Shock wave needle-zero mass jet aircraft resistance reduction and heat reduction multi-objective optimization method

Abstract

The invention discloses a shock wave needle-zero mass jet aircraft resistance reduction and heat reduction multi-objective optimization method. According to the method, approximate characterization is carried out based on three different proxy models of KRG, RBF and PRS, advantages and disadvantages between an interpolation type proxy model and a fitting type proxy model are comprehensively considered, and aerodynamic thermal characterization of the high-precision hypersonic aircraft is realized; meanwhile, the agent model is dynamically updated based on adaptive point adding of crowding degree sorting, the fusion agent model is optimized through a multi-objective optimization algorithm based on a Pareto dominating relation, and after pseudo Pareto front edges obtained by the fusion agent model are combined, crowding degree sorting is performed to select newly-added sample points, so that the pseudo Pareto front edges can be fully utilized, the diversity of a population is ensured, and the accuracy of the algorithm is improved. The optimization design efficiency of the aircraft is improved, and rapid optimization design of the hypersonic aircraft is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of aerodynamic optimization design of hypersonic aircraft, and in particular to a multi-objective optimization method for reducing drag and heat of a shock needle-massless jet aircraft. Background Art

[0002] With the development of aerospace technology, hypersonic vehicles have attracted widespread attention worldwide due to their significant research significance and potential application value. However, during hypersonic flight, vehicles face severe aerodynamic conditions due to viscous friction and shock waves, which in turn affect their flight range and safety. Therefore, research on drag and heat reduction for hypersonic vehicles is of great significance. In addition, with the rapid advancement of computer technology, high-precision modeling technologies such as Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) have become core tools for aircraft design. However, while these high-fidelity models improve computational accuracy, they also incur significant computational costs, severely limiting the efficiency of aircraft design optimization. Therefore, the development of advanced, fast, and reliable optimization design methods is essential.

[0003] Currently, shock needles are widely used in hypersonic aircraft to reduce drag and heat due to their simple structure. Wang et al. (2021) studied the combination of shock needles and channels. By slotting the head of the aerodynamic disk to bleed air and jetting from the middle of the shock needle, a zero-mass jet was realized, which can achieve a certain drag and heat reduction effect and avoid the carryover of high-pressure air source, greatly enhancing the engineering practicality. Furthermore, Wang, Guo et al. (2023) successively conducted multi-parameter drag and heat reduction performance studies on this configuration. The results showed that design variables such as shock needle length, aerodynamic disk diameter, slot angle, jet position and channel diameter have a significant impact on the drag and heat reduction performance. Subsequently, Meng et al. (2024) studied the drag and heat reduction performance of shock needle-zero-mass jets with different aerodynamic disk shapes. Their research results showed that the aerodynamic disk shape with a conical aviation dome can reduce drag by 20.71%, proving that the aerodynamic disk shape has a significant impact on the drag reduction of the channel concept. Qin et al. (2024) combined a shock needle-zero mass jet with a root jet. A comprehensive analysis of the results showed that the root jet can reduce the heat flux density and pressure on the bluff body, but it will increase the drag. This shows that the two goals of drag reduction and heat protection of the configuration are often not achievable at the same time. Overall, the shock needle-zero mass jet combined with the channel technology has a significant drag and heat reduction effect on bluff-body hypersonic aircraft. However, most of the existing research focuses on the analysis of the flow field mechanism, and the multi-parameter coupled drag and heat reduction optimization design has not yet been fully carried out.

[0004] Ahmed and Qin (2010) studied optimization design using an evolutionary genetic algorithm under four different surrogate models. They found that eliminating samples with poor aerodynamic performance significantly improved optimization efficiency. Furthermore, Ahmed et al. (2012) first employed a second-generation non-dominated sorting genetic algorithm (NSGA-II) based on the Krging (KRG) surrogate model to optimize six parameters in a shock needle-aerodynamic disk configuration, including shock needle length, aerodynamic disk diameter, and bluff body shape, as design variables. Considering flow stability as a constraint, they conducted an optimization study and constructed a response relationship between each parameter and the objective function. Zhang et al. (2016) employed the response surface methodology to optimize the parameters of a shock needle and forward jet combination. They found that the response surface methodology exhibited high reliability and practicality for parameter optimization. Huang et al. (2019) studied the drag and heat reduction mechanisms of a shock needle-root jet configuration and performed a multi-objective optimization design using four design variables, including rod length, total pressure ratio, and jet size. They investigated the relationship between the design variables' influence on the objective function and constraints, and obtained an optimal solution that matched the Pareto boundary calculated using the NSGA-II method by varying the weighting coefficients. Huang et al. (2019) also optimized a shock needle-aerodynamic disk configuration and found that the typical Pareto optimal solution reduced the bluff body drag coefficient and total heat flux by 35.90% and 46.97% respectively. Furthermore, Huang et al. (2020) studied the drag and heat reduction mechanisms of a composite non-ablative thermal protection system and performed single-objective and multi-objective aerodynamic optimization on the configuration, deeply exploring the aerodynamic performance of the composite non-ablative thermal protection system. Ou et al. (2019) constructed a multi-objective optimization algorithm based on a surrogate model to optimize the design of shock needle configurations. When total drag and bluff body heat flux are used as objective functions, the aerodynamic disk diameter is insensitive to drag and heat flux. In this case, the optimization problem can be transformed into a single-objective problem. The above optimization designs of shock needle-related configurations mostly use existing optimization methods, which leads to low optimization efficiency and is not conducive to the efficient and rapid design of aircraft.

[0005] In summary, the shock needle-massless jet configuration can effectively reduce the drag and heat of hypersonic blunt-body vehicles and alleviate the severe aerodynamic and thermal problems of hypersonic vehicles. Figure 1As shown, the incoming flow is strongly compressed after passing through the zero-mass jet inlet at the head of the drag-reducing disk. It is then accelerated and ejected at the zero-mass jet outlet, achieving a zero-mass jet. This can achieve drag reduction and heat protection without the need for a gas working medium. However, in shock needle-zero-mass jet aircraft, the numerous external parameters and the unclear coupling relationships between these parameters make it difficult to simultaneously achieve drag and heat reduction. Therefore, it is urgent to implement multi-objective optimization design through optimization design methods. However, existing aerodynamic shape optimization methods require a large number of simulation model calls, making it difficult to achieve efficient optimization. Summary of the Invention

[0006] In view of this, the present invention provides a multi-objective optimization method (KRP-MAOM) for drag reduction and heat reduction of shock needle-massless jet aircraft, which adopts three proxy model approximate characterization methods: KRG, RBF and PRSM. At the same time, interpolation and fitting proxy models are adopted, which have complementary effects and can improve the accuracy of aircraft approximate characterization. Moreover, dynamic adaptive addition of points through congestion sorting can make full use of the pseudo-Pareto frontier and effectively improve the efficiency of aircraft optimization design.

[0007] The multi-objective optimization method for reducing drag and heat of a shock needle-massless jet aircraft of the present invention comprises:

[0008] Step 1: Determine the optimization problem model:

[0009]

[0010] Where L is the length of the shock needle; W is the diameter of the lateral zero-mass jet hole; D d D is the diameter of the drag reduction disc; c is the zero-mass jet hole diameter; L R is the position of the lateral zero-mass jet hole; is the zero-mass jet hole inlet convergence half angle; is the left deviation angle of the lateral zero-mass jet hole; is the right deviation angle of the lateral zero-mass jet hole; C d is the drag coefficient; Q t is the average heat flux density; f(X) is the objective function, X LB is the lower bound of the design variable; X UB is the upper bound of the design variable; X is the design variable;

[0011] Step 2: Obtain the initial design variable sample points; call the CFD fluid simulation analysis model to calculate the aerodynamic and thermal simulation results of the shock needle-zero mass jet hypersonic aircraft at the initial design variable sample points, obtain the corresponding objective function values, and build an initial sample point database;

[0012] Step 3: Based on the current sample point database, three proxy models, KRG, RBF and PRSM, are constructed;

[0013] Step 4: Using the sample points in the current sample point database as the initial population, the three proxy models are optimized separately using a multi-objective optimization algorithm based on the Pareto dominance relationship to obtain three sets of pseudo Pareto solution sets; the three sets of pseudo Pareto solution sets are merged, and N(k) is selected from the merged solution set based on the spatial congestion ranking. add New sample points;

[0014] Call the CFD fluid simulation analysis model to calculate the aerodynamic and thermal simulation results of the aircraft at each newly added sample point design variable sample point, obtain the corresponding objective function value, obtain the newly added sample point data, and incorporate it into the current sample point database;

[0015] Step 5: Determine whether the current model call count exceeds the maximum model call count; if not, return to step 3; if so, output the current database.

[0016] Preferably, in step 2, optimal Latin hypersquare sampling is used to obtain multiple groups of design variable sample points, and the group with the best spatial uniformity is selected as the initial design variable sample points.

[0017] Preferably, in step 2, maximizing the minimum distance is used as the spatial uniformity indicator.

[0018] Better, space congestion d (i) crowd Using formula (2) we can obtain:

[0019]

[0020] Among them, m is the number of objective functions; f j min and f j max The minimum and maximum values ​​of the jth objective function respectively; f j (i-1) and f j (i+1) They are the two adjacent objective function values ​​after the j-th objective function value is sorted by size.

[0021] Better, add the number of sample points N(k) add for:

[0022]

[0023] Among them, N add The number of new sample points set; |X (k) opt | is the number of sample points in the pseudo-Pareto solution set in the merged solution set.

[0024] Preferably, in step 2, a CFD fluid simulation analysis model based on the finite volume method is used.

[0025] Preferably, the hypersonic aircraft is a waverider, lifting body or rotating body hypersonic aircraft.

[0026] Preferably, the multi-objective optimization algorithm based on Pareto dominance relationship adopts NSGA-Ⅱ, StrengthPareto Evolutionary Algorithm 2 or Pareto Envelope-based Selection AlgorithmII.

[0027] Beneficial effects:

[0028] The present invention overcomes the problem of insufficient approximate characterization accuracy of a traditional single proxy model. Approximate characterization is performed based on three different proxy models: KRG, RBF, and PRSM. This method comprehensively considers the advantages and disadvantages of interpolation-type and fitting-type proxy models, and realizes high-precision aerodynamic and thermal characterization of hypersonic aircraft. At the same time, the proxy model is dynamically updated based on adaptive addition of points based on congestion ranking. The three proxy models are optimized by a multi-objective optimization algorithm based on the Pareto dominance relationship. The pseudo-Pareto frontiers obtained by the three proxy models are combined and then sorted by congestion to select new sample points. This can fully utilize the pseudo-Pareto frontier, ensure the diversity of the population, improve the efficiency of aircraft optimization design, and realize rapid optimization design of hypersonic aircraft.

[0029] The present invention is applicable to the field of design optimization of waverider, lifting and rotating hypersonic aircraft, and can effectively improve the efficiency of aircraft design optimization and shorten the design cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 The geometric model diagram of the shock needle-zero mass jet configuration aircraft, where (a) is a schematic diagram of the three-dimensional model and (b) is a simplified diagram of the two-dimensional model.

[0031] Figure 2 Flow chart of the method of the present invention.

[0032] Figure 3 It is the Pareto solution set of resistance and average heat flux density of the optimization results of the method of the present invention.

[0033] Figure 4 The comparison results of the average heat flow and resistance corresponding to the typical Pareto solution set data points selected after optimization by the method of the present invention are as follows: Figure 3 The initial plan and plans A to E.

[0034] Figure 5 The flow field comparison diagrams before and after the optimization of the method of the present invention are shown in Figure 1. (a) is the initial solution; (b) to (f) are solutions A to E, respectively.

[0035] Figure 6 Comparison diagram of the local zero-mass jet flow field before and after optimization using the method of the present invention. (a) is the initial solution; (b) to (f) are solutions A to E, respectively. DETAILED DESCRIPTION

[0036] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0037] The present invention provides a multi-objective optimization method for reducing drag and heat of a shock needle-zero mass jet aircraft, also known as the KRP-MAOM method. The design variable sample points are obtained by optimal Latin hypersquare sampling, and the aerodynamic and thermal calculations of the shock needle-zero mass jet hypersonic aircraft are performed through a high-precision CFD flow simulation model to obtain a sample point database. Multi-model approximate characterization is performed through KRG, RBF and PRSM, and then a multi-objective optimization algorithm based on the Pareto dominance relationship is used to solve a set of pseudo-Pareto fronts of drag and aerodynamic heat. The pseudo-Pareto fronts are sorted by congestion, and the pseudo-Pareto front points with the largest congestion are screened and used as new sample points for CFD simulation calculations. The obtained results are added to the sample point database and the operation is repeated to achieve adaptive dynamic optimization until the convergence criterion is met.

[0038] After acquiring sample points through CFD, three proxy models, KRG, RBF, and PRSM, were constructed for approximate characterization. A multi-objective optimization algorithm based on the Pareto dominance relationship was then used to optimize the design. New sample points were selected by crowding sorting, enabling rapid optimization of the shock needle-massless jet hypersonic vehicle design.

[0039] The flow chart of the present invention is as follows Figure 2 As shown, the following steps are included:

[0040] Step 1: Determine the design variables, design space, method parameters and objective function according to the model to be solved.

[0041] The three elements of the optimization problem model in the present invention are shown in formula (4), and the main parameters of the method are shown in Table 1.

[0042]

[0043] Where X is the design variable; L is the shock needle length; W is the zero-mass jet hole width; D d is the diameter of the pneumatic disc; D c is the zero mass channel diameter; L Ris the zero-mass jet hole position; is the zero-mass jet inlet angle; is the left deflection angle of the zero-mass jet hole; is the right deflection angle of the zero-mass jet hole; C d is the drag coefficient; Q t is the average heat flux density; f(X) is the objective function; X LB is the lower bound of the design variable; X UB is the upper bound of the design variable.

[0044] Table 1 Algorithm parameters

[0045]

[0046] Step 2: Obtain initial design variable sample points.

[0047] To ensure better projection uniformity and spatial distribution of space-filling sampling, initial sample points were obtained using a Latin hypersquare experimental design method, generating 60 sets of initial sample points. The set with the best spatial distribution was then selected as the initial design variable sample points. This embodiment uses maximizing the minimum distance as the spatial distribution metric.

[0048] The high-precision CFD simulation analysis model is used to calculate the high-precision aerodynamic and thermal simulation results of the initial sample points of the shock needle-massless jet hypersonic aircraft, obtain the corresponding objective function value, and complete the initialization of the sample point database. This embodiment uses a high-precision CFD fluid simulation model based on the finite volume method.

[0049] Step 3: Based on the current sample point database, three proxy models, KRG, RBF and PRSM, are constructed for the objective function value to complete the construction of interpolation and fitting proxy models.

[0050] (1) KRG Proxy Model

[0051] The KRG proxy model is an unbiased optimal estimation interpolation model for spatially distributed data, which is composed of the superposition of the global model and the local deviation, as shown in formula (5):

[0052]

[0053] In the formula, g(x) is a polynomial global approximation model that reflects the overall change trend of the approximated object in the design space. When the numerical characteristics of the approximated object are unknown, a constant μ can be taken. The local deviation term Z(x) has a mean of zero and a variance of σ. 2 , a random process with non-zero covariance.

[0054] The approximation ability of KRG is mainly determined by the local deviation term Z(x). The covariance matrix of Z(x) can be expressed as

[0055] Cov[Z(x i ),Z(x j )]=σ 2 R[R(x i ,x j )] (6)

[0056] Where R is the Gaussian correlation function, R is the symmetric correlation matrix,

[0057]

[0058] μ and σ 2 The least squares estimate of can be obtained by formula (8)

[0059]

[0060] Using the maximum likelihood method, the correlation coefficient θ can be determined by solving the optimization problem in the following formula: k .

[0061]

[0062] (2) RBF Proxy Model

[0063] Radial basis function (RBF) is a multivariate spatial interpolation method that can be expressed as a linear weighted sum of radially symmetric basis functions.

[0064]

[0065] According to the interpolation conditions, the weight coefficient vector w can be solved as follows

[0066]

[0067] Where φ(r) is the radial function and r is the Euclidean distance between sample points.

[0068] The radial function can be expressed as the inverse multi-quadratic function (IMQ), which is expressed as

[0069] φ(r)=(r 2 +c 2 ) -0.5 (12)

[0070] The value of the shape coefficient c is

[0071]

[0072] (3) PRSM agent model

[0073] Polynomial response surface method (PRSM) is a surrogate model method that uses multiple linear regression to fit functions. The most commonly used quadratic PRSM in engineering can be expressed as

[0074]

[0075] Its undetermined coefficient matrix β can be determined by the least squares method and can be expressed as

[0076] β=(X T X) -1 X T y (15)

[0077] Where X is the design variable matrix associated with the constructed sample points; y is the column vector consisting of the response values ​​of the constructed sample points.

[0078] Step 4: Using the sample points in the current sample point database as the initial population, the three constructed proxy models are optimized using a multi-objective optimization algorithm based on the Pareto dominance relationship to obtain three sets of pseudo Pareto solution sets. The three sets of pseudo Pareto solution sets are merged and the combined pseudo Pareto solution set X is compared. (k) opt The number of sample points in |X (k) opt | and the number of new sample points N set by the algorithm parameters in step 1 add Determine the number of new sample points N(k) in the kth cycle add , as shown in formula (16):

[0079]

[0080] Among them, the multi-objective optimization algorithms based on Pareto dominance relationship can adopt NSGA-Ⅱ, Strength ParetoEvolutionary Algorithm 2, Pareto Envelope-based Selection Algorithm II, etc.

[0081] In order to ensure the diversity of the population during the optimization process, the solution set X(k) obtained from the congestion ranking is opt The new sample points are selected as follows:

[0082] The three sets of pseudo Pareto solution sets are merged. To ensure population diversity, the pseudo Pareto solution set X (k) opt In the example, based on the spatial congestion ranking, the top N(k) are selected. add samples as new sample points.

[0083] Spatial crowding d (i) crowd It can be obtained by formula (17):

[0084]

[0085] Among them, m, f j min , f j max , f j (i-1) , f j (i+1) They are the number of objective functions, the minimum and maximum values ​​of the j-th objective function, and the two objective function values ​​adjacent to the i-th objective function value after the j-th objective function value is sorted by size.

[0086] Step 5: Determine whether the termination condition is met: whether the current model call count exceeds the maximum model call count. If not, return to step 3; if yes, output the current database.

[0087] The KRP-MAOM method of the present invention can effectively improve the efficiency of aircraft design optimization and shorten the design cycle.

[0088] The aircraft system includes the fields of single-stage horizontal take-off and landing suborbital aircraft, two-stage horizontal take-off and landing suborbital aircraft, and vertical take-off and landing suborbital aircraft.

[0089] The hypersonic aircraft includes a waverider, a lifting body and a rotating body hypersonic aircraft.

[0090] Example 1: International numerical examples of similar methods

[0091] In order to verify the optimization performance of the KRP-MAOM method for solving multi-objective optimization problems, a set of standard numerical test cases were selected and compared with NSGA-Ⅱ and Pareto Efficient Global Optimization (ParEGO). In addition, the multi-objective optimization algorithm based on Pareto dominance relationship used in this embodiment is NSGA-Ⅱ. The parameters of each method are shown in Table 2. Inverted generational distance (IGD) is used as the method evaluation index, and its specific definition is shown in (18):

[0092]

[0093] Where, X *is the theoretical Pareto frontier of the test case, X is the Pareto frontier obtained after optimization, and d(x,X) is the minimum Euclidean distance between x and individuals in X; |X * | for X * The smaller the IGD value, the closer the optimized Parteo frontier is to the true Pareto frontier, the more evenly distributed it is, and the better the performance.

[0094] Table 2 Parameter settings of three methods

[0095]

[0096] Four standard numerical examples, ZDT1, ZDT2, ZDT3, and LZ08-F4, were selected for performance comparison of the optimization methods. The results are shown in Table 3. Compared with NSGA-II, the proposed KRP-MAOM method improved the global convergence of the tested examples by two orders of magnitude, while using 10 times fewer computational resources. Compared with ParEGO, the KRP-MAOM method improved the global convergence of the tested examples by one order of magnitude, while using the same computational resources.

[0097] Table 3 Comparison results of IGD values ​​of optimization methods

[0098]

[0099]

[0100] Note: The highlighted numbers are the best results among the KRP-MAOM method and the comparison methods.

[0101] Example 2: Shock needle-massless jet hypersonic vehicle drag reduction and heat reduction engineering case

[0102] Taking the case of shock needle-massless jet hypersonic aircraft drag reduction and heat reduction engineering as an example, the application of KRP-MAOM method in the field of multi-objective optimization design of hypersonic aircraft is introduced. fe max Except for setting it to 200, the other parameter settings are the same as Table 2.

[0103] First, confirm the three optimization elements, as shown in (19).

[0104]

[0105] Among them, the parameters and specific ranges corresponding to X in the design variable can be referred to Figure 1 (b) and Table 4; the objective functions are Figure 1(a) The aircraft drag and the average heat flux density of the bluff body wall; the constraints are the upper and lower bounds of the design variables. This embodiment adopts a 0° angle of attack flight, so Figure 1 The three-dimensional model of (a) is simplified to Figure 1 (b) Two-dimensional axisymmetric model.

[0106] Table 4 Design variable parameters

[0107]

[0108]

[0109] Multiple sets of initial sample points were generated using the Latin hypersquare experimental design method. The spatial uniformity metric, maximizing the minimum distance, was used to determine the best spatial uniformity. Sample points were calculated using CFD, and aerodynamic heat was calculated using the Shear stress transport (SST) k-ω turbulence model. The flight conditions for this example are shown in Table 5.

[0110] Table 5 Inflow conditions

[0111]

[0112] After that, the sample point data is used to construct three proxy models based on KRG, RBF and PRSM, and NSGA-Ⅱ (the multi-objective optimization algorithm based on Pareto dominance relationship used in this embodiment is NSGA-Ⅱ) is called to optimize the three proxy models. The pseudo Pareto fronts optimized by the three proxy models are merged, the congestion of the pseudo Pareto fronts is calculated, and the congestion is sorted. The sample point with the maximum spatial congestion is selected as the new sample point. The CFD high-precision fluid simulation model is continued to be called for calculation until the condition is met. Figure 2 The convergence conditions in .

[0113] Figure 3 The Pareto set for optimizing the drag and average heat flux of a shock needle-massless jet hypersonic vehicle is given. 42 non-inferior solutions are obtained by the KRP-MAOM method. The average heat flux of the Pareto set is less than the initial solution. Scheme A has the smallest total drag. Scheme B has the lowest average heat flux. Scheme C is the Pareto frontier whose total drag is not greater than that of the initial scheme. Schemes D and E are the solutions obtained on the Pareto frontier. Figure 4 Compared with the initial solution, the optimized shock needle-massless jet hypersonic vehicle has a drag reduction of 13.28% and an average heat flux density of 41.82%. Under the condition that the total drag is no greater than that of the initial solution, the average heat flux density can be reduced by 20.49%.

[0114] contrast Figure 5 From the Mach number and temperature cloud diagrams, it can be found that for schemes A and C, whose total drag is less than that of the initial scheme, the advancement of the separation point is more obvious. The recirculation zone of schemes A and C is significantly different from other cases. Two obvious vortex structures appear in the recirculation zone of these two schemes, and the rotation directions of the two vortex structures are opposite. The recirculation zone formed by the two vortex structures is more slender. For schemes B, D and E, their common characteristics are the longest shock needle length and larger aerodynamic disk diameter. From the current results, considering only the drag reduction goal, there is an optimal value for the shock needle length. This is because increasing the shock needle length does not always increase the size of the recirculation zone. Therefore, increasing the shock needle length does not always reduce drag. The aerodynamic disks of schemes B, D and E are larger, which increases the reattachment angle when the airflow reattaches to the bluff body surface, thereby improving the effect of aerodynamic thermal protection.

[0115] There are obvious changes at the zero-mass jet outlet. Figure 6 The Mach number and temperature curves are shown. Figure 6 In the optimized scheme, the jet phenomenon is more obvious than that of the initial scheme. In addition, the flow field near the zero-mass jet outlet also changes significantly. Figure 6 In (a), the initial solution generates three vortex structures on the left, and then the zero-mass jet structure has no obvious downstream tilt. Figure 6 In (bf), the zero-mass jet structure is obvious, and its influence on the vortex on the left is obvious, causing the three vortices on the left to become two. Figure 6 Comparison of the temperature contours reveals that the massless jet temperatures for all optimized configurations are lower than those of the initial design. This is because the optimized design can better accelerate the jet flow within the channel, thereby reducing the temperature. Accelerated jet cooling is equivalent to active jet cooling, providing aerodynamic thermal protection to the bluff body surface to a certain extent.

[0116] The two examples above demonstrate that the KRP-MAOM method offers significant advantages over internationally accepted algorithms in terms of optimization efficiency, robustness, and global convergence. Furthermore, the method has been successfully applied to aircraft design optimization. The engineering case study of drag and heat reduction for hypersonic vehicles using a shock needle and massless jet demonstrates the rationality, effectiveness, and engineering practicability of the KRP-MAOM method.

[0117] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for drag and heat reduction of shock needle-zero mass jet aircraft, characterized in that: include: Step 1: Determine the optimization problem model: Where L is the shock needle length; W and L R are the diameter and position of the lateral zero-mass jet hole, respectively; D d D is the diameter of the drag reduction disc; c is the zero-mass jet hole diameter; is the zero-mass jet hole inlet convergence half angle; are the left and right deflection angles of the lateral zero-mass jet hole, respectively; C d is the drag coefficient; Q t is the average heat flux density; Step 2: Obtain sample points of initial design variables; use CFD simulation to calculate the aerodynamic and thermal results corresponding to the sample points of initial design variables, and build a sample point database; Step 3: Based on the current sample point database, three proxy models, KRG, RBF and PRSM, are constructed; Step 4: Using the current sample point database sample points as the initial population, the three proxy models are optimized separately using a multi-objective optimization algorithm based on the Pareto dominance relationship to obtain three sets of pseudo Pareto solution sets; the three sets of pseudo Pareto solution sets are merged and N(k) is selected from them based on the spatial congestion ranking. add New sample points; Use CFD simulation to calculate the aerodynamic and thermal results of the newly added sample point design variables and incorporate them into the current sample point database; Step 5: Determine whether the number of times the current model is called exceeds the maximum value; if not, return to step 3; if so, output the current database.

2. The method according to claim 1, wherein In step 2, optimal Latin hypersquare sampling is used to obtain multiple groups of design variable sample points, and the group with the best spatial uniformity is selected as the initial design variable sample points.

3. The method according to claim 2, wherein In step 2, the minimum distance maximization is used as the spatial uniformity index.

4. The method according to claim 1, wherein Spatial crowding d (i) crowd Using formula (2) we can obtain: Where m is the number of objective functions; and The minimum and maximum values ​​of the j-th objective function respectively; and They are the two adjacent objective function values ​​after the j-th objective function value is sorted by size.

5. The method according to claim 1 or 4, wherein: The number of new sample points N(k) add for: Among them, N add The number of new sample points set; |X (k) opt | is the number of sample points in the pseudo-Pareto solution set in the merged solution set.

6. The method according to claim 1, wherein In the step 2, a CFD fluid simulation analysis model based on the finite volume method is adopted.

7. The method according to claim 1, wherein The hypersonic aircraft is a waverider, lifting body or rotating body hypersonic aircraft.

8. The method according to claim 1, wherein The multi-objective optimization algorithm based on Pareto dominance relationship adopts NSGA-Ⅱ, Strength Pareto Evolutionary Algorithm 2 or Pareto Envelope-based Selection Algorithm II.

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