzy input variables with prominent features. Step 6: Introduce an index to the n fuzzy input variables X obtained in Step 4. i The fuzzy process is abstracted, and the fuzzy input variable X is defined. i The fuzzy sensitivity index is T i The calculation formula is as follows: Among them, X i，j (j = 1, 2, ..., N) represents the fuzzy input variable X. i The j-th fixed value x′; Indicates the model output response The k-th value in the middle; the For slice cross section The traversal span is set during traversal, where M is the traversal span. Traversal The number of values ​​that can be taken from the domain; Step 7: Combining Steps 5 and 6, rank the influence of the n fuzzy processes based on both function graph features and index magnitude, and select one or more key fuzzy input variables X in the structural analysis. i ; Among them, when T i When →1, input variable X i The more significant the impact on the model's output, the greater T. i When the input variable X is 1, the input variable X is 1. i This plays a key and dominant role in the model; If the membership function The shape is triangular, T i When the value reaches 0.5, input variable X. i The smaller the impact on the model's output, the better T i Input variable X when = 0.5 i This has no effect on the model; If the membership function The shape is trapezoidal, when T i When →0, input variable X i The smaller the impact on the model's output, the better T i Input variable X when = 0 i This has no effect on the model.

2. The radome structure analysis method based on fuzzy variables according to claim 1, characterized in that, Step 3 also includes: Step 3.5: Based on X in Step 1 i The corresponding membership function middle The magnitude of the membership function curves in step 3.3 is respectively compared with the N membership function curves. Uneven coloring and drawing in step 3.4 In the diagram, let X represent the variable X in the fuzzy input. i The darker the color of the selected x′ probability, the more significant the difference in the fuzzy input variable X. i The higher the probability of selecting x′.

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