CN109885879B - Method, system, device and medium for measuring integrated interference type reliability - Google Patents

Abstract

The invention relates to a measurement method, system, device and medium of set interference type reliability. The method includes establishing a convex set model describing structural uncertainty, and dividing the convex set model into an interval model and a hyperellipsoid model; The interval model and the hyperellipsoid model are standardized to obtain the standardized interval model and the unit hypersphere model, and the standardized limit state equation is obtained according to the standardized interval model and the unit hypersphere model; according to the standardized limit state equation, the standardized interval model and the hypersphere model are respectively Uniform sampling is carried out to obtain interval model samples and hypersphere model samples; composite samples are obtained according to interval model samples and hypersphere model samples, and ensemble interference reliability is calculated according to the standardized limit state equation and composite samples. The sampling method of the invention is rigorous, effective, simple and practical, has strong operability, and effectively improves the measurement efficiency and precision of the interference reliability of a large complex structure set.

Description

A measurement method, system, device and medium for collective interference type reliability

Technical Field

The present invention relates to the field of structural reliability measurement, and in particular to a measurement method, system, device and medium for collective interference type reliability.

Background Art

In the reliability analysis and design of structures, many uncertainties are generated due to the complexity of the structural system itself and the limitations of people's cognition. These uncertainties often play a vital role in the performance and response of the structure, so it is necessary to reasonably and quantitatively deal with these uncertainties. The traditional description of these uncertainties is based on probability theory, but due to the limitations of probability theory, non-probabilistic reliability theory has been developed in recent years. The mathematical basis of non-probabilistic reliability theory is the convex set model.

At present, there are also a lot of studies on measuring the reliability of structures based on non-probabilistic reliability theory. The scope of each parameter combination in the convex set model is called the basic variable domain, and the basic variable domain has the situation of safety domain and failure domain. Among them, when the failure domain and the safety domain have an intersection, the reliability of the structure is called the set interference reliability. When the failure domain and the safety domain do not have an intersection, the reliability of the structure is called the set extension reliability.

The measurement of the collective interference reliability is based on the non-probabilistic collective interference model. Measuring the collective interference reliability based on the non-probabilistic collective interference model is to measure the reliability of the structure through the interference degree between the basic variable domain and the safety domain of the structure, that is, the ratio of the volume of the structural safety domain to the total volume of the basic variable domain is used as the structural collective interference reliability. The larger the ratio of this volume, the greater the reliability. The distinction between the safety domain and the failure domain is often determined by the limit state function. The limit state equation can divide the structural uncertainty variable space into two parts: the safety domain and the failure domain.

However, for large and complex structures, since their limit state functions involve many variables and are highly complex, it is often not feasible to solve their reliability using analytical methods. Therefore, it is necessary to use computer tools to seek simulation solutions.

For the reliability of set interference, the key and core of simulation solution is to realize uniform sampling of convex set model. According to existing literature, the sampling method for arbitrary-dimensional (hyper)ellipsoidal convex sets is often realized by uniform sampling of spherical coordinates. However, this method implies theoretical errors. After the uniformly distributed samples in the spherical coordinate system are transformed into the orthogonal coordinate system, they no longer obey the uniform distribution. The reliability simulation calculation results based on this method are bound to be distorted and unreliable.

Therefore, it is necessary to propose a new sampling method to establish a non-probabilistic collective interference model and achieve accurate measurement of collective interference reliability.

Summary of the invention

The technical problem to be solved by the present invention is to provide a method, system, device and medium for measuring the reliability of a collective interference type in view of the deficiencies of the above-mentioned prior art.

The technical solution of the present invention to solve the above technical problems is as follows:

A method for measuring collective interference reliability comprises the following steps:

Step 1: Establish a convex set model that describes structural uncertainty, and divide the convex set model into an interval model and a hyperellipsoid model;

Step 2: performing standardized transformation on the interval model and the hyper-ellipsoid model respectively to obtain a standardized interval model and a unit hyper-sphere model, and obtaining a standardized limit state equation according to the standardized interval model and the unit hyper-sphere model;

Step 3: uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized limit state equation to obtain interval model samples and hypersphere model samples respectively;

Step 4: Obtain a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculate the collective interference reliability of the structure according to the standardized limit state equation and the composite sample.

The beneficial effects of the present invention are as follows: firstly, a non-probabilistic model capable of describing structural uncertainty, namely a convex set model, is established, and the convex set model is divided into an interval model and a hyperellipsoid model, which can be convenient for describing the structural uncertainty of the coexistence of hyperellipsoid variables and interval variables; since the ratio of the volume of the structural safety domain to the total volume of the basic variable domain is used as the structural set interference type reliability in the set interference model, the standardized limit state equation is obtained by performing standardized transformation on the interval model and the hyperellipsoid model respectively, which is convenient for subsequent uniform sampling according to the standardized limit state equation to obtain a composite sample, thereby facilitating the acquisition of the ratio of the volume of the safety domain to the total volume of the basic variable domain, and providing a data basis for the subsequent measurement of the set interference reliability. It is convenient for efficient and accurate measurement of collective interference reliability; the measurement method of the present invention is rigorous in theory, and on the basis of the standardized limit state equation, it ensures the uniform distribution of sampling samples of arbitrary-dimensional (super) ellipsoid convex sets, overcomes the theoretical defects of traditional sampling methods, ensures the accuracy and credibility of reliability simulation results, and effectively solves the measurement problem of collective interference reliability containing (super) ellipsoid convex set models. It is suitable for convex set models in different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of reliability calculation results are guaranteed. The method is simple and practical, with strong operability, and effectively improves the calculation efficiency and accuracy of collective interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

On the basis of the above technical solution, the present invention can also be improved as follows:

Further: Step 1 specifically includes the following steps:

Step 11: establishing the original limit state equation of the structure according to the uncertain parameter variables of the structure, and obtaining the convex set model according to the original limit state equation;

The original limit state equation is:

M=G(X)=G(x ₁ ,x ₂ ,...,x _n )=0;

Wherein, M is the original limit state equation, G(X) is the original limit state function, X=(x ₁ ,x ₂ ,...,x _n ) is the uncertainty parameter variable, and n is the total number of the uncertainty parameter variables;

Step 12: Divide the convex set model into a p-dimensional interval model and m super-ellipsoid models;

The interval model is: _Xi = ( _x1 , _x2 , ..., _xp );

Wherein, _Xi is the interval variable of the interval model of p dimension, _x1 , _x2 ... _xp are all interval uncertainty parameter variables;

The hyperellipsoid model is:

为第i个所述超椭球模型的中心点向量，Ω_i为第i个正定矩阵，θ_i为第i个所述超椭球模型的尺度参数。Wherein, _Xi is the super-ellipsoid variable of the i-th super-ellipsoid model, _Ei ( _Xi , _θi ) is the set of the i-th super-ellipsoid variables,

is the center point vector of the i-th super-ellipsoid model, Ω _i is the i-th positive definite matrix, and θ _i is the scale parameter of the i-th super-ellipsoid model.

The beneficial effect of the above further scheme is: in order to obtain the basic variable domain and safety domain of the structure, when establishing the convex set model, the uncertainty parameter variables of the structure are first determined, and the original limit state equation of the convex set model is established based on the uncertainty parameter variables. Due to the differences in complex structures, the types of convex set models established for different structures will also be different, usually including interval models composed of interval variables, which are uniform box convex models, and also include multiple hyperellipsoid models composed of hyperellipsoid variables. Therefore, the convex set model is divided into interval model and hyperellipsoid model, which is convenient for measuring the collective interference reliability of different structures, can be applied to uncertainty measurement of different types of structures, and has a wide range of applications.

Further: Step 2 specifically includes the following steps:

Step 21: transform the interval variable according to the interval standardization transformation formula to obtain a standardized interval model;

The interval standardization transformation formula is:

为所述区间变量X_I的中心值向量，ΔX_I为所述区间变量X_I的离差向量，δ_I为p维的标准化区间变量且δ_I∈[-1,1]^p；in,

is the center value vector of the interval variable _Xi , _ΔXi is the deviation vector of the interval variable _Xi , _δI is a p-dimensional standardized interval variable and _δI∈ [-1,1] ^p ;

Step 22: transforming the m hyper-ellipsoid models according to the hyper-ellipsoid standardization transformation formula to obtain m unit hyper-sphere models;

The hyperellipsoid normalization transformation formula is:

The unit hypersphere model is: Δu _i ∈{Δu _i :Δu _i ^T Δu _i ≤1}, (i=1, 2, …, m);

为第i个所述正交矩阵的转置矩阵，D_i为第i个对角矩阵，Δu_i为第i个所述单位超球体模型的标准化超球体变量，Δu_i ^T为第i个所述标准化超球体变量的转置向量，u_i为第i个所述单位超球体模型的引入向量，

为第i个所述单位超球体模型的中心点向量，且

I_i为第i个单位矩阵；Among them, _Qi is the i-th orthogonal matrix,

is the transposed matrix of the i-th orthogonal matrix, _Di is the i-th diagonal matrix, _Δui is the standardized hypersphere variable of the i-th unit hypersphere model, _Δui ^T is the transposed vector of the i-th standardized hypersphere variable, _ui is the introduction vector of the i-th unit hypersphere model,

is the center point vector of the i-th unit hypersphere model, and

I _i is the i-th identity matrix;

Step 23: obtaining the standardized limit state equation according to the original limit state equation, the standardized interval model and the unit hypersphere model;

The normalized limit state equation is:

M′=G′(δ)=G′(δ ₁ ,Δu ₁ ,Δu ₂ ,…, _Δum )=0;

Wherein, M′ is the standardized limit state equation, δ is a standardized variable and δ=(δ ₁ , Δu ₁ , Δu ₂ , …, _Δum ), G′(δ) is a standardized limit state function, and Δu ₁ , Δu ₂ … _Δum are all the standardized hypersphere variables.

The beneficial effects of the above further scheme are: the standardized transformation is to introduce new variables, transform the interval variable vector into an equivalent standardized interval variable, transform each hyperellipsoid model into an equivalent unit hypersphere model, and then define the reliability index of the structure in the new variable space; the present invention transforms the interval variable into a standardized interval variable through the interval standardized transformation formula, and transforms the hyperellipsoid model into a unit hypersphere model through the hyperellipsoid standardized transformation formula, so as to facilitate the acquisition of the standardized limit state equation of the entire convex set model, and the "critical state" of the failure domain and the safety domain can be obtained according to the standardized limit state equation, so as to facilitate the acquisition of a more accurate ratio of the volume of the safety domain to the total volume of the basic variable domain;

Based on the analysis of the standardized interval variable vector, when the standardized interval variable is multidimensional, the multidimensional interval domain formed by the multidimensional standardized interval variables is called a hypercube. The hypercube is divided into a safety domain and a failure domain by the standardized limit state equation. Therefore, the reliability of the standardized interval variable is the ratio of the hypervolume of the safety domain to the total volume of the hypercube. Similarly, based on the analysis of the unit hypersphere model, the reliability of the unit hypersphere model is the ratio of the hypervolume of the safety domain to the total volume of the unit hypersphere model.

The present invention obtains a standardized interval model and a unit hypersphere model through standardized transformation, which is convenient for obtaining the standardized limit state equation of the entire convex set model, thereby facilitating subsequent uniform sampling of the standardized interval model and the unit hypersphere model according to the standardized limit state equation, and laying a theoretical foundation for measuring the collective interference type reliability by obtaining the ratio of the volume of the safety domain to the total volume of the basic variable domain based on the composite samples obtained after merging the uniform sampling. The obtained collective interference type reliability is more accurate and efficient.

Further: In step 3, the specific steps of obtaining the interval model sample include:

Step 31: Obtain a first random number of the standardized interval model within a first preset sampling range, and uniformly sample the standardized interval model according to the first random number and the standardized limit state equation to obtain the interval model sample.

The beneficial effect of the above further scheme is that: since the probability of the standardized interval variable taking each value within the interval is the same, the p-dimensional standardized interval variable in the present invention obeys a uniform distribution within the first preset sampling range, and therefore obtaining the first random number of the p-dimensional standardized interval variable within the first preset sampling range can achieve uniform sampling of the standardized interval variable, thereby facilitating the improvement of the accuracy of the subsequent measurement set interference reliability;

Among them, for obtaining the first random number, for example, the rand command can be used in MATLAB to extract the first random number of the standardized interval variable within [0,1] ^p (the first preset sampling range). Due to the relationship between the first preset sampling range and the range of the aforementioned standardized interval variable δ ₁ , the standardized interval variable can be converted to: δ ₁ =2δ _Δ -1 and δ _Δ ∈[0,1] ^p , thereby realizing the extraction of samples of the standardized interval variable δ ₁ .

Further: In step 3, the specific steps of obtaining the hypersphere model sample include:

Step 32: obtaining a radial probability density function of a radial distance component of the unit hypersphere model in the spherical coordinate system, obtaining a second random number of an elevation component of the unit hypersphere model in the spherical coordinate system within a second preset sampling range, and obtaining a third random number of an azimuth component of the unit hypersphere model in the spherical coordinate system within a third preset sampling range;

Step 33: uniformly sampling the elevation component according to the second random number to obtain elevation component samples; uniformly sampling the azimuth component according to the third random number to obtain azimuth component samples; and based on the Metropolis sampling method, sampling the radial distance component according to the radial probability density function to obtain radial distance component samples;

Step 34: obtaining an initial hypersphere model sample of the unit hypersphere model in the spherical coordinate system according to the elevation component sample, the azimuth component sample and the radial distance component sample;

Step 35: transforming the initial hypersphere model sample according to the transformation formula between the spherical coordinate system and the orthogonal coordinate system to obtain the hypersphere model sample of the unit hypersphere model in the orthogonal coordinate system;

The conversion formula between the spherical coordinate system and the orthogonal coordinate system is:

为第i个所述单位超球体模型在所述正交坐标系下的第n_i-1维坐标分量，

为第i个所述单位超球体模型在所述正交坐标系下的第n_i维坐标分量，r_i为第i个所述单位超球体模型在所述球坐标系下的所述径向距离分量，

均为第i个所述单位超球体模型在所述球坐标系下的所述仰角分量，

为第i个所述单位超球体模型在所述球坐标系下的所述方向角分量，且

Wherein, _ni is the dimension of the i-th unit hypersphere model, Δui _,1 is the first-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system, _Δui,2 is the second-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system,

is the n _i -1 th dimensional coordinate component of the i th unit hypersphere model in the orthogonal coordinate system,

is the n _{i -th} dimensional coordinate component of the i -th unit hypersphere model in the orthogonal coordinate system, _ri is the radial distance component of the i -th unit hypersphere model in the spherical coordinate system,

are the elevation angle components of the i-th unit hypersphere model in the spherical coordinate system,

is the direction angle component of the i-th unit hypersphere model in the spherical coordinate system, and

Among them, for the omitted part of the formula in the conversion formula between the spherical coordinate system and the orthogonal coordinate system, when 2≤h≤ni _- 1, the omitted part of the formula is Δui _,h = _{ri sinβ1 sinβ2} …sinβh _{-1 cosβh} , Δui _,h is the h-th dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system.

The beneficial effect of the above further scheme is: since the sampling method for the arbitrary-dimensional unit hypersphere model is often implemented by uniform sampling of spherical coordinates, when the uniformly distributed samples in the spherical coordinate system are transformed into the orthogonal coordinate system, they no longer obey the uniform distribution, resulting in distortion and unreliability of the reliability measurement result; among which, the most important factor is the radial distance component in the spherical coordinate system. Therefore, in order to ensure that the samples in the spherical coordinate system obey the uniform distribution after being transformed into the orthogonal coordinate system, the radial probability density function of the radial distance component can be obtained, and then the radial distance component can be sampled based on the Metropolis sampling method, so that Monte Carlo samples (Monte Carlo samples) that obey the radial probability density function can be obtained, that is, radial distance component samples;

The remaining components in the spherical coordinate system, namely the elevation angle component and the azimuth angle component, are respectively obtained according to a sampling method similar to the standardized interval variable, and the corresponding second random number and the third random number are respectively uniformly sampled. Finally, the coordinate transformation can ensure that the hypersphere model samples of the unit hypersphere model that conform to the uniform distribution are obtained, so as to facilitate the improvement of the accuracy of the subsequent measurement set interference reliability.

的样本抽取可先在MATLAB中采用rand命令抽取区间[0,1]的随机数再乘以π得到；方向角分量

的样本抽取，可先在MATLAB中采用rand命令抽取区间[0,1]的随机数再乘以2π得到。Among them, for the sampling of the elevation angle component and the azimuth angle component, for example, the elevation angle component

The sample extraction can be done by first using the rand command in MATLAB to extract a random number in the interval [0,1] and then multiplying it by π; the angular component

To extract samples, you can first use the rand command in MATLAB to extract a random number in the interval [0,1] and then multiply it by 2π.

Further: In step 32, the specific steps of obtaining the radial probability density function include:

Step 321: Calculate the volume and surface area of the unit hypersphere model in the spherical coordinate system respectively;

The volume is:

为n_i维的所述单位超球体模型的所述体积，R_i为n_i维的所述单位超球体模型的半径；in,

is the volume of the n _i -dimensional unit hypersphere model, and R _i is the radius of the n _i -dimensional unit hypersphere model;

当n_i为奇数时，

为给定常数，且

Γ(·) is the gamma function, and when n _i is an even number,

When n _i is an odd number,

is a given constant, and

The surface area is:

为所述单位超球体模型的n_i-1维球面的所述表面积；in,

is the surface area of the n _i -1 dimensional sphere of the unit hypersphere model;

Step 322: Obtain the radial probability density function according to the volume and the surface area;

The radial probability density function is:

Wherein, f( _ri ) is the radial probability density function of the i-th unit hypersphere model.

The beneficial effect of the above further scheme is that the radial probability density function can be used with the help of advanced mathematical knowledge to first obtain the volume and surface area of the unit hypersphere model respectively, and then take two hypertoroidal microelements at the radial distance components of r ₁ and r ₂ in the n _i -dimensional unit hypersphere model. The radial thicknesses of the two hypertoroidal microelements in the spherical coordinate system are dr ₁ and dr ₂ respectively, and the corresponding hypertoroidal microelement volumes are:

In order to ensure that the hypertoroidal element obtains uniformly distributed samples in the orthogonal coordinate system, the number of samples must be proportional to the volume of the hypertoroidal element. In other words, the probability accumulation of _ri at the micro-distances dr ₁ and dr ₂ is proportional to the volume of the hypertoroidal element, so:

The radial probability density function is obtained as follows:

Through the radial probability density function, it is convenient to sample the radial distance component, so as to ensure that the hypersphere model samples of the unit hypersphere model obey uniform distribution in the orthogonal coordinate system are obtained.

Further: in step 33, the specific steps of obtaining the radial distance component sample include:

Step 331: setting the initial value, candidate value and number of iterations in the Metropolis sampling method according to the radial probability density function, calculating the transition probability according to the initial value, the candidate value, the number of iterations and the radial probability density function, and determining the Markov chain for uniform sampling of the hyperellipsoid model according to the transition probability;

Step 332: Determine a fourth random number of the radial distance component within a fourth preset sampling range according to the Markov chain, and sample the radial coordinate component according to the fourth random number to obtain the initial hypersphere model sample.

The beneficial effects of the above further solution are: by using the above Metropolis sampling method, it is ensured that radial distance component samples that obey the radial probability density function are obtained;

For example: at t=0, select an initial value r ₀ , and f(r ₀ )≥0; at the t+1 iteration, extract a candidate value r ^c through the proposed distribution q(r _i |r _t ), and the proposed distribution is a symmetric type, such as a normal distribution or an interval uniform distribution; and set α=min[f(r ^c )/f(r _t ),1], and the transition probability of α satisfies r _t+1 =r ^c , and the transition probability of 1-α satisfies r _t+1 =r _t ; through the above sampling, a Markov chain with a probability distribution of f(r _i ) can be obtained, and the fourth random number of f(r _i ) can be obtained.

Further: In step 4, the specific steps of calculating the collective interference type reliability of the structure are:

Calculating the collective interference type reliability according to the standardized limit state equation, the composite sample and the collective interference type reliability calculation formula;

The collective interference reliability calculation formula is:

Wherein, R _set is the set interferometric reliability, q _all is the total number of sample points in the composite sample, and q _s is the number of sample points in the composite sample that satisfy G′(δ)＞0.

The beneficial effect of the above further scheme is that the total number of sample points in the composite sample can be equivalent to the total volume of the basic domain of the structure. According to the standardized limit state equation G′(δ)=0 in step 23, it can be known that the number of sample points in the composite sample that satisfy G′(δ)＞0 can be equivalent to the volume of the safety domain. Therefore, the collective interference reliability calculation formula according to the present invention can efficiently and accurately measure the collective interference reliability of the structure; the sampling technology is supported by rigorous mathematical theory, which ensures the rigor and effectiveness of the sampling, and ensures the accuracy and credibility of the reliability calculation results. The method is simple and practical, with strong operability, which effectively improves the calculation efficiency and accuracy of the collective interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

According to another aspect of the present invention, there is provided a measurement system for collective interferometric reliability, comprising a modeling module, a standardized transformation module, a sampling module and a calculation module;

The modeling module is used to establish a convex set model that describes structural uncertainty, and divide the convex set model into an interval model and a super ellipsoid model;

The standardized transformation module is used to perform standardized transformation on the interval model and the hyper-ellipsoid model respectively to obtain a standardized interval model and a unit hyper-sphere model, and obtain a standardized limit state equation according to the standardized interval model and the unit hyper-sphere model;

The sampling module is used to uniformly sample the standardized interval model and the unit hypersphere model according to the standardized limit state equation to obtain interval model samples and hypersphere model samples respectively;

The calculation module is used to obtain a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculate the collective interference reliability of the structure according to the standardized limit state equation and the composite sample.

The beneficial effects of the present invention are as follows: a convex set model is established through a modeling module, and the convex set model is divided into an interval model and a hyperellipsoid model, which can facilitate the description of the structural uncertainty of the coexistence of hyperellipsoid variables and interval variables; since the ratio of the volume of the structural safety domain to the total volume of the basic variable domain is used as the structural set interference type reliability in the set interference model, the standardized limit state equation is obtained after the interval model and the hyperellipsoid model are respectively standardized and transformed through the standardized transformation module, which is convenient for the subsequent sampling module to perform uniform sampling according to the standardized limit state equation to obtain a composite sample, thereby facilitating the acquisition of the ratio of the volume of the safety domain to the total volume of the basic variable domain, providing a data basis for the subsequent calculation module to measure the set interference reliability, and facilitating the efficient and accurate measurement of the set interference reliability;

The measurement system method of the present invention is rigorous in theory. On the basis of the standardized limit state equation, it ensures the uniform distribution of the sampling samples of the (hyper)ellipsoid convex set of any dimension, overcomes the theoretical defects of the traditional sampling method, ensures the accuracy and credibility of the reliability simulation results, and effectively solves the measurement problem of the set interference reliability of the (hyper)ellipsoid convex set model. It is suitable for convex set models in different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of the reliability calculation results are guaranteed. The method is simple and practical, with strong operability, and effectively improves the calculation efficiency and accuracy of the set interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

According to another aspect of the present invention, another device for measuring collective interference type reliability is provided, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program implements the steps of a method for measuring collective interference type reliability of the present invention when executed.

The beneficial effects of the present invention are: by storing a computer program on a memory and running it on a processor, the device for measuring the collective interference type reliability of the present invention is realized; the method is theoretically rigorous; on the basis of the standardized limit state equation, the uniform distribution of the sampling samples of the (super) ellipsoid convex set of any dimension is guaranteed; the theoretical defects of the traditional sampling method are overcome; the accuracy and credibility of the reliability simulation results are guaranteed; the problem of measuring the collective interference reliability of the (super) ellipsoid convex set model is effectively solved; the convex set model is applicable to different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of the reliability calculation results are guaranteed; the method is simple and practical, and has strong operability; it effectively improves the calculation efficiency and accuracy of the collective interference reliability of large and complex structures, and can be widely applied to the field of structural reliability measurement.

According to another aspect of the present invention, a computer storage medium is provided, wherein the computer storage medium comprises: at least one instruction, and when the instruction is executed, the steps in the method for measuring the reliability of a collective interference type of the present invention are implemented.

The beneficial effects of the present invention are as follows: by executing a computer storage medium containing at least one instruction, the measurement of the collective interference type reliability of the present invention is realized. The method is rigorous in theory. On the basis of the standardized limit state equation, the uniform distribution of the sampling samples of the (super) ellipsoid convex set of any dimension is guaranteed, the theoretical defects of the traditional sampling method are overcome, the accuracy and credibility of the reliability simulation results are guaranteed, and the measurement problem of the collective interference reliability of the (super) ellipsoid convex set model is effectively solved. The convex set model is applicable to different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of the reliability calculation results are guaranteed. The method is simple and practical, with strong operability, and effectively improves the calculation efficiency and accuracy of the collective interference reliability of large and complex structures, and can be widely applied to the field of structural reliability measurement.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for measuring the reliability of a collective interference type in a first embodiment of the present invention;

FIG2 is a cross-sectional view of a cylindrical shell reinforced with ring ribs in Embodiment 1 of the present invention;

FIG3 is a top view of a cylindrical shell reinforced with ring ribs in Embodiment 1 of the present invention;

FIG4 is a second flow chart of the method for measuring the reliability of the collective interference type in the first embodiment of the present invention;

FIG. 5 is a schematic diagram of the structure of a measurement system of collective interferometric reliability in the second embodiment of the present invention.

In the accompanying drawings, the components represented by the reference numerals are listed as follows:

1. Shell, 2. Ribs.

DETAILED DESCRIPTION

The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

The present invention will be described below in conjunction with the accompanying drawings.

Embodiment 1, as shown in FIG1 , a method for measuring the reliability of a collective interference type includes the following steps:

S1: Establish a convex set model to describe structural uncertainty, and divide the convex set model into an interval model and a hyper-ellipsoid model;

S2: performing standardized transformation on the interval model and the hyper-ellipsoid model respectively to obtain a standardized interval model and a unit hyper-sphere model, and obtaining a standardized limit state equation according to the standardized interval model and the unit hyper-sphere model;

S3: uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized limit state equation to obtain interval model samples and hypersphere model samples respectively;

S4: obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the collective interference reliability of the structure according to the standardized limit state equation and the composite sample.

The measurement method of this embodiment is rigorous in theory. On the basis of the standardized limit state equation, it ensures the uniform distribution of sampling samples of (hyper)ellipsoid convex sets of arbitrary dimensions, overcomes the theoretical defects of traditional sampling methods, ensures the accuracy and credibility of reliability simulation results, and effectively solves the measurement problem of the set interference reliability of (hyper)ellipsoid convex set models. It is suitable for convex set models in different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of reliability calculation results are guaranteed. The method is simple and practical, with strong operability, and effectively improves the calculation efficiency and accuracy of the set interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

The structure in this embodiment is a ring-rib reinforced cylindrical shell. The collective interference reliability of the ring-rib reinforced cylindrical shell is measured, and the instability reliability of the ring-rib reinforced cylindrical shell is mainly analyzed and calculated. The structure of the ring-rib reinforced cylindrical shell is shown in Figures 2 and 3 respectively, and includes a shell 1 and ribs 2 evenly distributed inside the shell 1.

Preferably, as shown in FIG4 , S1 specifically includes the following steps:

S11: establishing an original limit state equation of the structure according to the uncertain parameter variables of the structure, and obtaining the convex set model according to the original limit state equation;

The original limit state equation is:

M=G(X)=G(x ₁ ,x ₂ ,...,x _n )=0;

Wherein, M is the original limit state equation, G(X) is the original limit state function, X=(x ₁ ,x ₂ ,...,x _n ) is the uncertainty parameter variable, and n is the total number of the uncertainty parameter variables;

S12: dividing the convex set model into a p-dimensional interval model and m super-ellipsoid models;

The interval model is: _Xi = ( _x1 , _x2 , ..., _xp );

Wherein, _Xi is the interval variable vector of the interval model of p dimensions, and _x1 , _x2 ... _xp are all interval uncertainty parameter variables;

The hyperellipsoid model is:

为第i个所述超椭球模型的中心点向量，Ω_i为第i个正定矩阵，θ_i为第i个所述超椭球模型的尺度参数。Wherein, _Xi is the super-ellipsoid variable vector of the i-th super-ellipsoid model, _Ei ( _Xi , _θi ) is the set of the i-th super-ellipsoid variable vectors,

is the center point vector of the i-th super-ellipsoid model, Ω _i is the i-th positive definite matrix, and θ _i is the scale parameter of the i-th super-ellipsoid model.

In order to obtain the basic variable domain and safety domain of the structure, when establishing the convex set model, the uncertainty parameter variables of the structure are first determined, and the original limit state equation of the convex set model is established based on the uncertainty parameter variables. Due to the differences in complex structures, the types of convex set models established for different structures will also be different, usually including interval models composed of interval variables, which are uniform box convex models, and also include multiple hyper-ellipsoid models composed of hyper-ellipsoid variables. Therefore, the convex set model is divided into interval model and hyper-ellipsoid model, which is convenient for measuring the collective interference reliability of different structures, can be applied to uncertainty measurement of different types of structures, and has a wide range of applications.

Specifically, the calculation formula for the critical instability pressure p _cr of the plate and shell between adjacent ribs in Figure 2 of this embodiment is p _cr =C _g C _s p _E , wherein p _E is the instability Euler pressure, C _g is the first model correction coefficient considering the influence of the calculation itself and the initial geometric defects of the shell out-of-roundness, and C _s is the second model correction coefficient considering the influence of the calculation itself and the plasticity and residual stress.

其中，E为材料弹性模量，h为壳体厚度，r为壳体半径，u为无量纲参数，且

其中，l为肋骨间距。When the material Poisson's coefficient is 0.3, the calculation formula for p _E is:

Where E is the elastic modulus of the material, h is the shell thickness, r is the shell radius, u is a dimensionless parameter, and

Where l is the rib spacing.

According to the method described in step 11 of this embodiment, the original limit state equation for shell structural instability of the ring-rib reinforced cylindrical shell is established as G _sh (p, p _cr ) = p _cr -p = 0, where p is the actual pressure borne by the shell;

The actual shell pressure p, shell radius r, shell thickness h, material elastic modulus E, rib spacing l, first model correction coefficient _Cg and second model correction coefficient _Cs are taken as uncertain parameter variables, and a convex set model is established based on the above uncertain parameter vectors; the above original limit state equation can be further rewritten:

Specifically, in this embodiment, the actual pressure p of the shell is an interval variable, forming a one-dimensional interval model, _Xi = (r, h, E, l, _Cs , _Cg ) ^T is a hyperellipsoid variable, forming a six-dimensional hyperellipsoid model and i = 1, which is described by the hyperellipsoid model:

In this embodiment, it is known that θ ₁ =1, and the following vectors are known:

Ω ₁ = Diag(1/360 ² ,1/2.2 ² ,1/(0.34×10 ⁵ ) ² ,1/96 ² ,1/0.34 ² ,1/0.3 ² ),

p∈[2.44,3.44].

Preferably, as shown in FIG4 , S2 specifically includes the following steps:

S21: transforming the interval variable according to the interval standardization transformation formula to obtain a standardized interval model;

The interval standardization transformation formula is:

为所述区间变量X_I的中心值向量，ΔX_I为所述区间变量X_I的离差向量，δ_I为p维的标准化区间变量且δ_I∈[-1,1]^p；in,

is the center value vector of the interval variable _Xi , _ΔXi is the deviation vector of the interval variable _Xi , _δI is a p-dimensional standardized interval variable and _δI∈ [-1,1] ^p ;

S22: transforming the m hyper-ellipsoid models according to the hyper-ellipsoid standardization transformation formula to obtain m unit hyper-sphere models;

The hyperellipsoid normalization transformation formula is:

The unit hypersphere model is: Δu _i ∈{Δu _i :Δu _i ^T Δu _i ≤1}, (i=1, 2, …, m);

为第i个所述正交矩阵的转置矩阵，D_i为第i个对角矩阵，Δu_i为第i个所述单位超球体模型的标准化超球体变量，Δu_i ^T为第i个所述标准化超球体变量的转置向量，u_i为第i个所述单位超球体模型的引入向量，

为第i个所述单位超球体模型的中心点向量，且

I_i为第i个单位矩阵；Among them, _Qi is the i-th orthogonal matrix,

is the transposed matrix of the i-th orthogonal matrix, _Di is the i-th diagonal matrix, _Δui is the standardized hypersphere variable of the i-th unit hypersphere model, _Δui ^T is the transposed vector of the i-th standardized hypersphere variable, _ui is the introduction vector of the i-th unit hypersphere model,

is the center point vector of the i-th unit hypersphere model, and

I _i is the i-th identity matrix;

S23: Obtaining the standardized limit state equation according to the original limit state equation, the standardized interval model and the unit hypersphere model;

The normalized limit state equation is:

M′=G′(δ)=G′(δ ₁ ,Δu ₁ ,Δu ₂ ,…, _Δum )=0;

Wherein, M′ is the standardized limit state equation, δ is a standardized variable and δ=(δ ₁ , Δu ₁ , Δu ₂ , …, _Δum ), G′(δ) is a standardized limit state function, and Δu ₁ , Δu ₂ … _Δum are all the standardized hypersphere variables.

This embodiment obtains standardized interval variables and a unit hypersphere model through standardized transformation, which facilitates obtaining the standardized limit state equation of the entire convex set model, thereby facilitating subsequent uniform sampling of the interval model and the hyperellipsoid model according to the standardized limit state equation, and laying a theoretical foundation for measuring the collective interference type reliability by obtaining the ratio of the volume of the safety domain to the total volume of the basic variable domain based on the composite samples obtained after uniform sampling. The obtained collective interference type reliability is more accurate and efficient.

Specifically, the interval model of this embodiment is a one-dimensional interval model, and the hyperellipsoid model is a six-dimensional hyperellipsoid model. The hyperellipsoid model and the interval model are subjected to standardized transformations, and the obtained standardized limit state equation is:

Among them, r ₁ , h ₁ , E ₁ , l ₁ , C _s1 and C _g1 are the standardized hypersphere variables after the standardization transformation, p ₁ is the standardized interval variable after the standardization transformation, r ₁ , h ₁ , E ₁ , l ₁ , C _s1 and C _g1 constitute a six-dimensional unit hypersphere model, p ₁ constitutes a one-dimensional standardized interval variable and p ₁ ∈ [-1,1].

Preferably, as shown in FIG4 , in S3, the specific steps of obtaining the interval model sample include:

S31: Obtain a first random number of the standardized interval model within a first preset sampling range, and uniformly sample the standardized interval model according to the first random number and the standardized limit state equation to obtain the interval model sample.

Since the probability of a standardized interval variable taking each value within the interval is the same, the p-dimensional standardized interval variable in the present invention obeys a uniform distribution within a first preset sampling range. Therefore, obtaining a first random number of the p-dimensional standardized interval variable within the first preset sampling range can achieve uniform sampling of the standardized interval variable, thereby facilitating improving the accuracy of subsequent measurement set interference reliability.

Specifically, this embodiment first uses the rand command in MATLAB to extract the first random number of the standardized interval variable within [0,1] ^p (the first preset sampling range). Due to the relationship between the first preset sampling range and the range of the aforementioned standardized interval variable p ₁ , the standardized interval variable is converted to: p ₁ =2p _Δ -1 and p _Δ ∈[0,1], thereby realizing the extraction of the standardized interval variable p ₁ sample in this embodiment.

Preferably, as shown in FIG4 , in S3, the specific steps of obtaining the hypersphere model sample include:

S32: obtaining a radial probability density function of a radial distance component of the unit hypersphere model in the spherical coordinate system, obtaining a second random number of an elevation component of the unit hypersphere model in the spherical coordinate system within a second preset sampling range, and obtaining a third random number of an azimuth component of the unit hypersphere model in the spherical coordinate system within a third preset sampling range;

S33: uniformly sampling the elevation component according to the second random number to obtain elevation component samples; uniformly sampling the azimuth component according to the third random number to obtain azimuth component samples; and based on the Metropolis sampling method, sampling the radial distance component according to the radial probability density function to obtain radial distance component samples;

Step 34: obtaining an initial hypersphere model sample of the unit hypersphere model in the spherical coordinate system according to the elevation component sample, the azimuth component sample and the radial distance component sample;

Step 35: transforming the initial hypersphere model sample according to the transformation formula between the spherical coordinate system and the orthogonal coordinate system to obtain the hypersphere model sample of the unit hypersphere model in the orthogonal coordinate system;

The conversion formula between the spherical coordinate system and the orthogonal coordinate system is:

为第i个所述单位超球体模型在所述正交坐标系下的第n_i-1维坐标分量，

为第i个所述单位超球体模型在所述正交坐标系下的第n_i维坐标分量，r_i为第i个所述单位超球体模型在所述球坐标系下的所述径向距离分量，

均为第i个所述单位超球体模型在所述球坐标系下的所述仰角分量，

为第i个所述单位超球体模型在所述球坐标系下的所述方向角分量，且

Wherein, _ni is the dimension of the i-th unit hypersphere model, Δui _,1 is the first-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system, _Δui,2 is the second-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system,

is the n _i -1 th dimensional coordinate component of the i th unit hypersphere model in the orthogonal coordinate system,

is the n _{i -th} dimensional coordinate component of the i -th unit hypersphere model in the orthogonal coordinate system, _ri is the radial distance component of the i -th unit hypersphere model in the spherical coordinate system,

are the elevation angle components of the i-th unit hypersphere model in the spherical coordinate system,

is the direction angle component of the i-th unit hypersphere model in the spherical coordinate system, and

Among them, for the omitted part of the formula in the conversion formula between the spherical coordinate system and the orthogonal coordinate system, when 2≤h≤ni _- 1, the omitted part of the formula is Δui _,h = _{ri sinβ1 sinβ2} …sinβh _{-1 cosβh} , Δui _,h is the h-th dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system.

Through the above sampling method, it can be ensured that after the radial distance component in the spherical coordinate system and the components in the other spherical coordinate system (i.e., the elevation component and the azimuth component) are sampled respectively, the hypersphere model samples that conform to the uniform distribution of the unit hypersphere model are obtained through coordinate transformation, thereby facilitating the improvement of the accuracy of the subsequent measurement set interference reliability.

Specifically, for the sampling of the elevation component and the azimuth component in this embodiment, since n _i =6 in this embodiment, the samples of the elevation components β ₁ -β ₄ ∈ [0,π] are first extracted by using the rand command in MATLAB to extract a random number in the interval [0,1] and then multiplying it by π; the samples of the azimuth component β ₅ ∈ [0,2π] are first extracted by using the rand command in MATLAB to extract a random number in the interval [0,1] and then multiplying it by 2π.

Preferably, in S32, the specific step of obtaining the radial probability density function includes:

S321: Calculate the volume and surface area of the unit hypersphere model in the spherical coordinate system respectively;

The volume is:

为n_i维的所述单位超球体模型的所述体积，R_i为n_i维的所述单位超球体模型的半径；in,

is the volume of the n _i -dimensional unit hypersphere model, and R _i is the radius of the n _i -dimensional unit hypersphere model;

当n_i为奇数时，

为给定常数，且

Γ(·) is the gamma function, and when n _i is an even number,

When n _i is an odd number,

is a given constant, and

The surface area is:

为所述单位超球体模型的n_i-1维球面的所述表面积；in,

is the surface area of the n _i -1 dimensional sphere of the unit hypersphere model;

S322: Obtain the radial probability density function according to the volume and the surface area;

The radial probability density function is:

Wherein, f( _ri ) is the radial probability density function of the i-th unit hypersphere model.

Through the radial probability density function, it is convenient to sample the radial distance component and ensure that the hypersphere model samples of the unit hypersphere model obey uniform distribution in the orthogonal coordinate system are obtained.

Specifically, the radial probability density function of the six-dimensional unit hypersphere model of this embodiment is:

The process of using the Metropolis sampling method is: at t=0, select an initial value r ₀ , and f(r ₀ )≥0; at the t+1 iteration, extract a candidate value r ^c through a proposed distribution q(r ₁ |r _t ), and the proposed distribution is a symmetric type, such as a normal distribution or an interval uniform distribution; and set α=min[f(r ^c )/f(r _t ),1], and the transition probability of α satisfies r _t+1 =r ^c , and the transition probability of 1-α satisfies r _t+1 =r _t ; through the above sampling, a Markov chain with a distribution of f(r ₁ ) can be obtained, and a fourth random number of f(r ₁ ) is obtained, and the radial distance component is sampled according to the fourth random number.

Preferably, as shown in FIG2 , in S4, the specific steps of calculating the collective interference type reliability of the structure are:

Calculating the collective interference type reliability according to the standardized limit state equation, the composite sample and the collective interference type reliability calculation formula;

The collective interference reliability calculation formula is:

Wherein, R _set is the set interferometric reliability, q _all is the total number of sample points in the composite sample, and q _s is the number of sample points in the composite sample that satisfy G′(δ)＞0.

The total number of sample points in the composite sample is equivalent to the total volume of the basic domain of the structure. According to the standardized limit state equation G′(δ)=0 of S23, the number of sample points in the composite sample that satisfy G′(δ)＞0 is equivalent to the volume of the safety domain. Therefore, the collective interference reliability calculation formula according to the present invention can efficiently and accurately measure the collective interference reliability of the structure; the sampling technology is supported by rigorous mathematical theory, which ensures the rigor and effectiveness of the sampling, and ensures the accuracy and credibility of the reliability calculation results. The method is simple and practical, with strong operability, which effectively improves the calculation efficiency and accuracy of the collective interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

Specifically, the total number of sample points in the composite sample obtained in this embodiment is 10 million times, and the collective interference reliability of the ring-rib reinforced cylindrical shell calculated according to the collective interference reliability calculation formula is 0.9985185. In addition, this embodiment also adopts the traditional measurement method, that is, the radial distance component of the spherical coordinate system is also sampled according to a uniform distribution. Under the same total number of sample points, the obtained reliability result is 0.9997206. It can be seen that the traditional sampling strategy causes the obtained composite samples to gather in the middle of the unit hypersphere model due to method defects, that is, it presents a phenomenon of uneven density, which directly leads to a larger measurement result of the structural reliability, that is, more samples fall in the safety domain, and this error is difficult to predict, resulting in distortion and loss of credibility of the reliability result.

Embodiment 2, as shown in FIG5 , a measurement system of collective interference type reliability includes a modeling module, a standardized transformation module, a sampling module and a calculation module;

The modeling module is used to establish a convex set model that describes structural uncertainty, and divide the convex set model into an interval model and a super ellipsoid model;

The standardized transformation module is used to perform standardized transformation on the interval model and the hyper-ellipsoid model respectively to obtain a standardized interval model and a unit hyper-sphere model, and obtain a standardized limit state equation according to the standardized interval model and the unit hyper-sphere model;

The sampling module is used to uniformly sample the standardized interval model and the unit hypersphere model according to the standardized limit state equation to obtain interval model samples and hypersphere model samples respectively;

The calculation module is used to obtain a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculate the collective interference reliability of the structure according to the standardized limit state equation and the composite sample.

A convex set model is established through the modeling module, and the convex set model is divided into an interval model and a hyperellipsoid model, which can be used to describe the structural uncertainty of the coexistence of hyperellipsoid variables and interval variables; since the ratio of the volume of the structural safety domain to the total volume of the basic variable domain is used as the structural set interference type reliability in the set interference model, the standardized limit state equation is obtained after the interval model and the hyperellipsoid model are standardized through the standardized transformation module, which is convenient for the subsequent sampling module to perform uniform sampling according to the standardized limit state equation to obtain a composite sample, thereby facilitating the acquisition of the ratio of the volume of the safety domain to the total volume of the basic variable domain, providing a data basis for the subsequent calculation module to measure the set interference reliability, and facilitating the efficient and accurate measurement of the set interference reliability;

The measurement system method of this embodiment is rigorous in theory. On the basis of the standardized limit state equation, it ensures the uniform distribution of sampling samples of arbitrary-dimensional (hyper)ellipsoid convex sets, overcomes the theoretical defects of traditional sampling methods, ensures the accuracy and credibility of reliability simulation results, and effectively solves the measurement problem of the set interference reliability of (hyper)ellipsoid convex set models. It is suitable for convex set models in different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of reliability calculation results are guaranteed. The method is simple and practical, with strong operability, and effectively improves the calculation efficiency and accuracy of the set interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

Embodiment 3: Based on Embodiment 1 and Embodiment 2, this embodiment further discloses a device for measuring collective interferometric reliability, including a processor, a memory, and a computer program stored in the memory and executable on the processor. When the computer program is executed, the following steps are implemented as shown in FIG. 1:

S1: Establish a convex set model to describe structural uncertainty, and divide the convex set model into an interval model and a hyper-ellipsoid model;

S2: performing standardized transformation on the interval model and the hyper-ellipsoid model respectively, to obtain a standardized interval model and a unit hyper-sphere model, and obtaining a standardized limit state equation according to the standardized interval model and the unit hyper-sphere model;

S3: uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized limit state equation to obtain interval model samples and hypersphere model samples respectively;

S4: obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the collective interference reliability of the structure according to the standardized limit state equation and the composite sample.

The device for measuring the collective interference type reliability of the present invention is realized by a computer program stored in a memory and running on a processor. The method is rigorous in theory. On the basis of the standardized limit state equation, the uniform distribution of the sampling samples of the (super) ellipsoid convex set of any dimension is guaranteed, the theoretical defects of the traditional sampling method are overcome, the accuracy and credibility of the reliability simulation results are guaranteed, and the measurement problem of the collective interference reliability of the (super) ellipsoid convex set model is effectively solved. The method is suitable for convex set models in different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of the reliability calculation results are guaranteed. The method is simple and practical, with strong operability, and effectively improves the calculation efficiency and accuracy of the collective interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

This embodiment further provides a computer storage medium, on which at least one instruction is stored, and when the instruction is executed, the specific steps S1 to S4 are implemented.

The measurement of the collective interference type reliability of the present invention is realized by executing a computer storage medium containing at least one instruction. The method is rigorous in theory. On the basis of the standardized limit state equation, the uniform distribution of the sampling samples of the (super) ellipsoid convex set of any dimension is guaranteed, the theoretical defects of the traditional sampling method are overcome, the accuracy and credibility of the reliability simulation results are guaranteed, and the measurement problem of the collective interference reliability of the (super) ellipsoid convex set model is effectively solved. The method is suitable for convex set models in different situations, so that the reliability of different types of structures can be measured, and the accuracy and credibility of the reliability calculation results are guaranteed. The method is simple and practical, with strong operability, and effectively improves the calculation efficiency and accuracy of the collective interference reliability of large and complex structures, and can be widely used in the field of structural reliability measurement.

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

Claims (9)

1. A method for measuring collective interferometric reliability, comprising the following steps: Step 1: Establish a convex set model that describes structural uncertainty, and divide the convex set model into an interval model and a hyperellipsoid model; Step 2: performing standardized transformation on the interval model and the hyper-ellipsoid model respectively to obtain a standardized interval model and a unit hyper-sphere model, and obtaining a standardized limit state equation according to the standardized interval model and the unit hyper-sphere model; Step 3: uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized limit state equation to obtain interval model samples and hypersphere model samples respectively; Step 4: obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the collective interference type reliability of the structure according to the standardized limit state equation and the composite sample; In step 3, the specific steps of obtaining the hypersphere model sample include: Step 32: obtaining a radial probability density function of a radial distance component of the unit hypersphere model in the spherical coordinate system, obtaining a second random number of an elevation component of the unit hypersphere model in the spherical coordinate system within a second preset sampling range, and obtaining a third random number of an azimuth component of the unit hypersphere model in the spherical coordinate system within a third preset sampling range; Step 33: uniformly sampling the elevation component according to the second random number to obtain elevation component samples; uniformly sampling the azimuth component according to the third random number to obtain azimuth component samples; and based on the Metropolis sampling method, sampling the radial distance component according to the radial probability density function to obtain radial distance component samples; Step 34: obtaining an initial hypersphere model sample of the unit hypersphere model in the spherical coordinate system according to the elevation component sample, the azimuth component sample and the radial distance component sample; Step 35: transforming the initial hypersphere model sample according to the transformation formula between the spherical coordinate system and the orthogonal coordinate system to obtain the hypersphere model sample of the unit hypersphere model in the orthogonal coordinate system; The conversion formula between the spherical coordinate system and the orthogonal coordinate system is:

Wherein, _ni is the dimension of the i-th unit hypersphere model, Δui _,1 is the first-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system, _Δui,2 is the second-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system,

is the n _i -1 th dimensional coordinate component of the i th unit hypersphere model in the orthogonal coordinate system,

is the n _i -th dimensional coordinate component of the i -th unit hypersphere model in the orthogonal coordinate system, _ri is the radial distance component of the i -th unit hypersphere model in the spherical coordinate system, β ₁ ~

are the elevation angle components of the i-th unit hypersphere model in the spherical coordinate system,

is the direction angle component of the i-th unit hypersphere model in the spherical coordinate system, and β ₁ ~

,

2. The method for measuring the collective interferometric reliability according to claim 1, wherein step 1 specifically comprises the following steps: Step 11: establishing the original limit state equation of the structure according to the uncertain parameter variables of the structure, and obtaining the convex set model according to the original limit state equation; The original limit state equation is: M=G(X)=G(x ₁ ,x ₂ ,...,x _n )=0; Wherein, M is the original limit state equation, G(X) is the original limit state function, X=(x ₁ ,x ₂ ,...,x _n ) is the uncertainty parameter variable, and n is the total number of the uncertainty parameter variables; Step 12: Divide the convex set model into a p-dimensional interval model and m super-ellipsoid models; The interval model is: _Xi = ( _x1 , _x2 , ..., _xp ); Wherein, _Xi is the interval variable of the interval model of p dimension, _x1 , _x2 ... _xp are all interval uncertainty parameter variables; The hyperellipsoid model is:

Wherein, _Xi is the super-ellipsoid variable of the i-th super-ellipsoid model, _Ei ( _Xi , _θi ) is the set of the i-th super-ellipsoid variables,

is the center point vector of the i-th super-ellipsoid model, Ω _i is the i-th positive definite matrix, and θ _i is the scale parameter of the i-th super-ellipsoid model. 3. The method for measuring the collective interferometric reliability according to claim 2, wherein step 2 specifically comprises the following steps: Step 21: transform the interval variable according to the interval standardization transformation formula to obtain a standardized interval model; The interval standardization transformation formula is:

in,

is the center value vector of the interval variable _Xi , _ΔXi is the deviation vector of the interval variable _Xi , _δI is a p-dimensional standardized interval variable and _δI∈ [-1,1] ^p ; Step 22: transforming the m hyper-ellipsoid models according to the hyper-ellipsoid standardization transformation formula to obtain m unit hyper-sphere models; The hyperellipsoid normalization transformation formula is:

The unit hypersphere model is: Δu _i ∈{Δu _i :Δu _i ^T Δu _i ≤1}, i = 1, 2, …, m; Among them, _Qi is the i-th orthogonal matrix,

is the transposed matrix of the i-th orthogonal matrix, _Di is the i-th diagonal matrix, _Δui is the standardized hypersphere variable of the i-th unit hypersphere model, _Δui ^T is the transposed vector of the i-th standardized hypersphere variable, _ui is the introduction vector of the i-th unit hypersphere model,

is the center point vector of the ⁱ -th unit hypersphere model, and _Δui = _ui - _ui0 ,

I _i is the i-th identity matrix; Step 23: obtaining the standardized limit state equation according to the original limit state equation, the standardized interval model and the unit hypersphere model; The normalized limit state equation is: M′=G′(δ)=G′(δ ₁ ,Δu ₁ ,Δu ₂ ,…, _Δum )=0; Wherein, M′ is the standardized limit state equation, δ is a standardized variable and δ=(δ ₁ , Δu ₁ , Δu ₂ , …, _Δum ), G′(δ) is a standardized limit state function, and Δu ₁ , Δu ₂ … _Δum are all the standardized hypersphere variables. 4. The method for measuring the collective interferometric reliability according to claim 3, characterized in that in step 3, the specific steps of obtaining the interval model sample include: Step 31: Obtain a first random number of the standardized interval model within a first preset sampling range, and uniformly sample the standardized interval model according to the first random number and the standardized limit state equation to obtain the interval model sample. 5. The method for measuring the reliability of the collective interferometry according to claim 3, characterized in that, in the step 32, the specific step of obtaining the radial probability density function comprises: Step 321: Calculate the volume and surface area of the unit hypersphere model in the spherical coordinate system respectively; The volume is:

in,

is the volume of the n _i -dimensional unit hypersphere model, and R _i is the radius of the n _i -dimensional unit hypersphere model; Γ(·) is the gamma function, and when n _i is an even number,

When n _i is an odd number,

is a given constant, and

The surface area is:

in,

is the surface area of the n _i -1 dimensional sphere of the unit hypersphere model; Step 322: Obtain the radial probability density function according to the volume and the surface area; The radial probability density function is:

Wherein, f( _ri ) is the radial probability density function of the i-th unit hypersphere model. 6. The method for measuring the collective interferometry reliability according to claim 4, characterized in that in step 4, the specific steps of calculating the collective interferometry reliability of the structure are: Calculating the collective interference type reliability according to the standardized limit state equation, the composite sample and the collective interference type reliability calculation formula; The collective interference reliability calculation formula is:

Wherein, R _set is the set interferometric reliability, q _all is the total number of sample points in the composite sample, and q _s is the number of sample points in the composite sample that satisfy G′(δ)＞0. 7. A measurement system of collective interferometric reliability, characterized by comprising a modeling module, a standardization transformation module, a sampling module and a calculation module; The modeling module is used to establish a convex set model that describes structural uncertainty, and divide the convex set model into an interval model and a super ellipsoid model; The standardized transformation module is used to perform standardized transformation on the interval model and the hyper-ellipsoid model respectively to obtain a standardized interval model and a unit hyper-sphere model, and obtain a standardized limit state equation according to the standardized interval model and the unit hyper-sphere model; The sampling module is used to uniformly sample the standardized interval model and the unit hypersphere model according to the standardized limit state equation to obtain interval model samples and hypersphere model samples respectively; The calculation module is used to obtain a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculate the collective interference type reliability of the structure according to the standardized limit state equation and the composite sample; The sampling module is specifically used for: Obtaining a radial probability density function of a radial distance component of the unit hypersphere model in a spherical coordinate system, obtaining a second random number of an elevation component of the unit hypersphere model in the spherical coordinate system within a second preset sampling range, and obtaining a third random number of an azimuth component of the unit hypersphere model in the spherical coordinate system within a third preset sampling range; Uniformly sampling the elevation angle component according to the second random number to obtain elevation angle component samples; uniformly sampling the azimuth component according to the third random number to obtain azimuth component samples; and based on the Metropol is sampling method, sampling the radial distance component according to the radial probability density function to obtain radial distance component samples; Obtaining an initial hypersphere model sample of the unit hypersphere model in the spherical coordinate system according to the elevation component sample, the direction component sample and the radial distance component sample; According to the conversion formula between the spherical coordinate system and the orthogonal coordinate system, the initial hypersphere model sample is converted to obtain the hypersphere model sample of the unit hypersphere model in the orthogonal coordinate system; The conversion formula between the spherical coordinate system and the orthogonal coordinate system is:

Wherein, _ni is the dimension of the i-th unit hypersphere model, Δui _,1 is the first-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system, _Δui,2 is the second-dimensional coordinate component of the i-th unit hypersphere model in the orthogonal coordinate system,

is the n _i -1 th dimensional coordinate component of the i th unit hypersphere model in the orthogonal coordinate system,

is the n _{i -th} dimensional coordinate component of the i -th unit hypersphere model in the orthogonal coordinate system, _ri is the radial distance component of the i -th unit hypersphere model in the spherical coordinate system,

are the elevation angle components of the i-th unit hypersphere model in the spherical coordinate system,

is the direction angle component of the i-th unit hypersphere model in the spherical coordinate system, and

8. A device for measuring collective interference reliability, characterized in that it comprises a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program implements the method steps as claimed in any one of claims 1 to 6 when executed. 9. A computer storage medium, characterized in that the computer storage medium comprises: at least one instruction, which implements the method steps according to any one of claims 1 to 6 when the instruction is executed.

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