Aircraft structure uncertainty quantification method

Abstract

The invention belongs to the technical field of aircraft structure uncertainty quantification, and particularly relates to an aircraft structure uncertainty quantification method, which comprises the steps of 1, extracting N input samples xj (j = 1,..., N) according to probability distribution of structure model variables, and constructing an input sample pool S; 2, randomly selecting N0 input samples x0, j (j = 1,..., N0) from the input sample pool S, calculating output response y0, j (j = 1,..., N0) by using a finite element model to obtain an initial training sample set T0 = {x0, j, y0, j} (j = 1,..., N0), and constructing an initial Kriging model # imgabs0 #; 3, updating the initial Kriging model # imgabs1 # by using a composite learning function to obtain a Kriging model gK for calculation; 4, extracting an input sample xj (j = 1,..., M) according to probability distribution of input variables of the structure model, and predicting an output response # imgabs2 # corresponding to the input sample by using a Kriging model gK for calculation; 5, estimating a mean value and a variance of the output response by using the output response # imgabs3 # of the input sample, and estimating a failure probability of the structure model.

Description

Technical Field

[0001] The present application belongs to the technical field of aircraft structure uncertainty quantification, and specifically relates to an aircraft structure uncertainty quantification method. Background Art

[0002] In engineering practice, uncertainty factors are widely present in the design and use of aircraft structures due to the influence of processing errors, measurement errors, modeling errors, etc. Uncertainty factors often cause variability in the output performance of aircraft structures, and in severe cases even lead to failure of aircraft structures.

[0003] Uncertainty quantification is an important technical means to quantitatively analyze the degree of influence of uncertainty factors on aircraft structural performance in engineering. In order to predict and evaluate the performance of aircraft structures with high confidence, uncertainty quantification technology provides a rigorous and effective theoretical framework that can quantitatively analyze the influence of uncertainty factors on aircraft structural performance, which is of great significance for risk assessment of aircraft structures and improving the safety level of aircraft structures.

[0004] At present, quantitative analysis of aircraft structural uncertainty requires exploring the changes in model output performance when the input parameters of each structural model change 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 to implement uncertainty quantification is too high and the efficiency is low, which makes it difficult to meet the needs of rapid iteration of aircraft structural design and improvement.

[0005] This application is proposed in view of the above-mentioned technical defects. Summary of the invention

[0006] The purpose of the present application is to provide an aircraft structure uncertainty quantification method to overcome or alleviate at least one of the known technical deficiencies.

[0007] The technical solution of this application is:

[0008] A method for quantifying aircraft structural uncertainty, comprising:

[0009] Step 1: Extract N input samples x according to the probability distribution of the structural model variables 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), and use the finite element model to calculate the output response y 0,j (j=1,…,N0), and get the initial training sample set T0={x0,j ,y 0,j}(j=1,…,N0), to construct the initial Kriging model

[0011] Step 3: Update the initial Kriging model with a composite learning function Get the Kriging model g used for calculation K ;

[0012] Step 4: Extract input samples x according to the probability distribution of the structural model input variables j (j=1,…,M), using the Kriging model g 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 the present application, in the above-mentioned aircraft structure uncertainty quantification method, 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 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 the plate unit, and the external load concentrated force P.

[0015] According to at least one embodiment of the present application, in the above-mentioned aircraft structure uncertainty quantification method, in step 2, for the wing structure, the output response can be designed to be 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 the present application, in the above-mentioned aircraft structure uncertainty quantification method, 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 error training set Then based on the error training set Constructing an initial error Kriging model

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

[0019] S21, based on Kriging model Parameters, calculate the U′(x) learning function value U′(x) of all input samples in the sample pool S j )(j=1,…,N), based on the error model Predict E of all input samples in 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 ))<0.5,j=1,…,N), then exit the loop and get the Kriging model g K Otherwise, proceed to S23

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

[0022] S24, calculate the C(x) 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 maximum C(x) composite learning function value new , using the finite element model to calculate the corresponding output response y 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 the 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 in LOO (x) Learning function value E LOO (x i,j )(j=1,…,N0+i), construct a new error training set T i e ={x i,j ,E LOO (x i,j)}(j=1,…,N0+i), based on building a new error training set T i e Error Kriging Model Updated to

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

[0026] According to at least one embodiment of the present application, in the above-mentioned aircraft structure uncertainty quantification method, in S1, E is calculated LOO (x) Learning 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) learning function value, R is the correlation matrix between 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.

[0032] According to at least one embodiment of the present application, in the above-mentioned aircraft structure uncertainty quantification method, in S21, the U′(x) learning function value is calculated, specifically:

[0033]

[0034] in,

[0035] U(x i ) is the learning function value of U′(x), g K (x i ), are the predicted output of the Kriging model and its standard deviation respectively.

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

[0037]

[0038] According to at least one embodiment of the present application, in the above-mentioned aircraft structure uncertainty quantification method, in S24, the value of the composite learning function C(x) is calculated, specifically:

[0039]

[0040] in,

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

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

[0043] According to at least one embodiment of the present application, in the above-mentioned aircraft structure uncertainty quantification method, in step 5, estimating the failure probability of the structural model is specifically:

[0044]

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

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

[0047] A method for quantifying aircraft structural uncertainty is provided. The 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 estimation for the wing structure, but also provide accurate failure probability estimation, and can efficiently and accurately provide uncertainty quantification results based on statistical moments and failure probabilities for aircraft structural models. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0050] Figure 3is a schematic diagram of an aircraft structure uncertainty quantification method provided in an embodiment of the present application;

[0051] Figure 4 It is a schematic diagram of the failure probability error result of the Kriging model when α changes from 0 to 1 provided in an embodiment of the present application;

[0052] Figure 5 It is a schematic diagram of the output mean square error result of the Kriging model when α changes from 0 to 1 provided in an embodiment of the present application.

[0053] In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product. In addition, the drawings are only used for illustrative purposes and should not be construed as limitations on the present application. DETAILED DESCRIPTION

[0054] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be described in further detail in detail and in detail with reference to the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design.

[0055] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application shall have the usual meanings understood by those of ordinary skill in the art to which this application belongs. The words used in the description of this application to indicate orientation are only used to indicate relative directions or positional relationships. When the absolute position of the described object changes, its relative positional relationship may also change accordingly. The word "include" used in the description of this application indicates that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, but does not exclude other elements or objects.

[0056] In addition, it should be noted that, unless otherwise clearly specified and limited, the words "installation", "connection" and similar terms used in the description of this application should be understood in a broad sense. For example, the 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. Technical personnel in the field can understand its specific meaning in this application according to the specific circumstances.

[0057] In order to more comprehensively perform uncertainty quantitative analysis on the output performance of aircraft structures, the present invention aims to establish an uncertainty quantification method that can simultaneously provide output statistical moments and failure probabilities of aircraft structure models.

[0058] The method established by the present invention is described by taking a research object, that is, a simplified airplane wing model, as an example. Figure 1 As shown, the cross section of the aircraft wing structure is Figure 2 As shown, the entire wing structure can be regarded as a box segment extending from the cross section. The length of a box segment is recorded as variable L, and the cross-sectional area of ​​all rod units is represented by variable A. The thickness of the plate unit used for the rib and wing wall is θ2, and the thickness of the plate unit used for the skin is θ1. The elastic moduli of all rod units and plate units 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 functional function of the wing model can be expressed as formula (1):

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

[0060] When the functional 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 fails.

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

[0062] By performing ANSYS finite element modeling on the wing model, the displacement 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 expressed by Y = g(X), where X represents the input variable and Y represents the output variable. In order to quantify the uncertainty of Y, it is necessary to extract a large number of samples in the uncertainty space of X and calculate the corresponding Y values. This process is undoubtedly very time-consuming for simulation calculation models with high computational costs. To this end, the Kriging model of g(X) can be established to improve the computational efficiency. The basic principle is to use a mathematical model to approximate the input-output relationship of the original simulation model, and the Kriging model function can be expressed as formula (2):

[0063] g K (X) = f T (X)β+Z(X)…………(3)

[0064] Among them, f T (X)β is the global trend model, and Z(X) is the local deviation model.

[0065] 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.

[0066] By optimizing and solving the Kriging model parameters during the fitting process, the expression of the Kriging model prediction output can be finally obtained, formula (4):

[0067] g K (X) = f T (X)β+r T (X)R -1 (y-Fβ)…………(5)

[0068] The expression of the predicted output variance is:

[0069]

[0070] Among them, 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 samples and any input variable X, σ 2 is the variance of the local deviation model.

[0071] Theoretically, if there are enough modeling samples, the Kriging model g K (X) can provide accurate output prediction results for the original simulation model g(X). However, a large number of modeling samples often lead to a decrease in modeling efficiency and a waste of modeling samples. In addition, uncertainty quantification indicators have various forms. If you want to obtain more comprehensive uncertainty quantification results, you need to build different adaptive Kriging models to accurately estimate the corresponding quantitative indicators, but this process will undoubtedly bring complex calculation problems. To this end, a self-learning function can be used to select modeling samples in a targeted manner, so that the constructed model can provide accurate estimates for the output of interest.

[0072] In order to improve the efficiency of quantifying the uncertainty of the wing model output, only a Kriging model is constructed to obtain accurate estimates of the output moment and failure probability at the same time. The following composite learning function C(x) can be established:

[0073]

[0074] in, U′ s (x) is the normalized E LOO(x), U′(x) are learning functions, α is a balance parameter defined in the interval [0,1]. If the constructed Kriging model is expected to focus more on improving the accuracy of the predicted output value, the parameter α can be set to α>0.5, otherwise it can be set to α<0.5.

[0075]

[0076] And, U(x i )=1 / U(x i ).

[0077] E LOO (x) is a learning function for improving the prediction output accuracy of the Kriging model, and its specific form is shown in formula (7):

[0078]

[0079] Where, d = y - Fβ, H = F(F T F) -1 F T , 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.

[0080] Based on formula (7), we can approximate any input modeling sample x i The leave-one-out error of the predicted output value.

[0081] U(x) is a learning function that improves the accuracy of the Kriging model in estimating the output failure probability. Its specific form is shown in formula (8):

[0082]

[0083] Among them, g K (x i )and are the predicted output of the Kriging model and its standard deviation respectively.

[0084] Based on formula (8), the probability that the sign of the predicted output value of any input sample is accurately judged can be obtained.

[0085] Based on the above, the embodiment of the present application provides an aircraft structure uncertainty quantification method, which adopts adaptive Kriging modeling technology and hybrid adaptive learning functions to construct an aircraft structure agent model for uncertainty quantification. Based on the constructed low computational cost Kriging agent model, the calculation efficiency of the output statistical moment and failure probability of the aircraft structure model can be significantly improved, which can well meet the needs of rapid iteration of aircraft structure design and improvement. Specifically, Figure 3 shown.

[0086] Step 1: Extract N input samples x according to the probability distribution of the structural model variables j (j=1,…,N), construct the input sample pool S.

[0087] For the wing structure, the structural model variables include the length L of the box section, the cross-sectional area A of the rod element, the thickness θ2 of the plate element used for the 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 external load concentrated force P.

[0088] Step 2: Randomly select N0 input samples x from the input sample pool S 0,j (j=1,…,N0), and use the finite element model to calculate the output response y 0,j (j=1,…,N0), and get the initial training sample set T0={x 0,j ,y 0,j}(j=1,…,N0), to construct the initial Kriging model

[0089] 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.

[0090] Step 3: Update the initial Kriging model with a composite learning function Get the Kriging model g used for calculation K .

[0091] 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 error training set Then based on the error training set Constructing an initial error Kriging model

[0092] Calculate E LOO (x) Learning function value, specifically:

[0093]

[0094] d = y - Fβ;

[0095] H=F(F T F) -1 F T ;

[0096] in,

[0097] E LOO (xi ) is E LOO (x) learning function value, R is the correlation matrix between 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.

[0098] S2, let i=1 and loop:

[0099] S21, based on Kriging model Parameters, calculate the U′(x) learning function value U′(x) of all input samples in the sample pool S j )(j=1,…,N), based on the error model Predict E of all input samples in sample pool S LOO (x) Learning function value E LOO (x i-1,j )(j=1,…,N).

[0100] Calculate the value of the U′(x) learning function, specifically:

[0101]

[0102] in,

[0103] U(x i ) is the learning function value of U′(x), g K (x i ), are the predicted output of the Kriging model and its standard deviation respectively.

[0104] S22, if (max(E LOO (x i-1,j ))<ε,j=1,…,N0+i)&(max(U′(x j ))<0.5,j=1,…,N), then exit the loop and get the Kriging model g K Otherwise, proceed to S23

[0105] S23. Calculate the standardized U′(x) and E LOO (x) Learning function value U′ s (x j ),

[0106] The details are as follows:

[0107]

[0108] S24, calculate the C(x) 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 maximum C(x) composite learning function value new , using the finite element model to calculate the corresponding output response y new .

[0109] Calculate the value of the composite learning function C(x), specifically:

[0110]

[0111] in,

[0112] C(x i ) is the composite learning function value of C(x), and α is the balance parameter defined in the interval [0,1].

[0113] 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 the training sample set T i , based on the training sample set T i Kriging model Updated to

[0114] S26, Model-Based Calculate the training sample set T i E of all input samples in LOO (x) Learning function value E LOO (x i,j )(j=1,…,N0+i), construct a new error training set T i e ={x i,j ,E LOO (x i,j )}(j=1,…,N0+i), based on building a new error training set T i e Error Kriging Model Updated to

[0115] S27. Set i=i+1 and return to S21.

[0116] Step 4: Extract input samples x according to the probability distribution of the structural model input variables j (j=1,…,M), using the Kriging model g K Predict the output response corresponding to the input sample

[0117] 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.

[0118] Estimate the failure probability of the structural model, specifically:

[0119]

[0120] in, is the expectation operator, I F (x) is the failure domain indicator function, when g K When (x)≤0, I F (x) = 1, otherwise, I F (x)=0.

[0121] Based on the aircraft structure uncertainty quantification method disclosed in the above embodiment, a Kriging proxy model of a wing model can be obtained, and the proxy model is used to replace the wing model to quantify the output uncertainty.

[0122] In order to obtain the uncertainty quantification result of the output, a total of 5×10 4 The variability of the output is studied using input samples. The uncertainty quantification results of the outputs of the wing model and the Kriging proxy model are shown in the following table:

[0123] In the above table, the Monte Carlo method can provide reference results for the uncertainty quantification of the wing model. f represents the failure probability, μ Y , σ Y Represents the mean and standard deviation of the output, Err(P f ) is the relative error of the failure probability estimate, MSE is the mean square error of the Kriging proxy model prediction output, and N is the actual number of operations of the wing finite element model.

[0124] 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 estimation value as the Monte Carlo method, which proves that the established composite learning function can enable the Kriging model to provide accurate failure probability results.

[0125] In addition, it can be seen that based on E LOOThe learning function and the Kriging model constructed based on the composite learning function (when α is 0.6) have lower output prediction errors and more accurate estimates of the first two moments of the output, which proves that the established composite learning function can improve the accuracy of the Kriging model's output prediction.

[0126] Compared with the Monte Carlo method, the Kriging model established in the aircraft structure uncertainty quantification method disclosed in the above embodiment can significantly save the number of calculations of the wing finite element model. Its calculation amount is only 0.1% of the Monte Carlo method, which effectively improves the efficiency of uncertainty quantification.

[0127] Figure 4 , Figure 5 The failure probability error and output mean square error result of the Kriging model when α changes from 0 to 1 are shown in the figure. The failure probability estimation and output prediction accuracy of the Kriging model based on the composite learning function change as the balance parameter α changes from 0 to 1. It can be seen that when α gradually increases from 0 to 1, the error of 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.

[0128] In addition, from the above table 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 prediction ability for the reliability analysis of the wing model and the output value of the wing model. Therefore, if the constructed Kriging model is to have a more comprehensive uncertainty quantification analysis capability, the balance parameter α can be set near 0.5.

[0129] The aircraft structure uncertainty quantification method disclosed in the above embodiment is an uncertainty quantification method based on an adaptive Kriging proxy model. This method implements uncertainty quantification analysis by establishing a low computational cost proxy model of the aircraft structure model, thereby achieving the purpose of saving computational costs, and establishes a hybrid learning function to implement the adaptive Kriging modeling process, thereby improving the modeling efficiency of the adaptive Kriging.

[0130] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other. In the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other to obtain new embodiments.

[0131] So far, the technical solution of the present 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 the present application is obviously not limited to these specific embodiments. Without departing from the principles of the present 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 fall within the scope of protection of the present application.

Claims

1. A method for quantifying aircraft structural uncertainty, characterized in that: include: Step 1: Extract N input samples x according to the probability distribution of the structural model variables j (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 (j=1,…,N0), and use the finite element model to calculate the output response y 0,j (j=1,…,N0), and get the initial training sample set T0={x 0,j ,y 0,j }(j=1,…,N0), to construct the initial Kriging model Step 3: Update the initial Kriging model with a composite learning function Get the Kriging model g used for calculation K ; Step 4: Extract input samples x according to the probability distribution of the structural model input variables j (j=1,…,M), using the Kriging model g K Predict the output response corresponding to the input sample 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.

2. The aircraft structure uncertainty quantification method 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 unit, the thickness θ2 of the plate unit used for the 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 external load concentrated force P.

3. The aircraft structure uncertainty quantification method according to claim 2, characterized in that: In step 2, 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 aircraft structure uncertainty quantification method according to claim 3, characterized in that: 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 )(j=1,…,N0), construct error training set Then based on the error training set Constructing an initial error Kriging model S2, let i=1 and loop: S21, based on Kriging model Parameters, calculate the U′(x) learning function value U′(x) of all input samples in the sample pool S j )(j=1,…,N), based on the error model Predict E of all input samples in sample pool S LOO (x) Learning function value E LOO (x i-1,j )(j=1,…,N); S22, if (max(E LOO (x i-1,j ))<ε,j=1,…,N0+i)&(max(U′(x j ))<0.5,j=1,…,N), then exit the loop and get the Kriging model g K Otherwise, proceed to S23 S23. Calculate the standardized U′(x) and E LOO (x) Learning function value U′ s (x j ), S24, calculate the C(x) 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 maximum C(x) composite learning function value new , using the finite element model to calculate the corresponding output response y 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 the 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 in LOO (x) Learning function value E LOO (x i,j )(j=1,…,N0+i), construct a new error training set T i e ={x i,j ,E LOO (x i,j )}(j=1,…,N0+i), based on building a new error training set T i e Error Kriging Model Updated to S27. Set i=i+1 and return to S21.

5. The aircraft structure uncertainty quantification method according to claim 4, characterized in that: In S1, calculate E LOO (x) Learning function value, specifically: d = y - Fβ; H=F(F T F) -1 F T ; in, E LOO (x i ) is E LOO (x) learning function value, R is the correlation matrix between 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.

6. The aircraft structure uncertainty quantification method according to claim 5, characterized in that: In S21, the learning function value of U′(x) is calculated, specifically: in, U(x i ) is the learning function value of U′(x), g K (x i ), are the predicted output of the Kriging model and its standard deviation respectively.

7. The aircraft structure uncertainty quantification method according to claim 6, characterized in that: In S23, the standardized U′(x) and E are calculated. LOO (x) Learning function value U′ s (x j ), Specifically:

8. The aircraft structure uncertainty quantification method according to claim 7, characterized in that: In S24, the composite learning function value of C(x) is calculated, specifically: in, C(x i ) is the composite learning function value of C(x), and α is the balance parameter defined in the interval [0,1].

9. The aircraft structure uncertainty quantification method according to claim 8, characterized in that: In S24, the balance parameter α defined in the interval [0,1] is set to 0.

5.

10. The aircraft structure uncertainty quantification method according to claim 9, characterized in that: In step 5, the failure probability of the structural model is estimated, specifically: in, is the expectation operator, I F (x) is the failure domain indicator function, when g K When (x)≤0, I F (x) = 1, otherwise, I F (x)=0.

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