Method and apparatus for designing a baseline flow field based on multi-objective subproblem optimization

Abstract

The application relates to an internal contraction reference flow field design method and device based on multi-target sub-problem optimization. The method converts an internal turning inlet reference flow field design problem into a constraint optimization problem, optimizes through construction of an agent model, and provides multiple update points in one iteration through multi-target sub-problems. Multi-target sub-problem optimization includes finding optimal solutions in a positioning feasible region and a feasible region. When the positioning feasible region is positioned, a first multi-target optimization sub-problem constructed by a feasible probability function, a maximum violation degree and a constraint variance is solved to provide multiple update points, and the efficiency and capacity of the positioning feasible region are improved. When the feasible region is positioned, a second multi-target optimization sub-problem constructed by two CEI items and a constraint variance is solved to provide multiple update points, and the resolution of the constraint boundary is improved, which is beneficial to searching the constraint boundary. The method can effectively improve the optimization design efficiency of the reference flow field while ensuring the optimization design precision of the reference flow field.

Description

Technical Field

[0001] This application relates to the field of engineering design technology, and in particular to a design method and apparatus for an internally contracting reference flow field based on multi-objective sub-problem optimization. Background Technology

[0002] Hypersonic vehicles, characterized by high speed, high maneuverability, and long range, have received increasing attention from the academic community and major powers in recent years. The scramjet engine, as the propulsion system of hypersonic vehicles, is crucial to their development. A scramjet engine typically consists of four components: an inlet, an isolation section, a combustion chamber, and a tailpipe. The inlet, through its own compression structure, slows and pressurizes the high-speed airflow, providing the combustion chamber with the required flow rate and quality of air to ensure stable and reliable engine operation. Therefore, designing an efficient inlet is of great significance.

[0003] Scramjet engine inlets include axisymmetric inlets, two-dimensional inlets, three-dimensional side-pressure inlets, and internal rotation inlets. Among these, internal rotation inlets have advantages such as high compression efficiency, low total pressure loss, small wetted area, and full flow capture, making them an important inlet design. The design of internal rotation inlets typically involves the following steps: first, designing a contracting reference flow field; then, designing the projected flow profile according to aircraft integration requirements; finally, performing streamline tracing on the reference flow field using the projected flow profile and trunculating the traced streamlines at the leading shock wave surface to obtain the internal rotation inlet profile. Therefore, the performance of the reference flow field largely determines the performance of the internal rotation inlet, making the design of a high-performance reference flow field based on overall requirements a crucial step in internal rotation inlet design.

[0004] The "two-wave, three-zone" morphology of the inward-contracting reference flow field is a widely studied type of reference flow field. It consists of an axisymmetric outer compression surface and a central volume. The supersonic incoming flow is disturbed by the outer compression surface, forming a leading-edge conical shock wave. Then, under the influence of the inward-contracting outer compression surface, a series of isentropic compression waves are formed. These isentropic compression waves and the leading-edge shock wave converge and are reflected by the central volume, forming a reflected shock wave. The reference flow field compresses the incoming flow through the leading-edge shock wave, the isentropic compression wave, and the reflected shock wave. Currently, optimization designs for this reference flow field often utilize intelligent optimization algorithms. However, using intelligent optimization algorithms requires thousands of CFD simulations, each taking tens of minutes, resulting in a total optimization process that can take several days. Even with parallel computing on multi-core computers, the computational and time costs remain significant. Therefore, existing optimization methods for inward-contracting reference flow fields suffer from high computational and time costs and low optimization efficiency. Summary of the Invention

[0005] Therefore, it is necessary to provide a design method and apparatus for an internally contracting reference flow field based on multi-objective sub-problem optimization to address the aforementioned technical problems.

[0006] A design method for an internally contracting reference flow field based on multi-objective sub-problem optimization, the method comprising:

[0007] A coordinate system is established within the meridional plane of the reference flow field. The configuration of the reference flow field is parametrically designed in the coordinate system to determine the design space. The design space includes design parameters and their corresponding value ranges.

[0008] Based on the preset design requirements, the optimization design problem of the reference flow field is determined; the optimization design problem of the reference flow field includes: design objectives, design variables, constraints, and design conditions.

[0009] Based on the design space, the Latin hypercube sampling method is used to obtain a preset number of initial sampling points.

[0010] Use the initial sample point as the current sample point and set the number of iterations to 1.

[0011] Using CAD software, a reference flow field configuration corresponding to the current sample point is generated. Then, using mesh generation software, a mesh for the reference flow field is generated based on the reference flow field configuration.

[0012] For each current sample point, a CFD simulation is performed on the grid of the reference flow field.

[0013] The current sample point and the simulation response value are added to the sample library to obtain the current sample library.

[0014] Based on the current sample library, construct a Kriging proxy model with optimization objectives and constraints.

[0015] Determine whether there is a feasible solution that satisfies the constraints among all current sample points. When there is no feasible solution that satisfies the constraints, construct a first multi-objective optimization sub-problem based on the Kriging surrogate model, consisting of a feasible probability function, a maximum default degree, and a constraint variance function. Use the first type of point addition method to obtain multiple update points based on the Pareto solution set obtained by solving the first multi-objective optimization sub-problem.

[0016] When a feasible solution that satisfies the constraints exists, a second multi-objective optimization subproblem consisting of two CEI terms and a constraint variance function is constructed based on the Kriging surrogate model. The second type of point addition method is used to obtain multiple update points based on the Pareto solution set obtained by solving the second multi-objective optimization subproblem.

[0017] The current sample point is updated to the update point, the iteration count is incremented by 1, and the iteration continues until the iteration count is greater than the preset maximum iteration count, thus obtaining the optimal design variables for the internal contraction reference flow field.

[0018] An apparatus for designing an internally contracting reference flow field based on multi-objective sub-problem optimization, the apparatus comprising:

[0019] The parametric design module is used to establish a coordinate system in the meridional plane of the reference flow field, perform parametric design on the configuration of the reference flow field in the coordinate system, and determine the design space; the design space includes design parameters and their corresponding value ranges.

[0020] The benchmark flow field optimization design problem determination module is used to determine the benchmark flow field optimization design problem based on preset design requirements. The benchmark flow field optimization design problem includes: design objective, design variables, constraints, and design conditions.

[0021] The initial sampling module is used to obtain a preset number of initial sampling points based on the design space using the Latin hypercube sampling method; the initial sample points are used as the current sample points, and the number of iterations is set to 1.

[0022] The Kriging surrogate model construction module is used to generate a baseline flow field configuration corresponding to the current sample point using CAD software, and to generate a mesh of the baseline flow field using mesh generation software based on the baseline flow field configuration; to perform CFD simulation calculations on the mesh of the baseline flow field corresponding to each current sample point; to add the current sample point and the simulation response value to the sample library to obtain the current sample library; and to construct a Kriging surrogate model with optimization objectives and constraints based on the current sample library.

[0023] The feasible region localization module is used to determine whether there is a feasible solution that satisfies the constraints among all current sample points. When there is no feasible solution that satisfies the constraints, a first multi-objective optimization sub-problem consisting of a feasible probability function, a maximum default degree, and a constraint variance function is constructed based on the Kriging surrogate model. Based on the Pareto solution set obtained by solving the first multi-objective optimization sub-problem, a first type of point addition method is used to obtain multiple update points.

[0024] The module for finding the optimal solution in the feasible region is used to construct a second multi-objective optimization subproblem based on the Kriging surrogate model when a feasible solution that satisfies the constraints exists. The subproblem consists of two CEI terms and a constraint variance function. The second type of point addition method is used to obtain multiple update points based on the Pareto solution set obtained by solving the second multi-objective optimization subproblem.

[0025] The optimization result determination module is used to update the current sample point as the update point, increment the iteration count by 1, and continue iterating until the iteration count is greater than the preset maximum iteration count, thereby obtaining the optimal design variables for the internal contraction reference flow field.

[0026] The aforementioned method and apparatus for designing an inward-contracting reference flow field based on multi-objective sub-problem optimization transforms the design problem of the inward-contracting air intake reference flow field into a constrained optimization problem. By constructing a surrogate model for optimization, the number of simulation evaluations of the reference flow field can be significantly reduced. Furthermore, by utilizing the multi-objective sub-problem to provide multiple update points in a single iteration, the number of optimization iterations can be reduced. On the other hand, the multi-objective sub-problem surrogate model optimization includes the process of locating feasible regions and finding the optimal solution within them. When locating feasible regions, solving the first multi-objective optimization sub-problem constructed from the feasible probability function, maximum default degree, and constraint variance provides multiple update points, improving the efficiency and capability of locating feasible regions. When finding the optimal solution within feasible regions, solving the second multi-objective optimization sub-problem constructed from two CEI terms and constraint variance provides multiple update points, enabling the exploration and mining of feasible regions and improving the resolution of constraint boundaries, which is beneficial for searching constraint boundaries. This method can effectively improve the optimization design efficiency of the reference flow field while ensuring the accuracy of the design. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating an internal contraction baseline flow field design method based on multi-objective sub-problem optimization in one embodiment.

[0028] Figure 2 A schematic diagram of the contraction reference flow field within the "two waves and three zones" in another embodiment;

[0029] Figure 3 This is a schematic diagram of the reference flow field parameterization in another embodiment;

[0030] Figure 4 This is a flowchart illustrating the design method for an internally contracting reference flow field based on multi-objective sub-problem optimization in another embodiment;

[0031] Figure 5 This is an optimized convergence process in another embodiment;

[0032] Figure 6 The flow field Mach number contour plot is shown for the optimal reference flow field in another embodiment;

[0033] Figure 7 This is a structural block diagram of an internal contraction reference flow field design device based on multi-objective sub-problem optimization in one embodiment. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0035] In one embodiment, such as Figure 1 As shown, a design method for an internally contracting reference flow field based on multi-objective sub-problem optimization is provided. This method includes the following steps:

[0036] Step 100: Establish a coordinate system in the meridional plane of the reference flow field, perform parametric design of the reference flow field configuration in the coordinate system, and determine the design space; the design space includes design parameters and their corresponding value ranges.

[0037] Specifically, the schematic diagram of the contraction reference flow field within the "two waves and three zones" is as follows: Figure 2 As shown, a coordinate system is established in the meridional plane of the reference flow field, with the origin being the center of the inlet section of the axisymmetric reference flow field, the x-axis being the axis of symmetry of the reference flow field, and the y-axis being perpendicular to the x-axis and pointing towards the generatrix of the outer wall.

[0038] The baseline flow field configuration is parametrically designed. The outer compression wall consists of two cubic curve segments, and the central body consists of straight segments and cubic curve segments, as shown below. Figure 3 As shown. The entire configuration is controlled by 6 points, with point 1 being the starting point of the outer wall surface, and its coordinates are... Point 2 is the starting point of internal compression, with coordinates as follows: Point 3 is the endpoint of the outer wall surface, with coordinates as follows: Point 4 is the starting point of the central body, with coordinates of... Point 5 represents the lip position, with coordinates as follows: Point 6 is the endpoint of the central body, with coordinates of... The baseline flow field configuration is determined by 11 parameters, namely: inlet radius... Minimum radius of the central body Maximum radius of the central body Total length lip flow position Inlet compression angle Lower corner corners of the lips Exit angle Total shrinkage ratio and internal contraction ratio When the 11 parameters are determined, the ordinates of points 2 and 3 are calculated using the definitions of the total shrinkage ratio and the internal shrinkage ratio, i.e. , The shape of a cubic curve is obtained by substituting its endpoint coordinates and endpoint slopes into the expression. The parameters are obtained from the differential equations. A schematic diagram of the reference flow field parameterization is shown below. Figure 3 As shown.

[0039] Step 102: Determine the optimization design problem of the reference flow field according to the preset design requirements; the optimization design problem of the reference flow field includes: design objectives, design variables, constraints, and design conditions.

[0040] Specifically, this embodiment specifies the design objective as maximizing the total pressure recovery coefficient; there are three constraints: the exit Mach number is less than 3, and the distance between the reflection point of the leading shock wave in the central body and the lip. (See Figure 3 (less than) And calculate convergence; the design variable is the inlet compression angle. , lower corner lip corners Exit Angle Minimum radius of the central body Total shrinkage ratio and internal contraction ratio The range of values ​​for the design variables is , , , , , , The sizes of the remaining four variables are , , , The design operating conditions are Mach number 6 and altitude 25 kilometers.

[0041] The design variable dimension is given based on the number of design variables. In this embodiment, there are 7 design variables, therefore, the design variable dimension d=7.

[0042] Step 104: Based on the design space, use the Latin hypercube sampling method to obtain a preset number of initial sampling points.

[0043] Specifically, the number of initial sampling points is determined based on the baseline flow field optimization design problem and computational resources. As a preferred option, the number of initial sample points is n=35.

[0044] Step 106: Use the initial sample point as the current sample point and set the iteration count to 1.

[0045] Step 108: Using CAD software, generate the reference flow field configuration corresponding to the current sample point, and using mesh generation software, generate the mesh of the reference flow field based on the reference flow field configuration.

[0046] Step 110: Perform CFD simulation calculations on the grid of the reference flow field corresponding to each current sample point.

[0047] Step 112: Add the current sample point and the response value obtained from the simulation to the sample library to obtain the current sample library; based on the current sample library, construct the Kriging surrogate model of the optimization objective and constraints.

[0048] Step 114: Determine whether there is a feasible solution that satisfies the constraints among all current sample points. If there is no feasible solution that satisfies the constraints, construct a first multi-objective optimization sub-problem based on the Kriging surrogate model, consisting of a feasible probability function, a maximum default degree, and a constraint variance function. Based on the Pareto solution set obtained by solving the first multi-objective optimization sub-problem, use the first type of point addition method to obtain multiple update points.

[0049] Specifically, when locating feasible regions, a first multi-objective optimization sub-problem, constructed from the feasible probability function, the maximum default degree, and the constraint variance, provides multiple update points. The feasible probability function possesses both local and global search capabilities; the maximum default degree provides gradient information about the constraints, facilitating the search towards the feasible region; maximizing the constraint variance improves the accuracy of the constraint model. Therefore, this multi-objective sub-problem can simultaneously perform global exploration and local mining of constraints, providing multiple update points that balance global exploration and local mining, thereby efficiently locating feasible regions.

[0050] Step 116: When a feasible solution that satisfies the constraints exists, based on the Kriging surrogate model, a second multi-objective optimization subproblem consisting of two CEI terms and a constraint variance function is constructed. Based on the Pareto solution set obtained by solving the second multi-objective optimization subproblem, the second type of point addition method is used to obtain multiple update points.

[0051] Specifically, as a preferred option, the number of update points in steps 114 and 116 is determined by the baseline flow field optimization design problem and computational resources. As a preferred option, the number of update points q=3.

[0052] When searching for the optimal solution within the feasible region, a second multi-objective optimization subproblem, constructed from two CEI terms and constraint variance, is used to provide multiple update points. The two CEI terms enable global exploration and local mining of the feasible region; minimizing the constraint variance improves the resolution of the constraint boundaries, facilitating the search within those boundaries.

[0053] Step 118: Update the current sample point to the update point, increment the iteration count by 1, and continue iterating until the iteration count is greater than the preset maximum iteration count, thus obtaining the optimal design variables for the internal contraction reference flow field.

[0054] Specifically, the maximum number of iterations is preset as an optimal value. .

[0055] In the aforementioned design method for the inward contraction reference flow field based on multi-objective sub-problem optimization, the method transforms the design problem of the inward-turning inlet reference flow field into a constrained optimization problem. By constructing a surrogate model for optimization, the number of simulation evaluations of the reference flow field can be significantly reduced. Furthermore, by utilizing the multi-objective sub-problem to provide multiple update points in a single iteration, the number of optimization iterations can be reduced. On the other hand, the multi-objective sub-problem surrogate model optimization includes the process of locating feasible regions and finding the optimal solution within them. When locating feasible regions, solving the first multi-objective optimization sub-problem constructed from the feasible probability function, maximum default degree, and constraint variance provides multiple update points, improving the efficiency and capability of locating feasible regions. When finding the optimal solution within feasible regions, solving the second multi-objective optimization sub-problem constructed from two CEI terms and constraint variance provides multiple update points, enabling the exploration and mining of feasible regions and improving the resolution of constraint boundaries, which is beneficial for searching constraint boundaries. This method can effectively improve the optimization design efficiency of the reference flow field while ensuring the accuracy of the reference flow field optimization design.

[0056] In one embodiment, step 100 includes: establishing a coordinate system in the meridional plane of the reference flow field, with the origin of the coordinate system being the center of the inlet section of the axisymmetric reference flow field, the x-axis being the axis of symmetry of the reference flow field, and the y-axis being perpendicular to the x-axis and pointing towards the generatrix of the outer wall; parametrically designing the configuration of the reference flow field, wherein the outer compression wall is composed of two cubic curves, the central body is composed of straight line segments and cubic curves, and the configuration of the reference flow field is determined by 11 design parameters, including: inlet radius, minimum radius of the central body, maximum radius of the central body, total length, lip flow direction position, inlet compression angle, downwash angle, lip angle, outlet angle, total contraction ratio, and internal contraction ratio.

[0057] In one embodiment, the design objectives in step 102 include: total pressure recovery coefficient and outlet airflow uniformity; the constraints include: outlet Mach number, pitching moment, and flow coefficient; the design condition is the cruise state of a hypersonic vehicle; and the design variables are selected from the design parameters based on preset design requirements, optimization objectives, and constraints. Preferably, the design variables include: inlet compression angle, downwash angle, lip angle, outlet angle, minimum radius of the central body, total contraction ratio, and internal contraction ratio.

[0058] In one embodiment, the expression for the first multi-objective optimization subproblem in step 114 is:

[0059] (1)

[0060] Where PS represents the Pareto solution set of a multi-objective optimization problem; Let it be a feasible probability function; For the first i A constraint at point xThe predicted variance at that location Representing unknown points x The maximum degree of default. Representing unknown points x The maximum degree of default; For the i-th constraint at the unknown point x The degree of default at the location. The definition is as follows:

[0061] (2)

[0062] in, Indicates the number of constraints; express Positive integers above; Indicates an unknown observation point; Indicates the first One constraint For the first i A constraint at point x The predicted value at that location; Indicates the first The probability of satisfying a constraint; Let represent the normal distribution function. Solve this subproblem using a mature multi-objective optimization algorithm.

[0063] In one embodiment, the first type of point addition method in step 114 includes: deleting duplicate points in the Pareto solution set of the first multi-objective optimization sub-problem or points that are duplicates of the current sample point; duplicate points refer to points in the Pareto solution set of the first multi-objective optimization sub-problem where the Euclidean distance between two points is less than a preset value; points that are duplicates of the current sample point refer to points in the Pareto solution set of the first multi-objective optimization sub-problem where the Euclidean distance between two points and the current sample point is less than a preset value; normalizing the Pareto front of the first multi-objective optimization sub-problem and clustering the results using the K-means clustering method to obtain multiple groups, the number of groups being the same as the number of points to be added; and selecting the point with the largest feasible probability function value in each group as the update point.

[0064] Specifically, the number of clusters is the same as the number of points added, and the number of points added is the same as the number of update points. As a preferred option, the number of update points is q=3.

[0065] In one embodiment, the expression for the second multi-objective optimization sub-problem in step 116 is:

[0066] (3)

[0067] Where PS represents the Pareto solution set of a multi-objective optimization problem; For the first i A constraint at pointx The predicted variance at the location; , , Let be the feasible probability function. and These are two separate aspects: local mining and global exploration of EI functions. , ,in, This is the feasible optimal solution in the current sample set. This represents the probability density function of a normal distribution. and The objective function at points x The predicted value and prediction variance at the location.

[0068] In one embodiment, the second type of point addition method in step 116 includes: deleting duplicate points in the Pareto solution set of the second multi-objective optimization sub-problem or points that are duplicates of the current sample point; duplicate points refer to points in the Pareto solution set of the second multi-objective optimization sub-problem where the Euclidean distance between two points is less than a preset value; points that are duplicates of the current sample point refer to points in the Pareto solution set of the second multi-objective optimization sub-problem where the Euclidean distance between two points and the current sample point is less than a preset value; normalizing the Pareto front of the second multi-objective optimization sub-problem, and clustering the results using the K-means clustering method to obtain multiple groups, the number of groups being the same as the number of points to be added; selecting the points in each group that minimize the lower confidence bound function to form the update point set; the lower confidence bound function is:

[0069] (4)

[0070] in, and The objective function at points x Predicted values ​​and prediction variance at the location, The coefficient is a factor that decreases continuously with the number of iterations. For the number of iterations, This represents the maximum number of iterations.

[0071] Specifically, when selecting the update point from the Pareto solution set of the second multi-objective optimization subproblem, the coefficients are used... a The changes in these parameters cause the characteristics of the selected points to gradually transition from global exploration to local discovery as optimization progresses. This allows the algorithm to initially favor global exploration to improve the accuracy of the target surrogate model, while later shifting towards local search to improve the accuracy of the optimal solution. This is beneficial for finding the global optimum and enhances the search capability of this method.

[0072] The number of clusters is the same as the number of nodes added. The number of nodes added is the same as the number of update points. As a preferred option, the number of update points is q=3.

[0073] Preferably, the preset threshold for Euclidean distance is: .

[0074] As a preferred option, the solution algorithms used for the first and second multi-objective optimization sub-problems can be, but are not limited to, NSGA II or decomposition-based multi-objective evolutionary algorithms (MOEA / D).

[0075] In one embodiment, the CAD software in step 108 is either Catia or Solidworks; the mesh generation software is either ICEM or Pointwise.

[0076] In one embodiment, the CFD simulation calculation in step 110 uses the method of solving the Euler equation.

[0077] In a specific embodiment, such as Figure 4 As shown, a design method for an internally contracting reference flow field based on multi-objective sub-problem optimization is provided, which specifically includes the following steps.

[0078] S1. Establishing a coordinate system: Establish a coordinate system within the meridional plane of the reference flow field, with the origin at the center of the inlet section of the axisymmetric reference flow field. x The axis is the axis of symmetry of the reference flow field. y Axis perpendicular x The axis points to the generatrix of the outer wall surface;

[0079] S2. Configuration Parametric Design: The baseline flow field configuration is parametrically designed. The outer compression wall consists of two cubic curve segments, and the central body consists of straight line segments and cubic curve segments, such as... Figure 3 As shown. The entire configuration is controlled by 6 points, with point 1 being the starting point of the outer wall surface, and its coordinates are... Point 2 is the starting point of internal compression, with coordinates as follows: Point 3 is the endpoint of the outer wall surface, with coordinates as follows: Point 4 is the starting point of the central body, with coordinates of... Point 5 represents the lip position, with coordinates as follows: Point 6 is the endpoint of the central body, with coordinates of... The baseline flow field configuration is determined by 11 parameters, namely: inlet radius... Minimum radius of the central body Maximum radius of the central body Total length lip flow position Inlet compression angle Lower corner corners of the lips Exit angle Total shrinkage ratio and internal contraction ratio When the 11 parameters are determined, the ordinates of points 2 and 3 are calculated using the definitions of the total shrinkage ratio and the internal shrinkage ratio, i.e. , The shape of a cubic curve is obtained by substituting its endpoint coordinates and endpoint slopes into the expression. It is obtained by calculating its differential equation;

[0080] S3. Determine the optimization problem: Based on the design requirements, determine the optimization design problem of the reference flow field, including the design objective, design variables, constraints, and design conditions. In this embodiment, the design objective is to maximize the total pressure recovery coefficient. There are three constraints: the exit Mach number is less than 3, and the distance between the reflection point of the leading shock wave in the central body and the lip is... (See Figure 3 (less than) And calculate convergence; design variables are , , , , , , The range of values ​​for the design variables is , , , , , , The sizes of the remaining four variables are , , , The design operating conditions are Mach number 6 and altitude 25 kilometers.

[0081] S4. Optimize parameter settings: Based on the baseline flow field optimization design problem and computational resources, determine the dimension d of the design variables, the initial number of sampling points n, and the maximum number of iterations for optimization. The number of points is q; in this embodiment, the design variable dimension d=7, the initial number of sample points n=35, and the maximum number of iterations is optimized. The number of dots added is q=3;

[0082] S5. Initial Sampling: Use the Latin hypercube sampling method to obtain n initial sampling points throughout the design space;

[0083] S6. Configuration Generation: Using Catia software, generate the baseline flow field configuration corresponding to the sample points;

[0084] S7. Flow field mesh generation: Use Pointwise mesh generation software to generate the mesh for the reference flow field;

[0085] S8. Simulation Calculation: Perform CFD simulation calculations on the flow field mesh corresponding to each sample point to obtain the performance of the corresponding benchmark flow field;

[0086] S9. Add the sample points, their response values, and constraint values ​​to the sample library;

[0087] S10. Based on the current sample library, construct a Kriging surrogate model for the optimization objective and constraints;

[0088] S11. Feasible solution judgment: Determine whether there is a feasible solution that satisfies the constraints in the current sample set. If it exists, go to S14; otherwise, execute S12.

[0089] S12. Locating the feasible region: Construct the first multi-objective optimization subproblem for locating the feasible region. The expression of the first multi-objective optimization subproblem is shown in Equation (1).

[0090] S13. Selecting Update Points: In the multi-objective optimal solution set PS (Pareto solution set) of S12, select q points as update points using the following steps. The specific selection approach is as follows:

[0091] (a) Remove duplicate points: Remove duplicate points in PS or points that are duplicates of already sampled points. The criterion is that the Euclidean distance between the two points is less than 1 × 10⁻⁶. -6 ;

[0092] (b) Clustering: The Pareto front (PF) is normalized and then divided into q groups using the k-means clustering method;

[0093] (c) Selecting points: Select the point with the largest PoF function value from each group.

[0094] Go to S16.

[0095] S14. Local exploration and global mining of feasible regions: Construct a second multi-objective optimization subproblem for finding the optimal feasible solution. The expression of the first multi-objective optimization subproblem is shown in Equation (2).

[0096] S15. Selecting Update Points: In the multi-objective optimal solution set PS (Pareto set) of S9, select q points as simulation evaluation sample points using the following steps. The specific selection approach is as follows:

[0097] (a) Remove duplicate points: Remove duplicate points in PS or points that are duplicates of already sampled points. The criterion is that the Euclidean distance between the two points is less than 1 × 10⁻⁶. -6 ;

[0098] (b) Clustering: Normalize the Pareto front (PF) and then utilize... k-means Clustering methods divide them into q Group;

[0099] (c) Point selection: Select the point that minimizes the lower confidence bound (LCB) function value. The LCB function is: , and The objective function at points x Predicted values ​​and prediction variance at the location, This is a coefficient that decreases continuously as the number of iterations increases.

[0100] S16. Simulation Evaluation: Execute steps S6-S8 to obtain the response and constraint values ​​of the update points;

[0101] S17. Sample Library Update: Add the update point, its response value, and constraint value to the sample library;

[0102] S18. Convergence Check: Determine if the number of iterations exceeds the maximum allowed number of iterations. If yes, stop the iteration and output the result; otherwise, jump to S10, increment the iteration count by 1, and start the next iteration cycle.

[0103] In this embodiment, optimization requires a total of 95 simulation evaluations. Figure 5 The convergence process of the total pressure recovery coefficient during the optimization process is presented. From Figure 5 As can be seen, no feasible solution exists in the initial sample points. Therefore, the first multi-objective sub-problem is used to find a feasible solution. After 6 iterations, the algorithm finds a feasible solution that satisfies the constraints, with a total pressure recovery coefficient of 0.7483. Next, the second multi-objective sub-problem is used to find the optimal feasible solution. In the subsequent optimization process, the algorithm successively finds the optimal feasible solution with better performance, proving the convergence performance of the algorithm. After 20 iterations, the optimal reference flow field obtained in this embodiment has a total pressure recovery coefficient of 0.9489, corresponding to the design variables... , , , , , , The exit Mach number is 2.9994, which meets the requirement that the exit Mach number is less than 3. The distance between the reflection point of the leading shock wave at the central body and the lip is... The value is 0.054mm, which meets the requirements. The requirements are as follows. The exit Mach number is very close to the maximum value of the constraint, indicating that the constraint is an activation constraint, proving the algorithm's search capability within the constraint boundary. The Mach number contour plot of the optimal reference flow field in this embodiment is shown below. Figure 6 As shown.

[0104] It should be understood that, although Figure 1 and Figure 4 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 and Figure 4 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0105] In one embodiment, such as Figure 7 As shown, a design device for an internally contracting reference flow field based on multi-objective sub-problem optimization is provided, including: a parametric design module, a reference flow field optimization design problem determination module, an initial sampling module, a Kriging surrogate model construction module, a feasible region location module, an optimal solution search module in the feasible region, and an optimization result determination module, wherein:

[0106] The parametric design module is used to establish a coordinate system in the meridional plane of the reference flow field, perform parametric design on the configuration of the reference flow field in the coordinate system, and determine the design space; the design space includes design parameters and their corresponding value ranges.

[0107] The benchmark flow field optimization design problem determination module is used to determine the benchmark flow field optimization design problem based on preset design requirements. The benchmark flow field optimization design problem includes: design objective, design variables, constraints, and design conditions.

[0108] The initial sampling module is used to obtain a preset number of initial sampling points based on the Latin hypercube sampling method in the design space; the initial sample points are used as the current sample points, and the number of iterations is set to 1.

[0109] The Kriging surrogate model construction module is used to generate the baseline flow field configuration corresponding to the current sample point using CAD software, and to generate the baseline flow field mesh using mesh generation software based on the baseline flow field configuration; to perform CFD simulation calculations on the baseline flow field mesh corresponding to each current sample point; to add the current sample point and the simulation response value to the sample library to obtain the current sample library; and to construct the Kriging surrogate model with optimization objectives and constraints based on the current sample library.

[0110] The feasible region localization module is used to determine whether there is a feasible solution that satisfies the constraints among all current sample points. When there is no feasible solution that satisfies the constraints, a first multi-objective optimization sub-problem is constructed based on the Kriging surrogate model, consisting of a feasible probability function, a maximum default degree, and a constraint variance function. Based on the Pareto solution set obtained by solving the first multi-objective optimization sub-problem, the first type of point addition method is used to obtain multiple update points.

[0111] The module for finding the optimal solution in the feasible region is used to construct a second multi-objective optimization subproblem based on the Kriging surrogate model when a feasible solution that satisfies the constraints exists. This subproblem consists of two CEI terms and a constraint variance function. Based on the Pareto solution set obtained by solving the second multi-objective optimization subproblem, a second type of point addition method is used to obtain multiple update points.

[0112] The optimization result determination module is used to update the current sample point as the update point, increment the iteration count by 1, and continue iterating until the iteration count is greater than the preset maximum iteration count, thus obtaining the optimal design variables for the internal contraction reference flow field.

[0113] In one embodiment, the parametric design module is further used to establish a coordinate system in the meridional plane of the reference flow field. The origin of the coordinate system is the center of the inlet section of the axisymmetric reference flow field, the x-axis is the axis of symmetry of the reference flow field, and the y-axis is perpendicular to the x-axis and points to the generatrix of the outer wall. The reference flow field configuration is parametrically designed. The outer compression wall is composed of two cubic curves, and the central body is composed of straight line segments and cubic curves. The reference flow field configuration is determined by 11 design parameters, including: inlet radius, minimum radius of the central body, maximum radius of the central body, total length, lip flow direction position, inlet compression angle, downwash angle, lip angle, outlet angle, total contraction ratio, and internal contraction ratio.

[0114] In one embodiment, the design objectives in the benchmark flow field optimization design problem determination module include: total pressure recovery coefficient and outlet airflow uniformity; the constraints include: outlet Mach number, pitching moment, and flow coefficient; the design condition is the cruise state of a hypersonic vehicle; and the design variables include: inlet compression angle, downwash angle, lip angle, outlet angle, minimum radius of the central body, total contraction ratio, and internal contraction ratio.

[0115] In one embodiment, the expression for the first multi-objective optimization subproblem in the location feasible area positioning module is shown in equation (1).

[0116] In one embodiment, the first type of point addition method in the feasible region localization module includes: deleting duplicate points in the Pareto solution set of the first multi-objective optimization sub-problem or points that are duplicates of the current sample point; duplicate points refer to points in the Pareto solution set of the first multi-objective optimization sub-problem where the Euclidean distance between two points is less than a preset value; points that are duplicates of the current sample point refer to points in the Pareto solution set of the first multi-objective optimization sub-problem where the Euclidean distance between two points and the current sample point is less than a preset value; normalizing the Pareto front of the first multi-objective optimization sub-problem and clustering the results using the K-means clustering method to obtain multiple groups, the number of groups being the same as the number of points to be added; and selecting the point with the largest feasible probability function value in each group as the update point.

[0117] In one embodiment, the expression for the second multi-objective optimization subproblem in the module for finding the optimal solution in the feasible region is shown in equation (3).

[0118] In one embodiment, the second type of point addition method in the module for finding the optimal solution in the feasible region includes: deleting duplicate points in the Pareto solution set of the second multi-objective optimization subproblem or points that are duplicates of the current sample point; duplicate points refer to points in the Pareto solution set of the second multi-objective optimization subproblem where the Euclidean distance between two points is less than a preset value; points that are duplicates of the current sample point refer to points in the Pareto solution set of the second multi-objective optimization subproblem where the Euclidean distance between two points and the current sample point is less than a preset value; normalizing the Pareto front of the second multi-objective optimization subproblem and using the K-means clustering method to cluster the results to obtain multiple groups, the number of groups being the same as the number of points added; selecting the points in each group that minimize the lower confidence limit function value to form the update point set; the expression for minimizing the lower confidence limit function is shown in equation (4).

[0119] In one embodiment, the CAD software in the Kriging proxy model building module is either Catia or Solidworks; the meshing software is either ICEM or Pointwise.

[0120] In one embodiment, the CFD simulation calculation in the Kriging proxy model building module uses the method of solving the Euler equation.

[0121] Specific limitations regarding the design apparatus for the internally contracting reference flow field based on multi-objective sub-problem optimization can be found in the limitations of the design method for the internally contracting reference flow field based on multi-objective sub-problem optimization mentioned above, and will not be repeated here. Each module in the aforementioned internally contracting reference flow field design apparatus based on multi-objective sub-problem optimization can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0122] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0123] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0124] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A design method for an internally contracting reference flow field based on multi-objective sub-problem optimization, characterized in that, The method includes: A coordinate system is established within the meridional plane of the reference flow field. The configuration of the inwardly contracting reference flow field is parametrically designed within the coordinate system to determine the design space. The design space includes design parameters and their corresponding value ranges. Based on the preset design requirements, the optimization design problem of the reference flow field is determined; the optimization design problem of the reference flow field includes: design objectives, design variables, constraints, and design conditions; Based on the design space, a predetermined number of initial sampling points are obtained using the Latin hypercube sampling method. Use the initial sample point as the current sample point and set the iteration count to 1; Using CAD software, a reference flow field configuration corresponding to the current sample point is generated, and using mesh generation software, a mesh for the reference flow field is generated based on the reference flow field configuration. For each current sample point, a CFD simulation is performed on the grid of the reference flow field. The current sample point and the simulation response value are added to the sample library to obtain the current sample library; Based on the current sample library, construct a Kriging proxy model for the optimization objective and constraints; Determine whether there is a feasible solution that satisfies the constraints among all current sample points. When there is no feasible solution that satisfies the constraints, construct a first multi-objective optimization sub-problem based on the Kriging surrogate model, consisting of a feasible probability function, a maximum default degree, and a constraint variance function. Use the first type of point addition method to obtain multiple update points based on the Pareto solution set obtained by solving the first multi-objective optimization sub-problem. When a feasible solution that satisfies the constraints exists, based on the Kriging surrogate model, a second multi-objective optimization subproblem consisting of two CEI terms and a constraint variance function is constructed. Based on the Pareto solution set obtained by solving the second multi-objective optimization subproblem, a second type of point addition method is used to obtain multiple update points. The current sample point is updated to the update point, the iteration count is incremented by 1, and the iteration continues until the iteration count is greater than the preset maximum iteration count, thus obtaining the optimal design variables for the internal contraction reference flow field.

2. The method according to claim 1, characterized in that, A coordinate system is established within the meridional plane of the reference flow field. The configuration of the concentrated flow field is parametrically designed within this coordinate system to determine the design space, including: A coordinate system is established within the meridional plane of the reference flow field, with the origin of the coordinate system being the center of the circle at the inlet section of the axisymmetric reference flow field. x The axis is the axis of symmetry of the reference flow field. y Axis perpendicular x The axis points to the generatrix of the outer wall surface; The baseline flow field configuration is parametrically designed. The outer compression wall is composed of two cubic curves, and the central body is composed of straight lines and cubic curves. The baseline flow field configuration is determined by 11 design parameters, including: inlet radius, minimum radius of the central body, maximum radius of the central body, total length, lip flow direction, inlet compression angle, downwash angle, lip angle, outlet angle, total contraction ratio, and internal contraction ratio.

3. The method according to claim 2, characterized in that, Based on the preset design requirements, the optimization design problem of the reference flow field is determined. The design objectives mentioned in the steps include: total pressure recovery coefficient and outlet airflow uniformity. The constraints include: exit Mach number, pitching moment, and flow coefficient; The design condition is the cruise state of a hypersonic aircraft. The design variables are selected from the design parameters according to preset design requirements.

4. The method according to claim 1, characterized in that, Determine whether there is a feasible solution that satisfies the constraints among all current sample points. If no feasible solution satisfies the constraints, construct a first multi-objective optimization sub-problem based on the Kriging surrogate model, consisting of a feasible probability function, a maximum default degree, and a constraint variance function. Using the Pareto solution set obtained from solving the first multi-objective optimization sub-problem, employ the first type of point addition method to obtain a preset number of update points. The expression for the first multi-objective optimization sub-problem in this step is: Where PS represents the Pareto solution set of a multi-objective optimization problem; Let it be a feasible probability function; For the first i A constraint at the unknown point x Calculate the prediction variance. Representing unknown points x The maximum degree of default.

5. The method according to claim 4, characterized in that, Determine whether there is a feasible solution that satisfies the constraints among all current sample points. If no feasible solution satisfies the constraints, construct a first multi-objective optimization sub-problem based on the Kriging surrogate model, consisting of a feasible probability function, a maximum default degree, and a constraint variance function. Using the Pareto solution set obtained from solving the first multi-objective optimization sub-problem, employ a first-type point-addition method to obtain a preset number of update points. The first-type point-addition method includes: Delete duplicate points in the Pareto solution set of the first multi-objective optimization subproblem or points that are duplicates of the current sample point; the duplicate points refer to points in the Pareto solution set of the first multi-objective optimization subproblem where the Euclidean distance between two points is less than a preset value; the points that are duplicates of the current sample point refer to points in the Pareto solution set of the first multi-objective optimization subproblem where the Euclidean distance between two points is less than a preset value. The Pareto front of the first multi-objective optimization subproblem is normalized, and the results are clustered using the K-means clustering method to obtain multiple groups, with the number of groups being the same as the number of points added. Select the point with the largest feasible probability function value in each group as the update point.

6. The method according to claim 1, characterized in that, When a feasible solution satisfying the constraints exists, based on the Kriging surrogate model, a second multi-objective optimization subproblem consisting of two CEI terms and a constraint variance function is constructed. Using the Pareto solution set obtained from solving the second multi-objective optimization subproblem, a second type of point addition method is applied to obtain a preset number of update points. The expression for the second multi-objective optimization subproblem in this step is: Where PS represents the Pareto solution set of a multi-objective optimization problem; For the first i A constraint at point x The predicted variance at the location; , , Let be the feasible probability function. and These are two separate aspects: local mining and global exploration of EI functions. ,in, This is the feasible optimal solution in the current sample set. This represents the probability density function of a normal distribution. and The objective function at points x The predicted value and prediction variance at the location.

7. The method according to claim 1, characterized in that, When a feasible solution satisfying the constraints exists, based on the Kriging surrogate model, a second multi-objective optimization subproblem consisting of two CEI terms and a constraint variance function is constructed. The Pareto solution set obtained from solving the second multi-objective optimization subproblem is then processed using a second type of point-addition method to obtain a preset number of update points. The second type of point-addition method includes the following steps: Delete duplicate points in the Pareto solution set of the second multi-objective optimization subproblem or points that are duplicates of the current sample point; the duplicate points refer to points in the Pareto solution set of the second multi-objective optimization subproblem where the Euclidean distance between two points is less than a preset value; the points that are duplicates of the current sample point refer to points in the Pareto solution set of the second multi-objective optimization subproblem where the Euclidean distance between two points is less than a preset value. The Pareto front of the second multi-objective optimization subproblem is normalized, and the results are clustered using the K-means clustering method to obtain multiple groups, with the number of groups being the same as the number of points added. The update point set is formed by selecting the points with the smallest minimum confidence lower bound function value from each group; the minimum confidence lower bound function is: in, and The objective function at points x Predicted values ​​and prediction variance at the location, The coefficient is a factor that decreases continuously with the number of iterations. For the number of iterations, This represents the maximum number of iterations.

8. The method according to claim 1, characterized in that, Using CAD software, a reference flow field configuration corresponding to the current sample point is generated. Then, using mesh generation software, a mesh for the reference flow field is generated based on the reference flow field configuration. The CAD software mentioned in the steps is either Catia or Solidworks. The mesh generation software is either ICEM or Pointwise.

9. The method according to claim 1, characterized in that, For each current sample point, a CFD simulation is performed on the grid of the reference flow field. The CFD simulation is performed by solving the Euler equations.

10. A design device for an internally contracting reference flow field based on multi-objective sub-problem optimization, characterized in that, The device includes: The parametric design module is used to establish a coordinate system in the meridional plane of the reference flow field, perform parametric design on the configuration of the reference flow field in the coordinate system, and determine the design space; the design space includes design parameters and their corresponding value ranges; The benchmark flow field optimization design problem determination module is used to determine the optimization design problem of the benchmark flow field according to the preset design requirements. The benchmark flow field optimization design problem includes: design objective, design variables, constraints, and design conditions. The initial sampling module is used to obtain a preset number of initial sampling points based on the design space using the Latin hypercube sampling method; the initial sample points are used as the current sample points, and the iteration count is set to 1. The Kriging surrogate model construction module is used to generate a baseline flow field configuration corresponding to the current sample point using CAD software, and to generate a mesh of the baseline flow field using mesh generation software based on the baseline flow field configuration; to perform CFD simulation calculations on the mesh of the baseline flow field corresponding to each current sample point; to add the current sample point and the simulation response value to the sample library to obtain the current sample library; and to construct a Kriging surrogate model with optimization objectives and constraints based on the current sample library. The feasible region localization module is used to determine whether there is a feasible solution that satisfies the constraints among all current sample points. When there is no feasible solution that satisfies the constraints, a first multi-objective optimization sub-problem consisting of a feasible probability function, a maximum default degree, and a constraint variance function is constructed based on the Kriging surrogate model. Based on the Pareto solution set obtained by solving the first multi-objective optimization sub-problem, a first type of point addition method is used to obtain multiple update points. The module for finding the optimal solution in the feasible region is used to construct a second multi-objective optimization subproblem based on the Kriging surrogate model when a feasible solution that satisfies the constraints exists. The second type of point addition method is used to obtain multiple update points based on the Pareto solution set obtained by solving the second multi-objective optimization subproblem. The optimization result determination module is used to update the current sample point as the update point, increment the iteration count by 1, and continue iterating until the iteration count is greater than the preset maximum iteration count, thereby obtaining the optimal design variables for the internal contraction reference flow field.

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