Quantitative analysis method for thermal protection structure response under uncertain conditions

Abstract

According to the quantitative analysis method for the thermal protection structure response under the uncertain condition, an improved grey wolf optimization algorithm of an improved convergence factor and a nonlinear convergence algorithm is provided, the global search range is expanded, the search step length is shortened, the precision is high, the stability is good, and the convergence speed is high; the parameters of the model are dynamically updated by combining an adaptive radial basis function neural network model with an optimization algorithm and output data, so that the precision in the aspect of numerical prediction is improved; through the adaptive radial basis function neural network model, response prediction of the thermal protection structure can be completed only by a small number of initial samples, a propagation rule of uncertainty input can be quantified more efficiently and accurately, and uncertainty response distribution of the thermal protection structure can be represented.

Description

Technical Field

[0001] The present invention belongs to the technical field of thermal protection structure response analysis, and particularly relates to a quantitative analysis method for the response of a thermal protection structure under uncertain conditions. Background Art

[0002] The thermal protection structure is a key component covering the surface of a high-speed aircraft and used to block the external heat of the airframe. Due to process defects in actual production and spatio-temporal variations of atmospheric parameters during the service period, various conditions such as the geometric thickness, material elastic parameters, strength parameters of each component of the thermal protection structure, as well as the air static and dynamic pressures, aerodynamic heat, and vibration loads show obvious uncertainty characteristics. There are a large number of uncertain factors in the thermal protection structure model, making it difficult to obtain ideal results using the traditional analysis method based on a deterministic model plus a safety factor.

[0003] Monte Carlo simulation can effectively solve the problem of quantitative analysis of the uncertain response of complex structures, but the high computational cost is unacceptable. The surrogate model is a simplified mathematical model that simulates the mapping relationship between input and output parameters, which can effectively reduce the computational cost of Monte Carlo simulation and accelerate the analysis process of uncertain responses. Commonly used surrogate models include response surface models, regression splines, and neural networks, etc. Among them, the radial basis neural network has good non-linear prediction ability, but the prediction accuracy is greatly affected by the radial basis parameters.

[0004] The essence of improving the training result of the radial basis neural network can be regarded as an optimization process of expanding constants. Existing optimization strategies are generally based on genetic algorithms and particle swarm algorithms, etc. Such algorithms have the deficiencies of low solution accuracy and slow convergence speed, which easily lead to poor optimization of the radial basis parameters during iteration. At the same time, most of the research on improving the radial basis focuses on the numerical optimization of the expansion constant, while ignoring the beneficial contribution of the number of center points in the hidden layer to the prediction result. Eventually, the improved radial basis neural network model still has problems such as poor model fitting accuracy when facing complex non-linear problems or fewer data samples, and it is difficult to accurately quantify the response of the thermal protection structure under uncertain conditions. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a quantitative analysis method for the response of a thermal protection structure under uncertain conditions. The solution of the present invention can solve the problems existing in the above prior art.

[0006] The technical solution of the present invention:

[0007] A quantitative analysis method for the response of a thermal protection structure under uncertain conditions, comprising the following steps:

[0008] Set the uncertainty distribution characteristics of the air static and dynamic pressure loads, and establish a sample space through optimal Latin hypercube sampling;

[0009] Conduct a static analysis of the thermal protection structure and count the maximum stress value in the in-plane direction of the thermal protection structure;

[0010] Using the gas static and dynamic pressure loads as inputs and the obtained stress values as outputs, an adaptive radial basis neural network model is established. Its radial basis function is an extended Gaussian function, that is, the extended constant σ of the Gaussian c Add the overlap coefficient λ j ,

[0011]

[0012] where j = {1, 2, …, M}; c -j represents the center point other than c j ; c j is the center point of the j-th hidden layer; M is the total number of hidden layer units; λ j is the overlap coefficient;

[0013] Divide the sample space into training samples and correction samples. Use the training samples to train the adaptive radial basis neural network model, use the correction samples to predict the output of the trained adaptive radial basis neural network model, and calculate the root mean square error between the prediction result and the actual result;

[0014] Input the initial values of M and λ j into the improved grey wolf optimization algorithm model respectively. Use the obtained root mean square error as the optimization objective, and iteratively update the parameters of M and λ j through the improved grey wolf optimization algorithm. Judge whether the root mean square error meets the set accuracy. After meeting, obtain the optimal M and λ j ;

[0015] Use the optimal M and λ j to update the current Gaussian function, obtain the adaptive radial basis neural network model, and output the radial basis neural network model of the last iteration as the optimal model.

[0016] Furthermore, the extended Gaussian function is:

[0017]

[0018] where x i = [x i1 , x i2 , …, x iN , is the i-th N-dimensional input sample, representing the uncertain gas static and dynamic pressure loads.

[0019] Furthermore, the root mean square error between the predicted result and the actual result is:

[0020]

[0021] where y i =[y i1 , y i2 , …, y iH , is the i-th H-dimensional output sample, representing the stress response of the thermal protection structure; k = {1, 2, …, H}, H is the total number of output layer units; ω jk is the weight connecting the hidden layer to the output layer.

[0022] Furthermore, the number of training samples is 80 - 150.

[0023] Furthermore, the number of correction samples is 40 - 60.

[0024] Furthermore, the improved grey wolf optimization algorithm includes the following steps:

[0025] 1) Set the dimension of the variable and the upper and lower boundaries corresponding to each dimension, and initialize parameters such as the size of the wolf pack and the number of iterations t max and so on.

[0026] D = |C · P T (t) - P W (t)|

[0027] P W (t + 1) = |P W (t) - A · D|

[0028] A = 2a · r 1 - a

[0029] C = 2r 2

[0030] In the formula, P T is the position vector of the target value, that is, the initialized M or λ j ; P W is the position vector of the grey wolf, that is, the optimized output M or λ j ; t is the current iteration step, A and C are the cooperation coefficient vectors, r 1 and r 2 are random vectors within the range of [0, 1];

[0031] 2) Update the current cooperation coefficient vectors of A and C according to the improved convergence factor and the non-linear convergence algorithm. The improved convergence factor is as follows:

[0032] a = μ · l(t)

[0033] Where μ is the convergence coefficient and l(t) is the non - linear convergence algorithm, Sort(s,n) is the sorting function, which calculates the sorting value of the fitness of the s - th grey wolf among all n grey wolves and is used to update the positions of grey wolves in each iteration process; t is the current iteration step number, and t max is the maximum iteration step;

[0034] 3) Calculate the fitness of each grey - wolf individual, and select three randomly selected individuals with better position fitness according to the current fitness ranking, and save the position vectors as P α 、P β and P δ , representing the optimal solutions at the current iteration step, and use this to update the remaining P ω position vectors:

[0035]

[0036] In the formula, P ω represents the position vector of the current grey - wolf individual, and C 1 、C 2 and C 3 respectively represent the cooperation coefficients of the current grey - wolf individual with P α 、P β and P δ , and the values are random vectors within the range of [0, 2].

[0037] 4) Determine whether the iteration termination condition is met. If not, continue the iteration. If the condition is met, terminate the iteration, and use P α as the position vector of the grey wolf, that is, the optimized output M or λ j optimal solution output.

[0038] Furthermore, the iteration termination condition is that the number of iterations reaches the maximum value or the minimum error is less than the threshold.

[0039] Furthermore, the adaptive radial basis neural network model is a dynamic neural network model.

[0040] The beneficial effects of the present invention compared with the prior art:

[0041] (1) The present invention proposes an improved grey - wolf optimization algorithm that improves the convergence factor and non - linear convergence algorithm, expands the global search range, shortens the search step size, has high precision, good stability and fast convergence speed;

[0042] (2) The present invention dynamically updates the parameters of the model itself through the adaptive radial basis neural network model combined with the optimization algorithm and output data, improving the accuracy in numerical prediction;

[0043] (3) The adaptive radial basis neural network model of the present invention only requires a small number of initial samples to complete the response prediction of the thermal protection structure, and can more efficiently and accurately quantify the propagation law of uncertain inputs, and characterize the uncertain response distribution of the thermal protection structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The accompanying drawings included herein are used to provide a further understanding of the embodiments of the present invention, which form a part of the specification, are used to illustrate the embodiments of the present invention, and together with the written description are used to explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0045] Figure 1 Shows a schematic diagram of an improved grey wolf optimization algorithm provided according to an embodiment of the present invention;

[0046] Figure 2 Shows a schematic diagram of an adaptive radial basis neural network provided according to an embodiment of the present invention;

[0047] Figure 3 Shows a schematic diagram of a sample of an arc-shaped thermal protection structure provided according to an embodiment of the present invention;

[0048] Figure 4 Shows a schematic diagram of a comparison of uncertain response predictions provided according to an embodiment of the present invention;

[0049] Figure 5 Shows a schematic diagram of the steps of a quantitative analysis method for the response of a thermal protection structure under uncertain conditions provided according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. The description of at least one exemplary embodiment is actually only illustrative and in no way restrictive of the present invention and its application or use. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0051] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0052] Unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that, for the sake of convenience of description, the dimensions of the various parts shown in the drawings are not drawn in actual proportional relationships. Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the said technologies, methods, and devices should be regarded as part of the specification. In all the examples shown and discussed herein, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that like reference numerals and letters denote like items in the following drawings, and thus, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0053] As Figure 5 shown, according to an embodiment of the present invention, a quantitative analysis method for the response of a thermal protection structure under uncertain conditions is provided, including the following steps:

[0054] Set the uncertainty distribution characteristics of the gas static and dynamic pressure loads, and establish a sample space through optimal Latin hypercube sampling;

[0055] Conduct a static analysis of the thermal protection structure, and statistically analyze the maximum stress value in the in-plane direction of the thermal protection structure;

[0056] Taking the gas static and dynamic pressure loads as inputs and the obtained stress values as outputs, establish an adaptive radial basis neural network model, the radial basis function of which is an extended Gaussian function, that is, the extended constant σ of the Gaussian c Add the overlap coefficient λ j ,

[0057]

[0058] where j = {1, 2,..., M}; c -j represents the center point other than c j ; c j is the center point of the j-th hidden layer; M is the total number of hidden layer units; λ j is the overlap coefficient;

[0059] Divide the sample space into training samples and correction samples. Use the training samples to train the adaptive radial basis neural network model, use the correction samples to perform output prediction on the trained adaptive radial basis neural network model, and calculate the root mean square error between the prediction result and the actual result;

[0060] Input the initial values of M and λ j into the improved grey wolf optimization algorithm model respectively. Take the obtained root mean square error as the optimization objective, and iteratively update the parameters of M and λ j through the improved grey wolf optimization algorithm. Judge whether the root mean square error meets the set accuracy. After meeting, obtain the optimal M and λ j ;

[0061] Use the optimal M and λ j to update the current Gaussian function, obtain the adaptive radial basis neural network model, and output the radial basis neural network model of the last iteration as the optimal model.

[0062] Furthermore, in one embodiment, the extended Gaussian function is:

[0063]

[0064] where x i =[x i1 , x i2 , …, x iN is the i-th N-dimensional input sample, representing the uncertain aerodynamic static pressure load.

[0065] Furthermore, in one embodiment, the root mean square error between the prediction result and the actual result is:

[0066]

[0067] where y i =[y i1 , y i2 , …, y iH is the i-th H-dimensional output sample, representing the stress response of the thermal protection structure; k = {1, 2, …, H}, H is the total number of output layer units; ω jk is the weight connecting the hidden layer to the output layer.

[0068] Furthermore, in one embodiment, the number of training samples is 80 - 150.

[0069] Furthermore, in one embodiment, the number of correction samples is 40 - 60.

[0070] As can be seen from the above, only a small number of samples are required to complete the response prediction of the thermal protection structure, and the propagation law of uncertain inputs can be quantified more efficiently and accurately, and the uncertain response distribution of the thermal protection structure can be characterized.

[0071] Further, in one embodiment, the improved grey wolf optimization algorithm includes the following steps:

[0072] 1) Set the dimension of the variable and the upper and lower bounds corresponding to each dimension, and initialize the wolf pack size and the number of iterations t max and other parameters,

[0073] D = |C·P T (t) - P W (t)|

[0074] P W (t + 1) = |P W (t) - A·D|

[0075] A = 2a·r 1 -a

[0076] C = 2r 2

[0077] In the formula, P T is the position vector of the target value, that is, the initialized M or λ j ; P W is the position vector of the grey wolf, that is, the optimized output M or λ j ; t is the current iteration step, a is the improved convergence factor, A and C are the cooperation coefficient vectors, r 1 and r 2 are random vectors within the range of [0, 1];

[0078] 2) Update the current cooperation coefficient vectors of A and C according to the improved convergence factor and the non-linear convergence algorithm. The improved convergence factor is as follows:

[0079] a = μ·l(t)

[0080] In the formula, μ is the convergence coefficient, l(t) is the non-linear convergence algorithm, Sort(s, n) is the sorting function, which calculates the sorting value of the fitness of the s-th grey wolf among all n grey wolves, and is used to update the position of the grey wolf in each iteration process; t is the current iteration step, t max is the maximum iteration step;

[0081] 3) Calculate the fitness of each grey wolf individual, and select three random individuals with better position fitness according to the current fitness ranking, and save the position vectors as P α 、P β and Pδ , representing the optimal solution at the current iteration step, and updating the remaining P accordingly ω Position vector:

[0082]

[0083] In the formula, P ω represents the position vector of the current grey wolf individual, and C 1 , C 2 and C 3 respectively represent the cooperation coefficients of the current grey wolf individual with P α , P β and P δ , and the values are random vectors within the range of [0, 2];

[0084] 5) Determine whether the iteration termination condition is satisfied. If not, continue the iteration. If the condition is satisfied, terminate the iteration, and use P α as the position vector of the grey wolf, that is, the optimized output M or λ j Optimal solution output.

[0085] By proposing an improved grey wolf optimization algorithm with an improved convergence factor and a non - linear convergence algorithm, the global search range is expanded, the search step length is shortened, and it has high precision, good stability and fast convergence speed.

[0086] Furthermore, in one embodiment, the iteration termination condition is that the number of iterations reaches the maximum value or the minimum error is less than the threshold.

[0087] Furthermore, in one embodiment, the adaptive radial basis neural network model is a dynamic neural network model. By combining the adaptive radial basis neural network model with the optimization algorithm and the output data, the model's own parameters are dynamically updated to improve the accuracy in numerical prediction.

[0088] In order to have a further understanding of a quantitative analysis method for the response of a thermal protection structure under uncertain conditions provided by the present invention, the following will be described in detail with specific examples and drawings.

[0089] Taking the thermal protection structure as an arc - shaped thermal protection structure, such as Figure 3As shown, it consists of multiple layers of components, including the upper panel, the core layer, the lower panel, the adhesive layer, and the metal plate component. The panel is made of aluminosilicate material, the core layer is made of aerogel material, and the metal plate is made of titanium alloy. The designed dimensions of the standard thickness are: 2 mm for the upper panel, 20.5 mm for the core layer, 1 mm for the lower panel, 0.5 mm for the adhesive layer, and 4 mm for the metal plate; taking the structure with a metal plate arc radius of 500 mm as an example, assuming that the aerodynamic static and dynamic loads follow a uniform distribution within the range of [0.1, 0.2] MPa, and not considering the uncertainty of other parameters. A static analysis is carried out for the arc-shaped thermal protection structure, and the maximum stress value in the in-plane direction of the upper panel is statistically obtained. 1000 maximum stress values obtained from the test are selected as sample data for the calculation of the adaptive radial basis neural network model, and 100 training samples and 50 correction samples are selected from the calculation results to establish the adaptive radial basis neural network model.

[0090] This patent discloses a quantitative analysis method for the response of a thermal protection structure under uncertain conditions.

[0091] This method establishes an adaptive radial basis neural network model based on an improved grey wolf optimization algorithm to conduct quantitative analysis of the response of the thermal protection structure under uncertain conditions.

[0092] As Figure 1 shown, the improved grey wolf optimization algorithm improves the optimization accuracy and convergence speed by improving the convergence factor and the non-linear convergence algorithm. Specifically:

[0093] 1) Set the dimension of the variable and the upper and lower boundaries corresponding to each dimension, and initialize parameters such as the wolf pack size and the iteration number t max etc.,

[0094] D = |C·P T (t) - P W (t)| (3)

[0095] P W (t + 1) = |P W (t) - A·D| (4)

[0096] A = 2a·r 1 - a (5)

[0097] C = 2r 2 (6)

[0098] In the formula, P T is the position vector of the target value; P W is the position vector of the grey wolf, t is the current iteration number, A and C are the cooperative coefficient vectors, r 1 and r 2 are random vectors within the range of [0, 1].

[0099] 2) Update the collaborative coefficient vectors of the current A and C according to the improved convergence factor and the non-linear convergence algorithm. Further, the improved convergence factor is as follows:

[0100] a = μ·l(t) (7)

[0101] In the formula, μ is the convergence coefficient, and l(t) is the non-linear convergence algorithm.

[0102] Further, the convergence coefficient is determined by the following expression:

[0103]

[0104] In the formula, Sort(s,n) is the sorting function, which calculates the sorting value of the fitness of the s-th gray wolf among all n gray wolves, and is used to update the positions of gray wolves in each iteration process.

[0105] Further, the non-linear convergence algorithm is determined by the following expression:

[0106]

[0107] In the formula, t is the current iteration step, and t max is the maximum iteration step. In the initial stage of iteration, the non-linear convergence algorithm is beneficial to expanding the global search range; in the later stage of iteration, it can shorten the iteration step length and improve the local search accuracy.

[0108] 3) Calculate the fitness of each gray wolf individual, and select three random individuals with better position fitness according to the current fitness ranking, and save the position vectors as P α 、P β and P δ , representing the optimal solution at the current iteration step, and update the remaining P ω position vectors accordingly:

[0109]

[0110] 4) Determine whether the iteration termination condition (number of iterations / minimum error) is satisfied. If not, continue the iteration. If the condition is satisfied, terminate the iteration and output P α as the optimal solution.

[0111] As Figure 2 shown, combine the improved gray wolf optimization algorithm and the output data to dynamically update the model's own parameters to establish an adaptive radial basis neural network model. Specifically:

[0112] 1) Use the optimal Latin hypercube sampling to obtain the input sample points of the problem scenario, calculate the corresponding output results, and divide this part of the sample data into a training set and a correction set;

[0113] 2) Select the Gaussian function as the radial basis function of the model, and for the expansion constant σ of the Gaussian c Add the overlap coefficient λ j ,

[0114]

[0115] where j = {1, 2, …, M}; c -j represents the center point other than c j ; c j is the center point of the j-th hidden layer; j ∈ {1, 2, …, M}, M is the total number of hidden layer units; λ j is the overlap coefficient. M and λ j are initialized according to the empirical formula and optimized in the subsequent process;

[0116] Furthermore, the Gaussian function is shown by the following expression;

[0117]

[0118] where σ c is the expansion constant of the radial basis function. x i = [x i1 , x i2 , …, x iN , is the i-th N-dimensional input sample, representing the uncertain aerodynamic static pressure load.

[0119] 3) Update the current Gaussian function according to the M and λ j parameters, establish the corresponding radial basis neural network model in combination with the training data, bring the input data of the correction set into the current radial basis neural network model for output prediction, and calculate the root mean square error between the prediction result and the actual result.

[0120]

[0121] where y i = [y i1 , y i2 , …, y iH , is the i-th H-dimensional output sample, representing the stress response of the thermal protection structure; k = {1, 2, …, H}, H is the total number of output layer units; ω jk is the weight connecting the hidden layer to the output layer; φ(||x i - c j ||) is the radial basis function.

[0122] 4) Take the obtained root mean square error as the optimization goal, and use the improved grey wolf optimization algorithm for M and λ jIteratively update the parameters, and determine whether the root mean square error meets the set accuracy. After meeting the accuracy, output the radial basis neural network model of the last iteration as the optimal model.

[0123] Furthermore, the adaptive radial basis neural network model is a dynamic neural network model. In essence, it iteratively optimizes the composition parameters of the radial basis function itself by combining an optimization algorithm and output data, reducing the model prediction error.

[0124] A quantitative analysis method for the response of a thermal protection structure under uncertain conditions is proposed based on an improved grey wolf optimization algorithm and an adaptive radial basis neural network model. Only a small number of initial samples are required to efficiently and accurately quantify the uncertainty response distribution of the thermal protection structure.

[0125] Based on the improved grey wolf optimization algorithm and the adaptive radial basis neural network model, predict the stress response of the thermal protection structure under uncertain static pressure loads, obtain the probability density distribution of the stress response, and verify the innovation of the present invention by comparing with the actual distribution obtained by finite element calculation. After calculation, as Figure 4 shown, the predicted probability density distribution is consistent with the simulation probability density distribution.

[0126] In summary, a quantitative analysis method for the response of a thermal protection structure under uncertain conditions provided by the present invention has at least the following advantages compared with the prior art:

[0127] (1) The present invention proposes an improved grey wolf optimization algorithm with an improved convergence factor and a non-linear convergence algorithm, which expands the global search range, shortens the search step size, has high accuracy, good stability and fast convergence speed;

[0128] (2) The present invention dynamically updates the model's own parameters through the adaptive radial basis neural network model by combining an optimization algorithm and output data, improving the accuracy in numerical prediction;

[0129] (3) The adaptive radial basis neural network model of the present invention only needs a small number of initial samples to complete the response prediction of the thermal protection structure, and can more efficiently and accurately quantify the propagation law of uncertain inputs, characterizing the uncertainty response distribution of the thermal protection structure.

[0130] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A quantitative analysis method for the response of a thermal protection structure under uncertainty conditions, characterized in that: The following steps are involved: The uncertainty distribution characteristics of aerodynamic and static pressure loads are set, and the sample space is established through optimal Latin hypercube sampling; Conduct static analysis of the thermal protection structure and calculate the maximum stress value within the surface of the thermal protection structure; The aerodynamic and static pressure loads are taken as input, and the obtained stress values ​​are taken as output. An adaptive radial basis function neural network model is established, and its radial basis function is an extended Gaussian function, that is, the extended constant σ of Gaussian c Add overlap factor λ j , Where, j = {1, 2, ..., M}; c -j Indicates c j The center point outside the j is the jth hidden layer center point; M is the total number of hidden layer units; λ j is the overlap coefficient; The sample space is divided into training samples and correction samples, the training samples are used to train the adaptive radial basis function neural network model, the correction samples are used to predict the output of the trained adaptive radial basis function neural network model, and the root mean square error between the prediction result and the actual result is calculated; M and λ j Initialization values ​​are input into the improved gray wolf optimization algorithm model, and the obtained root mean square error is used as the optimization target. The improved gray wolf optimization algorithm is used to optimize M and λ. j The parameters are updated iteratively to determine whether the root mean square error meets the set accuracy. If it meets the set accuracy, the optimal solution M and λ are obtained. j ; Use the optimal solution of M and λ j Update the current Gaussian function to obtain an adaptive radial basis neural network model, and output the radial basis neural network model of the last iteration as the optimal model.

2. The quantitative analysis method of thermal protection structure response under uncertainty conditions according to claim 1, characterized in that: The extended Gaussian function is: Among them, x i =[x i1 ,x i2 ,…,x iN ], is the i-th N-dimensional uncertain aerodynamic and static pressure load.

3. The quantitative analysis method of the response of a thermal protection structure under uncertainty conditions according to claim 2 is characterized in that: The root mean square error between the predicted result and the actual result is: Among them, y i =[y i1 ,y i2 ,…,y iH ], is the i-th H-dimensional output sample, representing the stress response of the thermal protection structure; k = {1, 2, …, H}, H is the total number of output layer units; ω jk are the weights connecting the hidden layer to the output layer.

4. The quantitative analysis method of thermal protection structure response under uncertainty conditions according to claim 3 is characterized in that: The number of training samples is 80-150.

5. The quantitative analysis method of thermal protection structure response under uncertainty conditions according to claim 3, characterized in that: The corrected sample number is 40-60.

6. The quantitative analysis method of thermal protection structure response under uncertainty conditions according to claim 3, characterized in that: The improved gray wolf optimization algorithm comprises the following steps: 1) Set the dimension of the variable and the upper and lower boundaries corresponding to each dimension, and initialize the wolf pack size and number of iterations t max And other parameters, D=|C·P T (t)-P W (t)| P W (t+1)=|P W (t)-A·D| A=2a·r1-a C＝2r2 Where P T is the position vector of the target value, that is, the initialized M or λ j ;P W is the position vector of the gray wolf, that is, M or λ output after optimization j ; t is the current iteration step, A and C are the synergy coefficient vectors, r1 and r2 are random vectors in the range of [0,1]; 2) Update the current synergy coefficient vector of A and C according to the improved convergence factor and the nonlinear convergence algorithm, wherein the improved convergence factor is as follows: a=μ·l(t) Where μ is the convergence coefficient, l(t) is the nonlinear convergence algorithm, Sort(s,n) is a sorting function that calculates the ranking value of the fitness of the sth gray wolf among all n gray wolves, which is used to update the position of the gray wolf in each iteration process; t is the current iteration step number, t max is the maximum iteration step; 3) Calculate the fitness of each gray wolf individual, and select three random individuals with better position fitness according to the current fitness ranking, and save the position vector as P α , P β and P δ , represents the optimal solution for the current iteration, and updates the remaining P ω Position vector: Where P ω represents the position vector of the current gray wolf individual, C1, C2 and C3 represent the position vector of the current gray wolf individual and P α , P β and P δ The synergy coefficient is a random vector in the range of [0,2]. 4) Determine whether the iteration termination condition is met. If not, continue the iteration. If the condition is met, terminate the iteration and set P α As the position vector of the gray wolf, that is, the optimized output M or λ j Optimal solution output.

7. The quantitative analysis method of thermal protection structure response under uncertainty conditions according to claim 6, characterized in that: The iteration termination condition is that the number of iterations reaches a maximum value or the minimum error is less than a threshold value.

8. The quantitative analysis method of thermal protection structure response under uncertainty conditions according to claim 1, characterized in that: The adaptive radial basis function neural network model is a dynamic neural network model.

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