A launch vehicle aerodynamic force and thermal coupling multi-objective optimization design method
By employing a multi-objective optimization design method that couples aerodynamics and thermodynamics of launch vehicles, and utilizing surrogate models and global optimization algorithms, the problems of long time consumption and low efficiency in the aerodynamic shape design of launch vehicles were solved, achieving a globally optimal solution and efficient design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2023-07-06
- Publication Date
- 2026-07-10
AI Technical Summary
Existing aerodynamic design of launch vehicles is time-consuming, inefficient, and difficult to obtain the global optimal solution. Traditional methods consume a lot of manpower and resources and are difficult to achieve optimal overall benefits.
A multi-objective optimization design method for launch vehicle aerodynamic-thermal coupling is adopted, which includes determining the design objectives and constraints, constructing a surrogate model, optimizing the design using a global optimization algorithm and a point-addition criterion, and finding the Pareto leading edge of the launch vehicle aerodynamic design by combining the surrogate model with the global optimization algorithm.
It achieves efficient and refined aerodynamic shape design for launch vehicles, balancing optimization efficiency and overall performance, reducing manpower and material resource consumption, and obtaining the optimal global solution.
Smart Images
Figure CN116894403B_ABST
Abstract
Description
Technical Field
[0001] This invention presents a multi-objective optimization design method for aerodynamic-thermal coupling of launch vehicles, belonging to the field of launch vehicle shape design. Background Technology
[0002] Aerodynamic design is a crucial aspect of launch vehicle overall design. The aerodynamic shape of a launch vehicle significantly influences its flight performance. Key factors considered in the overall launch vehicle design, such as aerodynamic drag, aerodynamic heat, and volumetric efficiency, are all related to the launch vehicle's shape. It can be said that aerodynamic shape design is the soul of launch vehicle design. However, as a wide-speed-range, large-spacecraft launched from the ground to space, the launch vehicle operates in a complex and variable flight environment, and its missions require high safety. Therefore, the aerodynamic shape design of launch vehicles is becoming increasingly refined, ultimately resulting in a globally optimal solution rather than a locally feasible one. Traditional methods for launch vehicle shape design mostly involve iterative design after determining the initial shape, conducting extensive wind tunnel tests and numerical calculations, until an aerodynamic shape that meets the overall design requirements is obtained. While this method can yield a feasible solution, the human, material, and financial resources required increase dramatically with increasing design refinement, and it is unlikely to ultimately achieve a globally optimal solution, thus failing to achieve optimal overall efficiency. Summary of the Invention
[0003] This invention addresses the shortcomings of existing launch vehicle aerodynamic shape design technologies, such as long processing time, low efficiency, and difficulty in obtaining the global optimal solution, by proposing a multi-objective optimization design method for launch vehicle aerodynamic-thermal coupling.
[0004] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:
[0005] A multi-objective optimization design method for aerodynamic-thermal coupling of launch vehicles includes the following steps:
[0006] Step 1: Define the aerodynamic optimization design problem of the launch vehicle, including the design objectives and constraints;
[0007] Step 2: Determine the design variables based on the launch vehicle's geometric shape model;
[0008] Step 3: Obtain sample points by sampling in the design space;
[0009] Step 4: Import the sample points into the numerical calculation model to obtain the aerodynamic performance parameters corresponding to each sample point;
[0010] Step 5: Use the sample points and aerodynamic performance parameters to construct a surrogate model to replace the numerical calculation model;
[0011] Step 6: Check the prediction accuracy of the surrogate model. If the accuracy does not meet the requirements, use the point addition criterion to increase the sample points and rebuild the surrogate model until the prediction accuracy meets the requirements.
[0012] Step 7: Use a global optimization algorithm to optimize the surrogate model and obtain the Pareto leading edge of the surrogate model, which is the Pareto leading edge of the launch vehicle's aerodynamic design parameters.
[0013] The aerodynamic optimization design problem of the launch vehicle determined in step 1 includes the design objectives and constraints.
[0014] The design objectives are to minimize the drag coefficient of the launch vehicle booster and the peak value of the stagnation point heat flux; the constraints are that the position of the launch vehicle's pressure core remains unchanged, and the surface area of the booster tail fin is reduced by more than 30% compared to the initial shape.
[0015] Optionally, the design variables include: the geometric parameters of the booster head and the geometric parameters of the booster tail fin; the values of the design variables constitute the launch vehicle optimization design space.
[0016] In step 3, the optimal Latin hypercube sampling method is used to sample in the launch vehicle optimization design space to obtain sample points.
[0017] In step 5, optionally, the surrogate model is a Kriging model, a response surface model, or a radial basis function neural network (RBN) model; wherein the kernel function of the Kriging model is a Gaussian function, the response surface model is a second-order response surface, and the smoothing operator coefficient of the RBN model is 0.1. Different surrogate models allow for different addition criteria: the Kriging model can use one of the following addition criteria: MP addition criterion, EI addition criterion, LCB addition criterion, PI addition criterion, and RMSE addition criterion; the response surface model and the RBN model can use one of the following addition criteria: MP addition criterion and RMSE addition criterion.
[0018] The MP addition criterion is the minimum value criterion of the objective function, and the sample points added are the minimum values in the current surrogate model;
[0019] The EI addition criterion is that the added sample point is the one with the largest EI value among all current sample points. The formula for calculating the EI value is as follows:
[0020]
[0021] The LCB (Lower Scale Bound) criterion is a statistical minimum criterion. It adds the sample point with the smallest LCB value among all current sample points. The formula for calculating the LCB value is as follows:
[0022]
[0023] In the formula, A is a constant defined by the user.
[0024] The PI addition criterion is to maximize the probability increase. The sample points added are those with the largest PI values in the current surrogate model. The formula for calculating the PI value is as follows:
[0025]
[0026] Typically, T takes the value of: T = y min -k|y min |,k>0;
[0027] The RMSE addition criterion is the maximum root mean square error criterion, which adds the sample point with the largest RMSE value among all current sample points. The formula for calculating the RMSE value is as follows:
[0028]
[0029] In the formula, y i This represents the aerodynamic performance parameters obtained from the numerical calculation model using the actual values, i.e., the sample points. The predicted value represents the aerodynamic performance parameter obtained by fitting the sample points using a surrogate model, y min Φ is the minimum predicted value among all current sample points, Φ is the distribution function of the standard normal distribution, and s(x0) is the standard deviation at x.
[0030] The metric used in step 6 to determine the prediction accuracy of the surrogate model is: R 2 RMSE, ME;
[0031] R 2 It is a measure of the model's fit, and its calculation formula is:
[0032]
[0033] RMSE is the root mean square error, and the calculation formula has been given in claim 7;
[0034] ME is the maximum error, and its calculation formula is as follows:
[0035]
[0036] In the formula, y i This represents the aerodynamic performance parameters obtained from the numerical calculation model using the actual values, i.e., the sample points. This represents the predicted values, i.e., the aerodynamic performance parameters obtained by fitting the sample points using a surrogate model. max() represents the maximum value within the parentheses.
[0037] The R-value of the resulting proxy model is calculated using a test set obtained through random sampling. 2When RMSE and ME all meet the required values, it indicates that the surrogate model has achieved the required accuracy.
[0038] The global optimization algorithm used is a non-dominated sorting genetic algorithm with an elitist strategy; the algorithm parameters include: population size, maximum number of generations, threshold for determining if optimization is stuck, encoding method, etc.
[0039] The advantages of this invention compared to the prior art are:
[0040] This invention provides a multi-objective optimization design for launch vehicle aerodynamic-thermal coupling based on a surrogate model, comprising the following steps: first, defining the aerodynamic optimization design problem of the launch vehicle, including design objectives and constraints; determining design variables based on the launch vehicle's geometric shape model; sampling points in the design space; importing the sample points into a numerical calculation model to obtain the aerodynamic performance parameters corresponding to each sample point; constructing a surrogate model to replace the numerical calculation model using the sample points and aerodynamic performance parameters; checking the prediction accuracy of the surrogate model, and if the accuracy does not meet the requirements, adding sample points using the point addition criterion to reconstruct the surrogate model until the prediction accuracy meets the requirements; and using a global optimization algorithm to optimize the surrogate model to obtain the Pareto leading edge of the surrogate model, i.e., the Pareto leading edge of the launch vehicle's aerodynamic design parameters. This method introduces an optimization design method based on a surrogate model and point addition criteria into the aerodynamic shape design of launch vehicles, ensuring both optimization efficiency and the globality of the optimization results, achieving a highly reliable and refined aerodynamic shape design for launch vehicles. Attached Figure Description
[0041] Figure 1 A flowchart provided for the invention.
[0042] Figure 2 This is a schematic diagram of the parametric geometric shape mathematical model of a launch vehicle. Detailed Implementation
[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0044] Example
[0045] In the current embodiment, the aerodynamic optimization design problem of the launch vehicle is first determined, including the design objectives and constraints; design variables are determined based on the geometric shape model of the launch vehicle; sample points are obtained by sampling in the design space; the sample points are imported into the numerical calculation model to obtain the aerodynamic performance parameters corresponding to each sample point; a surrogate model is constructed using the sample points and aerodynamic performance parameters to replace the numerical calculation model; the prediction accuracy of the surrogate model is checked, and if the accuracy does not meet the requirements, sample points are added using the point addition criterion to reconstruct the surrogate model until the prediction accuracy meets the requirements; a global optimization algorithm is used to optimize the surrogate model to obtain the Pareto leading edge of the surrogate model, which is the Pareto leading edge of the launch vehicle aerodynamic design parameters. The flowchart is as follows: Figure 1 As shown, it specifically includes:
[0046] The aerodynamic optimization design problem of the launch vehicle is defined, including: design objectives and constraints. Here, the design objectives are to minimize the drag coefficient of the launch vehicle boosters and the peak heat flux at the stagnation point of the booster nose cone. The constraints are that the overall pressure center position of the launch vehicle remains unchanged and the surface area of the booster tail fins is reduced by 30% compared to the initial shape. The specific functions are as follows:
[0047] min C d Q ws
[0048] stX p =X pinitial
[0049] Area ≤ 0.7 × Area initial
[0050] Among them, C d Q is the drag coefficient of the launch vehicle booster. ws For the peak heat flux at the stagnation point of the booster nose cone, X p This refers to the overall pressure center position of the launch vehicle, Area refers to the surface area of the booster tail fin, and the subscript initial represents the initial shape.
[0051] In the embodiment, the geometric shape model of the launch vehicle is as follows: Figure 2 As shown, the design parameters are listed in the table below:
[0052] Table 1 Design parameters for the aerodynamic optimization design problem of launch vehicles
[0053] serial number Design variable name Remark 1 R booster head cone top radius 2 A booster head cone semi-cone angle 3 SL booster tail fin span 4 RCL booster tail fin root chord 5 TCL booster tail fin tip chord 6 LEA booster tail fin leading edge sweep angle 7 RCW booster tail fin root width 8 TCW booster tail fin tip width
[0054] Sample points are obtained by sampling within the design space: To ensure that the surrogate model established with a limited number of sample points can reflect the information of the launch vehicle's optimized design space to the greatest extent, the optimal Latin hypercube sampling method is used for sampling. Latin hypercube sampling is a stratified random sampling method with good space-filling ability, but as the number of design variables increases, some design space may still be lost. The optimal Latin hypercube sampling method improves the uniformity of Latin hypercube sampling, making the distribution of sample points more uniform and balanced.
[0055] After obtaining the sample points, the geometric shape model of the launch vehicle corresponding to the sample points is constructed using 3D modeling software such as Solidworks. The generated model is then imported into Pointwise software for mesh generation. After the mesh generation is completed, it is exported as a calculation example. The data calculation model is used to perform calculations to obtain the corresponding aerodynamic performance parameters.
[0056] After obtaining the sample points and corresponding aerodynamic performance parameters, the Kriging model was selected as the surrogate model for construction, with a Gaussian kernel function chosen. The R-value of the resulting surrogate model was calculated using a randomly sampled test set. 2 When RMSE and ME all meet the required values, it indicates that the surrogate model's accuracy meets the requirements. If the accuracy does not meet the requirements, the EI addition criterion is used to increase the sample points and reconstruct the Kriging model until the prediction accuracy meets the requirements. The non-dominated sorting genetic algorithm with elitist strategy is used in combination with the Kriging model constructed above to optimize the launch vehicle's shape within the constraints and obtain the optimal launch vehicle shape parameters. The parameter settings of the non-dominated sorting genetic algorithm with elitist strategy are as follows: population size: 40, maximum number of generations: 500, threshold for judging stagnation in optimization: 1e-10, encoding method: real integer mixed encoding.
[0057] This example uses an aerodynamic-thermal coupled multi-objective optimization design method to design the aerodynamic shape of a launch vehicle. The surrogate model, as a simple mathematical approximation model to replace expensive numerical calculation models in engineering problems, combined with a global optimization algorithm and a point-addition criterion, can balance global applicability and optimization efficiency. Introducing it into the aerodynamic design of launch vehicles, compared to traditional aerodynamic design methods, can effectively reduce manpower, material resources, and time consumption while achieving the engineering goals of drag reduction and heat dissipation.
[0058] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.
Claims
1. A multi-objective optimization design method for aerodynamic-thermal coupling of launch vehicles, characterized in that, Includes the following steps: Step 1: Define the aerodynamic optimization design problem of the launch vehicle, including the design objectives and constraints; Step 2: Determine the design variables based on the launch vehicle's geometric shape model; Step 3: Obtain sample points by sampling in the design space; Step 4: Import the sample points into the numerical calculation model to obtain the aerodynamic performance parameters corresponding to each sample point; Step 5: Use the sample points and aerodynamic performance parameters to construct a surrogate model to replace the numerical calculation model; Step 6: Check the prediction accuracy of the surrogate model. If the accuracy does not meet the requirements, use the point addition criterion to increase the sample points and rebuild the surrogate model until the prediction accuracy meets the requirements. Step 7: Use a global optimization algorithm to optimize the surrogate model and obtain the Pareto leading edge of the surrogate model, which is the Pareto leading edge of the launch vehicle's aerodynamic design parameters. The surrogate model that can be used in step 5 is one of the following models: Kriging model, response surface model, or radial basis function neural network model; wherein the kernel function of the Kriging model is a Gaussian function, the response surface model is a second-order response surface, and the smoothing operator coefficient of the radial basis function neural network model is 0.
1. Depending on the proxy model used in step 5, the available point-addition criteria vary: the Kriging model can use one of the following point-addition criteria: MP point-addition criterion, EI point-addition criterion, LCB point-addition criterion, PI point-addition criterion, RMSE point-addition criterion. Response surface models and radial basis function neural network models can use one of the following addition criteria: MP addition criterion and RMSE addition criterion; The MP addition criterion is the minimum value criterion of the objective function, and the sample points added are the minimum values in the current surrogate model; The EI addition criterion is that the added sample point is the one with the largest EI value among all current sample points. The formula for calculating the EI value is as follows: ； The LCB (Lower Scale Bound) criterion is a statistical minimum criterion. It adds the sample point with the smallest LCB value among all current sample points. The formula for calculating the LCB value is as follows: ； In the formula, A is a constant defined by the user. The PI addition criterion is to maximize the probability increase. The sample points added are those with the largest PI values in the current surrogate model. The formula for calculating the PI value is as follows: ； Typically, T takes the following values: ; The RMSE addition criterion is the maximum root mean square error criterion, which adds the sample point with the largest RMSE value among all current sample points. The formula for calculating the RMSE value is as follows: ； In the formula, This represents the aerodynamic performance parameters obtained from the numerical calculation model using the actual values, i.e., the sample points. This indicates that the predicted values are the aerodynamic performance parameters obtained by fitting the sample points using a surrogate model. It is the minimum value among all predicted values for all current sample points. The distribution function of the standard normal distribution. Let x be the standard deviation at x.
2. The aerodynamic-thermal coupling multi-objective optimization design method for launch vehicles according to claim 1, characterized in that: In step 1, the design objectives are to minimize the drag coefficient of the launch vehicle booster and the peak value of the stagnation point heat flux; the constraints are that the position of the launch vehicle's pressure core remains unchanged, and the surface area of the booster tail fin is reduced by more than 30% compared to the initial external surface area.
3. The aerodynamic-thermal coupling multi-objective optimization design method for launch vehicles according to claim 1, characterized in that: In step 2, the design variables include: the geometric parameters of the booster head and the geometric parameters of the booster tail fin; the values of the design variables constitute the launch vehicle optimization design space.
4. The multi-objective optimization design method for aerodynamic-thermal coupling of launch vehicles according to claim 1, characterized in that: In step 3, the optimal Latin hypercube sampling method is used to sample in the launch vehicle optimization design space to obtain sample points.
5. The aerodynamic-thermal coupling multi-objective optimization design method for launch vehicles according to claim 1, characterized in that: The metric used in step 6 to determine the prediction accuracy of the surrogate model is: R 2 RMSE, ME; R 2 It is a measure of the model's fit, and its calculation formula is: ； RMSE stands for Root Mean Square Error. ME is the maximum error, and its calculation formula is as follows: ； In the formula, This represents the aerodynamic performance parameters obtained from the numerical calculation model using the actual values, i.e., the sample points. This indicates that the predicted values are the aerodynamic performance parameters obtained by fitting the sample points using a surrogate model. Indicates the maximum value within the parentheses; The R-value of the resulting proxy model is calculated using a test set obtained through random sampling. 2 When RMSE and ME all meet the required values, it indicates that the surrogate model has achieved the required accuracy.
6. The multi-objective optimization design method for aerodynamic-thermal coupling of launch vehicles according to claim 1, characterized in that: The global optimization algorithm used is a non-dominated sorting genetic algorithm with an elitist strategy; the algorithm parameters include: population size and iteration termination condition.