A robust optimization method, medium and program product based on D-optimality and considering the influence of intake and exhaust

Abstract

The present invention discloses a robust optimization method, medium and program product based on D-optimality and considering the influence of intake and exhaust, belonging to the technical field of aircraft aerodynamic optimization design. The present invention constructs a representative small sample set by introducing the D-optimality criterion, realizes the optimal coverage of the design space by maximizing the determinant of the information matrix, and the optimization objective function is composed of the weighted sum of the mean and standard deviation of the aerodynamic performance to balance performance improvement and robust optimization. The FFD method is used for geometric parameterization modeling of the aircraft aerodynamic shape and intake and exhaust systems, and the GPCE method is used to establish an uncertainty quantification surrogate model to analytically calculate the statistical characteristics and gradient information of the objective function, and the gradient optimization algorithm is used for iterative update to ensure meeting the design constraints and convergence criteria. The present invention fully considers the uncertainty influence of geometric parameters and intake and exhaust conditions, improves the aircraft aerodynamic performance, and enhances the adaptability and robustness under actual flight conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerodynamic optimization design of aircraft, and relates to uncertainty quantification, robust optimization, and coupled optimization of intake and exhaust systems and external configuration layout. Specifically, it is a robust optimization method, medium, and program product based on D-optimality and considering the influence of intake and exhaust, which is used to solve the uncertainty optimization problem of aircraft with intake and exhaust systems under real flight conditions. Background Technique

[0002] Modern high-performance aircraft usually adopt a layout with a high degree of integration of the fuselage and intake and exhaust systems. As an important part of the aircraft aerodynamic layout, the intake and exhaust systems not only have a significant impact on the external flow field of the aircraft, but also are closely coupled with the internal flow field of the engine. Moreover, the mutual influence between the external flow field of the aircraft and the internal flow of the intake and exhaust systems has an important impact on the overall performance of the aircraft. In addition, under real flight conditions, the aircraft is affected by uncertainty factors such as fluctuations in oncoming flow conditions, structural deformations, and external environmental disturbances, and its aerodynamic performance may change significantly. Therefore, in the process of aircraft design optimization, it is necessary to not only consider the performance under nominal conditions, but also consider the influence of various uncertainty factors on the performance to ensure that the aircraft can maintain good aerodynamic performance under various flight conditions.

[0003] At present, the research on integrated optimization design considering the influence of intake and exhaust mainly focuses on deterministic single-objective or multi-objective optimization. For example: using the inverse design idea to optimize the conformal nozzle considering the coupling of internal and external flows of the aircraft to obtain a nozzle profile with excellent robustness and aerodynamic characteristics, conducting multi-objective optimization for the unilateral expansion surface of the flying wing rear body to reduce the adverse effects of engine jet flow on the flight handling and stability characteristics of the flying wing, conducting three-dimensional optimization design with multiple objectives and multiple constraints for the aircraft considering the intake and exhaust systems to obtain better comprehensive performance, or conducting adjoint-based optimization design for the intake duct profile of the hybrid wing to obtain an optimization result with obvious drag reduction and obvious improvement in intake duct distortion, etc. Although these studies have improved the aerodynamic performance of the aircraft to a certain extent, due to ignoring the influence of uncertainty factors, their optimization results may show poor robustness under actual flight conditions.

[0004] In recent years, with the development of mathematical modeling and computing technology, uncertainty optimization design methods have gradually been applied to the aviation field to improve the robustness of optimization results. For example, by constructing a robust optimization design framework for full turbulence, the random perturbations of a small number of geometric design variables are considered, and the non-gradient optimization algorithm is used to optimize the uncertainty of power unit components. There are also studies that combine the gradient optimization method based on discrete adjoints with the polynomial chaos expansion method to achieve aerodynamic performance optimization under random perturbations. However, current research mainly focuses on the optimization of the aerodynamic shape of aircraft, and the research on the coupling between the internal flow field and the external aerodynamic flow field of the intake and exhaust system is relatively limited, and the uncertainty problem under the coupling of internal and external flows has not been effectively solved. On the other hand, although there are a large number of mathematical literatures studying methods for improving the accuracy of uncertainty prediction, the existing optimization methods still have room for improvement in sample efficiency and computational accuracy, especially when dealing with high-dimensional design spaces and complex flow field problems. In addition, traditional uncertainty quantification methods often require a large number of computational samples and have high computational costs.

[0005] In summary, how to achieve efficient and robust optimization design of aircraft while considering the influence of intake and exhaust, and how to improve the prediction accuracy and stability of uncertainty optimization methods in the aerodynamic field are technical problems that need to be solved urgently in the field of aircraft design. Summary of the invention

[0006] 1. Purpose of the invention

[0007] In view of the above defects and deficiencies of the prior art, the purpose of the present invention is to solve the problem of robust optimization of aircraft uncertainty under real flight conditions taking into account the effects of intake and exhaust, and to construct a robust optimization method, medium and program product based on D-optimality and taking into account the effects of intake and exhaust. By combining an efficient adjoint method, an uncertainty analysis method based on gradient-enhanced polynomial chaos expansion (GPCE) and a D-optimal sampling strategy, efficient and accurate aerodynamic shape optimization design of aircraft including intake and exhaust systems is achieved. The method can effectively quantify and propagate the uncertainty of flight state parameters, and select the optimal sample point combination according to the D-optimality criterion, so as to obtain high-precision prediction results at a relatively low computational cost, and finally achieve aerodynamic optimization including the effects of internal flow in the intake and exhaust system, while taking into account the uncertainty of flight conditions, and meeting the overall performance and robustness requirements of the aircraft in the optimization process.

[0008] (II) Technical solution

[0009] In order to achieve the purpose of the invention and solve the technical problems, the present invention adopts the following technical solutions:

[0010] The first object of the present invention is to provide a robust optimization method based on D-optimality and considering the influence of intake and exhaust, which is used for the optimization design of the intake and exhaust system and the overall aerodynamic layout of an aircraft under real flight uncertainty conditions, so as to improve the aerodynamic performance and design robustness. The method is characterized by including:

[0011] SS1. Definition of optimization objectives and geometric parameterization design

[0012] Define the optimization objectives, including the improvement of the aerodynamic performance of the aircraft and the optimization of the design result robustness. The objective function is composed of the weighted sum of the mean and standard deviation of the target aerodynamic performance, and the weight coefficient is dynamically adjusted according to the design requirements; use the Free-Form Deformation (FFD) method to perform geometric parameterization modeling on the aerodynamic shape and intake and exhaust system of the aircraft, and impose constraint conditions based on the geometric parameterization model; define the optimization design variables, including at least geometric design variables and aerodynamic design variables, and divide them into deterministic design variables and uncertain design variables according to whether they are affected by uncertain factors.

[0013] SS2. Construct a small sample set that meets statistical characteristics based on the D-optimality criterion

[0014] According to the probability distribution of the uncertain design variables, use the random sampling method to generate an initial large-scale candidate sample set; based on the D-optimality criterion, adopt the greedy algorithm of QR decomposition, and maximize the product of the eigenvalues of the information matrix of the basis function matrix to screen out a representative small sample set from the initial large-scale candidate sample set. Adjust the balance between the sample number and eigenvalue maximization to optimize the representativeness of the sample points, and form an optimal sampling set that meets statistical characteristics and has a controllable computational cost.

[0015] SS3. Internal and external flow field solution and gradient calculation based on the discrete adjoint method

[0016] For each sample point in the small sample set, perform computational fluid dynamics (CFD) numerical simulation on the internal and external flow fields of the aircraft. The simulation process considers the interaction between the intake and exhaust system and the external flow field to ensure the calculation accuracy of aerodynamic parameters. Obtain the target aerodynamic performance parameters corresponding to each sample point through numerical solution, and use the discrete adjoint method to calculate the gradient information of the target aerodynamic performance parameters with respect to each design variable.

[0017] SS4. Construct a GPCE uncertainty quantification surrogate model

[0018] Based on the CFD calculation results of a small sample set, the Gradient-Enhanced Polynomial Chaos Expansion (GPCE) method is used to model the uncertainty quantification problem. By combining the objective function values and their gradient information, a GPCE surrogate model containing orthogonal polynomial basis functions and their derivative terms is constructed. The statistical moments of the objective function and its gradients with respect to the design variables are analytically calculated using the obtained GPCE surrogate model.

[0019] SS5. Robust Optimization Design and Iterative Update of Aircraft

[0020] Based on the statistical moments of the objective function and its gradients with respect to the design variables calculated by the GPCE surrogate model, a gradient optimization algorithm is used to iteratively update all design variables. During the optimization iteration process, the update of geometric design variables is achieved by adjusting the positions of FFD control points. According to the updated FFD control points, the surface grids of the aircraft aerodynamic shape and the intake and exhaust systems are regenerated, and the volume grids are updated using the Inverse Distance Weighting (IDW) method. The update of uncertainty design variables is adjusted according to the search direction and step size of the gradient optimization algorithm. During the optimization iteration process, the update of all design variables must strictly satisfy the constraint conditions until the convergence criterion is met.

[0021] SS6. Verification of Optimization Results and Robustness Evaluation

[0022] After the optimization is completed, the final optimization results are output, and the optimized aircraft configuration is verified and its robustness is evaluated. The coupling characteristics between the intake and exhaust systems and the external flow field are analyzed, and the comprehensive performance of the optimized configuration is evaluated to ensure that the design meets the actual flight requirements.

[0023] The second object of the present invention is to provide a computer program product, including computer instructions, for executing the above-mentioned robust optimization method based on D-optimal and considering the influence of intake and exhaust.

[0024] The third object of the present invention is to provide a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned robust optimization method based on D-optimal and considering the influence of intake and exhaust of the present invention is implemented.

[0025] (III) Technical Effects

[0026] Compared with the prior art, the robust optimization method, medium, and program product based on D-optimal and considering the influence of intake and exhaust of the present invention have the following beneficial and significant technical effects:

[0027] (1) The present invention adopts the D-optimal criterion and constructs a small sample set from a large number of candidate samples through a greedy method of QR decomposition. Combining with the GPCE uncertainty quantification surrogate model of gradient-enhanced polynomial chaos expansion, by introducing the gradient information of the objective function into the surrogate model and combining with the change trend of the objective function in the optimization iteration, it can accurately capture the change direction of the design variables, improve the prediction accuracy of the model for the objective function, significantly improve the prediction accuracy and stability of the robust optimization method in the aerodynamic field, enable aerodynamic optimization including the influence of the internal flow of the intake and exhaust systems, and at the same time consider the uncertainty of flight conditions, meeting the overall performance and robustness requirements of the flying wing layout in the optimization process.

[0028] (2) In the optimization of the intake and exhaust systems, the present invention considers the coupling influence between the intake and exhaust systems and the overall aerodynamic layout, improving the comprehensive performance of the aircraft. By incorporating the mutual influence between the intake and exhaust systems and the aerodynamic layout into the optimization model, the present invention can more accurately capture the coupling effects between various components of the aircraft during the optimization process, and ultimately achieve more efficient and stable aerodynamic performance optimization. In addition, by introducing uncertainty quantification and robust optimization strategies, the present invention can consider various uncertain factors that the aircraft may encounter under different flight conditions during the design process, ensuring that the optimization results can still maintain high performance and stability under uncertain conditions, not only improving the aerodynamic performance of the aircraft, but also enhancing the adaptability and robustness of the design in an uncertain environment.

[0029] (3) The present invention uses the D-optimal experimental design method to generate the initial sampling point set. By maximizing the determinant of the information matrix to optimize the sampling point distribution, it can effectively screen out the sample points that contribute the most to the uncertainty quantification of the objective function, thereby constructing a representative small sample set, ensuring good space filling and uniformity of the sampling points in the design space, and improving the prediction accuracy and generalization ability of the surrogate model. At the same time, the present invention uses the GPCE method to construct a high-precision surrogate model using the function values and gradient information of a small number of sample points. On the premise of ensuring the optimization accuracy, it significantly reduces the required CFD calculation amount, can obtain higher-precision optimization results under the same computing resources, or significantly reduces the calculation time under the same accuracy requirements. Description of the Drawings

[0030] Figure 1 is the flow chart of the robust optimization method based on D-optimal and considering the influence of intake and exhaust in the present invention;

[0031] Figure 2 is the schematic diagram of the robust optimization framework based on D-optimal and considering the influence of intake and exhaust in the present invention;

[0032] Figure 3 shows the schematic diagram of the FFD box for the initial configuration optimization layout in Embodiment 2 of the present invention;

[0033] Figure 4 Shown are the schematic diagrams of the total pressure recovery coefficient distribution of the inlet before and after optimization and the changes in the inlet center axis and area. In the figures: (a) is the contour map of the end face total pressure recovery coefficient σ distribution of the initial configuration (left half) and the configuration after uncertainty optimization (right half); (b) is the distribution curve of the inlet area along the axial direction x of the initial configuration, the deterministic optimization configuration, and the uncertainty optimization configuration; (c) is the distribution curve of the height z of the center axis of the three configurations along the axial direction.

[0034] Figure 5 Shown are the schematic diagrams of the pressure coefficient distribution and its statistical response at different wingspan positions in Embodiment 2 of the present invention. In the figures, (a) to (d) correspond to the pressure coefficient distributions at four different wingspan positions of Y / b = 0.3, Y / b = 0.5, Y / b = 0.7, and Y / b = 0.9, respectively. Specific Embodiments

[0035] The present invention aims to provide a robust optimization method, medium, and program product based on D-optimal and considering the influence of intake and exhaust. By combining an efficient adjoint method, a GPCE uncertainty analysis method based on gradient-enhanced polynomial chaos expansion, and a D-optimal sampling strategy, aerodynamic optimization considering the influence of the internal flow of the intake and exhaust system is realized, while considering the uncertainty of flight conditions to meet the overall performance and robustness requirements of the aircraft during the optimization process. To make the purpose, technical solutions, and advantages of the implementation of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are some, but not all, of the embodiments of the present invention, and the described embodiments are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0036] Embodiment 1: Implementation Process of the Robust Optimization Method

[0037] As a specific example, Figure 1 shows the implementation process of the robust optimization method provided by the present invention based on D-optimal and considering the influence of intake and exhaust. Figure 2 Further shows the implementation framework of this robust optimization method. As Figure 1 、 2 shown, when implementing this robust optimization method, it mainly includes the following steps:

[0038] SS1. Definition of Optimization Objectives and Geometric Parameterization Design

[0039] Define the optimization objectives, including the improvement of the aerodynamic performance of the aircraft and the optimization of the robustness of the design results. The objective function is composed of the weighted sum of the mean and standard deviation of the target aerodynamic performance, and the weight coefficients are dynamically adjusted according to the design requirements. Use the FFD method to perform geometric parameterization modeling on the aerodynamic shape and inlet and exhaust systems of the aircraft, and impose constraint conditions based on the geometric parameterization model. Define the optimization design variables, including geometric design variables and aerodynamic design variables, etc., and divide them into deterministic design variables and uncertain design variables according to whether they are affected by uncertain factors.

[0040] In the embodiment of the present invention, the objective function I ( μ , σ ) is defined as the weighted sum of the statistical moments of the target aerodynamic performance and satisfies I ( μ , σ ) = K 1· μ + K 2· σ , where μ is the mean value, σ is the standard deviation, K 1, K 2 are the weight coefficients respectively and satisfy K 1 + K 2 = 1. When the optimization objective pays more attention to performance improvement, K 1 > K 2 is preferably set, while when the optimization objective pays more attention to robustness, K 1 < K 2 is preferably set; the mean value μ and the standard deviation σ of the objective function are calculated based on the statistical moments of the aerodynamic performance analyzed and calculated by the surrogate model, and are obtained by weighted averaging and standard deviation calculation of the responses of the sample points under various flight conditions. In addition, the optimization state condition is set to the actual flight state under cruise flight conditions and the influence of uncertainty is considered. The flight state parameters include at least Mach number, incoming flow angle of attack, sideslip angle, and / or internal flow parameters of the inlet. For the Mach number and incoming flow angle of attack with uncertain quantities, their probability distribution types and statistical characteristics are given to ensure that the variable distribution in the optimization process can accurately reflect the actual flight conditions.

[0041] In the embodiments of the present invention, the FFD method adopted in geometric parametric modeling is realized by generating a control framework around the geometric shape of the aircraft. The control framework is composed of B-spline control points. The FFD control points perform parametric modeling on the aerodynamic shape of the aircraft, the shape of the inlet lip, and the shape of the internal flow path of the inlet by adjusting their positions. The number and distribution of the FFD control points are allocated according to the complexity of the aircraft design area, and a higher density of control points is arranged in the wing and inlet areas to meet the refined requirements of geometric deformation during the optimization process.

[0042] In the embodiments of the present invention, the constraint conditions applied to the geometric parametric model include aerodynamic performance constraints, geometric shape constraints, and / or constraints related to the intake and exhaust systems, etc. The aerodynamic performance constraints include moment balance constraints and / or lift coefficient constraints, etc. The geometric shape constraints include thickness constraints and / or volume constraints, etc. The constraints related to the intake and exhaust systems include total pressure recovery coefficient constraints and / or distortion coefficient constraints of the inlet.

[0043] In the embodiments of the present invention, geometric design variables are defined by the FFD method, covering the aerodynamic shape of the aircraft and the geometric shapes of the intake and exhaust systems, and at least including FFD control points for controlling the aerodynamic shape of the aircraft, FFD control points for controlling the geometric shape of the inlet, and FFD control points for controlling the deformation of the inlet lip; the aerodynamic design variables include parameters related to the flight state, at least including Mach number, angle of attack of the oncoming flow, sideslip angle, and / or internal flow parameters of the inlet; the deterministic design variables are used to define fixed geometric shapes and aerodynamic characteristics, and the uncertain design variables are used to characterize the random influence of flight conditions and environmental disturbances on aerodynamic performance. The probability density distribution of the uncertain design variables is determined through statistical analysis, and it is assumed to follow a normal distribution or a uniform distribution to meet the requirements of random response modeling.

[0044] SS2. Construct a small sample set that meets statistical characteristics based on the D-optimal criterion

[0045] According to the probability distribution of the uncertain design variables, an initial large-scale candidate sample set is generated using a random sampling method; based on the D-optimal criterion, a greedy algorithm using QR decomposition is adopted to screen out a representative small sample set from the initial large-scale candidate sample set by maximizing the product of the eigenvalues of the information matrix of the basis function matrix. The representativeness of the sample points is optimized by adjusting the balance between the number of samples and the maximization of the eigenvalues, forming an optimal sampling set that meets statistical characteristics and has a controllable computational cost.

[0046] In the embodiments of the present invention, the process of constructing a small sample set based on the D-optimal criterion includes the following sub-steps:

[0047] SS21. Generation of the initial large-scale candidate sample set: According to the probability distribution type and statistical characteristics of the uncertainty design variables, the initial large-scale candidate sample set is generated by Monte Carlo sampling or Latin hypercube sampling methods. The sample points cover the complete range of the uncertainty design variables and their distribution characteristics are consistent with the probability distribution of the uncertainty design variables. The number of samples is reasonably set according to the number of uncertainty design variables and the order of the subsequent polynomial chaos expansion (PCE) to ensure that the candidate sample set can fully represent the statistical characteristics of the uncertainty variables.

[0048] SS22. Construction of the basic information matrix for the small sample set: Based on the generated initial large-scale candidate sample set, a polynomial basis function matrix related to the uncertainty design variables is constructed. The basis functions are the orthogonal polynomial basis functions of the polynomial chaos expansion (PCE). Each element of the basis function matrix consists of the values of the basis functions at the candidate sample points, reflecting the correlation between each candidate sample point and the objective function. And based on the basis function matrix, a basic information matrix for D-optimal criterion screening is formed. The information matrix is defined as the product of the transpose matrix of the polynomial basis function matrix and itself. The eigenvalues and determinant value of the information matrix directly determine the representativeness and prediction accuracy of the candidate sample set for the uncertainty quantification of the objective function.

[0049] SS23. Greedy algorithm screening based on QR decomposition: Using the constructed information matrix, the greedy algorithm based on QR decomposition is used to screen the candidate sample points. By QR decomposing the basis function matrix into an orthogonal matrix Q and an upper triangular matrix R, the sample points with the largest absolute values of the diagonal elements of the upper triangular matrix R are preferentially selected. According to the greedy algorithm and combined with the distribution uniformity among the sample points, the sample points that maximize the determinant value of the information matrix are iteratively selected to be added to the small sample set to update the basis function matrix information matrix, so as to maximize the product of the eigenvalues of the basis function matrix information matrix until the small sample set reaches the preset scale or meets the stopping criterion.

[0050] SS24. Optimization balance of the number of samples and eigenvalues: During the screening process, the number of the small sample set is dynamically adjusted according to the complexity of the objective function and the computational cost requirements to ensure that the sample set can effectively improve the accuracy of the surrogate model without increasing the computational cost due to excessive number of samples. After optimization, a small sample set that meets the statistical characteristics is formed.

[0051] SS25. Quality verification of the sample set: Quality verification is carried out on the screened small sample set. By calculating the eigenvalue distribution of the information matrix and the minimum distance between samples, the coverage and distribution uniformity of the sample points are evaluated to ensure that the sample set can comprehensively reflect the influence range of the uncertainty design variables and support the construction and optimization iteration of the subsequent GPCE surrogate model.

[0052] Preferably, the method for generating the initial large-scale candidate sample set is Monte Carlo sampling or Latin hypercube sampling, where: Monte Carlo sampling is applicable to the case where uncertain design variables follow a complex or non-uniform distribution. By randomly generating sample points, it simulates the probability distribution characteristics of the variables. The sampling density is dynamically adjusted according to the distribution range of the variables and their importance in affecting the objective function to ensure sufficient coverage of the candidate sample set for the true distribution; Latin hypercube sampling is applicable to the case where uncertain design variables are uniformly distributed or normally distributed. By means of stratified sampling, the variable range is divided into several equal sub-intervals, and a sample point is randomly generated in each interval to ensure the uniformity and representativeness of the candidate sample set, while reducing the possibility of sample point overlap and improving the sample utilization efficiency.

[0053] SS3. Internal and external flow field solution and gradient calculation based on the discrete adjoint method

[0054] For each sample point in the small sample set, based on the Reynolds-Averaged Navier-Stokes (RANS) equations and combined with a turbulence model, a computational fluid dynamics (CFD) numerical simulation of the internal and external flow fields of the aircraft is carried out. The interaction between the intake and exhaust systems and the external flow field is considered in the simulation process to ensure the calculation accuracy of the aerodynamic parameters. The target aerodynamic performance parameters corresponding to each sample point are obtained through numerical solution, and the gradient information of the target aerodynamic performance parameters with respect to each design variable is calculated using the discrete adjoint method.

[0055] In the embodiments of the present invention, the CFD numerical simulation solves the RANS equations based on the finite volume method and combines the Spalart-Allmaras turbulence model to simulate the influence of turbulent viscosity. The viscous fluxes in the flow field calculation are discretized using standard central differences, and the inviscid fluxes are discretized using artificially dissipated central differences; when solving the residual equation, the Runge-Kutta method and the Newton-Krylov method are combined to dynamically switch to optimize the solution efficiency, and the residual norm is ensured to be reduced by at least five orders of magnitude to ensure the stability and accuracy of the flow field solution; the interaction between the intake and exhaust systems and the external flow field is simulated using the overlapping grid technique, and the exchange of internal and external flow field information is realized through interpolation methods to couple the solution of the internal and external flow fields; the discrete adjoint method is used to calculate the gradient of the target aerodynamic performance parameters with respect to the design variables, including geometric design variables and aerodynamic design variables.

[0056] In the embodiments of the present invention, the target aerodynamic performance parameters include the aerodynamic shape performance parameters of the aircraft and the performance parameters of the intake and exhaust systems. Among them, the aerodynamic shape performance parameters of the aircraft are the drag coefficient, the lift coefficient, and / or the moment coefficient. The performance parameters of the intake and exhaust systems include the total pressure recovery coefficient and / or the distortion coefficient of the intake duct. The total pressure recovery coefficient of the intake duct is defined as the ratio of the average total pressure at the outlet of the intake duct to the total pressure of the free stream. The distortion coefficient is composed of the sum of the circumferential non-uniformity of the total pressure and the surface average pulsation intensity. The circumferential non-uniformity of the total pressure is calculated based on the total pressure distribution at the outlet section of the intake duct, reflecting the circumferential non-uniformity of the flow field at the outlet of the intake duct. The surface average pulsation intensity is a time-varying random variable related to the total pressure fluctuation on the plane at the outlet of the intake duct.

[0057] SS4. Construct a GPCE uncertainty quantification surrogate model

[0058] Based on the CFD calculation results of a small sample set, the Gradient-Enhanced Polynomial Chaos Expansion (GPCE) method is used to model the uncertainty quantification problem. A surrogate model containing orthogonal polynomial basis functions and their derivative terms is constructed by combining the objective function values and their gradient information, and the statistical moments of the objective function and their gradients with respect to the design variables are analytically calculated using the obtained GPCE surrogate model.

[0059] In the embodiments of the present invention, the construction process of the GPCE uncertainty quantification surrogate model at least includes:

[0060] SS41. Determine the orthogonal polynomial basis function and the model framework

[0061] First, according to the probability distribution type of the uncertain design variables, select the appropriate form of the multivariate orthogonal polynomial basis function. If the variable follows a normal distribution, select the Hermite polynomial; if the variable follows a uniform distribution, select the Legendre polynomial.

[0062] Secondly, apply the effect sparsity principle and the hyperbolic truncation method to limit the interaction order of the multivariate orthogonal polynomial basis functions, retain the main effects and important low-order interaction effects, and eliminate the high-order non-linear interaction terms.

[0063] After that, model the uncertainty quantification problem of the objective function, and expand the random response of the objective function Y ( D , ξ ) into a linear combination of orthogonal polynomial basis functions:

[0064]

[0065] Where: Dis the deterministic design variable vector, ξ is n dimensional uncertainty design variable vector and ξ =( ξ 1, ξ 2,..., ξ n ); Ψ j ( ξ ) is the j -th order basis function, c j ( D ) is the expansion coefficient of the j -th order basis function, P +1 is the total number of basis functions and , n is ξ dimensionality, p is the highest order of expansion;

[0066] SS42. Introduce the gradient information of the objective function to construct the GPCE surrogate model

[0067] Introduce the gradient information of the objective function with respect to the design variables into the model framework to construct the gradient-enhanced GPCE surrogate model. The gradient expansion form of the objective function is:

[0068]

[0069] where is the uncertainty design variable ξ i in the standard random variable form, μ i , σ i are respectively the mean and standard deviation of the i -th uncertainty design variable ξ i , i =1,2,… n , n is ξ dimensionality;

[0070] SS43. Solve the expansion coefficients of the orthogonal polynomials

[0071] Construct the augmented linear equations , where Ψ is the augmented basis function matrix composed of the basis functions and their derivatives, c is the vector of expansion coefficients to be solved, Y is the vector composed of the function values and gradient values of the sample points; The equations are based on N sThe N s (1 + n ) equations are constructed, n where ξ is the dimension of , and Ψ j is the number of sample points in the small sample set. The partial derivative term ξ i of the uncertainty design variable is calculated through the analytical expression of the orthogonal polynomial. The partial derivative X i of the standard random variable ξ i is σ i analytically determined based on the probability density function of the uncertainty design variable, and the least squares method is used to solve to obtain the expansion coefficients c j ( D ) of the orthogonal polynomial expansion;

[0072] SS44. Analytically calculate the statistical moments and gradients of the objective function

[0073] Based on the constructed GPCE surrogate model and the obtained expansion coefficients, the statistical moments of the objective function are analytically calculated. The mean μ Y of the objective function is given by the constant term coefficient c 0( D ), and , the variance of the objective function satisfies , is the normalization factor of the basis function, and based on this, the gradients D of the statistical moments with respect to the deterministic design variable and are calculated;

[0074] SS45. Verification and optimization of the GPCE surrogate model accuracy

[0075] Calculate the normal root mean square deviation to verify the prediction accuracy of the GPCE surrogate model, where Y i is the true value of the objective function, is the predicted value of the GPCE surrogate model. The closer the value of NRMSD is to 0, the higher the prediction accuracy; according to the verification results, adjust the highest order p of the orthogonal polynomial basis function, the truncation strategy, and / or the number of sample points N s, to improve the model accuracy and reduce the computational cost.

[0076] SS5. Robust Optimization Design and Iterative Update of Aircraft

[0077] Based on the statistical moments of the objective function calculated by the GPCE surrogate model and their gradient information with respect to the design variables, use the gradient optimization algorithm to iteratively update all design variables; during the optimization iteration process, the update of the geometric design variables is achieved by adjusting the positions of the FFD control points. Regenerate the surface grids of the aircraft aerodynamic shape and the intake and exhaust systems according to the updated FFD control points, and update the volume grids using the Inverse Distance Weighting (IDW) method. The update of the uncertainty design variables is adjusted according to the search direction and step size of the gradient optimization algorithm; during the optimization iteration process, the update of all design variables must strictly satisfy the constraint conditions until the convergence criterion is met.

[0078] Preferably, during the iterative update process of the gradient optimization algorithm, the line search or trust region method is used to determine the appropriate step size to ensure the convergence and efficiency of the algorithm. The penalty function method or barrier function method is used to handle the constraint conditions to ensure that the optimization results meet the design requirements; if the change amount of the objective function value is less than the set threshold, the gradient norm of the objective function with respect to the design variables is less than the set threshold, the change amount of the design variables is less than the set threshold, the residuals of all constraints are less than the preset allowable error, and / or the number of iterations reaches the preset maximum value, it is considered that the uncertainty optimization design process meets the convergence criterion.

[0079] SS6. Verification of Optimization Results and Robustness Evaluation

[0080] After the optimization is completed, output the final optimization results, verify and evaluate the robustness of the optimized aircraft configuration, analyze the coupling characteristics between the intake and exhaust systems and the external flow field, evaluate the comprehensive performance of the optimized configuration, and ensure that the design meets the actual flight requirements.

[0081] Preferably, the CFD numerical simulation method is used for the verification of the optimization results. The optimized aircraft configuration is subjected to CFD calculations under deterministic conditions, and the calculation results are compared with the initial design to evaluate the optimization effect; the Monte Carlo method is used for the robustness evaluation to perform uncertainty analysis on the optimized aircraft configuration and evaluate the changes in its aerodynamic performance under different values of uncertainty variables to verify the robustness of the design; and during the robustness evaluation process, analyze the coupling characteristics between the intake and exhaust systems and the external flow field, including the changes in the total pressure recovery coefficient and / or distortion coefficient of the intake duct, and the influence of the intake and exhaust systems on the overall aerodynamic performance of the aircraft.

[0082] The above Example 1 provides a robust optimization method of the present invention based on D-optimality and considering the influence of intake and exhaust, which significantly improves the performance and robustness of aircraft design by combining accurate aircraft aerodynamic performance modeling and uncertainty analysis. Through an efficient optimization algorithm and surrogate model, this method can ensure that the optimization results have excellent aerodynamic performance and reliability under actual flight conditions, meet the design requirements of high precision and high stability, and have important engineering application value.

[0083] Example 2: Uncertainty Optimization of a Flying Wing Configuration with an Inlet

[0084] On the basis of the above Example 1, as a further application, Example 2 performs uncertainty optimization on the X1 flying wing configuration including an inlet. By comparing the results of deterministic optimization and uncertainty optimization, the improved aerodynamic performance and robustness after optimization are analyzed.

[0085] On the basis of Example 1, in this Example 2, the X1 flying wing configuration including an inlet is selected for uncertainty optimization. Among the optimized state parameters, the Mach number Ma and the angle of attack of the oncoming flow AoA are taken as uncertain design variables, and are respectively assumed to follow normal distributions Ma ~N(0.75, 0.03 2 ), AoA ~N(3, 0.4 2 ). The optimization objective is to minimize the objective function I ( μ , σ ) under the optimized state, where the weighted sum of the mean μ and the standard deviation σ of the aerodynamic performance constitutes the objective function, and the aerodynamic constraint is the moment balance under the optimized state, C my =-0.002. The optimized design variables are: ① 266 FFD control points for controlling the deformation of the wing; ② 64 FFD control points for controlling the deformation of the inlet lip; ③ 72 FFD control points for controlling the deformation of the inlet; ④ the cruise angle of attack. During the optimization process, thickness constraints are imposed on the wing and the fuselage, the constraint positions are 5% - 95%, and the constraint range is to make the thickness not less than 98% of the initial thickness, and a total of 154 thickness constraints are applied. The FFD box used for the initial configuration optimization is as shown in Figure 3 .

[0086] Meanwhile, in order to compare and analyze the optimization effect, this Example 2 also performs deterministic optimization with the optimization parameters consistent with the uncertainty optimization. Its optimized state is set as: Ma =0.75, C l =0.20, and the optimization objective is the objective function 5 under the optimized state CD - σ AV is minimized, where C D is the drag coefficient, σ AV is the standard deviation of the lift coefficient, and the aerodynamic constraint is moment trimming in the optimized state. C my = -0.002, ensuring that the aircraft has balanced aerodynamic characteristics in the optimized state. By comparing the results of uncertainty optimization and deterministic optimization, Example 2 analyzes in detail the differences between the two in terms of robustness, performance improvement, and the number of optimization iterations, thus providing guidance for the robust optimization of aircraft design.

[0087] In Example 2, the uncertainty optimization results (labeled Unopt) and the deterministic optimization results (labeled Deopt) are shown in Table 1 below. Compared with the initial configuration, the statistical moments of the configuration after uncertainty optimization μ ( C D ) + σ ( C D ) are reduced by 6.8%, indicating that the optimized design not only improves the mean value of the aerodynamic performance μ ( C D ), but also reduces the standard deviation σ ( C D ), effectively enhancing the robustness of the design. Compared with the initial configuration, the optimized configuration based on uncertainty has a lower standard deviation.

[0088] Table 1 Comparison of Deterministic and Uncertainty Optimization Before and After

[0089]

[0090] Under the benchmark conditions, the drag coefficient C D of the uncertainty optimization configuration is 139.44, which is 5.3 counts lower than 144.74 of the initial configuration, while the drag coefficient of the deterministic optimization configuration is reduced by 5.5 counts. Although the drag of the uncertainty optimization is slightly higher, its advantage in terms of robustness is more prominent. The main reason for this difference is that the deterministic optimization has gone through more than 200 rounds of optimization, but due to time constraints, the robustness optimization has only been carried out 4 rounds. Nevertheless, the uncertainty optimization can provide a significant improvement in the stability and robustness of the aircraft performance while ensuring a relatively low drag.

[0091] Figure 4Presents the schematic diagrams of the total pressure recovery coefficient distribution of the inlet before and after optimization and the changes in the inlet center axis and area. In the figure: (a) is the contour map of the end face total pressure recovery coefficient σ distribution of the initial configuration (left half) and the configuration after uncertainty optimization (right half). The color of the contour map ranges from blue to red corresponding to the change range of the σ value from 0.85 to 1.0; (b) is the distribution curve of the inlet area along the axial direction (x) of the initial configuration, the deterministic optimization configuration, and the uncertainty optimization configuration; (c) is the distribution curve of the height z of the center axis of the three configurations along the axial direction. It can be seen from the figure that for the initial and uncertainty optimization configurations, the low total pressure recovery region ( σ <0.91) is concentrated at the end face edge, and the high total pressure recovery region ( σ >0.97) is concentrated at the center of the end face. Compared with the initial configuration, the high total pressure recovery region of the uncertainty optimization configuration is larger, indicating that the aerodynamic performance of the inlet after optimization has been improved. From Figure 4 the area distribution curve in (b) of the figure, it can be seen that the overall inlet area of the uncertainty optimization configuration is larger than that of the initial configuration, and there are two peaks near x = 0.8 and x = 1.2. In addition, Figure 4 the center axis distribution in (c) of the figure shows that the optimized configuration shifts downward more significantly in the region of x > 0.8, but the overall trend is similar to that of the initial configuration. This moderate geometric change helps to maintain a smooth transition of the flow channel and avoid severe flow separation.

[0092] Figure 5 Shows the schematic diagrams of the pressure coefficient distribution and its statistical response at different span positions of the wing. In the figure, (a) - (d) are the pressure coefficient distributions at the span positions of Y / b = 0.3, Y / b = 0.5, Y / b = 0.7, and Y / b = 0.9 respectively. Each sub - figure contains the pressure coefficient curves of the initial configuration (solid line), the deterministic optimization configuration (red dashed line), and the uncertainty optimization configuration (blue dotted line), and at the same time shows the statistical response intervals (±2 times the standard deviation, represented by the gray shaded area) of the pressure coefficients of each configuration. To explore the robust design more deeply, the statistical responses of the pressure coefficients and lift distributions at different span positions of the wing are analyzed. For the pressure coefficient, the results of the initial configuration show the worst robustness. Since the robust optimization results have not fully converged, it can be seen that the pressure distribution is not smooth enough, but the variance perturbation range (blue shaded area) of the uncertainty optimization is significantly better than that of the initial configuration. The statistical response of the pressure coefficient distribution further explains the robustness of the uncertainty - based optimization.

[0093] Through the above embodiments, the object of the present invention is fully and effectively achieved. Those skilled in the art can understand that the present invention includes but is not limited to the content described in the drawings and the above specific embodiments. Although the present invention has been described with respect to the presently considered most practical and preferred embodiments, it should be understood that the present invention is not limited to the disclosed embodiments, and any modifications that do not deviate from the functional and structural principles of the present invention will be included within the scope of the claims.

Claims

1. A robust optimization method based on D-optimality and considering the influence of intake and exhaust, characterized in that: include: SS1. Define the optimization objective, where the objective function is the weighted sum of the mean and standard deviation of the target aerodynamic performance; use the FFD method to perform geometric parameterized modeling of the aerodynamic shape and intake and exhaust system of the aircraft, and impose constraints accordingly; Define optimization design variables, including geometric design variables and aerodynamic design variables, and divide them into deterministic design variables and uncertain design variables; SS2. Generate an initial large-scale candidate sample set using random sampling method according to the probability distribution of uncertain design variables; Based on the D-optimal criterion, the greedy algorithm of QR decomposition is used to screen out a small sample set from the candidate sample set by maximizing the product of the eigenvalues ​​of the basis function matrix and the information matrix. SS3. For each sample point in the small sample set, perform CFD numerical simulation on the external aerodynamic flow field of the aircraft and the internal flow field of the intake and exhaust system. The internal and external flow fields include the external aerodynamic flow field of the aircraft and the internal flow field of the intake and exhaust system, obtain the target aerodynamic performance parameters, and use the discrete adjoint method to calculate the gradient information of the target aerodynamic performance parameters; SS4. Use the GPCE method to model the uncertainty quantification problem. By combining the objective function value and its gradient information, a GPCE proxy model containing orthogonal polynomial basis functions and their derivatives is constructed. The proxy model is used to calculate the objective function statistical moment and its gradient information. SS5. Based on the objective function statistical moment and its gradient information, the design variables are iteratively updated using the gradient optimization algorithm. The geometric design variables are updated by adjusting the position of the FFD control points, the surface mesh is regenerated based on the updated FFD control points, and the volume mesh is updated using the IDW method. The update of the uncertain design variables is adjusted according to the search direction and step size of the gradient optimization algorithm. The update of all design variables must strictly meet the constraints until the objective function meets the convergence criteria; SS6. Output the optimization results and verify and evaluate the robustness of the optimized aircraft configuration.

2. A robust optimization method based on D-optimality and considering the effects of intake and exhaust according to claim 1, characterized in that: In step SS1, the objective function I ( μ , σ ) is defined as the weighted sum of the statistical moments of the target aerodynamic performance and satisfies I ( μ , σ )= K 1. μ + K 2. σ , μ is the mean, σ is the standard deviation; K 1. K 2 are weight coefficients and satisfy K 1+ K 2=1; mean μ and standard deviation σ The calculation is based on the statistical moment of the objective function calculated analytically by the proxy model; the optimization state condition is set to the actual flight state under cruise flight conditions and the influence of uncertainty is taken into account. The flight state parameters include at least Mach number, incoming flow angle of attack, sideslip angle and / or inlet flow parameters. For the Mach number and incoming flow angle of attack with uncertain quantities, their probability distribution type and statistical characteristics must be given.

3. A robust optimization method based on D-optimality and considering the effects of intake and exhaust according to claim 1, characterized in that: In step SS1, the FFD method is implemented by generating a control frame around the geometric shape of the aircraft, and the FFD control points perform geometric parameterized modeling of the aircraft's aerodynamic shape, inlet lip shape, and inlet internal flow path shape by adjusting their positions; the number and distribution of FFD control points are allocated according to the complexity of the aircraft design area; the constraints include at least aerodynamic performance constraints, geometric shape constraints, and / or intake and exhaust system-related constraints, the aerodynamic performance constraints include moment balancing constraints and / or lift coefficient constraints, the geometric shape constraints include thickness constraints and / or volume constraints, and the intake and exhaust system-related constraints include inlet total pressure recovery coefficient constraints and / or distortion coefficient constraints.

4. A robust optimization method based on D-optimality and considering the effects of intake and exhaust according to claim 3, characterized in that: In step SS1, the geometric design variables are defined by the FFD method, including at least the FFD control points that control the aerodynamic shape of the aircraft, the FFD control points that control the geometric shape of the inlet, and the FFD control points that control the deformation of the inlet lip; the aerodynamic design variables include parameters related to the flight state, including at least the Mach number, the incoming flow angle of attack, the sideslip angle and / or the inlet flow parameters; the deterministic design variables are used to define the fixed geometric shape and aerodynamic characteristics, and the uncertain design variables are used to characterize the random effects of flight conditions and environmental disturbances on the aerodynamic performance. The probability density distribution of the uncertain design variables is determined by statistical analysis, and it is assumed that they obey the normal distribution or uniform distribution.

5. A robust optimization method based on D-optimal and considering the influence of intake and exhaust according to claim 4, characterized in that: In step SS2, the small sample set construction process includes at least the following sub-steps: SS21. Generate an initial large-scale candidate sample set based on the probability distribution type and statistical characteristics of the uncertain design variables by Monte Carlo sampling or Latin hypercube sampling method. The sample points cover the full range of the uncertain design variables and the distribution characteristics are consistent with the probability distribution of the variables. The number of samples is set according to the number of uncertain design variables and the order of the subsequent polynomial chaos expansion. SS22. Based on the initial large-scale candidate sample set, a polynomial basis function matrix related to the uncertain design variables is constructed. The basis function adopts the orthogonal polynomial basis function of the polynomial chaos expansion PCE. Each element of the basis function matrix consists of the value of the orthogonal polynomial basis function at the candidate sample point. Based on the basis function matrix, a basic information matrix of the small sample set for D optimal criterion screening is formed. The information matrix is ​​defined as the product of the transposed matrix of the basis function matrix and itself. SS23. Using the constructed information matrix, the greedy algorithm of QR decomposition is used to screen the candidate sample points. By decomposing the basis function matrix QR into an orthogonal matrix Q and an upper triangular matrix R, the sample points with the largest absolute value of the diagonal elements of the upper triangular matrix R are selected. According to the greedy algorithm and the distribution uniformity among the sample points, the sample points with the largest determinant value of the information matrix are iteratively selected to add to the small sample set to update the basis function matrix information matrix, so as to maximize the product of the eigenvalues ​​of the basis function matrix information matrix, until the small sample set reaches the preset size or meets the stopping criterion; SS24. During the screening process, the number of small sample sets is dynamically adjusted according to the complexity of the objective function and the computational cost requirements, and after the optimization is completed, a small sample set that meets the statistical characteristics is formed; SS25. Perform quality verification on the small sample set that has been screened, and evaluate the coverage and distribution uniformity of the sample points by calculating the eigenvalue distribution of the information matrix and the minimum distance between samples.

6. A robust optimization method based on D-optimal and considering the influence of intake and exhaust according to claim 5, characterized in that: In step SS2, the initial large-scale candidate sample set is generated by Monte Carlo sampling or Latin hypercube sampling, where Monte Carlo sampling simulates the probability distribution characteristics of variables by randomly generating sample points, and the sampling density is dynamically adjusted according to the distribution range of the variables and the importance of their impact on the objective function; Latin hypercube sampling divides the variable range into several equal intervals by stratified sampling, and randomly generates a sample point in each interval.

7. A robust optimization method based on D-optimality and considering the effects of intake and exhaust according to claim 1, characterized in that: In step SS3, the CFD numerical simulation solves the RANS equations based on the finite volume method and combines the turbulence model to simulate the influence of turbulent viscosity. The viscous flux in the flow field calculation is discretized using the standard central difference, and the inviscid flux is discretized using the artificial dissipative central difference. When solving the residual equation, the Runge-Kutta method and the Newton-Krilov method are dynamically switched to optimize the solution efficiency to ensure that the residual norm is reduced by at least five orders of magnitude to ensure the stability and accuracy of the flow field solution. The interaction between the intake and exhaust system and the external flow field is simulated using the overlapping grid technology, and the exchange of internal and external flow field information is achieved through the interpolation method. The discrete adjoint method is used to calculate the gradient of the target aerodynamic performance to the design variables.

8. A robust optimization method based on D-optimality and considering the effects of intake and exhaust according to claim 1, characterized in that: In step SS3, the target aerodynamic performance parameters include aircraft aerodynamic shape performance parameters and intake and exhaust system performance parameters, wherein the aircraft aerodynamic shape performance parameters are drag coefficient, lift coefficient and / or moment coefficient, and the intake and exhaust system performance parameters include inlet duct total pressure recovery coefficient and / or distortion coefficient, the inlet duct total pressure recovery coefficient is defined as the ratio of the average total pressure at the inlet duct outlet to the free flow total pressure, the distortion coefficient is composed of the sum of the circumferential non-uniformity of the total pressure and the surface average pulsation intensity, the circumferential non-uniformity of the total pressure is calculated based on the total pressure distribution of the inlet duct outlet cross section, and the surface average pulsation intensity is a time-varying random variable associated with the total pressure fluctuation on the inlet duct outlet plane.

9. A robust optimization method based on D-optimal and considering the influence of intake and exhaust according to claim 1, characterized in that: In step SS4, the construction process of the GPCE proxy model includes: SS41. Select the appropriate multivariate orthogonal polynomial basis function form according to the probability distribution type of the uncertain design variable; apply the effect sparsity principle and hyperbolic truncation method to limit the interaction order of the multivariate orthogonal polynomial basis function, retain the main effect and important low-order interaction effects; model the uncertainty quantification problem of the objective function and convert the random response of the objective function into Y ( D , ξ ) is expanded into a linear combination of orthogonal polynomial basis functions: in: D is the deterministic design variable vector, ξ =( ξ 1, ξ 2,..., ξ n )for n dimensional uncertain design variable vector; Ψ j ( ξ ) is the j The order basis function, c j ( D ) is the j The expansion coefficients of the order basis functions, the total number of basis functions is , n for ξ The dimension of p is the highest order of expansion; SS42. The gradient information of the objective function relative to the design variables is introduced to construct a gradient-enhanced GPCE agent model. The gradient expansion form of the objective function is: in, Designing variables for uncertainty ξ i The standard random variable form of μ i , σ i Respectively i Uncertain design variables ξ i The mean and standard deviation of i =1,2,… n , n for ξ The dimension of SS43. Constructing Augmented Linear Systems , [ Ψ ] is the augmented basis function matrix composed of basis functions and their derivatives, c is the expansion coefficient vector to be solved, Y is a vector consisting of the function value and gradient value of the sample point; the system of equations is based on N s The sampling points were constructed N s (1+ n ) equations, n for ξ The dimension of is the number of sample points in the small sample set, the basis function Ψ j Design variables for uncertainty ξ i The partial derivative of The standard random variables are calculated by the analytical expression of orthogonal polynomials. X i right ξ i The partial derivative of σ i The probability density function of the uncertain design variables is determined analytically and solved using the least squares method. Get the expansion coefficient c j ( D ); SS44. Based on the GPCE proxy model and the solved expansion coefficients, the statistical moments and mean of the objective function are calculated analytically. μ Y By the constant coefficient c 0( D ) is given and , the variance of the objective function satisfy , is the normalization factor of the basis function, and on this basis, the statistical moment is calculated for the deterministic design variables D Gradient and ; SS45. Calculate the normal root mean square deviation , verify the prediction accuracy of the GPCE proxy model, where Y i is the true value of the objective function, is the predicted value of the GPCE proxy model; according to the verification results, adjust the highest order of the orthogonal polynomial basis function in the GPCE proxy model p , truncation strategy and / or number of sampling points in small sample sets N s .

10. A robust optimization method based on D-optimality and considering the effects of intake and exhaust according to claim 1, characterized in that: In step SS5, during the iterative update process, a line search or trust region method is used to determine the appropriate step size to ensure the convergence and efficiency of the algorithm, and the constraint conditions are processed using a penalty function method or a barrier function method to ensure that the optimization results meet the design requirements; if the change in the objective function value is less than a set threshold, the gradient norm of the objective function relative to the design variable is less than a set threshold, the change in the design variable is less than a set threshold, the residuals of all constraints are less than the preset allowable error and / or the number of iterations reaches a preset maximum value, then the convergence criterion is considered to be met.

11. A robust optimization method based on D-optimality and considering the effects of intake and exhaust according to claim 1, characterized in that: In step SS6, the optimization result is verified by using the CFD numerical simulation method, and the optimized aircraft configuration is subjected to CFD calculation under deterministic conditions, and the calculation results are compared with the initial design to evaluate the optimization effect; the robustness evaluation adopts the Monte Carlo method to perform uncertainty analysis on the optimized aircraft configuration, evaluate the changes in its aerodynamic performance under different values ​​of uncertainty variables, and verify the robustness of the design; and in the process of robustness evaluation, analyze the coupling characteristics of the intake and exhaust system and the external flow field, including the changes in the total pressure recovery coefficient and / or distortion coefficient of the inlet duct, and the influence of the intake and exhaust system on the overall aerodynamic performance of the aircraft.

12. A computer program product, characterized in that: It includes computer instructions for executing the robust optimization method based on D optimality and considering the influence of intake and exhaust as described in any one of claims 1 to 11.

13. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the robust optimization method based on D optimality and taking into account the influence of intake and exhaust as described in any one of claims 1 to 11 is implemented.

Images