Thermal insulation structure reliability optimization method based on Bootstrap sampling

Abstract

The invention discloses a thermal insulation structure reliability optimization method based on Bootstrap sampling, and relates to the field of thermal insulation of high-speed aircrafts, and the method comprises the steps: S1, setting model parameters and uncertain distribution parameters of thermal insulation structure design based on actual demands; s2, in a particle swarm optimization (PSO) method, generating K1 groups of uncertain variable parameter samples for each particle in the population, and calculating each particle in the population according to a heat transfer equation and a boundary condition to obtain K1 groups of # imgabs0 # and # imgabs1 #; s3, based on a Bootstrap sampling method, the # imgabs2 # and the # imgabs3 # are expanded to the # imgabs4 # and the # imgabs5 # of the K2 group, and the failure probability # imgabs6 # of all particles in the current iteration population is obtained through statistics and traversal and serves as a reliability constraint condition of an optimization target; and S4, based on the model parameters and the uncertain distribution parameters in the S1, solving the reliability optimization model to obtain design variables of the heat insulation structure. According to the heat insulation structure reliability optimization method based on Bootstrap sampling, the consistency of the heat insulation structure optimization design result and the actual result is higher.

Description

Technical Field

[0001] The present invention relates to the field of heat insulation of high-speed aircraft, and more specifically, to a heat insulation structure reliability optimization method based on Bootstrap sampling. Background Art

[0002] The thermal insulation structure is a key factor in protecting the safety of high-speed aircraft and completing various tasks. An effective thermal insulation structure can meet the basic needs of high-speed aircraft for heat protection and insulation, protecting it from damage in extreme aerodynamic thermal environments. Figure 2 As shown, its thermal insulation structure mainly includes an anti-ablation layer K, a thermal insulation layer G, and a bearing layer C from the outside to the inside. h K , h G , h C are the thickness of the anti-ablation layer, the heat insulation layer, and the bearing layer, respectively. T H is the temperature load outside the anti-ablation layer, T L is the ambient temperature in the cabin, T in is the temperature of the inner surface of the bearing layer, T out It is the temperature of the outer surface of the anti-ablation layer. In actual application, the extremely high temperature thermal environment that high-speed aircraft are subjected to during flight heats the high-temperature resistant layer of the multi-layer insulation structure through forced convection heat transfer, and at the same time, the burn-resistant layer radiates heat to the external space to remove part of the heat. The main heat of the remaining heat is blocked by the insulation layer, and a small part of the heat is absorbed, stored and transferred to the base layer by the burn-resistant layer's own material. The base layer structure and the internal air undergo natural convection heat exchange. The quality of the thermal insulation performance of the multi-layer insulation structure mainly depends on the insulation layer material parameters and the thickness of each layer. The equivalent mechanical properties of the overall structure are mainly determined by the base material parameters. Therefore, the base layer is sometimes called a load-bearing layer according to its function. However, in the current optimization design of the multi-layer insulation structure of high-speed aircraft, the emphasis is different, and the more mature technologies are mainly divided into the following categories: First, when designing the multi-layer thermal insulation structure of a high-speed aircraft, the focus is mainly on optimizing the multi-layer thermal insulation structure by considering the material type selection under the determined material parameters. For example, the patent application is named "A method for optimizing the design of a multi-layer thermal insulation structure of a high-speed aircraft". The case mainly establishes an optimization model by considering the material selection of each layer to achieve the purpose of lightweight optimization of the structure; Second, when designing multi-layer thermal insulation structures for high-speed aircraft, the focus is mainly on the consideration of bionic optimization methods. For example, the patent application is titled "Optimization method and system for thermal protection scheme of integrated thermal insulation structure". This case mainly uses particle swarm algorithm to optimize the structure and obtain the optimized thickness of each layer; Third, in the multi-layer thermal insulation structure of high-speed aircraft, the main focus is on solving the non-steady-state heat transfer equation. For example, the patent application is named "A rapid analysis and design method for aerospace vehicle thermal protection system". This case mainly solves the one-dimensional non-steady-state heat transfer equation through a one-dimensional heat conduction finite difference format to achieve the goal of obtaining the structural temperature response, and optimizes the thickness of each layer with the goal of lightweight.

[0003] However, when using the above three methods to design multi-layer thermal insulation structures for high-speed aircraft, the uncertainty of material parameters and temperature loads is not taken into account. In actual applications, there is a certain uncertainty in material properties and loads compared with theoretical design values. This leads to the problem that after the thermal insulation structure is designed, there will be inconsistency between the optimized design results and the actual results. Summary of the invention

[0004] An object of the present invention is to solve at least the above problems and / or disadvantages and to provide at least the advantages which will be described hereinafter.

[0005] In order to achieve these purposes and other advantages of the present invention, a reliability optimization method for a thermal insulation structure based on Bootstrap sampling is provided, comprising: S1. Set the model parameters and uncertain distribution parameters of the thermal insulation structure design based on actual needs; S2. In the particle swarm optimization PSO method, for each particle in the population, a K 1 set of uncertain variable parameter samples, and then calculate each particle in the population according to the heat transfer equation and boundary conditions to obtain K Temperature of the inner surface of the bearing layer 1 and equivalent modulus ; S3, based on the Bootstrap sampling method, , Expand to K Temperature of the inner surface of the 2 groups of bearing layers and equivalent modulus , the failure probability of all particles in the current iteration population is obtained by statistics and traversal , as the reliability constraint of the optimization objective; S4, based on the model parameters and uncertain distribution parameters in S1, the reliability optimization model is solved to obtain the design variables of the thermal insulation structure; Among them, in S2, the particles refer to the thickness of the anti-ablation layer, the bearing layer, and the thermal insulation layer.

[0006] Optionally, in S1, the model parameters include: the minimum equivalent modulus allowed E min , Maximum allowable temperature of the bearing layer , Ambient temperature in the cabin T L , Temperature load outside the anti-ablation layer T H , minimum thickness of the anti-ablation layer x 1min , the maximum thickness of the anti-ablation layer x 1max , minimum thickness of the bearing layer x 2min , Maximum thickness of the bearing layer x 2max , minimum thickness of insulation layer x 3min , Maximum thickness of thermal insulation layer x 3max , forced convection heat transfer coefficient between the outer surface of the anti-ablation layer and the temperature load , the natural convection heat transfer coefficient between the inner surface of the bearing layer and the static fluid at room temperature , stop calculating time t end , the minimum equivalent modulus allowed E min , maximum allowable failure probability P max , the number of samples of the first group of uncertain variable parameters K 1. The number of samples of the second group of uncertain variable parameters K 2; The uncertain distribution parameters include: temperature load variation coefficient, E K is the Young's modulus of the anti-ablation layer K, E G is the Young's modulus of the thermal insulation layer G, E C is the Young’s modulus of the load-bearing layer C.

[0007] Optionally, in S2, the heat transfer equation is characterized by the following formula: In the above formula, T is temperature, t is time, ρ is the density, β is the specific heat capacity, is the thermal conductivity, z is the thickness direction coordinate; The boundary condition is characterized by the following formula: In the above formula, is the thermal conductivity parameter of the anti-ablation layer material, h K-HTF is the forced convection heat transfer coefficient between the outer surface of the anti-ablation layer and the temperature load, ε is the emissivity, σ is the Stefan-Boltzmann constant, T out is the temperature of the outer surface of the anti-ablation layer, is the thermal conductivity parameter of the bearing layer material, h C-NTF is the natural convection heat transfer coefficient between the inner surface of the bearing layer and the static fluid at room temperature, is the gradient of temperature T with respect to spatial coordinate z, t is time, h K is the thickness of the anti-ablation layer, h G is the thickness of the insulation layer, h C is the thickness of the bearing layer, is the temperature of the inner surface of the bearing layer at time t, T L is the ambient temperature in the cabin; Equivalent modulus It is characterized by the following formula: In the above formula, E K is the Young's modulus of the anti-ablation layer K, E G is the Young's modulus of the thermal insulation layer G, Ec is the Young's modulus of the load-bearing layer C; Among them, the The temperature response of the inner surface of the K1 group calculated under different parameters of the K1 group is obtained based on the heat transfer equation and boundary conditions and is solved and calculated by the pde function in MATLAB.

[0008] Optionally, in S3, the failure probability The acquisition process includes: S30, for the observed samples ,make , i =1,2,… n ,and n = K 1 , If the distribution function is unknown, then the empirical distribution function constructed by the observed sample is Fn It is characterized by the following formula: In the above formula, Yes x 1, x 2,…, x n The order statistics obtained after sorting from small to large, k =1,2,…,n-1; S31. Take a random variable with a Dirichlet distribution Perform sample extraction to obtain a regenerated self-service sample ,and N = K 2, ; S32. Estimation of error is performed by the following formula: In the above formula, is the empirical distribution function of the bootstrap sample, R n is a random variable and F n The function of is the overall parameter The estimated value of ; S33, estimate the unknown parameters, and repeat S30 to S33 to obtain the stable value of the desired parameter; S33, based on and Statistically obtain the failure probability of the corresponding particles P f , by traversing all particles in the population, the failure probability of all particles in this iteration population is obtained .

[0009] Optionally, in S4, the reliability optimization model is characterized by the following formula: In the above formula, x represents the variable to be optimized, t is the time, ρ obj To optimize the objective function, x min is the lower limit of the design variable, x max is the upper limit of the design variable, , , are variables in the uncertain distribution parameters, and , , , , , They are , , The probability density function is obeyed, T H is the temperature load outside the anti-ablation layer, for T H The probability density function obeyed at time t is, t end To stop counting time, θ max is the maximum allowable temperature of the bearing layer, E min To allow for a minimum equivalent modulus, P max is the maximum allowed failure probability, E eff is the equivalent modulus, T in The temperature of the inner surface of the bearing layer, P f is the failure probability of the corresponding particle, , , are the thermal conductivity parameters of the anti-ablation layer, thermal insulation layer, and bearing layer materials, β K , β G , β C They are the specific heat capacities of the anti-ablation layer, thermal insulation layer and bearing layer materials respectively.

[0010] The present invention includes at least the following beneficial effects: Compared with the prior art, in the process of optimizing the design of multi-layer thermal insulation structures of high-speed aircraft, the present invention introduces failure probability constraints into the optimization design model to solve the problem of optimizing the thermal insulation structure under reliability constraints. The obtained solution is more in line with the needs of practical applications and effectively reduces the risk of failure during use.

[0011] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flow chart of the reliability optimization method of thermal insulation structure based on Bootstrap sampling of the present invention; Figure 2It is a schematic diagram of the layout of the heat insulation structure of the present invention; Figure 3 A schematic diagram of temperature load in an embodiment of the present invention; Figure 4 It is a schematic diagram of the optimization result in the embodiment of the present invention. DETAILED DESCRIPTION

[0013] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0014] Aiming at the optimization design of multi-layer thermal insulation structures of high-speed aircraft, the present invention proposes a thermal insulation structure reliability optimization method based on Bootstrap sampling, which is used to solve the problem that the existing optimization design method of multi-layer thermal insulation structures of high-speed aircraft does not consider the uncertainty of material parameters and loads. The failure probability constraint condition is introduced into the optimization design model to solve the optimization design problem of the thermal insulation structure under reliability constraints, which is more in line with the needs of practical applications.

[0015] A reliability optimization method for thermal insulation structures based on Bootstrap sampling, comprising: S10, setting the number of iterations, the number of populations, the material parameters involved in the optimization model parameters, the uncertain distribution parameters related to the load, etc.; S20, for each particle in the population, generates K 1 set of uncertain variable parameter samples, for most cases K 1 cannot be very large; S30, for each particle in the population, that is, the thickness of each group, is calculated according to the heat transfer equation and boundary conditions. K Temperature of the inner surface of the bearing layer 1 and equivalent modulus ; The heat transfer equation is: in, T is temperature, t is time, ρ is the density, β is the specific heat capacity, is the thermal conductivity, z is the thickness direction coordinate.

[0016] The boundary conditions are: in, is the thermal conductivity parameter of the anti-ablation layer material, h K-HTF is the forced convection heat transfer coefficient between the outer surface of the anti-ablation layer and the temperature load, ε is the emissivity (between 0 and 1), σ is the Stefan-Boltzmann constant, T out is the temperature of the outer surface of the anti-ablation layer, is the thermal conductivity parameter of the bearing layer material, h C-HT is the natural convection heat transfer coefficient between the inner surface of the bearing layer and the static fluid at room temperature, , is the gradient of temperature T with respect to spatial coordinate z, and t is time.

[0017] for K Calculated under 1 set of different parameters K 1 set of internal surface temperature responses, based on the heat transfer equation and boundary conditions, are calculated by solving the pde function in MATLAB; The equivalent modulus is: in, , E K is the Young's modulus of the anti-ablation layer K, E G is the Young's modulus of the thermal insulation layer G, Ec is the Young's modulus of the load-bearing layer C, one(3)=[1 1 1 ], x=[ h K h G h C ], h K is the thickness of the anti-ablation layer, h G is the thickness of the insulation layer, h C is the thickness of the bearing layer.

[0018] S40, according to the Bootstrap sampling method, K 1 group of bearing layer inner surface temperature and equivalent modulus extended to K 2 groups of bearing layer inner surface temperature and equivalent modulus This step mainly solves the problem that the uncertainty parameters under small samples are difficult to estimate. Therefore, the Bootstrap sampling method is used to estimate the uncertainty parameters during structural optimization. By considering the structural failure probability constraint, a design scheme that meets the actual engineering situation is obtained. It specifically includes the following sub-steps: S401, Empirical distribution function construction Due to observation sample The sample size of is limited. , i=1,2,… n , is an unknown distribution function, then the empirical distribution function constructed by the observed sample is: In the formula, is an order statistic, x 1, x 2,…, x n After sorting from small to large, here n= K 1.

[0019] Assumptions is some parameter of the population, such as mean and variance, is the overall parameter The estimated value of is defined as: in, error n for The estimation error is error n is a random variable X and F function.

[0020] S402, sample extraction Take a random variable with a Dirichlet distribution ,in Let be a uniformly distributed random number from (0,1) and arranged from small to large. , , then: These N groups of resampled samples are defined as: , the regenerated resampled sample is called a bootstrap sample, and Each time a computer sampling is performed, a set of V i , and accordingly we can get a resampled sample . j changes sampling n times to get a set of data, a total of N groups of samples, here N = K 2.

[0021] S403, error estimation calculation The error estimate is calculated as follows: R n : In the formula, is the empirical distribution function of the bootstrap sample, R nis a random variable and F n The function of , with the help of computer multiple sampling, can be obtained R n The probability distribution of .

[0022] S404, unknown parameter estimation error n The distribution and R n The distribution of joint, we can get: Computer Simulated Sampling K 2 times, K 2 can be 10000 or larger, and we can get K2 , unknown parameters The distribution and characteristic values ​​of can be calculated using corresponding statistical methods.

[0023] Repeat S402 to S404 to gradually obtain the stable value of the desired parameter.

[0024] S50, based on K 2 sets of inner surface temperature and equivalent modulus of the bearing layer, statistically obtained the failure probability of the particle P f ; S60, traverse all particles in the population and obtain the failure probability of all particles in the population in this iteration ; S70, finding all particles that meet the failure probability requirement, obtaining the particle with the best objective function as the best particle of this generation, and recording the characteristic parameters of the particle; The optimization model is: in, x represents the variables to be optimized, specifically the thickness of the anti-ablation layer, the thermal insulation layer and the bearing layer, t is the time, ρ obj To optimize the objective function (i.e., surface mass density), x min is the lower limit of the design variable, x max is the upper limit of the design variable, , , are variables in the uncertain distribution parameters, and , , , , , They are , , The probability density function is obeyed, T H is the temperature load outside the anti-ablation layer, for T H The probability density function obeyed at time t is, t end To stop counting time, θ max is the maximum allowable temperature of the bearing layer, E min To allow for a minimum equivalent modulus, P max is the maximum allowed failure probability, E eff is the equivalent modulus, T in The temperature of the inner surface of the bearing layer, P f is the failure probability of the corresponding particle, , , are the thermal conductivity parameters of the anti-ablation layer, thermal insulation layer, and bearing layer materials, β K , β G , β C They are the specific heat capacities of the anti-ablation layer, thermal insulation layer and bearing layer materials respectively.

[0025] S80, update the population particles, update the particle position and speed to generate a new population, repeat S20-S70, if the new optimal particle is better than the previous optimal particle, then update the optimal particle, otherwise do not update; S90, when the number of iteration updates reaches the maximum number of iterations, the iteration is stopped and the optimized design variables (i.e., the geometric dimensions of each part of the thermal insulation structure) are output.

[0026] Example: like Figure 1 As shown, the steps of the practical application of the present invention include: S1. Set the value of the uncertain distribution parameter in the optimization model to: x 1min =0.5mm, x 1max =3mm, x 2min =5mm, x 2max =50mm, x3min =2mm, x 3max =5mm, E min =10Gpa, T H =1200℃, T L =25℃, θ max =70℃, h K-HTF =230W / (m 2 ℃) h C-NTF =10 W / (m 2 ℃) t end =600s, K1=50, K2=10000, P max =0.01, E min =140GPa.

[0027] Setting temperature loads in uncertain distribution parameters T H The coefficient of variation is 0.05. For the settings of Young's modulus, thermal conductivity, specific heat capacity, etc., the parameter data set of the anti-ablation layer material parameters Inconel 718 is shown in Table 1: Table 1 The parameter data set of the insulation layer material parameters Saffil is shown in Table 2: Table 2 The parameter data set of the bearing layer material parameters 2024 aluminum alloy is shown in Table 3: Table 3 S2. In the particle swarm optimization PSO method, for each particle in the population, a K 1 A set of uncertain variable parameter samples is then calculated for each particle in the population according to the heat transfer equation and boundary conditions to obtain K 1 Inner surface temperature of bearing layer and equivalent modulus ; S3, based on the Bootstrap sampling method, , Expand to K Temperature of the inner surface of the 2 groups of bearing layers and equivalent modulus , the failure probability of all particles in the current iteration population is obtained by statistics and traversal , as the reliability constraint of the optimization objective; S4, based on the model parameters and uncertain distribution parameters in S1, the reliability optimization model is solved to obtain the design variables of the thermal insulation structure; Among them, the change of temperature load in the above process is as follows: Figure 3 As shown (in Figure 3 In the figure, the solid line is the temperature curve, the dashed line is the upper limit of 3σ, and the dotted line is the lower limit of 3σ); In the above process, PSO optimization is used, the population size is 50, and the number of iterations is 200. The optimization results are as follows: Figure 4 As shown (in Figure 4 In the figure, the solid line is the objective function curve, the dotted line is the failure probability curve, and the design variables at A are: [1.0183, 47.7569, 2.2089] mm, 16.8211 kg / m 2 ; The design variables at B are: [0.6491, 46.6154, 2.0856] mm, 13.4285 kg / m 2 ; D is the maximum allowable failure probability). According to the optimization results, the optimal value of the objective function is 13.4285kg / m 2 , the corresponding design variables are: x = (0.6491, 46.6154, 2.0856) mm. During the entire optimization process, the probability of particle failure is less than 0.01, which meets the reliability constraints.

[0028] In actual engineering applications, 100% reliable situations do not exist. In most cases, it is sufficient to meet the requirements of failure probability. This method introduces failure probability into structural optimization design to make the optimization design results more in line with actual conditions.

[0029] The above solution is only an illustration of a preferred embodiment, but is not limited thereto. When implementing the present invention, appropriate replacement and / or modification can be performed according to user needs.

[0030] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and the embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily realized. Therefore, without departing from the general concept defined by the claims and equivalent scope, the present invention is not limited to the specific details and the illustrations shown and described here.

Claims

1. A reliability optimization method for thermal insulation structure based on Bootstrap sampling, characterized in that: include: S1. Set the model parameters and uncertain distribution parameters of the thermal insulation structure design based on actual needs; S2. In the particle swarm optimization PSO method, for each particle in the population, a K 1 set of uncertain variable parameter samples, and then calculate each particle in the population according to the heat transfer equation and boundary conditions to obtain K Temperature of the inner surface of the bearing layer 1 and equivalent modulus ; S3, based on the Bootstrap sampling method, , Expand to K Temperature of the inner surface of the 2 groups of bearing layers and equivalent modulus , the failure probability of all particles in the current iteration population is obtained by statistics and traversal , as the reliability constraint of the optimization objective; S4, based on the model parameters and uncertain distribution parameters in S1, the reliability optimization model is solved to obtain the design variables of the thermal insulation structure; Among them, in S2, the particles refer to the thickness of the anti-ablation layer, the bearing layer, and the thermal insulation layer.

2. The reliability optimization method of thermal insulation structure based on Bootstrap sampling according to claim 1, characterized in that: In S1, the model parameters include: the minimum equivalent modulus allowed E min , Maximum allowable temperature of the bearing layer , Ambient temperature in the cabin T L , Temperature load outside the anti-ablation layer T H , minimum thickness of the anti-ablation layer x 1min , the maximum thickness of the anti-ablation layer x 1max , minimum thickness of the bearing layer x 2min , Maximum thickness of the bearing layer x 2max , minimum thickness of insulation layer x 3min , Maximum thickness of thermal insulation layer x 3max , forced convection heat transfer coefficient between the outer surface of the anti-ablation layer and the temperature load , the natural convection heat transfer coefficient between the inner surface of the bearing layer and the static fluid at room temperature , stop calculating time t end , the minimum equivalent modulus allowed E min , maximum allowable failure probability P max , the number of samples of the first group of uncertain variable parameters K 1. The number of samples of the second group of uncertain variable parameters K 2; The uncertain distribution parameters include: temperature load variation coefficient, E K is the Young's modulus of the anti-ablation layer K, E G is the Young's modulus of the thermal insulation layer G, E C is the Young’s modulus of the load-bearing layer C.

3. The reliability optimization method of thermal insulation structure based on Bootstrap sampling according to claim 1, characterized in that: In S2, the heat transfer equation is characterized by the following formula: In the above formula, T is temperature, t is time, ρ is the density, β is the specific heat capacity, is the thermal conductivity, z is the thickness direction coordinate; The boundary condition is characterized by the following formula: In the above formula, is the thermal conductivity parameter of the anti-ablation layer material, h K-HTF is the forced convection heat transfer coefficient between the outer surface of the anti-ablation layer and the temperature load, ε is the emissivity, σ is the Stefan-Boltzmann constant, T out is the temperature of the outer surface of the anti-ablation layer, is the thermal conductivity parameter of the bearing layer material, h C-NTF is the natural convection heat transfer coefficient between the inner surface of the bearing layer and the static fluid at room temperature, is the gradient of temperature T with respect to spatial coordinate z, t is time, h K is the thickness of the anti-ablation layer, h G is the thickness of the insulation layer, h C is the thickness of the bearing layer, is the temperature of the inner surface of the bearing layer at time t, T L is the ambient temperature in the cabin; Equivalent modulus It is characterized by the following formula: In the above formula, E K is the Young's modulus of the anti-ablation layer K, E G is the Young's modulus of the thermal insulation layer G, Ec is the Young's modulus of the load-bearing layer C; Among them, the The temperature response of the inner surface of the K1 group calculated under different parameters of the K1 group is obtained based on the heat transfer equation and boundary conditions and is solved and calculated by the pde function in MATLAB.

4. The reliability optimization method of thermal insulation structure based on Bootstrap sampling as claimed in claim 3, characterized in that: In S3, the failure probability The acquisition process includes: S30, for the observed samples ,make , i =1,2,… n ,and n = K 1 , If the distribution function is unknown, then the empirical distribution function constructed by the observed sample is F n It is characterized by the following formula: In the above formula, Yes x 1, x 2,…, x n The order statistics obtained after sorting from small to large, k =1,2,…,n-1; S31. Take a random variable with a Dirichlet distribution Perform sample extraction to obtain a regenerated self-service sample ,and N = K 2, ; S32. Estimation of error is performed by the following formula: In the above formula, is the empirical distribution function of the bootstrap sample, R n is a random variable and F n The function of is the overall parameter The estimated value of ; S33, estimate the unknown parameters, and repeat S30 to S33 to obtain the stable value of the desired parameter; S33, based on and Statistically obtain the failure probability of the corresponding particles P f , by traversing all particles in the population, the failure probability of all particles in this iteration population is obtained .

5. The reliability optimization method of thermal insulation structure based on Bootstrap sampling according to claim 4 is characterized in that: In S4, the reliability optimization model is characterized by the following formula: In the above formula, x represents the variable to be optimized, t is the time, ρ obj To optimize the objective function, x min is the lower limit of the design variable, x max is the upper limit of the design variable, , , are variables in the uncertain distribution parameters, and , , , , , They are , , The probability density function is obeyed, T H is the temperature load outside the anti-ablation layer, for T H The probability density function obeyed at time t is, t end To stop counting time, θ max is the maximum allowable temperature of the bearing layer, E min To allow for a minimum equivalent modulus, P max is the maximum allowed failure probability, E eff is the equivalent modulus, T in The temperature of the inner surface of the bearing layer, P f is the failure probability of the corresponding particle, , , are the thermal conductivity parameters of the anti-ablation layer, thermal insulation layer, and bearing layer materials, β K , β G , β C They are the specific heat capacities of the anti-ablation layer, thermal insulation layer and bearing layer materials respectively.

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