Wing structure thermal vibration coupling reliability analysis method based on GEP-Kriging double-layer proxy model

Abstract

The invention discloses a wing structure thermal vibration coupling reliability analysis method based on a GEP-Kriging double-layer agent model. The method comprises the steps that design variables, uncertain parameters and value intervals of the design variables and the uncertain parameters in wing structure reliability analysis are determined; establishing a discourse domain of design variables and uncertain parameters, and obtaining an initial sample point set in the discourse domain; calculating the vibration response of the wing structure in the thermal environment; establishing a first-layer GEP agent model, and obtaining an explicit fitting expression of the vibration response about the initial sample point set and an error predicted by the first-layer GEP agent model; establishing a second-layer error Kriging model, adaptively increasing test points, establishing a GEP-Kriging double-layer proxy model, and calculating a vibration response interval of the wing structure; and the reliability of the wing structure in the thermal vibration coupling environment is calculated. The method can improve the reliability evaluation precision and efficiency of the wing structure in the thermal vibration coupling environment.

Description

Technical Field

[0001] This invention belongs to the field of aircraft structure analysis and design, specifically relating to a method for thermal vibration coupling reliability analysis of wing structures based on the GEP-Kriging double-layer surrogate model. Background Technology

[0002] Reliability is used to assess a structure's ability to perform its intended function under specified conditions and within a specified time. It is a measure of the impact of uncertainties in a structure on its ability to fulfill its intended function. Real-world engineering structures inevitably contain various uncertainties related to material properties, loads, and boundary conditions. Under extreme service conditions, the uncertainty of structural vibration response increases significantly. Accurate analysis of these uncertainties is crucial for predicting structural performance degradation and potential failure modes. Traditional deterministic analysis struggles to accurately define the structural safety boundaries under uncertain disturbances. Therefore, conducting thermal-vibrational coupling reliability analysis on wing structures while considering uncertainties is of significant engineering importance for improving their service safety.

[0003] Currently, reliability analysis of airfoil structures heavily relies on surrogate modeling techniques. These methods avoid time-consuming, high-precision simulations by constructing an approximate mapping between input parameters and system response. Common surrogate models include polynomial response surfaces, radial basis functions, Kriging models, and artificial neural networks. For problems with limited complexity, a single surrogate model can usually achieve good fitting results. However, airfoil structures are characterized by strong nonlinearity, complex intrinsic physical laws, and high computational costs. A single surrogate model struggles to balance accuracy and efficiency, limiting its applicability and accuracy in complex reliability analyses.

[0004] Therefore, there is an urgent need to develop a two-layer surrogate model that can effectively integrate the advantages of different models, so as to not only deeply characterize the intrinsic laws of the vibration response of the wing structure, but also achieve efficient and high-precision fitting and prediction of the response value. Summary of the Invention

[0005] In view of the above problems, this invention provides a method for thermal vibration coupling reliability analysis of wing structures based on the GEP-Kriging double-layer surrogate model, which is used to solve the reliability assessment problem of wing structures under the combined action of thermal vibration coupling environment and uncertain parameters.

[0006] This invention provides a method for thermal vibration coupling reliability analysis of wing structures based on a GEP-Kriging double-layer surrogate model, comprising:

[0007] Step 1: Determine the design variables and uncertain parameters in the reliability analysis of the wing structure, as well as the value ranges of the design variables and uncertain parameters;

[0008] Step 2: Establish the universe of discourse for the design variables and the uncertain parameters through Cartesian product operation, and obtain the initial sample point set within the universe of discourse using the Latin hypercube sampling method;

[0009] Step 3: Calculate the vibration response of the wing structure under thermal conditions using a finite element model. The vibration response includes the maximum stress and maximum vibration displacement of the wing structure within the vibration period.

[0010] Step 4: Based on the initial sample point set and the corresponding vibration response, establish a first-layer GEP surrogate model, and obtain the error between the explicit fitting expression of the vibration response with respect to the initial sample point set and the prediction of the first-layer GEP surrogate model;

[0011] Step 5: Based on the initial sample point set and the error predicted by the first-layer GEP surrogate model, establish a second-layer error Kriging model and adaptively add test points to the initial sample point set to update the second-layer error Kriging model and establish a GEP-Kriging double-layer surrogate model. Use the GEP-Kriging double-layer surrogate model to calculate the vibration response range of the wing structure in the universe of discourse.

[0012] Step 6: Determine the stress and vibration displacement bearing limit strength ranges of the wing structure respectively, and calculate the reliability of the wing structure under thermal vibration coupling environment using the stress-strength interference theory in interval form.

[0013] In some possible implementations, based on the initial set of sample points and the corresponding vibration response, the GEP algorithm is used to obtain an explicit fit expression of the vibration response with respect to the design variables and the uncertain parameters.

[0014] In some possible implementations, the GEP algorithm includes:

[0015] The design variables and the uncertain parameters are combined into a terminal set TS, wherein the terminal set TS is:

[0016] TS = {x1, x2, ..., x m};

[0017] Where TS is the union of the design variables and the uncertain parameters, and m is the total number of the design variables and the uncertain parameters;

[0018] Based on basic mathematical operators, a function set FS for the gene encoding is established, wherein the function set FS is:

[0019]

[0020] A fixed-size population is generated and encoded. Each individual in the population consists of genes composed of a head and a tail. The elements that make up the head are selected from the function set FS and the terminal set TS, and the elements that make up the tail are selected only from the terminal set TS.

[0021] The expression tree method is used to decode all the genes in the population to obtain the explicit fitting expression corresponding to the gene.

[0022] In some possible implementations, a first-layer GEP surrogate model is established based on the initial sample point set and the corresponding vibration response. The error between the explicit fitted expression of the vibration response with respect to the initial sample point set and the prediction of the first-layer GEP surrogate model is obtained, including:

[0023] Substitute the initial sample point set into the calculation of the prediction of the vibration response for each explicit fitting expression, and the training error between the prediction and the vibration response calculated by the finite element model;

[0024] The individual with the smallest training error is selected to establish the first-layer GEP surrogate model, and the vibration response predicted by the first-layer GEP surrogate model is calculated by substituting the initial sample point set into the model.

[0025] The vibration response y calculated based on the finite element model FEM Vibration response predicted by the first-layer GEP surrogate model The error Δy predicted by the first-layer GEP surrogate model is obtained:

[0026]

[0027] In some possible implementations, a second-layer error Kriging model is established based on the initial sample point set and the error predicted by the first-layer GEP surrogate model. Test points are adaptively added to the initial sample point set to update the second-layer error Kriging model and establish a GEP-Kriging dual-layer surrogate model. The vibration response range of the wing structure within the universe of discourse is calculated using the GEP-Kriging dual-layer surrogate model, including:

[0028] Based on the error Δy predicted by the first-layer GEP surrogate model, a second-layer error Kriging model is established to obtain the Kriging fitting function for the prediction error of the first-layer GEP surrogate model. and the corresponding mean square error

[0029] Searching for the mean square error in the universe of discourse The largest test point is added to the initial sample point set to update the second-layer error Kriging model;

[0030] The vibration response predicted by the first-layer GEP surrogate model is linearly superimposed. The Kriging fitting function of the second-layer error Kriging model to the prediction error of the first-layer surrogate model. The GEP-Kriging two-layer proxy model is obtained as follows:

[0031]

[0032] The maximum stress response σ D and the maximum vibration displacement response u D Within the universe of discourse, the vibration response range of the wing structure is calculated using the GEP-Kriging two-layer surrogate model, and the vibration response range includes the maximum stress response range. and the maximum vibration displacement response range

[0033] The reliability analysis method for thermal vibration coupling of wing structures based on the GEP-Kriging double-layer surrogate model provided in this invention has at least the following advantages:

[0034] (1) The analysis method provided in this embodiment of the invention is applicable to the evaluation and analysis of the vibration reliability of the wing structure under thermo-coupling environment, considering different design variable values ​​and uncertain parameters, thus expanding the scope of aircraft structure reliability analysis.

[0035] (2) The GEP-Kriging double-layer surrogate model in this embodiment of the invention ensures high-precision prediction and fitting of vibration response while improving the solution speed, thereby improving the computational efficiency of the entire reliability analysis process.

[0036] (3) Compared with reliability analysis methods using a single surrogate model, the GEP-Kriging two-layer surrogate model can not only achieve high-precision prediction, but also further establish an explicit expression of vibration response, thereby directly characterizing the quantitative relationship between design variables and uncertain parameters and vibration response. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method for thermal vibration coupling reliability analysis of wing structure based on GEP-Kriging double-layer surrogate model in an embodiment of the present invention;

[0038] Figure 2This is a simplified flowchart of a reliability analysis method for thermal vibration coupling of wing structure based on the GEP-Kriging double-layer surrogate model in an embodiment of the present invention.

[0039] Figure 3 This is a schematic diagram of the aircraft wing structure and the distribution of force and thermal loads in an embodiment of the present invention.

[0040] Explanation of reference numerals in the attached figures:

[0041] 10-Internal framework;

[0042] 20-Skin. Detailed Implementation

[0043] To make the above-mentioned objectives, features, and advantages of the embodiments of the present invention more apparent and understandable, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] refer to Figure 1 and Figure 2 This invention provides a method for thermal vibration coupling reliability analysis of wing structures based on the GEP-Kriging double-layer surrogate model. The method specifically includes the following steps:

[0045] Step 1: Determine the design variables and uncertain parameters in the reliability analysis of the wing structure, as well as the range of values ​​for the design variables and uncertain parameters.

[0046] In the embodiments of this application, see Figure 3 The wing structure includes an internal frame 10 and a skin 20. The internal frame 10 is designed as an integral structural frame integrating the spars and ribs, and can be made of Al7050 material. The skin 20 and the internal frame 10 are connected by a rigid direct contact, and the skin 20 is made of Al2024 material.

[0047] Considering processing and measurement errors, the Young's modulus, coefficient of thermal expansion, and specific heat capacity of Al2024 material used in skin 20 and Al7050 material used in internal frame 10 are used as uncertain parameters.

[0048] Each uncertain parameter α i The range of (1≤i≤6) For the smallest closed set containing all possible values:

[0049]

[0050] The superscript "I" indicates an interval.

[0051] For example, the range of a set of uncertain parameters obtained by the above method is shown in Table 1.

[0052] Table 1. Range of Uncertainty Parameters for Wing Structure

[0053]

[0054] In the embodiments of this application, the sparsity width, sparsity web thickness, rib thickness, and skin thickness of the wing structure are used as design variables.

[0055] Each design variable β j The range of (1≤j≤4) For the smallest closed set containing all possible values:

[0056]

[0057] For example, the range of a set of design variables As shown in Table 2.

[0058] Table 2. Range of wing structure design variables

[0059]

[0060] Step 2: Establish the universe of discourse for the design variables and uncertain parameters through Cartesian product operation, and obtain the initial sample point set within the universe of discourse using the Latin hypercube sampling method.

[0061] The aforementioned design variables and uncertain parameters form the multi-source parameter γ in the reliability analysis of the wing structure. I .

[0062] For parameters with multiple sources The wing structure, whose universe of discourse can be expressed as a Cartesian product of the range of each parameter:

[0063]

[0064] Based on the range of variables designed in step one and the range of uncertain parameters The domain of discourse can be determined:

[0065] U(γ I = [27,41]×[3.6,5.4]×[8,12]×[3,7]×[2.375×10 -5 2.625×10 -5]×[142.5,157.5]×[757.3,846.4]×[2.234×10 -5 2.468×10 -5 [67.45, 74.55] × [832.7, 967.8]

[0066] Using the Latin hypercube sampling method in the universe of discourse U(γ) I Obtain the initial sample point set within )

[0067] Specifically, taking n in the universe of discourse s The initial sample point set consists of n sample points ζ. d Dimensional components, the initial set of sample points forms a sample point matrix. Each matrix element is represented as x. ij (1≤i≤n s ,1≤j≤n d ), x ij The calculation formula is as follows:

[0068]

[0069] Where U is a random number in the interval [0,1]. Let the j-th dimension component be a random value at the i-th sample point:

[0070]

[0071] The function random(·) represents randomly selecting an element from all elements of the set, π j Let be the set of values ​​for the j-th component. The total set of values ​​Π = {0, 1, ..., n} s -1}, then the set of values ​​π j It is the difference between the total set of possible values ​​and the set of values ​​already taken, that is:

[0072]

[0073] For example, in this embodiment of the application, the initial sample point set contains 300(n) s =300) sample points, each sample point consisting of 10(n d =10) dimensional components.

[0074] Step 3: Use the finite element model to calculate the vibration response of the wing structure under thermal conditions. The vibration response includes the maximum stress and maximum vibration displacement of the wing structure within the vibration period.

[0075] The influence of the thermal environment on the structural vibration response is represented by the temperature-dependent properties of material parameters. The change of Young's modulus of metallic materials with temperature is characterized using a linear model.

[0076] E k =E 0k [1-25α k (T-T0)];

[0077] Among them, E 0k α represents the temperature variation coefficient of Young's modulus for different materials. k For different materials, T0 = 273.15K.

[0078] linear expansion coefficient α k (unit K) -1 The change with temperature is characterized using a linear model, as shown in the following formula:

[0079] α k =1.0×10 -8 (T-T0)+α kC ;

[0080] Where, α kC is the temperature constant for the coefficient of linear expansion of different materials.

[0081] Specific heat capacity c k (unit: J·kg) -1 ·K -1 The linear increase with temperature follows the following pattern:

[0082]

[0083] For example, the material parameters of Al2024 and Al7050 are given in Table 3.

[0084] Table 3 Material parameters of Al2024 and Al7050

[0085]

[0086] In the embodiments of this application, reference is made to Figure 3 A geometric model of the wing structure was established, and the material parameters of the internal frame 10 and the skin 20 were set respectively. The internal frame 10 was meshed using tetrahedral solid elements, and the skin 20 was meshed using quadrilateral shell elements to obtain the finite element model of the wing structure.

[0087] The thermal vibration coupling problem of the wing structure is solved by using a sequential coupling method.

[0088] refer to Figure 3 The average heat flux density applied to the leading edge of the wing is 48.41 kW / m². 2The emissivity of the skin 20 surface radiating heat to the environment is 0.85, and the structural temperature field was obtained through thermal analysis. In the stress analysis based on the structural temperature field, a constant external load of 0.11 MPa was applied to the upper surface of the skin 20, while the wing root end face was fixedly supported. The first six natural frequencies of the structure were obtained in modal analysis. In the vibration analysis, a simple harmonic external load with an amplitude of 0.11 MPa and a frequency of 200 Hz was applied to the upper surface of the skin 20. Thermo-vibration coupling calculations were performed on the initial sample point set to obtain the vibration response y of the wing structure at each sample point. FEM The vibration response y FEM This includes the maximum stress and maximum vibration displacement of the wing structure during the vibration period.

[0089] Step 4: Based on the initial sample point set and the corresponding vibration response, establish the first-layer GEP surrogate model, and obtain the error between the explicit fitting expression of the vibration response with respect to the initial sample point set and the prediction of the first-layer GEP surrogate model.

[0090] Based on the initial sample point set The corresponding vibration response is obtained, and the explicit fitting expression of the vibration response with respect to the design variables and uncertain parameters is obtained using the GEP (Gene Expression Programming) algorithm.

[0091] The design variables and uncertain parameters are combined into a terminal set TS, which is:

[0092] TS = {x1, x2, ..., x m};

[0093] Where TS is the union of design variables and uncertain parameters, and m is the total number of design variables and uncertain parameters.

[0094] In this embodiment, m = 10, x i (i = 1, 2, ..., 4) represent the four design variables shown in Table 2, x i (i = 5, 6, ..., 10) are the six uncertain parameters shown in Table 1.

[0095] Based on basic mathematical operators, a function set FS for gene encoding is established. The function set FS is:

[0096]

[0097] The GEP algorithm consists of two steps: population generation and population evolution. Specifically, during population generation, a fixed-size population is randomly generated. Each individual in the population is a gene composed of a head and a tail. The elements that make up the gene head can be arbitrarily selected from the function set FS and the terminal set TS, while the elements that make up the tail can only be selected from the terminal set TS. The gene is randomly encoded in this manner.

[0098] For example, the gene head length is set to 16, the tail length is set to 145, and a population of size 40 is randomly generated.

[0099] During population evolution, the expression tree method is used to decode all genes in the population to obtain the explicit fitting expression corresponding to each gene.

[0100] Substitute the initial sample point set to calculate the prediction of the vibration response for each explicit fitted expression, and the training error between this prediction and the vibration response calculated by the finite element model.

[0101] The individual with the smallest training error is selected to build the first-layer GEP surrogate model, and the vibration response predicted by the first-layer GEP surrogate model is calculated by substituting the initial sample point set into it.

[0102] The GEP explicit fit expression for the maximum stress response with respect to the initial sample point set was calculated.

[0103]

[0104] The GEP explicit fitting expression for the maximum vibration displacement response with respect to the initial sample point set was calculated.

[0105]

[0106] Vibration response y calculated based on finite element model FEM Vibration response predicted by the first-layer GEP surrogate model The error Δy predicted by the first-layer GEP surrogate model is obtained:

[0107]

[0108] Step 5: Based on the initial sample point set and the error predicted by the first-layer GEP surrogate model, establish the second-layer error Kriging model and adaptively add test points to the initial sample point set to update the second-layer error Kriging model and establish the GEP-Kriging double-layer surrogate model. Use the GEP-Kriging double-layer surrogate model to calculate the vibration response range of the wing structure in the universe of discourse.

[0109] A second-layer error Kriging model is established based on the error Δy predicted by the first-layer GEP surrogate model, in the universe of discourse U(γ). I Arbitrarily select the input vector x = (x1, x2, ..., xn) 10 ) T The Kriging fitting function for the prediction error Δy of the first-layer GEP surrogate model is obtained as follows:

[0110]

[0111] Where r is the correlation vector, which is the input vector x and each sample point ζ. i (1≤i≤n s The correlation function value R between ) K (x,ζ i )composition, Let ζ be a unit vector, and C be the correlation matrix, composed of the correlation function values ​​between all sample points ζ. ij =R K (ζ i ,ζ j ).

[0112] In this embodiment, the Gaussian model is selected as the correlation function, that is:

[0113]

[0114] The variance σ in the second-level error Kriging model is obtained using the maximum likelihood estimation method. 2 :

[0115]

[0116] Where, β0=(F T C -1 F) -1 F T C -1 y S Further calculate the second-layer error predictions from the Kriging model. Mean square error:

[0117]

[0118] Searching for the mean square error in the universe of discourse The largest test point is selected and added to the initial sample point set to update the second-layer error Kriging model. Specifically, n samples are drawn in the universe of discourse using the Latin hypercube sampling method. t The test points form a test point matrix X. T The test point matrix X TInput the second-layer error Kriging model, and solve for the mean squared error using an optimization method. The largest test point x Tk ,Right now:

[0119] find x Tk

[0120]

[0121] stx Tk ∈X T

[0122] 1≤k≤n t

[0123] Test point x Tk Add to the initial sample point set, and calculate the test point x using the finite element model in step three. Tk The corresponding vibration response is used to update the error predicted by the first-layer GEP surrogate model using the explicit fitting expression in step four, and the second-layer error Kriging model is iteratively updated.

[0124] In this embodiment of the application, the convergence condition for adaptive iteration is set to MSE. max <δ=1×10 -6 The maximum number of iterations is N. max =20.

[0125] Vibration response predicted by the linear superposition of the first layer of the GEP surrogate model Kriging fitting function of the second-layer error Kriging model to the prediction error of the first-layer GEP surrogate model The GEP-Kriging two-layer proxy model is obtained:

[0126]

[0127] For the maximum stress response σ D and maximum vibration displacement response u D Within the universe of discourse, the vibration response range of the aircraft wing structure is calculated using the GEP-Kriging two-layer surrogate model. The vibration response range includes the maximum stress response range. and the maximum vibration displacement response range

[0128] Based on the above GEP-Kriging two-layer surrogate model, the vibration response range of the wing structure is calculated within the range of the uncertain parameters in step one:

[0129]

[0130] Step 6: Determine the stress and vibration displacement bearing limit strength ranges of the wing structure respectively, and use the stress-strength interference theory in interval form to calculate the reliability of the wing structure under thermal vibration coupling environment.

[0131] The vibration response is expressed as a generalized stress σ, and the corresponding ultimate bearing strength is the generalized strength S. Under the influence of uncertainties, the generalized strength is also a random variable with a distributed state:

[0132]

[0133] When the parameter is represented by an interval variable, it can be assumed that the parameter is a random variable that follows a uniform distribution within a known interval. Then the probability density functions of the generalized stress σ and the generalized intensity S are as follows:

[0134]

[0135] For example, the range of the generalized intensity S corresponding to the generalized stress σ is given in Table 4.

[0136] Table 4. Range of Generalized Strength in Reliability Calculation

[0137]

[0138] According to the stress-strength interference theory, the reliability R is defined as the probability that the strength is greater than the stress throughout the entire stress range, that is:

[0139]

[0140] In particular, when the generalized stress range σ I With generalized intensity range S I When they do not overlap, if the lower bound σ of the generalized stress interval is completely greater than the upper bound of the generalized strength interval... Then the reliability is 0; if the upper bound of the generalized stress range... If the value is completely less than the lower bound S of the generalized strength interval, then the reliability is 1. The median σ of the generalized stress interval is defined. c and radius Δσ, and the median S of the generalized intensity range. c And radius ΔS. When the generalized stress interval and the generalized strength interval interfere with each other, according to the interval midpoint σ c and S c The size relationship can be divided into the following two cases:

[0141] When the median of the generalized stress interval σ c Not less than the median S of the generalized intensity range c At this point, it can be further divided into three cases: the first is the generalized stress range σ I Completely encompasses the generalized intensity range S IIn this case, the reliability calculation formula is:

[0142]

[0143] Secondly, the generalized intensity range S I Completely encompasses the generalized stress range σ I In this case, the reliability calculation formula is:

[0144]

[0145] Thirdly, there is the case where the generalized stress range and the generalized strength range do not completely overlap. In this case, the reliability calculation formula is:

[0146]

[0147] And when the median of the generalized stress range σ c Less than the median S of the generalized intensity range c At this point, it can still be subdivided into three cases. The first is the generalized stress range σ I Completely encompasses the generalized intensity range S I In this case, the reliability calculation formula is:

[0148]

[0149] Secondly, the generalized intensity range S I Completely encompasses the generalized stress range σ I In this case, the reliability calculation formula is:

[0150]

[0151] Thirdly, there is the case where the generalized stress range and the generalized strength range do not completely overlap. In this case, the reliability calculation formula is:

[0152]

[0153] For strength reliability Take the generalized stress range σ I =y1 I The corresponding generalized intensity range is For stiffness reliability Take the generalized stress range σ I =y2 I The corresponding generalized intensity range is

[0154] Based on the strength threshold in Table 4 and the vibration response range calculated in step 5, the strength and stiffness reliability of the thermal-vibration coupling of the wing structure are calculated as follows:

[0155]

[0156] The analysis method provided in this application is applicable to the assessment and analysis of wing structure vibration reliability under thermo-coupling environments, considering different design variable values ​​and uncertain parameters, thus expanding the scope of aircraft structural reliability analysis. The GEP-Kriging two-layer surrogate model in this embodiment of the invention ensures high-precision prediction and fitting of the vibration response while improving the solution speed, thereby enhancing the computational efficiency of the entire reliability analysis process. Compared with reliability analysis methods using a single surrogate model, the GEP-Kriging two-layer surrogate model not only achieves high-precision prediction but also further establishes an explicit expression for the vibration response, thereby directly characterizing the quantitative relationship between design variables and uncertain parameters and the vibration response.

[0157] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reliability analysis method for thermal-vibration coupling of wing structures based on the GEP-Kriging double-layer surrogate model, characterized in that, include: Step 1: Determine the design variables and uncertain parameters in the reliability analysis of the wing structure, as well as the value ranges of the design variables and uncertain parameters; Step 2: Establish the universe of discourse for the design variables and the uncertain parameters through Cartesian product operation, and obtain the initial sample point set within the universe of discourse using the Latin hypercube sampling method; Step 3: Calculate the vibration response of the wing structure under thermal conditions using a finite element model. The vibration response includes the maximum stress and maximum vibration displacement of the wing structure within the vibration period. Step 4: Based on the initial sample point set and the corresponding vibration response, establish a first-layer GEP surrogate model, and obtain the error between the explicit fitting expression of the vibration response with respect to the initial sample point set and the prediction of the first-layer GEP surrogate model; Step 5: Based on the initial sample point set and the error predicted by the first-layer GEP surrogate model, establish a second-layer error Kriging model and adaptively add test points to the initial sample point set to update the second-layer error Kriging model and establish a GEP-Kriging double-layer surrogate model. Use the GEP-Kriging double-layer surrogate model to calculate the vibration response range of the wing structure in the universe of discourse. Step 6: Determine the stress and vibration displacement bearing limit strength ranges of the wing structure respectively, and calculate the reliability of the wing structure under thermal vibration coupling environment using the stress-strength interference theory in interval form.

2. The analytical method according to claim 1, characterized in that, Based on the initial sample point set and the corresponding vibration response, the GEP algorithm is used to obtain an explicit fitting expression of the vibration response with respect to the design variables and the uncertain parameters.

3. The analytical method according to claim 2, characterized in that, The GEP algorithm includes: The design variables and the uncertain parameters are combined into a terminal set TS, wherein the terminal set TS is: TS={x1,x2,...,x m }; Where TS is the union of the design variables and the uncertain parameters, and m is the total number of the design variables and the uncertain parameters; Based on basic mathematical operators, a function set FS for the gene encoding is established, wherein the function set FS is: A fixed-size population is generated and encoded. Each individual in the population consists of genes composed of a head and a tail. The elements that make up the head are selected from the function set FS and the terminal set TS, and the elements that make up the tail are selected only from the terminal set TS. The expression tree method is used to decode all the genes in the population to obtain the explicit fitting expression corresponding to the gene.

4. The analytical method according to claim 1, characterized in that, A first-layer GEP surrogate model is established based on the initial sample point set and the corresponding vibration response. The error between the explicit fitting expression of the vibration response with respect to the initial sample point set and the prediction of the first-layer GEP surrogate model is obtained, including: Substitute the initial sample point set into the calculation of the prediction of the vibration response for each explicit fitting expression, and the training error between the prediction and the vibration response calculated by the finite element model; The individual with the smallest training error is selected to establish the first-layer GEP surrogate model, and the vibration response predicted by the first-layer GEP surrogate model is calculated by substituting the initial sample point set into the model. The vibration response y calculated based on the finite element model FEM Vibration response predicted by the first-layer GEP surrogate model The error Δy predicted by the first-layer GEP surrogate model is obtained:

5. The analytical method according to claim 1, characterized in that, Based on the initial sample point set and the error predicted by the first-layer GEP surrogate model, a second-layer error Kriging model is established, and test points are adaptively added to the initial sample point set to update the second-layer error Kriging model and establish a GEP-Kriging dual-layer surrogate model. The vibration response range of the wing structure within the universe of discourse is calculated using the GEP-Kriging dual-layer surrogate model, including: Based on the error Δy predicted by the first-layer GEP surrogate model, a second-layer error Kriging model is established to obtain the Kriging fitting function for the prediction error of the first-layer GEP surrogate model. and the corresponding mean square error Searching for the mean square error in the universe of discourse The largest test point is added to the initial sample point set to update the second-layer error Kriging model; The vibration response predicted by the first-layer GEP surrogate model is linearly superimposed. The Kriging fitting function of the second-layer error Kriging model to the prediction error of the first-layer surrogate model. The GEP-Kriging two-layer proxy model is obtained as follows: The maximum stress response σ D and the maximum vibration displacement response u D Within the universe of discourse, the vibration response range of the wing structure is calculated using the GEP-Kriging two-layer surrogate model, and the vibration response range includes the maximum stress response range. and the maximum vibration displacement response range

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