High-speed aircraft thermal protection system design and optimization method

Abstract

A design and optimization method for a thermal protection system of a high-speed aircraft considers uncertainty of physical property parameters, heat flux density, geometric shape and the like and probability distribution characteristics of the parameters in design and application of the thermal protection system, the uncertainty and the probability distribution characteristics are embedded into a design process, and uncertainty analysis and design optimization of the thermal protection system are achieved; the method comprises the following steps: performing uncertainty modeling on small subsample characteristic parameters such as material attribute parameters, input environment parameters and machining process parameters in thermal protection design by utilizing a nuclear density theory to realize accurate modeling of input parameter uncertainty distribution characteristics; design parameters are optimized through the agent model based on physical information, so that a design model and a result have interpretability, and very high extrapolation and generalization capabilities are achieved.

Description

Technical Field

[0001] The invention relates to a design and optimization method for a high-speed aircraft thermal protection system, and belongs to the technical field of aircraft thermal protection. Background Art

[0002] The thermal protection system of high-speed aircraft plays a vital role in the reliability and structural integrity of the aircraft. The optimization design of the thermal protection system has always been an important part of aircraft design. Making the best use of the thermal protection system has always been an important goal of thermal protection design. The aircraft thermal protection system is the most important system to ensure the completion of flight missions, the integrity of the aircraft structure, and the safety of internal equipment. Its design level is an important indicator of the design level of the aircraft.

[0003] In the design of thermal protection systems, there are many uncertain factors in the system, mainly including dimensional deviations caused by parts manufacturing and installation, aerodynamic thermal changes caused by changes in the external environment, and instability of material performance due to temperature changes. In traditional thermal protection design, the extreme deviation design method is usually adopted based on the concept of redundant design to deal with possible extreme situations and to ensure the effectiveness of thermal protection with sufficient margin. With the current trend of aircraft design becoming increasingly lightweight and integrated, traditional design methods often lead to a large design weight for thermal protection systems, resulting in a low flight quality-efficiency ratio. Therefore, in order to improve aircraft performance, it is necessary to provide more sophisticated and efficient design and optimization methods for thermal protection systems. Summary of the invention

[0004] The technical problem to be solved by the present invention is: to overcome the shortcomings of the prior art, to provide a design and optimization method for a high-speed aircraft thermal protection system, to adopt a multi-objective and multi-parameter uncertainty optimization design method for the thermal protection system, to effectively reduce the design margin of the system, to improve the design accuracy and efficiency of the thermal protection system, and to make the thermal protection system more efficient.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A high-speed aircraft thermal protection system design and optimization method comprises the following steps:

[0007] Step (1): Model the thermal protection system. Model the aircraft thermal protection system to simulate the real physical system;

[0008] Step (2): Based on the deterministic model of step (1), the uncertainty parameters and variables in the system are considered to perform quantitative characterization modeling. According to the performance and configuration requirements determined by the real environment of the thermal protection system, the uncertainty parameters that need to be considered are preliminarily determined. For multi-layer thermal protection systems, the thermal flow environment constraints, geometric constraints, material property constraints, etc. are involved;

[0009] Step (3): Select the uncertainty sources in step (2) as system uncertainty parameters, and obtain small sub-samples of specific heat capacity, density, thermal conductivity, heat flux density, system surface emissivity, and geometric size parameters. Based on the actual working condition samples, use the kernel density estimation method to characterize the uncertainty of the small sample data and determine the probability distribution of each variable;

[0010] Step (4): According to the probability distribution of the uncertainty parameters in step (3), sample each parameter separately to obtain N different sample combinations X of uncertainty parameters. (i) ;

[0011] Step (5): The uncertainty parameters and coordinates selected in step (3) are used as the input of the model in step (2), and the known physical information such as control equations and boundary conditions are embedded into the model to construct a parameterized physical information neural network proxy model and establish a mapping relationship between the uncertainty input parameters and the system back temperature field;

[0012] Step (6): According to the Bayesian theorem, the parameters of the proxy model constructed in step (5) are optimized using the real system back-temperature field data obtained from the experiment, thereby correcting the uncertainty of the model constructed in step (5);

[0013] Step (7): Combine the sample combination X of the uncertainty parameters obtained in step (4) (i) , input into the proxy model constructed in step (5), the corresponding back temperature field can be quickly obtained;

[0014] Step (8): Based on the temperature field obtained in step (7), quantitatively analyze the distribution statistical characteristics such as mean and variance of the target temperature field under the influence of uncertainty, and calculate the reliability of the thermal protection system;

[0015] Step (9): If the reliability of the thermal protection system meets the requirements, the method ends; otherwise, sensitivity analysis is performed on each input uncertainty parameter, and the parameter with the highest sensitivity coefficient is selected for further optimization;

[0016] Step (10): For the parameters selected in step (9), perform multi-objective and multi-parameter uncertainty optimization on the system to obtain the optimal uncertainty distribution of each parameter under the current state. Based on this result, adjust the probability distribution of the uncertainty parameters and perform steps (4) to (10) again until the system finally meets the design requirements.

[0017] A computer program product stored on a non-transitory computer-readable medium, the computer program product comprising program codes for implementing the above-mentioned high-speed aircraft thermal protection system design and optimization method.

[0018] In a further preferred embodiment, in the method for designing and optimizing a high-speed aircraft thermal protection system, the estimation method of the uncertainty parameters in step (3) uses a non-parametric kernel density estimation method to estimate the uncertainty of the small sample parameters. It is not necessary to assume in advance the probability distribution type obeyed by the variable. The probability density function is obtained by selecting an appropriate kernel function and bandwidth and using a small sample of known samples. The parameter probability density function obtained is:

[0019]

[0020] Where K[·] is the kernel function; h is the bandwidth parameter used to control the smoothness of the kernel density estimation; and x represents the selected uncertainty parameter.

[0021] A further preferred embodiment is that in the method for designing and optimizing a thermal protection system for a high-speed aircraft, the sampling methods involved in step (4) include Monte Carlo sampling, Latin hypercube sampling, importance sampling, Sobol sequence sampling, and sampling result evaluation based on the Kolmogorov-Smirnov test.

[0022] In a further preferred embodiment, in the method for designing and optimizing a high-speed aircraft thermal protection system, a proxy model including parameter probability distribution characteristics is constructed in step (5) to solve the problem of high computational cost and low efficiency of traditional high-precision simulation models; the proxy model has the characteristics of fast simulation and high fitting accuracy. By approximating the original high-precision model with the proxy model, a fast and low-cost replacement of the high-precision model is achieved.

[0023] A further preferred solution is that in the method for designing and optimizing a high-speed aircraft thermal protection system, the parameterized physical information neural network proxy model in step (5) uses the design parameters containing uncertainty distribution information as the input of the neural network, and embeds the heat conduction physical equations, boundary constraints, etc. into the loss function of the neural network, so that the output results of the neural network are constrained within the scope of real physical information, getting rid of the dependence of traditional models on experimental or simulated data, and thus being more suitable for small sample situations. In addition, the interpretability of the model is enhanced by physical information constraints, so that the model can obtain predictions consistent with physical information, and the model has strong extrapolation and generalization capabilities.

[0024] In a further preferred embodiment, the method for designing and optimizing a high-speed aircraft thermal protection system, the Bayesian method in step (6) first assumes that the parameters of the proxy model obey a certain distribution, and then updates the posterior parameters using the actual system back-temperature field data obtained from the experiment according to the Bayesian theorem, and then uses the posterior distribution of the parameters to obtain the response prediction. The posterior update formula is:

[0025]

[0026] Where Y represents the system back-temperature field data obtained through the experiment; X represents the input parameter (material thermal conductivity, specific heat capacity, density, etc.) vector; w represents the model parameter.

[0027] A further preferred embodiment is the method for designing and optimizing a thermal protection system for a high-speed aircraft, in which the multi-objective and multi-parameter uncertainty optimization process of the thermal protection system in step (10) is optimized again based on the results of sensitivity analysis so that the design results meet the design requirements.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] (1) The present invention provides a thermal protection system design optimization method that takes into account the uncertainty of physical parameters, heat flux density, geometric shape, etc. in the design and application of the thermal protection system and the probability distribution characteristics of the parameters, and embeds it into the design process, thereby realizing uncertainty analysis of the thermal protection system and its design optimization, and reducing the design margin.

[0030] (2) The present invention uses kernel density theory to perform uncertainty modeling on small sample characteristic parameters such as material property parameters, input environment parameters, and processing technology parameters in thermal protection design, thereby achieving accurate modeling of the uncertainty distribution characteristics of the input parameters.

[0031] (3) In the process of design optimization, the present invention optimizes the design parameters through a proxy model based on physical information, so that the design model and results are interpretable and have strong extrapolation and generalization capabilities.

[0032] (4) The present invention adopts a probability-based optimization method to perform multi-parameter and multi-objective optimization, which can realize the refined design of the thermal protection system and effectively improve the performance of the thermal protection system and reduce the weight of the system while ensuring reliability.

[0033] (5) The present invention has improvements in small sample characterization, construction of proxy models and uncertainty correction, and provides a multi-objective and multi-parameter uncertainty optimization process for a thermal protection system, providing more scientific guidance for subsequent design optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flowchart of thermal protection system design and optimization method.

[0035] Figure 2 Schematic diagram of thermal protection structure.

[0036] Figure 3 This is the schematic diagram of the parameterized physical information neural network structure.

[0037] Figure 4 Schematic diagram of the multi-objective particle swarm optimization algorithm. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0039] A design and optimization method for a high-speed aircraft thermal protection system, such as Figure 1 As shown, including:

[0040] Step (1): Deterministically model the thermal protection system. Model the aircraft thermal protection system to simulate the real physical system. The thermal protection structure is as follows: Figure 2 As shown. The heat conduction process involved in the thermal protection system can be represented by the following partial differential equation model:

[0041]

[0042] In the formula, x is the spatial coordinate vector, t is time, T is the longest time to reach the maximum back temperature of the thermal protection system; u represents the solution of the equation, k, ρ, and c are the three physical parameters of the thermal insulation material, which are respectively expressed as the thermal conductivity, density, and specific heat capacity of the material, which can be uniformly expressed as λ; Ω represents the spatial domain.

[0043] The boundary conditions can be expressed as:

[0044]

[0045] The initial conditions can be expressed as:

[0046] u(x,t0)=g0(x),x∈Ω (5)

[0047] Among them, g0(x) and g Γ (x) represent the initial conditions and boundary conditions of the equation respectively; Ω represents a bounded region, and to its corresponding boundary.

[0048] Step (2): Based on the deterministic model, the uncertainty parameters of the thermal protection system design variables are quantitatively modeled. According to the performance and configuration requirements of the thermal protection system determined by the real environment, the uncertainty parameters of the material property parameters, the external environment heat flux density, the structural geometric parameters, etc. in the design process are quantitatively modeled for thermal protection design to form a quantitative characterization model containing uncertainty parameters.

[0049] Step (3): Select the uncertainty source in step (2) as the system uncertainty parameter to quantitatively characterize the uncertainty. Use kernel density estimation to characterize the probability distribution of small sample data of uncertain parameters such as material specific heat capacity, density, thermal conductivity, external environment heat flux density, thermal protection system structure thickness, layer spacing geometric parameters, etc. Through known samples, select kernel function and bandwidth, estimate probability density function, determine its probability distribution, and obtain parameter probability density function. for:

[0050]

[0051] Where K[·] is the kernel function; h is the bandwidth parameter, which controls the smoothness of the kernel density estimate; x represents the selected uncertainty parameter variable; N is the number of samples; i is the sample point number; X i is the ith sample.

[0052] Step (4): According to the probability distribution of the uncertainty parameters in step (3), Monte Carlo sampling, Latin hypercube sampling, and Sobol sequence sampling methods are used to sample each parameter respectively, and the sampling results of different sampling methods are evaluated and compared using the Kolmogorov-Smirnov test to screen out the optimal sampling result, thereby obtaining N different sample combinations X of uncertainty parameters. (i) .

[0053] The screening process of the Kolmogorov-Smirnov test is as follows:

[0054] First, based on the cumulative distribution function, by comparing the frequency distribution f(x) with the theoretical distribution g(x), the sample statistics are obtained to quantitatively analyze the degree of difference between the two distributions.

[0055] Secondly, assuming that the sample distribution and the theoretical distribution follow the same distribution, the sample statistic D = max|f(x)-g(x)| is used to evaluate the results, where D represents the maximum value of the distance between the two distributions. The smaller the value of this statistic, the closer the two distributions are.

[0056] Finally, based on the results of the Kolmogorov-Smirnov test, the optimal sampling method can be selected to make the obtained samples closer to the theoretical distribution and more representative.

[0057] Step (5): Based on step (3), a parameterized physical information neural network agent model is constructed to establish a fitting relationship between the uncertain input parameters and the system background temperature field.

[0058] Constructing a proxy model for rapid simulation and high-precision fitting of the thermal protection system avoids the high cost and low efficiency of direct simulation of high-precision models, and achieves rapid and low-cost replacement. By parameterizing the physical information neural network proxy model, the heat conduction equation of the thermal protection system is embedded into the loss function of the neural network, and the output results of the neural network are constrained by the physical process of heat conduction, so as to achieve high-precision applicability in simulation design under small sample conditions. In addition, the interpretability of the simulation model is enhanced through physical information constraints, so that the model can obtain predictions consistent with the physical constraints of the heat transfer process of the thermal protection system, realize the extrapolation and generalization capabilities of the simulation model, and improve the accuracy of extrapolation and generalization.

[0059] The structure of parameterized physical information neural network model is as follows Figure 3 As shown, the approximation theorem is used to make the network infinitely close to the continuous function. The automatic differentiation algorithm is used to make the output result the exact derivative of any input parameter. By embedding the physical constraint information of the thermal protection system into the loss function of the neural network, the output result of the neural network is constrained within the known physical information range. In the parameterized physical information neural network, a fully connected neural network is used to approximate the solution u(x, t). An M-layer neural network consists of an input layer, (M-2) hidden layers and an output layer. The spatial and time coordinates (x, t) and the uncertainty parameter λ are the input parameters (x, t, λ) of the neural network. The output value of the last layer is the approximate value of the solution u of the equation. Let the output vector of the nth hidden layer be z n , then the neural network can be expressed as:

[0060]

[0061] In the formula, z 0 represents the input layer of the neural network, z n (n=1,…,M-2) represents the output vector of (M-2) hidden layers, σ is the nonlinear activation function, W n and b n Represent the weight matrix and bias vector of the nth hidden layer, respectively, and are the parameters optimized during model training; z M-1 This is the approximate value of the solution u of the equation.

[0062] The loss function after adding physical constraints to the parameterized physical information neural network is:

[0063] L=α1L PDE +α2L IC +α3L BC (8)

[0064] Where, L PDE , L IC , L BCare the residuals of the control equation, initial condition and boundary condition respectively, where the partial differential operator is obtained by the method of automatic differentiation; α1, α2, α3 are the weight coefficients of the corresponding loss terms.

[0065] The optimal design result is obtained by training the parameterized physical information neural network. The training process is to optimize the parameters W n and b n , so that the loss function is minimized, so that the results learned by the neural network meet the physical information constraints. Generally, the mean square error (MSE) is used to measure the loss of L, and its loss function form is as follows:

[0066]

[0067] In the formula, the subscripts PDE, IC, and BC are the control equation, initial condition, and boundary condition equations, respectively; α1, α2, and α3 are the weight coefficients of the corresponding loss terms; N is the number of samples; i is the sample number, indicating the i-th sample; F is the residual of the partial differential control equation; x is the spatial coordinate vector; t is the time, and t0 is the initial time; g0(x) and g Γ (x) represent the initial conditions and boundary conditions of the equation respectively.

[0068] Step (6): First assume that the parameters of the proxy model obey a uniform distribution, then use the system background temperature field data obtained from the experiment to update the posterior parameters, and then use the posterior distribution of the parameters to obtain the response prediction. The posterior update formula P is:

[0069]

[0070] Where Y represents the system back-temperature field data obtained through the experiment; X represents the input parameter (such as material thermal conductivity, specific heat capacity, density, etc.) vector; w represents the model parameter.

[0071] Step (7): Combine the sample combination X of the uncertainty parameters obtained in step (4) (i) , input into the proxy model of step (5), the corresponding back temperature field can be quickly obtained;

[0072] Step (8): Based on the temperature field obtained in step (7), quantitatively analyze the distribution characteristics of the target temperature field under the influence of uncertainty and calculate the mean value. The formula is:

[0073]

[0074] Where N is the number of calculation results, U (i) Calculate the result for the i-th temperature field.

[0075] Variance σ UThe calculation formula is:

[0076]

[0077] In the formula, N is the number, U is (i) is the calculation result of the i-th temperature field, is the mean.

[0078] At the beginning of thermal protection design, reliability needs to be set, and the preferred reliability is 99.99%. The reliability R of the thermal protection system can be directly obtained from the statistical output results:

[0079]

[0080] Where, T lim is the maximum temperature that the system can withstand, T max is the highest temperature of the system, N represents the total number of repeated calculations using Monte Carlo sampling, and N(﹒) represents the number of times the corresponding situation occurs.

[0081] Step (9): If the reliability of the thermal protection system meets the requirements, the design is completed; otherwise, sensitivity analysis is performed on each input uncertainty parameter, and the parameter with the highest sensitivity coefficient is selected, adjusted within the probability distribution range, and redesigned. Sensitivity can be obtained based on the correlation coefficient.

[0082] The correlation coefficient of the output parameters to the input parameters in the thermal protection system design is expressed as:

[0083]

[0084] In the formula, r i The correlation coefficient between the i random input variables and the random output variable y can indicate the degree of correlation between the two. ij is the jth value of the ith random input variable; is the mean of the values ​​of the i-th random input variable; y j is the jth value of the random output variable; is the mean of the values ​​of the random output variable.

[0085] Based on the correlation, the sensitivity of the parameter can be obtained. The sensitivity coefficient can measure the influence of the variability of each random input variable on the system reliability. The sensitivity coefficient can be obtained by the correlation coefficient r i It turns out that its specific expression is:

[0086]

[0087] Step (10): For the parameters selected in step (9), perform multi-objective and multi-parameter uncertainty optimization on the system, such as Figure 4 As shown, the TOPSIS decision method is preferably used for implementation.

[0088] TOPSIS decision method assumes that the set of multi-attribute decision solutions is D = d1, d2, ..., d m , the attribute variables for measuring the quality of the scheme are x1, x2,…, x n , then each solution d in solution set D i (i=1,…,m) is a vector consisting of n attribute values ​​[a i_1 ,…,a i_n ], which, as a point in n-dimensional space, can uniquely characterize solution d i . Positive ideal solution C * is a virtual optimal solution that does not exist in the solution set D. Each of its attribute values ​​is the optimal value of the attribute in the decision matrix. The negative ideal solution C 0 is the virtual worst solution, and each of its attribute values ​​is the worst value of the attribute in the decision matrix. i With positive ideal solution C * and negative ideal solution C 0 The distance between the positive ideal solution and the negative ideal solution is compared. The solution that is close to the positive ideal solution and far away from the negative ideal solution is the optimal solution in the solution set D; and the priority of each alternative solution in the solution set D can be ranked accordingly. The key to the ideal solution method is to define an appropriate distance measure in the attribute space, so that the distance between the alternative solution and the ideal solution can be calculated. The TOPSIS method uses the Euclidean distance. When two alternative solutions have the same distance from the positive ideal solution, the distance between these two solutions and the negative ideal solution is calculated. The solution with the same distance to the positive ideal solution and far away from the negative ideal solution is the best. Based on the obtained set of optimal frontier solutions, the final design decision solution is obtained in the optimal solution set using the TOPSIS decision method.

[0089] Based on this result, the probability distribution of the uncertainty parameters is adjusted, and steps (4) to (10) are performed again until the system finally meets the design requirements.

[0090] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

[0091] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the above methods and technical contents without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the contents of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for designing and optimizing a high-speed aircraft thermal protection system, characterized in that: include: Step (1): Modeling the thermal protection system to simulate the real physical system; Step (2): Based on the deterministic model in step (1), the uncertain parameters and variables in the system are considered to perform quantitative characterization modeling; Step (3): Select the uncertainty source in step (2) as the system uncertainty parameter, and obtain the specific heat capacity, density, thermal conductivity, heat flux density, system surface emissivity and geometric size parameters as small sub-samples; According to the actual working condition samples, the kernel density estimation method is used to characterize the uncertainty of the small sample data and determine the probability distribution of each variable; Step (4): According to the probability distribution of the uncertainty parameters in step (3), sample each parameter separately to obtain N different sample combinations X of uncertainty parameters. (i) ; Step (5): The uncertainty parameters and coordinates selected in step (3) are used as the input of the model in step (2), and the known physical information is embedded into the model to construct a parameterized physical information neural network proxy model and establish a mapping relationship between the uncertainty input parameters and the system background temperature field; Step (6): According to the Bayesian theorem, the real system back temperature field data obtained from the experiment is used to optimize the parameters of the proxy model constructed in step (5), thereby correcting the uncertainty of the proxy model constructed in step (5); Step (7): Combine the sample combination X of the uncertainty parameters obtained in step (4) (i) , input into the proxy model constructed in step (5) to quickly obtain its corresponding back temperature field; Step (8): Based on the temperature field obtained in step (7), quantitatively analyze the distribution statistical characteristics of the target temperature field under the influence of uncertainty, and calculate the reliability of the thermal protection system; Step (9): If the reliability of the thermal protection system meets the requirements, the method ends; otherwise, sensitivity analysis is performed on each input uncertainty parameter, and the parameter with the highest sensitivity coefficient is selected for further optimization; Step (10): For the parameters selected in step (9), perform multi-objective and multi-parameter uncertainty optimization on the system to obtain the optimal uncertainty distribution of each parameter under the current state. Based on this result, adjust the probability distribution of the uncertainty parameters and return to steps (4) to (10) until the system finally meets the design requirements.

2. The high-speed aircraft thermal protection system design and optimization method according to claim 1, characterized in that: The uncertainty parameter estimation method in step (3) adopts the non-parametric kernel density estimation method.

3. The high-speed aircraft thermal protection system design and optimization method according to claim 2, characterized in that: The uncertainty estimation of small sample parameters is carried out by selecting appropriate kernel functions and bandwidths and using known samples of small samples to obtain the probability density function. The obtained parameter probability density function is: Where K[·] is the kernel function; h is the bandwidth parameter, which controls the smoothness of the kernel density estimate; x represents the selected uncertainty parameter variable; N is the number of samples; i is the sample point number; X i is the ith sample.

4. The high-speed aircraft thermal protection system design and optimization method according to claim 1, characterized in that: The sampling method in step (4) is one of the following methods: Monte Carlo sampling, Latin hypercube sampling, importance sampling, Sobol sequence sampling; and the sampling results based on the Kolmogorov-Smirnov test are used for evaluation and comparison.

5. The high-speed aircraft thermal protection system design and optimization method according to claim 1, characterized in that: The parameterized physical information neural network proxy model described in step (5) takes the design parameters containing uncertainty distribution information as the input of the neural network, and embeds the heat conduction physical equations, boundary constraints, etc. into the loss function of the neural network, so that the output results of the neural network are constrained within the range of real physical information.

6. The high-speed aircraft thermal protection system design and optimization method according to claim 1, characterized in that: The Bayesian method described in step (6) first assumes that the parameters of the proxy model obey a certain distribution, and then updates the posterior parameters using the actual system background temperature field data obtained from the experiment according to the Bayesian theorem, and then uses the posterior distribution of the parameters to obtain the response prediction; The posterior update formula is Where Y represents the system back-temperature field data obtained through the experiment; X represents the input parameter vector; and w represents the model parameter.

7. The high-speed aircraft thermal protection system design and optimization method according to claim 6, characterized in that: The input parameters are material thermal conductivity, specific heat capacity, and density.

8. The high-speed aircraft thermal protection system design and optimization method according to claim 1, characterized in that: In step (10), the multi-objective and multi-parameter uncertainty optimization process of the thermal protection system is optimized again based on the results of the sensitivity analysis so that the design results meet the design requirements.

9. The high-speed aircraft thermal protection system design and optimization method according to claim 1, characterized in that: In step (10), the TOPSIS decision method is used to achieve multi-objective and multi-parameter uncertainty optimization.

10. A computer program product stored on a non-transitory computer readable medium, the computer program product comprising a program code for carrying out the method according to any one of claims 1 to 9.

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