CN115828414A - Reliability and sensitivity analysis method for uncertainty of distributed parameters of radome structure - Google Patents

Abstract

The disclosure relates to a distributed parameter uncertainty reliability sensitivity analysis method of a radome structure, relating to the field of uncertainty analysis, and comprising the following steps: constructing an adaptive kriging proxy model based on the first initial training sample set; calculating a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to the self-adaptive kriging agent model, and calculating the main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value; calculating a second conditional variance value of the output failure probability according to the self-adaptive kriging agent model, and calculating a conditional expected value of the output failure probability according to the second conditional variance value; and calculating the total sensitivity of the real radome structure model according to the second condition variance value and the condition expected value, and analyzing the sensitivity of the real radome structure model according to the main sensitivity and the total sensitivity. The present disclosure improves sensitivity analysis efficiency.

Description

Reliability and sensitivity analysis method for uncertainty of distributed parameters of radome structure

Technical Field

The embodiment of the disclosure relates to the field of uncertainty analysis, in particular to a reliability and sensitivity analysis method for uncertainty of distribution parameters of a radome structure.

Background

Under severe environment, the aircraft radar antenna can be affected by lightning stroke, hail and other environments to cause failure, and even more serious flight accidents are caused. An aircraft radome is an important structural component in an aircraft, can protect a radar antenna system and provides safety guarantee for a radar antenna, so that the normal realization of the function of the radar system is directly influenced by the quality of the performance of the radome. While the uncertainty existing in the aspects of material characteristics, geometric parameters and the like of the radome structure has a non-negligible influence on the output performance of the structure, so that the propagation of the uncertainty and the influence degree thereof are necessary to be evaluated, and a sensitivity analysis method is a key method for achieving the purpose.

The sources of uncertainty described above generally fall into two categories: objective uncertainties (e.g., uncertainties in input variables) and subjective uncertainties (e.g., uncertainties in distribution parameters). The global reliability sensitivity analysis, when considering the distribution parameter uncertainty of the radome structure, can measure the individual contributions of the distribution parameters of the input variables as they vary throughout their uncertainty and the average contribution of the interactions with other distribution parameter variables to the probability of output failure due to the subjective uncertainty of the distribution parameters due to lack of knowledge and insufficient information collection of the structure. And then the importance sequence of each distribution parameter is given, so that guidance suggestion is provided for reducing the influence effect of structural output failure caused by uncertainty, and meanwhile, the wider application of the radome structure is ensured.

When uncertainty of distribution parameters is considered, a Monte Carlo (Monte Carlo) method is a basic method for realizing global reliability sensitivity analysis in a digital simulation method, but the Monte Carlo method is difficult to accept due to too large calculation amount when the Monte Carlo method is used for solving engineering problems. Therefore, in order to reduce the amount of computation when reliability sensitivity analysis is applied to an engineering structure, in some schemes, a global reliability sensitivity index of a distribution parameter may be defined by simplifying the process of transferring the uncertainty of the distribution parameter to the failure probability into a "black box" model, and the amount of computation in the index computation process may be reduced by a Kriging (Kriging) method. However, for the radome structure, due to the characteristics of a complex structure, a high variable dimension and the like, how to model the radome structure and efficiently analyze the sensitivity of the radome structure based on the modeling are problems which need to be solved urgently.

It is to be noted that the information invented in the background section above is only for enhancement of understanding of the background of the present disclosure, and thus may include information that does not constitute prior art known to those of ordinary skill in the art.

Disclosure of Invention

The purpose of the present disclosure is to provide a method for analyzing the reliability and sensitivity of distributed parameter uncertainty of a radome structure, so as to overcome, at least to a certain extent, the problem that the sensitivity of the radome structure cannot be efficiently analyzed due to the limitations and defects of the related art.

According to one aspect of the present disclosure, there is provided a distributed parameter uncertainty reliability sensitivity analysis method of a radome structure, comprising:

constructing a first initial training sample set according to original distribution parameters of a real radome structure model, and constructing an adaptive kriging agent model based on the first initial training sample set;

calculating a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to the self-adaptive kriging agent model, and calculating the main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value;

calculating a second conditional variance value of the output failure probability according to the self-adaptive kriging agent model, and calculating a conditional expected value of the output failure probability according to the second conditional variance value;

and calculating the total sensitivity of the real radome structure model according to the second condition variance value and the condition expected value, and analyzing the sensitivity of the real radome structure model according to the main sensitivity and the total sensitivity.

In an exemplary embodiment of the present disclosure, constructing a first initial training sample set according to original distribution parameters of a real radome structure model includes:

acquiring original distribution parameters of a real radome structure model, and sampling the original input variables by using a first target proxy important sampling probability density function to obtain a plurality of sampling results;

constructing a first sample pool according to the plurality of sampling results, and randomly extracting a plurality of first original sample points from the first sample pool;

calculating a first distance between the first original sample point and an origin of the real radome structure model, and selecting a plurality of first target sample points from the first original sample points according to the first distance;

and calculating a first buckling response value of each first target sample point through an original model function of the real radome structure model, and constructing the first initial training sample set according to the first buckling response value.

In an exemplary embodiment of the present disclosure, sampling the original input variable by using a first target proxy significant sampling probability density function to obtain a plurality of sampling results, including:

determining a first original proxy sampling probability density function of the real radome structure model according to a selection principle of the proxy sampling probability density function;

in an independent standard normal space, calculating a design point and a reliability index of the real radome structure model by using an improved first-order and second-order moment method;

translating the first original proxy sampling probability density function to the design point from the sampling center to obtain a first target proxy important sampling probability density function;

and sampling the original input variable by using a first target proxy important sampling probability density function to obtain a plurality of sampling results.

In an exemplary embodiment of the present disclosure, constructing an adaptive kriging agent model based on a first initial training sample set comprises:

constructing a target function according to an original model function of the real radome structure model and a preset failure condition, and constructing the initial kriging proxy model according to the target function and the first initial training sample set;

calculating a U learning function value of the sampling result included in the first sample pool by using the initial kriging proxy model, and selecting a sample point to be updated from the sampling result in the first sample pool according to the U learning function value;

and when the U learning function value of the sample point to be updated is determined to be larger than or equal to a preset threshold value, taking the initial kriging agent model as an adaptive kriging agent model.

In an exemplary embodiment of the present disclosure, calculating a total variance value of the output failure probability of the real radar cover structure model according to an adaptive kriging proxy model includes:

calculating a first multi-dimensional distribution parameter variable of the original distribution parameter under an independent standard normal space, and calculating a first variable integral point and a first weight value of the first multi-dimensional distribution parameter variable;

transforming the independent standard normal space by using the first variable integral point to obtain a first original model space, and selecting a plurality of sampling results from a first sample pool to construct a first input variable sample in the first original model space;

calculating a first failure domain indicating function according to the self-adaptive kriging proxy model and a first input variable sample, and calculating a first failure probability integral point of the output failure probability of the real radome structure model according to a first target proxy important sampling probability density function, a first subjective probability density function, a first beta sphere indicating function, a first failure domain indicating function and a first variable integral point of the first input variable sample;

and calculating the total variance value of the output failure probability according to the first failure probability integral point and the first weight value.

In an exemplary embodiment of the present disclosure, calculating a first conditional variance value of an output failure probability of the real radar cover structure model according to an adaptive kriging proxy model includes:

under the first original model space, calculating a second variable integral point and a second weight value of a second multi-dimensional distribution parameter variable included in the first original model space, and transforming the second variable integral point to the first original model space to obtain a second original model space;

determining a second original proxy sampling probability density function in the second original model space, and determining a second target proxy important sampling probability density function according to the second original proxy sampling probability density function;

extracting a second input variable sample from the first sample pool based on a second target proxy important sampling probability density function, and calculating a second failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model;

calculating a difference value between the first multi-dimensional distribution parameter variable and the second multi-dimensional distribution parameter variable to obtain a third multi-dimensional distribution parameter variable, and transforming a third variable integral point of the third multi-dimensional distribution parameter variable to a second original model space to obtain a third original model space;

under the third original model space, calculating a second failure probability integral point of the output failure probability of the real radome structure model according to a second input variable sample, a second subjective probability density function of the second input variable sample, a second beta sphere indicating function, a second failure domain indicating function and a third variable integral point;

and calculating a first condition expected value of the output failure probability according to the second failure probability integral point, and calculating a first condition variance value of the output failure probability according to the first condition expected value and a third weight value.

In an exemplary embodiment of the disclosure, calculating the second conditional variance value of the output failure probability according to an adaptive kriging agent model includes:

calculating a fourth variable integral point and a fourth weight value of a third multidimensional distribution parameter variable, and transforming the fourth variable integral point to an independent standard normal space to obtain a fourth original model space;

determining a third original proxy sampling probability density function under the fourth original model space, and determining a third target proxy important sampling probability density function according to the third original proxy sampling probability density function;

extracting a third input variable sample from the first sample pool based on a third target proxy important sampling probability density function, and calculating a third failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model;

converting a second variable integral point of a second multidimensional distribution parameter variable into an independent standard normal space to obtain a fifth original model space, and calculating a third failure probability integral point of the output failure probability according to a third input variable sample and a third subjective probability density function, a third beta sphere indicating function, a third failure domain indicating function and a second variable integral point of the third variable input sample in the fifth original model space;

and calculating a second conditional variance value of the output failure probability according to a third failure probability integral point and a second weight value of the second multi-dimensional distribution parameter variable.

In an exemplary embodiment of the disclosure, calculating the conditional expectation value of the output failure probability according to the second conditional variance value includes:

and calculating the condition expectation value of the output failure probability according to the second condition variance value and a second weight value of a second multi-dimensional distribution parameter variable.

In an exemplary embodiment of the disclosure, the method for analyzing reliability sensitivity of uncertainty of distributed parameters of a radome structure further comprises:

the method comprises the steps of obtaining a subjective probability density function of original distribution parameters and an original failure domain indicating function of a real radome structure model, and calculating the output failure probability of the real radome structure model according to the subjective probability density function and the original failure domain indicating function.

In an exemplary embodiment of the present disclosure, the main sensitivity is used to measure the contribution of any original distribution parameter to the total variance value of the output failure probability under the action of itself;

the total sensitivity is used for measuring the contribution degree of the independent action of any original distribution parameter and the interaction with other distribution parameters to the total variance value of the output failure probability.

According to the method for analyzing the reliability and the sensitivity of the uncertainty of the distribution parameters of the radome structure, on one hand, a first initial training sample set can be constructed according to the original distribution parameters of a real radome structure model, and an adaptive kriging agent model is constructed on the basis of the first initial training sample set; further, calculating a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to the self-adaptive kriging agent model, and calculating the main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value; calculating a second conditional variance value of the output failure probability according to the self-adaptive kriging agent model, and calculating a conditional expected value of the output failure probability according to the second conditional variance value; finally, the total sensitivity of the real radome structure model is calculated according to the second condition variance value and the condition expected value, and the sensitivity of the real radome structure model is analyzed according to the main sensitivity and the total sensitivity, so that the sensitivity of the real radome structure model is analyzed based on the self-adaptive kriging proxy model, the problems that the radome structure cannot be modeled in the prior art and the sensitivity of the radome structure is analyzed based on the modeling high efficiency are solved, and the sensitivity analysis efficiency is improved; on the other hand, the sensitivity of the real radome structure model can be analyzed based on the main sensitivity and the total sensitivity, so that the accuracy of the reliability sensitivity analysis result is improved.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure. It is to be understood that the drawings in the following description are merely exemplary of the disclosure, and that other drawings may be derived from those drawings by one of ordinary skill in the art without the exercise of inventive faculty.

FIG. 1 schematically illustrates a flow chart of a distributed parameter uncertainty reliability sensitivity analysis method of a radome structure according to an example embodiment of the present disclosure.

Fig. 2 schematically illustrates a cellular sandwich radome structural model schematic in accordance with an example embodiment of the present disclosure.

Fig. 3 schematically illustrates a flowchart of a method for constructing a first initial training sample set according to original distribution parameters of a real radome structure model according to an exemplary embodiment of the present disclosure.

Fig. 4 schematically illustrates a flowchart of a method of constructing an adaptive kriging agent model based on a first initial training sample set, according to an example embodiment of the present disclosure.

FIG. 5 schematically illustrates an unconditional failure probability with N according to an example embodiment of the present disclosure _X The increased convergence curves illustrate the graph.

Fig. 6 schematically illustrates an example graph of alignment results of one kind of main sensitivities according to an example embodiment of the present disclosure.

Fig. 7 schematically illustrates an example graph of alignment results of an overall sensitivity according to an example embodiment of the present disclosure.

Fig. 8 schematically illustrates a block diagram of a distributed parameter uncertainty reliability sensitivity analysis apparatus of a radome structure according to an example embodiment of the present disclosure.

Fig. 9 schematically illustrates an electronic device for implementing the distributed parameter uncertainty reliability sensitivity analysis method of the radome structure described above, according to an example embodiment of the present disclosure.

Detailed Description

Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the subject matter of the present disclosure can be practiced without one or more of the specific details, or with other methods, components, devices, steps, and the like. In other instances, well-known technical solutions have not been shown or described in detail to avoid obscuring aspects of the present disclosure.

Furthermore, the drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repetitive description will be omitted. Some of the block diagrams shown in the figures are functional entities and do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in the form of software, or in one or more hardware modules or integrated circuits, or in different networks and/or processor devices and/or microcontroller devices.

In the present exemplary embodiment, first, a method for analyzing reliability and sensitivity of uncertainty of distributed parameters of a radome structure is provided, where the method may be performed in a server, a server cluster, a cloud server, or the like; of course, a person skilled in the art may also run the method of the present disclosure on other platforms as needed, which is not limited in this exemplary embodiment. Specifically, referring to fig. 1, the method for analyzing the reliability sensitivity of the radome structure may include the following steps:

s110, constructing a first initial training sample set according to original distribution parameters of a real radome structure model, and constructing an adaptive kriging agent model based on the first initial training sample set;

step S120, calculating a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to an adaptive kriging agent model, and calculating the main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value;

step S130, calculating a second conditional variance value of the output failure probability according to the self-adaptive Krigin agent model, and calculating a conditional expected value of the output failure probability according to the second conditional variance value;

and S140, calculating the total sensitivity of the real radome structure model according to the second condition variance value and the condition expected value, and analyzing the sensitivity of the real radome structure model according to the main sensitivity and the total sensitivity.

In the reliability sensitivity analysis method for the radome structure, on one hand, a first initial training sample set can be constructed according to original distribution parameters of a real radome structure model, and an adaptive kriging agent model is constructed based on the first initial training sample set; further, calculating a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to the self-adaptive kriging agent model, and calculating the main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value; calculating a second conditional variance value of the output failure probability according to the self-adaptive kriging agent model, and calculating a conditional expected value of the output failure probability according to the second conditional variance value; finally, the total sensitivity of the real radome structure model is calculated according to the second condition variance value and the condition expected value, and the sensitivity of the real radome structure model is analyzed according to the main sensitivity and the total sensitivity, so that the sensitivity of the real radome structure model is analyzed based on the self-adaptive kriging proxy model, the problems that the radome structure cannot be modeled in the prior art and the sensitivity of the radome structure is analyzed based on the modeling high efficiency are solved, and the sensitivity analysis efficiency is improved; on the other hand, the sensitivity of the real radome structure model can be analyzed based on the main sensitivity and the total sensitivity, so that the accuracy of the reliability sensitivity analysis result is improved.

Hereinafter, a distributed parameter uncertainty reliability sensitivity analysis method of a radome structure according to an exemplary embodiment of the present disclosure will be explained and explained in detail with reference to the accompanying drawings.

First, an application scenario and an object of the exemplary embodiment of the present disclosure are explained and explained. Specifically, the method for analyzing uncertainty reliability sensitivity of distribution parameters of a radome structure according to the exemplary embodiment of the present disclosure relates to a problem of analyzing overall reliability sensitivity of the radome structure when the distribution parameters have uncertainty; meanwhile, the reliability sensitivity analysis method of the radome structure, which is disclosed by the embodiment of the disclosure, provides an efficient global reliability sensitivity analysis algorithm aiming at the problem of difficult analysis of the traditional method; in the global reliability sensitivity analysis algorithm, the main applied technologies are as follows: on the one hand, the Formula of quadrature (Cubasic Formula, CF); on the other hand, the proxy Sampling Probability Density Function (SSPDF), and on the other hand, the Kriging proxy model method (Kriging method); further, truncated Importance Sampling (TIS) is a method for extracting samples.

The method for analyzing the reliability and the sensitivity of the uncertainty of the distribution parameters of the radome structure, which is disclosed by the embodiment of the disclosure, aims to efficiently analyze the degree of influence of each distribution parameter on the output failure probability in the radome structure so as to improve the reliability and the safety of the radome structure in practical application; in a specific implementation process, an SSPDF method (STISFF method) combined with TIS (TIS) can be introduced into an adaptive Kriging proxy model method to establish a proxy model of a real radome structure model, and based on the proxy model, a CF method is further applied to global reliability sensitivity analysis under uncertainty of distribution parameters, so that a method for efficiently solving global reliability sensitivity indexes of radome structure distribution parameters is provided: an integral formula (AKS-CF) method based on an adaptive Kriging agent model and combined with a TIS method and an SSPDF method.

Next, a description will be given of a model of a real radome structure described in the exemplary embodiments of the present disclosure. Specifically, an example diagram of the real radome structural model can be referred to fig. 2. Specifically, in the real radome structure model shown in fig. 2, 15 intensity variables may be included, and the distribution parameter of each intensity variable may be a 21-dimensional variable; wherein, each intensity variable and the corresponding distribution parameter can be specifically shown in the following table 1:

TABLE 1 distribution parameters of input variables of a radome construction

Further, it is assumed that the original input variables and the mean values thereof of the real radome structure model have uncertainty and distribution information is listed in table 1, wherein the input variables and the mean values thereof respectively obey normal distribution and uniform distribution, and the variation coefficients of the input variables are all 0.2; meanwhile, a constrained and constrained relation exists between the original input variable and the original distribution parameter; that is, the original input variables may be constrained by the original distribution parameters. Therefore, considering the buckling failure analysis of the real radome structural model, the definition of the failure domain can be shown as the following formula (1):

f = { x: g (x) = gamma (x) -Force × M ≦ 0}; formula (1)

Wherein γ (x) is a buckling response function; force is wind load, and because the air environment is complex and the real wind load fluctuation is large, the Force needs to be reviewed from an uncertain visual angle; for example, assume that the original load is 1 as a whole, and assume that the original wind load is normally distributed as a whole: n (1, 1 Xcov); wherein cov is the coefficient of variation of wind load; in practical application, when cov =0.1, the wind load is distributed normally N (1,0.1); when the sampling value is 0.95, the wind load is multiplied by 0.95 at all positions; furthermore, M is a safety margin (M > 1) taken by a real radar cover structure model, and the setting of M is to prevent the consequences caused by factors such as sudden increase of wind load and the like, so that the assessment cannot be continuously carried out according to the given load, but the original load value is multiplied by the safety margin M, thereby actually increasing the safety assessment standard of the structure, providing more rigorous requirements for the structure design, and ensuring that the structure is more reliable; further, in combination with the actual situation, the wind load of the structure in this disclosure has a coefficient of variation cov =0.2 and a safety margin M =3.

Then, the output failure probability of the real radome structure model described in the exemplary embodiments of the present disclosure is explained and explained. Specifically, the method for calculating the output failure probability includes: the method comprises the steps of obtaining a subjective probability density function of original distribution parameters and an original failure domain indicating function of a real radome structure model, and calculating the output failure probability of the real radome structure model according to the subjective probability density function and the original failure domain indicating function. That is, in the practical application process, for a structure with parameter uncertainty, the function is expressed as: y = g (X, Θ); wherein the content of the first and second substances,

is d _X Input variables with mutually independent dimensions, namely the recorded original distribution parameters;

is d of the input variable X _Θ Distribution parameter variables which are mutually independent in dimension; wherein the subjective uncertainty of the parameter can be determined by a subjective probability density function f _Θ (θ). At this time, the output failure probability is no longer influenced by the uncertainty of the input variable X, but can be described as a function of the distribution parameter Θ, that is:

wherein, f _X (X | theta) is input variable X under distributed parameter conditionsThe subjective probability density function of the probability of the user,

as a space of input variables, I _F (x | theta) is a failure domain indicator function when x ∈ I _F When (x | theta), then there is I _F (x | θ) =1; otherwise, I _F (x|θ)＝0；P _f Is the output failure probability of the radome structural model. Therefore, similar to the variance-based sensitivity analysis method, the definition of the global reliability sensitivity index and the total sensitivity index of the distribution parameters to the output failure probability can be shown as the following equations (3) and (4):

the main sensitivity is used for measuring the contribution degree of any original distribution parameter to the total variance value of the output failure probability under the independent action; the total sensitivity is used for measuring the contribution degree of the independent action of any original distribution parameter and the interaction with other distribution parameters to the total variance value of the output failure probability; i.e. the main sensitivity index S _i For measuring the distribution parameter theta _i Under the independent action, the failure probability P _f Variance contribution, total sensitivity index used to measure distribution parameter theta _i Acting alone and interacting with other distribution parameters on failure probability P _f The contribution of the variance.

Next, the principle of use of the product formula involved in the exemplary embodiments of the present disclosure is explained and explained. Specifically, as can be seen from the above equations (3) and (4), the key of the index solution is the calculation of the nested expectation and variance; thus, to efficiently solve for nested expectation and variance operators, the present disclosure utilizes the theory of CF (quadrature formula) to simplify this solving process; where the statistical moments of the CF estimate variables are performed in the standard normal space, thus, by the Rosenblatt transform or Nataf transformConverting the model of formula (2) into an independent standard normal variable

The function of (3) can be specifically expressed by the following formula (5):

P _f ＝ψ(Θ)＝ψ[R ^-1 (λ)]= ρ (λ); formula (5)

Wherein R is ^-1 (. -) represents the Rosenblatt transform or the Nataf transform, and ρ (λ) represents a multivariate function of the independent normal variable λ; meanwhile, according to the formula (5), the output failure probability P can be known _f The expectation and variance of (c) may be shown in the form of an integral in the following equation (6) and equation (7), respectively:

wherein f is _λ (λ) represents the joint probability density function of the independent standard normal variable λ. Further, according to the theory of the product formula, the integrals in the formula (6) and the formula (7) can be efficiently calculated by using a small number of suitable integral points and corresponding weights, which can be specifically represented by the following formula (8) and formula (9):

based on the foregoing description, it can be seen that the expression form of the product formula used in the calculation of the expectation and variance of the nesting in the present disclosure can be specifically shown in the following formula (10):

wherein I () represents an abbreviation of integral if one considers that in equation (8)

And in equation (9)

R () in the formula (10) can be expressed as ρ (λ) and

further, the principle of the proxy truncated significant sample probability density function according to the exemplary embodiments of the present disclosure is explained and illustrated. Specifically, by introducing the CF, nested expectations and variances can be efficiently and accurately solved, whereas a two-tier sampling of input variables and distribution parameters is required when the distribution parameter uncertainty is passed to the output failure probability, to solve this problem, the present disclosure resorts to the SSPDF approach. In practical application, the method solves the problem that the calculated amount of uncertainty depends on the parameter dimension in the process of transferring from the distribution parameters to the failure probability, and has the advantages of reducing the number of nested sampling layers and improving the uncertainty transfer efficiency. For example, by introducing the SSPDF into the index solution, the output failure probability in equation (2) can be shown as equation (11) below

Wherein h is _X (x|θ ^* ) In order to be the SSPDF,

represents an average value with respect to SSPDF; meanwhile, according to the formula (11), it can be known that the SSPDFh is introduced in the calculation process of the output failure probability _X (x|θ ^* ) Generated, independent of the true distribution parameters. Thus, in calculating P _f In time, the distribution parameter Θ varies at the outer layer, and the sample of the input variable X produced by the inner layer can be reused.

From the above analysis, it can be known that SSPDFh _X (x|θ ^* ) Is critical, in some embodiments, when the input variable X changes with its distribution parameter Θ with uncertainty, h _X (x|θ ^* ) The entire range of variation of the input variable X should be covered. One simple and straightforward way is to determine the limit distribution of the responsive input variable X according to the variation range of the distribution parameter theta and then determine SSPDFh according to the limit distribution _X (x|θ ^* ). Meanwhile, in order to effectively improve the sampling efficiency of the radome structure under the condition of small failure probability, the method introduces the thought of the TIS method into the SSPDF method, and further constructs the STISPDF. The TIS method described herein is a sampling method formed by combining an important sampling method and an idea of truncation sampling, wherein the basic idea of the important sampling method is as follows: samples are extracted through the important sampling probability density function, and a large number of extracted sample points fall in a failure domain, so that the estimated value of the failure probability is converged to a true value quickly, and the problem of small failure probability can be solved effectively. The point in the failure domain of the functional function that contributes most to the failure probability is the design point, and therefore the density center is generally set at the design point when constructing the significant sampling density function. The invention further moves the sampling center of SSPDF to the design point to construct the important sampling proxy density function (SISPDF) so as to further improve the efficiency. The basic idea of the truncation significant sampling method is as follows: in a standard normal space, an original point is taken as a sphere center, a reliability index (the shortest distance from a coordinate original point to an extreme state surface) is taken as a radius to establish a beta hypersphere, and after sample points are extracted by SISPDF, the sample points falling into the beta hypersphere are in a safe domain, so that the sample points can be cut off, and the calculation amount for estimating the failure probability is further reduced.

Further, the indicator function in the outer region of the beta hypersphere can be defined as I _β (x) In that respect Wherein the indication function I _β (x) Specifically, the following formula (12) can be used:

therefore, the expression of the failure probability at this time can be expressed as the following formula (13):

wherein the content of the first and second substances,

representing SISPDF, E ^* []Mean values for SISPDF are shown.

The use principle of the Kriging surrogate model in combination with the truncated significant sample and the surrogate sample probability density function will be explained and explained below. Specifically, for the problem of small failure probability of the engineering structure, a function needs to be repeatedly called when the structure is calculated and output, particularly a complex implicit structure system, and the cost for repeatedly calling a finite element model is extremely high.

Because the original Kriging agent model cannot solve the contradiction between precision and efficiency, a self-adaptive agent model is needed to deal with the problem; and the number of the first and second electrodes,

the learning function considers the distance between the predicted value of the Kriging agent model and the failure surface and the standard deviation of the estimated value, after a rough Kriging model is established by using a small number of sample points, the learning function screens sample points meeting requirements from the rest candidate sample points and adds the sample points into the current training sample set to update the Kriging model, and minU (x) is selected to be more than or equal to 2 as a convergence termination condition of the Kriging agent model adaptive updating process. Meanwhile, the U learning function is only suitable for a structural system with a limit state face of 0, and for a system with a threshold value of e and failure when the condition Y = g (X) is less than or equal to e, a new function Y needs to be constructed according to the original function and the failure condition _reb ＝g _reb (X) = g (X) -e, and then, the description Y is created using a U learning function _reb ＝g _reb Kriging model of (X). Accordingly, exemplary embodiments of the present disclosureIn the recorded reliability sensitivity analysis method of the radome structure, an AK-STISPF proxy model is also established based on a U learning function; namely, an AK-STIPDF method is utilized to establish an input-output proxy model of the radar cover structure, and a CF is utilized to calculate the global reliability sensitivity index of the distribution parameter based on the proxy model. Meanwhile, an AKS-CF method can be established, and the method solves the parameter theta _i And Θ _i When the output failure probability under the condition is satisfied, the following equations (14) and (15) can be obtained by transforming equation (13):

wherein, theta _i 'and θ' _i Respectively expressed in the parameter theta _i And theta _i Fixed value of the parameter under the condition. Therefore, the conditional output failure probabilities of the indices described in the formula (3) and the formula (4) can be calculated by the formula (14) and the formula (15), respectively, and the index S can be calculated _i And

and then the sensitivity of the radome structure model is analyzed.

Hereinafter, the reliability sensitivity analysis method of the radome structure shown in fig. 1 will be further explained and explained in conjunction with the above-described principle. Specifically, the method comprises the following steps:

in step S110, a first initial training sample set is constructed according to the original distribution parameters of the real radome structure model, and an adaptive kriging proxy model is constructed based on the first initial training sample set.

In the present exemplary embodiment, first, a first initial training sample set is constructed from the original distribution parameters of the real radome structure model. Specifically, as shown in fig. 3, the method may include the following steps:

step S310, obtaining original distribution parameters of a real radome structure model, and sampling the original input variables by using a first target proxy important sampling probability density function to obtain a plurality of sampling results;

step S320, constructing a first sample pool according to the plurality of sampling results, and randomly extracting a plurality of first original sample points from the first sample pool;

step S330, calculating a first distance between the first original sample point and an origin of the real radome structure model, and selecting a plurality of first target sample points from the first original sample points according to the first distance;

step S340, calculating a first buckling response value of each first target sample point through an original model function of the real radome structure model, and constructing the first initial training sample set according to the first buckling response value.

In an exemplary embodiment, sampling the original input variable by using a first target proxy significant sampling probability density function to obtain a plurality of sampling results may be implemented as follows: firstly, determining a first original proxy sampling probability density function of the real radome structure model according to a selection principle of a proxy sampling probability density function; secondly, calculating a design point and a reliability index of the real radome structure model by using an improved first-order and second-order moment method in an independent standard normal space; then, translating the first original proxy sampling probability density function from a sampling center to the design point to obtain a first target proxy important sampling probability density function; and finally, sampling the original input variable by using a first target proxy important sampling probability density function to obtain a plurality of sampling results.

Hereinafter, steps S310 to S340 will be explained and explained. Specifically, in the actual application process, first, a first original proxy sampling probability density function h of the radome structure model may be determined according to a selection principle of SSPDF (proxy sampling probability density function) _X (x|θ ^* ) (ii) a Then, in an independent standard normal space, an AFOSM (Advanced First Order and Second Order Moment) method is utilized to solve the design point and the reliability index beta of the real radome structure model, and then the First original proxy sampling probability density function h is sampled _X (x|θ ^* ) The sampling center is translated to a design point to construct a first target proxy significant sampling probability density function SISPDF

Further, a first target proxy significant sampling probability density function SISPDF is utilized

Extracting N of input variable (original distribution parameter) X _K One sample (sampling result) x _k (k＝1,,N _K ) And forming a first sample pool S from the samples _TIS (ii) a Further, from the first sample pool S _TIS In randomly selecting N _T (N _T N _K ) Input variable samples (first original sample points), and calculates each first original sample point

Distance to origin

And further select out the coincidence

Constitutes a new input variable sample x _k (k＝1,,N′ _T ) (ii) a Finally, calculating the buckling response value of each first target sample point, and further constructing a first initial training sample set T _TIS ＝{(x _k ,γ(x _k )-Force×M),k＝1,,N′ _T }。

Secondly, after the first initial training sample set is obtained, the self-adaptive kriging agent model can be constructed based on the first initial training sample set. Specifically, as shown in fig. 4, the method may include the following steps:

step S410, constructing a target function according to an original model function of the real radome structure model and a preset failure condition, and constructing the initial Krigin agent model according to the target function and the first initial training sample set;

step S420, calculating a U learning function value of sampling results included in the first sample pool by using the initial Krigin proxy model, and selecting a sample point to be updated from the sampling results in the first sample pool according to the U learning function value;

and step S430, when the U learning function value of the sample point to be updated is determined to be greater than or equal to a preset threshold value, taking the initial kriging proxy model as an adaptive kriging proxy model.

Hereinafter, steps S410 to S430 will be explained and explained. Specifically, first, according to a first initial training sample set T _TIS Function Y is established by using tool kit DACE (Design and Analysis of Computer Experiments) _reb First initial Kriging proxy model g of = gamma (X) -Force × M and X _eK (X); then, a first sample pool S is calculated by utilizing the first initial Kriging model _TIS The U learning function value corresponding to each sample point (sampling result) is selected, and the next sample point (to-be-updated sample point) to be updated is selected

When in use

When the self-adaptive learning process is stopped, the self-adaptive Kriging agent model is established, namely the initial Kriging agent model can be used as the self-adaptive Kriging agent model; of course, if

Then x needs to be reduced _u ,g(x _u )＝γ(x _u ) -Force x M } is added to the first initial training sample set T _TIS And reconstructing the initial Krigin agent model based on the updated first initial training sample set until the U learning function value of the sample point to be updated is more than or equal to 2. It should be added that, in the process of the adaptive learning of the first initial kriging model, the first initial training sample set may be updated by continuously using the sample point whose U learning function value is less than 2 to obtain the target training sample set, and then the initial kriging proxy model is reconstructed based on the updated target training sample set, so as to implement the adaptive learning of the initial kriging proxy model to obtain the adaptive kriging proxy model, and further achieve the purpose of improving the accuracy of the obtained output failure probability, and finally achieve the purpose of improving the accuracy of the reliability sensitivity analysis result.

In step S120, a total variance value and a first conditional variance value of the output failure probability of the real radome structure model are calculated according to the adaptive kriging proxy model, and a main sensitivity of the real radome structure model is calculated according to the total variance value and the first conditional variance value.

In the present exemplary embodiment, first, a total variance value of the output failure probability of the real radar cover structure model is calculated from an adaptive kriging proxy model. Specifically, the method can be realized by the following steps: firstly, calculating a first multi-dimensional distribution parameter variable of the original distribution parameter under an independent standard normal space, and calculating a first variable integral point and a first weight value of the first multi-dimensional distribution parameter variable; secondly, transforming the independent standard normal space by using the first variable integration point to obtain a first original model space, and selecting a plurality of sampling results from a first sample pool to construct a first input variable sample in the first original model space; then, calculating a first failure domain indicating function according to the self-adaptive kriging proxy model and the first input variable sample, and calculating a first failure probability integral point of the output failure probability of the real radome structure model according to a first target proxy important sampling probability density function, a first subjective probability density function, a first beta sphere indicating function, a first failure domain indicating function and a first variable integral point of the first input variable sample; and finally, calculating the total variance value of the output failure probability according to the first failure probability integral point and the first weight value.

Hereinafter, a specific calculation process of outputting the total variance value of the failure probability will be explained and explained, specifically, the first variable integration point and the first weight value are calculated based on the aforementioned formula (10) in the independent standard normal space. Specifically, the formula (10) can be as follows:

wherein the first multidimensional distribution parameter variable d is calculated based on the formula (10) _Θ The integral point of the first variable obtained by calculation is

The first weight value is

Then, the first variable integral point is transformed to an independent standard normal space to obtain a first original model space

Further, when

From the first sample pool S _TIS N of the selected input variable X _X A sample x _k (k＝1,,N _X ) Calculating each sample

Distance to origin

And select out the coincidence

Make up a new input variable sample x _k (k＝1,…,N′ _X ) (first input variable samples); i.e. I _β (x _k |θ ^* )(k＝1,…,N′ _X ) =1, bringing the first input variable sample to adaptive kriging proxy modeAfter modeling, obtaining a first failure domain indication function I _F (x _k |θ ^* )(k＝1,…,N′ _X ) (ii) a Further, a first target proxy significant sampling probability density function based on the first input variable samples

First subjective probability density function f _X (x _k |θ)(k＝1,…,N′ _X ) First beta sphere indicating function I _β (x _k |θ ^* )(k＝1,…,N′ _X ) And a first failure domain indication function I _F (x _k |θ ^* )(k＝1,…,N′ _X ) And a first variable integration point of Θ

Solving the output failure probability P using equation (13) _f First failure probability integration point of

Wherein, equation (13) can be as follows:

finally, the integration point can be integrated according to the first failure probability

And a first weight value

P is obtained by solving the above-mentioned equation (10) _f Total variance value V (P) _f ). Wherein, the formula (10) can be as follows:

and secondly, calculating a first conditional variance value of the output failure probability of the real radar cover structure model according to the self-adaptive kriging agent model. Specifically, the method can be realized by the following steps: firstly, under the first original model space, calculating a second variable integral point and a second weight value of a second multi-dimensional distribution parameter variable included in the first original model space, and transforming the second variable integral point to the first original model space to obtain a second original model space; secondly, determining a second original proxy sampling probability density function in the second original model space, and determining a second target proxy important sampling probability density function according to the second original proxy sampling probability density function; then, extracting a second input variable sample from the first sample pool based on a second target proxy important sampling probability density function, and calculating a second failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model; further, calculating a difference value between the first multidimensional distribution parameter variable and the second multidimensional distribution parameter variable to obtain a third multidimensional distribution parameter variable, and transforming a third variable integral point of the third multidimensional distribution parameter variable to a second original model space to obtain a third original model space; further, under the third original model space, calculating a second failure probability integral point of the output failure probability of the real radome structure model according to a second input variable sample, a second subjective probability density function of the second input variable sample, a second beta sphere indicating function, a second failure domain indicating function and a third variable integral point; and finally, calculating a first condition expected value of the output failure probability according to the second failure probability integration point, and calculating a first condition variance value of the output failure probability according to the first condition expected value and a third weight value.

Hereinafter, a specific calculation process of the first conditional variance value will be explained and explained. Specifically, first, a second multidimensional distribution parameter variable (i-dimensional) and a second variable integration point are calculated in the first prototype space based on the aforementioned product equation (i.e., equation (10))

And a second weight value

And will be secondIntegral point of variable

Transforming to the first original model space to obtain a second original model space

Secondly, when

When a new SSPDF is determined

(i.e., the second original proxy sampling probability density function), and constructing the SSPDF based on the second original proxy sampling probability density function

(second target proxy significant sampling probability density function) and the second target proxy significant sampling probability density function

Extracting N of input variable X _X Sample x' _k (k＝1,,N _X ) Calculating each sample

Distance to origin

Select out the coincidence

Constitutes the new input variable sample x' _k (k＝1,,N′ _X ) (second input variable sample), i.e.

Wherein, (k =1, N' _X ) Substituting the second input variable sample into the adaptive kriging proxy model to obtain a second failure domain indicator function

Then, the product formula based on the above description(i.e., equation 10) to produce d _Θ -third variable integration points of 1-dimensional distribution parameters (third multidimensional parametric distribution variables)

And a third weight value

And integrating the third variable into a point

Transforming to the second original model space to obtain a third original model space

Further, when

While inputting samples according to a second variable

Second subjective probability density function of second input variable samples

Second beta sphere indicator function

Second failure domain indicator function

And theta _i Integral point of (third variable integral point)

Solving the failure probability P under the condition of parameters by using the formula (14) described above _f Second point of probability of failure integration

Further, according to the second failure probability integration point and the third weight value

Solving for the output using the equation (10) set forth aboveProbability of failure P _f Is expected for the first condition

Finally, the expected value is expected according to the first condition

And a third weight value

Calculating a first conditional expectation of an output failure probability using the previously described equation (10)

Up to this point, the calculation process of the conditional expectation value of the output failure probability and the first conditional expectation value has been fully realized. On the premise again, the expected value V (P) can be obtained according to the condition _f ) And first conditional expected value

Calculating and obtaining the main sensitivity S of the real radome structure model based on the recorded formula (3) _i 。

In step S130, a second conditional variance value of the output failure probability is calculated according to the adaptive kriging proxy model, and a conditional expected value of the output failure probability is calculated according to the second conditional variance value.

In the present exemplary embodiment, first, the second conditional variance value of the output failure probability is calculated from the adaptive kriging agent model. Specifically, the method can be realized by the following steps: firstly, calculating a fourth variable integral point and a fourth weight value of a third multidimensional distribution parameter variable, and transforming the fourth variable integral point to an independent standard normal space to obtain a fourth original model space; secondly, determining a third original proxy sampling probability density function under the fourth original model space, and determining a third target proxy important sampling probability density function according to the third original proxy sampling probability density function; then, extracting a third input variable sample from the first sample pool based on a third target proxy important sampling probability density function, and calculating a third failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model; further, converting second variable integral points of a second multidimensional distribution parameter variable into an independent standard normal space to obtain a fifth original model space, and calculating third failure probability integral points of the output failure probability according to a third input variable sample and a third subjective probability density function, a third beta-sphere indicating function, a third failure domain indicating function and second variable integral points of the third variable input sample in the fifth original model space; and finally, calculating a second conditional variance value of the output failure probability according to a third failure probability integration point and a second weight value of the second multi-dimensional distribution parameter variable.

Hereinafter, a specific calculation process of the second conditional variance value will be explained and explained. Specifically, first, the third multidimensional distribution parameter variable d is calculated according to the aforementioned product formula (i.e., formula (10)) _Θ -1 fourth variable integration point

And a fourth weight value

And a fourth variable integration point

Transforming to independent standard normal space to obtain fourth original model space

Secondly, the first step is to carry out the first,

then, a third original proxy sampling probability density function SSPDF is determined

And constructing a third target proxy significant sampling probability density function SSPDF according to the third original proxy sampling probability density function

And the third target agent is used for substituting the important sampling probability density function

N of the input variable X _X Sample x' _k ′(k＝1,…,N _X ) Calculating each sample

Distance to origin

Select out the coincidence

Constitutes a new third input variable sample x' _k ′(k＝1,…,N′ _X ) I.e. by

Substituting a third input variable sample into the self-adaptive Krigin proxy model to obtain a third failure domain indicator function

Then, a second variable integration point of the 1-dimensional distribution parameter (second multidimensional distribution parameter variable) is generated based on the aforementioned integration formula (i.e., formula (10))

And a second weight value

Integrating the points of the second variable by the Rosenblatt transform or the Nataf transform

Transforming to independent standard normal space to obtain fifth original model space

Further, when

According to the third input variable sample

Third subjective probability density function of third variable input samples

Third beta sphere indicator function

Third failure domain indicator function

And theta _i Integral point of

(second variable integration point) for solving the output failure probability P based on the above-mentioned formula (15) _f Third failure probability integration point of

Then the third failure probability integration point

And a second weight value

Solving the output failure probability P by using the formula (10) described above _f Second conditional variance of (2)

Up to this point, the specific calculation process of the second conditional variance has been fully implemented. Under this condition, the conditional expectation value of the output failure probability may be calculated based on the second conditional variance value. Specifically, the method can be realized by the following steps: and calculating the condition expectation value of the output failure probability according to the second condition variance value and a second weight value of a second multi-dimensional distribution parameter variable. That is, the second conditional variance value can be used

And a second weight value

Solving the expected value of the condition by using the above-mentioned formula (10)

In step S140, the total sensitivity of the real radome structure model is calculated according to the second conditional variance value and the conditional expectation value, and the sensitivity of the real radome structure model is analyzed according to the main sensitivity and the total sensitivity.

Specifically, after obtaining the second conditional variance value and the conditional expectation value, the second conditional variance value V (P) may be obtained _f ) And expected value of condition

The total sensitivity can be obtained by substituting the above-mentioned formula (4)

And finally, analyzing the sensitivity of the real radome structure model based on the main sensitivity and the total sensitivity.

In practical application, when the reliability sensitivity index is calculated by the MCS, the original radome structure model needs to be repeatedly called for many times, so that the calculation cost is too high, and the analysis process is difficult to realize. Therefore, the present disclosure firstly compares the unconditional output failure probability calculated by calling the real radome structure model and the Kriging agent model, and a specific obtained comparison result exemplary graph can be shown in table 2 below. Specifically, in Table 2, N _X For the sample size of the input variable selected in the sample pool, NPFE is the Number of times of calling an original model function (NPFE), wherein NPFE is 206 times when a Kriging proxy model is established for the radome structure model, and NPFE is 521 times when the design point is iteratively solved by using an AFOSM method. As can be seen from Table 2, the failure probability calculated by calling the Kriging proxy model established by AK-STISFF method is better matched with the failure probability calculated by calling the original model by MCS, while the NPFE of the Kriging proxy model is much smaller than that of MCS, which shows that the established Kriging proxy modelThe calculation cost can be reduced while the calculation precision is ensured, and an analysis basis is provided for the radome model with the complex structure.

TABLE 2 unconditional failure probability of radome structures

In addition, in order to visually display the excellence of the Kriging model established by the AK-STISFF method, FIG. 5 lists the failure probability obtained by the MCS method as a contrast solution, and the failure probability solved by the Kriging proxy model along with N _X Convergence curve when varied. From FIG. 5, it can be seen that at N _X And if the failure probability is 5000, the failure probability can reach convergence and meet the calculation accuracy requirement, which indicates that a Kriging model established by the AK-STISPF method can replace an original model to realize the reliability and sensitivity analysis of the structure.

In order to compare the calculation efficiency of the AKS-CF method, the built Kriging proxy model is used for replacing an implicit function, a Monte Carlo method (marked as AKS-MCS) based on the Kriging model is used as a comparison method, and the results obtained by the two methods are listed in Table 3. The parenthesized values in the table are the coefficient of variation of the corresponding results, and are obtained by circularly calculating the reliability sensitivity index and the failure probability 30 times. N is the calling times of the Kriging agent model, and N for calculating the reliability sensitivity index by the AKS-MCS and AKS-CF methods is d _Θ ×N _Θ ×N _Θ ×N _X +N _Θ ×N _X And

TABLE 3 reliability sensitivity index of radar cover structure distribution parameters

It should be added here that, because of the large number of structural variables, only the numerical results with the index greater than 0.01 are listed in the table. The results can be seen from the tableOn the premise of meeting the convergence of the calculation result, the result obtained by the AKS-CF method has good calculation accuracy. When the method obtains a convergence solution, N is 8.4425 × 10 ⁷ Compared with 8.4004 × 10 of MCS method ¹⁰ The calculation amount can be greatly reduced, and the high-efficiency calculation efficiency is embodied. Meanwhile, in order to clearly compare the sizes of the indexes, histograms of the indexes obtained under the two methods are listed in fig. 6 and 7, from which the importance ranks of the distribution parameters derived from the main and total sensitivity indexes are summarized as μ _M2 ＞μ _Mat3G13 ＞μ _M1 ＞μ _Mat1E22 ＞μ _M3 ＞μ _Mat1G12 (ii) a This illustrates the parameter μ for the honeycomb sandwich thickness _M2 Has the greatest influence on the failure probability and, therefore, on the parameter mu _M2 Effective adjustment can reduce the failure probability of the structure to the maximum extent. In addition, the parameter μ _Mat3G13 、μ _M2 And mu _Mat1E22 The influence on the failure probability of the structure is large, and the subjective information of the structure needs to be collected more to improve the reliability of the structure. While the remaining distribution parameters, which have little effect on the failure probability, can be fixed to arbitrary values within an uncertain range to simplify the analysis and design process of the structure.

Up to this point, the distributed parameter uncertainty reliability sensitivity analysis method of the radome structure described in the exemplary embodiment of the present disclosure has been fully implemented. Based on the content recorded in the foregoing, it can be known that, in the method for analyzing reliability and sensitivity of uncertainty of distribution parameters of a radome structure according to the exemplary embodiment of the present disclosure, on one hand, for a problem that a conventional method is difficult to implement global reliability and sensitivity analysis of a high-dimensional nonlinear radome structure, the present disclosure combines an SSPDF method, and moves a sampling center of an SSPDF to a design point, so that more extracted sample points fall into a failure domain, and a built β -sphere is used to truncate sample points falling into a security domain within the sphere, thereby constructing an stipdf method, and a proxy model of an AK-stipdf proxy model of the radome structure is built based on the stipdf, thereby avoiding repeatedly calling a function when calculating a global reliability and sensitivity index of the distribution parameters, and overcoming a problem of huge calculation amount in an index solving process to a certain extent; on the other hand, the traditional product formula is applied to a structural model with subjective parameter uncertainty, nested expectation and variance in the overall reliability sensitivity index of the distributed parameters are solved efficiently, and an AKS-CF method is further established to solve the parameter reliability sensitivity index of the radome structure efficiently; on the other hand, the radar cover structure is analyzed by the aid of the new algorithm, effectiveness of establishing the Kriging proxy model by the AK-STIPDF method is proved, calculation accuracy of indexes and failure probability can be guaranteed, calculation efficiency of reliability and sensitivity analysis can be improved, and good applicability is shown. In addition, the importance ranking of the parameters is obtained from the calculation results, which can provide guidance for reducing the failure probability of the structure and simplifying the analysis and design process.

The disclosed example embodiment also provides a distributed parameter uncertainty reliability sensitivity analysis device of the radome structure. Specifically, referring to fig. 8, the apparatus for analyzing reliability and sensitivity of a radome structure may include an adaptive kriging proxy model building module 810, a main sensitivity calculating module 820, a condition expectation value calculating module 830, and a reliability and sensitivity analyzing module 840. Wherein:

the adaptive kriging agent model building module 810 may be configured to build a first initial training sample set according to the original distribution parameters of the real radome structure model, and build an adaptive kriging agent model based on the first initial training sample set;

a main sensitivity calculation module 820, configured to calculate a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to an adaptive kriging proxy model, and calculate a main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value;

the conditional expected value calculation module 830 may be configured to calculate a second conditional variance value of the output failure probability according to the adaptive kriging agent model, and calculate a conditional expected value of the output failure probability according to the second conditional variance value;

the reliability sensitivity analysis module 840 may be configured to calculate a total sensitivity of the real radome structure model according to the second conditional variance value and the conditional expectation value, and analyze the sensitivity of the real radome structure model according to the main sensitivity and the total sensitivity.

In an exemplary embodiment of the present disclosure, constructing a first initial training sample set according to original distribution parameters of a real radome structure model includes: acquiring original distribution parameters of a real radome structure model, and sampling the original input variables by using a first target proxy important sampling probability density function to obtain a plurality of sampling results; constructing a first sample pool according to the plurality of sampling results, and randomly extracting a plurality of first original sample points from the first sample pool; calculating a first distance between the first original sample point and an origin of the real radome structure model, and selecting a plurality of first target sample points from the first original sample points according to the first distance; and calculating a first buckling response value of each first target sample point through an original model function of the real radome structure model, and constructing the first initial training sample set according to the first buckling response value.

In an exemplary embodiment of the present disclosure, sampling the original input variable by using a first target proxy significant sampling probability density function to obtain a plurality of sampling results, including: determining a first original proxy sampling probability density function of the real radome structure model according to a selection principle of the proxy sampling probability density function; in an independent standard normal space, calculating a design point and a reliability index of the real radome structure model by using an improved first-order and second-order moment method; translating the first original proxy sampling probability density function to the design point from the sampling center to obtain a first target proxy important sampling probability density function; and sampling the original input variable by using a first target proxy important sampling probability density function to obtain a plurality of sampling results.

In an exemplary embodiment of the present disclosure, constructing an adaptive kriging proxy model based on a first initial training sample set includes: constructing a target function according to an original model function of the real radome structure model and a preset failure condition, and constructing the initial kriging proxy model according to the target function and the first initial training sample set; calculating a U learning function value of the sampling result included in the first sample pool by using the initial kriging proxy model, and selecting a sample point to be updated from the sampling result in the first sample pool according to the U learning function value; and when the U learning function value of the sample point to be updated is determined to be larger than or equal to a preset threshold value, taking the initial kriging proxy model as an adaptive kriging proxy model.

In an exemplary embodiment of the present disclosure, calculating a total variance value of the output failure probability of the real radar cover structure model according to an adaptive kriging proxy model includes: calculating a first multi-dimensional distribution parameter variable of the original distribution parameter under an independent standard normal space, and calculating a first variable integral point and a first weight value of the first multi-dimensional distribution parameter variable; transforming the independent standard normal space by using the first variable integral point to obtain a first original model space, and selecting a plurality of sampling results from a first sample pool to construct a first input variable sample in the first original model space; calculating a first failure domain indicating function according to the self-adaptive kriging proxy model and a first input variable sample, and calculating a first failure probability integral point of the output failure probability of the real radome structure model according to a first target proxy important sampling probability density function, a first subjective probability density function, a first beta sphere indicating function, a first failure domain indicating function and a first variable integral point of the first input variable sample; and calculating the total variance value of the output failure probability according to the first failure probability integral point and the first weight value.

In an exemplary embodiment of the present disclosure, calculating a first conditional variance value of an output failure probability of the real radar cover structure model according to an adaptive kriging proxy model includes: under the first original model space, calculating a second variable integral point and a second weight value of a second multi-dimensional distribution parameter variable included in the first original model space, and transforming the second variable integral point to the first original model space to obtain a second original model space; determining a second original proxy sampling probability density function in the second original model space, and determining a second target proxy important sampling probability density function according to the second original proxy sampling probability density function; extracting a second input variable sample from the first sample pool based on a second target proxy important sampling probability density function, and calculating a second failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model; calculating a difference value between the first multi-dimensional distribution parameter variable and the second multi-dimensional distribution parameter variable to obtain a third multi-dimensional distribution parameter variable, and transforming a third variable integral point of the third multi-dimensional distribution parameter variable to a second original model space to obtain a third original model space; calculating a second failure probability integral point of the output failure probability of the real radome structure model according to a second input variable sample, a second subjective probability density function of the second input variable sample, a second beta sphere indicating function, a second failure domain indicating function and a third variable integral point in the third original model space; and calculating a first condition expected value of the output failure probability according to the second failure probability integral point, and calculating a first condition variance value of the output failure probability according to the first condition expected value and a third weight value.

In an exemplary embodiment of the disclosure, calculating the second conditional variance value of the output failure probability according to an adaptive kriging agent model includes: calculating a fourth variable integral point and a fourth weight value of a third multi-dimensional distribution parameter variable, and transforming the fourth variable integral point to an independent standard normal space to obtain a fourth original model space; determining a third original proxy sampling probability density function under the fourth original model space, and determining a third target proxy important sampling probability density function according to the third original proxy sampling probability density function; extracting a third input variable sample from the first sample pool based on a third target proxy important sampling probability density function, and calculating a third failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model; converting a second variable integral point of a second multidimensional distribution parameter variable into an independent standard normal space to obtain a fifth original model space, and calculating a third failure probability integral point of the output failure probability according to a third input variable sample and a third subjective probability density function, a third beta sphere indicating function, a third failure domain indicating function and a second variable integral point of the third variable input sample in the fifth original model space; and calculating a second conditional variance value of the output failure probability according to the third failure probability integration point and a second weight value of the second multi-dimensional distribution parameter variable.

In an exemplary embodiment of the disclosure, calculating the conditional expectation value of the output failure probability according to the second conditional variance value includes: and calculating the condition expectation value of the output failure probability according to the second condition variance value and a second weight value of a second multi-dimensional distribution parameter variable.

In an exemplary embodiment of the present disclosure, the distributed parameter uncertainty reliability sensitivity analysis apparatus of a radome structure further includes:

the output failure probability calculation module can be used for acquiring a subjective probability density function of original distribution parameters and an original failure domain indication function of a real radome structure model, and calculating the output failure probability of the real radome structure model according to the subjective probability density function and the original failure domain indication function.

In an exemplary embodiment of the present disclosure, the main sensitivity is used to measure the contribution of any original distribution parameter to the total variance value of the output failure probability under the action of itself; the total sensitivity is used for measuring the contribution degree of the independent action of any original distribution parameter and the interaction with other distribution parameters to the total variance value of the output failure probability.

The details of each module in the reliability sensitivity analysis apparatus for a radome structure are described in detail in the sensitivity method for a corresponding radome structure, and therefore are not described herein again.

It should be noted that although in the above detailed description several modules or units of the device for action execution are mentioned, such a division is not mandatory. Indeed, the features and functionality of two or more modules or units described above may be embodied in one module or unit, according to embodiments of the present disclosure. Conversely, the features and functions of one module or unit described above may be further divided into embodiments by a plurality of modules or units. Moreover, although the steps of the methods of the present disclosure are depicted in the drawings in a particular order, this does not require or imply that the steps must be performed in this particular order, or that all of the depicted steps must be performed, to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken into multiple step executions, etc.

In an exemplary embodiment of the present disclosure, an electronic device capable of implementing the above method is also provided.

As will be appreciated by one skilled in the art, aspects of the present disclosure may be embodied as a system, method or program product. Accordingly, various aspects of the present disclosure may be embodied in the form of: an entirely hardware embodiment, an entirely software embodiment (including firmware, microcode, etc.) or an embodiment combining hardware and software aspects that may all generally be referred to herein as a "circuit," module "or" system.

An electronic device 900 according to this embodiment of the disclosure is described below with reference to fig. 9. The electronic device 900 shown in fig. 9 is only an example and should not bring any limitations to the functionality or scope of use of the embodiments of the present disclosure.

As shown in fig. 9, the electronic device 900 is embodied in the form of a general purpose computing device. Components of electronic device 900 may include, but are not limited to: the at least one processing unit 910, the at least one storage unit 920, a bus 930 connecting different system components (including the storage unit 920 and the processing unit 910), and a display unit 940.

Wherein the storage unit stores program code that is executable by the processing unit 910 to cause the processing unit 910 to perform steps according to various exemplary embodiments of the present disclosure described in the above section "exemplary method" of the present specification. For example, the processing unit 910 may execute step S110 as shown in fig. 1: constructing a first initial training sample set according to original distribution parameters of a real radome structure model, and constructing an adaptive kriging agent model based on the first initial training sample set; step S120: calculating a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to the self-adaptive kriging agent model, and calculating the main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value; step S130: calculating a second conditional variance value of the output failure probability according to the self-adaptive kriging agent model, and calculating a conditional expected value of the output failure probability according to the second conditional variance value; step S140 calculates a total sensitivity of the real radome structure model according to the second conditional variance value and the conditional expectation value, and analyzes the sensitivity of the real radome structure model according to the main sensitivity and the total sensitivity.

The storage unit 920 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 9201 and/or a cache memory unit 9202, and may further include a read only memory unit (ROM) 9203.

Storage unit 920 may also include a program/utility 9204 having a set (at least one) of program modules 9205, such program modules 9205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which, or some combination thereof, may comprise an implementation of a network environment.

Bus 930 can be any of several types of bus structures including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

The electronic device 900 may also communicate with one or more external devices 1000 (e.g., keyboard, pointing device, bluetooth device, etc.), with one or more devices that enable a user to interact with the electronic device 900, and/or with any devices (e.g., router, modem, etc.) that enable the electronic device 900 to communicate with one or more other computing devices. Such communication may occur via input/output (I/O) interfaces 950. Also, the electronic device 900 may communicate with one or more networks (e.g., a Local Area Network (LAN), a Wide Area Network (WAN) and/or a public network, such as the Internet) via the network adapter 960. As shown, the network adapter 960 communicates with the other modules of the electronic device 900 via the bus 930. It should be appreciated that although not shown in the figures, other hardware and/or software modules may be used in conjunction with the electronic device 900, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, among others.

Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein may be implemented by software, or by software in combination with necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure may be embodied in the form of a software product, which may be stored in a non-volatile storage medium (which may be a CD-ROM, a usb disk, a removable hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which may be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the embodiments of the present disclosure.

In an exemplary embodiment of the present disclosure, there is also provided a computer-readable storage medium having stored thereon a program product capable of implementing the above-described method of the present specification. In some possible embodiments, various aspects of the disclosure may also be implemented in the form of a program product comprising program code for causing a terminal device to perform the steps according to various exemplary embodiments of the disclosure described in the "exemplary methods" section above of this specification, when the program product is run on the terminal device.

According to the program product for implementing the above method of the embodiments of the present disclosure, it may employ a portable compact disc read only memory (CD-ROM) and include program codes, and may be run on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto, and in this document, a readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

The program product may employ any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the readable storage medium include: an electrical connection having one or more wires, a portable disk, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

A computer readable signal medium may include a propagated data signal with readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A readable signal medium may also be any readable medium that is not a readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

Program code embodied on a readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

Program code for carrying out operations for the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, C + + or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computing device, partly on the user's device, as a stand-alone software package, partly on the user's computing device and partly on a remote computing device, or entirely on the remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any kind of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computing device (e.g., through the internet using an internet service provider).

Furthermore, the above-described drawings are merely schematic illustrations of processes involved in methods according to exemplary embodiments of the present disclosure, and are not intended to be limiting. It will be readily understood that the processes shown in the above figures are not intended to indicate or limit the chronological order of the processes. In addition, it is also readily understood that these processes may be performed synchronously or asynchronously, e.g., in multiple modules.

Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.

Claims (10)

1. A method for analyzing reliability and sensitivity of uncertainty of distributed parameters of a radome structure is characterized by comprising the following steps:

constructing a first initial training sample set according to original distribution parameters of a real radome structure model, and constructing an adaptive kriging agent model based on the first initial training sample set;

calculating a total variance value and a first conditional variance value of the output failure probability of the real radome structure model according to the self-adaptive kriging agent model, and calculating the main sensitivity of the real radome structure model according to the total variance value and the first conditional variance value;

calculating a second conditional variance value of the output failure probability according to the self-adaptive kriging agent model, and calculating a conditional expected value of the output failure probability according to the second conditional variance value;

and calculating the total sensitivity of the real radome structure model according to the second condition variance value and the condition expected value, and analyzing the sensitivity of the real radome structure model according to the main sensitivity and the total sensitivity.

2. The method of claim 1, wherein constructing a first initial training sample set from the original distribution parameters of the real radome structure model comprises:

acquiring original distribution parameters of a real radome structure model, and sampling the original input variables by using a first target proxy important sampling probability density function to obtain a plurality of sampling results;

constructing a first sample pool according to the plurality of sampling results, and randomly extracting a plurality of first original sample points from the first sample pool;

calculating a first distance between the first original sample point and an origin of the real radome structure model, and selecting a plurality of first target sample points from the first original sample points according to the first distance;

and calculating a first buckling response value of each first target sample point through an original model function of the real radome structure model, and constructing the first initial training sample set according to the first buckling response value.

3. The radome structure distributed parameter uncertainty reliability sensitivity analysis method of claim 2 wherein sampling the raw input variables using a first target agent significant sampling probability density function to obtain a plurality of sampling results comprises:

determining a first original proxy sampling probability density function of the real radome structure model according to a selection principle of the proxy sampling probability density function;

in an independent standard normal space, calculating a design point and a reliability index of the real radome structure model by using an improved first-order and second-order moment method;

translating the first original proxy sampling probability density function from a sampling center to the design point to obtain a first target proxy important sampling probability density function;

and sampling the original input variable by using a first target proxy important sampling probability density function to obtain a plurality of sampling results.

4. The method of claim 1, wherein constructing an adaptive kriging proxy model based on a first initial training sample set comprises:

constructing a target function according to an original model function of the real radome structure model and a preset failure condition, and constructing the initial kriging proxy model according to the target function and the first initial training sample set;

calculating a U learning function value of the sampling result included in the first sample pool by using the initial kriging proxy model, and selecting a sample point to be updated from the sampling result in the first sample pool according to the U learning function value;

and when the U learning function value of the sample point to be updated is determined to be larger than or equal to a preset threshold value, taking the initial kriging agent model as an adaptive kriging agent model.

5. The method of claim 1, wherein calculating a total variance value of the output failure probability of the real radome structure model according to an adaptive kriging proxy model comprises:

calculating a first multi-dimensional distribution parameter variable of the original distribution parameter under an independent standard normal space, and calculating a first variable integral point and a first weight value of the first multi-dimensional distribution parameter variable;

transforming the independent standard normal space by using the first variable integral point to obtain a first original model space, and selecting a plurality of sampling results from a first sample pool to construct a first input variable sample in the first original model space;

calculating a first failure domain indicating function according to the self-adaptive kriging proxy model and a first input variable sample, and calculating a first failure probability integral point of the output failure probability of the real radome structure model according to a first target proxy important sampling probability density function, a first subjective probability density function, a first beta sphere indicating function, a first failure domain indicating function and a first variable integral point of the first input variable sample;

and calculating the total variance value of the output failure probability according to the first failure probability integral point and the first weight value.

6. The method of claim 1, wherein calculating a first conditional variance value of an output failure probability of the true radome structure model from an adaptive kriging proxy model comprises:

under the first original model space, calculating a second variable integral point and a second weight value of a second multi-dimensional distribution parameter variable included in the first original model space, and transforming the second variable integral point to the first original model space to obtain a second original model space;

determining a second original proxy sampling probability density function in the second original model space, and determining a second target proxy important sampling probability density function according to the second original proxy sampling probability density function;

extracting a second input variable sample from the first sample pool based on a second target proxy important sampling probability density function, and calculating a second failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model;

calculating a difference value between the first multi-dimensional distribution parameter variable and the second multi-dimensional distribution parameter variable to obtain a third multi-dimensional distribution parameter variable, and transforming a third variable integral point of the third multi-dimensional distribution parameter variable to a second original model space to obtain a third original model space;

calculating a second failure probability integral point of the output failure probability of the real radome structure model according to a second input variable sample, a second subjective probability density function of the second input variable sample, a second beta sphere indicating function, a second failure domain indicating function and a third variable integral point in the third original model space;

and calculating a first condition expected value of the output failure probability according to the second failure probability integral point, and calculating a first condition variance value of the output failure probability according to the first condition expected value and a third weight value.

7. The method of claim 1, wherein calculating a second conditional variance value of the output failure probability based on an adaptive kriging proxy model comprises:

calculating a fourth variable integral point and a fourth weight value of a third multidimensional distribution parameter variable, and transforming the fourth variable integral point to an independent standard normal space to obtain a fourth original model space;

determining a third original proxy sampling probability density function under the fourth original model space, and determining a third target proxy important sampling probability density function according to the third original proxy sampling probability density function;

extracting a third input variable sample from the first sample pool based on a third target proxy important sampling probability density function, and calculating a third failure domain indication function according to the second input variable sample and the self-adaptive kriging proxy model;

converting a second variable integral point of a second multidimensional distribution parameter variable into an independent standard normal space to obtain a fifth original model space, and calculating a third failure probability integral point of the output failure probability according to a third input variable sample and a third subjective probability density function, a third beta sphere indicating function, a third failure domain indicating function and a second variable integral point of the third variable input sample in the fifth original model space;

and calculating a second conditional variance value of the output failure probability according to the third failure probability integration point and a second weight value of the second multi-dimensional distribution parameter variable.

8. The method of claim 1, wherein calculating the conditional expectation value for the output failure probability based on a second conditional variance value comprises:

and calculating the condition expectation value of the output failure probability according to the second condition variance value and a second weight value of a second multi-dimensional distribution parameter variable.

9. The method of claim 1, further comprising:

the method comprises the steps of obtaining a subjective probability density function of original distribution parameters and an original failure domain indicating function of a real radome structure model, and calculating the output failure probability of the real radome structure model according to the subjective probability density function and the original failure domain indicating function.

10. The method for analyzing reliability of distributed parameters of a radome structure of any one of claims 1-9, wherein the main sensitivity is used for measuring the contribution of any original distributed parameter to the total variance value of the output failure probability under the action of the original distributed parameter alone; the total sensitivity is used for measuring the contribution degree of the independent action of any original distribution parameter and the interaction with other distribution parameters to the total variance value of the output failure probability.

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