Analysis method of time-varying reliability for complex aerostructure under mixed uncertainty

Abstract

The application discloses a kind of complex aviation structure under mixed uncertainty Time-varying reliability analysis method, and its basic flow is as follows: the finite element simulation model of complex aviation structure is established, the examination site is selected and the failure criterion is determined, the finite element simulation model is parameterized, and the response function of complex aviation structure is constructed;Generate training sample set, and establish the multiple Kriging surrogate model of complex aviation structure response function according to training sample set and corresponding structure response, and the KL divergence is combined with limit state surface projection profile method to construct adaptive learning function under mixed uncertainty, and the new training sample is screened to update and enhance Kriging surrogate model;Global accuracy index of multiple Kriging surrogate model is used to adjust multiple surrogate models in the proxy model set, and local accuracy index is used to solve the time-varying reliability result of complex aviation structure under mixed uncertainty.

Description

Technical Field

[0001] This invention relates to the field of aerospace structural technology, and more specifically to an analytical method for the time-varying reliability of complex aerospace structures under mixed uncertainties. Background Technology

[0002] Complex aerospace products are subjected to various uncertainties during operation, including geometric dimensions, material properties, and load environments. These uncertainties significantly impact the product's operation and consequently its safety and reliability. Furthermore, due to the varying data volumes and uncertainty types of the different uncertain input variables, quantification using only probabilistic uncertainty quantification methods is insufficient; a comprehensive approach combining probabilistic and non-probabilistic uncertainty quantification methods is necessary to obtain quantitative results that accurately reflect the actual situation. Simultaneously, variables such as loads in complex aerospace products often change continuously over time, necessitating the quantitative analysis of these variables through stochastic processes. Therefore, time-varying reliability analysis of complex aerospace structures under mixed uncertainties is crucial.

[0003] Reliability analysis of complex aerospace structures often requires multiple calls to the time-consuming finite element model for calculation, a process that incurs significant time and economic costs. Structural reliability analysis methods based on Kriging surrogate models, by explicitly expressing the implicit relationships of the finite element model, can greatly improve computational efficiency. However, traditional methods based on Kriging surrogate models require manually setting the order of the regression terms, introducing a degree of subjective uncertainty into the final reliability analysis results. Different individuals may set different regression terms, which can lead to varying computational accuracy and costs in the constructed surrogate model. Furthermore, the optimal regression term is problem-related and unknown beforehand. Summary of the Invention

[0004] The purpose of this invention is to provide an analytical method for time-varying reliability of complex aerospace structures under mixed uncertainties. This method can effectively balance the impact of different regression terms on the final result and determine one or more optimal regression terms to construct a surrogate model, thereby avoiding the drawbacks of manually setting regression terms.

[0005] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0006] This invention provides a method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties, comprising:

[0007] S1: Constructing the response function of complex aerospace structures based on simulation models of complex aerospace structures;

[0008] S2: Obtain the quantification results of input uncertainty variables for complex aerospace structures;

[0009] S3: Based on the quantization result, obtain the sample matrix and sample pool corresponding to the quantization result;

[0010] S4: Calculate the response function result of the current training sample using the aforementioned response function;

[0011] S5: Based on the quantization results and the response function results, establish a multiple Kriging surrogate model for the response function of complex aerospace structures;

[0012] S6: Use the multiple Kriging proxy model to predict the samples in the sample matrix to obtain the first prediction mean and the first prediction standard value;

[0013] S7: Based on the first predicted mean and the first predicted standard value, obtain the average KL divergence and the maximum average KL divergence;

[0014] S8: Determine the globally optimal proxy model of the multiple Kriging proxy model based on the average KL divergence, the maximum average KL divergence, and the global accuracy of the multiple Kriging proxy model;

[0015] S9: Based on the local accuracy index, use the global optimal surrogate model to calculate the second predicted mean of the samples in the sample pool;

[0016] S10: Determine the number of failed samples based on the second predicted mean;

[0017] S11: Based on the number of failed samples, the upper limit of the number of misjudged samples in the failure domain, and the upper limit of the number of misjudged samples in the safety domain, the result of the error-based adaptive update stopping criterion is obtained;

[0018] S12: Determine whether the result of the error-based adaptive update stopping criterion has converged. If it has converged, proceed to step S13; otherwise, proceed to step S14.

[0019] S13: Calculate the upper boundary value of the time-varying failure probability under mixed uncertainty based on the number of failure samples, and output the upper boundary value of the time-varying failure probability under mixed uncertainty as the analysis result of the time-varying reliability of the complex aerospace structure under mixed uncertainty;

[0020] S14: Update the average KL divergence based on the global optimal proxy model and obtain new training samples based on the updated average KL divergence, then return to step S4.

[0021] Alternatively, in step S1, the simulation model of the complex aerospace structure is established using finite element software, and step S1 includes:

[0022] S101: Establishing a three-dimensional model of a complex aerospace structure using Abaqus software;

[0023] S102: Based on the three-dimensional model, as well as the material properties, external loads and boundary conditions, analysis steps and mesh generation of the complex aerospace structure, a simulation model of the complex aerospace structure is obtained;

[0024] S103: Utilize command flow analysis and parameterize the corresponding variables of the simulation model of the complex aerospace structure to obtain parameterization results;

[0025] S104: Establish the call between Matlab and Abaqus software, complete the sampling process of the corresponding variables of the simulation model of the complex aerospace structure in Matlab, send the parameterization results into Abaqus and read the analysis results of Abaqus, thereby realizing the joint simulation of Matlab and Abaqus and the construction of the response function of the complex aerospace structure.

[0026] The response function G GJQ1 for:

[0027]

[0028] Among them, g GJQ1 (X,Y(t),Q,t) represents the response function, X represents the random input variable, Y(t) represents the random process input variable, Q represents the interval input variable, and S represents the random input variable. XY S represents the allowable stress of the aircraft wing structure. GJQ1 E1 represents the elastic modulus of the first material, ρ1 represents the density of the first material, E2 represents the elastic modulus of the second material, and ρ2 represents the density of the second material. Indicates the thickness of the upper and lower edge strips of the main beam. Indicates the thickness of the web of the main beam. n represents the skin thickness, n0 represents the maneuver overload, θ represents the flight pitch angle, m(t) represents the aircraft mass at time t, and t represents the time parameter.

[0029] Optionally, in step S2, the input uncertainty variables of the complex aerospace structure include: the geometric dimensions of the complex aerospace structure, the load environment, and the material properties; step S2 includes: using random variables, interval variables, and random processes to perform quantitative analysis on the corresponding input uncertainty variables of the complex aerospace structure to obtain the quantitative results.

[0030] Alternatively, step S3 may include:

[0031] S301: The time parameter t is uniformly discretized into N values ​​within its time interval [0,T]. t That moment, namely

[0032] S302: Quantification results (x) of the input uncertainty variables of the complex aerospace structure extracted using the Latin hypercube technique. (i) ,ξ (i) ,q (i) (i = 1, 2, ..., N), to obtain the sample pool, wherein the sample pool includes N S Samples [x] *(i) ,ξ *(i) ,q *(i) ,t *(i) (i = 1, 2, ..., N) S );

[0033] S303: Construct a sample matrix based on the sample pool. Among them, the sample matrix The sample in the i-th row and j-th column is [x (i) ,y (i) (t (j) ),q (i) ,t (j) ](i=1,2,...,N; j=1,2,...,N t ), where y (i) (t (j) ) by ξ (i) and t (j) t is calculated based on the orthogonal series extension method. (j) At time j, the interval input variable sample q (i) (i = 1, 2, ..., N) represents the extraction of interval input variables as uniformly distributed variables within their respective intervals, x (i) Let ξ represent the i-th group of random input variable samples. (i) Let λ represent the i-th group of standard normal variables. jk Y represents the input variable of the random process. j The k-th eigenvalue of the orthogonal expansion of (t) and Y represents the input variable of the random process. j The mean of (t), and and κ i (t) represents the k-th value of the eigenvector and the fundamental orthogonal function, respectively. jk This represents the input variable Y corresponding to the random process. jM is the k-th standard normal random variable of (t). j Y represents the input variable of the random process. j The number of terms in the expansion of (t), where k represents the indicator parameter.

[0034] Alternatively, in step S4, the current training sample is obtained from the sample pool, i.e., using the formula... ξ *(i) Convert to y *(i) (t *(i) ), to obtain training samples [x *(i) ,y *(i) (t *(i) ),q *(i) ,t *(i) (i = 1, 2, ..., N) S ).

[0035] Alternatively, in step S6, the first predicted mean is:

[0036]

[0037] The first prediction standard deviation is:

[0038]

[0039] In step S9, the second predicted mean is:

[0040]

[0041] Where, x (i) Let y represent the i-th group of random input variable samples. (i) (t (j) ) represents the value of the random process vector of the i-th sample and the j-th time step, t (j) Let q represent the j-th time. (i) This represents a range of input variable samples.

[0042] Alternatively, in step S7, the average KL divergence is:

[0043]

[0044] The maximum average KL divergence is:

[0045]

[0046] Alternatively, step S8 may include:

[0047] S801: Determine whether the maximum average KL divergence is less than the average KL divergence. If yes, proceed to step S802; otherwise, proceed to step S803.

[0048] S802: Output the current Kriging proxy model as the globally optimal proxy model;

[0049] S803: Determine whether there exists a multiple Kriging proxy model that satisfies the condition in two iterations. If a proxy model exists, delete it; otherwise, retain all proxy models. This represents the global accuracy of the multiple Kriging proxy model. This represents the global precision threshold.

[0050] Alternatively, in step S11, the error-based adaptive update stopping criterion result... for:

[0051]

[0052] Where, N f Indicates the number of failed samples. and These represent the upper limit of the number of samples that are misjudged in the failure domain and the upper limit of the number of samples that are misjudged in the security domain, respectively.

[0053] Alternatively, in step S13, the upper boundary value of the time-varying failure probability under mixed uncertainties... for:

[0054]

[0055] in, For failure indication function and

[0056] This represents the minimum second predicted mean and This represents the time corresponding to the minimum second predicted mean and This represents the range of values ​​of the interval variable corresponding to the minimum second predicted mean, and This indicates that when the interval variable takes the value The second predicted mean result, This indicates that when the time parameter takes the value The second predicted mean result.

[0057] The present invention has the following beneficial effects:

[0058] This invention establishes an effective strategy based on the Kriging surrogate model to weigh the impact of different regression terms on the final result, and determines one or more optimal regression terms to construct a surrogate model for complex aerospace structures, thereby effectively avoiding the shortcomings of the traditional Kriging surrogate model method that involves manually setting regression terms. Attached Figure Description

[0059] Figure 1 This is a flowchart of the analysis method for time-varying reliability of complex aerospace structures under mixed uncertainties according to the present invention;

[0060] Figure 2 This is a geometric model of a complex aerospace structure disclosed herein;

[0061] Figure 3 This is a description of the mesh generation for complex aerospace structures disclosed in this publication;

[0062] Figure 4 The results of stress analysis of complex aerospace structures disclosed herein;

[0063] Figure 5 The results are the time-varying failure probability evolution diagrams for complex aerospace structures disclosed herein. Detailed Implementation

[0064] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0065] Example

[0066] This invention provides an analytical method for the time-varying reliability of complex aerospace structures under mixed uncertainties, with reference to... Figure 1 As shown, it includes:

[0067] S1: Constructing the response function of complex aerospace structures based on simulation models of complex aerospace structures;

[0068] The simulation model of the complex aerospace structure (e.g., aircraft wing structure) is established using finite element software. Step S1 includes:

[0069] S101: A three-dimensional model of a complex aerospace structure was created using Abaqus software, such as... Figure 2 As shown (partial skin is hidden to show the internal structure);

[0070] S102: Based on the three-dimensional model, as well as the material properties, external loads and boundary conditions, analysis steps and mesh generation of the complex aerospace structure, a simulation model of the complex aerospace structure is obtained;

[0071] Material properties of complex aerospace structures. Specifically, in this invention, the wing spars of the constructed wing structure use 30CrMnSiNi2A alloy steel, while the stringers, wing ribs, and skin all use 2024 aluminum alloy. The elastic modulus, density, and Poisson's ratio of 30CrMnSiNi2A alloy steel are E1 = 207000 MPa, ρ1 = 7.77 × 10⁻⁶ MPa, and ρ1 = 7.77 × 10⁻⁶ MPa, respectively. -9 ton / mm 3 And ν1 = 0.3. The elastic modulus, density, and Poisson's ratio of 2024 aluminum alloy are E2 = 68000 MPa, ρ2 = 2.8 × 10⁻⁶, and ν1 = 0.3, respectively. -9 ton / mm 3 And ν2 = 0.3.

[0072] External loads and boundary conditions. Since the aircraft wing structure uses a straight wing, the aerodynamic load distribution of a single wing can be approximated as an elliptical distribution along the span and a triangular distribution along the chord. Based on this, aerodynamic loads are added, and the displacement and rotational degrees of freedom in the three directions of the wing rib at the wing root are fixed as boundary conditions.

[0073] Mesh generation. The wing structure model is meshed, with an approximate global mesh size of 10mm selected. The meshed wing structure model is shown below. Figure 3 As shown, some of the skin has been hidden to demonstrate the effect.

[0074] Deterministic finite element model analysis. The structural strength of the wing structure under aerodynamic loads was analyzed using Abaqus finite element software. The results are shown below. Figure 4 As shown.

[0075] S103: Utilize command flow analysis and parameterize the corresponding variables of the simulation model of the complex aerospace structure to obtain parameterization results;

[0076] Before proceeding, the assessment points and failure criteria must be determined. Strength analysis of the wing structure shows that the areas with higher principal stresses are the upper and lower edge strips on the main wing spars near the wing root. The area with the highest stress is the outermost unit where the upper and lower edge strips at the front of the main wing spars connect to the wing rib at the wing root. Figure 4 The B-cell display shows the location of maximum stress on the upper edge slat. Therefore, in the subsequent reliability analysis, the principal stress output of the B-cell will be used as the output of the aircraft wing structure.

[0077] Then, the position of the pre-parameterized variable is recorded during the command stream generation process. The variable is then used to replace the variable value in the implementation process at that position, thus achieving the parameterization of the variable in the .py file.

[0078] S104: Establish the call between Matlab and Abaqus software, complete the sampling process of the corresponding variables of the simulation model of the complex aerospace structure in Matlab, send the parameterization results into Abaqus, and read the analysis results of Abaqus, thereby realizing the joint simulation of Matlab and Abaqus and the construction of the response function of the complex aerospace structure.

[0079] The response function G GJQ1 for:

[0080]

[0081] Among them, g GJQ1 (X,Y(t),Q,t) represents the response function, X represents the random input variable, Y(t) represents the random process input variable, Q represents the interval input variable, and S represents the random input variable. XY S represents the allowable stress of the aircraft wing structure. GJQ1 E1 represents the elastic modulus of the first material, ρ1 represents the density of the first material, E2 represents the elastic modulus of the second material, and ρ2 represents the density of the second material. Indicates the thickness of the upper and lower edge strips of the main beam. Indicates the thickness of the web of the main beam. n represents the skin thickness, n0 represents the maneuver overload, θ represents the flight pitch angle, m(t) represents the aircraft mass at time t, and t represents the time parameter.

[0082] S2: Obtain the quantification results of input uncertainty variables for complex aerospace structures;

[0083] Optionally, in step S2, the input uncertainty variables of the complex aerospace structure include: the geometric dimensions of the complex aerospace structure, the load environment, and the material properties; step S2 includes: using random variables, interval variables, and random processes to perform quantitative analysis on the corresponding input uncertainty variables of the complex aerospace structure to obtain the quantitative results.

[0084] When quantifying the input uncertainties of complex aerospace structures, various quantification methods, including random variables, interval variables, and stochastic processes, were employed based on the actual situation. The stochastic processes were calculated using the Orthogonal Series Extension (OSE) method. The basic idea is as follows:

[0085] The orthogonal function used in the OSE method is:

[0086]

[0087] Among them Le i (·) is the i-th Legendre polynomial and In general, for a random process Y j (t)(j=1,2,...,n Y This can be expressed as:

[0088]

[0089] In the above formula, Δ ji (i = 1, 2, ..., ∞) is a set of correlated, zero-mean, normally distributed random variables. The core of the OSE method is to transform this set of correlated normally distributed random variables into uncorrelated, standard normally distributed random variables. This is based on the fundamental orthogonal function κ. i The orthogonality property of (t)(i=1,2,...,∞) can be used to determine Δ ji With Δ jk Covariance function between Written as:

[0090]

[0091] Through eigenvalue decomposition, the covariance function can be determined. Satisfy the following formula:

[0092]

[0093] Where λ j It is a diagonal matrix, and the diagonal element λ jk for Γ is an eigenvalue. j It is an eigenvector matrix, and each of its columns Γ ji All The eigenvectors of the relevant random variables Δ. ji (i = 1, 2, ..., ∞) are expressed as independent standard normal random variables ξ j =(ξ j1 ,ξ j2 ,...,ξ j∞ ):

[0094]

[0095] in It is the eigenvector Γ ji The k-th value. Furthermore, the random process Y can be... j (t)(j=1,2,...,n Y This can be expressed as:

[0096]

[0097] Because it is actually very difficult to obtain Since there are infinitely many eigenvalues ​​and eigenvectors, the first M are often selected. jThe term is used as an approximation, thus allowing the stochastic process Y to be approximated. j (t)(j=1,2,...,n Y This can be further expressed as:

[0098]

[0099] In the above formula Based on the above process, the random process can be input into Y. j (t)(j=1,2,...,n Y It can be expressed as a series of independent standard normal variables. This invention defines Let Y(t) represent the input of the random process.

[0100] The uncertainties considered include load uncertainty, material uncertainty, dimensional uncertainty, and safety limit uncertainty. Load uncertainty is determined by the randomness of aircraft mass and the randomness of maneuvering overload. This invention assumes that the aircraft mass m(t) is a Gaussian random process, and the maneuvering overload n0 is a uniformly distributed variable varying from g to 1.5g, where g = 9800 mm / s². 2 This represents gravitational acceleration. Material uncertainty is measured by the randomness of material parameters, specifically including the elastic modulus E1, density ρ1, and Poisson's ratio ν1 of 30CrMnSiNi2A alloy steel, and the elastic modulus E2, density ρ2, and Poisson's ratio ν2 of 2024 aluminum alloy. Dimensional uncertainty is measured by the randomness of the thickness of each component of the wing structure, including the thickness of the upper and lower edge strips of the main spars. Main beam web thickness Sub-beam upper and lower edge strip thickness Sub-beam web thickness Rib thickness stringer thickness and skin thickness The uncertainty of the safety limit is determined by the corresponding allowable stress S XY Perhaps use strain E XY Measurement. All random inputs are assumed to have a coefficient of variation of 0.05. The distribution type and parameters are shown in Table 1. For the aircraft's flight angle of attack θ, in the absence of flight statistics, it may be more reasonable to assume it as an interval input variable. Here, the flight angle of attack θ is assumed to be an interval variable taking values ​​in the interval [0°, 10°].

[0101] Table 1 Random Input Distribution Parameters of Wing Structure

[0102]

[0103] S3: Based on the quantization result, obtain the sample matrix and sample pool corresponding to the quantization result;

[0104] S301: The time parameter t is uniformly discretized into N values ​​within its time interval [0,T]. t That moment, namely

[0105] The aircraft wing structure has an operating time of T = 5 years. To calculate the upper boundary of the time-varying failure probability, the time parameter t is uniformly discretized into N values ​​within its range [0,5]. t = 100 moments.

[0106] S302: Quantification results (x) of the input uncertainty variables of the complex aerospace structure extracted using the Latin hypercube technique. (i) ,ξ (i) ,q (i) (i = 1, 2, ..., N), to obtain the sample pool, wherein the sample pool includes N S Samples [x] *(i) ,ξ *(i) ,q *(i) ,t *(i) (i = 1, 2, ..., N) S );

[0107] This invention utilizes the Latin hypercube technique to extract 100,000 input samples (x (i) ,ξ (i) ,q (i) (i = 1, 2, ..., 100000), generate N S =26 samples [x *(i) ,ξ *(i) ,q *(i) ,t *(i) ](i=1,2,...,26), where the time parameter samples are drawn by treating the time parameter as a uniform distribution over its value range.

[0108] S303: Construct a sample matrix based on the sample pool. Wherein, sample matrix The sample in the i-th row and j-th column is [x (i) ,y (i) (t (j) ),q (i) ,t (j) ](i=1,2,...,N; j=1,2,...,N t ), where y (i) (t (j) ) by ξ (i) and t (j) t is calculated based on the orthogonal series extension method. (j) At time j, the interval input variable sample q (i)(i = 1, 2, ..., N) represents the extraction of interval input variables as uniformly distributed variables within their respective intervals, x (i) Let ξ represent the i-th group of random input variable samples. (i) Let λ represent the i-th group of standard normal variables. jk Y represents the input variable of the random process. j The k-th eigenvalue of the orthogonal expansion of (t) and Y represents the input variable of the random process. j The mean of (t), and and κ i (t) represents the k-th value of the eigenvector and the fundamental orthogonal function, respectively. jk This represents the input variable Y corresponding to the random process. j M is the k-th standard normal random variable of (t). j Y represents the input variable of the random process. j The number of terms in the expansion of (t), where k represents the indicator parameter.

[0109] Constructing the sample matrix The sample in the i-th row and j-th column of the sample matrix is ​​[x (i) ,y (i) (t (j) ),q (i) ,t (j) (i = 1, 2, ..., 100000; j = 1, 2, ..., 100), where y (i) (t (j) ) by ξ (i) and t (j) The interval input variable sample q is calculated using the following formula. (i) (i = 1, 2, ..., 100000) is a method of extracting interval input variables as uniformly distributed variables in their respective intervals.

[0110] S4: Calculate the response function result of the current training sample using the aforementioned response function;

[0111] Among them, the current training samples are obtained through ξ *(i) Convert to y *(i) (t *(i) ), thereby obtaining the current training sample [x] *(i) ,y *(i) (t *(i) ),q *(i) ,t *(i) [i = 1, 2, ..., 26], and the response under these training samples is calculated using a finite element model of complex aerospace structures.

[0112] S5: Based on the quantization results and the response function results, establish a multiple Kriging surrogate model for the response function of complex aerospace structures;

[0113] When constructing the Kriging surrogate model, the number of samples in the training set must be no less than the number of regression parameters p = n. X +n Y +n Q +1, where n X n Y and n Q These represent the number of input random variables, random processes, and interval variables, respectively. Therefore, when constructing a multiple Kriging surrogate model, the number of samples N in the training set can be used as a basis. S The relationship between the size of the regression parameters and the number of regression parameters p determines the type of surrogate model constructed, i.e.:

[0114] (a) If 1 <N S ≤n X +n Y +n Q +2, then construct a surrogate model for the 0th-order regression term;

[0115] (b) If Then a surrogate model with both 0th-order and 1st-order regression terms is constructed simultaneously;

[0116] (c) If Then, surrogate models with 0th-order, 1st-order, and 2nd-order regression terms are constructed simultaneously.

[0117] Since the multiple Kriging proxy model is built using the same set of training samples and responses, building the multiple Kriging proxy model does not introduce additional computational costs.

[0118] S6: Use the multiple Kriging proxy model to predict the samples in the sample matrix to obtain the first prediction mean and the first prediction standard value;

[0119] Simultaneously calculate the corresponding U-learning function U. l (x (i) ,y (i) (t (j) ),q (i) ,t (j) )(i=1,2,...,N; j=1,2,...,N t )

[0120] The first prediction mean is:

[0121]

[0122] The first prediction standard deviation is:

[0123]

[0124] S7: Based on the first predicted mean and the first predicted standard value, obtain the average KL divergence and the maximum average KL divergence;

[0125] The average KL divergence is:

[0126]

[0127] The maximum average KL divergence is:

[0128]

[0129]

[0130] Where N K This represents the number of proxy models in the proxy model set Ω. and These represent the results obtained based on the surrogate model l under the inputs px, y(t), q, t], respectively. and The probability of:

[0131]

[0132]

[0133] and Let each represent a proxy model for [ ] ∈ Ω. and The average probability of is defined as follows:

[0134]

[0135]

[0136] S8: Determine the globally optimal proxy model of the multiple Kriging proxy model based on the average KL divergence, the maximum average KL divergence, and the global accuracy of the multiple Kriging proxy model;

[0137] Specifically, step S8 includes:

[0138] S801: Determine whether the maximum average KL divergence is less than the average KL divergence. If yes, proceed to step S802; otherwise, proceed to step S803.

[0139] S802: Output the current Kriging proxy model as the globally optimal proxy model;

[0140] S803: Determine whether there exists a multiple Kriging proxy model that satisfies the condition in two iterations. If a proxy model exists, delete it; otherwise, retain all proxy models. This represents the global accuracy of the multiple Kriging proxy model. This represents the global precision threshold.

[0141] For each Kriging proxy model, its prediction mean Minimum values ​​of time parameters and interval variables This is crucial for calculating the upper bound of the time-varying failure probability, where:

[0142]

[0143]

[0144] The corresponding U-learning function is:

[0145]

[0146] In the above formula This represents the standard deviation of the forecast.

[0147] Therefore, the following measure ω ] It can be used to measure the global accuracy of the proxy models in the proxy model set Ω.

[0148]

[0149] Where N represents the number of random input samples, Indicates corresponding to U ] (x,y(t minl ),q minl ,t minl The number of samples where ω < 2. l It can be viewed as the prediction error when the surrogate model l predicts samples in the sample pool, and therefore has the minimum ω. l The surrogate model for the value has the best global accuracy. Further analysis of ω... ] The following standardization will be implemented:

[0150]

[0151] Where, N K This indicates the number of proxy models in the proxy model set Ω. ω represents all proxy models in the proxy model set Ω. l The sum of . Therefore, The smaller the value, the higher the accuracy of the proxy model. Exceeding a certain value In such cases, the proxy model can be considered insufficiently accurate. In this invention... If set to 1.5, then when a certain proxy model's If the value is greater than 1.5, it indicates that the proxy model is not accurate enough compared to other proxy models and should be removed from the proxy model set Ω.

[0152] S9: Based on the local accuracy index, use the global optimal surrogate model to calculate the second predicted mean of the samples in the sample pool;

[0153] The second predicted mean is:

[0154]

[0155] Where, x (i) Let y represent the i-th group of random input variable samples. (i) (t (j) ) represents the value of the random process vector of the i-th sample and the j-th time step, t (j) Let q represent the j-th time. (i) This represents a range of input variable samples.

[0156] S10: Determine the number of failed samples based on the second predicted mean;

[0157] S11: Based on the number of failed samples, the upper limit of the number of misjudged samples in the failure domain, and the upper limit of the number of misjudged samples in the safety domain, the result of the error-based adaptive update stopping criterion is obtained;

[0158] The error-based adaptive update stopping criterion results for:

[0159]

[0160] Where, N f Indicates the number of failed samples. and These represent the upper limit of the number of samples that are misjudged in the failure domain and the upper limit of the number of samples that are misjudged in the security domain, respectively.

[0161] Specifically, the local precision index is used to predict samples and calculate the upper bound of time-varying failure probability. The basic idea is as follows: the multiple Kriging surrogate model method contains multiple surrogate models, and each surrogate model has a prediction mean and a prediction standard deviation. That is, directly using the constructed multiple Kriging surrogate model will result in multiple sets of prediction results, while the calculation of time-varying failure probability only requires one set of prediction results. Because the learning function U... lThe expression (x,y(t),q,t) can, to some extent, measure the accuracy of the surrogate model in predicting the response. Therefore, a locally optimal surrogate model for input [x,y(t),q,t] is defined as the surrogate model with the maximum U-learning function value. Using l... local Describing a locally optimal surrogate model, then

[0162]

[0163] For different inputs, the corresponding locally optimal surrogate model may be different. If using Let U(x,y(t),q,t) represent the mean, standard deviation, and learning function of the locally optimal surrogate model under the input [x,y(t),q,t], respectively.

[0164]

[0165]

[0166]

[0167] By using the local optimal surrogate model l local It can integrate multiple sets of prediction results from multiple Kriging surrogate models into a single set of prediction results, which can then be used to solve for the upper bound of the time-varying failure probability.

[0168] S12: Determine whether the result of the error-based adaptive update stopping criterion has converged. If it has converged, proceed to step S13; otherwise, proceed to step S14.

[0169] The convergence criteria are:

[0170]

[0171] S13: Calculate the upper boundary value of the time-varying failure probability under mixed uncertainty based on the number of failure samples, and output the upper boundary value of the time-varying failure probability under mixed uncertainty as the analysis result of the time-varying reliability of the complex aerospace structure under mixed uncertainty;

[0172] Upper boundary value of time-varying failure probability under mixed uncertainties for:

[0173]

[0174] in, For failure indication function and This represents the minimum second predicted mean and This represents the time corresponding to the minimum second predicted mean and This represents the range of values ​​of the interval variable corresponding to the minimum second predicted mean, and This indicates that when the interval variable takes the value The second predicted mean result, This indicates that when the time parameter takes the value The second predicted mean result.

[0175] exist and In the calculation and Estimate using the following formulas respectively:

[0176]

[0177]

[0178]

[0179] In the above formulas, For corresponding The predictive standard deviation, [x (i)f ,y (i)f (t min (i = 1, 2, ..., N) f ) and [x (i)s ,y (i)s (t min (i = 1, 2, ..., N) f ) respectively represent the proxy model The identified failure domain samples and security domain samples.

[0180] Upper bound of time-varying failure probability The calculation is as follows:

[0181]

[0182] in The failure indication function is expressed as follows:

[0183]

[0184] In the above formula and Upper bound of the calculated time-varying failure probability coefficient of variation for:

[0185]

[0186] S14: Update the average KL divergence based on the global optimal proxy model and obtain new training samples based on the updated average KL divergence, then return to step S4.

[0187] Let the sample obtained by filtering based on the KKT conditions for the interval input variable be denoted as . Construct a new average KL divergence The learning function is as follows:

[0188]

[0189] New training samples are obtained through the following process: the response under the training sample is calculated based on the response function, and the training sample and the corresponding response are added to the training sample set and the response set, and then the process returns to step S4.

[0190]

[0191] By combining the limit state projection contour method with KL divergence, a new adaptive update learning function is constructed, the basic idea of ​​which is as follows:

[0192] For a response function G = g(X,Y(t),Q,t) under mixed uncertain input variables, its limit state surface can be expressed as:

[0193] {g(X,Y(t),Q,t)=0|t∈[0,T],Q∈[Q L Q U ]} (1)

[0194] The upper boundary of the time-varying failure probability at different times t∈[0,T] The calculated limit state surface projected boundary is:

[0195]

[0196] in Let be a sample consisting of random input variables and random process input variables on the projected boundary. Based on the above equation, the projected profile of the limit state surface can be obtained as:

[0197]

[0198] In the above formula This represents the upper boundary of the time-varying failure probability at different times t∈[0,T]. The set of points on the projection profile of the limit state surface. If the constructed surrogate model can accurately identify this projection profile of the limit state surface, it can accurately calculate the upper boundary of the time-varying failure probability under mixed uncertainty input.

[0199] In the above formula At least one of the following Karush-Kuhn-Tucker (KKT) conditions must be satisfied:

[0200]

[0201]

[0202] in, and The first There are interval variables, a lower bound of the interval variable, an upper bound of the interval variable, and the values ​​of the interval variable projected onto the limit state surface profile, where l = 1, 2, ..., n Q Based on this KKT condition and combined with the idea of ​​multiple Kriging surrogate models, during the adaptive update process of the Kriging surrogate model, the sample points on the projection contour of the limit state surface should be added to the training sample set to update the surrogate model.

[0203] Let the sample obtained by filtering through KKT conditions regarding the interval input variable be denoted as... Then a new average KL divergence can be constructed. The learning function is as follows:

[0204]

[0205] By maximizing This will allow us to obtain new training sample points.

[0206] The final calculated upper boundary results of the time-varying failure probability are shown in Table 2, and the convergence evolution diagram is shown in... Figure 5 As shown.

[0207] Table 2. Upper Boundary Results of Time-Varying Failure Probability of Aircraft Wing Structure under Mixed Uncertainty

[0208]

[0209] By combining Table 2 Figure 5 It can be seen that, compared with the traditional Kriging surrogate model method, the established multiple Kriging surrogate model method not only has higher computational accuracy, but also significantly improves the computational efficiency of time-varying reliability analysis under mixed uncertainties, and has great engineering application value.

[0210] The present invention has the following beneficial effects:

[0211] This invention establishes an effective strategy based on the Kriging surrogate model to weigh the impact of different regression terms on the final result, and determines one or more optimal regression terms to construct a surrogate model for complex aerospace structures, thereby effectively avoiding the shortcomings of the traditional Kriging surrogate model method that involves manually setting regression terms.

[0212] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties, characterized in that, include: S1: Constructing the response function of complex aerospace structures based on simulation models of complex aerospace structures; S2: Obtain the quantification results of input uncertainty variables for complex aerospace structures; S3: Based on the quantization result, obtain the sample matrix and sample pool corresponding to the quantization result; S4: Calculate the response function result of the current training sample using the aforementioned response function; S5: Based on the quantization results and the response function results, establish a multiple Kriging surrogate model for the response function of complex aerospace structures; S6: Use the multiple Kriging proxy model to predict the samples in the sample matrix to obtain the first prediction mean and the first prediction standard value; S7: Based on the first predicted mean and the first predicted standard value, obtain the average KL divergence and the maximum average KL divergence; S8: Determine the globally optimal proxy model of the multiple Kriging proxy model based on the average KL divergence, the maximum average KL divergence, and the global accuracy of the multiple Kriging proxy model; S9: Based on the local accuracy index, use the global optimal surrogate model to calculate the second predicted mean of the samples in the sample pool; S10: Determine the number of failed samples based on the second predicted mean; S11: Based on the number of failed samples, the upper limit of the number of misjudged samples in the failure domain, and the upper limit of the number of misjudged samples in the safety domain, the result of the error-based adaptive update stopping criterion is obtained; S12: Determine whether the result of the error-based adaptive update stopping criterion has converged. If it has converged, proceed to step S13. Otherwise, proceed to step S14; S13: Calculate the upper boundary value of the time-varying failure probability under mixed uncertainty based on the number of failure samples, and output the upper boundary value of the time-varying failure probability under mixed uncertainty as the analysis result of the time-varying reliability of the complex aerospace structure under mixed uncertainty; S14: Update the average KL divergence based on the global optimal proxy model and obtain new training samples based on the updated average KL divergence, then return to step S4.

2. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 1, characterized in that, In step S1, the simulation model of the complex aerospace structure is established using finite element software. Step S1 includes: S101: Establishing a three-dimensional model of a complex aerospace structure using Abaqus software; S102: Based on the three-dimensional model, as well as the material properties, external loads and boundary conditions, analysis steps and mesh generation of the complex aerospace structure, a simulation model of the complex aerospace structure is obtained; S103: Utilize command flow analysis and parameterize the corresponding variables of the simulation model of the complex aerospace structure to obtain parameterization results; S104: Establish the call between Matlab and Abaqus software, complete the sampling process of the corresponding variables of the simulation model of the complex aerospace structure in Matlab, send the parameterization results into Abaqus and read the analysis results of Abaqus, thereby realizing the joint simulation of Matlab and Abaqus and the construction of the response function of the complex aerospace structure. The response function G GJQ1 for: Among them, g GJQ1 (X,Y(t),Q,t) represents the response function, X represents the random input variable, Y(t) represents the random process input variable, Q represents the interval input variable, and S represents the random input variable. XY S represents the allowable stress of the aircraft wing structure. GJQ1 E1 represents the elastic modulus of the first material, ρ1 represents the density of the first material, E2 represents the elastic modulus of the second material, and ρ2 represents the density of the second material. Indicates the thickness of the upper and lower edge strips of the main beam. Indicates the thickness of the web of the main beam. n represents the skin thickness, n0 represents the maneuver overload, θ represents the flight pitch angle, m(t) represents the aircraft mass at time t, and t represents the time parameter.

3. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 1, characterized in that, In step S2, the input uncertainty variables of the complex aerospace structure include: the geometric dimensions of the complex aerospace structure, the load environment, and the material properties; step S2 includes: using random variables, interval variables, and random processes to perform quantitative analysis on the corresponding input uncertainty variables of the complex aerospace structure to obtain the quantitative results.

4. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 1, characterized in that, Step S3 includes: S301: The time parameter t is uniformly discretized into N values ​​within its time interval [0,T]. t That moment, namely S302: Quantification results (x) of the input uncertainty variables of the complex aerospace structure extracted using the Latin hypercube technique. (i) ,ξ (i) ,q (i) (i = 1, 2, ..., N), to obtain the sample pool, wherein the sample pool includes N S Samples [x] *(i) ,ξ *(i) ,q *(i) ,t *(i) (i = 1, 2, ..., N) S ); S303: Construct a sample matrix based on the sample pool. Wherein, sample matrix The sample in the i-th row and j-th column is [x (i) ,y (i) (t (j) ),q (i) ,t (j) ](i=1,2,...,N; j=1,2,...,N t ), where y (i) (t (j) ) by ξ (i) and t (j) t is calculated based on the orthogonal series extension method. (j) At time j, the interval input variable sample q (i) (i = 1, 2, ..., N) represents the extraction of interval input variables as uniformly distributed variables within their respective intervals, x (i) Let ξ represent the i-th group of random input variable samples. (i) Let λ represent the i-th group of standard normal variables. jk Y represents the input variable of the random process. j The kth eigenvalue of the orthogonal expansion of (t) and Y represents the input variable of the random process. j The mean of (t), and and κ i (t) represents the k-th value of the eigenvector and the fundamental orthogonal function, respectively. jk This represents the input variable Y corresponding to the random process. j M is the k-th standard normal random variable of (t). j Y represents the input variable of the random process. j The number of terms in the expansion of (t), where k represents the indicator parameter.

5. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 4, characterized in that, In step S4, the current training sample is obtained from the sample pool, i.e., using the formula... ξ *(i) Convert to y *(i) (t *(i) ), to obtain training samples [x *(i) ,y *(i) (t *(i) ),q *(i) ,t *(i) (i = 1, 2, ..., N) S ).

6. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 1, characterized in that, In step S6, the first predicted mean is: The first prediction standard deviation is: In step S9, the second predicted mean is: Where, x (i) Let y represent the i-th group of random input variable samples. (i) (t (j) ) represents the value of the random process vector of the i-th sample and the j-th time step, t (j) Let q represent the j-th time. (i) This represents a range of input variable samples.

7. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 6, characterized in that, In step S7, the average KL divergence is: The maximum average KL divergence is: .

8. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 5, characterized in that, Step S8 includes: S801: Determine whether the maximum average KL divergence is less than the average KL divergence. If yes, proceed to step S82; otherwise, proceed to step S83. S802: Output the current Kriging proxy model as the globally optimal proxy model; S803: Determine whether there exists a multiple Kriging proxy model that satisfies the condition in two iterations. If a proxy model exists, delete it; otherwise, retain all proxy models. This represents the global accuracy of the multiple Kriging proxy model. This represents the global precision threshold.

9. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to claim 1, characterized in that, In step S11, the error-based adaptive update stopping criterion result for: Where, N f Indicates the number of failed samples. and These represent the upper limit of the number of samples that are misjudged in the failure domain and the upper limit of the number of samples that are misjudged in the security domain, respectively.

10. The method for analyzing the time-varying reliability of complex aerospace structures under mixed uncertainties according to any one of claims 1-9, characterized in that, In step S13, the upper boundary value of the time-varying failure probability under mixed uncertainty for: in, For failure indication function and This represents the minimum second predicted mean and This represents the time corresponding to the minimum second predicted mean and This represents the range of values ​​of the interval variable corresponding to the minimum second predicted mean, and This indicates that when the interval variable takes the value The second predicted mean result, This indicates that when the time parameter takes the value The second predicted mean result.

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