Global sensitivity analysis method for radome structures

Abstract

This disclosure relates to the field of reliability technology, specifically to a method for global sensitivity analysis of a radome structure. The method includes: obtaining important sampled samples of the input variables of the radome structure and a sample pool of the distribution parameters of the input variables; obtaining a training set for a Kriging failure model of the radome structure based on the important sampled samples, and training the Kriging failure model using the training set; when it is determined that each sample in the sample pool meets preset conditions, substituting the samples of the distribution parameters into the Kriging failure model to obtain the global sensitivity analysis result of the radome structure. This disclosure can improve the performance and reliability of radome structures.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the field of reliability, and in particular, to a method for analyzing global sensitivity of radome structure. BACKGROUND

[0002] With the development of aviation technology in China, it has become an urgent task to research and manufacture high-precision and high-gain antennas suitable for aircraft. In order to protect the antenna system of the aircraft from the external environment, the reliability research on the electrical performance design and structural design of the radome of the aircraft is particularly important. In order to meet the requirements of weight reduction and electromagnetic wave transmission, fiber-reinforced composite materials are widely used in the radome structure of the aircraft. This material has designability, and by changing the type, content, and stacking direction and order of the material, the optimal design of the radome structure of the aircraft can be achieved. Therefore, it is necessary to study the influence of parameters such as material type, content, and stacking order on the structure of the radome of the aircraft, that is, to analyze the reliability sensitivity of the radome of the aircraft.

[0003] The existing method for analyzing the reliability sensitivity of the radome structure of the aircraft studies the global sensitivity of the radome structure of the aircraft under the objective uncertainty of the input variable. The global sensitivity can measure the degree of contribution of the uncertainty of the input variable to the statistical characteristics of the output performance (such as failure probability) of interest in engineering design from the entire distribution range of the input variable. However, the use of the existing technology will lead to a decrease in the structural performance and reliability of the radome of the aircraft, and thus when the flight strategy is formulated according to the optimization design result, flight decision errors will occur, and even disastrous consequences will occur during the flight process.

[0004] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present disclosure, and thus can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The purpose of the present disclosure is to provide a method for analyzing the global sensitivity of the radome structure, and to at least partially overcome one or more problems caused by the limitations and defects of the related art.

[0006] Other characteristics and advantages of the present disclosure will become apparent from the following detailed description, or will be learned by practice of the present disclosure.

[0007] The present disclosure provides a method for analyzing the global sensitivity of the radome structure, comprising:

[0008] obtaining an important sampling sample of an input variable of a radome structure and a sample pool of distribution parameters of the input variable;

[0009] According to the important sampling sample, a training set of a Kriging failure model of the radome structure is obtained, and the Kriging failure model is trained by using the training set.

[0010] When it is determined that each sample in the sample pool satisfies a preset condition, the sample of the distribution parameter is substituted into the Kriging failure model, and a global sensitivity analysis result of the radome structure is obtained.

[0011] In an example embodiment of the present application, the important sampling sample of the input variable of the radome structure comprises:

[0012] An importance sampling probability density function of the input variable is obtained.

[0013] A sampling center of the importance sampling probability density function is set as a design point of the radome structure, and an importance probability density sampling function of the input variable is obtained.

[0014] According to the importance probability density sampling function, the important sampling sample of the input variable is extracted.

[0015] In an example embodiment of the present application, the importance probability density sampling function of the input variable comprises:

[0016] When the input variable is subject to a normal distribution, a variation interval of the input variable is determined according to a mean value and a standard deviation of the input variable.

[0017] A lower limit and an upper limit of the distribution of the input variable are determined according to the variation interval.

[0018] The importance probability density sampling function of the input variable is determined according to the lower limit and the upper limit of the distribution of the input variable.

[0019] In an example embodiment of the present application, the training set of the Kriging failure model of the radome structure according to the important sampling sample comprises:

[0020] The important sampling sample is substituted into a failure function of the radome structure, and an output response value of the important sampling sample is calculated.

[0021] A failure domain indicator function of the important sampling sample is determined according to the output response value.

[0022] A sample set is obtained from the sample pool.

[0023] Failure probabilities corresponding to each sample in the sample set are calculated according to the failure domain indicator function.

[0024] The failure probability corresponding to each sample and the sample set are taken as the training set.

[0025] In an example embodiment of the present application, the determining that each sample in the sample pool satisfies the preset condition comprises:

[0026] Each sample in the sample pool is substituted into the U-learning function, and a value of the U-learning function corresponding to each sample is calculated.

[0027] A minimum value is determined from the values of the U-learning function corresponding to each sample point, and it is determined that the preset condition is satisfied when the minimum value is greater than or equal to a first preset threshold.

[0028] In an example embodiment of the present application, the method further comprises:

[0029] If the minimum value is less than the first preset threshold, a target sample is determined from the sample pool according to the minimum value.

[0030] A target failure probability corresponding to the target sample is calculated according to the failure domain indicator function.

[0031] The target sample and the target failure probability are added to the training set, and the training set is updated.

[0032] The Kriging failure model is trained using the updated training set, and an updated Kriging failure model is obtained.

[0033] In an example embodiment of the present application, before the global sensitivity analysis result of the radome structure is obtained, the method further comprises:

[0034] Each sample in the sample pool is substituted into the Kriging failure model, and a failure probability value corresponding to each sample is obtained.

[0035] A total variance value of the failure probability of the radome structure is calculated according to the failure probability values corresponding to each sample.

[0036] In an example embodiment of the present application, the substituting the sample of the distribution parameter into the Kriging failure model to obtain the global sensitivity analysis result of the radome structure comprises:

[0037] The sample of the target distribution parameter is substituted into the Kriging failure model to obtain a first failure probability variance value of the target distribution parameter, the target distribution parameter being any one distribution parameter.

[0038] The main sensitivity index is determined according to the first expected failure probability variance value and the total variance value of the failure probability.

[0039] In an example embodiment of the present application, the step of inputting the sample of the target distribution parameter into the Kriging failure model to obtain the expected failure probability variance value of the target distribution parameter comprises:

[0040] The step of inputting each sample of the target distribution parameter and each sample of each of the other distribution parameters into the Kriging failure model to obtain a first failure probability value corresponding to each sample of the target distribution parameter for each sample of each of the other distribution parameters comprises:

[0041] The step of determining a first failure probability expectation value of each of the other distribution parameters corresponding to the target distribution parameter according to the first failure probability value comprises:

[0042] The step of determining the first failure probability variance value according to the first failure probability expectation value comprises:

[0043] In an example embodiment of the present application, the step of inputting the sample of the distribution parameter into the Kriging failure model to obtain the global sensitivity analysis result of the radome structure comprises:

[0044] The step of inputting the sample of the other distribution parameter into the Kriging failure model to obtain a second failure probability variance value of the other distribution parameter, wherein the other distribution parameter is a distribution parameter other than the target distribution parameter in the distribution parameter comprises:

[0045] The step of determining a total sensitivity index according to the second failure probability variance value and the total failure probability variance value comprises:

[0046] In an example embodiment of the present application, the step of inputting the sample of the target distribution parameter into the Kriging failure model to obtain the second failure probability variance value of the other distribution parameter comprises:

[0047] The step of inputting each sample of each of the other distribution parameters and each sample of the target distribution parameter into the Kriging failure model to obtain a second failure probability value corresponding to each sample of the target distribution parameter for each sample of each of the other distribution parameters comprises:

[0048] The step of determining a second failure probability expectation value of the target distribution parameter corresponding to each of the other distribution parameters according to the second failure probability value comprises:

[0049] The step of determining the second failure probability variance value of the other distribution parameter according to the second failure probability expectation value comprises:

[0050] The technical scheme provided by the embodiments of the present application can have the following beneficial effects:

[0051] In summary, the method provided by the present disclosure, by obtaining the important sampling samples of the input variables of the radome structure and the sample pool of the distribution parameters of the input variables; obtaining the training set of the Kriging failure model of the radome structure according to the important sampling samples, and training the Kriging failure model by using the training set; when determining that each sample in the sample pool meets the preset condition, substituting the sample of the distribution parameter into the Kriging failure model to obtain the global sensitivity analysis result of the radome structure, and when using the global sensitivity analysis result obtained according to the distribution parameter to optimize the reliability of the radome structure, the structural performance and reliability of the radome structure can be improved, and when the flight strategy is formulated according to the optimization design result, the problem of flight decision error can be avoided, and the safety of the aircraft in the flight process is improved.

[0052] It should be understood that the foregoing general description and the following detailed description are only exemplary and explanatory and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0053] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and serve to explain the principles of the present disclosure. It is readily apparent to one of ordinary skill in the art that the accompanying drawings are merely exemplary of embodiments of the present disclosure and that other drawings of other embodiments of the present disclosure can be derived from the drawings without departing from the spirit of the present disclosure.

[0054] Figure 1 A flowchart of a global sensitivity analysis method of a radome structure in an exemplary embodiment of the present disclosure is schematically shown;

[0055] Figure 2 A schematic diagram of a finite element analysis model of a radome structure in an exemplary embodiment of the present disclosure is schematically shown;

[0056] Figure 3 A schematic diagram of a global sensitivity bar contrast chart of a radome structure in an exemplary embodiment of the present disclosure is schematically shown Figure 1 ;

[0057] Figure 4 A schematic diagram of a global sensitivity bar contrast chart of a radome structure in an exemplary embodiment of the present disclosure is schematically shown Figure 2 ;

[0058] Figure 5 A schematic diagram of a failure probability convergence curve of a radome structure in an exemplary embodiment of the present disclosure is schematically shown.

[0059] In the drawings, identical or corresponding reference signs indicate identical or corresponding parts. DETAILED DESCRIPTION

[0060] The principles and spirits of the present application will be described below with reference to several exemplary embodiments. It should be understood that the embodiments are given only so that those skilled in the art can better understand and implement the present application, and do not limit the scope of the present application in any way. On the contrary, the embodiments are provided so that the disclosure is more thorough and complete, and the scope of the disclosure is fully conveyed to those skilled in the art.

[0061] Those skilled in the art understand that the embodiments of the present application can be implemented as a system, device, apparatus, method or computer program product. Therefore, the present disclosure can be embodied in the form of a complete hardware, complete software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.

[0062] The existing antenna cover structure reliability sensitivity analysis method studies the global sensitivity of the antenna cover structure of the aircraft under the condition of objective uncertainty of the input variable. However, in engineering practice, the distribution parameters of the input variable are generally obtained through experimental data and experience. However, due to the incompleteness of information and subjectivity of understanding, the distribution parameters of the input variable usually have subjective uncertainty, and the subjective uncertainty of the distribution parameters will have a certain impact on the performance and reliability of the aircraft. Therefore, when the existing technology is used to determine the local sensitivity and global sensitivity for the optimization design of the antenna cover structure of the aircraft, the performance and reliability of the antenna cover structure of the aircraft will be reduced, and then when the flight strategy is formulated according to the optimization design result, flight decision errors will occur, and even disastrous consequences will occur in the flight process.

[0063] In view of the above defects in the prior art, the present example embodiment first provides an antenna cover structure global sensitivity analysis method, which can obtain the global sensitivity analysis result of the antenna cover structure according to the distribution parameters, and when the global sensitivity analysis result obtained according to the distribution parameters is used for reliability optimization of the antenna cover structure, the performance and reliability of the antenna cover structure can be improved, and then when the flight strategy is formulated according to the optimization design result, the problem of flight decision errors is avoided, and the safety of the aircraft in the flight process is improved.

[0064] In order to describe the antenna cover structure global sensitivity analysis method in the example embodiment, first, how to establish the Kriging failure model of the antenna cover structure will be described.

[0065] In an exemplary embodiment of the present application, if the input variable objective uncertainty and the distribution parameter subjective uncertainty exist in the antenna cover structure at the same time, the failure function can be expressed as:

[0066] (1);

[0067] where, is the output response, are independent input variables, subjective variables is a dimensional distribution parameter and independent of each other.

[0068] The subjective uncertainty of the distribution parameter can be described by the subjective probability density function , which will decrease or even disappear with the accumulation of information about the input variables. The subjective uncertainty of the distribution parameter can be described by the conditional probability density function , which affects the uncertainty of the random input variable , and then passes through the function function of the radome structure to the output response, resulting in the uncertainty of the output failure probability, that is, “distribution parameter → input variable → output response → failure probability”. Therefore, the idea of studying the contribution of the subjective uncertainty of the distribution parameter to the failure probability of the output failure function is:

[0069] (2);

[0070] As can be seen from equation (2), is a function of , but it is difficult to directly give a certain expression of the corresponding relationship between and In order to reduce the computational cost of solving global sensitivity by numerical simulation method, the implicit function relationship between them can be established:

[0071] (3);

[0072] Based on the definition of sensitivity Sobol index, the main sensitivity index and the global sensitivity index of the subjective uncertainty distribution parameter to the failure probability of the radome structure can be defined:

[0073] (4);

[0074] (5);

[0075] where, is the set of other distribution parameters in the distribution parameter population except for the single distribution parameter . represents a single distribution parameter Failure probability Contribution of uncertainty. Characterize the distribution parameters Its own effect and the interaction with the remaining other distribution parameters The overall impact of the failure probability Uncertainty.

[0076] It can be seen that the difficulty of calculating the global sensitivity lies in the solution of the molecules of formula (4) and formula (5), which requires fixing the distribution parameters at different implementation values for cyclic sampling calculation, which requires a large amount of operation. An efficient method is to use Kriging surrogate model for calculation. As a kind of unbiased estimation model with minimum variance, Kriging model has the characteristics of global approximation combined with local random error, and through a small number of sample tests, a semi-parametric prediction model can be determined to approximate the relationship between failure probability And distribution parameters Avoid repeated calls to the real model.

[0077] Kriging surrogate model is essentially an improved linear regression analysis technique, which is composed of a parametric linear regression model and a non-parametric random process, that is:

[0078] (6);

[0079] Where, Is the unknown Kriging failure model, Is the basis function of the distribution parameters , which can provide a global approximation model in the design space; its value is shown in Table 1; Is the regression function to be determined coefficient, its value can be estimated by the known response value; Is a random process that can provide an approximation of simulating local deviation, and it obeys normal distribution , whose covariance matrix components can be expressed as:

[0080] (7);

[0081] Where, Is the standard deviation to be determined, Is the number of samples in the training set, Is the component of the correlation matrix , which represents the correlation function of any two sample points in space, which determines the simulation accuracy. There are many forms of correlation function to choose from, among which the calculation effect of Gaussian correlation function is the best, and its expression is:

[0082] (8);

[0083] in, It is an unknown correlation parameter.

[0084] According to Kriging theory, the unknown parameters in the model and The estimated value can be expressed as:

[0085] (9);

[0086] (10);

[0087] in, A column vector consisting of the response values ​​of the training sample data. For the reason The regression model consists of 10 sample points. 1-th order matrix , for The transpose matrix. The regression model is shown in Table 1:

[0088]

[0089] Table 1

[0090] Relevant parameters It can be obtained through maximum likelihood estimation, i.e.

[0091] (11);

[0092] The result obtained by solving formula (11) Substituting the values ​​into formula (8), and then substituting formula (9) into formula (10), the calculated result and formula (8) into formula (7) are used to obtain the Kriging failure model of the radome structure based on formula (7) and formula (6). This Kriging failure model is the surrogate model with the best fitting accuracy. The Kriging failure model is shown below:

[0093] (12);

[0094] in, This is the correlation function vector between the training samples and the predicted failure probability.

[0095] Therefore, for any unknown distribution parameter The distribution parameter can be accurately predicted using formula (12). failure probability of output response Failure probability obey The normal distribution, where the mean is and variance The calculation formula is:

[0096] (13);

[0097] (14).

[0098] Further, after obtaining the Kriging failure model of the radome structure, a global sensitivity analysis method of the radome structure provided by the present example embodiment is described. In an example embodiment of the present application, referring to the description shown in Figure 1 , the global sensitivity analysis method of the radome structure described above can include the following steps:

[0099] S1, obtaining an important sampling sample of an input variable of a radome structure and a sample pool of distribution parameters of the input variable;

[0100] S2, obtaining a training set of a Kriging Kriging failure model of the radome structure according to the important sampling sample, and training the Kriging failure model using the training set;

[0101] S3, when it is determined that each sample in the sample pool meets a preset condition, substituting the sample of the distribution parameter into the Kriging failure model to obtain a global sensitivity analysis result of the radome structure.

[0102] The global sensitivity analysis method of the radome structure provided by the present application, by obtaining an important sampling sample of an input variable of a radome structure and a sample pool of distribution parameters of the input variable; obtaining a training set of a Kriging Kriging failure model of the radome structure according to the important sampling sample, and training the Kriging failure model using the training set; when it is determined that each sample in the sample pool meets a preset condition, substituting the sample of the distribution parameter into the Kriging failure model to obtain a global sensitivity analysis result of the radome structure, and then using the global sensitivity analysis result obtained according to the distribution parameter to optimize the reliability of the radome structure, the structure performance and reliability of the radome structure can be improved, and then when the flight strategy is formulated according to the optimization design result, the problem of flight decision error is avoided, and the safety during flight is improved.

[0103] In the following, the steps in the global sensitivity analysis method of the radome structure in the present example embodiment will be described in more detail in conjunction with the drawings and examples.

[0104] In S1, an important sampling sample of an input variable of a radome structure and a sample pool of distribution parameters of the input variable are obtained.

[0105] In an example embodiment of the present disclosure, the obtaining the importance sampling samples of the input variables of the radome structure comprises:

[0106] S11, obtaining a proxy sampling probability density function of the input variables;

[0107] S12, setting a sampling center of the proxy sampling probability density function as a design point of the radome structure, to obtain a proxy importance probability density sampling function of the input variables;

[0108] S13, extracting importance sampling samples of the input variables according to the proxy importance probability density sampling function.

[0109] In an example embodiment of the present disclosure, the radome structure is a composite laminated plate structure, and a finite element model of the radome structure is as shown in Figure 2 The radome structure is under the action of external aerodynamic load and is fixed on the fuselage through three joints.

[0110] In an example embodiment of the present disclosure, 17 uncertain input variables of the radome structure are determined based on the Tsai-Wu criterion, and the 17 uncertain input variables are subject to normal distribution. The distribution parameters of the input variables are as shown in Table 2. The distribution parameters of the input variables, such as the mean value, have subjective uncertainty and are interval data.

[0111]

[0112] Table 2

[0113] Based on the above, in an example embodiment of the present disclosure, the obtaining the proxy sampling probability density function of the input variables comprises:

[0114] S111, when the input variables are subject to normal distribution, determining a variation interval of the input variables according to the mean value and the standard deviation of the input variables;

[0115] S112, determining a lower limit and an upper limit of the distribution of the input variables according to the variation interval;

[0116] S113, determining the proxy sampling probability density function of the input variables according to the lower limit and the upper limit of the distribution of the input variables.

[0117] For example, if the input variables are subject to normal distribution, wherein , , according to the Tsai-Wu criterion, it can be considered that , , , , The change interval of the input variable and is respectively The lower limit of the corresponding distribution is , and the upper limit of the distribution is The proxy sampling probability density function can be The criterion can be determined as Since the input variable is subject to a normal distribution, the proxy sampling probability density function can also select the same distribution type, and the distribution parameters and can be obtained by solving the following formula:

[0118] (15).

[0119] Solving formula (15) can obtain the proxy sampling probability density function of the input variable .

[0120] In an exemplary embodiment of the present disclosure, the design point of the radome structure finite element analysis model can be obtained by a second moment matrix method or other methods, and then the sampling center of the proxy sampling probability density function is set to the design point and the variance is kept consistent, to obtain the proxy important probability density sampling function of the input variable, and important sampling samples of the input variable are extracted according to the proxy important probability density sampling function.

[0121] In step S2, a training set of a Kriging failure model of the radome structure is obtained according to the important sampling samples, and the Kriging failure model is trained by using the training set.

[0122] Based on the above, in an exemplary embodiment of the present disclosure, the above obtaining a training set of a Kriging failure model of the radome structure according to the important sampling samples comprises:

[0123] S21, substituting the important sampling samples into the failure function of the radome structure to calculate the output response value of the important sampling samples;

[0124] S22, determining the failure domain indicator function of the important sampling samples according to the output response value;

[0125] S23, obtaining a sample set from the sample pool;

[0126] S24, calculating the failure probability corresponding to each sample in the sample set according to the failure domain indicator function;

[0127] S25, taking the failure probability corresponding to each sample and the sample set as the training set.

[0128] Specifically, according to the agent sampling probability density function extracting an important sampling sample , substitute into the failure function of formula (1), get an important sampling sample corresponding to the output response value , determine whether the output response value falls into the failure domain , and further determine the failure domain indication function of the important sampling sample according to the failure domain . Wherein, is the failure domain indication function, and satisfies .

[0129] In an exemplary embodiment of the present disclosure, according to the marginal probability density distribution function of the distribution parameter a plurality of distribution parameter samples are generated by spatial uniform sampling (such as Sobol sequence) to form a sample pool ; a plurality of distribution parameter samples are randomly extracted from the sample pool as a sample set; the failure probability corresponding to each sample is calculated according to formula (16) based on the value of at each sample in the sample set , and the failure probability corresponding to each sample and the sample set are taken as the training set, and the training set is .The calculation formula of the failure probability is as follows: .

[0130] (16);

[0131] Wherein, represents the failure probability, represents the probability density function, represents the mathematical expectation of the agent important sampling density function .

[0132] Further, after obtaining the training set , the Kriging failure model is trained using the training set.

[0133] Based on the above, in an exemplary embodiment of the present disclosure, the determination that each sample in the sample pool satisfies the preset condition comprises: ​

[0134] S311. Substitute each sample in the sample pool into the U learning function and calculate the value of the U learning function corresponding to each sample;

[0135] S312. If the minimum value is greater than or equal to the first preset threshold, it is determined that the preset condition is met.

[0136] Specifically, the Kriging model is used to calculate the sample pool. The minimum value is determined from the values ​​of the U function corresponding to each sample point. .

[0137] in, (17).

[0138] In one exemplary embodiment of this disclosure, if If the value is greater than or equal to a preset threshold, then the preset condition is determined to be met. In an exemplary embodiment of this disclosure, the preset threshold can be 2, 3, or other values, and no specific limitation is made here.

[0139] Based on the above, in one exemplary embodiment of this disclosure, the method further includes:

[0140] S313. If the minimum value is less than the first preset threshold, then the target sample is determined from the sample pool based on the minimum value;

[0141] S314. Calculate the target failure probability corresponding to the target sample based on the failure domain indication function;

[0142] S315. Add the target sample and the target failure probability to the training set, and update the training set;

[0143] S316. Train the Kriging failure model using the updated training set to obtain the updated Kriging failure model.

[0144] In one exemplary embodiment of this disclosure, if If the sample is less than the preset threshold, the target sample is determined according to formula (18):

[0145] (18);

[0146] Among them, samples For the target sample. Further, in the target sample... to The values ​​are accumulated, and the target failure probability corresponding to the target sample is calculated according to formula (16). and will Add to training set In some embodiments, the training set is updated and the updated training set is used to train the Kriging failure model. The Kriging failure model is trained to obtain an updated Kriging failure model.

[0147] Based on the above, in an example embodiment of the present disclosure, before the global sensitivity analysis result of the radome structure is obtained, the method further comprises:

[0148] S41, each sample in the sample pool is substituted into the Kriging failure model to obtain a failure probability value corresponding to each sample;

[0149] S42, the total variance value of the failure probability of the radome structure is calculated according to the failure probability value corresponding to each sample.

[0150] Specifically, a sample of a distribution parameter is randomly selected from a sample pool , substituted into the Kriging failure model to obtain a failure probability value corresponding to each sample , and the total variance of the failure probability value is calculated , that is, the total variance value of the failure probability of the radome structure.

[0151] Based on the above, in an example embodiment of the present disclosure, the global sensitivity analysis result of the radome structure is obtained by substituting the sample of the distribution parameter into the Kriging failure model, which comprises:

[0152] S321, the sample of the target distribution parameter is substituted into the Kriging failure model to obtain a first failure probability variance value of the target distribution parameter, and the target distribution parameter is any one distribution parameter;

[0153] S322, the main sensitivity index is determined according to the first expected failure probability variance value and the total variance value of the failure probability.

[0154] In an example embodiment of the present disclosure, each sample of the target distribution parameter and each sample of each of the other distribution parameters are input into the Kriging failure model to obtain a first failure probability value corresponding to each sample of the target distribution parameter for each sample of each of the other distribution parameters; a first failure probability expected value of each of the other distribution parameters corresponding to the target distribution parameter is determined according to the first failure probability value; and the first failure probability variance value is determined according to the first failure probability expected value.

[0155] ​​​​Specifically, the distribution parameters Set as target distribution parameter samples Then, combine the samples with other distribution parameters. ,Will Substituting into the Kriging failure model, we get and When fixed, the target distribution parameters The corresponding first failure probability value , recorded as traversed , can be obtained Fixed target distribution parameters of The first failure probability value corresponding to each sample , recorded as and according to The first failure probability value of each sample calculate When fixed, The expected first failure probability of each sample traversed The target distribution parameters can be obtained. Expected value of the first expected failure probability for each sample Then calculate the expected value of the first expected failure probability. variance This is the variance of the first failure probability.

[0156] Furthermore, obtain the variance of the first failure probability. and total variance Then, by substituting into formula (4), the target distribution parameters can be calculated. Main sensitivity index .

[0157] Based on the above, in an exemplary embodiment of this disclosure, substituting the samples of the distribution parameters into the Kriging failure model to obtain the global sensitivity analysis results of the radome structure includes:

[0158] S331. Substitute the samples of the other distribution parameters into the Kriging failure model to obtain the second failure probability variance value of the other distribution parameters, wherein the other distribution parameters are the distribution parameters other than the target distribution parameter among the distribution parameters;

[0159] S331. Determine the total sensitivity index based on the second failure probability variance value and the total failure probability variance value.

[0160] In an exemplary embodiment of this disclosure, each sample of each of the other distribution parameters and each sample of the target distribution parameter are respectively input into the Kriging failure model to obtain the second failure probability value of each sample of the target distribution parameter corresponding to each sample of the other target distribution parameters; the second failure probability expectation value of each of the other distribution parameters corresponding to the target distribution parameter is determined based on the second failure probability value; and the second failure probability variance value of the other distribution parameters is determined based on the second failure probability expectation value.

[0161] Specifically, the distribution parameters Set to other distribution parameters samples Then, combined with the sample of the target distribution parameters ,Will Substituting into the established Kriging model, we can obtain and When fixed, other distribution parameters The corresponding second failure probability value , recorded as traversed , can be obtained When fixed, other distribution parameters of The second failure probability value corresponding to each sample , recorded as and according to The second failure probability value of each sample calculate When fixed The expected value of the second expected failure probability of each sample traversed Then other distribution parameters can be obtained. Expected value of the second expected failure probability for each sample Then calculate the expected value of the second expected failure probability. variance This is the variance of the second failure probability.

[0162] Furthermore, obtain the variance of the second failure probability. and total variance Then, by substituting into formula (5), the target distribution parameters can be calculated. Total sensitivity index .

[0163] In one exemplary embodiment of this disclosure, the results of the analysis of the global sensitivity of an aircraft radome structure employing a conformal material laminate using quasi-Monte Carlo (QMC), the Kriging model and the surrogate sampling method (AK-SS), and the method of this disclosure are as follows: Figure 3 and Figure 4 As shown.

[0164] From 3 and Figure 4 It can be clearly seen from the data that the distributed parameters for this radome structure are... Most importantly, followed by distribution parameters Finally, the distribution parameters , , and The influence of other distribution parameters is negligible. Therefore, in the optimized design of radome structures, attention should be paid to accumulating data on the subjective uncertainty distribution parameters of important input variables, especially the mean value of the thickness of a single layer of material. The mean of the modulus in the 11th direction of the material This minimizes the probability of radome structure failure, and the interaction between distributed parameters and remaining distributed parameters cannot be completely ignored when adjusting them. Furthermore, less important distributed parameters, such as the mean material density, can be reduced in dimensionality during the design process to alleviate computational burden. Etc. can be fixed at the nominal value during calculation.

[0165] The global sensitivity results of global sensitivity analysis calculations for radome structures of aircraft using conformal material laminates, performed using the quasi-Monte Carlo (QMC) method, the Kriging model and the surrogate sampling method (AK-SS), and the method provided in this disclosure, are shown in Table 3.

[0166]

[0167] Table 3

[0168] Table 3 details the global sensitivity index and failure probability values ​​obtained from the calculation of six important distributed parameters of the radome structure using three methods. The values ​​in parentheses in the table are the coefficients of variation obtained after 30 iterations of the calculation. This represents the number of samples for the input variables, and NPFE represents the total number of model calls. The comparison results show that the global sensitivity and importance ranking results calculated by the three methods are basically consistent, verifying the accuracy of the method provided in this disclosure. Furthermore, when the failure probability is very small, given the dimension of the distribution parameters... and the number of sample points of the to-be-tested distribution parameter The QMC method extracts the distribution parameter sample in the outer layer, and a large number of input variable samples are needed in the inner layer to ensure the convergence of the result, and the calculation time is long. The AK-SS method always uses the same set of input variable sample values in the process of establishing the Kriging model, so that the calculation model is independent of the true distribution parameter, improves the sample utilization rate and reduces the number of model calls. For the method provided in the present disclosure, the number of iterations of the design point optimization is The number of input variable samples is only 11% of the number of samples of the AK-SS method, and accurate sensitivity index results are further provided with fewer sample amounts, and the method has better robustness compared with the QMC algorithm.

[0169] Further, the convergence of the sensitivity index of the radome structure solved by different methods is as shown in Figure 5 It can be seen from Figure 5 that the failure probability changes with the sample amount of the input variable , that is, the convergence when solving the sensitivity index of the radome structure. The results show that, compared with the AK-SS calculation method, the convergence speed of the method provided in the present disclosure is obviously faster, which again proves the superiority of the calculation of the optimized proxy sampling probability density function.

[0170] In summary, the radome structure global sensitivity analysis method of the present disclosure can analyze the global sensitivity of the radome structure according to the subjective uncertainty of the distribution parameters of the input variables, and obtain the global sensitivity analysis result of the radome structure. When the global sensitivity analysis result obtained according to the distribution parameters is used to optimize the reliability of the radome structure, the structural performance and reliability of the radome structure can be improved, thereby avoiding the problem of flight decision errors when the flight strategy is formulated according to the optimization design result, and improving the safety during flight. And a global sensitivity index based on variance of failure probability suitable for aircraft radome structure is established, so as to quantitatively measure the influence of the uncertainty of the distribution parameters of each input variable on the failure probability of the radome structure, and play a guiding role in performance prediction and design optimization of the radome structure under uncertain environment. And for the global sensitivity index, the present disclosure further proposes an efficient solving method based on Kriging model and proxy importance sampling. By establishing the Kriging failure model between the distribution parameters and the failure probability, the problem of exponential growth of global sensitivity analysis calculation amount with the increase of the dimension of input variables and their distribution parameters is solved; then the proxy sampling probability density function is introduced to sample the input variables, which eliminates the dependence of the calculation amount on the dimension of the distribution parameters of the input variables when solving the failure probability; and for engineering practice, by shifting the sampling center to the design point, the probability of the sample falling into the failure domain is increased, which improves the calculation efficiency and convergence speed of the global sensitivity of the radome structure while ensuring the accuracy.

[0171] It should be noted that, although the operations of the method of the present application are described in a particular order in the accompanying drawings, this does not require or imply that the operations must be performed in this particular order, or that all of the shown operations must be performed to achieve the desired result. Additionally or alternatively, certain steps can be omitted, combined into one step, and / or divided into multiple steps.

[0172] Although the spirit and principles of the present application have been described with reference to several specific embodiments, it should be understood that the present application is not limited to the disclosed specific embodiments, and the division of aspects does not mean that the features in these aspects cannot be combined for the benefit. This division is only for the convenience of expression. The present application is intended to cover various modifications and equivalent arrangements included in the spirit and scope of the appended claims.

Claims

1. A method for global sensitivity analysis of a radome structure, characterized in that, The method comprises the following steps: obtaining an important sampling sample of an input variable of the radome structure and a sample pool of distribution parameters of the input variable; obtaining a training set of a Kriging failure model of the radome structure according to the important sampling sample, and training the Kriging failure model by using the training set; when it is determined that each sample in the sample pool meets a preset condition, substituting the sample of the distribution parameter into the Kriging failure model to obtain a global sensitivity analysis result of the radome structure; wherein, the step of obtaining the training set of the Kriging failure model of the radome structure according to the important sampling sample comprises the following steps: substituting the important sampling sample into a failure function of the radome structure to calculate an output response value of the important sampling sample; determining a failure domain indicator function of the important sampling sample according to the output response value; obtaining a sample set from the sample pool; calculating a failure probability corresponding to each sample in the sample set according to the failure domain indicator function; and taking the failure probability corresponding to each sample and the sample set as the training set; before the step of obtaining the global sensitivity analysis result of the radome structure, the method further comprises the following steps: substituting each sample in the sample pool into the Kriging failure model to obtain a failure probability value corresponding to each sample; and calculating a total variance value of the failure probability of the radome structure according to the failure probability value corresponding to each sample.

2. The method of claim 1, wherein, The step of obtaining the important sampling sample of the input variable of the radome structure comprises the following steps: obtaining a proxy sampling probability density function of the input variable; setting a sampling center of the proxy sampling probability density function as a design point of the radome structure to obtain a proxy important probability density sampling function of the input variable; extracting the important sampling sample of the input variable according to the proxy important probability density sampling function.

3. The method of claim 2, wherein, The step of obtaining the proxy sampling probability density function of the input variable comprises the following steps: when the input variable is subject to a normal distribution, determining a variation interval of the input variable according to a mean value and a standard deviation of the input variable; determining a lower limit and an upper limit of the distribution of the input variable according to the variation interval; determining the proxy sampling probability density function of the input variable according to the lower limit and the upper limit of the distribution of the input variable.

4. The method of claim 1, wherein, The step of determining that each sample in the sample pool meets the preset condition comprises the following steps: substituting each sample in the sample pool into a U-learning function to calculate a value of the U-learning function corresponding to each sample; determining a minimum value from the value of the U-learning function corresponding to each sample point, and determining that the preset condition is met when the minimum value is greater than or equal to a first preset threshold.

5. The method of claim 4, wherein, The method further comprises the following steps: if the minimum value is less than the first preset threshold, determining a target sample from the sample pool according to the minimum value; calculating a target failure probability corresponding to the target sample according to the failure domain indicator function; adding the target sample and the target failure probability to the training set to update the training set; training the Kriging failure model by using the updated training set to obtain an updated Kriging failure model.

6. The method of claim 1, wherein, The global sensitivity analysis result of the radome structure comprises: selecting any parameter as a target distribution parameter from a sample pool of distribution parameters; substituting samples of the target distribution parameter into the Kriging failure model to obtain a first failure probability variance value of the target distribution parameter; determining a main sensitivity index according to the first failure probability variance value and a total failure probability variance value.

7. The method of claim 6, wherein, The step of substituting samples of the target distribution parameter into the Kriging failure model to obtain a first failure probability variance value of the target distribution parameter comprises: inputting each sample of the target distribution parameter and each sample of each other distribution parameter into the Kriging failure model to obtain a first failure probability value corresponding to each sample of the target distribution parameter and each sample of each other distribution parameter; determining a first failure probability expectation value of each other distribution parameter corresponding to the target distribution parameter according to the first failure probability value; determining the first failure probability variance value according to the first failure probability expectation value.

8. The method of claim 7, wherein The global sensitivity analysis result of the radome structure comprises: substituting samples of the other distribution parameters into the Kriging failure model to obtain a second failure probability variance value of the other distribution parameters, the other distribution parameters being distribution parameters other than the target distribution parameter; determining a total sensitivity index according to the second failure probability variance value and the total failure probability variance value.

9. The method of claim 8, wherein, The step of substituting samples of the target distribution parameter into the Kriging failure model to obtain a second failure probability variance value of the other distribution parameters comprises: inputting each sample of each other distribution parameter and each sample of the target distribution parameter into the Kriging failure model to obtain a second failure probability value corresponding to each sample of the target distribution parameter and each sample of each other distribution parameter; determining a second failure probability expectation value of the target distribution parameter corresponding to each other distribution parameter according to the second failure probability value; determining the second failure probability variance value of the other distribution parameters according to the second failure probability expectation value.

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