A Design and Optimization Method for Thermal Protection System of High-Speed ​​Aircraft

Abstract

A design and optimization method for a high-speed aircraft thermal protection system is proposed. This method considers the uncertainties and probability distribution characteristics of physical properties, heat flux density, and geometry in the design and application of the thermal protection system, embedding these factors into the design process to achieve uncertainty analysis and design optimization of the thermal protection system. Kernel density theory is used to model the uncertainties of small sample characteristic parameters such as material properties, input environment parameters, and processing parameters in the thermal protection design, achieving accurate modeling of the uncertainty distribution characteristics of input parameters. The design parameters are optimized through a surrogate model based on physical information, making the design model and results interpretable and possessing strong extrapolation and generalization capabilities.

Description

Technical Field

[0001] This invention relates to a design and optimization method for a thermal protection system for high-speed aircraft, belonging to the field of aircraft thermal protection technology. Background Technology

[0002] The thermal protection system of a high-speed aircraft plays a crucial role in its reliability and structural integrity. Optimizing the design of the thermal protection system has always been a vital aspect of aircraft design. Achieving optimal utilization of the thermal protection system has always been a key objective of thermal protection design. The aircraft's thermal protection system is the most critical system for ensuring the completion of flight missions and safeguarding the airframe's structural integrity and internal equipment safety; its design level is a significant indicator of the overall aircraft design level.

[0003] In the design of thermal protection systems, many uncertainties exist, primarily including dimensional deviations during component manufacturing and installation, aerodynamic and thermal changes caused by external environmental variations, and material instability due to temperature changes. Traditional thermal protection designs typically rely on redundancy design principles and extreme deviation design methods to address potential extreme situations, ensuring sufficient margin for effective thermal protection. However, with the current trend towards lightweight and integrated aircraft design, traditional methods often result in excessively heavy thermal protection systems, leading to low flight performance-to-weight ratios. Therefore, to improve aircraft performance, more refined and efficient design and optimization methods for thermal protection systems are essential. Summary of the Invention

[0004] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and provide a design and optimization method for a high-speed aircraft thermal protection system. The method adopts a multi-objective, multi-parameter uncertainty optimization design method for the thermal protection system, which effectively reduces the design margin of the system, improves the design accuracy and efficiency of the thermal protection system, and makes the thermal protection system more efficient.

[0005] The objective of this invention is achieved through the following technical solutions:

[0006] A method for designing and optimizing a thermal protection system for high-speed aircraft, comprising the following steps:

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

[0008] Step (2): Based on the deterministic model in step (1), consider the uncertain parameters and variables in the system to perform quantitative characterization modeling. According to the performance and configuration requirements determined by the real environment of the thermal protection system, the uncertain parameters that need to be considered are initially determined. For multilayer thermal protection systems, 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 sample data such as specific heat capacity, density, thermal conductivity, heat flux density, system surface emissivity, and geometric dimensions. Based on the actual working condition samples, use kernel density estimation to characterize the uncertainty of the small sample data and determine the probability distribution of each variable;

[0010] Step (4): Based on 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 inputs to the model in step (2), and the known control equations, boundary conditions and other physical information 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): Based on Bayes' theorem, the parameters of the surrogate 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 X of the uncertainty parameters obtained in step (4) (i) Inputting this into the proxy model constructed in step (5) allows for the rapid acquisition of its corresponding back temperature field.

[0014] 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, such as mean and variance, 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, perform sensitivity analysis on each input uncertainty parameter, select the parameter with the highest sensitivity coefficient, and perform further optimization.

[0016] Step (10): For the parameters selected in step (9), perform multi-objective 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 repeat steps (4) to (10) 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 code for implementing the above-described high-speed aircraft thermal protection system design and optimization method.

[0018] A further preferred embodiment of the high-speed aircraft thermal protection system design and optimization method, in step (3), the uncertainty parameter estimation method adopts a non-parametric kernel density estimation method to estimate the uncertainty of the small sample parameters. It does not require prior assumption of the probability distribution type followed by the variables. It only selects an appropriate kernel function and bandwidth, and uses known samples of the small sample to obtain the probability density function. The obtained parametric probability density function is:

[0019]

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

[0021] In a further preferred embodiment, the sampling methods involved in step (4) of the aforementioned high-speed aircraft thermal protection system design and optimization method include Monte Carlo sampling, Latin hypercube sampling, importance sampling, Sobol sequence sampling, and sampling result evaluation based on the Kolmogorov-Smirnov test.

[0022] A further preferred embodiment of the high-speed aircraft thermal protection system design and optimization method, in step (5), constructs a surrogate model containing parameter probability distribution characteristics to solve the problems of high computational cost and low efficiency of traditional high-precision simulation models; the surrogate model has the characteristics of fast simulation and high fitting accuracy. By approximating the original high-precision model with the surrogate model, a fast and low-cost replacement of the high-precision model is achieved.

[0023] A further preferred embodiment of the high-speed aircraft thermal protection system design and optimization method, in step (5), the parameterized physical information neural network proxy model uses design parameters containing uncertainty distribution information as input to the neural network, and embeds the heat conduction physical equation, boundary constraints, etc., into the loss function of the neural network. This constrains the output of the neural network within the range of real physical information, freeing it from the dependence of traditional models on experimental or simulated data, thus making it more suitable for small sample situations. In addition, the physical information constraint enhances the interpretability of the model, enabling the model to obtain predictions consistent with physical information. The model has strong extrapolation and generalization capabilities.

[0024] A further preferred embodiment of the high-speed aircraft thermal protection system design and optimization method, in step (6) the Bayesian method, first assumes that the parameters of the surrogate model follow a certain distribution, then updates the posterior parameters using the actual system back-end temperature field data obtained from experiments according to Bayes' theorem, and then uses the posterior distribution of the parameters to obtain the response prediction. The posterior update formula is as follows:

[0025]

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

[0027] In a further preferred embodiment, the design and optimization method for a high-speed aircraft thermal protection system, step (10) of the thermal protection system multi-objective multi-parameter uncertainty optimization process, is further optimized 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 advantages:

[0029] (1) The present invention provides a design optimization method for thermal protection systems that takes into account the uncertainty of physical property parameters, heat flux density and geometric shape and the probability distribution characteristics of parameters in the design and application of thermal protection systems. It embeds these into the design process, realizes the uncertainty analysis and design optimization of thermal protection systems, and reduces the design margin.

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

[0031] (3) In the process of optimizing the design, the present invention optimizes the design parameters by using 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 uses a probability-based optimization method to perform multi-parameter and multi-objective optimization, which can realize the fine design of the thermal protection system and effectively improve the performance of the thermal protection system and reduce the system weight while ensuring reliability.

[0033] (5) This invention has made improvements in small sample characterization, surrogate model construction and uncertainty correction, and provides a multi-objective multi-parameter uncertainty optimization process for thermal protection systems, providing more scientific guidance for subsequent design optimization. Attached Figure Description

[0034] Figure 1 A flowchart illustrating the design and optimization methodology for thermal protection systems.

[0035] Figure 2 This is a schematic diagram of a thermal protection structure.

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

[0037] Figure 4 This is a schematic diagram of the optimization algorithm for multi-objective particle swarm optimization. Detailed Implementation

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

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

[0040] Step (1): Deterministically model the thermal protection system. Model the aircraft's thermal protection system to simulate a 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 a 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 three physical property parameters of the thermal insulation material, which are respectively represented as the thermal conductivity, density, and specific heat capacity of the material, and can be uniformly represented 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] Where g0(x) and g Γ (x) represent the initial and boundary conditions of the equation, respectively; Ω represents a bounded region, and Its corresponding boundary.

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

[0049] Step (3): Select the sources of uncertainty from step (2) as system uncertainty parameters for quantitative characterization of uncertainty. Kernel density estimation is used to characterize the probability distribution of small sample data of uncertain parameters such as the specific heat capacity, density, and thermal conductivity of the material, the heat flux density of the external environment, and the structural thickness and interlayer spacing geometric parameters of the thermal protection system. Using known samples, the kernel function and bandwidth are selected to estimate the probability density function and determine its probability distribution. The resulting parameter probability density function... for:

[0050]

[0051] In the formula, K[·] is the kernel function; h is the bandwidth parameter, which controls the smoothness of the kernel density estimation; x represents the selected uncertainty parameter variable; N is the number of samples; i is the sample point number; X i Let i be the i-th sample.

[0052] Step (4): Based on 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 separately. The Kolmogorov-Smirnov test is used to evaluate and compare the sampling results of different sampling methods, and the optimal sampling result is selected to obtain N different sample combinations X of uncertainty parameters. (i) .

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

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

[0055] Secondly, it is assumed 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 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 sample closer to the theoretical distribution and the sample more representative.

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

[0058] A surrogate model is constructed for rapid simulation and high-precision fitting of thermal protection systems, avoiding the high computational cost and low efficiency of direct simulation of high-precision models, thus achieving a fast and low-cost alternative. By using a parameterized physical information neural network surrogate model, the heat conduction equations of the thermal protection system are embedded into the loss function of the neural network. The output results of the neural network are constrained by the physical process of heat conduction, achieving high-precision applicability in simulation design under small sample conditions. Furthermore, the physical information constraints enhance the interpretability of the simulation model, enabling it to obtain predictions consistent with the physical constraints of the heat transfer process in the thermal protection system, improving the extrapolation and generalization capabilities of the simulation model and enhancing the accuracy of extrapolation and generalization.

[0059] The structure of a parameterized physical information neural network model is as follows: Figure 3 As shown, an approximation theorem is used to make the network infinitely close to a continuous function. An automatic differentiation algorithm is used to ensure the output result has an exact derivative with respect to any input parameters. 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 range of known physical information. 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 temporal 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 an approximation of the solution u. Let the output vector of the nth hidden layer be z. n Then the neural network can be represented as:

[0060]

[0061] In the formula, z 0 z represents the input layer of the neural network. n (n = 1, ..., M-2) represents the output vectors of (M-2) hidden layers, σ is the non-linear activation function, and W... n and b n These represent the weight matrix and bias vector of the nth hidden layer, respectively, and are obtained by optimizing the parameters during model training; z M-1 This is an approximate value of the solution u to the equation.

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

[0063] L=α1L PDE +α2L IC +α3L BC (8)

[0064] In the formula, L PDE L IC L BCThese are the residuals of the governing equations, initial conditions, and boundary conditions, respectively, where the partial differential operators are obtained through automatic differentiation; α1, α2, and α3 are the weight coefficients of the corresponding loss terms.

[0065] The optimal design result is obtained by training a parameterized physical information neural network. The training process involves optimizing the parameter W. n and b n This minimizes the loss function, ensuring that the results learned by the neural network satisfy the physical information constraints. Generally, the mean squared error (MSE) is used to measure the loss of L, and its loss function is as follows:

[0066]

[0067] In the formula, subscripts PDE, IC, and BC represent the governing equation, initial condition equation, and boundary condition equation, 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, representing the i-th sample; F is the residual of the partial differential governing equation; x is the spatial coordinate vector; t is time, and t0 is the initial time; g0(x) and g Γ (x) represent the initial and boundary conditions of the equation, respectively.

[0068] Step (6): First, assume that the parameters of the surrogate model follow a uniform distribution. Then, update the posterior parameters using the system back-temperature field data obtained from the experiment. Finally, use the posterior distribution of the parameters to obtain the response prediction. The posterior update formula P is:

[0069]

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

[0071] Step (7): Combine the sample X of the uncertainty parameters obtained in step (4) (i) Inputting this into the proxy model in step (5) allows for the rapid acquisition of its corresponding back temperature field.

[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. The formula is:

[0073]

[0074] In the formula, N represents the number of calculation results, and U (i) This is the calculation result for the i-th temperature field.

[0075] Variance σ UThe calculation formula is:

[0076]

[0077] In the formula, N represents the quantity, and U (i) The result of the calculation for the i-th temperature field. This is the mean.

[0078] At the initial stage of thermal protection design, a reliability level needs to be set, with 99.99% being the preferred level. The reliability R of the thermal protection system can be directly obtained from the statistical output results:

[0079]

[0080] In the formula, T lim T is the maximum temperature that the system can withstand. max The highest temperature of the system is N, which represents the total number of times the Monte Carlo sampling was repeated, and N(﹒) represents the number of times the corresponding condition occurred.

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

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

[0083]

[0084] In the formula, r i The correlation coefficient between the i-th random input variable and the random output variable y represents the degree of correlation between them; the x-th... ij Let j be the j-th value of the i-th random input variable; Let y be the mean of the values ​​of the i-th random input variable; j This is the j-th value of the random output variable; This is the mean of the values ​​taken by the random output variable.

[0085] Based on correlation, the sensitivity of parameters can be obtained. The sensitivity coefficient measures the impact of the variability of each random input variable on the reliability of the system. The sensitivity coefficient can be derived from the correlation coefficient r. i Therefore, its specific expression is:

[0086]

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

[0088] The TOPSIS decision method assumes a multi-attribute decision set as D = d1, d2, ..., d m The attribute variables for evaluating the merits of a solution are x1, x2, ..., x. n At this point, each solution d in the solution set D... i A vector (i = 1, ..., m) consisting of n attribute values ​​is [a i_1 ,…,a i_n As a point in n-dimensional space, it can uniquely represent scheme d. i The ideal solution C * A virtual optimal solution is a solution that does not exist in the solution set D, and each of its attribute values ​​is the optimal value of that attribute in the decision matrix; while the negative ideal solution C... 0 This represents a virtual worst-case scenario, where each attribute value is the worst value of that attribute in the decision matrix. In n-dimensional space, each alternative scenario d in the solution set D is considered... i With the ideal solution C * and negative ideal solution C 0 The optimal solution in solution set D is determined by comparing the distances to the positive ideal solution and the negative ideal solution. The solution that is both close to the positive ideal solution and far from the negative ideal solution is then ranked according to its distance from the positive ideal solution. The key to the ideal solution method is defining an appropriate distance measure in the attribute space to calculate the distances between the alternative solutions and the ideal solution. The TOPSIS method uses Euclidean distance. When two alternative solutions have the same distance from the positive ideal solution, the distances between these two solutions and the negative ideal solution are calculated. The alternative solution with the same distance from the positive ideal solution but farther from the negative ideal solution is considered superior. Based on the obtained set of optimal frontier solutions, the TOPSIS decision method is used to obtain the final design decision solution from the optimal solution set.

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

[0090] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0091] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention using the above methods and techniques without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for designing and optimizing a thermal protection system for high-speed aircraft, characterized in that, include: Step (1): Model the thermal protection system to simulate the real physical system; Step (2): Based on the deterministic model in step (1), consider the uncertain parameters and variables in the system to perform quantitative characterization modeling; Step (3): Select the uncertainty sources in step (2) as system uncertainty parameters, and obtain specific heat capacity, density, thermal conductivity, heat flux density, system surface emissivity and geometric size parameters as small sample samples; Based on actual working condition samples, the kernel density estimation method is used to characterize the uncertainty of small sample data and determine the probability distribution of each variable. Step (4): Based on 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 inputs to 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 back temperature field. Step (6): Based on Bayes' theorem, the parameters of the surrogate 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 surrogate model constructed in step (5). Step (7): Combine the sample X of the uncertainty parameters obtained in step (4) (i) Input it 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 statistics 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, perform sensitivity analysis on each input uncertainty parameter, select the parameter with the highest sensitivity coefficient, and perform further optimization. Step (10): For the parameters selected in step (9), perform multi-objective 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 design and optimization method for a high-speed aircraft thermal protection system according to claim 1, characterized in that, In step (3), the uncertainty parameter is estimated using a non-parametric kernel density estimation method.

3. The design and optimization method for a high-speed aircraft thermal protection system according to claim 2, characterized in that, Uncertainty estimation of small sample parameters can be performed by selecting an appropriate kernel function and bandwidth, and obtaining the probability density function using known samples of the small sample. The resulting parametric probability density function is as follows: In the formula, K[·] is the kernel function; h is the bandwidth parameter, which controls the smoothness of the kernel density estimation; x represents the selected uncertainty parameter variable; N is the number of samples; i is the sample point number; X i Let i be the i-th sample.

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

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

6. The design and optimization method for a high-speed aircraft thermal protection system according to claim 1, characterized in that, The Bayesian method described in step (6) first assumes that the parameters of the surrogate model follow a certain distribution, and then updates the posterior parameters using the real system back temperature field data obtained from the experiment according to Bayes' theorem. After that, the posterior distribution of the parameters is used to obtain the response prediction. The posterior update formula is In the formula, Y represents the system back temperature field data obtained through experiments; X represents the input parameter vector; and w represents the model parameters.

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

8. The design and optimization method for a high-speed aircraft thermal protection system 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 further optimized based on the results of sensitivity analysis, so that the design results meet the design requirements.

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

10. A computer program product stored on a non-transitory computer-readable medium, the computer program product comprising program code for performing the method as described in any one of claims 1 to 9.

Images