Prediction and selection method of critical burst pressure of shock tunnel diaphragm
By constructing a second-order polynomial response surface surrogate model and a genetic algorithm, the problems of predicting and selecting the critical rupture pressure and geometric parameters of the diaphragm in a shock tunnel were solved. This enabled accurate prediction of the critical rupture pressure and intelligent selection of the diaphragm's geometric parameters, improving the efficiency and accuracy of shock tunnel test preparation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2026-03-13
- Publication Date
- 2026-06-12
Smart Images
Figure CN122192691A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of shock tunnel diaphragm technology, and more specifically, relates to a method for predicting and selecting the critical rupture pressure of a shock tunnel diaphragm. Background Technology
[0002] As one of the main facilities for studying the aerodynamic and thermal characteristics of hypersonic vehicles on land, the shock tunnel simulates the hypersonic flight state of the vehicle by generating hypersonic gas flow. The diaphragm of the wind tunnel is a key initiation component for the release of driving gas, and its critical rupture pressure directly determines the release effect of the driving gas and the quality of shock wave formation.
[0003] Determining the critical burst pressure of shock tunnel diaphragms with different geometric parameters quickly, and rapidly determining the diaphragm's geometric parameters given the critical burst pressure, remain challenging problems in the pre-test preparation for shock tunnels. On one hand, the geometric dimensions of the shock tunnel, such as the slot depth and width, are key parameters affecting the critical burst pressure, and a complex nonlinear relationship exists between them. On the other hand, determining the diaphragm's geometry based on the critical burst pressure is a typical inverse problem, often exhibiting ill-posedness. The rapid development of machine learning technology may offer new solutions to this complex problem, but how to efficiently utilize machine learning for predicting the critical burst pressure of shock tunnel diaphragms still requires further research. Summary of the Invention
[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for predicting and selecting the critical rupture pressure of shock tunnel diaphragms. By constructing a surrogate model between the shape parameters of the shock tunnel diaphragm and the critical rupture pressure, the critical rupture pressure of diaphragms with different geometric parameters can be accurately predicted. Furthermore, a genetic algorithm is combined to achieve intelligent selection of shock tunnel diaphragms.
[0005] To achieve the above-mentioned objective, the method for predicting the critical rupture pressure of a shock tunnel diaphragm according to the present invention includes the following steps:
[0006] S1.1: The shock tunnel diaphragm should be configured according to actual needs. Each shape parameter is obtained by taking values within the shape parameter sample space. A vector of shape parameters ,in Indicates the first In the shape parameter vector, the first... The values of the shape parameters, , Then, the vector of each shape parameter is obtained. Corresponding critical membrane rupture pressure Thus obtain Each data sample constitutes a data sample set;
[0007] S1.2: Using the data sample set data obtained in step S1.1, a second-order polynomial response surface surrogate model is fitted with the shape parameter vector as the input variable and the critical membrane rupture pressure as the output variable;
[0008] S1.3: For the shock tunnel diaphragm to be predicted, obtain its... The external parameters are substituted into the second-order polynomial response surface surrogate model obtained by fitting in step S1.2 to obtain the predicted value of the critical membrane rupture pressure.
[0009] This invention also proposes a method for selecting shock tunnel diaphragms, comprising the following steps:
[0010] S2.1: The shock tunnel diaphragm should be configured according to actual needs. Each shape parameter is obtained by taking values within the shape parameter sample space. A vector of shape parameters ,in Indicates the first In the shape parameter vector, the first... The values of the shape parameters, , Then, the vector of each shape parameter is obtained. Corresponding critical membrane rupture pressure Thus obtain Each data sample constitutes a data sample set;
[0011] S2.2: Using the data sample set data obtained in step S2.1, a second-order polynomial response surface surrogate model is fitted with the shape parameter vector as the input variable and the critical membrane rupture pressure as the output variable;
[0012] S2.3: Set the target critical membrane rupture pressure according to actual needs, and use the second-order polynomial response surface surrogate model obtained in step S2.2 for inversion to obtain the shock tunnel membrane shape parameters; the specific method for inverting the shock tunnel membrane shape parameters is as follows:
[0013] S2.3.1: Generation A vector of shape parameters As individuals in the initial population of the genetic algorithm, Indicates the first Among the individuals, the first The values of the shape parameters, ;
[0014] S2.3.2: Calculate the fitness of each individual in the current population, using the following method:
[0015] For each individual, select the shape parameter vector of the data sample that is closest to the current individual from the data sample set, and determine whether the error between the two is less than the preset absolute tolerance. If so, the negative of the absolute difference between the critical membrane rupture pressure and the target critical membrane rupture pressure of the data sample is used as the fitness value of the current individual; otherwise, the morphological parameter vector of the current individual is substituted into the second-order polynomial response surface surrogate model to obtain the predicted critical membrane rupture pressure value, and the negative of the absolute difference between the predicted critical membrane rupture pressure value and the target critical membrane rupture pressure is used as the fitness value of the current individual.
[0016] S2.3.3: Based on fitness, perform selection, crossover, and mutation operations on the current population to generate a new generation of population;
[0017] S2.3.4: Determine whether the termination condition has been met. If it has, proceed to step S2.3.5; otherwise, return to step S2.3.2.
[0018] S2.3.5: Select the individual with the highest fitness value from the current population and use its corresponding morphological parameter vector as the inversion result.
[0019] The present invention discloses a method for predicting and selecting the critical rupture pressure of a shock tunnel diaphragm. First, several sets of shape parameter vectors and their corresponding critical rupture pressures are obtained to form a data sample set. Based on this, a second-order polynomial response surface surrogate model is fitted, with the shape parameter vectors as input variables and the critical rupture pressure as the output variable. When predicting the critical rupture pressure, the shape parameters of the shock tunnel diaphragm to be predicted are input into the second-order polynomial response surface surrogate model to obtain the predicted critical rupture pressure value. When selecting the shock tunnel diaphragm, a target critical rupture pressure is set according to actual needs, and a genetic algorithm is used to invert the diaphragm based on the second-order polynomial response surface surrogate model to obtain the shape parameters of the shock tunnel diaphragm.
[0020] This invention establishes a quantitative mapping relationship between the shape parameters of a shock tunnel diaphragm and the critical rupture pressure, enabling forward prediction of the critical rupture pressure and inverse inversion of the diaphragm's geometric parameters. Simulation results show that the second-order polynomial response surface surrogate model used in this invention can not only accurately predict the critical rupture pressure within the training set parameter range, but also solve the corresponding diaphragm geometric parameters within a certain range using a genetic algorithm, thus achieving intelligent selection of shock tunnel diaphragms. Attached Figure Description
[0021] Figure 1 This is a flowchart illustrating a specific implementation method for predicting the critical rupture pressure of a shock tunnel diaphragm according to the present invention.
[0022] Figure 2 This is a flowchart of the method for selecting shock tunnel diaphragms according to the present invention;
[0023] Figure 3 This is a flowchart of the shock tunnel diaphragm shape parameter inversion method based on genetic algorithm in this invention;
[0024] Figure 4 This is a schematic diagram of the shock tunnel diaphragm shape parameters in this embodiment;
[0025] Figure 5 This is a visual schematic diagram of the second-order polynomial response surface surrogate model in this embodiment;
[0026] Figure 6 This is a schematic diagram illustrating the determination of the critical membrane rupture pressure prediction range in this embodiment;
[0027] Figure 7 This is a schematic diagram of the inversion range of the diaphragm shape parameters in this embodiment. Detailed Implementation
[0028] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.
[0029] Example
[0030] Figure 1 This is a flowchart illustrating a specific implementation method for predicting the critical rupture pressure of a shock tunnel diaphragm according to the present invention. Figure 1 As shown, the critical rupture pressure prediction method for the shock tunnel diaphragm of the present invention includes the following steps:
[0031] S101: Obtain the data sample set:
[0032] The shock tunnel diaphragm is set according to actual needs. Each shape parameter is obtained by taking values within the shape parameter sample space. A vector of shape parameters ,in Indicates the first In the shape parameter vector, the first... The values of the shape parameters, , Then we obtain the vector of each shape parameter. Corresponding critical membrane rupture pressure Thus obtain The data sample set consists of several data samples.
[0033] In this embodiment, the shape parameters of the shock tunnel diaphragm include the diaphragm thickness, groove depth, and groove width. The shape parameter sample space is determined using an experimental method based on central composite design. Each shape parameter vector... The corresponding critical rupture pressure was obtained through numerical simulation calculation, and the specific method is as follows:
[0034] Based on the shape parameter vector A shock tunnel diaphragm model was constructed, and the finite element method (FEM) was used to discretize the diaphragm model into a finite number of elements, resulting in the diaphragm finite element model. After determining the initial boundary conditions and applying loads, the deformation and failure process of the diaphragm was solved using the Dyna explicit dynamics module in ANSYS simulation software to obtain the critical rupture pressure. During the diaphragm failure process, the failure status of the elements was recorded in the ANSYS message file. When the number of failed mesh elements gradually accumulated and reached a threshold, it was determined that the diaphragm was about to rupture. Specifically, if the diaphragm began to rupture in the simulation animation, and the crack did not continue to extend over time, this was the critical rupture state, and the corresponding rupture pressure was the critical rupture pressure.
[0035] In practical applications, to ensure that the critical rupture pressure is independent of the mesh, the finite element module can be further verified for mesh independence. The critical rupture pressure that satisfies the mesh independence condition is the final critical rupture pressure.
[0036] S102: Constructing a second-order polynomial response surface surrogate model:
[0037] Using the data sample set data obtained in step S1, a second-order polynomial response surface surrogate model is fitted, with the shape parameter vector as the input variable and the critical membrane rupture pressure as the output variable.
[0038] In this embodiment, the expression for the second-order polynomial response surface surrogate model is as follows:
[0039] ,
[0040] in, Indicates the critical membrane rupture pressure. , , , These are the fitting coefficients. Indicates the first The values of the shape parameters are as follows: Indicates the error term. .
[0041] In practical applications, to improve the prediction accuracy of the second-order polynomial response surface surrogate model, a genetic algorithm can be used to fine-tune the model. The specific method is as follows:
[0042] Several sets of shape parameter vectors and their corresponding true values of critical membrane rupture pressure are obtained separately. The range of values for each coefficient is determined based on the fitted values of each coefficient and error term in the fitted second-order polynomial response surface surrogate model. Individuals in the genetic algorithm are set as coefficient vectors composed of coefficients and error terms in the surrogate model. The particle fitness function is set as the reciprocal of the error between the predicted and true critical membrane rupture pressure values. After several rounds of genetic iteration, the optimized values of each coefficient and error term in the second-order polynomial response surface surrogate model are obtained.
[0043] S103: Predicted critical rupture pressure:
[0044] For the diaphragm of the shock tunnel to be predicted, obtain its The external parameters are substituted into the second-order polynomial response surface surrogate model obtained by fitting in step S102 to obtain the predicted value of the critical membrane rupture pressure.
[0045] To facilitate the design of shock tunnel diaphragms for engineering applications, this invention also provides a method for selecting shock tunnel diaphragms. Figure 2 This is a flowchart of the method for selecting the shock tunnel diaphragm according to the present invention. For example... Figure 2 As shown, the specific steps of the shock tunnel diaphragm selection method of the present invention include:
[0046] S201: Obtain the data sample set:
[0047] The shock tunnel diaphragm is set according to actual needs. Each shape parameter is obtained by taking values within the shape parameter sample space. A vector of shape parameters ,in Indicates the first In the shape parameter vector, the first... The values of the shape parameters, , Then we obtain the vector of each shape parameter. Corresponding critical membrane rupture pressure Thus obtain The data sample set consists of several data samples.
[0048] Similarly, each shape parameter vector The corresponding critical rupture pressure can also be obtained through the aforementioned numerical simulation calculation, as follows:
[0049] Based on the shape parameter vector A shock tunnel diaphragm model was constructed, and the finite element method (FEM) was used to discretize the diaphragm model into a finite number of elements, resulting in the diaphragm finite element model. After determining the initial boundary conditions and applying loads, the deformation and failure process of the diaphragm was solved using the Dyna explicit dynamics module in ANSYS simulation software to obtain the critical rupture pressure. During the diaphragm failure process, the failure status of the elements was recorded in the ANSYS message file. When the number of failed mesh elements gradually accumulated and reached a threshold, it was determined that the diaphragm was about to rupture.
[0050] S202: Constructing a second-order polynomial response surface surrogate model:
[0051] Using the data sample set data obtained in step S201, a second-order polynomial response surface surrogate model is fitted, with the shape parameter vector as the input variable and the critical membrane rupture pressure as the output variable.
[0052] Similarly, the second-order polynomial response surface surrogate model can be expressed as follows:
[0053] ,
[0054] in, Indicates the critical membrane rupture pressure. , , , These are the fitting coefficients. Indicates the first The values of the shape parameters are as follows: Indicates the error term. .
[0055] In practical applications, in order to improve the prediction accuracy of the second-order polynomial response surface surrogate model, a genetic algorithm can also be used to fine-tune the second-order polynomial response surface surrogate model.
[0056] S203: Shock Tunnel Diaphragm Shape Parameters:
[0057] The target critical membrane rupture pressure is set according to actual needs, and the second-order polynomial response surface surrogate model obtained by fitting in step S202 is used for inversion to obtain the shock tunnel membrane shape parameters.
[0058] To improve the accuracy of the inverted shape parameters, this invention adopts a shock tunnel diaphragm shape parameter inversion method based on genetic algorithm. Figure 3 This is a flowchart of the shock tunnel diaphragm shape parameter inversion method based on genetic algorithm in this invention. Figure 3 As shown, the specific steps of the shock tunnel diaphragm shape parameter inversion method based on genetic algorithm in this invention include:
[0059] S301: Generate the initial population:
[0060] generate A vector of shape parameters As individuals in the initial population of the genetic algorithm, Indicates the first Among the individuals, the first The values of the shape parameters, .
[0061] In this embodiment, the initial population is generated using the following method: randomly selecting from the data sample set data in step S201. Given a vector of shape parameters, a new shape parameter vector is generated by mutating each vector within a preset parameter neighborhood. The initial population consists of individuals. This approach guides the search starting point closer to the known data region, improving convergence speed.
[0062] S302: Calculate fitness:
[0063] The fitness of each individual in the current population is calculated using the following method:
[0064] For each individual, select the shape parameter vector of the data sample that is closest to the current individual from the data sample set, and determine whether the error between the two is less than the preset absolute tolerance. (In this embodiment) If so, the negative of the absolute difference between the critical rupture pressure and the target critical rupture pressure of the data sample is used as the fitness value of the current individual; otherwise, the shape parameter vector of the current individual is substituted into the second-order polynomial response surface surrogate model to obtain the predicted critical rupture pressure value, and the negative of the absolute difference between the predicted critical rupture pressure value and the target critical rupture pressure is used as the fitness value of the current individual.
[0065] S303: Generate a new generation of population:
[0066] Based on fitness, the current population is selected, crossovered, and mutated to generate a new generation of population.
[0067] S304: Determine whether the termination condition has been met. If it has, proceed to step S305; otherwise, return to step S302.
[0068] Termination conditions can be set as needed, generally set to the maximum number of iterations or the optimal fitness value for convergence.
[0069] S305: Selecting the optimal individual:
[0070] Select the individual with the highest fitness value from the current population and use its corresponding morphological parameter vector as the inversion result.
[0071] To better illustrate the technical effects of the present invention, specific examples are used to experimentally verify the present invention.
[0072] In this embodiment, a central composite design is adopted to generate a sample space for membrane shape parameters. Figure 4 This is a schematic diagram of the shock tunnel diaphragm shape parameters in this embodiment. For example... Figure 4 As shown, in this embodiment, the reference model is centered at (diaphragm thickness, groove depth, groove width) = (1.80, 1.40, 3.50). An axial distance coefficient of 0.1 (parameter variation range ±10%) is set, and the sample space for the external parameters is determined as follows: diaphragm thickness ∈ [1.62, 1.98] mm, groove depth ∈ [1.26, 1.54] mm, and groove width ∈ [3.15, 3.85] mm. Within this space, 36 sample points are generated as the training set according to the experimental design scheme of the central composite design. Then, 6 sample points are generated as the test set, with 3 sets within the training set space and the other 3 sets generated outside the training set space with the center point as the reference and an axial distance coefficient of 0.2 (parameter variation range ±20%). Finally, 6 sets of sample points were generated as the validation set: 4 sets of sample points were generated outside the training set space with the center point as the reference and the axial distance coefficient of 0.3 (parameter variation range ±30%), and 2 sets of sample points were added by randomly selecting samples from the training set.
[0073] This embodiment is based on the Windows 11 operating system platform, with an 11th generation Intel® Core™ i7-11800H processor. Python programs were written using the Anaconda 24.7.1 platform to construct the experimental framework. The PolynomialFeatures (order 2) and LinearRegression modules from the scikit-learn library were used for model fitting, ultimately obtaining a second-order polynomial response surface surrogate model. Figure 5 This is a visual schematic diagram of the second-order polynomial response surface surrogate model in this embodiment.
[0074] The membrane shape parameters are inversely derived using a genetic algorithm based on a second-order polynomial response surface surrogate model. Specifically, the genetic algorithm from the DEAP library in Python is used to solve for the membrane parameters in reverse. The initial population is set to n = 100, the crossover probability is set to Pc = 0.5, the mutation probability is set to Pm = 0.2, and the initial number of iterations is set to ngen = 100. After inputting the target critical membrane rupture pressure, the algorithm outputs the membrane shape parameters: membrane thickness, groove depth, and groove width.
[0075] Using the center point of the central composite design as a reference, the groove depth is fixed at 1.4 mm and the groove width at 3.5 mm, and the diaphragm thickness is scaled proportionally with 1.8 mm as the reference. Figure 6 This is a schematic diagram illustrating the determination of the critical membrane rupture pressure prediction range in this embodiment. (See diagram below.) Figure 6 As shown, when the relative error is allowed to be within 10%, the membrane thickness expands from the original training set range of 1.62~1.98 mm to approximately 1.53~2.88 mm, and the groove depth expands from 1.26~1.54 mm to approximately 0.98~1.61 mm, thus verifying the effective prediction range of the single parameter of the second-order polynomial response surface surrogate model.
[0076] To test the accuracy of the inversion of this invention, this embodiment extends the target critical membrane rupture pressure to outside the training set parameter range (1.2~5.9 MPa) for testing, and records the relative deviation between the critical membrane rupture pressure corresponding to the inverted membrane geometric parameters and the initial target set critical membrane rupture pressure. Figure 7 This is a schematic diagram illustrating the inversion range of the membrane shape parameters in this embodiment. For example... Figure 7 As shown, when the relative error is within 10%, the effective range for inverting the membrane shape parameters based on the critical rupture pressure can be extended from the original training set range of 1.2~5.9 MPa to approximately 1.2~14.5 MPa, and within this range, the absolute error of the inversion does not exceed 0.5 MPa (e.g., Figure 7 (As shown by the red dashed line), this illustrates the accuracy of the inverse inversion within the specified range.
[0077] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.
Claims
1. A method for predicting the critical rupture pressure of a shock tunnel diaphragm, characterized in that... Includes the following steps: S1.1: The shock tunnel diaphragm should be configured according to actual needs. Each shape parameter is obtained by taking values within the shape parameter sample space. A vector of shape parameters ,in Indicates the first In the shape parameter vector, the first... The values of the shape parameters, , Then, the vector of each shape parameter is obtained. Corresponding critical membrane rupture pressure Thus obtain Each data sample constitutes a data sample set; S1.2: Using the data sample set data obtained in step S1.1, a second-order polynomial response surface surrogate model is fitted with the shape parameter vector as the input variable and the critical membrane rupture pressure as the output variable; S1.3: For the shock tunnel diaphragm to be predicted, obtain its... The external parameters are substituted into the second-order polynomial response surface surrogate model obtained by fitting in step S1.2 to obtain the predicted value of the critical membrane rupture pressure.
2. The method for predicting the critical rupture pressure of a shock tunnel diaphragm according to claim 1, characterized in that, The shape parameters include the membrane thickness, groove depth, and groove width of the shock tunnel diaphragm.
3. The method for predicting the critical rupture pressure of a shock tunnel diaphragm according to claim 1, characterized in that, The critical membrane rupture pressure was obtained using the following method: Based on the shape parameter vector A shock tunnel diaphragm model was constructed, and the finite element method was used to discretize the shock tunnel diaphragm model into a mesh of finite elements to obtain the diaphragm finite element model. After determining the initial boundary conditions and applying the load, the deformation and failure process of the diaphragm was solved using the Dyna explicit dynamics module in ANSYS simulation software to obtain the critical rupture pressure.
4. The method for predicting the critical rupture pressure of a shock tunnel diaphragm according to claim 1, characterized in that, The expression for the second-order polynomial response surface surrogate model is as follows: ， in, Indicates the critical membrane rupture pressure. , , , These are the fitting coefficients. Indicates the first The values of the shape parameters are as follows: Indicates the error term. .
5. The method for predicting the critical rupture pressure of a shock tunnel diaphragm according to claim 1, characterized in that, The surrogate model is optimized using a genetic algorithm, specifically as follows: Several sets of shape parameter vectors and corresponding true values of critical membrane rupture pressure are obtained separately; the range of values of each coefficient is determined according to the fitted values of each coefficient and error term in the fitted second-order polynomial response surface surrogate model; individuals in the genetic algorithm are set as coefficient vectors composed of coefficients and error terms in the surrogate model; the particle fitness function is set as the reciprocal of the error between the predicted and true values of critical membrane rupture pressure; after several rounds of genetic iteration, the optimized values of each coefficient and error term in the second-order polynomial response surface surrogate model are obtained.
6. A method for selecting a shock tunnel diaphragm, characterized in that, Includes the following steps: S2.1: The shock tunnel diaphragm should be configured according to actual needs. Each shape parameter is obtained by taking values within the shape parameter sample space. A vector of shape parameters ,in Indicates the first In the shape parameter vector, the first... The values of the shape parameters, , Then, the vector of each shape parameter is obtained. Corresponding critical membrane rupture pressure Thus obtain Each data sample constitutes a data sample set; S2.2: Using the data sample set data obtained in step S2.1, a second-order polynomial response surface surrogate model is fitted with the shape parameter vector as the input variable and the critical membrane rupture pressure as the output variable; S2.3: Set the target critical membrane rupture pressure according to actual needs, and use the second-order polynomial response surface surrogate model obtained in step S2.2 for inversion to obtain the shock tunnel membrane shape parameters; the specific method for inverting the shock tunnel membrane shape parameters is as follows: S2.3.1: Generation A vector of shape parameters As individuals in the initial population of the genetic algorithm, Indicates the first Among the individuals, the first The values of the shape parameters, ; S2.3.2: Calculate the fitness of each individual in the current population, using the following method: For each individual, select the shape parameter vector of the data sample that is closest to the current individual from the data sample set, and determine whether the error between the two is less than the preset absolute tolerance. If so, the negative of the absolute difference between the critical membrane rupture pressure and the target critical membrane rupture pressure of the data sample is used as the fitness value of the current individual; otherwise, the morphological parameter vector of the current individual is substituted into the second-order polynomial response surface surrogate model to obtain the predicted critical membrane rupture pressure value, and the negative of the absolute difference between the predicted critical membrane rupture pressure value and the target critical membrane rupture pressure is used as the fitness value of the current individual. S2.3.3: Based on fitness, perform selection, crossover, and mutation operations on the current population to generate a new generation of population; S2.3.4: Determine whether the termination condition has been met. If it has, proceed to step S2.3.5; otherwise, return to step S2.3.
2. S2.3.5: Select the individual with the highest fitness value from the current population and use its corresponding morphological parameter vector as the inversion result.
7. The method for selecting a shock tunnel diaphragm according to claim 6, characterized in that, The shape parameters include the membrane thickness, groove depth, and groove width of the shock tunnel diaphragm.
8. The method for selecting a shock tunnel diaphragm according to claim 6, characterized in that, The critical membrane rupture pressure was obtained using the following method: Based on the shape parameter vector A shock tunnel diaphragm model was constructed, and the finite element method was used to discretize the shock tunnel diaphragm model into a mesh of finite elements to obtain the diaphragm finite element model. After determining the initial boundary conditions and applying the load, the deformation and failure process of the diaphragm was solved using the Dyna explicit dynamics module in ANSYS simulation software to obtain the critical rupture pressure.
9. The method for selecting a shock tunnel diaphragm according to claim 6, characterized in that, The expression for the second-order polynomial response surface surrogate model is as follows: ； in, Indicates the critical membrane rupture pressure. , , , These are the fitting coefficients. Indicates the first The values of the shape parameters are as follows: Indicates the error term. .
10. The method for selecting a shock tunnel diaphragm according to claim 6, characterized in that, The initial population in step S2.3.1 is generated using the following method: randomly selecting from the data sample set data in step S2.1 Given a vector of shape parameters, a new shape parameter vector is generated by mutating each vector within a preset parameter neighborhood. The initial population of individuals.