Wing structure efficient distribution parameter global sensitivity analysis method and related system

Abstract

The invention belongs to the field of wing structure analysis, discloses an efficient distribution parameter global sensitivity analysis method of a wing structure and a related system, and aims to describe the influence of distribution parameters on an output statistical moment under the condition that the distribution parameters of a structure system also have uncertainty. According to the method, implicit function relationships among the distribution parameters, the mean values and the variances are established. Meanwhile, in order to measure the influence of the uncertainty of the distribution parameters on the output statistical moment of the structural system, a main sensitivity index and a total sensitivity index of the distribution parameters for the output mean value and the variance are established in view of the basic idea of the traditional sensitivity index based on the variance. According to the method, a Kriging proxy model method is applied to an inner layer, a proxy sampling probability density function is introduced, and a Kriging proxy model between an input variable and an output response is established by using fewer training sample points, so that a large amount of repeated calling of actual performance functions is reduced.

Description

Technical Field

[0001] The invention belongs to the field of wing structure analysis, and in particular relates to an efficient distributed parameter global sensitivity analysis method of a wing structure and a related system. Background Art

[0002] For aircraft wing structures in the aviation field, in order to ensure their long-term normal operation in complex working environments, it is necessary to ensure the safety and reliability of the structure. However, there are a lot of uncertainties in the structural system, and the analysis of these uncertainties is a crucial part of the structural design, analysis and optimization process. By identifying the influencing process and effect of uncertainty, the structural system can be effectively evaluated and improved. The main goal of global sensitivity analysis is to study how the uncertainty of output performance is distributed to the input uncertainty from different sources and to rank the degree of influence of these input uncertainties. This process is particularly important for guiding the analysis, prediction and optimization of structural systems. However, due to insufficient understanding of the structural system, the distribution parameters of the input variables in the structural system are often uncertain.

[0003] In order to measure the impact of the uncertainty of the distribution parameters of the input variables in the wing nine-box section structure on the statistical moment of the system output, the global sensitivity index under the distribution parameter uncertainty can measure this impact. Directly solving this index requires cyclic nested sampling of the input variables at each distribution parameter value, which has a high computational cost. Summary of the invention

[0004] The purpose of the present invention is to overcome the disadvantage of too high calculation cost when solving the above-mentioned indicators, and to provide an efficient distributed parameter global sensitivity analysis method and related system for wing structures.

[0005] In order to achieve the above object, the present invention adopts the following technical solution: In a first aspect, the present invention provides an efficient distributed parameter global sensitivity analysis method for a wing structure, comprising the following steps: Obtain the distribution parameters of the nine-box section structure of the wing; According to each distribution parameter, an initial training sample set is formed; Construct the Kriging initial proxy model based on the processed training sample set; Obtain the required distribution parameter sample points in the training sample set, and send the obtained distribution parameter sample points into the constructed Kriging initial proxy model to obtain training samples; Determine the basis function, weight function and compact support radius according to the requirements, and obtain the quadratic basis function according to the basis function, weight function and compact support radius combined with the distribution parameters; A number of test points are selected from the training samples, and weighted calculation is performed on the test points to obtain fitting values. A coefficient vector is calculated according to the fitting values, and a fitting function is established according to the coefficient vector. The fitting function is combined with the quadratic basis function to obtain a statistical moment sample. The sensitivity of the statistical moment samples is calculated, and the sensitivity index of each distribution parameter in the wing nine-box section structure is obtained.

[0006] A further improvement of the present invention is that, according to each distribution parameter, a specific method of forming an initial training sample set is as follows: Select the corresponding proxy density function according to each distribution parameter; Draw a sample pool of random variables in the proxy density function; Select the required samples from the random variable sample pool, calculate the corresponding output response values, and form an initial training sample set based on the samples and output response values.

[0007] A further improvement of the present invention is that, based on processing the training sample set, the DACE toolbox is used to construct the Kriging initial proxy model.

[0008] A further improvement of the present invention is that when constructing the Kriging initial proxy model, the Kriging initial proxy model needs to be updated, and the specific method is as follows: The updated sample points are selected in the random variable sample pool, and the model prediction value and the true response value of the updated sample points are calculated. When the relative error of the model prediction value is less than the preset threshold, the updated sample points are added to the training sample set and the Kriging initial proxy model is rebuilt; otherwise, the Kriging initial proxy model is built. A further improvement of the present invention is that the method for screening and updating sample points in the random variable sample pool is as follows:

[0009] in, To update the sample points, is the prediction variance, is the Kriging initial surrogate model, is a random variable sample pool.

[0010] A further improvement of the present invention is that the quadratic basis function is:

[0011] in, is a quadratic basis function, are different distribution parameters.

[0012] A further improvement of the present invention is that the fitting function is:

[0013] in, is the fitting function, is the dimension of the coefficient vector, is the index variable in the sum operation, is the first Quantity, is the basis function Quantity, is the distribution parameter, is the transposed matrix of the quadratic basis function, is the coefficient vector to be determined.

[0014] In a second aspect, the present invention provides an efficient distributed parameter global sensitivity analysis system for a wing structure, comprising the following steps: A parameter acquisition module is used to obtain various distribution parameters in the wing nine-box section structure; An initial sample set acquisition module is used to form an initial training sample set according to various distribution parameters; The model building module is used to build the Kriging initial proxy model based on the processed training sample set; The training sample establishment module is used to obtain the required distribution parameter sample points in the training sample set, and send the obtained distribution parameter sample points into the constructed Kriging initial proxy model to obtain the training samples; A quadratic basis function establishment module is used to determine the basis function, weight function and compact support radius according to the requirements, and obtain the quadratic basis function according to the basis function, weight function and compact support radius combined with the distribution parameters; The statistical moment sample establishment module is used to select a number of test points in the training sample, perform weighted calculation on the test points to obtain fitting values, calculate coefficient vectors according to the fitting values, establish a fitting function according to the coefficient vector, and combine the fitting function with the quadratic basis function to obtain a statistical moment sample; The sensitivity index building module is used to calculate the sensitivity of the statistical moment sample and obtain the sensitivity index of each distribution parameter in the wing nine-box section structure.

[0015] In a third aspect, the present invention provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of an efficient distributed parameter global sensitivity analysis method for a wing structure when executing the computer program.

[0016] In a fourth aspect, the present invention provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of an efficient distributed parameter global sensitivity analysis method for wing structures.

[0017] Compared with the prior art, the present invention has the following beneficial effects: In the case that the distribution parameters of the structural system also have uncertainty, in order to describe the influence of the distribution parameters on the output statistical moments, the present invention establishes an implicit functional relationship between the distribution parameters and the mean and variance. At the same time, in order to measure the influence of the distribution parameter uncertainty on the output statistical moments of the structural system, in view of the basic idea of ​​the traditional variance-based sensitivity index, the main sensitivity index and the total sensitivity index of the distribution parameters for the output mean and variance are established. The present invention uses the Kriging proxy model method in the inner layer, and introduces the proxy sampling probability density function at the same time. With fewer training sample points, the Kriging proxy model between the input variable and the output response is established, which reduces the large number of repeated calls of the actual function function. In the outer layer, the moving least squares method is used to establish a fitting function between the output statistical moment and the distribution parameter. First, the appropriate basis function is determined, and then the appropriate tight support radius is selected. After determining the influence area, it is necessary to further determine the weight function to measure the influence of the training sample points in the influence area on the value of the fitting function at the test point. Thereby fitting the relationship between the distribution parameter and the output statistical moment, and evaluating the influence of the parameter on the output statistical moment by analyzing the coefficient of the regression model.

[0018] Furthermore, the present invention applies the established MLS-K method to the nine-box segment model of the wing structure through MATLAB and ANSYS joint simulation, calculates the distribution parameter sensitivity index, and verifies the accuracy and efficiency of the method established by the present invention by comparing the results obtained with the existing AK-S-MCS method. The importance ranking of the distribution parameters of each input variable obtained by calculation provides an important basis for reducing the uncertainty of output performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flow chart of the present invention; Figure 2 is a system diagram of the present invention; Figure 3 It is a schematic diagram of the nine-box section structure of the wing; Figure 4 The sensitivity index histogram of the output statistical moment of the nine-box section of the wing; Figure 5 This is a system schematic diagram of Example 2. DETAILED DESCRIPTION

[0020] In order to further understand the content of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0021] The schematic diagram of the nine-box structure of the wing is as follows Figure 3As shown in Figure 1, the structure consists of 64 rod elements and 42 plate elements. The 64 rod elements are divided into three groups according to their directions. x, y, z Three directions. The lengths of the rod elements in each group are , and The elastic modulus of the bar element and the plate element are E , Poisson's ratio is 0.3, the skin thickness is 0.2cm, P Indicates the effect Figure 3 The external loads at the positions shown. Each input variable of the wing nine-box section structure obeys an independent normal distribution, and its distribution parameters are shown in Table 1. At the same time, it is assumed that the mean of the input variable has subjective uncertainty and obeys the normal distribution shown in Table 2.

[0022] Table 1 Distribution parameters of input variables of the nine-box wing structure

[0023] Table 2 Distribution parameters of the mean of subjective uncertainty of the nine-box section of the wing

[0024] See also Figure 1 , an efficient distributed parameter global sensitivity analysis method for wing structures, comprising the following steps: S1, obtain the distribution parameters of the wing nine-box segment structure.

[0025] S2: Form an initial training sample set based on each distribution parameter.

[0026] S3, constructing a Kriging initial proxy model based on the processed training sample set.

[0027] S4, obtaining the required distribution parameter sample points in the training sample set, and sending the obtained distribution parameter sample points to the constructed Kriging initial proxy model to obtain training samples.

[0028] S5, determining the basis function, weight function and compact support radius according to the requirements, and obtaining the quadratic basis function according to the basis function, weight function and compact support radius combined with the distribution parameters.

[0029] S6, selecting a number of test points in the training sample, performing weighted calculation on the test points to obtain fitting values, calculating coefficient vectors according to the fitting values, establishing a fitting function according to the coefficient vector, combining the fitting function with the quadratic basis function, and obtaining a statistical moment sample.

[0030] S7, calculate the sensitivity of the statistical moment sample and obtain the sensitivity index of each distribution parameter in the wing nine-box section structure.

[0031] See also Figure 2, an efficient distributed parameter global sensitivity analysis system for wing structures, including the following steps: A parameter acquisition module is used to obtain various distribution parameters in the wing nine-box section structure; An initial sample set acquisition module is used to form an initial training sample set according to various distribution parameters; The model building module is used to build the Kriging initial proxy model based on the processed training sample set; The training sample establishment module is used to obtain the required distribution parameter sample points in the training sample set, and send the obtained distribution parameter sample points into the constructed Kriging initial proxy model to obtain the training samples; A quadratic basis function establishment module is used to determine the basis function, weight function and compact support radius according to the requirements, and obtain the quadratic basis function according to the basis function, weight function and compact support radius combined with the distribution parameters; The statistical moment sample establishment module is used to select a number of test points in the training sample, perform weighted calculation on the test points to obtain fitting values, calculate coefficient vectors according to the fitting values, establish a fitting function according to the coefficient vector, and combine the fitting function with the quadratic basis function to obtain a statistical moment sample; The sensitivity index building module is used to calculate the sensitivity of the statistical moment sample and obtain the sensitivity index of each distribution parameter in the wing nine-box section structure.

[0032] Embodiment 1: The specific method of this embodiment is as follows: Step 1: Select an appropriate proxy sampling density function ; Step 2: Extract the input variable sample pool: Use the spatial uniform sampling method (this method uses normal distribution samples) to extract The size is N K A random variable sample pool ; Step 3: Generate training samples: S MC Randomly select N T Samples , and the corresponding output response value is calculated by the real function , forming the initial training sample set , let the number of iteration steps be initialized to N M =0; Step 4: Construct the Kriging initial proxy model : Use existing T MC In the information, the Kriging initial surrogate model is constructed with the help of DACE toolbox ; Step 5: Update the proxy model: In the sample pool S MC Filter and update sample points , specifically through the formula:

[0033] Calculate the model prediction value and the true response value of this point, let N M = N M +1, when the relative error of the predicted value is greater than 1%, it is added to the training set T MC In the process, return to step 4); otherwise, stop the adaptive learning process and complete The construction of Step 6: Get the training sample of distribution parameters: Generate n The distribution parameter sample points are used as known data and substituted into the constructed inner layer Kriging proxy model to calculate and obtain the output mean and variance to obtain the training samples. Step 7: Determine the basis function P T , weight function w and tight support radius S max :This method uses quadratic basis functions ,in n is the dimension of the distribution parameter; determine the appropriate tight support radius so that the influence area can ensure the local fitting accuracy and obtain better fitting effect without making the calculation too large. At the same time, a sufficient number of training sample points must fall into the influence area to avoid singular phenomena; determine the weight function to measure the influence of the training sample points in the influence area on the value of the fitting function at the test point. The weight function should meet the following two conditions: it is a non-negative function that decreases monotonically with the increase of the distance between the test point and the training sample point, and meets certain smoothness requirements, so the selected weight function is a cubic spline function; Step 8: Establish a fitting function between distribution parameters and output statistical moments: Select N points to be tested, perform weighted calculation on each point, obtain the fitting value, and find the coefficient vector to establish the fitting function: , get the sample of output statistical moment; Step 9: Substitute the obtained output statistical moment samples into the sensitivity index calculation formula to obtain the distribution parameters Four sensitivity indicators for the output mean e and variance v.

[0034] The present invention considers the structural system of input variable uncertainty, and its function can be expressed as: ,in, Y is the output response value, X yes n dimensional input vectors, which are independent of each other and can be expressed as: When there is uncertainty in the distribution parameters of the input variables of the structural system, the actual performance function can be expressed as: .in, express n Dimensional independent distribution parameter variables The subjective uncertainty of the distribution parameters can be expressed through the conditional probability density function The uncertainty of the input variable is caused, which is then transferred to the output response through the function, further causing the uncertainty of the output statistical moment. This uncertainty transfer process can be expressed as: distribution parameter → input variable → output response → output statistical moment. In the case of uncertainty in the distribution parameter, the output statistical moment of the structural system is no longer a fixed value, but has a one-to-one correspondence with the distribution parameter. In order to describe the influence of the distribution parameter on the output statistical moment, the present invention establishes an implicit functional relationship between the distribution parameter and the output mean and variance: .in, C is the output statistical moment, such as the mean e and variance v .

[0035] Therefore, according to the basic idea of ​​variance-based sensitivity indicators, the distribution parameters can be written For the output mean e and variance v The four sensitivity indicators are as follows.

[0036] Main sensitivity index: (1) (2) Overall sensitivity index: (3) (4) In the formula, Does not contain a single distribution parameter The set of distribution parameter variables, the main sensitivity index and Represents a single distribution parameter Contribution to mean and variance uncertainty, overall sensitivity index and Represents a single distribution parameter itself and the remaining distribution parameters The total contribution of the interaction between to the uncertainty in the mean and variance.

[0037] For the established distribution parameter sensitivity index, the key is to calculate the nested expectation and variance. The traditional Monte Carlo simulation method requires three layers of nested distribution parameters and input variable sampling to solve the index. The calculation cost is too high and it is difficult to be accepted by engineering practice. It is usually only used as a reference solution in theoretical analysis. Therefore, the present invention constructs a double-layer proxy model method based on Kriging proxy model and moving least squares. The Kriging proxy model is used in the inner layer to establish a Kriging proxy model between input and output to reduce the number of calls to the function function. The moving least squares method is used in the outer layer to construct the functional relationship between the distribution parameter and the output statistical moment, and the coefficient of the regression model is analyzed to evaluate the influence of the parameter on the output statistical moment.

[0038] The Kriging surrogate model is an unbiased estimation model for obtaining the minimum estimation variance. By combining local random errors with global approximations, the effectiveness of the model does not depend on the existence of random errors. It combines a parameterized linear regression model with a nonparametric random process to approximate the failure probability of the test point by weighted averaging the failure probabilities of the training points around the test point. Through the Kriging method, the mapping relationship between cognitive parameters and failure probabilities can be directly obtained, thereby simplifying the calculation of the conditional expectation of failure probability and avoiding the complex sampling process.

[0039] The Kriging surrogate model can be expressed as follows: (5) In the formula, is the unknown Kriging model, is the input variable X The basis functions of can provide a global approximate model in the design space; Represents the unknown regression coefficient, which can be calculated from the actual function value; n Indicates the number of basis functions used in the model. It is a random process created on the basis of global simulation, which can represent the local deviation of the model and obeys an expectation of 0 and a variance of σ 2 The normal distribution of .

[0040] According to Kriging theory, the point to be measured x The output value at can be expressed as follows: (6) In the formula, gis a column vector consisting of the true function values ​​of the training samples, f is the unit column vector, r ( x ) is the training sample point X T With the test point x The vector composed of the correlation functions between is expressed as follows: (7) The estimated value of and the estimated variance of and It can be expressed as: (8) (9) Related parameters The maximum value of the maximum likelihood estimate can be obtained by solving, that is, (10) By solving the formula λ A Kriging surrogate model with optimal fitting accuracy can be constructed.

[0041] Therefore, for any test point x , whose Kriging surrogate model has a mean and variance of The Gaussian distribution of can be calculated by the following formula: (11) (12) The DACE toolbox in MATLAB can be used to calculate the mean and variance of equations 11 and 12. In the process of modeling the Kriging surrogate model, the mean at the training sample is equal to the true response value of the system, and the variance is equal to 0. At other points, the predicted value of the functional function of the input variable sample is generally not 0. If the variance is large, it means that there is a large gap between the predicted value and the true value. Therefore, the predicted value at this point can be used to measure the prediction accuracy of the Kriging model at this point, thereby providing a good indicator for updating the Kriging surrogate model.

[0042] In order to simplify the two-layer nested sampling in the process of solving the output statistical moment, Li proposed a theoretical method of surrogate sampling probability density function in his article "A new algorithm for importance analysis of the inputs with distribution parameter uncertainty". This method determines the output variable under the distribution parameter uncertainty.X , using the proxy sampling probability density function Sampling the input variables, where To determine the distribution parameters, the double-layer nested sampling in the output statistical moment solution step is simplified to a single-layer calculation.

[0043] Considering the model with output mean, SS-PDF is introduced After that, the output mean can be expressed by the following formula e : (13) In the formula, R n represents the sample space of the input variable X, When the distribution parameter is fixed, the input variable X The probability density function of is the mean obtained with the aid of the proxy sampling probability density function.

[0044] Combined variance calculation formula , by introducing SS-PDF To the model of output variance, the output variance v The calculation formula is as follows: (14) According to the above formula, it can be observed that after introducing SS-PDF To calculate the output mean and variance, we can use To generate input variables X Therefore, during the calculation process, when the distribution parameters of the outer layer change, the samples of the inner layer X Can be reused.

[0045] In summary, SS-PDF The selection of is very critical, as it has an important impact on the accuracy and efficiency of the calculation. Li detailed its principles and specific selection methods in his article.

[0046] Moving least squares is a regression method for fitting data. It determines the best fitting curve by minimizing the residual sum of squares. In distribution parameter sensitivity analysis, MLS can be used to fit the relationship between input and output, and evaluate the degree of influence of input on output by analyzing the coefficients of the regression model. MLS first needs to obtain the basic information of a set of observation points, namely the training samples. The traditional least squares method treats the training samples in the same way and can be regarded as a global regression. Its disadvantage is that it is not suitable for models with a high degree of nonlinearity. For general functions, it is difficult to fit globally with a polynomial function, and when fitting piecewise, the smoothness of the fitting function is difficult to guarantee, which will bring great difficulties. The moving least squares method is a piecewise regression method that can capture the drastic changes in the local part of the model, so it can better deal with problems with a high degree of nonlinearity. MLS defines an influence domain centered on the point to be tested and uses the weighted average of the training samples in the influence domain to approximate the model value at the point to be tested.

[0047] In the field of discrete data fitting, there are many optional methods, the most common of which is the least squares method. However, the least squares method assigns the same weight to all sample points during the fitting process, resulting in the equal influence of each point on the value of the fitting function. Therefore, when dealing with complex data sets, the least squares method is difficult to accurately capture drastic changes in the data. In fact, it is unreasonable to treat all sample points equally. When fitting discrete data, more attention should be paid to the true values ​​of sample points within a certain range near the test point, while the influence of farther sample points can be ignored. This idea is the core concept of MLS. With this method, the fitting function can be adjusted more flexibly to more accurately reflect the local characteristics and changing trends of the data, thereby providing more accurate fitting results even in complex situations.

[0048] In the global sensitivity analysis of wing structures, the MCS method samples the distribution parameters in the outer layer and cyclically samples the input variables in the inner layer when calculating the main sensitivity index and the total sensitivity index. This method has a very large amount of calculation (Number of performance function evaluation, NPFE) and is difficult to apply to the sensitivity analysis of distribution parameter uncertainty of wing structures. Therefore, the present invention uses the results obtained by the existing single-layer Kriging (AK-S-MCS) method in the article "Distribution Parameter Uncertainty Sensitivity Analysis Method Based on Kriging Model and Proxy Sampling" as a comparative solution to verify the efficiency and accuracy of the double-layer proxy model method constructed by the present invention.

[0049] The AK-S-MCS method only calls the real function when establishing the Kriging proxy model from the distribution parameters to the output statistical moments, and its calculation amount is 45,000 times the input variable samples are substituted into the real function. The double-layer proxy model method based on the Kriging model and the moving least squares method constructed by the present invention also has a NPFE limited to the calculation amount when modeling the inner and outer layers, that is, N T + N M ,in N M is the number of iterations during modeling.

[0050] According to the selection principle of the proxy probability density function, in this example, SS-PDF should be in the form of normal distribution, as shown in Table 3.

[0051] Table 4 lists the sensitivity indices calculated by the AK-S-MCS method and the MLS-K method constructed by the present invention for comparison.

[0052] In order to more intuitively compare the index sizes calculated by the two double-layer proxy model methods, Figure 4 The main sensitivity index and total sensitivity index of each distribution parameter to the output mean and variance are shown in the bar graph. The influence of three important distribution parameters on the output mean is compared in the figure, and the importance is ranked as follows: Therefore, in order to enhance the robustness of the wing nine-box segment, more subjective information of these parameters needs to be collected, and at the same time, the interaction between each distribution parameter can be ignored.

[0053] In addition, the figure also compares the impact of each distribution parameter on the output variance. The results show and These are the two most important parameters. and The variability of the output response can be effectively reduced. In addition, the impact of the interaction between distribution parameters on the output variance also needs attention.

[0054] Table 3 Probability density function of proxy sampling of input variables of the nine-box section of the wing

[0055] Table 4 Calculation results of sensitivity index of wing nine-box section structure

[0056] Embodiment 2: See also Figure 5As shown, the present invention also provides an electronic device 100 for an efficient distributed parameter global sensitivity analysis method for a wing structure; the electronic device 100 includes a memory 101, at least one processor 102, a computer program 103 stored in the memory 101 and executable on the at least one processor 102, and at least one communication bus 104.

[0057] The memory 101 can be used to store the computer program 103, and the processor 102 implements the steps of the efficient distributed parameter global sensitivity analysis method of the wing structure described in Example 1 by running or executing the computer program stored in the memory 101 and calling the data stored in the memory 101. The memory 101 can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, an application required for at least one function (such as a sound playback function, an image playback function, etc.), etc.; the data storage area can store data (such as audio data) created according to the use of the electronic device 100, etc. In addition, the memory 101 can include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other non-volatile solid-state storage devices.

[0058] The at least one processor 102 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor 102 may be a microprocessor or any conventional processor, etc. The processor 102 is the control center of the electronic device 100, and uses various interfaces and lines to connect various parts of the entire electronic device 100.

[0059] The memory 101 in the electronic device 100 stores a plurality of instructions to implement an efficient distributed parameter global sensitivity analysis method for a wing structure, and the processor 102 can execute the plurality of instructions to implement: Obtain the distribution parameters of the nine-box section structure of the wing; According to each distribution parameter, an initial training sample set is formed; Construct the Kriging initial proxy model based on the processed training sample set; Obtain the required distribution parameter sample points in the training sample set, and send the obtained distribution parameter sample points into the constructed Kriging initial proxy model to obtain training samples; Determine the basis function, weight function and compact support radius according to the requirements, and obtain the quadratic basis function according to the basis function, weight function and compact support radius combined with the distribution parameters; A number of test points are selected from the training samples, and weighted calculation is performed on the test points to obtain fitting values. A coefficient vector is calculated according to the fitting values, and a fitting function is established according to the coefficient vector. The fitting function is combined with the quadratic basis function to obtain a statistical moment sample. The sensitivity of the statistical moment samples is calculated, and the sensitivity index of each distribution parameter in the wing nine-box section structure is obtained.

[0060] Embodiment 3: If the module / unit integrated in the electronic device 100 is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device that can carry the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory and read-only memory (ROM, Read-Only Memory).

[0061] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0062] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0063] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0064] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. An efficient distributed parameter global sensitivity analysis method for wing structures, characterized in that: The following steps are involved: Obtain the distribution parameters of the nine-box section structure of the wing; According to each distribution parameter, an initial training sample set is formed; Construct the Kriging initial proxy model based on the processed training sample set; Obtain the required distribution parameter sample points in the training sample set, and send the obtained distribution parameter sample points into the constructed Kriging initial proxy model to obtain training samples; Determine the basis function, weight function and compact support radius according to the requirements, and obtain the quadratic basis function according to the basis function, weight function and compact support radius combined with the distribution parameters; A number of test points are selected from the training samples, and weighted calculation is performed on the test points to obtain fitting values. A coefficient vector is calculated according to the fitting values, and a fitting function is established according to the coefficient vector. The fitting function is combined with the quadratic basis function to obtain a statistical moment sample. The sensitivity of the statistical moment samples is calculated, and the sensitivity index of each distribution parameter in the wing nine-box section structure is obtained.

2. The efficient distributed parameter global sensitivity analysis method for wing structure according to claim 1, characterized in that: According to each distribution parameter, the specific method of forming the initial training sample set is as follows: Select the corresponding proxy density function according to each distribution parameter; Draw a sample pool of random variables in the proxy density function; Select the required samples from the random variable sample pool, calculate the corresponding output response values, and form an initial training sample set based on the samples and output response values.

3. The efficient distributed parameter global sensitivity analysis method for wing structure according to claim 1, characterized in that: According to the processing training sample set, the DACE toolbox is used to build the Kriging initial surrogate model.

4. The efficient distributed parameter global sensitivity analysis method for wing structure according to claim 1, characterized in that: When constructing the Kriging initial proxy model, the Kriging initial proxy model needs to be updated. The specific method is as follows: The updated sample points are selected in the random variable sample pool, and the model prediction value and the true response value of the updated sample points are calculated. When the relative error of the model prediction value is less than the preset threshold, the updated sample points are added to the training sample set and the Kriging initial proxy model is rebuilt. Otherwise, the construction of the Kriging initial surrogate model is completed.

5. The efficient distributed parameter global sensitivity analysis method for wing structure according to claim 4, characterized in that: The method for screening and updating sample points in the random variable sample pool is as follows: in, To update the sample points, is the prediction variance, is the Kriging initial surrogate model, is a random variable sample pool.

6. The efficient distributed parameter global sensitivity analysis method for wing structure according to claim 1, characterized in that: The quadratic basis functions are: in, is a quadratic basis function, are different distribution parameters.

7. The efficient distributed parameter global sensitivity analysis method for wing structure according to claim 1, characterized in that: The fitting function is: in, is the fitting function, is the dimension of the coefficient vector, is the index variable in the sum operation, is the first Quantity, is the basis function Quantity, is the distribution parameter, is the transposed matrix of the quadratic basis function, is the coefficient vector to be determined.

8. An efficient distributed parameter global sensitivity analysis system for wing structures, characterized by: The following steps are involved: A parameter acquisition module is used to obtain various distribution parameters in the wing nine-box section structure; An initial sample set acquisition module is used to form an initial training sample set according to various distribution parameters; The model building module is used to build the Kriging initial proxy model based on the processed training sample set; The training sample establishment module is used to obtain the required distribution parameter sample points in the training sample set, and send the obtained distribution parameter sample points into the constructed Kriging initial proxy model to obtain the training samples; A quadratic basis function establishment module is used to determine the basis function, weight function and compact support radius according to the requirements, and obtain the quadratic basis function according to the basis function, weight function and compact support radius combined with the distribution parameters; The statistical moment sample establishment module is used to select a number of test points in the training sample, perform weighted calculation on the test points to obtain fitting values, calculate coefficient vectors according to the fitting values, establish a fitting function according to the coefficient vector, and combine the fitting function with the quadratic basis function to obtain a statistical moment sample; The sensitivity index building module is used to calculate the sensitivity of the statistical moment sample and obtain the sensitivity index of each distribution parameter in the wing nine-box section structure.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the efficient distributed parameter global sensitivity analysis method for the wing structure according to any one of claims 1 to 7 are implemented.

10. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the efficient distributed parameter global sensitivity analysis method for a wing structure according to any one of claims 1 to 7 are implemented.

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