A method for quantifying aircraft structure uncertainty

Abstract

The application belongs to the technical field of aircraft structure uncertainty quantification, and particularly relates to an aircraft structure uncertainty quantification method, which comprises the following steps: step one, according to the probability distribution of a structure model variable, extracting N input samples x j (j=1,...,N) to construct an input sample pool S; step two, randomly selecting N0 input samples x 0,j (j=1,...,N0) from the input sample pool S, and using a finite element model to calculate output responses y 0,j (j=1,...,N0), obtaining an initial training sample set T0={x 0,j ,y 0,j}(j=1,...,N0), and constructing an initial Kriging model; step three, using a composite learning function to update the initial Kriging model to obtain a calculation Kriging model g K ; step four, according to the probability distribution of a structure model input variable, extracting input samples x j (j=1,...,M), and using the calculation Kriging model g K to predict output responses corresponding to the input samples; and step five, estimating the mean and variance of the output responses of the input samples, and estimating the failure probability of the structure model.

Description

Technical Field

[0001] This application belongs to the field of aircraft structural uncertainty quantification technology, specifically involving a method for quantifying aircraft structural uncertainty. Background Technology

[0002] In engineering practice, uncertainties are prevalent in the design and use of aircraft structures due to factors such as manufacturing errors, measurement errors, and modeling errors. These uncertainties often cause variability in the output performance of aircraft structures, and in severe cases, can even lead to structural failure.

[0003] Uncertainty quantification is an important technical means to quantitatively analyze the impact of uncertainties on aircraft structural performance in engineering. To enable high-confidence performance prediction and evaluation of aircraft structures, uncertainty quantification provides a rigorous and effective theoretical framework that can quantitatively analyze the impact of uncertainties on aircraft structural performance. This is of great significance for risk assessment of aircraft structures and for improving the safety level of aircraft structures.

[0004] Currently, the quantitative analysis of uncertainties in aircraft structures requires exploring how the output performance of each structural model changes when the input parameters vary within their uncertainty range. This process needs to be based on a large number of repeated deterministic experiments. For complex aircraft structural models, such as wing structures, fuselage structures, and key aircraft structural component models such as engines, the computational cost required for uncertainty quantification is too high and the efficiency is low, making it difficult to meet the needs of rapid iteration for aircraft structural design and improvement.

[0005] This application is made in view of the aforementioned technical deficiencies. Summary of the Invention

[0006] The purpose of this application is to provide a method for quantifying aircraft structural uncertainties in order to overcome or mitigate at least one of the known technical deficiencies.

[0007] The technical solution of this application is:

[0008] A method for quantifying aircraft structural uncertainties includes:

[0009] Step 1: Based on the probability distribution of the structural model variables, draw N input samples x. j (j = 1, ..., N), construct the input sample pool S;

[0010] Step 2: Randomly select N0 input samples x from the input sample pool S. 0,j (j=1,…,N0), calculate the output response y using the finite element model. 0,j (j=1,…,N0), thus obtaining the initial training sample set T0={x0,j ,y 0,j}(j=1,…,N0), thus constructing the initial Kriging model.

[0011] Step 3: Update the initial Kriging model using a composite learning function. The calculation was performed using the Kriging model g. K ;

[0012] Step 4: Based on the probability distribution of the input variables in the structural model, extract the input sample x. j (j=1,…,M), using the Kriging model g for computation K Predict the output response corresponding to the input sample

[0013] Step 5: Output response based on input samples Estimate the mean and variance of the output response, and estimate the failure probability of the structural model.

[0014] According to at least one embodiment of this application, in the above-described method for quantifying the uncertainty of aircraft structures, in step one, for the wing structure, the structural model variables include the length L of the box segment, the cross-sectional area A of the rod unit, the thickness θ2 of the plate unit used for the wing ribs and wing walls, the thickness θ1 of the plate unit used for the skin, the elastic moduli E1 and E2 of the rod unit and plate unit, and the concentrated external load P.

[0015] According to at least one embodiment of this application, in the above-described method for quantifying the uncertainty of aircraft structures, in step two, for the wing structure, the output response can be designed as the difference between the displacement of the wing structure in the Y direction and the displacement limit.

[0016] According to at least one embodiment of this application, in the above-described method for quantifying aircraft structural uncertainties, step three includes:

[0017] S1, Based on the initial Kriging model Parameters, calculate E corresponding to all input training samples LOO (x) Learning function value E LOO (x 0,j (j = 1, ..., N0), construct the error training set Then, based on this error training set Construct an initial error Kriging model

[0018] S2, Let i = 1 and loop:

[0019] S21, Based on the Kriging model Parameters, calculate the U′(x) learning function value U′(x) for all input samples in the sample pool S. j (j=1,…,N), based on error model Predict the E of all input samples in the sample pool S LOO (x) Learning function value E LOO (x i-1,j (j=1,…,N);

[0020] S22, If (max(E) LOO (x i-1,j ))<ε,j=1,…,N0+i)&(max(U′(x j If ))<0.5, j=1,…,N), then exit the loop and obtain the result using the Kriging model g. K Otherwise, proceed to S23.

[0021] S23. Calculate the standardized U′(x) and E. LOO (x) Learn the function value U′ s (x j ),

[0022] S24. Calculate the composite learning function value C(x) corresponding to all input samples in the sample pool S. j (j=1,…,N), find the input sample x corresponding to the largest C(x) composite learning function value. new The corresponding output response y is calculated using the finite element model. new ;

[0023] S25, (x) new ,y new Add to the current training sample set T i-1 and the current training sample set T i-1 Update to training sample set T i Based on the training sample set T i Kriging model Updated to

[0024] S26, Model-based Calculate the training sample set T i E of all input samples LOO (x) Learning function value E LOO (x i,j Construct a new error training set T (j = 1, ..., N0+i). i e ={x i,j E LOO (x i,j)}(j=1,…,N0+i), based on the newly constructed error training set T i e Error Kriging model Updated to

[0025] S27. Let i = i + 1, and return to S21.

[0026] According to at least one embodiment of this application, in the above-described aircraft structural uncertainty quantification method, in S1, E is calculated. LOO (x) Learn the function value, specifically:

[0027]

[0028] d = y - Fβ;

[0029] H = F(F) T F) -1 F T ;

[0030] in,

[0031] E LOO (x i ) is E LOO (x) is the numerical value of the learning function, R is the correlation matrix between the input modeling samples, d and H are intermediate calculation variables, y is the output modeling sample, F is the regression function matrix of the global model, β is the regression parameter, i,: and :,i represent the i-th row and i-th column of the matrix, and ii represents the i-th diagonal element of the matrix.

[0032] According to at least one embodiment of this application, in the above-described aircraft structural uncertainty quantification method, in step S21, the calculation of the U′(x) learning function value specifically involves:

[0033]

[0034] in,

[0035] U(x i ) represents the learning function value of U′(x), g K (x i ), These are the predicted outputs and standard deviations of the Kriging model, respectively.

[0036] According to at least one embodiment of this application, in the above-described aircraft structural uncertainty quantification method, in step S23, the standardized U′(x) and E are calculated. LOO (x) Learn the function value U′ s (x j ), Specifically:

[0037]

[0038] According to at least one embodiment of this application, in the above-described method for quantifying aircraft structural uncertainties, in step S24, the calculation of the C(x) composite learning function value is specifically as follows:

[0039]

[0040] in,

[0041] C(x i ) represents the composite learning function value of C(x), and α is the equilibrium parameter defined on the interval [0,1].

[0042] According to at least one embodiment of this application, in the above-described aircraft structure uncertainty quantification method, in S24, the balance parameter α defined on the interval [0,1] is taken as 0.5.

[0043] According to at least one embodiment of this application, in the above-described method for quantifying aircraft structural uncertainties, step five, estimating the failure probability of the structural model, specifically involves:

[0044]

[0045] in, For the expectation operator, I F (x) is the failure domain indicator function, when g K When (x)≤0, I F (x) = 1, conversely, I F (x) = 0.

[0046] This application has at least the following beneficial technical effects:

[0047] This paper presents a method for quantifying uncertainties in aircraft structures. This method mainly utilizes the low computational cost advantage of the Kriging model and establishes a new hybrid learning function to accelerate Kriging adaptive modeling. Ultimately, the established Kriging model can not only provide accurate output moment estimates for wing structures, but also accurate failure probability estimates. It can efficiently and accurately provide uncertainty quantification results for aircraft structure models based on statistical moments and failure probabilities. Attached Figure Description

[0048] Figure 1 This is a simplified schematic diagram of an aircraft wing model provided in an embodiment of this application;

[0049] Figure 2 This is a schematic diagram of the cross-section of an aircraft wing structure provided in an embodiment of this application;

[0050] Figure 3This is a schematic diagram of the aircraft structural uncertainty quantification method provided in the embodiments of this application;

[0051] Figure 4 This is a schematic diagram of the failure probability error results of the Kriging model when α changes from 0 to 1, as provided in the embodiments of this application.

[0052] Figure 5 This is a schematic diagram of the mean square error of the Kriging model output when α changes from 0 to 1, as provided in the embodiments of this application.

[0053] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. Furthermore, the drawings are for illustrative purposes only and should not be construed as limiting this application. Detailed Implementation

[0054] To make the technical solution and advantages of this application clearer, the technical solution of this application will be described in a clearer and more complete manner below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some embodiments of this application, and are only used to explain this application, not to limit this application. It should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, and other related parts can be referred to the general design.

[0055] Furthermore, unless otherwise defined, the technical or scientific terms used in this application description shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms indicating direction used in this application description are used only to indicate relative direction or positional relationship; when the absolute position of the described object changes, its relative positional relationship may also change accordingly. The word "comprising" as used in this application description indicates that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, but does not exclude other elements or objects.

[0056] Furthermore, it should be noted that, unless otherwise explicitly specified and limited, terms such as "installation" and "connection" used in the description of this application should be interpreted broadly. For example, a connection can be a fixed connection or a detachable connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand its specific meaning in this application according to the specific circumstances.

[0057] In order to conduct a more comprehensive uncertainty quantification analysis of the output performance of aircraft structures, this invention aims to establish an uncertainty quantification method that can simultaneously provide the output statistical moments and failure probability of the aircraft structure model.

[0058] The method established in this invention will be illustrated using a simplified aircraft wing model as an example. Figure 1 As shown, the cross-section of the aircraft wing structure is as follows: Figure 2 As shown, the entire wing structure can be considered as a box segment extending from the cross section. The length of a box segment is denoted as variable L, and the cross-sectional area of ​​all rod elements is represented by variable A. The thickness of the plate element used for the wing ribs and wing walls is θ2, and the thickness of the plate element used for the skin is θ1. The elastic moduli of all rod elements and plate elements in the wing structure are E1 and E2, respectively, and the Poisson's ratio is set to 0.3. If all external loads are approximated as concentrated force P, the maximum displacement of the wing structure in the Y direction can be studied through the ANSYS finite element model. When the displacement limit of the wing structure is set to 0.185m, the function of the wing model can be expressed as equation (1):

[0059] g(A,E1,E2,θ1,θ2,P,L)=0.185-|dis(A,E1,E2,θ1,θ2,P,L)|…………(1)

[0060] When the function g(·)≤0, that is, when the displacement of the wing structure in the Y direction exceeds the displacement limit, it indicates that the wing structure has failed.

[0061] The above wing model has uncertain input random variables, and the specific parameter distribution is shown in the table below:

[0062] variable Distribution type mean Standard deviation <![CDATA[A / m 2 ]]> normal <![CDATA[1×10 -4 ]]> <![CDATA[1×10 -5 ]]> <![CDATA[E1 / Pa]]> normal <![CDATA[7×10 10 ]]> <![CDATA[7×10 9 ]]> <![CDATA[E2 / Pa]]> normal <![CDATA[2.1×10 11 ]]> <![CDATA[2.1×10 10 ]]> <![CDATA[θ1 / m]]> normal <![CDATA[3×10 -3 ]]> <![CDATA[3×10 -4 ]]> <![CDATA[θ2 / m]]> normal <![CDATA[2×10 -2 ]]> <![CDATA[2×10 -3 ]]> P / N normal 2000 200 L / m normal 3 0.3

[0063] By performing ANSYS finite element modeling on the wing model, the displacement and deformation results of the wing model in the Y direction (or other required characteristics) can be obtained. Due to the existence of uncertainty, the functional relationship between input and output can be represented by Y = g(X), where X represents the input variable and Y represents the output variable. In order to quantify the uncertainty of Y, a large number of samples need to be extracted from the uncertainty space of X and the corresponding Y values ​​need to be calculated. This process is undoubtedly very time-consuming for simulation calculation models with high computational cost. Therefore, the computational efficiency can be improved by establishing a Kriging model of g(X). Its basic principle is to approximate the input-output relationship of the original simulation model through a mathematical model, and the Kriging model function can be expressed as Equation (2):

[0064] g K (X)=f T (X)β+Z(X)…………(3)

[0065] Among them, f T Z(X)β represents the global trend model, and Z(X) represents the local deviation model.

[0066] Through global and local fitting, the Kriging model g K (X) can replace the original simulation model g(X) to obtain the value of the output Y under a given input sample.

[0067] By optimizing the Kriging model parameters during the fitting process, the expression for the predicted output of the Kriging model can be obtained, Equation (4):

[0068] g K (X)=f T (X)β+r T (X)R -1 (y-Fβ)…………(5)

[0069] The expression for the predicted output variance is given by equation (6):

[0070]

[0071] Where F(X) is the regression function matrix of the global model, β is the regression parameter, y is the output modeling sample, R is the correlation matrix between the input modeling samples, r(X) is the correlation matrix between the input modeling sample and any input variable X, and σ 2 This represents the variance of the local bias model.

[0072] Theoretically, if there are enough modeling samples, the constructed Kriging model g will... K While g(X) can provide accurate output predictions for the original simulation model, a large number of modeling samples often leads to decreased modeling efficiency and wasted samples. Furthermore, uncertainty quantification indices come in various forms. To obtain more comprehensive uncertainty quantification results, different adaptive Kriging models need to be constructed to accurately estimate the corresponding quantification indices, but this process undoubtedly introduces complex computational problems. Therefore, a self-learning function can be used to selectively choose modeling samples, ultimately enabling the constructed model to provide accurate estimates of the output quantities of interest.

[0073] To improve the efficiency of quantifying the output uncertainty of the wing model, and to obtain accurate estimates of both the output moment and the failure probability simultaneously by constructing only a Kriging model, the following composite learning function C(x) can be established:

[0074]

[0075] in, U′ s (x) is the standardized E LOOThe learning functions are U(x) and U′(x), where α is a balance parameter defined on the interval [0,1]. If it is desired that the constructed Kriging model focuses more on improving the accuracy of the predicted output value, the parameter α can be set to α>0.5, and otherwise it can be set to α<0.5.

[0076]

[0077] And there is, U(x) i )=1 / U(x i ).

[0078] E LOO (x) is the learning function to improve the prediction accuracy of the Kriging model, and its specific form is shown in equation (7):

[0079]

[0080] Where d = y - Fβ, H = F(F T F) -1 F T , i,:、:,i represent the i-th row and i-th column of the matrix, and ii represent the i-th diagonal element of the matrix.

[0081] Based on equation (7), any input modeling sample x can be approximately estimated. i The one-left error of the predicted output value.

[0082] U(x) is the learning function that improves the accuracy of the Kriging model in estimating the output failure probability, and its specific form is shown in Equation (8):

[0083]

[0084] Among them, g K (x i )and These are the predicted outputs and standard deviations of the Kriging model, respectively.

[0085] Based on equation (8), the probability that the sign of the predicted output value of any input sample is accurately determined can be obtained.

[0086] Based on the above, this application provides a method for quantifying uncertainties in aircraft structures. It employs adaptive Kriging modeling technology and a hybrid adaptive learning function to construct a surrogate model for uncertainty quantification of the aircraft structure. Based on the constructed low-computational-cost Kriging surrogate model, the computational efficiency of the output statistical moments and failure probability of the aircraft structure model can be significantly improved, effectively meeting the needs of rapid iteration in aircraft structure design and improvement. Specifically, as shown below... Figure 3 As shown.

[0087] Step 1: Based on the probability distribution of the structural model variables, draw N input samples x. j (j=1,…,N), construct the input sample pool S.

[0088] For the wing structure, the structural model variables include the length L of the box segment, the cross-sectional area A of the rod element, the thickness θ2 of the plate element used for the wing ribs and wing walls, the thickness θ1 of the plate element used for the skin, the elastic moduli E1 and E2 of the rod and plate elements, and the concentrated external load P.

[0089] Step 2: Randomly select N0 input samples x from the input sample pool S. 0,j (j=1,…,N0), calculate the output response y using the finite element model. 0,j (j=1,…,N0), thus obtaining the initial training sample set T0={x 0,j ,y 0,j}(j=1,…,N0), thus constructing the initial Kriging model.

[0090] For an airfoil structure, the output response can be designed as the difference between the displacement of the airfoil structure in the Y direction and the displacement limit.

[0091] Step 3: Update the initial Kriging model using a composite learning function. The calculation was performed using the Kriging model g. K .

[0092] S1, Based on the initial Kriging model Parameters, calculate E corresponding to all input training samples LOO (x) Learning function value E LOO (x 0,j (j = 1, ..., N0), construct the error training set Then, based on this error training set Construct an initial error Kriging model

[0093] Calculate E LOO (x) Learn the function value, specifically:

[0094]

[0095] d = y - Fβ;

[0096] H = F(F) T F) -1 F T ;

[0097] in,

[0098] E LOO (xi ) is E LOO (x) is the numerical value of the learning function, R is the correlation matrix between the input modeling samples, d and H are intermediate calculation variables, y is the output modeling sample, F is the regression function matrix of the global model, β is the regression parameter, i,:,i represents the i-th row and i-th column of the matrix, and ii represents the i-th diagonal element of the matrix.

[0099] S2, Let i = 1 and loop:

[0100] S21, Based on the Kriging model Parameters, calculate the U′(x) learning function value U′(x) for all input samples in the sample pool S. j (j=1,…,N), based on error model Predict the E of all input samples in the sample pool S LOO (x) Learning function value E LOO (x i-1,j (j = 1, ..., N).

[0101] The learning function value of U′(x) is calculated as follows:

[0102]

[0103] in,

[0104] U(x i ) represents the learning function value of U′(x), g K (x i ), These are the predicted outputs and standard deviations of the Kriging model, respectively.

[0105] S22, If (max(E) LOO (x i-1,j ))<ε,j=1,…,N0+i)&(max(U′(x j If ))<0.5, j=1,…,N), then exit the loop and obtain the result using the Kriging model g. K Otherwise, proceed to S23.

[0106] S23. Calculate the standardized U′(x) and E. LOO (x) Learn the function value U′ s (x j ),

[0107]

[0108] Specifically as follows:

[0109]

[0110] S24. Calculate the composite learning function value C(x) corresponding to all input samples in the sample pool S. j (j=1,…,N), find the input sample x corresponding to the largest C(x) composite learning function value. new The corresponding output response y is calculated using the finite element model. new .

[0111] The value of the composite learning function C(x) is calculated as follows:

[0112]

[0113] in,

[0114] C(x i ) represents the composite learning function value of C(x), and α is the equilibrium parameter defined on the interval [0,1].

[0115] S25, (x) new ,y new Add to the current training sample set T i-1 and the current training sample set T i-1 Update to training sample set T i Based on the training sample set T i Kriging model Updated to

[0116] S26, Model-based Calculate the training sample set T i E of all input samples LOO (x) Learning function value E LOO (x i,j (j=1,…,N0+i), construct a new error training set

[0117] T i e ={x i,j E LOO (x i,j )}(j=1,…,N0+i), based on the newly constructed error training set T i e Error Kriging model Updated to

[0118] S27. Let i = i + 1, and return to S21.

[0119] Step 4: Based on the probability distribution of the input variables in the structural model, extract the input sample x. j (j=1,…,M), using the Kriging model g for computation KPredict the output response corresponding to the input sample

[0120] Step 5: Output response based on input samples Estimate the mean and variance of the output response, and estimate the failure probability of the structural model.

[0121] Estimate the failure probability of the structural model, specifically as follows:

[0122]

[0123] in, For the expectation operator, I F (x) is the failure domain indicator function, when g K When (x)≤0,

[0124] I F (x) = 1, conversely, I F (x) = 0.

[0125] Based on the aircraft structure uncertainty quantification method disclosed in the above embodiments, a Kriging surrogate model for a wing model can be obtained, and the surrogate model can be used to replace the wing model for output uncertainty quantification.

[0126] To obtain the uncertainty quantification result of the output, a total of 5 × 10⁻⁶ samples were drawn based on the probability distribution of the input variables. 4 The variability of the output of each input sample was studied, and the uncertainty quantification results of the output of the wing model and the Kriging surrogate model are shown in the table below:

[0127]

[0128] In the table above, the Monte Carlo method can provide reference results for quantifying the uncertainty of wing models, P f μ represents the failure probability. Y σ Y This represents the mean and standard deviation of the output, Err(P). f ) represents the relative error of the failure probability estimate, MSE represents the mean square error of the Kriging surrogate model prediction output, and N represents the actual number of calculations performed on the wing finite element model.

[0129] It can be seen that, for the reliability analysis results, the Kriging model based on the U learning function and the composite learning function (when α is 0.4 and 0.5) can obtain the same failure probability estimate as the Monte Carlo method. This proves that the established composite learning function enables the Kriging model to provide accurate failure probability results.

[0130] In addition, it can be seen that, based on E LOOThe learning function and the Kriging model built based on the composite learning function (when α is 0.6) have lower output prediction error and more accurate estimation of the first two moments of the output. This proves that the established composite learning function can improve the accuracy of the Kriging model in predicting the output.

[0131] Compared to the Monte Carlo method, the Kriging model established in the aircraft structure uncertainty quantification method disclosed in the above embodiments can significantly reduce the number of calculations for the wing finite element model, with its computational load being only 0.1% of that of the Monte Carlo method, effectively improving the efficiency of uncertainty quantification.

[0132] Figure 4 , Figure 5 The graph shows the failure probability error and output mean square error of the Kriging model as α changes from 0 to 1. It also shows the change in the accuracy of the failure probability estimation and output prediction of the Kriging model based on the composite learning function as the equilibrium parameter α changes from 0 to 1. It can be seen that as α gradually increases from 0 to 1, the error in the failure probability gradually increases, while the output mean square error gradually decreases. This result is consistent with the expected effect of the defined composite learning function.

[0133] In addition, from the table above and Figure 4 , Figure 5 It can be seen that when α = 0.5, the Kriging model constructed based on the composite learning function has the best predictive ability for both the reliability analysis and the output value of the wing model. Therefore, to make the constructed Kriging model have a more comprehensive and complete uncertainty quantification analysis capability, the balance parameter α can be set around 0.5.

[0134] The aircraft structural uncertainty quantification method disclosed in the above embodiments is an uncertainty quantification method based on an adaptive Kriging surrogate model. This method implements uncertainty quantification analysis by establishing a low-computational-cost surrogate model of the aircraft structural model, thereby saving computational costs. It also establishes a hybrid learning function to implement the adaptive Kriging modeling process, thereby improving the modeling efficiency of adaptive Kriging.

[0135] The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to mutually. In the absence of conflict, the embodiments and technical features in the embodiments of this application can be combined to obtain new embodiments.

[0136] The technical solution of this application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of this application is obviously not limited to these specific embodiments. Without departing from the principles of this application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of this application.

Claims

1. A method for quantifying uncertainties in aircraft structures, characterized in that, include: Step 1: Based on the probability distribution of the structural model variables, draw N input samples x. j Where j = 1, ..., N, construct the input sample pool S; Step 2: Randomly select N0 input samples x from the input sample pool S. 0,j Where j = 1, ..., N0, the output response y is calculated using the finite element model. 0,j Where j = 1, ..., N0, the initial training sample set T0 = {x 0,j ,y 0,j }, where j = 1, ..., N0, to construct the initial Kriging model. Step 3: Update the initial Kriging model using a composite learning function. The calculation was performed using the Kriging model g. K ; Step 4: Based on the probability distribution of the input variables in the structural model, extract the input sample x. j Where j = 1, ..., M, the Kriging model g is used for calculation. K Predict the output response corresponding to the input sample Where j = 1, ..., M; Step 5: Output response based on input samples Where j = 1, ..., M, the mean and variance of the output response are estimated, and the failure probability of the structural model is estimated; Step three includes: S1, Based on the initial Kriging model Parameters, calculate E corresponding to all input training samples LOO (x) Learning function value E LOO (x 0,j ), where j = 1, ..., N0, construct the error training set. Where j = 1, ..., N0, and then based on this error training set... Construct an initial error Kriging model S2, Let i = 1 and loop: S21, Based on the Kriging model Parameters, calculate the U′(x) learning function value U′(x) for all input samples in the sample pool S. j ), where j = 1, ..., N, based on the error model Predict the E of all input samples in the sample pool S LOO (x) Learning function value E LOO (x i-1,j ), where j = 1, ..., N; S22, If (max(E) LOO (x i-1,j ))<ε,j=1,…,N0+i)&(max(U′(x j If ))<0.5, j=1,…,N}, then exit the loop and obtain the result using the Kriging model g. K Otherwise, proceed to S23. S23. Calculate the standardized U′(x) and E. LOO (x) Learn the function value U′ s (x j ), S24. Calculate the composite learning function value C(x) corresponding to all input samples in the sample pool S. j ), where j = 1, ..., N, find the input sample x corresponding to the largest C(x) composite learning function value. new The corresponding output response y is calculated using the finite element model. new ; S25, (x) new ,y new Add to the current training sample set T i-1 and the current training sample set T i-1 Update to training sample set T i Based on the training sample set T i Kriging model Updated to S26, Model-based Calculate the training sample set T i E of all input samples LOO (x) Learning function value E LOO (x i,j ), where j = 1, ..., N0+i, construct a new error training set T. i e ={x i,j E LOO (x i,j )}, where j=1,…,N0+i, based on the newly constructed error training set T i e Error Kriging model Updated to S27. Let i = i + 1, and return to S21; In S1, calculate E LOO (x) Learn the function value, specifically: d = y - Fβ; H=F(F T F) -1 F T ; in, E LOO (x i ) is E LOO (x) The numerical value of the learning function, R is the correlation matrix between the input modeling samples, d and H are intermediate calculation variables, y is the output modeling sample, F is the regression function matrix of the global model, β is the regression parameter, i,:,:i represent the i-th row and i-th column of the matrix, and ii represents the i-th diagonal element of the matrix; In S21, the learning function value of U′(x) is calculated as follows: in, U(x i ) represents the learning function value of U′(x), g K (x i ), These are the predicted outputs and standard deviations of the Kriging model, respectively. In S23, calculate the standardized U′(x) and E. LOO (x) Learn the function value U′ s (x j ), Specifically: U′ s (x i )=U′(x i ) / max(U′(x i ); In S24, the value of the composite learning function C(x) is calculated as follows: in, C(x i ) represents the composite learning function value of C(x), and α is the equilibrium parameter defined on the interval [0,1].

2. The method for quantifying aircraft structural uncertainties according to claim 1, characterized in that, In step one, for the wing structure, the structural model variables include the length L of the box segment, the cross-sectional area A of the rod element, the thickness θ2 of the plate element used for the wing ribs and wing walls, the thickness θ1 of the plate element used for the skin, the elastic moduli E1 and E2 of the rod element and plate element, and the concentrated external load P.

3. The method for quantifying aircraft structural uncertainties according to claim 2, characterized in that, In step two, for the wing structure, the output response can be designed as the difference between the displacement of the wing structure in the Y direction and the displacement limit.

4. The method for quantifying aircraft structural uncertainties according to claim 3, characterized in that, In S24, the equilibrium parameter α, defined on the interval [0,1], is set to 0.

5.

5. The method for quantifying aircraft structural uncertainties according to claim 4, characterized in that, In step five, the failure probability of the structural model is estimated, specifically as follows: in, For the expectation operator, I F (x) is the failure domain indicator function, when g K When (x)≤0, I F (x) = 1, conversely, I F (x) = 0.

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