CN106874588B - A kind of analysis of multilayer thermal protection system non-probabilistic uncertainty and optimum design method based on experimental design - Google Patents

Abstract

The analysis of multilayer thermal protection system non-probabilistic uncertainty and optimum design method that the invention discloses a kind of based on experimental design, its step are as follows：(1) thermal coefficient, density and specific heat capacity are chosen as uncertain parameter, realizes the section expression of each uncertain parameter；(2) it extracts each layer thickness and uncertain parameter is characterized parameter, realize Full Parameterized modeling, analysis and solve；(3) consider uncertain parameter correlation, propose correlation factors arbitrary sampling method, choose test sample；(4) approximate model is built according to sample, influence of the analysis uncertain parameter to response is simultaneously preferred, establishes multilayered structure temperature field Uncertainty Analysis Method；(5) the non-Probability mapping networks of multilayer thermal protection system are realized so that each layer thickness, each layer temperature are less than allowable value, quality is minimised as design variable, constraints and object function build Optimized model respectively.The present invention improves thermal protection system structure efficiency by efficient analysis of uncertainty and optimization.

Description

A non-probabilistic uncertainty analysis and analysis of multi-layer thermal protection system based on experimental design Optimal Design Method

technical field

The invention relates to the field of optimal design of a multi-layer thermal protection system, in particular to a method for non-probability uncertainty analysis and optimal design of a multi-layer thermal protection system based on test design.

Background technique

Due to the advantages of fast flight speed, short reaction time, large combat radius, good concealment, and strong defense penetration capabilities, hypersonic vehicles have a prominent position in the future war space and God's battlefield, and have become the world's major powers in the arms race. commanding heights. Hypersonic vehicles have been in service for a long time in the extreme environment of multi-field coupling dominated by aerodynamic heat and force, and thermal protection technology has become a bottleneck that directly restricts its development. In order to ensure the safety of pilots and the normal operation of airborne equipment, it is necessary to lay a large area of thermal protection structure on the surface of the aircraft, coupled with the sensitivity of the aircraft to the weight of the structure, the thermal protection system has faced urgent safety issues and structural weight reduction issues since its birth. . Therefore, it is of great significance for the development of high-performance hypersonic vehicles to conduct research on optimal design technology based on thermal protection structures with low cost, high reliability, and high thermal insulation performance.

The thermal protection system of a hypersonic vehicle mostly presents a typical multi-layer structure, that is, a multi-layer thermal protection system. The thermal analysis of the multi-layer thermal protection system involves the complex heat transfer mechanism under the coupling of severe aerodynamic heat load, multi-layer structure and multiple heat transfer modes. During the service process of the aircraft, the first choice is that the aerodynamic thermal load on the structure shows a highly nonlinear change with time; secondly, the three heat transfer mechanisms of heat conduction, heat radiation and heat convection exist simultaneously in the structure, and the three interact and couple each other in the Together, it presents the characteristics of composite heat transfer; finally, as far as the thermal protection structure itself is concerned, the material properties and structural functions affect each other between layers, and the thermal physical properties of each layer of materials, including thermal conductivity, density, specific heat capacity, etc. The changes of pressure and temperature are non-linear, and all of the above lead to complex and difficult to distinguish the response mechanism of the temperature field. Therefore, in order to achieve high thermal insulation performance of the thermal protection system, the heat transfer mechanism of the multilayer thermal protection system must be thoroughly studied.

Traditional multi-layer thermal protection system design optimization incorporates the influence of uncertainty into the empirical safety factor without further investigation, often resulting in some layer redundancy and some layer failure, which is contrary to the requirements of low cost and high safety and reliability In particular, ignoring the uncertainty of material thermophysical parameters under the severe aerodynamic and thermal intensity will directly affect the structural anti-insulation performance, and then have a subversive impact on the safe service of the aircraft. Therefore, in order to improve the safety and reliability of the aircraft in service and reduce the cost, it is necessary to design the structure of the multi-layer thermal protection system considering the uncertainty. However, the heat transfer and heat storage efficiencies of each layer structure are different and the layers are coupled with each other. It is difficult to distinguish the influence of the thermophysical parameters of each material on the temperature field response, which makes the uncertainty analysis of the multilayer thermal protection structure more difficult. Therefore, in-depth research on the influence of various uncertain factors, the development of high-precision uncertainty analysis and optimal design methods, and the improvement of a refined structural design system that comprehensively considers various uncertainties will become a low-cost, high-reliability thermal protection system in the future. The inevitable trend of design.

Contents of the invention

The technical problem to be solved by the present invention is: to overcome the deficiencies of the prior art, and to provide a non-probabilistic uncertainty analysis and optimal design method for multi-layer thermal protection systems based on experimental design, which can ensure that the multi-layer thermal protection On the premise of safe and reliable thermal performance, the structure quality is effectively reduced and the performance of the thermal protection system is improved.

The technical solution adopted by the present invention is: a method for non-probabilistic uncertainty analysis and optimal design of a multi-layer thermal protection system based on experimental design, the method includes the following steps:

Step (1), according to the performance and configuration requirements determined by the actual service environment of the thermal protection system, the multi-layer thermal protection system is composed of n layers of different material structures with different functions; It will change with temperature, and the material property curve of each thermal physical property parameter changing with temperature needs to be obtained by interpolation fitting of a series of thermal physical property parameter values corresponding to a specific temperature. Record the thermal conductivity, density and specific heat capacity of each layer as k _ij , ρ _ij and c _ij , i=1,2,…,n, j=1,2,…,m, where i and j are variable numbers, n is the total number of layers of the multi-layer thermal protection structure, and m is the number of selected specific temperatures , the specific temperature corresponding to the thermal conductivity, density, and specific heat capacity are recorded as and

Step (2), considering the various uncertainties of the thermophysical parameters of the materials in each layer due to material dispersion, measurement errors, etc., select k _ij , ρ _ij and c _ij in step (1) as uncertain parameters; according to the engineering test Obtain the distribution law of each uncertain parameter, obtain the distribution range of each uncertain parameter, and quantify it into k _ij ∈[ _{kij_min} , _{kij_max} ], ρ _ij ∈[ρ _{ij_min} ,ρ _{ij_max} ] and c _ij ∈[ _{cij_min} , c _{ij_max} ], where k _{ij_min} , ρ _{ij_min} and c _{ij_min} are the minimum value of each parameter distribution range, k _{ij_max} , ρ _{ij_max} and c _{ij_max} are respectively the maximum value of each parameter distribution range;

Step (3), select the thickness of each layer in step (1) as a design variable, denoted as X, X=(x ₁ ,x ₂ ,...,x _n ), n is the multi-layer involved in step (1) The number of thermal protection structure layers; each thickness is limited within a given range, that is, x _i ∈ [ _{xi_min} , x _{i_max} ], i=1,2,...,n, where x _{i_min} is the minimum value of the given range of x _i , _{xi_max} is the maximum value of a given range of _xi , which is generally determined by engineering experience and project cost conditions;

Step (4), in the process of geometric modeling, each design variable is extracted as the design characteristic parameter of the control 3D geometric model, when each design variable is arbitrarily changed within their respective given ranges, the geometric automatic modeling can be realized, thereby completing the process based on Geometric parametric modeling of selected design variables;

Step (5), on the basis of the geometric model, through the secondary development function of the finite element software, extract each uncertain parameter as an uncertain characteristic parameter for controlling the thermophysical properties of the material in the finite element model, when each uncertain parameter is in the respective When the distribution range is changed arbitrarily, the automatic assignment of the thermophysical properties of the finite element model material can be realized, so as to establish a parameterized finite element model of the multi-layer thermal protection structure based on the design characteristic parameters and uncertain characteristic parameters;

Step (6), based on the ballistic data of the reentry process, adopt the heat transfer analysis method combined with multiple heat transfer modes of radiation, convection and conduction, and consider the interaction between aerodynamic heat and structural heat transfer to realize the multi-layer The transient temperature field of the thermal protection system is analyzed and solved, and the temperature history T ^s (t) of the interface of each layer of the multilayer thermal protection structure is obtained over time, and the highest temperature at the interface of each layer is extracted as the response output, which is denoted as s=0,1,...,n, where s increases from 0 to n refers to the interface of all layers of the multi-layer thermal protection structure from the outer surface to the inner surface;

Step (7), considering the law of temperature variation of each thermal physical property parameter under deterministic conditions as a sampling constraint, and compiling a sampling algorithm through data analysis and processing software, compared with the traditional completely random sampling method, realizing random sampling considering constraints The sampling process is a random sampling method for correlation factors; based on this method, a group of random combinations considering factor correlations are selected from the distribution intervals of the uncertain parameters k _ij , ρ _ij and c _ij in step (2). Sample point, denoted as P, P=(p ₁ ,p ₂ ,…, _{pu u} ,…p _r ), p _u =(k ₁₁ ,k ₁₂ ,…,k _ij ,…,k _nm ,ρ ₁₁ ,ρ ₁₂ ,…,ρ _ij ,…,ρ _nm ,c ₁₁ ,c ₁₂ ,…,c _ij ,…,c _nm ) _u , where r is the total number of sample points, p _u refers to a certain sample point, k _ij , ρ _ij and c _ij constitute the factors in the sample point, ( ) _u is the specific level of a factor in a sample point;

Step (8), extract the sample point p _u of P in step (7), u=1,...,r as the uncertainty characteristic parameter in step (5), repeat steps (4) to (6) r times , to obtain a set of discrete maximum temperature responses at the interface of each layer of the thermal protection system, denoted as According to the response surface method, fitting the sample set P and the response set Then construct the description of each factor k _ij in P, ρ _ij and c _ij and Approximate Functional Model of Relation

Step (9), through the approximate model in step (8) Analyze the output of each factor k _ij , ρ _ij and c _ij and the maximum temperature response of each layer interface of the multilayer thermal protection structure The relationship and trend between; considering the calculation cost and accuracy, the distribution intervals [k _{ij_min} , _{kij_max} ], [ρ _{ij_min} , ρ _{ij_max} ] and [ _{cij_min} , c _{ij_max} ] in step (2) are normalized to In the same range, compare and analyze k _ij , ρ _ij and c _ij for each response The degree of contribution, identify the key parameters first; combined with the analysis of k _ij , ρ _ij and c _ij and The relationship between the uncertainty response distribution interval after the sensitivity analysis is obtained, that is in and respectively The lower and upper bounds of the uncertainty distribution range;

Step (10), based on the above analysis, take the thickness X of each layer in step (3) as the design variable, and use the upper bound of the uncertainty distribution of the maximum temperature of each layer interface of the multilayer thermal protection structure in step (10) Less than the allowable limit temperature of the interface of each layer as constraints, that is Taking the minimization of the nominal value of structural mass as the optimization objective function, a non-probabilistic optimal design mathematical model of the multi-layer thermal protection system is established, and finally the non-probabilistic optimal design of the multi-layer thermal protection system considering the uncertainty is realized.

Wherein, in the step (7), the correlation factor random sampling method is applicable to each uncertain thermophysical parameter k _ij , and the adjacent factors corresponding to the adjacent specific temperature of ρ _ij and c _ij have correlation and uncertainty distribution In the case of interval interference, take the specific heat capacity c _ij as an example, where the adjacent factors corresponding to a specific temperature are c _ij and c _ij+1 , assuming that under deterministic conditions, there is a law of c _ij ≤ c _ij+1 changing with temperature , that is, adjacent factors are correlated, and under the condition of considering uncertainty, the uncertainty distribution intervals of adjacent factors c _ij and c _{ij +1} [ _{cij_min} , _{cij_max} ] and [ _{cij+1_min} ,cij _{+1_max} ] there is interference, that is, c _{ij_max} >cij _{+1_min} , in the above case, the correlation factor random sampling method, compared with the traditional random sampling method, considers the rule that c _ij ≤ c _ij+1 needs to be satisfied as a sampling constraint , so as to avoid the effect of c _ij > _cij+1 which is contrary to the law of thermophysical properties changing with temperature.

Wherein, in the step (10), the non-probabilistic optimal design mathematical model of the multi-layer thermal protection system is shown in the following formula:

Compared with the prior art, the present invention has the advantages that: the present invention provides a new idea for the optimal design of the multi-layer thermal protection system, and fully considers the effects of actual engineering processing errors, test measurement errors, and material dispersion on the thermal physical properties of the thermal protection system materials. The influence of parameters, the influence law and degree of influence of various uncertain thermophysical parameters of multi-layer coupled complex structures on the temperature field response are explored, and the efficient uncertainty analysis of the temperature field of the multi-layer thermal protection system is realized. On this basis, the idea of non-probability optimization is introduced to realize the refined design of the multi-layer thermal protection system under the premise of ensuring the anti-heat insulation performance, which greatly improves the safety and reliability of the thermal protection system and effectively reduces the quality of the thermal protection system.

Description of drawings

Fig. 1 is the flow chart of method implementation of the present invention;

Fig. 2 is the schematic layout diagram of the multi-layer thermal protection system aimed at by the present invention;

Fig. 3 is the schematic diagram of the finite element model of the multi-layer thermal protection system aimed at by the present invention;

Fig. 4 is the transient temperature history curve of each layer interface of the multilayer thermal protection system aimed at by the present invention;

Fig. 5 is a schematic diagram of the superiority of the correlation factor random sampling method proposed by the present invention;

Fig. 6 is a schematic diagram of the importance ranking of uncertain parameters of the multi-layer thermal protection system aimed at by the present invention;

Fig. 7 is the iterative course curve of the multi-layer thermal protection system uncertainty optimization design aimed at by the present invention.

Detailed ways

The present invention proposes a non-probabilistic uncertainty analysis and optimal design method for multi-layer thermal protection systems based on experimental design. In order to fully understand the characteristics of the invention and its applicability to engineering practice, the basis is shown in Figure 1 The program flow realizes the optimal design of the multi-layer thermal protection system, including the following steps:

Step (1), according to the performance and configuration requirements determined by the actual service environment of the thermal protection system, the multi-layer thermal protection system is composed of 6 layers of different material structures with different functions, as shown in Figure 2, including from the outer surface to the inner surface Reinforced C/C layer, room temperature curing adhesive layer, high temperature insulation layer, low temperature insulation layer, strain isolation cushion layer and skin cold structure layer; considering that thermal physical parameters such as material thermal conductivity, density and specific heat capacity will change with temperature , the material property curve of each thermophysical parameter changing with temperature needs to be obtained by interpolation fitting of a series of thermophysical parameter values corresponding to a specific temperature, record the thermal conductivity, density and specific heat capacity of each layer as k _ij , ρ _ij and c _ij , i =1,2,...,n, j=1,2,...,m, where i and j are variable numbers, n is the total number of layers of the multi-layer thermal protection structure, m is the number of selected specific temperatures, thermal conductivity, The specific temperature corresponding to the density and specific heat capacity is recorded as and For the structure shown in Fig. 2, the sum of specific temperatures of all layer thermophysical parameters is

Step (2), considering the various uncertainties caused by material dispersion and measurement error of each thermal physical parameter of each layer of material, selecting k _ij in step (1), ρ _ij and c _ij as uncertain parameters; according to The engineering test obtains the distribution law of each uncertain parameter, obtains the distribution range of each uncertain parameter, and uses the interval form to quantify k _ij ∈ [k _{ij_min} , k _{ij_max} ], ρ _ij ∈ [ρ _{ij_min} , ρ _{ij_max} ] and c _ij ∈ [ c _{ij_min} , c _{ij_max} ], where k _{ij_min} , ρ _{ij_min} and c _{ij_min} are the minimum value of the distribution range of each parameter, k _{ij_max} , ρ _{ij_max} and c _{ij_max} are the maximum value of the distribution range of each parameter;

Step (3), select the thickness of each layer in step (1) as a design variable, denoted as X, X=(x ₁ ,x ₂ ,...,x ₆ ); each thickness is limited within a given range, namely x _i ∈ [ _{xi_min} , _{i_max} ], i=1,2,…,6, where _{xi_min} is the minimum value of the given range of _xi , and _{xi_max} is the maximum value of the given range of _xi , generally relying on engineering experience and The project cost conditions are given;

Step (4), in the geometric modeling process, through the secondary development function of the geometric modeling software, the three-dimensional geometric model of the multi-layer thermal protection structure is established, and each design variable is extracted as the design characteristic parameter of the control three-dimensional geometric model, when When each design variable changes arbitrarily within its respective given range, automatic geometric modeling can be realized, thereby completing geometric parametric modeling based on the selected design variables;

Step (5), on the basis of the geometric model, through the secondary development function of the finite element software, sequentially set the thermal analysis unit types of radiation, convection and conduction, the nonlinear material properties defined as a function of temperature and the temperature-independent linear Material properties, finite element grid division, etc., the geometric model obtained in step (4) is transformed into a finite element model; each uncertain parameter is extracted as an uncertain characteristic parameter controlling the thermophysical properties of the material in the finite element model, when each uncertain When the parameters are changed arbitrarily within their respective distribution ranges, the automatic assignment of the thermophysical properties of the finite element model material can be realized, so as to establish a parametric finite element model of the multi-layer thermal protection structure based on the design characteristic parameters and uncertain characteristic parameters;

Step (6), based on the ballistic data of the re-entry process, adopt the heat transfer analysis method of radiation, convection and conduction combined with multiple heat transfer methods, consider the interaction between aerodynamic heat and structural heat transfer, and set the outer surface and inner surface in sequence Apply heat loads that change with time on the surface, completely insulate the rest of the surface, apply multi-step loads and solve multi-load steps, etc., to realize the analysis and solution of the transient temperature field of the multi-layer thermal protection system in the whole ballistic process, and obtain the multi-layer thermal protection The temperature history T ^s (t) of the interface of each layer of the structure changes with time, as shown in Figure 4, the highest temperature at the interface of each layer is extracted as the response output, which is recorded as s=0,1,...,6, where s increases from 0 to 6 refers to the interface of all layers of the multi-layer thermal protection structure from the outer surface to the inner surface;

Step (7), considering the law of temperature variation of each thermal physical property parameter under deterministic conditions as a sampling constraint, and compiling a sampling algorithm through data analysis and processing software, compared with the traditional completely random sampling method, realizing random sampling considering constraints The sampling process is a random sampling method for correlation factors; based on this method, a group of random combinations considering factor correlations are selected from the distribution intervals of the uncertain parameters k _ij , ρ _ij and c _ij in step (2). Sample point, denoted as P, P=(p ₁ ,p ₂ ,…,p _u ,…p ₂₅₀₀ ), p _u =(k ₁₁ ,k ₁₂ ,…,k _ij ,…,k _nm ,ρ ₁₁ ,ρ ₁₂ ,…,ρ _ij ,…,ρ _nm ,c ₁₁ ,c ₁₂ ,…,c _ij ,…,c _nm ) _u , where 2500 is the total number of sample points, p _u refers to a certain sample point, k _ij , ρ _ij and c _ij constitute the factors in the sample point, ( ) _u is the specific level of a factor in a sample point;

Step (8), extract the sample point p _u of P in step (7), u=1,2,...,2500 as the uncertainty characteristic parameter in step (5), repeat steps (4) to (6) 2500 times, a set of discrete maximum temperature responses of the interface of each layer of the thermal protection system is obtained, denoted as According to the response surface method, fitting the sample set P and the response set Then construct the description of each factor k _ij in P, ρ _ij and c _ij and Multivariate Quadratic Regression Approximate Functional Model of Relationship Expressed as:

Step (9), through the approximate model in step (8) Analyze the output of each factor k _ij , ρ _ij and c _ij and the maximum temperature response of each layer interface of the multilayer thermal protection structure The relationship and trend between; considering the calculation cost and accuracy, the distribution intervals [k _{ij_min} , _{kij_max} ], [ρ _{ij_min} , ρ _{ij_max} ] and [ _{cij_min} , c _{ij_max} ] in step (2) are normalized to In the same range [-1,+1], compare and analyze k _ij , ρ _ij and c _ij for each response through the normalized approximation function model coefficient φ _v degree of contribution, through v=1,2,...,903, convert φ _v into the percentage of contribution rate, and sort the contribution rate according to the absolute value through the Pareto diagram, as shown in Figure 6, identify the key parameters first; combine the k _ij obtained by analysis , ρ _ij and c _ij and The relationship between, and the uncertainty response distribution interval after the sensitivity analysis is obtained, that is in and respectively The lower and upper bounds of the uncertainty distribution range;

Step (10), based on the above analysis, take the thickness X of each layer in step (3) as the design variable, and use the upper bound of the uncertainty distribution of the maximum temperature of each layer interface of the multilayer thermal protection structure in step (10) Less than the allowable limit temperature of the interface of each layer as constraints, that is Taking the minimization of the nominal value of the structural mass as the optimization objective function, a non-probabilistic optimal design mathematical model of the multi-layer thermal protection system is established as shown in the following formula:

Among them, f(ρ _ij , x _i ) is the nominal value function of the structural mass; the optimization iteration process curve is shown in Fig. 7, and the non-probabilistic optimal design of the multi-layer thermal protection system considering the uncertainty is finally realized.

In summary, the present invention proposes a method for non-probabilistic uncertainty analysis and optimal design of a multi-layer thermal protection system based on experimental design. When deterministic, the upper limit of the maximum service temperature distribution of each layer is less than the allowable limit temperature of each layer as the constraint condition, and the nominal value of the thermal protection system quality is the optimization objective function, and the structural mass is minimized on the basis of ensuring the thermal insulation performance. Considering that the upper limit of the maximum service temperature distribution of each layer as a constraint condition must be safe and reliable, the present invention introduces the non-probability interval theory considering the uncertainty limit to quantify the uncertainty of the thermophysical parameters of each layer of materials, and based on the correlation factor random test The design method realizes the interval uncertainty analysis of the service maximum temperature of each layer interface of the multi-layer thermal protection system and the structural optimization design based on the uncertainty analysis. Among them, the correlation factor random experiment design method in the present invention refers to the process of continuing to complete the approximate model construction, analyzing the relationship between factors and responses, and identifying the priority key parameters on the basis of the selection of test samples by the proposed correlation factor random sampling method. A complete set of uncertainty analysis methods; compared with other uncertainty analysis methods, this method is not only suitable for the correlation between uncertain parameters, but also has compatibility with other methods, and its physical meaning is clearer. The analysis and optimization results obtained by the proposed method are more reliable.

The above are only the specific steps of the present invention, and do not constitute any limitation to the scope of protection of the present invention; it can be extended and applied to the field of heat transfer optimization design of multi-layer structures, and all technical solutions formed by equivalent transformation or equivalent replacement fall within the scope of the present invention. Within the protection scope of the present invention.

Parts not described in detail in the present invention belong to the known techniques of those skilled in the art.

Claims (3)

1. a kind of analysis of multilayer thermal protection system non-probabilistic uncertainty and optimum design method based on experimental design, feature It is, this method realizes that steps are as follows：

Step (1), the performance determined according to the true Service Environment of thermal protection system and configuration demand, multilayer thermal protection system is by n The different materials structure composition of layer different function；In view of the thermal physical property parameters such as material thermal conductivity, density and specific heat capacity can It varies with temperature, the material properties curve that each thermal physical property parameter varies with temperature need to pass through a series of corresponding hot object of specific temperatures Property parameter value interpolation fitting obtains, and remembers that each layer thermal coefficient, density and specific heat capacity are respectively k_ij, ρ_ijAnd c_ij, i=1,2 ..., n, J=1,2 ..., m, wherein i and j numbers for variable, and n is the total number of plies of multilayer thermal protection structure, and m is the number for choosing specific temperature Amount, the corresponding specific temperature of thermal coefficient, density, specific heat capacity are denoted as respectively With

Step (2) considers layers of material thermal physical property parameter due to various uncertain caused by material scatter, measurement error etc. Property, k in selecting step (1)_ij、ρ_ijAnd c_ijAs uncertain parameter；Each uncertain parameter distribution rule are obtained according to engineering test Rule, obtains the distribution of each uncertain parameter, range format is used in combination to be quantified as k_ij∈[k_{ij_min},k_{ij_max}], ρ_ij∈ [ρ_{ij_min},ρ_{ij_max}] and c_ij∈[c_{ij_min},c_{ij_max}], wherein k_{ij_min}, ρ_{ij_min}And c_{ij_min}Respectively each parameter distribution range is most Small value, k_{ij_max}, ρ_{ij_max}And c_{ij_max}Respectively each parameter distribution range maximum value；

Each layer thickness in step (3), selecting step (1) is denoted as X, X=(x as design variable₁,x₂,…,x_n), n is step (1) the involved multilayer thermal protection structure number of plies in；Each thickness is limited in given range, i.e. x_i∈[x_{i_min},x_{i_max}], i =1,2 ..., n, wherein x_{i_min}To give x_iThe minimum value of range, x_{i_max}To give x_iThe maximum value of range, generally relies on engineering Experience and project cost condition are given；

Step (4), during Geometric Modeling, extract each design variable as control 3-D geometric model design feature ginseng Number, when each design variable arbitrarily changes in respective given range, can realize geometry automatic modeling, to complete to be based on institute The geometric parameterization of design variable is selected to model；

Step (5), on the basis of geometrical model, by the secondary development function of finite element software, extract each uncertain parameter As the uncertain characteristic parameter of the control hot physical property attribute of finite element model material, when each uncertain parameter is in respectively distribution model When enclosing interior arbitrary change, the automatic assignment of the hot physical property attribute of finite element model material can be realized, it is special based on design to establish Levy the multilayer thermal protection structure parameter finite element model of parameter and uncertain characteristic parameter；

Step (6), based on reentering process ballistic data, using radiation, convection current and the compound heat transfer point of a variety of heat transfer types of conduction Analysis method considers influencing each other between Aerodynamic Heating and structural thermal, realizes the multilayer thermal protection system transient state of overall trajectory process Temperature field analysis solves, and obtains the temperature history T that each bed boundary of multilayer thermal protection structure changes over time^s(t), each stratum boundary is extracted Maximum temperature at face exports in response, is denoted asS=0,1 ..., n, wherein s increase to n from 0 and refer to multilayer thermal protection structure From outer surface to the interface of all layers of inner surface；

Step (7) considers under the conditions of certainty the rule varied with temperature that is presented of each thermal physical property parameter as sampling restraint, Sampling algorithm is worked out by data analyzing and processing software, compared to traditional completely random methods of sampling, realizes and considers constraints Random sampling procedure, be for correlation factors arbitrary sampling method；Based on the method, from each uncertain parameter k of step (2)_ij, ρ_ijAnd c_ijDistributed area in, select the sample point of the random combine of one group of consideration factor correlativity, be denoted as P, P=(p₁, p₂,…,p_u,…p_r), p_u=(k₁₁,k₁₂,…,k_ij,…,k_nm,ρ₁₁,ρ₁₂,…,ρ_ij,…,ρ_nm,c₁₁,c₁₂,…,c_ij,…,c_nm )_u, wherein r is sample point sum, p_uSome sample point of acute pyogenic infection of finger tip, k_ij, ρ_ijAnd c_ijForm the factor in sample point, ()_uFor certain The specific level of the sample point factor；

The sample point p of P in step (8), extraction step (7)_u, u=1 ..., r as the uncertain characteristic parameter in step (5), It repeats step (4) to (6) r times, obtains one group of discrete maximum temperature response of each bed boundary of thermal protection system, be denoted as Face method according to response is fitted sample set P and response setsThen each factor k in description P is constructed_ij, ρ_ijAnd c_ijWithThe approximate function model of relationship

Step (9) passes through approximate model in step (8)Analyze each factor k_ij、ρ_ijAnd c_ij It is exported with each bed boundary maximum temperature response of multilayer thermal protection structureBetween relationship and trend；Consider to calculate cost and essence Degree, by the distributed area [k in step (2)_{ij_min},k_{ij_max}], [ρ_{ij_min},ρ_{ij_max}] and [c_{ij_min},c_{ij_max}] normalize to Same range, comparative analysis k_ij, ρ_ijAnd c_ijTo each responsePercentage contribution, identification preferentially go out key parameter；Binding analysis The k obtained_ij, ρ_ijAnd c_ijWithBetween relationship, obtain the uncertain response distributed area after sensitivity analysis, i.e.,WhereinWithRespectivelyThe lower bound of Uncertainty distribution range and upper Boundary；

Step (10) is in summary analyzed, anti-with Multi-layer thermal in step (10) using each layer thickness X in step (3) as design variable Each bed boundary maximum temperature Uncertainty distribution upper bound of protection structureLess than each bed boundary acceptability limit temperature To constrain, i.e.,To minimize architecture quality nominal value mass as optimization object function, Multi-layer thermal is established The non-Probability mapping networks mathematical model of guard system, final realize consider probabilistic non-probability optimization of multilayer thermal protection system Design.

2. the analysis of multilayer thermal protection system non-probabilistic uncertainty and optimization according to claim 1 based on experimental design Design method, it is characterised in that：In the step (7), correlation factors arbitrary sampling method is suitable for each hot object of uncertainty Property parameter k_ij, ρ_ijAnd c_ijThere is the corresponding adjacent factor of adjacent specific temperature correlation and Uncertainty distribution section to interfere Situation, with specific heat capacity c_ijFor illustrate, wherein the corresponding adjacent factor of specific temperature be c_ijAnd c_ij+1, it is assumed that in certainty Under the conditions of have c_ij≤c_ij+1Vary with temperature rule, i.e., the adjacent factor has correlation, and considers probabilistic condition Under, adjacent factor c_ijAnd c_ij+1Uncertainty distribution section [c_{ij_min},c_{ij_max}] and [c_{ij+1_min},c_{ij+1_max}] there is interference, That is c_{ij_max}>c_{ij+1_min}, in these cases, correlation factors arbitrary sampling method compares traditional arbitrary sampling method, considers It need to meet c_ij≤c_ij+1Rule as sampling restraint, avoid generating c to reach_ij>c_ij+1It is this run counter to hot physical property with The effect of temperature changing regularity result.

3. the analysis of multilayer thermal protection system non-probabilistic uncertainty and optimization according to claim 1 based on experimental design Design method, it is characterised in that：In the step (10), the non-Probability mapping networks mathematical model such as following formula of multilayer thermal protection system It is shown：