A Dynamic Global Sensitivity Analysis Method for Flap Mechanisms Based on Vine Copula

Abstract

This invention discloses a dynamic global sensitivity analysis method for flap mechanisms based on Vine Copula. First, a rigid-flexible coupling simulation is performed on the moving mechanism. Stress-critical regions, deformation-critical regions, and jamming-critical regions are identified based on stress distribution. A new structural failure criterion—a time-varying stress-strain-driving force joint criterion—is proposed based on the dynamic multi-parameter coupling concept. The input random parameters are then defined according to the motion characteristics of the flap mechanism. Next, a time-varying correlation model considering autocorrelation and cross-correlation is established based on Vine Copula theory and a stochastic process model. This model generates conditional samples, and the required input random variables are generated through inverse transformation. Finally, the dynamic samples are divided into several sub-intervals using a spatial segmentation method, and the Sobol index is solved to determine the importance measure of each input parameter during the flap mechanism's motion process.

Description

Technical Field

[0001] This invention relates to the field of aircraft design, and in particular to a dynamic global sensitivity analysis method for flap mechanisms based on Vine Copula. Background Technology

[0002] With the rapid development of aerospace technology, the requirements for aircraft performance, reliability, and safety are increasing. However, aircraft structures and mechanisms face many complex factors, such as manufacturing errors, fluctuations in material properties, and uncertainties related to varying environmental conditions during actual operation. As a crucial lift-enhancing device for aircraft, the flap mechanism is vital to flight safety. Therefore, conducting global sensitivity analysis on flaps is essential. Global sensitivity analysis can identify key influencing factors, helping to optimize design parameters, reduce the impact of uncertainties, and provide strong support for the design optimization and reliability improvement of flap mechanisms. For flap mechanisms, the potential strength, stiffness, and jamming failures during their extension and retraction are major challenges currently faced in flap design.

[0003] The flap mechanism has numerous input variables, and these variables are coupled with each other. Therefore, the correlation between variables needs to be considered before conducting a global sensitivity analysis. Furthermore, the flap mechanism operates as a dynamic extension and retraction process, with varying importance and coupling levels of the input variables at different times. Global sensitivity analysis based on static correlations is insufficient to accurately determine the global sensitivity index (Sobol index), leading to inaccurate results. Therefore, dynamic correlation modeling is essential. Summary of the Invention

[0004] To overcome the shortcomings of existing methods and technologies and address the issue of prioritizing the importance of input variables in a flap mechanism at various time points, this invention proposes a dynamic global sensitivity analysis method for flap mechanisms based on Vine Copula. This method effectively considers the complete motion process of the flap mechanism and the correlations between its input variables, ranking their importance accordingly. Simultaneously, this method improves the computational efficiency of general global sensitivity analysis methods.

[0005] The technical solution of this invention is as follows:

[0006] A dynamic global sensitivity analysis method for flap mechanisms based on Vine Copula includes the following steps:

[0007] Step 1: Based on finite element simulation and multibody dynamics simulation, perform rigid-flexible coupling analysis on the flap motion mechanism. Select the rocker arm, sinking hinge, connecting bracket and connecting tube as the key parts of the flap mechanism. Extract the analysis results of Mises stress, equivalent displacement and actuator driving force to obtain the motion characteristics of the flap mechanism within 100 seconds of operation and identify the danger zone.

[0008] Step 2: Based on Minner's linear cumulative damage theory and engineering experience (engineering design manual or standard), conduct preliminary work for global sensitivity analysis, namely, determine the failure modes as strength failure, stiffness failure, jamming failure and system failure, establish failure criteria as insufficient strength, insufficient stiffness, insufficient driving force and excessive coupling criteria, clarify the types and distribution of input random variables, and fit the relationship between input and output.

[0009] Step 3: Perform dynamic global sensitivity analysis based on Vine Copula and spatial segmentation to calculate the importance measure of the input random variables. First, discretize the operating time into continuous non-overlapping intervals and construct a Kriging surrogate model for each failure mode. Fit the limiting state function using a finite number of sample points. Then, establish a time-varying correlation model. By considering the cross-correlation between different dimensions of the input random variables and the autocorrelation between different times of a single variable, establish a time-varying Vine Copula model and perform correlation processing on the samples to generate input random variable samples. Finally, divide the input random variable samples into n continuous non-overlapping sub-intervals and solve the Sobol index through spatial segmentation.

[0010] Step 4: Rank the importance of the input random variables according to the aforementioned indicators.

[0011] Preferably, in step 2, the three independent failure modes of the flap mechanism are determined to be strength failure, stiffness failure, and jamming failure, and the single failure criterion for each of the three failure modes is:

[0012] Failure criterion due to insufficient strength: In the formula For the maximum stress of the flap mechanism, For the allowable stress of the material, This is the strength reserve coefficient;

[0013] Insufficient stiffness failure criterion In the formula This represents the maximum deformation of the flap mechanism. This is the maximum allowable deformation;

[0014] Failure criteria for jamming phenomenon: In the formula For real-time driving torque, The driving torque required for the retraction and extension operation.

[0015] Preferably, in step 2, the construction of the multi-level failure criterion is as follows: To address the risk of compound failure, a time-varying comprehensive failure criterion is proposed based on the uncertainty of the flap mechanism's motion process and the single failure criterion: In the formula, This is a stress-based fatigue accumulation term. These are the weighting coefficients for a single failure mode. The threshold values ​​are used as comprehensive criteria; for flap mechanisms, when Fatigue accumulation failure is triggered when When the instantaneous over-limit failure is triggered, The system fails when the time is right.

[0016] Preferably, in step 2, the input random variables include: aerodynamic load coefficients a1, a2 that follow a Gaussian random process, assembly error d that follows a normal distribution, and hinge dynamic friction coefficient f that follows a normal distribution.

[0017] As a preferred embodiment, in step 3, the method for establishing the Kriging model is as follows: the input random variables determined in step 2 are sampled to obtain non-repeating input data of the flap mechanism, which are then substituted into the rigid-flexible coupling simulation to obtain the response values ​​under each failure mode as output data, and an input-output dataset is constructed; a Kriging surrogate model is established based on the dataset, and the Kriging model is adaptively learned using the U learning function until convergence, and the surrogate model is used to replace the rigid-flexible coupling simulation for subsequent global sensitivity analysis.

[0018] As a preferred embodiment, the method for establishing the time-varying correlation model in step 3 is as follows: a set of uniformly distributed samples is randomly sampled as the initial samples, and a Vine Copula tree is constructed. In each layer of the model tree, the optimal Copula function is selected for samples of different dimensions according to the AIC criterion, and the correlation parameters are calculated to establish the cross-correlation matrix between variables at different times. ; will conform to the matrix Corresponding samples of the correlation Transform the sample into one that follows a standard normal distribution and calculate the covariance. ,right SVD decomposition is performed to obtain matrix A, and the time-varying composite coefficient matrix containing autocorrelation and cross-correlation is solved. Based on the time-varying comprehensive coefficient matrix And the correlation vector obtained from the covariance matrix decomposition results. The required samples are generated through inverse transformation. .

[0019] As a preferred option The cross-correlation matrix between variables at time points for: In the formula Let i be a standard Gaussian random process with i-th dimension variable. For the standard deviation operator, For expectation operators.

[0020] As a preferred option Time-varying composite coefficient matrix containing autocorrelation and cross-correlation for: In the formula The result of covariance matrix decomposition. The standard deviation is given by the subscripts i and j, which indicate the dimension of the variable, l = 1, 2, ..., n, t. n t l t j They represent t respectively n Time, t l Time and t j time.

[0021] As a preferred option, in step 3, the Sobol index is solved by spatial segmentation as follows: the input sample is divided into n consecutive non-overlapping sub-intervals, and the Sobol index based on the traditional MCS method is converted into a spatial segmentation form containing the first-order Sobol index and the second-order Sobol index by calculating the probability of the sample falling into each sub-interval and the conditional variance within each sub-interval.

[0022] Preferably, for the first-order Sobol index, the input random variable is divided into s continuous non-overlapping sub-intervals. And based on the definition of expectation and the integral mean value theorem, the transformed Sobol index is converted into a spatial partitioning form, i.e.: as well as In the formula for Falling into the range The probability, Let v be the variance of the sample falling into each subinterval; for the second-order Sobol index, the input random variable is divided into v continuous non-overlapping subspaces. And based on mathematical expectation and numerical integration, it is transformed into a spatial partitioning form, namely: as well as In the formula Let be the probability that a sample falls into the subspace. This represents the variance of the sample falling into each subspace.

[0023] Beneficial effects

[0024] 1. This invention proposes a Vine Copula-based dynamic global sensitivity analysis method for flap mechanisms, used to quantify the importance of single input variables and two-dimensional interactive input variables of flap mechanisms. Currently, there is a gap in research on the uncertainty of flap mechanisms, making it difficult to effectively derive hazardous input variables through theoretical analysis. The method disclosed in this invention is applied to the field of aircraft design. It identifies hazardous parts and critical moments of flap mechanisms through rigid-flexible coupling analysis, and then uses the Vine Copula-spatial segmentation method based on stochastic processes to solve for the first and second order Sobol indices of the flap mechanism, thereby obtaining the importance ranking of single input variables and interactive variables, filling a gap in related fields.

[0025] 2. This invention employs Vine Copula and spatial partitioning to solve for the global variance sensitivity Sobol index, significantly expanding its application scope compared to existing methods. ① It introduces stochastic processes into correlation analysis. Existing ordinary Copula methods considering time-varying processes cannot effectively handle multidimensional correlations simultaneously. This invention introduces stochastic processes into Vine Copula, effectively considering time-varying effects when processing sample correlations, greatly improving analysis efficiency compared to single-time Copula analysis methods; ② When performing correlation modeling based on stochastic processes, this invention simultaneously considers the autocorrelation of the same variable at different times, as well as the cross-correlation between different random variables at the same time, compensating for the incomplete consideration of input variable correlations in aircraft design; ③ When using spatial partitioning to solve the Sobol index, this invention introduces a combination of the second-order Sobol index and time-varying Vine Copula, thereby quantifying the impact of two-dimensional interaction effects of input variables on the output response of the flap mechanism, filling previous research gaps. Compared to other global sensitivity analysis methods, this invention has higher computational efficiency while ensuring the accuracy of the calculation results. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below.

[0027] Figure 1 This is a schematic diagram of a flap mechanism according to an embodiment of the present invention;

[0028] Figure 2 This is a stress simulation cloud diagram of a flap mechanism according to an embodiment of the present invention;

[0029] Figure 3 This is a simulation cloud diagram of the deformation of the flap mechanism according to an embodiment of the present invention;

[0030] Figure 4This is a diagram showing the driving force curve of the flap mechanism according to an embodiment of the present invention;

[0031] Figure 5 This is the calculation result of the first-order global sensitivity index for stiffness failure according to an embodiment of the present invention;

[0032] Figure 6 This is the calculation result of the first-order global sensitivity index of strength failure according to an embodiment of the present invention;

[0033] Figure 7 This is the calculation result of the first-order global sensitivity index for jamming failure according to an embodiment of the present invention;

[0034] Figure 8 This is the calculation result of the first-order global sensitivity index of system failure according to an embodiment of the present invention;

[0035] Figure 9 This is the calculation result of the second-order global sensitivity index for stiffness failure according to an embodiment of the present invention;

[0036] Figure 10 This is the calculation result of the second-order global sensitivity index for strength failure according to an embodiment of the present invention;

[0037] Figure 11 This is the calculation result of the second-order global sensitivity index for jamming failure according to an embodiment of the present invention;

[0038] Figure 12 This is the calculation result of the second-order global sensitivity index of system failure according to an embodiment of the present invention;

[0039] Figure 13 This is a schematic diagram illustrating the verification of global sensitivity analysis results according to an embodiment of the present invention;

[0040] Figure 14 This is a schematic diagram of the frame structure and stress distribution according to an embodiment of the present invention;

[0041] Figure 15 This is a schematic diagram of the known sample distribution of the initial time sample according to an embodiment of the present invention;

[0042] Figure 16 This is a schematic diagram of the sample distribution generated based on Vine Copula according to an embodiment of the present invention;

[0043] Figure 17 This is the global sensitivity calculation result of the frame structure according to an embodiment of the present invention;

[0044] Figure 18 The result of calculating the second-order Sobol index of the framework structure according to an embodiment of the present invention;

[0045] Figure 19Aerodynamic load factor of one embodiment of the present invention , A schematic diagram showing the location distribution. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0047] Step 1: Based on finite element simulation and multibody dynamics simulation, perform rigid-flexible coupling analysis on the flap motion mechanism. Select the rocker arm, sinking hinge, connecting bracket and connecting tube as the key parts of the flap mechanism. Extract the analysis results of Mises stress, equivalent displacement and actuator driving force to obtain the motion characteristics of the flap mechanism within 100 seconds of operation and identify the danger zone.

[0048] First of all Figure 1 Considering the aircraft flap mechanism as shown, a deterministic analysis based on structural design should be performed before conducting a global sensitivity analysis. Mesh generation and boundary conditions are applied to the important components of the flap mechanism according to the finite element method. Flexible bodies are generated for components of key interest. A 100-second multibody dynamics simulation model is established based on the flap mechanism's operating state. The flexible bodies are imported into the multibody dynamics model, and rigid-flexible coupling analysis is performed to obtain the results shown below. Figure 2 The stress cloud diagram of the flap mechanism shown is as follows: Figure 3 The deformed cloud map shown and as Figure 4 The diagram shows the driving force curve, and the dangerous parts and moments of danger of the flap mechanism are clearly identified.

[0049] Consider using 300M steel, 7050 aluminum alloy, and TC4 alloy as the production materials for the flap mechanism. The properties of these materials are shown in Table 1.

[0050] surface Material properties

[0051] .

[0052] In the rigid-flexible coupling analysis model of the flap mechanism, the flap driving load is applied to the flap surface according to the STEP function. Considering that the lowering and retraction process is completed within 100 seconds, the stress, deformation and driving force data at each moment can be obtained by performing rigid-flexible coupling analysis. The expression of the STEP function is as follows.

[0053] ,

[0054] In the formula, , i, x, , , as well as These are the force sequence number, time variable, initial time value, initial force value, end time value, and end force value.

[0055] Based on the rigid-flexible coupling analysis of the flap, the single failure modes of the flap mechanism during operation were selected as insufficient strength, decreased stiffness, and jamming. For the insufficient strength failure mode, the Mises stress value was selected for comparison; for the decreased stiffness failure mode, the maximum deformation value was selected for comparison; and for the jamming failure mode, the driving force value was selected for comparison.

[0056] For the complete movement process of the flap mechanism, the maximum stress occurs at 70s, and the maximum stress location is on the connecting rod between the outer rocker arm and the wing surface. At this time, the maximum stress value is 834.01MPa. The maximum deformation of the flap mechanism occurs at 73s, located at the connecting tube, and the maximum deformation value is 0.277mm. The maximum driving force of the flap mechanism occurs at 70s, and the driving force value is 11400N.

[0057] Step 2: Based on Miner's linear cumulative damage theory and engineering design manuals or standards, determine the failure modes of the flap mechanism, including three basic failure modes (strength failure, stiffness failure, and jamming failure) and system failure. Establish failure criteria as insufficient strength, insufficient stiffness, insufficient driving force, and excessive coupling criterion indicators, and construct a multi-level failure mode structure. Select input random variables based on the uncertainty of the flap mechanism's motion process and establish a mathematical distribution model for the input random variables.

[0058] Step 2.1, establish failure criteria for three independent failure modes:

[0059] For the insufficient strength failure mode of the flap mechanism, the failure criterion is established as follows: the structure fails when the actual stress exceeds the allowable stress. According to the strength design manual, the allowable stress of the material corresponding to the most dangerous part at the most critical stress moment is obtained as follows:

[0060] ,

[0061] In the formula, This is the strength reserve coefficient.

[0062] For the stiffness reduction failure mode of the flap mechanism, the failure criterion is established as follows: structural failure occurs when the maximum deformation exceeds the allowable value. The location of the maximum deformation of the flap mechanism can be simplified to a bending beam element. Assuming it is an ideal beam element unaffected by shear force or moment during loading, its allowable deformation is:

[0063] ,

[0064] In the formula M, L, E, and I represent the bending deformation value, the bending moment of the beam element, the length of the beam, the Young's modulus of the beam material, and the second moment, respectively.

[0065] For the jamming failure mode of the flap mechanism, the failure criterion is established as follows: when the maximum driving force does not meet the required driving force, the mechanism will be blocked and jammed. According to engineering experience, the driving force of this type of flap should not be less than 11000N.

[0066] Step 2.2: Based on the above single failure modes and criteria, establish a system coupled failure criterion. Based on the uncertainty of the flap mechanism's motion process, construct a time-varying comprehensive failure criterion as follows:

[0067] ,

[0068] In the formula This is a stress-based fatigue accumulation term. These are the weighting coefficients for a single failure mode. The threshold values ​​are used as comprehensive judgment criteria. For flap mechanisms, when... Fatigue accumulation failure is triggered when When the instantaneous over-limit failure is triggered, The system malfunctions due to timing issues. In this embodiment, the flap mechanism is selected... .

[0069] Step 2.3, considering the randomness of load and material, as well as random processes, the input random variables and their distributions for the flap mechanism are shown in Table 2.

[0070] Table 2 Input Random Variable Parameters

[0071] .

[0072] Aerodynamic loads vary randomly due to flight conditions, and assembly errors and friction coefficients fluctuate due to manufacturing tolerances and wear. These parameters also vary over time (e.g., ...). Figure 2 As shown, the maximum stress occurs at 70s) and spatial dimensions (such as... Figure 3 The external rocker arm and wing connecting rod shown exhibit significant randomness. Aerodynamic load coefficient , These are load parameters at two locations; the aerodynamic load acts at two points, such as... Figure 19 As shown; , It is a constant, a coefficient in the aerodynamic load parameters, and the parameter distribution is determined according to manuals or engineering experience.

[0073] Step 3: Based on the dynamic Vine Copula and spatial partitioning method, calculate the first-order and second-order Sobol indices of each input random variable in Step 2 and rank them by importance. This includes:

[0074] Step 3.1, Discretization of the stochastic process:

[0075] Based on the actual working conditions of the flap mechanism, the actual working time of the flap mechanism was determined to be 100 seconds through rigid-flexible coupling simulation. This process considers two processes: lowering and retraction. The working time is discretized into 100 continuous non-overlapping intervals, with a single step size of 1 second.

[0076] Step 3.2, Limit state function fitting:

[0077] ① Using the LHS random sampling method, non-repeating input data for the flap mechanism is obtained by sampling according to the sample distribution in Table 2. The input variables are then substituted into the rigid-flexible coupling simulation analysis to obtain the corresponding output response values. The inputs are a1(t), a2(t), d, and f, and the outputs are stress σ(t), deformation u(t), and driving force T(t). The input-output samples generated in this step will be used as initial samples to construct the surrogate model. In this embodiment, 60 sets of input-output sample pools are constructed.

[0078] ② Select 8 samples as initial sample points, establish a Kriging surrogate model based on the initial sample points, and use the U learning function for adaptive learning until the surrogate model converges.

[0079] The Kriging surrogate models for each failure mode of the flap mechanism are used to replace the complex rigid-flexible coupling simulation for subsequent global sensitivity analysis, thus solving the problems of excessive computation time in rigid-flexible coupling simulation and the need for massive samples in sensitivity analysis. The limit state function g(X(t)) fitted by the Kriging surrogate model can be used to quickly calculate the failure response value (failure) of any output sample X=[a1(t),a2(t),d,f] at time t (failure is indicated by a limit state function less than 0), providing the response values ​​(stress, deformation, driving force) of the flap mechanism at each discrete time point, which is crucial for constructing the correlation coefficient matrix. Provides dynamic data sources. Subsequent Vine Copula modeling requires joint distribution data of a large number of samples, which come directly from the g(X(t)) response sequences generated by the surrogate model.

[0080] Step 3.3, Time-varying correlation modeling and sample generation

[0081] ① A uniformly distributed sample is generated using random sampling, and a Vine Copula model tree is built using this sample. In each level of the model tree, the optimal Copula function is selected for samples of different dimensions according to the AIC criterion, and the correlation parameters are calculated to establish the cross-correlation matrix between variables at different time points. .

[0082] The cross-correlation matrix between variables at time points for:

[0083] ,

[0084] In the formula Let i be a standard Gaussian random process with i-th dimension variable. For the standard deviation operator, For expectation operators.

[0085] ② Calculate the consistency matrix between variables at different times. Cross-correlation sample matrix of correlations :

[0086] .

[0087] ③ Through inverse transformation Will Transform each element into a standard normal distribution In the form of.

[0088] ④ Using D-vine copula to transform the covariance matrix of arbitrary distributions Convert to a standard normal distribution and calculate the covariance matrix of the distribution. .

[0089] ⑤ Perform matrix decomposition to obtain matrix A, and obtain the true correlation coefficient (considering autocorrelation and cross-correlation). and related vectors ,based on and The inverse transform of the marginal CDF is used to generate input samples. .in It can be represented as:

[0090] .

[0091] The existing samples (several experimental data before the flap analysis can be used as existing samples / initial sample points) are correlated using the correlation coefficient matrix to calculate the dynamic correlation between variables. The processed samples are then transformed to generate input samples that conform to the actual distribution of the flap mechanism. These samples will be used for subsequent global sensitivity analysis.

[0092] Because the Sobol index requires input samples to be independent and identically distributed (i.i.d.), but the input variables of the flap mechanism exhibit autocorrelation (dependence between different variables at the same time) and cross-correlation (dependence of the same variable at different times), directly using the original samples for calculation would lead to mismatched contributions due to cross-correlation, and the failure of variance decomposition due to autocorrelation, resulting in repeated calculation of interaction effects. This application transforms the original distribution into a uniform distribution using the Copula function, decomposes cross-correlation using a Vine tree structure, separates time dependencies through SVD decomposition of the time-varying covariance matrix, and finally generates i.i.d. samples through inverse transformation. Correlated samples ensure that the Sobol index identifies the true principal cause and avoids misjudging low-risk variables.

[0093] Step 3.4, Global Sensitivity Analysis of Flap Mechanism Spatial Segmentation:

[0094] For first-order and second-order Sobol indices, the input random variable is divided into s continuous non-overlapping subintervals. and v consecutive non-overlapping subspaces Based on the definition of expectation and the integral mean value theorem, the space partition form of the first-order Sobol index is obtained as follows:

[0095] , .

[0096] The spatial partitioning form of the second-order Sobol index is:

[0097] , .

[0098] In the formula for Falling into the range The probability is obtained by directly calculating the number of samples within the sub-interval; The variance of the sample falling into each sub-interval is calculated by performing variance calculation on the sample in each sub-interval to obtain the output response. Let be the probability that a sample falls into the subspace. This represents the variance of the sample falling into each subspace.

[0099] First-order indicators refer to the degree of influence of a single input variable on the output, such as indicator 1 > indicator 2 > greater than indicator 3; second-order indicators refer to the interaction effect of two indicators, used to quantify the interaction effect, such as the combined effect of indicator 1 + indicator 2 on the output > indicator 2 + indicator 3.

[0100] Step 4: Substitute the engine wheel-related data into steps 1-3 to calculate the importance ranking of the wheel input variables. The two calculation methods for the Sobol index mentioned above (the empty partition form of the first-order Sobol index in step 3.4) The results of the comparison with the simplified MCS method (the universal Monte Carlo method) are as follows: Figures 5-12 As shown. Among them, Figure 5-8 This is the analysis result of the first-order index under various failure modes. Each cell in the graph represents the importance level of each index at each time point. The darker the cell color, the higher the sensitivity index value at that time point. Figure 9-12 These are the calculation results of second-order indices for each failure mode; the darker the color, the larger the index value.

[0101] Step 5: Verify the importance calculation results of the input variables at a single time point using the controlled variable method. The verification results are as follows: Figure 13 As shown, the results indicate that variables with larger Sobol index calculations do indeed have a significant impact on the variance of the response value, and the method proposed in this invention is consistent with the actual situation.

[0102] In this embodiment, a frame structure is described as follows: Figure 14 As shown, the load is applied to the left side of the structure. The lower end of the frame is fixed to the ground. The input random variables and their distributions are shown in Table 3 below. The equivalent displacement of the upper right corner is selected as the structural output response.

[0103] Table 3 Input Random Variables

[0104] .

[0105] To reduce the computational cost of the steel frame, a Kriging surrogate model is used to establish the relationship between input variables and output response. Taking the initial time step as an example, the known sample distribution at the initial time step is shown below. Figure 15 . Figure 15 The diagram shows the known parameter distributions between pairs of variables.

[0106] By processing the aforementioned known samples using the time-varying Vine Copula method, a large number of samples meeting the correlation requirements can be obtained. The sample distribution generated based on Vine Copula is as follows: Figure 16 As shown.

[0107] Using Vine Copula samples as input samples, the output response value is predicted through the constructed Kriging surrogate model. Substituting the obtained input and output values ​​into the Sobol index calculation method proposed in this invention yields the global sensitivity calculation result of this framework structure. Figure 17 .

[0108] By extracting the three most important parameters from the first-order index and performing a two-dimensional interaction sensitivity analysis, the calculation results of the second-order Sobol index can be obtained (see [link to Sobol index]). Figure 18 .

[0109] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. 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 dynamic global sensitivity analysis method for flap mechanisms based on Vine Copula, characterized in that, Applied to aircraft flap movement mechanisms, the following steps are included: Step 1: Obtain the stress distribution, displacement deformation, and driving force parameters of each component of the flap mechanism through rigid-flexible coupling analysis, and identify high failure risk areas. Step 2: Based on the rigid-flexible coupling analysis results and engineering standards from Step 1, determine the independent failure modes and multi-level failure criteria of the flap mechanism; select input random variables according to the uncertainty of the flap mechanism's motion process, and establish a mathematical distribution model for the input random variables. Specifically, The three independent failure modes of the flap mechanism are identified as strength failure, stiffness failure, and jamming failure. The single failure criterion for each of these three failure modes is as follows: The failure criterion for insufficient strength is: ， In the formula For the maximum stress of the flap mechanism, For the allowable stress of the material, This is the strength reserve coefficient; The failure criterion for insufficient stiffness is: ， In the formula This represents the maximum deformation of the flap mechanism. This is the maximum allowable deformation; The failure criterion for the jamming phenomenon is: ， In the formula For real-time driving torque, The driving torque required for the retraction and extension operation; The construction of the multi-level failure criterion is as follows: To address the risk of compound failure, based on the uncertainty of the flap mechanism's motion process and the single failure criterion, a time-varying comprehensive failure criterion is proposed as follows: ， In the formula, This is a stress-based fatigue accumulation term. The actual number of load cycles for the i-th stress amplitude level at time t. This corresponds to the fatigue life limit of the SN curve for the material. For stress range, The stress value at time t. Let be the deformation at time t. Let be the driving force value at time t. These are the weighting coefficients for a single failure mode. The threshold values ​​are used as comprehensive criteria; for flap mechanisms, when Fatigue accumulation failure is triggered when When the instantaneous over-limit failure is triggered, The system fails when the time is right. Step 3: Perform dynamic global sensitivity analysis based on Vine Copula and spatial segmentation to calculate the importance measure of the input random variables. First, discretize the operating time into continuous non-overlapping intervals and construct a Kriging surrogate model for each failure mode. Fit the limiting state function using a finite number of sample points. Then, establish a time-varying correlation model. By considering the cross-correlation between different dimensions of the input random variables and the autocorrelation between different times of a single variable, establish a time-varying Vine Copula model and perform correlation processing on the samples to generate input random variable samples. Finally, divide the input random variable samples into n continuous non-overlapping sub-intervals and solve the Sobol index through spatial segmentation. Step 4: Rank the importance of the input random variables according to the aforementioned indicators.

2. The analytical method according to claim 1, characterized in that, In step 2, the input random variables include: aerodynamic load coefficients a1 and a2 that follow a Gaussian random process, assembly error d that follows a normal distribution, and hinge dynamic friction coefficient f that follows a normal distribution.

3. The analytical method according to claim 1, characterized in that, In step 3, the method for establishing the Kriging model is as follows: sample the input random variables determined in step 2 to obtain non-repeating input data of the flap mechanism and substitute them into the rigid-flexible coupling simulation to obtain the response values ​​of each failure mode as output data, and construct an input-output dataset. A Kriging surrogate model is established based on the dataset. The Kriging model is adaptively learned using the U learning function until it converges. The surrogate model is then used to replace the rigid-flexible coupling simulation for subsequent global sensitivity analysis.

4. The analytical method according to any one of claims 1-3, characterized in that, In step 3, the method for establishing the time-varying correlation model is as follows: a set of uniformly distributed samples is randomly sampled as the initial samples, and a Vine Copula tree is constructed. In each layer of the model tree, the optimal Copula function is selected for samples of different dimensions according to the AIC criterion, and the correlation parameters are calculated to establish the cross-correlation matrix between variables at different times. ; will conform to the matrix Corresponding samples of the correlation Transform the sample into one that follows a standard normal distribution and calculate the covariance. ,right SVD decomposition is performed to obtain matrix A, and the time-varying composite coefficient matrix containing autocorrelation and cross-correlation is solved. ; Based on the time-varying comprehensive coefficient matrix And the correlation vector obtained from the covariance matrix decomposition results. The required samples are generated through inverse transformation. In the formula It is the normal cumulative distribution function. The vector is a corresponding normal distribution. This is the inverse transform operation of the marginal cumulative probability density function.

5. The analytical method according to claim 4, characterized in that, The cross-correlation matrix between variables at time points for: ， In the formula Let i be a standard Gaussian random process with i-th dimension variable. For the standard deviation operator, For expectation operators.

6. The analytical method according to claim 5, characterized in that, Time-varying composite coefficient matrix containing autocorrelation and cross-correlation for: ， In the formula The result of covariance matrix decomposition. The standard deviation is given by the subscripts i and j, which indicate the dimension of the variable, and l = 1, 2, ..., n. , , Represent time, time, time.

7. The analytical method according to claim 1, characterized in that, In step 3, the Sobol index is solved by spatial segmentation as follows: the input sample is divided into n consecutive non-overlapping sub-intervals, and the Sobol index based on the traditional MCS method is converted into a spatial segmentation form containing the first-order Sobol index and the second-order Sobol index by calculating the probability of the sample falling into each sub-interval and the conditional variance within each sub-interval.

8. The analytical method according to claim 7, characterized in that, For the first-order Sobol index, the input random variable is divided into s continuous non-overlapping sub-intervals. And based on the definition of expectation and the integral mean value theorem, the transformed Sobol index is converted into a spatial partitioning form, i.e.: as well as In the formula for Falling into the range The probability, The variance of the sample falling into each subinterval; For the second-order Sobol index, the input random variable is divided into v continuous non-overlapping subspaces. And based on mathematical expectation and numerical integration, it is transformed into a spatial partitioning form, namely: as well as In the formula Let be the probability that a sample falls into the subspace. This represents the variance of the sample falling into each subspace.

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