Integrated Optimization Design Method and System for Bearing and Transmitting Waves Applied to Dot Array Antenna Windows

Abstract

This invention discloses a method and system for integrated load-bearing and wave-transmission optimization design of array antenna windows, relating to the field of computational electromagnetics structural strength cross-section and optimization technology. The invention includes: S1: Constructing a load-bearing and wave-transmission optimization model for the array antenna window, and obtaining initial sample points using the Latin hypercube sampling method; S2: Obtaining the actual response values ​​of the initial sample points using an integrated load-bearing and wave-transmission simulation analysis method for the array antenna window, and constructing a load-bearing and wave-transmission surrogate optimization model for the array antenna window using a Kriging surrogate model. This invention can solve the problems of high time cost and the inability to simultaneously optimize load-bearing / wave-transmission performance during the optimization design of array antenna windows, obtaining an array antenna window structure with optimal wave-transmission performance under load constraints with less time cost, thus reducing the optimization design cycle and cost of array antenna windows.

Description

Technical Field

[0001] This invention relates to the field of computational electromagnetic structural strength cross-section and optimization technology, specifically to an integrated optimization design method for wave transmission and load bearing of array antenna windows. Background Technology

[0002] Antenna windows are the electromagnetic windows of antenna systems in aircraft, requiring both high wave transmission and load-bearing capacity. Maintaining both load-bearing and wave transmission characteristics is crucial in the face of harsh load environments during aircraft service. Array structures offer advantages such as high specific stiffness, good heat resistance, strong load-bearing capacity, excellent wave transmission, and high design flexibility, meeting the multi-functional requirements of high-speed aircraft antenna windows. However, the complexity of array structures, the diversity of antenna window requirements, and the extreme nature of load environments have led to problems such as a lack of analytical methods and long optimization design cycles for current array structure antenna windows. Therefore, this invention proposes an integrated load-bearing and wave transmission optimization design method and system for array antenna windows. Summary of the Invention

[0003] The purpose of this invention is to provide an integrated optimization design method and system for load-bearing and wave-transmission of dot array antenna windows, which solves the problems of high time cost and inability to simultaneously optimize load-bearing and wave-transmission performance during the optimization design of dot array antenna windows. It obtains a dot array antenna window structure with optimal wave-transmission performance under load-bearing constraints with less time cost, thereby reducing the optimization design cycle and cost of dot array antenna windows.

[0004] According to a first aspect of the present invention, in order to achieve the above-mentioned objective, the present invention provides the following technical solution: an integrated optimization design method for wave transmission and load bearing of a dot array antenna window, comprising the following steps:

[0005] S1: Construct a dot array antenna window bearing-transmission optimization model and obtain initial sample points using the Latin hypercube sampling method;

[0006] S2: The actual response values ​​of the initial sample points are obtained by using the integrated simulation analysis method of the array antenna window bearing and wave transmission, and the Kriging surrogate model is used to construct the array antenna window bearing and wave transmission surrogate optimization model.

[0007] S3: The particle swarm optimization algorithm is used to solve the dot array antenna window bearing-transmission surrogate optimization model in S2 to obtain the optimal solution of the surrogate optimization model;

[0008] S4: Calculate the actual response of the optimal solution of the proxy optimization model and determine whether it converges. If it does not converge, add new sample points to the sample set using the mixed addition criterion, and repeat steps S2 and S3 to continue iterating. If it converges, output the optimal design scheme.

[0009] Furthermore, in step S1, an optimization model for the window bearing and wave transmission of the array antenna is established, and the initial sample points are obtained using the Latin hypercube sampling method, as detailed below:

[0010] (21) Establish the window-bearing-transmission optimization model for the array antenna, as follows:

[0011] Using the cell rod diameter, side length, and core layer thickness of the array antenna window as optimization variables, and the objective function of the optimization model is established with the goal of maximizing the minimum transmittance of the array antenna window within a specified incident angle range:

[0012]

[0013] In the formula, d is the rod diameter of the lattice cell, l is the side length of the lattice cell, h is the thickness of the antenna window core layer, and T(d,l,h) is the transmittance of the lattice antenna window. The transmittance of the array antenna window at a specific incident angle;

[0014] The constraints include the maximum deformation of the antenna window under force and heat loads and the temperature of the lower surface of the antenna window. Based on these constraints, the load-bearing and wave-transmission optimization model of the array antenna window is established as follows:

[0015]

[0016] In the formula, δ max (d,l,h) represents the maximum deformation of the dot matrix antenna window. It is the maximum allowable deformation of the dot array antenna window, t down (d,l,h) is the temperature of the lower surface of the antenna window. A is the maximum allowable temperature of the lower surface of the antenna window, and A is the characteristic parameter of the lattice cell. The range of values ​​for B is the range of values ​​for the thickness d of the dot matrix antenna window core layer;

[0017] (22) n initial sample points are obtained using the Latin hypercube sampling method, as follows:

[0018] The cumulative density functions of the variable lattice cell parameters d / l and the lattice antenna window core layer thickness h are divided into n equal partitions. Then, a data point is randomly selected in each partition. After that, these two sample lists are randomly combined into a two-dimensional random combination set, which yields a sample set consisting of n initial sample points.

[0019] Furthermore, in step S2, the actual response values ​​of the sample points are obtained through the integrated simulation analysis method of the array antenna window bearing and wave transmission, and the Kriging surrogate model is used to establish an optimized model of the array antenna window bearing and wave transmission surrogate, specifically including:

[0020] (31) Sample X was obtained through the integrated simulation analysis method of dot array antenna window bearing and wave transmission. i The actual response T(X) i ), δ max (X i ), t down (X i The details are as follows:

[0021] (31.1) Calculate the equivalent mechanical, thermal and electromagnetic parameters of the lattice structure according to the optimization variables in the sample, and establish an equivalent model of the lattice antenna window;

[0022] (31.2) Apply force and thermal loads to the equivalent model of the dot array antenna window respectively, and perform force-thermal-electric coupling analysis to obtain its mechanical, thermal, and electromagnetic properties, including the maximum deformation δ of the dot array antenna window. max (X i ), lower panel temperature t down (X i ) and transmittance T(X) i );

[0023] (32) The Kriging surrogate model is used to establish surrogate models for the optimization objective and constraints respectively. The setup method is as follows:

[0024] (32.1) The Kriging model consists of a regression model and a nonparametric Gaussian stochastic process, expressed as:

[0025]

[0026] In the formula, f is the model's predicted value. m (x) is the regression basis function; λ m These are the corresponding regression coefficients; Z(x) is a regression coefficient with a mean of 0 and a variance of σ. 2 Covariance is The static stochastic process represents the systematic deviation between the regression term and the response; It is a correlation function that is only related to spatial distance;

[0027] Optimize objective T(d,l,h) and constraint δ max (d,l,h),t down (d,l,h) are all predicted using the Kriging surrogate model;

[0028] (33) Proxy model based on optimization objective and constraints The optimization model for the window-bearing and wave-transmitting proxy of the array antenna is established as follows:

[0029]

[0030] In the formula, This is the predicted value of the transmittance of the array antenna window. This is the predicted value of the maximum deformation of the dot matrix antenna window. It is the predicted value of the temperature on the lower surface of the antenna window.

[0031] Furthermore, in step S3, the particle swarm optimization algorithm is used to solve the surrogate optimization model of the array antenna window in S2 to obtain the optimal solution of the surrogate optimization model, specifically including:

[0032] (41) Set the initial population size and number of iterations;

[0033] (42) The surrogate optimization model in S2 is solved using the particle swarm optimization algorithm to obtain the optimal solution of the surrogate optimization model. and the optimal predicted value The solution method is as follows:

[0034] (42.1) Particles have only two attributes: velocity and position. In each iteration, the particles in the population update their velocity and position according to the individual optimal solution and the global optimal solution, as shown in equation (5):

[0035]

[0036] In the formula, and These are the velocities of the i-th particle in the d-th and d+1-th iterations, respectively; and These represent the positions of the i-th particle in the d-th and d+1-th iterations, respectively; ω d is the inertia weight for the d-th iteration; c1 and c2 are the individual and social learning factors of the particle, respectively, set to 2; r1 and r2 are both random numbers between 0 and 1; and These are the individual solution in the d-th iteration and the global optimal solution, respectively.

[0037] The dynamic inertia weight ω is obtained by employing a linearly decreasing weight strategy. d As shown in the error message: "Error! Reference source not found."

[0038] ω d =(ω ini -ω end (Dd) / D+ω end (6)

[0039] In the formula, ω ini ω is the initial inertia weight, which is also the maximum value of the inertia weight, and is set to 0.9;end This is the final inertia weight, which is also the minimum value of the inertia weight, and is set to 0.4.

[0040] Further, in step S4, the actual response of the optimal solution of the surrogate optimization model is calculated and its convergence is determined. If it does not converge, a new sample point is added to the sample set using the mixed addition criterion, and steps S2 and S3 are repeated for further iteration. If it converges, the optimal design scheme is output, specifically including:

[0041] (51) Calculate the optimal solution of the proxy optimization model according to step (31). Actual response

[0042] (52) Based on the optimal solution, the predicted value is obtained. The accuracy is used as a termination condition to determine whether it has converged:

[0043]

[0044] In the formula, The predicted value is for the surrogate model; ε is the actual response value. error This represents the prediction error;

[0045] (53) If convergence is not achieved, the new sample points are added to the sample set using the mixed addition criterion. Then return to step S2 to continue the iteration process;

[0046] (54) If convergence occurs, output the optimal solution. And the actual response corresponding to the optimal solution: optimal transmittance Maximum deformation δ max Lower panel temperature t down .

[0047] Furthermore, the hybrid point-addition criterion includes the MSP criterion, which is beneficial for local optimization, and the EI criterion, which is beneficial for global optimization, wherein:

[0048] The MSP criterion is the optimal surrogate model prediction criterion. Its principle is to directly add the optimal solution of the surrogate model to the sample set.

[0049] The EI criterion is an improvement expectation criterion. Its principle is to find the maximum value of EI, and its expression is as follows:

[0050]

[0051] In the formula, Φ and φ are the standard normal cumulative distribution function and the standard normal probability density function, respectively; y min This represents the current optimal objective function value. s(x) represents the predicted value from the Kriging model, and s(x) represents the standard deviation of the predicted value.

[0052] Using the MSP criterion, the optimal solution of the surrogate model is obtained. Add to the sample set; using the EI criterion plus the point criterion, add the sample points at the maximum EI value. Add to sample set, update sample set

[0053] According to a second aspect of the present invention, the present invention provides an integrated optimization design system for the carrier and wave transmission of a dot array antenna window, for implementing the above-mentioned integrated optimization design method for the carrier and wave transmission of a dot array antenna window, comprising:

[0054] The first construction module is used to build the array antenna window bearing-transmission optimization model, and the initial sample points are obtained by using the Latin hypercube sampling method.

[0055] The second construction module is used to obtain the actual response values ​​of the initial sample points using the integrated simulation analysis method of the array antenna window bearing-transmission, and to construct the array antenna window bearing-transmission proxy optimization model using the Kriging proxy model.

[0056] The calculation module is used to solve the surrogate optimization model of the array antenna window in S2 using the particle swarm optimization algorithm, and obtain the optimal solution of the surrogate optimization model.

[0057] The output module is used to calculate the actual response of the optimal solution of the surrogate optimization model and determine whether it has converged. If it has not converged, the new sample points are added to the sample set using the mixed addition criterion, and the iteration is repeated. If it has converged, the optimal design scheme is output.

[0058] According to a third aspect of the present invention, the present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor, and when the processor loads and executes the computer program, it employs the above-described integrated wave-transmitting optimization design method for dot matrix antenna windows.

[0059] According to a fourth aspect of the present invention, the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the above-described integrated wave-transmitting optimization design method for a dot matrix antenna window.

[0060] According to a fifth aspect of the present invention, the present invention provides a computer program product comprising a computer program, which, when executed by a processor, is used to load and execute the above-described integrated wave-transmitting optimization design method for a dot matrix antenna window.

[0061] The present invention has at least the following beneficial effects:

[0062] This invention embeds the load-transmission simulation analysis method of a dot matrix antenna window into the optimization design process. With optimal wave transmission performance as the objective and load-bearing capacity as the constraint, an optimization model is established. Combined with the Kriging surrogate model, a dot matrix antenna window optimization design method based on the Kriging model-assisted particle swarm optimization algorithm is proposed. This method considers load-bearing performance while optimizing the antenna window's wave transmission performance. The use of the load-transmission simulation analysis method takes into account the influence of force and thermal loads on electromagnetic performance. The use of the Kriging surrogate model greatly improves the efficiency of the optimization design. This method can obtain the dot matrix antenna window structure with optimal wave transmission performance under load-bearing constraints in a short time, significantly shortening the optimization design time of the dot matrix antenna window and possessing high engineering value.

[0063] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0064] Figure 1 This is a flowchart illustrating the optimization design method described in this invention;

[0065] Figure 2 This is a schematic diagram illustrating the principle of the optimization design method described in this invention.

[0066] Figure 3 A schematic diagram of the dot array antenna window model in an embodiment of the present invention;

[0067] Figure 4 A schematic diagram of the initial sample points in an embodiment of the present invention;

[0068] Figure 5 A schematic diagram of the equivalent model of the dot array antenna window in this embodiment of the invention;

[0069] Figure 6 Surface temperature curves during flight in this embodiment of the invention;

[0070] Figure 7 This is a schematic diagram of the proxy model for transmittance in an example of the present invention;

[0071] Figure 8 This is a schematic diagram of the proxy model for the maximum deformation in an example of the present invention;

[0072] Figure 9 This is a schematic diagram of the proxy model for the lower panel temperature in an example of the present invention;

[0073] Figure 10 This is a schematic diagram of the convergence process for optimizing the dot matrix antenna window in an embodiment of the present invention;

[0074] Figure 11This is a displacement cloud map of the dot array antenna window in an embodiment of the present invention;

[0075] Figure 12 This is a temperature cloud map of the dot matrix antenna window in an embodiment of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0077] Please see Figure 1 This invention provides a technical solution: an integrated optimization design method for wave transmission and load bearing of a dot array antenna window, comprising the following steps:

[0078] S1: Construct a dot matrix antenna window bearing-transmission optimization model, and obtain initial sample points using the Latin hypercube sampling method, as follows:

[0079] S1.1: Construct the dot array antenna window bearing-transmission optimization model, as follows:

[0080] To address the integrated optimization problem of the load-bearing and wave-transmitting capabilities of a dot matrix antenna window, the cell rod diameter, side length, and core layer thickness of the dot matrix antenna window are used as optimization variables, and the objective function of the optimization model is established with the goal of maximizing the minimum wave transmittance of the dot matrix antenna window within a specified incident angle range.

[0081]

[0082] In the formula, d is the rod diameter of the lattice cell, l is the side length of the lattice cell, h is the thickness of the antenna window core layer, and T(d,l,h) is the transmittance of the lattice antenna window. The transmittance of the array antenna window at a specific incident angle;

[0083] Considering that the antenna window not only needs to meet electrical performance requirements but also needs to withstand harsh external environments, the array antenna window also needs to meet certain mechanical and thermal load-bearing requirements. Therefore, the constraints include the maximum deformation of the antenna window under mechanical and thermal loads and the temperature of the lower surface of the antenna window. Based on this, the load-bearing and wave-transmission optimization model of the array antenna window is established as follows:

[0084]

[0085] In the formula, δ max (d,l,h) represents the maximum deformation of the dot matrix antenna window. It is the maximum allowable deformation of the dot array antenna window, tdown (d,l,h) is the temperature of the lower surface of the antenna window. A is the maximum allowable temperature of the lower surface of the antenna window, and A is the characteristic parameter of the lattice cell. The range of values ​​for B is the range of values ​​for the thickness d of the dot matrix antenna window core layer;

[0086] S1.2: n initial sample points are obtained using the Latin hypercube sampling method, as follows:

[0087] The cumulative density functions of the variable lattice cell parameters d / l and the lattice antenna window core layer thickness h are divided into n equal partitions. Then, a data point is randomly selected in each partition. After that, these two sample lists are randomly combined into a two-dimensional random combination set, which yields a sample set consisting of n initial sample points.

[0088] S2: The actual response values ​​of the initial sample points are obtained using the integrated simulation analysis method of the array antenna window bearing and wave transmission. A Kriging surrogate model is then used to construct an optimized model of the array antenna window bearing and wave transmission surrogate, as detailed below:

[0089] S2.1: Sample X was obtained through the integrated simulation analysis method of dot array antenna window bearing and wave transmission. i The actual response T(X) i ), δ max (X i ), t down (X i The details are as follows:

[0090] (S2.11) Calculate the equivalent mechanical, thermal, and electromagnetic parameters of the lattice structure based on the optimization variables in the sample, and establish an equivalent model of the lattice antenna window;

[0091] (S2.12) Apply force and thermal loads to the equivalent model of the dot array antenna window respectively, and perform force-thermal-electric coupling analysis to obtain its mechanical, thermal, and electromagnetic properties, including the maximum deformation δ of the dot array antenna window. max (X i ), lower panel temperature t down (X i ), and transmittance T(X) i );

[0092] S2.2: Using the Kriging surrogate model, surrogate models for the optimization objective and constraints are established respectively. The setup method is as follows:

[0093] The Kriging model consists of a regression model and a nonparametric Gaussian stochastic process, expressed as:

[0094]

[0095] In the formula, f is the model's predicted value. m (x) is the regression basis function; λ m These are the corresponding regression coefficients; Z(x) is a regression coefficient with a mean of 0 and a variance of σ. 2 Covariance is The static stochastic process represents the systematic deviation between the regression term and the response; It is a correlation function that is only related to spatial distance;

[0096] Optimize objective T(d,l,h) and constraint δ max (d,l,h),t down (d,l,h) are all predicted using the Kriging surrogate model;

[0097] S2.3: A surrogate model based on optimization objectives and constraints The optimization model for the window-bearing and wave-transmitting proxy of the array antenna is established as follows:

[0098]

[0099] In the formula, This is the predicted value of the transmittance of the array antenna window. This is the predicted value of the maximum deformation of the dot matrix antenna window. It is the predicted value of the temperature of the lower surface of the antenna window;

[0100] S3: The particle swarm optimization algorithm is used to solve the surrogate optimization model of the array antenna window in S2, and the optimal solution of the surrogate optimization model is obtained as follows:

[0101] S3.1: Set the initial population size and number of iterations;

[0102] S3.2: The surrogate optimization model in S2 is solved using the particle swarm optimization algorithm to obtain the optimal solution of the surrogate optimization model. and the optimal predicted value The solution method is as follows:

[0103] The PSO algorithm is a population-based search algorithm, where each individual in the population is a point in the N-dimensional search space, and each particle represents a potential solution to the optimization problem. Particles have only two attributes: velocity and position. In each iteration, the particles in the population update their velocity and position based on the individual optimal solution and the global optimal solution, as shown in Equation (5):

[0104]

[0105] In the formula, and These are the velocities of the i-th particle in the d-th and d+1-th iterations, respectively; and These represent the positions of the i-th particle in the d-th and d+1-th iterations, respectively; ω d is the inertia weight for the d-th iteration; c1 and c2 are the individual and social learning factors of the particle, respectively, which are generally set to 2; r1 and r2 are both random numbers between 0 and 1; and These are the individual solution in the d-th iteration and the global optimal solution, respectively.

[0106] To balance the global and local search capabilities of the PSO algorithm, a Linear Decreasing Weight (LDW) strategy is adopted to obtain the dynamic inertia weight ω. d As shown in the example: Error! Reference source not found;

[0107] ω d =(ω ini -ω end (Dd) / D+ω end (14)

[0108] In the formula, ω ini ω is the initial inertia weight, which is also the maximum value of the inertia weight, and is generally taken as 0.9; end This is the final inertia weight, which is also the minimum value of the inertia weight, and is generally taken as 0.4;

[0109] S4: Calculate the actual response of the optimal solution of the surrogate optimization model and determine whether it has converged. If it has not converged, add new sample points to the sample set using the mixed addition criterion, and repeat steps S2 and S3 to continue iterating. If it has converged, output the optimal design scheme, as follows:

[0110] S4.1: Calculate the optimal solution of the surrogate optimization model according to the steps in S2.1. Actual response

[0111] S4.2: Predict the value based on the optimal solution The accuracy is used as a termination condition to determine whether it has converged:

[0112]

[0113] In the formula, The predicted value is for the surrogate model; ε is the actual response value. error This represents the prediction error;

[0114] S4.3: If convergence fails, the new sample points are added to the sample set using the mixed addition criterion. And return to S2 to continue the iteration process;

[0115] The hybrid addition criterion comprises the MSP criterion, which favors local optimization, and the EI criterion, which favors global optimization. The MSP criterion, or Optimal Surrogate Model Prediction Criterion, works by directly adding the optimal solution of the surrogate model to the sample set. The EI criterion, or Improvement Expectation Criterion, works by finding the maximum value of EI, and its expression is as follows:

[0116]

[0117] In the formula, Φ and φ are the standard normal cumulative distribution function and the standard normal probability density function, respectively; y min This represents the current optimal objective function value. s(x) represents the predicted value from the Kriging model, and s(x) represents the standard deviation of the predicted value.

[0118] Using the MSP criterion, the optimal solution of the surrogate model is obtained. Add to the sample set; using the EI criterion plus the point criterion, add the sample points at the maximum EI value. Add to sample set; Update sample set

[0119] S4.4: If convergence occurs, output the optimal solution. And the actual response corresponding to the optimal solution: optimal transmittance Maximum deformation δ max Lower panel temperature t down .

[0120] The present invention will be further described below with reference to specific embodiments:

[0121] like Figure 1 and Figure 2 As shown, this embodiment proposes an integrated load-transmission optimization design method for array antenna windows, to achieve... Figure 3 Taking the dot matrix antenna window model shown as an example, the method is explained in detail. The inner dimensions of the dot matrix antenna window are 140×100mm. The upper and lower skin materials are Pyroceram9606, both with a thickness of 2mm. The core layer adopts a dot matrix structure composed of body-centered cubic cells, and the material is 3Al2O3·2SiO2. The material parameters are shown in Tables 1 and 2, respectively. The core layer thickness h and the dimensions of the unit cell, including the rod diameter d and side length l of the cell, are the structural parameters to be determined in the design.

[0122] Table 1. Material parameters for the window skin of the dot matrix antenna

[0123]

[0124] Table 2 Material parameters of the core layer of the dot array antenna

[0125]

[0126]

[0127] The method provided by this invention is used to perform integrated load-transmission optimization design on the above-mentioned dot array antenna window, specifically including the following steps:

[0128] S1: Establish a dot array antenna window bearing-transmission optimization model, and use the Latin hypercube sampling method to obtain initial sample points;

[0129] S1.1: For the integrated optimization problem of the load-bearing and wave-transmitting structure of the array antenna window, the cell rod diameter d, side length l, and core layer thickness h of the array antenna window are used as optimization variables, and the objective of the optimization model is to maximize the minimum wave transmittance of the array antenna window within the 0-50° incident angle range. The objective function of the optimization model is established as follows:

[0130] T(d,l,h,)=min(T 10 ,T 20 ,T 30 ,T 40 ,T 50 )

[0131] Antenna windows need to meet load-bearing and wave-transmission performance requirements during service. Therefore, a dot-array antenna window needs to be designed to maximize wave transmission while meeting load-bearing requirements. Specifically, the thickness h of the dot-array core layer, the rod diameter d of the dot-array cell, and the side length l are optimized to ensure that the maximum deformation of the antenna window does not exceed 2mm, the lower surface temperature does not exceed 20℃, and the wave transmission is optimal. The optimization model is as follows:

[0132] maxT(d,l,h)

[0133]

[0134] S1.2: Twenty initial sample points were obtained using the Latin hypercube sampling method, such as... Figure 4 As shown;

[0135] S2: The actual response values ​​of the sample points are obtained through the integrated simulation analysis method of the array antenna window bearing and wave transmission, and the Kriging proxy model is used to establish the array antenna window bearing and wave transmission proxy optimization model.

[0136] S2.1: Obtain the equivalent thermal parameters of the lattice structure by calling Abaqus through MATLAB, obtain the electromagnetic parameters of the lattice structure by calling HFSS and using the S-parameter inversion program, and establish the equivalent model of the lattice antenna window by calling HyperMesh, such as... Figure 5As shown; apply to the upper surface of the dot matrix antenna window Figure 6 The temperature load and the uniformly distributed force load of 9.2 MPa are shown. The boundary conditions are set as follows: the antenna window is fixed around the perimeter, the antenna operating frequency is set to 6 GHz, and the incident angle is calculated every 10° from 0 to 50°. The force-thermal-electric coupling analysis of the array antenna window is performed by calling simulation modeling software such as Abaqus, FEKO, and HyperMesh through MATLAB program. The maximum deformation of the array antenna window, the temperature of the lower panel, and the transmittance of the sample points in the sample set are obtained.

[0137] S2.2: Using the Kriging surrogate model, surrogate models are established for the optimization objective (transmittance of the array antenna window) and constraints (maximum deformation of the array antenna window, temperature of the lower panel). A set of surrogate models for the optimization process is as follows: Figures 7 to 9 As shown;

[0138] S2.3: Based on the optimization objective and constraints, the proxy model for the array antenna window bearing-transmission is established as follows:

[0139]

[0140] S3: The surrogate optimization model in S2 is solved using the particle swarm optimization algorithm to obtain the optimal solution of the surrogate optimization model;

[0141] S3.1: Set the initial population size to 50 and the number of iterations to 50;

[0142] S3.2: The surrogate optimization model in S2 is solved using the particle swarm optimization algorithm to obtain the optimal solution of the surrogate optimization model. and the optimal predicted value

[0143] S4: Calculate the actual response of the optimal solution of the surrogate optimization model and determine whether it has converged. If it has not converged, use the mixed addition criterion to add new sample points to the sample set and return to S2 to continue the iteration process until convergence, then output the final optimization result.

[0144] S4.1: Repeat the steps in S2.1 to calculate the actual response of the optimal solution of the surrogate optimization model;

[0145] S4.2: Use the accuracy of the predicted value at the optimal solution being less than 10⁻³ as the termination condition to determine whether it has converged;

[0146] S4.3: If convergence is not achieved, the new sample point is added to the sample set using the mixed addition criterion, and the process returns to S2 to continue the iteration.

[0147] S4.4: Continue until the optimization program converges, then output the final optimization result. The final optimization shows that the antenna window has the best wave transmission performance when the core layer thickness is 11.838 mm and the aspect ratio (d / l) is 0.237. The optimization convergence process is as follows: Figure 10 As shown; after optimization, the minimum transmittance is 80.11% within the scanning angle range of 0-50°, the maximum deformation of the antenna window under the above load is 0.96mm, and the lower surface temperature is 20℃. Figure 11 and Figure 12 As shown, it meets the load-bearing performance requirements.

[0148] In summary, this invention embeds the load-transmission simulation analysis method of array antenna windows into the optimization design process. With optimal transmission performance as the objective and load-bearing capacity as the constraint, an optimization model is established. Furthermore, by combining the Kriging surrogate model, a Kriging-assisted particle swarm optimization algorithm-based optimization design method for array antenna windows is proposed. This method considers load-bearing performance while optimizing the transmission performance of the antenna window. The use of the load-transmission simulation analysis method takes into account the influence of force and thermal loads on electromagnetic performance. The use of the Kriging surrogate model greatly improves the efficiency of the optimization design. This method can obtain the array antenna window structure with optimal transmission performance under load-bearing constraints in a short time, significantly shortening the optimization design time of array antenna windows and possessing high engineering value.

[0149] Example 2:

[0150] This invention provides an integrated wave-transmission optimization design system for a dot array antenna window, used to implement the integrated wave-transmission optimization design method for a dot array antenna window described in Embodiment 1, comprising:

[0151] The first construction module is used to build the array antenna window bearing-transmission optimization model, and the initial sample points are obtained by using the Latin hypercube sampling method.

[0152] The second construction module is used to obtain the actual response values ​​of the initial sample points using the integrated simulation analysis method of the array antenna window bearing-transmission, and to construct the array antenna window bearing-transmission proxy optimization model using the Kriging proxy model.

[0153] The calculation module is used to solve the surrogate optimization model of the array antenna window in S2 using the particle swarm optimization algorithm, and obtain the optimal solution of the surrogate optimization model.

[0154] The output module is used to calculate the actual response of the optimal solution of the surrogate optimization model and determine whether it has converged. If it has not converged, the new sample points are added to the sample set using the mixed addition criterion, and the iteration is repeated. If it has converged, the optimal design scheme is output.

[0155] Specifically, the first construction module, the second construction module, the calculation module, and the output module can be embedded into a computer processing system. The computer, based on the aforementioned integrated optimization design method for the carrier-transmitter antenna window, calls each of the above modules to complete the task of optimizing the design of the array antenna window. The first construction module, the second construction module, the calculation module, and the output module can perform operations according to the specific steps given in the aforementioned integrated optimization design method for the carrier-transmitter antenna window.

[0156] It should be noted that the division of the various modules in the above system is merely a division of logical functions. In actual implementation, they can be fully or partially integrated into a single physical entity, or they can be physically separated. These modules can be implemented entirely in software through processing element calls; they can be fully implemented in hardware; or some modules can be implemented by processing element calls to software, while others are implemented in hardware. For example, the output module can be a separate processing element or integrated into a chip in the aforementioned device. Alternatively, it can be stored as program code in the memory of the aforementioned device, and called and executed by a processing element of the device. The implementation of other modules is similar. Furthermore, these modules can be fully or partially integrated together or implemented independently. The processing element mentioned here can be an integrated circuit with signal processing capabilities. During implementation, each step of the above method or each of the above modules can be completed through integrated logic circuits in the hardware of the processor element or through software instructions.

[0157] For example, these modules can be one or more integrated circuits configured to implement the above methods, such as one or more Application Specific Integrated Circuits (ASICs), one or more Digital Signal Processors (DSPs), or one or more Field Programmable Gate Arrays (FPGAs). As another example, when a module is implemented using processing element scheduler code, the processing element can be a general-purpose processor, such as a Central Processing Unit (CPU) or other processor capable of calling program code. Furthermore, these modules can be integrated together to form a system-on-a-chip (SOC).

[0158] Example 3:

[0159] The present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it adopts the above-mentioned integrated wave-transmitting optimization design method for dot array antenna windows.

[0160] It should be noted that the terminal device can be a computer device such as a desktop computer, a laptop computer, or a cloud server, and the terminal device includes, but is not limited to, a processor and a memory. For example, the terminal device may also include input / output devices, network access devices, and buses.

[0161] Furthermore, the processor can be a central processing unit (CPU). Of course, depending on the actual use, other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0162] Example 4:

[0163] The present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the above-described integrated wave-transmitting optimization design method for a dot matrix antenna window.

[0164] The computer program can be stored in a computer-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The computer-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the computer-readable medium includes, but is not limited to, the above-mentioned components.

[0165] Example 5:

[0166] The present invention provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it is used to load and execute the above-mentioned integrated wave-transmitting optimization design method for a dot matrix antenna window.

[0167] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0168] For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances. When an element is referred to as being "assembled on," "mounted on," "fixed to," or "set on" another element, it may be directly on the other element or there may be an intermediate element present. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be an intermediate element present. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible embodiments.

[0169] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

[0170] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

Claims

1. A carrying wave-transparent integrated optimization design method applied to a dot matrix antenna window, characterized in that, The method comprises the following steps: S1: Constructing a point array antenna window bearing-transmission optimization model, and obtaining initial sample points by using a Latin hypercube sampling method; S2: Obtaining actual response values of the initial sample points by using a point array antenna window bearing-transmission integrated simulation analysis method, and constructing a point array antenna window bearing-transmission surrogate optimization model by using a Kriging surrogate model; S3: Solving the point array antenna window bearing-transmission surrogate optimization model in S2 by using a particle swarm optimization algorithm to obtain an optimal solution of the surrogate optimization model; S4: Calculating an actual response of the optimal solution of the surrogate optimization model and judging whether the actual response converges, if not, adding a new sample point to a sample set by using a hybrid sampling criterion, and repeating steps S2 and S3 to continue iteration, and if the actual response converges, outputting an optimal design scheme; In step S1, the point array antenna window bearing-transmission optimization model is established, and initial sample points are obtained by using a Latin hypercube sampling method, and the specific process is as follows: The point array antenna window bearing-transmission optimization model is established, and the specific process is as follows: Taking the cell rod diameter, the side length of the point array antenna window and the thickness of the core layer as optimization variables, and taking the minimum value of the maximum transmission rate of the point array antenna window in a specified incident angle range as an optimization target, a target function of the optimization model is established: （1） In the formula, d is the rod diameter of the lattice cell, l is the side length of the lattice cell, h is the thickness of the antenna window core layer, is the transmittance of the lattice antenna window, is the transmittance of the lattice antenna window at a specific incident angle; The constraint conditions include the maximum deformation of the antenna window under the force and thermal load and the temperature of the lower surface of the antenna window, and the point array antenna window bearing-transmission optimization model is established based on this as follows: （2） wherein, is the maximum deformation of the lattice antenna window, is the maximum allowable deformation of the lattice antenna window, is the temperature of the lower surface of the antenna window, is the maximum allowable temperature of the lower surface of the antenna window, is the value range of the characteristic parameter of the lattice cell is the value range of the characteristic parameter of the lattice cell is the value range of the thickness of the core layer of the lattice antenna window is the value range of the thickness of the core layer of the lattice antenna window The initial sample points are obtained using a Latin hypercube sampling method, as follows: n two initial sample points, as follows: The variable dot cell parameters d / l And the cumulative density function of the dot antenna window core layer thickness h Respectively into n Equal sub-area, then randomly select a data point in each sub-area, then, randomly combine the two sample lists into a two-dimensional random combination set, that is, a sample set composed of n Initial sample points , i =0. 2.The carrying wave-transparent integrated optimization design method applied to the dot matrix antenna window according to claim 1, wherein, In step S2, the actual response values of the sample points are obtained by using a point array antenna window bearing-transmission integrated simulation analysis method, and a point array antenna window bearing-transmission surrogate optimization model is established by using a Kriging surrogate model, and the specific process includes: (21) A sample is obtained by a simulation analysis method of carrying and wave-transmitting integration of a dot matrix antenna window actual response , , , as follows: (21.1) The equivalent mechanical, thermal and electromagnetic parameters of the point array structure are calculated according to the optimization variables in the sample, and an equivalent model of the point array antenna window is established; (21.2) The force-thermal load is applied to the equivalent model of the lattice antenna window respectively, the force-thermal-electric coupling analysis is carried out, and the mechanical, thermal and electromagnetic performances are obtained, including the maximum deformation of the lattice antenna window , the temperature of the lower panel and the wave transmittance ; (22) Kriging surrogate models are used to establish surrogate models of the optimization objectives and constraint conditions, respectively , , , and are established as follows: (22.1) The Kriging model is composed of a regression model and a non-parametric Gaussian random process, and the expression is as follows: （3） wherein is the model prediction; is the regression basis function; is the corresponding regression coefficient; is a stationary stochastic process with mean 0, variance , and covariance , representing systematic bias between the regressors and the response; is a correlation function depending only on spatial distance; Optimization objectives and constraints , The prediction values of the optimization objectives and constraints are obtained by Kriging surrogate model. (23) Agent model based on optimization target and constraint condition , , The lattice antenna window bearing-transmitting agent optimization model is established as follows: （4） wherein is the predicted value of the transmission of the lattice antenna window, is the predicted value of the maximum deformation of the lattice antenna window, is the predicted value of the temperature of the lower surface of the antenna window. 3.The carrying wave-transparent integrated optimization design method applied to the dot matrix antenna window according to claim 1, wherein, In step S3, the point array antenna window bearing-transmission surrogate optimization model in S2 is solved by using a particle swarm optimization algorithm to obtain an optimal solution of the surrogate optimization model, and the specific process includes: (31) The initial population size and the iteration number are set; (32) The agent optimization model in S2 is solved by using a particle swarm optimization algorithm to obtain the optimal solution of the agent optimization model and the optimal prediction value The solving method is as follows: (32.1) The particle only has two attributes of speed and position, and in each iteration, the particle updates its speed and position according to the individual optimal solution and the global optimal solution, as shown in formula (5): （5） where, and are the velocity of the th particle at the th and th iteration, respectively; and are the position of the th particle at the th and th iteration, respectively; is the inertia weight at the th iteration; and are the individual and social learning factors of the particle, respectively, set to 2; and are random numbers between 0 and 1; and are the individual and global best solutions at the th iteration, respectively; A linearly decreasing weight strategy is used to obtain dynamic inertia weights As shown in equation \ MERGEFORMAT (6): （6） In the formula, is the initial inertia weight, which is also the maximum value of the inertia weight, and is taken as 0.9; is the final inertia weight, which is also the minimum value of the inertia weight, and is taken as 0.

4. 4.The carrying wave-transparent integrated optimal design method applied to a dot matrix antenna window according to claim 1, wherein, In step S4, the actual response of the optimal solution of the surrogate optimization model is calculated and judged whether the actual response converges, if not, a new sample point is added to the sample set by using a hybrid sampling criterion, and steps S2 and S3 are repeated to continue iteration; If the actual response converges, an optimal design scheme is output, and the specific process includes: (41) optimizing the solution of the agent model according to step (21) the actual response ; (42) The predicted value at the optimal solution as a termination condition to determine whether it converges: （7） wherein is the proxy model prediction value; is the actual response value, is the prediction error; (43) If not, a hybrid point selection rule is used to add a new sample point to the sample set and go back to step S2 to continue the iteration process; (44) If converged, output the optimal solution and the actual response corresponding to the optimal solution: optimal transmittance , maximum deformation , lower panel temperature .

5. The load-carrying wave-transparent integrated design method for a dot matrix antenna window according to claim 4, characterized in that: The hybrid sampling criterion includes an MSP criterion which is beneficial to local optimization and an EI criterion which is beneficial to global optimization, wherein: The MSP criterion is an optimal surrogate model prediction criterion, and the principle is to directly add the optimal solution of the surrogate model to the sample set; The EI criterion is an improved expected criterion, and the principle is to solve the maximum value of EI, and the expression is as follows: （8） wherein and are the standard normal cumulative distribution function and the standard normal probability density function, respectively; is the current best objective function value; is the predicted value of the Kriging model, is the standard deviation of the predicted value; Adopting the MSP criterion, the optimal solution of the surrogate model is found = The sample set is updated by adding the sample point with the maximum EI value The sample set is updated by adding the sample point with the maximum EI value .

6. A carrying and wave-transparent integrated optimization design system applied to a dot matrix antenna window, used to implement the carrying and wave-transparent integrated optimization design method applied to a dot matrix antenna window in any one of claims 1 to 5, characterized in that, The method comprises the following steps: The first construction module is configured to construct a dot matrix antenna window load-transmission optimization model, and to obtain initial sample points by using a Latin hypercube sampling method; The second construction module is configured to obtain actual response values of the initial sample points by using a dot matrix antenna window load-transmission integrated simulation analysis method, and to construct a dot matrix antenna window load-transmission surrogate optimization model by using a Kriging surrogate model; The calculation module is configured to solve the dot matrix antenna window load-transmission surrogate optimization model in S2 by using a particle swarm optimization algorithm, and to obtain an optimal solution of the surrogate optimization model; The output module is configured to calculate an actual response of the optimal solution of the surrogate optimization model and to determine whether the actual response converges, if the actual response does not converge, to add new sample points to a sample set by using a hybrid point addition criterion, and to repeat iteration, and if the actual response converges, to output an optimal design scheme.

7. A terminal device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The memory stores a computer program capable of running on the processor, and when the processor loads and executes the computer program, the load-transmission integrated optimization design method for the dot matrix antenna window is used.

8. A storage medium containing computer-executable instructions, characterized in that, The computer executable instructions are used to execute the load-transmission integrated optimization design method for the dot matrix antenna window when executed by the computer processor.

9. A computer program product, characterised in that, The computer program product includes a computer program, and when the computer program is executed by the processor, the load-transmission integrated optimization design method for the dot matrix antenna window is loaded and executed.

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