Method for efficiently optimizing variable-elongation inflatable wing structure based on pneumatic structure thermal coupling

Abstract

The invention discloses a method for efficiently optimizing a variable-elongation inflatable wing structure based on thermal coupling of a pneumatic structure. The method comprises the following steps: step 1, parameterization; step 2, sampling; thirdly, for the first set of working conditions, variable-elongation inflatable wing structure parameters in the first set of working conditions are used as design variables, and for other working conditions, an improved KTS method is used for processing; 4, establishing a geometric model, and performing simulation analysis; 5, calculating a target function; step 6, constructing an agent model; and 7, comparing a simulation result with an optimization algorithm predicted value, judging whether an expectation is reached, if so, ending, and otherwise, returning to the step 3 to continue iteration. The method has the advantages that the KTS method is improved, the optimal point is corrected, the evaluation frequency is reduced, and the solving efficiency is improved; the cross-domain flight performance of the inflatable wing is accurately analyzed; efficient optimization of the variable-span inflatable wing structure is achieved; and an efficient numerical method and an agent model are developed, so that the calculation cost of a high-precision model in an optimization process is reduced.

Description

Technical Field

[0001] The present invention relates to a method for efficiently optimizing the structure of a variable-span inflatable wing based on aerodynamic-structure-thermal coupling, and belongs to the technical field of aircraft technology. Background Art

[0002] The inflatable wing is a widely used aerospace structure with characteristics such as deployability and light weight. This flexible membrane structure is usually used within a limited height range to avoid potential risks. Specifically, due to its limited load-bearing capacity, a high aspect ratio inflatable wing may experience structural instability during a low-altitude descent. On the other hand, a low aspect ratio wing faces the challenge of providing sufficient lift at high altitudes. Therefore, it is particularly important to improve the flight performance of the inflatable wing under extreme conditions. Variable-span design is considered to have potential in expanding the flight altitude range of inflatable wing aircraft, and some related studies have demonstrated the effectiveness of this technology. To achieve cross-domain flight between different altitudes, the concept of a variable-span inflatable winged aircraft has been proposed, and a swept-back baffle structure is used to improve its overall performance. However, in the proposed concept, some unconventional design variables need to be considered, such as the aspect ratio and sweep angle of the baffle, which will result in higher optimization costs. Considering the potentially fatal impacts of aerodynamic loads, internal pressure loads, and thermal loads on flight efficiency and safety, it is necessary to develop an optimization framework to effectively solve the optimal solutions of the inflatable wing under different flight environments. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for efficiently optimizing the structure of a variable-span inflatable wing based on aerodynamic-structure-thermal coupling, a multidisciplinary comprehensive optimization framework considering aerodynamic and structural characteristics, so as to achieve efficient optimization of the variable-span inflatable wing structure; develop efficient numerical methods and surrogate models to reduce the computational cost of high-precision models during the optimization process.

[0004] The present invention is achieved through the following solutions: A method for efficiently optimizing the structure of a variable-span inflatable wing based on aerodynamic-structure-thermal coupling, comprising the following steps:

[0005] Step 1: Parametrize the variable-span inflatable wing structure;

[0006] Step 2: Sample within the design region of the variable-span inflatable wing structure parameters to generate an initial sample set;

[0007] Step 3: For the sample set obtained for the first group of working conditions, directly use the variable-span inflatable wing structure parameters therein as design variables. For the sample sets obtained for other working conditions, use the improved KTS method for processing to obtain a refined sample set;

[0008] Step 4: Based on the initial sample set and the refined sample set, establish a geometric model of the variable-span inflatable wing structure, and transfer it to the corresponding analysis module to perform a simulation analysis on the performance of the variable-span inflatable wing during cross-domain flight;

[0009] Step 5: Calculate the objective function response and the constraint response according to the simulation analysis results;

[0010] Step 6: Construct a surrogate model, use a global optimization algorithm to optimize the constructed surrogate model, and obtain the optimal structural parameters of the variable-span inflatable wing;

[0011] Step 7: Compare the simulation results with the predicted values of the optimization algorithm to determine whether the desired residual level is reached. If so, end. Otherwise, add this sample point to the sample set and return to Step 3 to continue the iteration until the convergence accuracy is satisfied, and obtain the optimal variable-span inflatable wing structure.

[0012] A method for efficiently optimizing the variable-span inflatable wing structure based on aerodynamic-structural-thermal coupling includes the following steps:

[0013] Step 1: Parametrize the variable-span inflatable wing structure, determine that the main design variables are the sweep angle θ and the span length l of the baffle, and the positive angle of attack i specified to obtain sufficient lift. To meet the load-bearing requirements, the internal pressure p and the film thicknesses t1, t2, and t3 need to be considered;

[0014] Step 2: Use the maximum Latin hypercube design method to sample within the design region of the variable-span inflatable wing structure parameters to generate an initial sample set;

[0015] Step 3: For the sample set obtained from the first set of working conditions, directly use the variable-span inflatable wing structure parameters therein as design variables. For the sample sets obtained from other working conditions, use the improved KTS method for processing to obtain a refined sample set;

[0016] Step 4: Based on the initial sample set and the refined sample set, establish a geometric model of the variable-span inflatable wing structure, and transfer it to the corresponding analysis module to perform a simulation analysis on the performance of the variable-span inflatable wing during cross-domain flight, where the calculation and application of aerodynamic and thermal loads are prioritized and integrated into the structural model;

[0017] Step 5: Through simulation analysis, obtain and record the lift L and the lift-to-drag ratio K obtained from the aerodynamic characteristic analysis, as well as the structural mass m, the maximum stress σ1, and the wrinkled area ratio RW obtained from the structural characteristic analysis, and calculate the objective function response and the constraint response;

[0018] Step 6: Taking the achievement of a balanced lift-to-drag ratio K and the minimum structural mass m while ensuring sufficient lift and structural stability as the optimization goal, use a global optimization algorithm to optimize the constructed surrogate model, and use a surrogate-assisted differential evolution algorithm for further optimization and refinement to obtain the optimal structural parameters of the variable-span inflatable wing;

[0019] Step 7: Simulate the optimization results obtained in Step 6, and compare the obtained objective function results with the predicted values using the surrogate model and the optimization algorithm to determine whether the desired residual level is achieved. If so, end the process; otherwise, add this sample point to the sample set and return to Step 3 for continued iteration until the convergence accuracy is met to obtain the optimal variable-span inflatable wing structure.

[0020] The simulation analysis in Step 4 includes aerodynamic characteristic analysis, thermal effect analysis, and structural characteristic analysis.

[0021] The aerodynamic characteristic analysis is to analyze the aerodynamic characteristics of the variable-span inflatable wing structure by establishing an aerodynamic model, and establish a three-dimensional incompressible Navier-Stokes equation based on continuity and momentum conservation. This equation is expressed as:

[0022]

[0023] where ρ is the fluid density, u, v, and w are the velocity components in the X, Y, and Z directions respectively, p is the pressure, and τ ij is the shear stress. Integrate the control equation into each element to derive the discretized equation, and then solve each term in the equation using the corresponding interpolation function.

[0024] The thermal effect analysis is to analyze the thermal effect of the variable-span inflatable wing by establishing a thermal model of the inflatable wing. The influence of the thermal environment on the flight performance of the inflatable wing can be divided into two main aspects: the heating of the membrane structure and the heating of the internal gas. The thermal balance of the inflatable wing is achieved through the balance of the external environment and the internal environment, including convective heat transfer, external thermal radiation, convection between the skin and the internal gas, and infrared radiation of the skin. The solar radiant energy Q sunc obtained by the inflatable wing can be expressed as:

[0025] Q sunc =α e τS sin H (2)

[0026] In the formula, α e is the absorption coefficient of the membrane material, τ is the atmospheric transmittance, S is the solar constant, whose value is 1367 W / m2, and H is the solar declination angle;

[0027] The solar diffuse heat flux Q se can be expressed as:

[0028]

[0029] S se is the diffuse sky radiation intensity, and θ me is the angle between the film unit and the horizontal plane.

[0030] The absorbed and reflected radiant heat flux Q ge can be expressed as:

[0031]

[0032] S g is the intensity of the ground radiation;

[0033] The atmospheric infrared radiant heat flux Q es and the ground infrared radiant heat flux Q eg can be expressed as:

[0034]

[0035] Q eg = ε e σΔT eg 4 φ eg (6)

[0036] ε e is the emissivity, σ is the Boltzmann constant, and ΔT es is the temperature difference between the skin and the atmosphere, and φ es is the radiation angle factor between the skin and the atmosphere, and ΔT eg is the temperature difference between the skin and the ground, and φ eg is the radiation angle factor between the skin and the ground;

[0037] The external convective heat flux convolution Q convout can be expressed as:

[0038] Q convout = h e (T e - T s ) (7)

[0039] h e is the convective coefficient, T e is the temperature of the film material, and T s is the atmospheric temperature;

[0040] For a single film element, the heat balance can be expressed as:

[0041]

[0042] m e is the mass of the film element, and ce is the specific heat capacity of the membrane material, and Q convout is the convective heat flux.

[0043] The finite volume method is used to solve the thermal effect of the inflatable wing by using a CFD solver. Its definition is the same as that in Equation (1), and the implementation of the mixed boundary condition is applied to the inflatable wing with variable span. In order to establish the boundary conditions of the heat transfer coefficient and the external radiation temperature, a user-defined function (UDF) program is created and compiled into the CFD solver. This program facilitates the accurate description of the complex heat transfer phenomenon occurring on the surface of the inflatable wing. This includes the interaction of convective and radiative heat transfer with the surrounding environment. The internal flow field of the inflatable wing with variable span is solved by the above method to determine the overall temperature distribution and the average temperature in the flow field. For the heating of the internal gas, according to the ideal gas law:

[0044]

[0045] where V is the volume, T is the temperature, the subscript wa represents the inflatable wing with variable span in the air considering the influence of the thermal environment, and wg represents the inflatable wing with variable span on the ground;

[0046] For a fully inflated inflatable wing, the volume change caused by the pressure change within a certain range can be ignored:

[0047]

[0048] The preset ground pressure p wg and the actual pressure p of the inflatable wing wa are related as follows:

[0049]

[0050] The method for the above-mentioned structural characteristic analysis is as follows: When exposed to excessive aerodynamic loads, the inflatable wing is prone to a unique type of failure, namely buckling. According to the membrane hypothesis, the stress of the membrane element consists of the spanwise stress, the circumferential stress, and the shear stress structure. The spanwise stress σ Y and the circumferential stress σ H can be expressed as:

[0051]

[0052]

[0053] is the internal pressure generated by the axial tensile stress, is the bending moment generated by the pressure, p i is the inflation pressure, A is the envelope area, A walls is the cross-sectional area of the membrane wing profile, M X and MZ The bending moments of the cross-section act about the X-axis and Z-axis respectively, I XX and I ZZ The moments of inertia of the cross-section about the X-axis and Z-axis, where x and z are the coordinate values of the membrane element in the cross-section coordinate system, and t m is the membrane thickness.

[0054] When there is no wrinkling in the wing cross-section, the stress remains continuously linearly distributed along the span in the z-axis direction. The tensile stress distribution of the non-wrinkled cross-section is expressed as:

[0055]

[0056] When local wrinkling occurs in the cross-section, the load-bearing capacity of the wrinkled area decreases. Assuming a linear distribution from the maximum stress to the minimum stress, the wrinkled cross-section distribution is expressed as:

[0057]

[0058] where t d is the thickness ratio, σ max is the maximum stress, z0 is the minimum z-coordinate of the wrinkled area, and σ Y The distribution of the type of load satisfies axial force balance and moment balance:

[0059]

[0060] The principal stresses of the membrane element are:

[0061]

[0062] where σ1 is the maximum principal stress of the membrane element and σ2 is the minimum principal stress of the membrane element;

[0063] Criterion for wrinkling of the membrane element:

[0064]

[0065] On this premise, a factor F w is established to determine whether wrinkling exists in the component. When F w = -1, the component wrinkles:

[0066]

[0067] The inflatable wing structure is divided into skin, baffle, and wing tip. The calculation of the aerodynamic load is completed by a CFD solver, and the conservative streamline preservation method is used to transfer the load to the skin and tip. The thermal load determined by the thermodynamic principle is distributed throughout the inflatable wing structure, fixed at the root, and the high-pressure gas is simulated by applying a uniform pressure to the skin and tip.

[0068] In the improved KTS method in Step 3, the correlation between design parameters and performance is considered. To improve the coverage effect of samples on the region where the potential optimal solution lies, the correction step of the optimal point is integrated into KTS. This process includes two basic stages: reuse of the optimal solution and calibration of the modified inferior points:

[0069] In the process of optimal solution reuse, first, the optimal solution of the source optimization task is and the initial sample point X ini are normalized to [0, 1]. Then, the normalized best source solution is calculated and the Euclidean distance d between each normalized initial sample i . Finally, the initial sample point with the smallest d i is replaced by the normalized best source solution as shown in Equation (21):

[0070]

[0071]

[0072] The sample points of the source optimization task are normalized to [0, 1], and the normalized are sorted according to the feasibility rules. Then, based on the N in the source task e best sample points, the size of the superior source sample points , i.e., N e , is obtained from the following formula:

[0073]

[0074] Finally, the points in the source task are divided into two categories, as shown in Equation (23):

[0075]

[0076] where is 's classification index, is the classification index set, and the binary LS - SVM classifier uses and 's input for training to embed prior optimization knowledge. It predicts the classification index of the initial sample points and divides the points into superior and inferior initial samples according to the prediction index.

[0077] For specific problems where the distribution of the optimal value is more significantly correlated, it is desired that the samples cluster into the region of interest in the same trend. Therefore, before reuse and calibration, all samples are modified according to the following steps:

[0078] Step 1: Record the source optimal solution Determine the target region of interest And its centroid D0. For an inflatable wing, the centroid D0 contains two variables: span length l and internal pressure p. Assuming that the lift coefficient of the inflatable wing remains constant with height, the span length l at the centroid can be obtained from Equation (24):

[0079]

[0080] According to previous research, the boundary of l can be determined within ±20%:

[0081] l ∈ [0.8l0, 1.2l0] (25) For the internal pressure P required for a given bending moment M, the equation is expressed as:

[0082]

[0083] In the formula, M is the bending moment, and r is the cross-sectional radius of the inflatable structure

[0084] Assuming that the lift is uniformly distributed along the span, the corresponding span length after the change of P with the airspace is:

[0085]

[0086] The boundary of P is determined by Equation (28):

[0087] p ∈ [0.8p0, 1.2p0] (28) [[ID=3〕

[0088] Step 2: Rotation: For the sample point X, the corresponding sphering X (Spher) Is expressed as:

[0089]

[0090]

[0091] e i Is the unit vector pointing from o to x i And Is the distance from the rotation center along e i To the boundary of the design domain. ub and lb are the upper and lower limits respectively, and o is the rotation center, which is a point on the perpendicular bisector of the line connecting the centroid D0 and It can be customized according to the specific nature of the problem

[0092] The transformation matrix T is derived from Equation (31):

[0093]

[0094] The rotated sample X (Rot) Can be expressed as:

[0095] X (Rot) = TX (Spher) (32)

[0096] Perform the reverse operation and project the sample points into the original design domain.

[0097] The new distribution of the design variable X[[ID=1②]] (Regression) :

[0098]

[0099]

[0100] The optimal solution of the regression source is reused, and after regression, D0 coincides with ;

[0101] Step 3. Reallocate high-quality samples and reallocate the high-quality samples to as follows:

[0102]

[0103]

[0104] x j is the optimal sample in x ini , is the unit vector from pointing to , is the distance from along the direction to the boundary, is the distance from through x j to the modified sample X of the boundary of the rotated LS-SVM classifier (T1)′ is expressed as:

[0105]

[0106] According to the modified sample, normalize X (T1)′ to In the KTS method, sample reuse and calibration are performed. If it is considered inferior, it is calibrated using equations (23) and (38). The LS-SVM classifier is used to retain high-quality samples and improve inferior samples.

[0107]

[0108] where α is the correction factor, is the point closest to in ,

[0109] After the optimal solution reuse and inferior point calibration procedures, the optimized initial sample points are mapped into the design space:

[0110]

[0111] The beneficial effects of the present invention are as follows:

[0112] 1. The present invention improves the KTS method and corrects the optimal points, solving the problem of low correlation between the source condition and the target condition in the design of variable-span inflatable wings. This strategy aims to increase the spatial coverage density of the potential feasible region while maintaining the overall distribution pattern of the samples, helping to reduce the number of evaluations of expensive functions in the inflatable wing design, thereby improving the solution efficiency;

[0113] 2. Based on the parametric modeling method proposed in the developed optimization framework of the present invention, a CFD-based aerodynamic model, a precision thermal model based on the UDF program, and a finite element structural model considering the wrinkling area are integrated. Through the iterative call and integration of sub-disciplinary solvers, the performance of the inflatable wing during cross-domain flight can be accurately analyzed;

[0114] 3. The present invention considers a multi-disciplinary comprehensive optimization framework for aerodynamic and structural characteristics to achieve efficient optimization of the variable-span inflatable wing structure; develops efficient numerical methods and surrogate models to reduce the computational cost of high-precision models in the optimization process and improve the convergence speed. Description of the Drawings

[0115] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0116] Figure 2 It is a schematic flow diagram of the optimal point correction in the improved KTS method of the present invention;

[0117] Figure 3 It is a schematic diagram of the aerodynamic model of the inflatable wing in the embodiment of the present invention;

[0118] Figure 4 It is a schematic diagram of the thermal model of the inflatable wing in the embodiment of the present invention;

[0119] Figure 5 It is a schematic diagram of the structural model of the inflatable wing in the embodiment of the present invention. Detailed Embodiment

[0120] The following further describes the present invention in conjunction with Figures 1-5 However, the protection scope of the present invention is not limited to the above content.

[0121] For clarity, not all features of the actual embodiments are described. In the following description, well-known functions and structures are not described in detail because they would obscure the present invention with unnecessary details. It should be considered that in the development of any actual embodiment, numerous implementation details must be made to achieve the specific goals of the developer, such as changing from one embodiment to another according to the relevant system or business constraints. Additionally, it should be considered that such development work may be complex and time-consuming, but it is only routine work for those skilled in the art.

[0122] A method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling includes the following steps:

[0123] Step 1: Parametrize the variable-span inflatable wing structure, and determine that the main design variables are the sweep angle θ and the span length l of the baffle, and the positive angle of attack i specified to obtain sufficient lift. To meet the load-bearing requirements, the internal pressure p and the film thicknesses t1, t2, and t3 need to be considered.

[0124] Step 2: Use the maximum Latin hypercube design method to sample within the design region of the variable-span inflatable wing structure parameters to generate an initial sample set.

[0125] Step 3: For the sample set obtained from the first group of working conditions, directly use the variable-span inflatable wing structure parameters therein as design variables. For the sample sets obtained from other working conditions, use the improved KTS method for processing to obtain a refined sample set.

[0126] Step 4: According to the initial sample set and the refined sample set, establish a geometric model of the variable-span inflatable wing structure, and transfer it to the corresponding analysis module to perform a simulation analysis on the performance of the variable-span inflatable wing during cross-domain flight, where the calculation and application of aerodynamic and thermal loads are prioritized and integrated into the structural model.

[0127] Step 5: Through the simulation analysis, obtain and record the lift L and the lift-to-drag ratio K obtained from the aerodynamic characteristic analysis, as well as the structural mass m, the maximum stress σ1, and the wrinkled area ratio RW obtained from the structural characteristic analysis, and calculate the objective function response and the constraint response.

[0128] Step 6: Taking the realization of a balanced lift-to-drag ratio K and the minimum structural mass m under the premise of ensuring sufficient lift and structural stability as the optimization goal, use a global optimization algorithm to optimize the constructed surrogate model, and use a surrogate-assisted differential evolution algorithm for further optimization and refinement to obtain the optimal structural parameters of the variable-span inflatable wing.

[0129] Step 7: Simulate the optimization results obtained in Step 6, compare the obtained objective function results with the predicted values using the surrogate model and the optimization algorithm, and determine whether the desired residual level is achieved. If so, end the process; otherwise, add this sample point to the sample set and return to Step 3 to continue the iteration until the convergence accuracy is met, and obtain the optimal variable-span inflatable wing structure.

[0130] The simulation analysis in Step 4 includes aerodynamic characteristic analysis, thermal effect analysis, and structural characteristic analysis.

[0131] The aerodynamic characteristic analysis is to perform aerodynamic characteristic analysis on the variable-span inflatable wing structure by establishing an aerodynamic model, and establish the three-dimensional incompressible Navier-Stokes equations based on continuity and momentum conservation. The equation is expressed as:

[0132]

[0133] where ρ is the fluid density, u, v, and w are the velocity components in the X, Y, and Z directions respectively, p is the pressure, and τ ij is the shear stress. Integrate the control equation into each element to derive the discretized equation, and then solve each term in the equation using the corresponding interpolation function.

[0134] The thermal effect analysis is to perform thermal effect analysis on the variable-span inflatable wing by establishing a thermal model of the inflatable wing. The influence of the thermal environment on the flight performance of the inflatable wing can be divided into two main aspects: the heating of the membrane structure and the heating of the internal gas. The thermal balance of the inflatable wing is achieved through the balance of the external environment and the internal environment, including convective heat transfer, external thermal radiation, convection between the skin and the internal gas, and infrared radiation of the skin. The solar radiation energy Q obtained by the inflatable wing sunc can be expressed as:

[0135] Q sunc = α e τS sin H (2)

[0136] In the formula, α e is the absorption coefficient of the membrane material, τ is the atmospheric transmittance, S is the solar constant, whose value is 1367 W / m2, and H is the solar declination angle;

[0137] The solar diffuse heat flux Q se can be expressed as:

[0138]

[0139] S se is the diffuse sky radiation intensity, and θ me is the angle between the membrane unit and the horizontal plane,

[0140] The absorbed and reflected radiant heat flux Qge It can be expressed as:

[0141]

[0142] S g is the intensity of ground radiation;

[0143] The atmospheric infrared radiation heat flux Q es and the ground infrared radiation heat flux Q eg can be expressed as:

[0144]

[0145] Q eg = ε e σΔT eg 4 φ eg (6)

[0146] ε e is the emissivity, σ is the Boltzmann constant, ΔT es is the temperature difference between the skin and the atmosphere, φ es is the radiation angle factor between the skin and the atmosphere, ΔT eg is the temperature difference between the skin and the ground, φ eg is the radiation angle factor between the skin and the ground;

[0147] The outer convection heat flux convolution Q convout can be expressed as:

[0148] Q convout = h e (T e - T s ) (7)

[0149] h e is the convection coefficient, T e is the membrane material temperature, T s is the atmospheric temperature;

[0150] For a single membrane element, the heat balance can be expressed as:

[0151]

[0152] m e is the membrane element mass, c e is the specific heat capacity of the membrane material, Q convout is the convection heat flux.

[0153] The thermal effect of the inflatable wing is solved by using the finite volume method with a CFD solver, which has the same definition as Equation (1), and the implementation of the mixed boundary condition is applied to the variable-span inflatable wing. To establish the boundary conditions for the heat transfer coefficient and the external radiation temperature, a user-defined function (UDF) program is created and compiled into the CFD solver. This program facilitates the accurate description of the complex heat transfer phenomena occurring on the surface of the inflatable wing. This includes the interaction of convective and radiative heat transfer with the surrounding environment. The internal flow field of the variable-span inflatable wing is solved using the above method to determine the overall temperature distribution. And the average temperature in the flow field. For the heating of the internal gas, according to the ideal gas law:

[0154]

[0155] Where V is the volume, T is the temperature, and the subscript wa represents the variable-span inflatable wing in the air considering the influence of the thermal environment, and wg represents the variable-span inflatable wing on the ground.

[0156] For a fully inflated inflatable wing, the volume change caused by the pressure change within a certain range can be ignored:

[0157]

[0158] The preset ground pressure p wg And the actual pressure p of the inflatable wing wa The relationship can be expressed as:

[0159]

[0160] The method for the above-mentioned structural characteristic analysis is as follows: When exposed to excessive aerodynamic loads, the inflatable wing is prone to a unique type of failure, namely buckling. According to the membrane hypothesis, the stress of the membrane element consists of the spanwise stress, circumferential stress, and shear stress structures. The spanwise stress σ Y And the circumferential stress σ H Can be expressed as:

[0161]

[0162]

[0163] Is the internal pressure generated by the axial tensile stress, Is the bending moment generated by the pressure, p i Is the inflation pressure, A is the envelope area, A walls Is the cross-sectional area of the membrane wing profile, M X And M Z The bending moments of the cross-sections are about the X-axis and Z-axis respectively, I XX And I ZZThe moments of inertia of the cross-section about the X and Z axes, where x and z are the coordinate values of the film element in the cross-sectional coordinate system, and t m is the film thickness.

[0164] When there is no wrinkling in the wing cross-section, the stress remains continuously linearly distributed along the span in the z-axis direction. The tensile stress distribution of the non-wrinkled cross-section is expressed as:

[0165]

[0166] When local wrinkling occurs in the cross-section, the load-bearing capacity of the wrinkled area decreases. Assuming a linear distribution from the maximum stress to the minimum stress, the distribution of the wrinkled cross-section is expressed as:

[0167]

[0168] where t d is the thickness ratio, σ max is the maximum stress, z0 is the minimum z coordinate of the wrinkled area, and σ Y The distribution of the type of load satisfies axial force balance and moment balance:

[0169] pA = ∮ s σ Y tds (16)

[0170] The principal stresses of the film element are:

[0171]

[0172] where σ1 is the maximum principal stress of the film element and σ2 is the minimum principal stress of the film element;

[0173] Criterion for wrinkling of the film element:

[0174]

[0175] On this premise, a factor F w is established to determine whether there is wrinkling in the component. When F w = -1, the component wrinkles:

[0176]

[0177] The inflatable wing structure is divided into skin, baffle, and wing tip. The calculation of the aerodynamic load is completed by a CFD solver, and a conservative streamline preservation method is used to transfer the load to the skin and the tip. The thermal load determined by the thermodynamics principle is distributed throughout the inflatable wing structure, fixed at the root, and high-pressure gas is simulated by a uniform pressure on the skin and the tip.

[0178] In the improved KTS method in step three, the correlation between design parameters and performance is considered. To improve the coverage effect of samples on the region where the potential optimal solution lies, the correction step of the optimal point is integrated into KTS. This process includes two basic stages: reuse of the optimal solution and calibration of the modified inferior points:

[0179] In the process of optimal solution reuse, first, the optimal solution of the source optimization task is and the initial sample point X ini are normalized to [0, 1]. Then, the normalized best source solution is calculated and the Euclidean distance d between each normalized initial sample i . Finally, the initial sample point with the smallest d i is replaced with the normalized best source solution as shown in Equation (21):

[0180]

[0181]

[0182] The sample points of the source optimization task are normalized to [0, 1], and the normalized are sorted according to the feasibility rules. Then, based on the N in the source task e best sample points, the size of the superior source sample points , i.e., N e , is obtained from the following formula:

[0183]

[0184] Finally, the points in the source task are divided into two categories, as shown in Equation (23):

[0185]

[0186] where is 's classification index, is the classification index set, and the binary LS - SVM classifier uses and 's input for training to embed prior optimization knowledge. It predicts the classification index of the initial sample points and divides the points into superior and inferior initial samples according to the prediction index.

[0187] For specific problems where the distribution of the optimal value is more significantly correlated, it is desired that the samples cluster in the region of interest in the same trend. Therefore, before reuse and calibration, all samples are modified according to the following steps:

[0188] Step 1: Record the source optimal solution Determine the target region of interest And its centroid D0. For an inflatable wing, the centroid D0 contains two variables: span length l and internal pressure p. Assuming that the lift coefficient of the inflatable wing remains constant with altitude, the span length l at the centroid can be obtained from Equation (24):

[0189]

[0190] According to previous research, the boundary of l can be determined within ±20%:

[0191] l ∈ [0.8l0, 1.2l0] (25)

[0192] The internal pressure P required for a given bending moment M is expressed by the equation:

[0193]

[0194] In the formula, M is the bending moment and r is the cross-sectional radius of the inflatable structure

[0195] Assuming that the lift is uniformly distributed along the span, the corresponding span length for the changed P value in the airspace is:

[0196]

[0197] The boundary of P is determined by Equation (28):

[0198] p ∈ [0.8p0, 1.2p0] (28)

[0199] Step 2: Rotation: For the sample point X, the corresponding sphering X (Spher) Is expressed as:

[0200]

[0201]

[0202] e i Is the unit vector pointing from o to x i Of Is the distance from the rotation center along e i To the boundary of the design domain. ub and lb are the upper and lower limits respectively, and o is the rotation center, which is a point on the perpendicular bisector of the line connecting the centroid D0 and And can be customized according to the specific nature of the problem

[0203] The transformation matrix T is derived from Equation (31):

[0204]

[0205] The rotated sample X(Rot) Can be expressed as:

[0206] X (Rot) = TX (Spher) (32)

[0207] Perform the reverse operation and project the sample points into the original design domain.

[0208] The new distribution X of the design variables (Regression) :

[0209]

[0210]

[0211] Regression source optimal solution Is reused, and after regression, D0 coincides with Coincide;

[0212] Step 3. Reallocate high-quality samples and reallocate the high-quality samples to As follows:

[0213]

[0214]

[0215] x j Is the optimal sample in x ini Among them, Is from Pointing to Unit vector of Is from Along Direction to Distance to the boundary, Is from Passing through x j To the distance from the modified sample X to the boundary of the rotated LS-SVM classifier (T1)′ Is expressed as:

[0216]

[0217] According to the modified sample, X (T1)′ Is normalized to In the KTS method, the reuse and calibration of samples are carried out. If it is considered inferior, it is calibrated using formulas (23) and (38). The LS-SVM classifier is used to retain high-quality samples and improve inferior samples.

[0218]

[0219] Where α is the correction factor, Is the closest to In terms of points,

[0220] After the optimal solution reuse and inferior point calibration procedures, the optimized initial sample points are mapped into the design space:

[0221]

[0222] Example: Based on the method flow of the present invention disclosed as shown in Figure 1 and the relationship between the optimization objective and design variables in the embodiment, a basic optimization process as shown in Figure 2 is constructed. The specific implementation steps are as follows:

[0223] Step 1: Parametrize the variable-span inflatable wing structure. The main design variables are the sweep angle θ and the span length l of the baffle. The value range of the sweep angle θ is [3, 90] and [-90, -3]; the aspect ratio of the inflatable wing is restricted within the range of [1.5, 3], and the value range of the span length l is determined accordingly. In addition, a positive installation angle i is specified to obtain sufficient lift, and its value range is [0, 20]. To meet the load-bearing requirements, the value range of the internal pressure p to be considered is [5, 2000] kPa, and the value ranges of the film thicknesses t1, t2, and t3 are set to [0.1, 1] mm.

[0224] Step 2: For the control parameters θ, l, i, p, t1, t2, t3 of the variable-span inflatable wing structure considering the aerodynamic-structure-thermal coupling, uniform sampling is performed using the maximum Latin hypercube design within the design range, and it is determined that the swept baffle inflatable wing at an altitude of 8 km is working condition 1, and the swept baffle inflatable wing at an altitude of 4 km is working condition 2.

[0225] Step 3: For the sample set generated for working condition 1, directly use the inflatable wing structure parameters in it as design variables. For the sample points generated for working condition 2, use the improved KTS for processing to obtain a refined sample set, and use the inflatable wing structure parameters in the obtained sample set as design variables. With the goal of achieving a balanced lift-to-drag ratio and minimum structural mass while ensuring sufficient lift and structural stability, the objective function QM is jointly constructed, and a surrogate model is built. Among them, the formula of QM is as shown in the formula:

[0226] find x = [x1, x2, x3, x4, x5, x6, x7] = [θ, l, i, p, t1, t2, t3]

[0227]

[0228] w.r.t x l ≤x≤x u

[0229] s.t.(1) Δσ≥0

[0230]

[0231] (3) ΔL ≥ 0

[0232] Step 4: Based on the parameters obtained in Step 2, establish the geometric model of the inflatable wing structure and use the CFD solver to conduct corresponding simulation analyses of aerodynamic characteristics, thermal effects, and structural characteristics; for the settings of aerodynamic characteristics analysis, generate anisotropic triangular meshes in the boundary layer near the wall and isotropic hybrid meshes in the entire flow field, and adopt the minimum near-surface mesh spacing y+ = 1 to capture high-resolution information of the boundary layer. The chord length of the ideal airfoil is set to 500 mm, while the chord length of the chord-length inflatable airfoil is approximately 460 mm. There are approximately 1.2 million meshes in the entire flow field. By defining symmetric boundary conditions, the span is halved. The wing surface is set as a non-slip boundary. The inlet velocity is set to 100 km / h, and the outlet gauge pressure is set to 0. The k-ω SST 2-equation turbulence model is used to solve the Reynolds-averaged Navier-Stokes (RANS) equations to calculate the aerodynamic characteristics of the inflatable wing. The atmospheric parameters are shown in Table 1:

[0233] Table 1 Atmospheric Parameters

[0234]

[0235]

[0236] Use the CFD solver to solve the thermal effects of the inflatable wing by the finite volume method, and apply the implementation of the mixed boundary conditions to the inflatable wing. Create a user-defined function (UDF) program and compile it into the CFD solver to establish the boundary conditions of the heat transfer coefficient and the external radiation temperature.

[0237] Analyze the mechanical structural performance of the inflatable wing by the finite element method. Model the structure using unstructured Shell41 elements, and the material parameters are shown in Table 2:

[0238] Table 2 Material Parameters

[0239]

[0240] Step 5: Obtain and record the lift L and lift-to-drag ratio K obtained from each aerodynamic characteristics analysis, as well as the mass m, maximum stress σ1, and wrinkled area ratio RW obtained from the structural characteristics analysis, and calculate the response of the objective function and the constraint response based on the data obtained each time.

[0241] Step 6: With the goal of achieving a balanced lift-to-drag ratio K and minimizing the structural mass m while ensuring sufficient lift and structural stability, use a global optimization algorithm to optimize the constructed surrogate model, and use a surrogate-assisted differential evolution algorithm for further optimization and refinement to obtain the optimal structural parameters and objective function of the inflatable wing.

[0242] Step 7: Simulate the optimization results obtained in Step 6, and compare the calculated objective function results with the predicted values using the surrogate model and the optimization algorithm to determine whether the desired residual level is achieved. If so, stop; otherwise, add this sample point to the sample set and return to Step 3 to continue the iteration until the convergence accuracy is met, and obtain the optimal inflatable wing structure corresponding to the two working conditions of 8 km high altitude and 4 km low altitude for the swept baffle type.

[0243] Based on the above ideas, using the improved KTS method, Kriging surrogate model and global search optimization algorithm, the global optimal solution of the inflatable wing structure parameters is obtained through multiple iterative solutions. The results of the optimization process are shown in Table 3. The results show that the improved KTS shows favorable effects in terms of improving efficiency and global search ability. In the case of using the improved KTS method, Working Condition 2 shows a significant efficiency level, confirming the efficiency advantage of using the improved KTS method to optimize the inflatable wing structure.

[0244] Table 3 Optimization Results

[0245]

[0246] Although the technical solutions of the present invention have been described and listed in detail, it should be understood that for those skilled in the art, making modifications to the above embodiments or adopting equivalent alternative solutions are obvious to those skilled in the art. These modifications or improvements made without departing from the spirit of the present invention all fall within the scope of protection required by the present invention.

Claims

1. A method for efficiently optimizing the structure of an inflatable wing with variable wingspan based on aerodynamic-thermal coupling, characterized in that It includes the following steps: Step 1: Parametrize the variable-span inflatable wing structure; Step 2: Sample within the design region of the variable-span inflatable wing structure parameters to generate an initial sample set; Step 3: For the sample set obtained from the first group of working conditions, directly use the variable-span inflatable wing structure parameters therein as design variables. For the sample sets obtained from other working conditions, use the improved KTS method for processing to obtain a refined sample set; Step 4: Based on the initial sample set and the refined sample set, establish a geometric model of the variable-span inflatable wing structure and transfer it to the corresponding analysis module to perform a simulation analysis on the performance of the variable-span inflatable wing during cross-domain flight; Step 5: Calculate the objective function response and the constraint response according to the simulation analysis results; Step 6: Construct a surrogate model, use a global optimization algorithm to optimize the constructed surrogate model, and obtain the optimal structure parameters of the variable-span inflatable wing; Step 7: Compare the simulation results with the predicted values of the optimization algorithm to determine whether the desired residual level is reached. If so, end. Otherwise, add this sample point to the sample set and return to Step 3 to continue the iteration until the convergence accuracy is met to obtain the optimal variable-span inflatable wing structure.

2. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 1, wherein It includes the following steps: Step 1: Parametrize the variable-span inflatable wing structure, and determine that the main design variables are the sweep angle θ and the span length l of the baffle, as well as the positive installation angle i specified to obtain sufficient lift; Step 2: Adopt the maximum Latin hypercube design method to sample within the design region of the variable-span inflatable wing structure parameters to generate an initial sample set; Step 3: For the sample set obtained from the first group of working conditions, directly use the variable-span inflatable wing structure parameters therein as design variables. For the sample sets obtained from other working conditions, use the improved KTS method for processing to obtain a refined sample set; Step 4: Based on the initial sample set and the refined sample set, establish a geometric model of the variable-span inflatable wing structure and transfer it to the corresponding analysis module to perform a simulation analysis on the performance of the variable-span inflatable wing during cross-domain flight; Step 5: Through simulation analysis, obtain and record the lift L and the lift-to-drag ratio K obtained from the aerodynamic characteristic analysis, as well as the structural mass m, the maximum stress σ1, and the wrinkled area ratio RW obtained from the structural characteristic analysis, and calculate the objective function response and the constraint response; Step 6: Take the minimum lift-to-drag ratio K and structural mass m as the optimization objectives, use a global optimization algorithm to optimize the constructed surrogate model, and use the surrogate-assisted differential evolution algorithm for further optimization and refinement to obtain the optimal structure parameters of the variable-span inflatable wing; Step 7: Simulate the optimization results obtained in Step 6, and compare the obtained objective function results with the predicted values using the surrogate model and the optimization algorithm to determine whether the desired residual level is reached. If so, end. Otherwise, add this sample point to the sample set and return to Step 3 to continue the iteration until the convergence accuracy is met to obtain the optimal variable-span inflatable wing structure.

3. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 1, characterized in that The simulation analysis in Step 4 includes aerodynamic characteristic analysis, thermal effect analysis, and structural characteristic analysis.

4. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 3, wherein The aerodynamic characteristics analysis is to conduct an aerodynamic characteristics analysis on the variable-span inflatable wing structure by establishing an aerodynamic model, and establish a three-dimensional incompressible Navier-Stokes equation based on the conservation of continuity and momentum. This equation is expressed as: where ρ is the fluid density, u, v, and w are the velocity components in the X, Y, and Z directions respectively, p is the pressure, and τ ij is the shear stress.

5. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 3, wherein The thermal effect analysis of the variable-span inflatable wing is carried out by establishing a thermal model of the inflatable wing. The solar radiant energy Q obtained by the inflatable wing sunc can be expressed as: Q sunc = α e τS sin H (2) where α e is the absorption coefficient of the membrane material, τ is the atmospheric transmittance, and S is the solar constant with a value of 1367 W / m2 H is the solar day angle; Solar diffuse heat flux Q se can be expressed as: S se is the diffuse sky radiation intensity, θ me is the angle between the membrane unit and the horizontal plane, Absorbed and reflected radiant heat flux Q ge can be expressed as: S g is the intensity of ground radiation; Atmospheric infrared radiation heat flux Q es and ground infrared radiation heat flux Q eg can be expressed as: Q eg = ε e σΔT eg 4 φ eg (6) ε e is the emissivity, σ is the Boltzmann constant, ΔT es is the temperature difference between the skin and the atmosphere, φ es is the radiation view factor between the skin and the atmosphere, ΔT eg is the temperature difference between the skin and the ground, φ eg is the radiation view factor between the skin and the ground; External convective heat flux convolution Q convout Can be expressed as: Q convout = h e (T e - T s ) (7) h e is the convective coefficient, T e is the membrane material temperature, T s is the atmospheric temperature; For a single membrane element, the heat balance can be expressed as: m e is the mass of the membrane element, c e is the specific heat capacity of the membrane material, Q convout is the convective heat flux.

6. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 5, wherein The finite volume method is used to solve the internal flow field of the variable-span inflatable wing by using a CFD solver, so as to determine the overall temperature distribution and the average temperature in the flow field. For the heating of the internal gas, according to the ideal gas law: In the formula, V is the volume, T is the temperature, the subscript wa represents the variable-span inflatable wing in the air considering the influence of the thermal environment, and wg represents the variable-span inflatable wing on the ground; The preset ground pressure p wg and the actual pressure p of the inflatable wing wa are related as follows:

7. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 3, wherein The method for analyzing the structural characteristics is as follows: According to the membrane hypothesis, the stress of the membrane element consists of the spanwise stress, circumferential stress, and shear stress structures. The spanwise stress σ Y and the circumferential stress σ H can be expressed as: is the internal pressure generated by the axial tensile stress, is the bending moment generated by the pressure, p i is the inflation pressure, A is the envelope area, A walls is the cross-sectional area of the membrane wing profile, M X and M Z the bending moments of the cross-section about the X-axis and Z-axis respectively, I XX and I ZZ the moments of inertia of the cross-section about the X-axis and Z-axis, x and z are the coordinate values of the membrane element in the cross-sectional coordinate system, t m is the membrane thickness.

8. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 7, characterized in that When there is no wrinkling in the wing section, the stress remains continuously linearly distributed along the span in the z-axis direction. The tensile stress distribution of the non-wrinkling section is expressed as: When local wrinkling occurs in the section, the load-bearing capacity of the wrinkling area decreases. The distribution of the wrinkling section is expressed as: where t d is the thickness ratio, σ max is the maximum stress, z0 is the minimum z coordinate of the wrinkling region, and the distribution of the σ Y -type load satisfies the axial force balance and the moment balance: pA = ∮ s σ Y tds (16) The principal stress of the membrane element is: Among them, σ1 is the maximum principal stress of the membrane element, and σ2 is the minimum principal stress of the membrane element; The criterion for the membrane element to wrinkle: On this premise, establish factor F w to determine whether the component wrinkles. When F w = -1, the component wrinkles:

9. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 1, wherein The improved KTS method in step three integrates the correction step of the optimal point into KTS. This process includes two basic stages: the reuse of the optimal solution and the calibration of the modified inferior point: In the optimal solution reuse process, first, the optimal solution of the source optimization task is normalized to [0, 1] according to Equation (20). and the initial sample point X ini Then, the Euclidean distance d between the normalized best source solution and each normalized initial sample is calculated. Finally, the initial sample point with the minimum d i is replaced with the normalized best source solution i as shown in Equation (21): ​ Normalize the sample points of the source optimization task to [0, 1], and according to the feasibility rules, the normalized are sorted. Then, based on the source task Among the N e best sample points, construct the excellent source sample points The size of, that is, N e is obtained by the following formula: Finally, the points in the source task are divided into two categories, as shown in Equation (23): In the formula is classification index of is the classification index set. The binary LS-SVM classifier uses and as inputs for training, embedding prior optimization knowledge. It predicts the classification index of the initial sample points and divides the points into excellent and poor initial samples according to the prediction index.

10. The method for efficiently optimizing the variable-span inflatable wing structure based on pneumatic-structure thermal coupling according to claim 9, characterized in that, Before the reuse and calibration, all samples are modified according to the following steps: Step 1: Record the source optimal solution Determine the target region of interest And its centroid D0. For an inflatable wing, the centroid D0 contains two variables: the span length l and the internal pressure p. The span length l at the centroid is obtained from Equation (24): Determine that the boundary of l is within ±20%: l∈[0.8l0,1.2l0](25) The equation for expressing the required internal pressure P for a given bending moment M is: In the formula, M is the bending moment, and r is the cross-sectional radius of the inflatable structure, The corresponding span length after varying with the airspace for the P value is: The boundary of P is determined by Equation (28): p ∈ [0.8p0, 1.2p0] (28) Step 2. Rotation: For the sample point X, the corresponding spheroidization X (Spher) is expressed as: e i is the unit vector pointing from o to x i , and is the distance from the rotation center along e i to the boundary of the design domain. ub and lb are the upper and lower limits respectively, o is the rotation center, and it is a point on the perpendicular bisector of the line connecting the centroid D0 and a point on the perpendicular bisector of the line connecting the centroid D0 and The transformation matrix T is derived from Equation (31): Rotated sample X (Rot) Can be expressed as: X (Rot) = TX (Spher) (32) Perform the reverse operation and project the sample points into the original design domain, New distribution X of design variables (Regression) : Regression source optimal solution is reused, after regression, D0 coincides with coincide; Step 3. Reallocate high-quality samples and reallocate the high-quality samples to as follows: x j is the optimal sample in ini and is the unit vector pointing from to . is the distance from along the direction to the boundary, is the distance from through x j to the modified sample X of the distance to the boundary of the rotated LS-SVM classifier (T1)′ is expressed as: According to the modified sample, X (T1)′ is normalized to In the KTS method, the reuse and calibration of samples are carried out. If it is considered inferior, calibration is performed using equations (23) and (38). The LS-SVM classifier is used to retain high-quality samples and improve inferior samples. where α is a correction factor, is the closest to in the point After the optimal solution reuse and inferior point calibration procedures, the optimized initial sample points are mapped into the design space:

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