CN109885879B - Method, system, device and medium for measuring integrated interference type reliability - Google Patents
Method, system, device and medium for measuring integrated interference type reliability Download PDFInfo
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Abstract
The invention relates to a measurement method, a system, a device and a medium of set interference type reliability, wherein the method comprises the steps of establishing a convex set model for describing structural uncertainty, and dividing the convex set model into an interval model and a hyper-ellipsoid model; respectively carrying out standardized transformation on the interval model and the hyperellipsoid model to obtain a standardized interval model and a unit hypersphere model, and obtaining a standardized extreme state equation according to the standardized interval model and the unit hypersphere model; respectively and uniformly sampling the standardized interval model and the hypersphere model according to a standardized extreme state equation to obtain an interval model sample and a hypersphere model sample; and obtaining a composite sample according to the interval model sample and the hypersphere model sample, and calculating the set interference type reliability according to the standardized extreme state equation and the composite sample. The sampling method is rigorous, effective, simple, convenient and practical, has strong operability, and effectively improves the measurement efficiency and precision of the interference reliability of the large complex structure set.
Description
Technical Field
The present invention relates to the field of structural reliability measurement, and in particular, to a method, a system, an apparatus, and a medium for measuring aggregate interference reliability.
Background
In the reliability analysis and design of the structure, a plurality of uncertainties are generated due to the complexity of a structural system and the cognitive limitation, the uncertainties often play a crucial role in the performance and the response of the structure, and therefore reasonable quantitative processing is needed. The traditional description of these uncertainties is based on probabilistic theory, but due to the limitations of probabilistic theory, non-probabilistic reliability theory has been developed in recent years, whose mathematical basis is a convex set model.
Currently, there is also a lot of research 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 as a basic variable domain, and the basic variable domain has a safe domain and a failure domain, wherein when the failure domain and the safe domain have a cross condition, the reliability of the structure is called as set interference type reliability, and when the failure domain and the safe domain do not have a cross condition, the reliability of the structure is called as set extension type reliability.
The metric for collective interferometric reliability is based on a non-probabilistic collective interference model. The reliability of the structure is measured by the interference degree of a basic variable domain and a security domain of the structure, namely, the ratio of the volume of the security domain of the structure to the total volume of the basic variable domain of the structure is used as the reliability of the structure set interference type, and the reliability is higher if the ratio of the volumes is higher. The distinction between the safe domain and the invalid domain is often determined by an extreme state function, and the extreme state equation can divide the structure uncertainty variable space into two parts, namely the safe domain and the invalid domain.
However, for a large complex structure, because the extreme state functions of the complex structure involve a large number of variables and have high complexity, the reliability of solving the complex structure by an analytical method is generally infeasible, and therefore, it is necessary to search for a simulation solution method by a computer tool.
For the set interference reliability, the key and core of the simulation solution is to realize uniform sampling of the convex set model. According to the existing literature, the sampling method for the convex set of the (hyper) ellipsoid in any dimension is often realized by uniformly sampling the spherical coordinate, however, the method has a theoretical error, the uniformly distributed samples in the spherical coordinate system are transformed into the orthogonal coordinate system and do not obey uniform distribution, and the reliability simulation calculation result based on the method is necessarily distorted and unreliable.
Therefore, a new sampling method is needed to establish a non-probabilistic ensemble interference model and to achieve an accurate measurement of the reliability of the ensemble interference type.
Disclosure of Invention
The present invention provides a method, system, device and medium for measuring the reliability of the collective interference type, aiming at the above-mentioned deficiencies of the prior art.
The technical scheme for solving the technical problems is as follows:
a method for measuring reliability of an aggregate interference type, comprising the steps of:
step 1: establishing a convex set model for describing structural uncertainty, and dividing the convex set model into an interval model and a hyper-ellipsoid model;
and 2, step: respectively carrying out standardized transformation on the interval model and the hyperellipsoid model to obtain a standardized interval model and a unit hypersphere model, and obtaining a standardized limit state equation according to the standardized interval model and the unit hypersphere model;
and step 3: respectively and uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized extreme state equation to respectively obtain an interval model sample and a hypersphere model sample;
and 4, step 4: and obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the set interference type reliability of the structure according to the standardized extreme state equation and the composite sample.
The invention has the beneficial effects that: firstly, establishing a non-probability model capable of describing structural uncertainty, namely a convex set model, and dividing the convex set model into an interval model and a hyper-ellipsoid model, so that the structural uncertainty of the coexistence condition of hyper-ellipsoid variables and interval variables can be conveniently described; because the ratio of the volume of the structure security domain to the total volume of the basic variable domain is taken as the structure set interference type reliability in the set interference model, the normalized extreme state equation is obtained by respectively performing normalized transformation on the interval model and the hyper-ellipsoid model, so that uniform sampling is performed according to the normalized extreme state equation subsequently, and a composite sample is obtained, thereby facilitating the acquisition of the ratio of the volume of the security domain to the total volume of the basic variable domain, providing a data base for the measurement of the subsequent set interference reliability, and facilitating the efficient and accurate measurement of the set interference reliability; the measuring method of the invention has strict theory, ensures the uniform distribution of the sampling samples of the (super) ellipsoid convex set with any dimension on the basis of the standardized extreme state equation, overcomes the theoretical defects of the traditional sampling method, ensures the accuracy and credibility of the reliability simulation result, effectively solves the measuring problem of the set interference reliability of the (super) ellipsoid convex set model, is suitable for convex set models with different conditions, can measure the reliability of different types of structures, and ensures the accuracy and credibility of the reliability calculation result, has simple, convenient and practical method and strong operability, effectively improves the calculation efficiency and precision of the set interference reliability of large-scale complex structures, and can be widely applied to the field of measuring the structural reliability.
On the basis of the technical scheme, the invention can be further improved as follows:
further: the step 1 specifically comprises the following steps:
step 11: establishing an original extreme state equation of the structure according to the uncertainty parameter variable of the structure, and obtaining the convex set model according to the original extreme state equation;
the original extreme state equation is:
M＝G(X)＝G(x 1 ,x 2 ,...,x n )＝0；
where M is the original extreme state equation, G (X) is the original extreme state function, and X = (X) 1 ,x 2 ,...,x n ) Is said toA deterministic parametric variable, n being the total number of said uncertain parametric variables;
step 12: dividing the convex set model into a p-dimensional interval model and m hyper-ellipsoid models;
the interval model is as follows: x I ＝(x 1 ,x 2 ,...,x p )；
Wherein X I Interval variable, x, of the interval model in p dimension 1 、x 2 …x p All are interval uncertainty parameter variables;
the hyperellipsoid model is as follows:
wherein, X i A hyper-ellipsoid variable, E, for the ith said hyper-ellipsoid model i (X i ,θ i ) For the ith set of the hyper-ellipsoid variables,
is the central point vector, omega, of the ith hyper-ellipsoid model i Is the ith positive definite matrix, theta i Is the scale parameter of the ith super ellipsoid model.
The beneficial effects of the further scheme are as follows: in order to obtain a basic variable domain and a safety domain of a structure, when a convex set model is established, firstly, an uncertain parameter variable of the structure is determined, an original extreme state equation of the convex set model is established according to the uncertain parameter variable, and due to the difference of complex structures, the types of the convex set models established by different structures are different.
Further: the step 2 specifically comprises the following steps:
step 21: converting the interval variable according to an interval standard conversion formula to obtain a standard interval model;
the interval standardization transformation formula is as follows:
wherein the content of the first and second substances,
is the interval variable X I Of the central value vector, Δ X I Is the interval variable X I Of the dispersion vector, delta I Is a normalized interval variable of dimension p and delta I ∈[-1,1] p ；
Step 22: transforming the m hyper-ellipsoid models according to a hyper-ellipsoid standardized transformation formula to obtain m unit hyper-sphere models;
the normalized transformation formula of the hyperellipsoid is as follows:
the unit hypersphere model is: Δ u i ∈{Δu i :Δu i T Δu i ≤1},(i＝1,2,…,m)；
Wherein Q is i Is the (i) th orthogonal matrix and,
as a transpose of the ith said orthogonal matrix, D i For the ith diagonal matrix, Δ u i Normalized hypersphere variable, Δ u, for the ith said unit hypersphere model i T As the transposed vector, u, of the ith said normalized hypersphere variable i For the introduction vector of the i-th said unit hypersphere model, <>
Is the center point vector of the ith said unit hypersphere model, and &>
I i Is the ith identity matrix;
step 23: obtaining the standardized extreme state equation according to the original extreme 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 ,…,Δu m )＝0；
wherein M' is the normalized extreme state equation, δ is the normalized variable and δ = (δ) 1 ,Δu 1 ,Δu 2 ,…,Δu m ) G' (delta) is a normalized limit state function, Δ u 1 、Δu 2 …Δu m Are all the normalized hyper-sphere variables.
The beneficial effects of the above further scheme are: the standardized transformation is to introduce a new variable, transform the interval variable vector into an equivalent standardized interval variable, transform each hyper-ellipsoid model into an equivalent unit hyper-sphere model, and then define the reliability index of the structure in a new variable space; the interval variable is converted into the standardized interval variable through the interval standardized transformation formula, the super-ellipsoid model is converted into the unit super-sphere model through the super-ellipsoid standardized transformation formula, the standardized extreme state equation of the whole convex set model is convenient to obtain, and the 'critical state' of the failure domain and the security domain can be obtained according to the standardized extreme state equation, so that the more accurate ratio of the volume of the security domain to the total volume of the basic variable domain is convenient to obtain;
based on the analysis of the normalized interval variable vector, when the normalized interval variable is multidimensional, a multidimensional interval domain formed by the multidimensional normalized interval variable is called a super-rectangular solid, the super-rectangular solid is divided into a security domain and a failure domain by a normalized extreme state equation, and therefore the reliability of the normalized interval variable is the ratio of the super volume of the security domain to the total volume of the super-rectangular solid; similarly, based on the analysis of the unit hyper-sphere model, the reliability of the unit hyper-sphere model is the ratio of the hyper-volume of the security domain to the total volume of the unit hyper-sphere model.
The standardized interval model and the unit hypersphere model are obtained through standardized transformation, the standardized extreme state equation of the whole convex set model is convenient to obtain, the standardized interval model and the unit hypersphere model are beneficial to being uniformly sampled respectively according to the standardized extreme state equation, a theoretical basis is laid for measuring the reliability of the set interference type according to the ratio of the volume of a security domain to the total volume of a basic variable domain obtained by combining the composite samples obtained after uniform sampling, and the reliability of the set interference type is more accurate and efficient.
Further: in the step 3, the specific step of obtaining the interval model sample includes:
step 31: and acquiring a first random number of the standardized interval model in a first preset sampling range, and uniformly sampling the standardized interval model according to the first random number and the standardized limit state equation to obtain the interval model sample.
The beneficial effects of the above further scheme are: because the possibility that the standardized interval variable takes various values in the interval is the same, the standardized interval variable of the p dimension in the invention is uniformly distributed in the first preset sampling range, so that the first random number of the standardized interval variable of the p dimension in the first preset sampling range is obtained, the uniform sampling of the standardized interval variable can be realized, and the accuracy of the interference reliability of the subsequent measurement set is convenient to improve;
wherein for the acquisition of the first random number, for example, a normalized interval variable of [0,1 ] may be first extracted in MATLAB by a rand command] p (first predetermined sampling range) due to the first predetermined sampling range and the aforementioned normalized interval variable δ 1 The normalized interval variable may be converted to: delta 1 ＝2δ Δ -1 and δ Δ ∈[0,1] p Realizing standardized intervalsVariable delta 1 And (4) extracting a sample.
Further: in the step 3, the specific steps of obtaining the hypersphere model sample include:
step 32: acquiring a radial probability density function of a radial distance component of the unit hyper-sphere model in a spherical coordinate system, acquiring a second random number of an elevation angle component of the unit hyper-sphere model in the spherical coordinate system in a second preset sampling range, and acquiring a third random number of a direction angle component of the unit hyper-sphere model in the spherical coordinate system in a third preset sampling range;
step 33: uniformly sampling the elevation component according to the second random number to obtain an elevation component sample; uniformly sampling the direction angle component according to the third random number to obtain a direction angle component sample; based on a Metropolis sampling method, sampling the radial distance component according to the radial probability density function to obtain a radial distance component sample;
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 direction angle component sample and the radial distance component sample;
step 35: converting the initial hyper-sphere model sample according to a conversion formula of a spherical coordinate system and an orthogonal coordinate system to obtain the hyper-sphere model sample of the unit hyper-sphere model in the orthogonal coordinate system;
the conversion formula of the spherical coordinate system and the orthogonal coordinate system is as follows:
wherein n is i Dimension of the ith said unitary hyper-sphere model, au i,1 Is the 1 st dimensional coordinate component, delauu, of the ith unit hyper-sphere model in the orthogonal coordinate system i,2 Is the 2 nd dimension coordinate component of the unit hyper-sphere model under the orthogonal coordinate system,
for the ith said unit hyper-sphere model in said orthogonal coordinate system i -a 1-dimensional coordinate component, based on the measured value of the sensor>
For the ith said unit hyper-sphere model in said orthogonal coordinate system i Component of dimensional coordinate, r i For said radial distance component of the ith said unit hypersphere model in said spherical coordinate system,/->
The elevation component, in the spherical coordinate system, of each ith unit hyper-sphere model is greater than or equal to>
For the direction angle component of the ith unit hyper-sphere model in the spherical coordinate system, and->
Wherein, for the formula of omitting part in the conversion formula of the spherical coordinate system and the orthogonal coordinate system, when h is more than or equal to 2 and less than or equal to n i In case of-1, the formula of the omitted portion is Δ u i,h ＝r i sinβ 1 sinβ 2 …sinβ h-1 cosβ h ，Δu i,h Is the h-dimension coordinate component of the ith unit hyper-sphere model in the orthogonal coordinate system.
The beneficial effects of the above further scheme are: because the sampling method for the hypersphere model of any dimension unit is usually realized by uniformly sampling the spherical coordinate, when the uniformly distributed samples in the spherical coordinate system are transformed to the orthogonal coordinate system, the uniformly distributed samples are not subjected to uniform distribution, so that the reliability measurement result is distorted and unreliable; the method comprises the following steps that a radial distance component in a spherical coordinate system is the most main factor, so that samples in the spherical coordinate system are transformed to an orthogonal coordinate system and then are uniformly distributed, a radial probability density function of the radial distance component can be obtained, and then the radial distance component is sampled based on a Metropolis sampling method, so that Monte Carlo samples (Monte Carlo samples) which obey the radial probability density function, namely radial distance component samples, can be obtained;
the components under the other spherical coordinate systems, namely the elevation angle component and the direction angle component, respectively obtain the corresponding second random number and the third random number according to the sampling method of the similar standardized interval variable, respectively perform uniform sampling, and finally ensure to obtain a hypersphere model sample which accords with uniform distribution of the unit hypersphere model through coordinate transformation, thereby being convenient for improving the accuracy of the interference reliability of the subsequent measurement set;
wherein the elevation component and the direction angle component are sampled, e.g. the elevation component
The sample extraction of (2) may first employ a range command extraction interval [0,1 ] in MATLAB]Multiplying the random number by pi to obtain the random number; angular component of direction
The sample extraction of (2) can be performed by first extracting the interval [0,1 ] in MATLAB by using the rand command]And then multiplying the random number by 2 pi.
Further: in step 32, the specific step of obtaining the radial probability density function includes:
step 321: respectively calculating the volume and the surface area of the unit hypersphere model under the spherical coordinate system;
the volume is:
wherein the content of the first and second substances,
is n i The volume, R, of the unit hyper-sphere model of dimensions i Is n i A radius of the unit hyper-sphere model of dimensions; />
Γ (-) is a gamma function, and when n i In the case of an even number, the number of the first,
when n is i In the case of an odd number of the groups,
is given constant, and +>
The surface area is:
wherein the content of the first and second substances,
is n of the unit hyper-sphere model i -said surface area of a 1-dimensional sphere;
step 322: obtaining the radial probability density function according to the volume and the surface area;
the radial probability density function is:
wherein, f (r) i ) The radial probability density function for the ith said unit hyper-sphere model.
The beneficial effects of the above further scheme are: the radial probability density function can firstly and respectively obtain the volume and the table of the unit hyper-sphere model by means of high-class mathematical knowledgeArea, then n i The radial distance components of the unit hypersphere model of dimension are r 1 And r 2 Two toroidal microelements are taken, and then the radial thicknesses of the two toroidal microelements are dr respectively under the spherical coordinate system 1 And dr 2 The corresponding toroidal infinitesimal volumes are respectively:
to ensure that the torroidal microelements obtain uniformly distributed samples in the orthogonal coordinate system, the number of samples is necessarily proportional to the volume of the torroidal microelements, in other words, r i At a microspur dr 1 And dr 2 The probability accumulation above is proportional to the toroid infinitesimal volume, then:
the radial probability density function can be derived as:
through the radial probability density function, the radial distance component is conveniently sampled, and the hypersphere model sample of the unit hypersphere model which obeys uniform distribution under the orthogonal coordinate system is ensured to be obtained.
Further: in step 33, the specific step of obtaining the radial distance component sample includes:
step 331: setting an initial value, a candidate value and iteration times in the Metropolis sampling method according to the radial probability density function, calculating transition probability according to the initial value, the candidate value, the iteration times and the radial probability density function, and determining a Markov chain for uniformly sampling the hyper-ellipsoid model according to the transition probability;
step 332: and determining a fourth random number of the radial distance component in a fourth preset sampling range according to the Markov chain, and sampling the radial coordinate component according to the fourth random number to obtain the initial hypersphere model sample.
The beneficial effects of the further scheme are as follows: by the Metropolis sampling method, a radial distance component sample obeying a radial probability density function is guaranteed to be obtained;
for example: when t =0, selecting an initial value r 0 And f (r) 0 ) Not less than 0; at t +1 iterations, the distribution q (r) is distributed by suggestion i |r t ) Extracting a candidate value r c And the distribution is proposed to be symmetrical, such as normal distribution or interval uniform distribution; and let α = min [ f (r) c )/f(r t ),1]And the transition probability of alpha satisfies r t+1 ＝r c The transition probability of 1-alpha satisfies r t+1 ＝r t (ii) a The probability distribution f (r) can be obtained by the sampling i ) And f (r) is obtained from the Markov chain (Markov chain) i ) The fourth random number of (2).
Further: in the step 4, the specific step of calculating the set interference type reliability of the structure is as follows:
calculating the set interference type reliability according to the standardized extreme state equation, the composite sample and a set interference type reliability calculation formula;
the set interference type reliability calculation formula is as follows:
wherein R is set For said collective interferometric type reliability, q all For the total number of sample points in the composite sample, q s The number of sample points in the composite sample that satisfy G' (δ) > 0.
The beneficial effects of the further scheme are as follows: the total number of sample points in the composite sample can be equivalent to the total volume of the structural fundamental domain, and according to the normalized extreme state equation G '(δ) =0 in step 23, the number of sample points satisfying G' (δ) > 0 in the composite sample can be equivalent to the volume of the safety domain, so that the set interference reliability calculation formula according to the present invention can efficiently and accurately measure the set interference reliability of the structure; the sampling technology is supported by strict mathematical theory, the rigidness and the effectiveness of sampling are ensured, the accuracy and the credibility of a calculation result of the reliability are ensured, the method is simple, convenient and practical, the operability is strong, the calculation efficiency and the precision of the set interference reliability of the large-scale complex structure are effectively improved, and the method can be widely applied to the field of structural reliability measurement.
According to another aspect of the present invention, there is provided a system for measuring reliability of an ensemble interference type, comprising a modeling module, a normalization transformation module, a sampling module, and a calculation module;
the modeling module is used for establishing a convex set model for describing structural uncertainty and dividing the convex set model into an interval model and a hyper-ellipsoid model;
the standardized transformation module is used for respectively carrying out standardized transformation on the interval model and the hyperellipsoid model to obtain a standardized interval model and a unit hypersphere model, and obtaining a standardized extreme state equation according to the standardized interval model and the unit hypersphere model;
the sampling module is used for respectively and uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized extreme state equation to respectively obtain an interval model sample and a hypersphere model sample;
and the calculation module is used for obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the set interference type reliability of the structure according to the standardized extreme state equation and the composite sample.
The beneficial effects of the invention are: the convex set model is established through the modeling module and is divided into an interval model and a hyperellipsoid model, so that the structural uncertainty of the coexistence condition of hyperellipsoid variables and interval variables can be conveniently described; because the ratio of the volume of the structural security domain to the total volume of the basic variable domain is taken as the structural set interference type reliability in the set interference model, the normalized transformation module is used for respectively performing normalized transformation on the interval model and the hyperellipsoid model to obtain a normalized extreme state equation, so that the subsequent sampling module can perform uniform sampling according to the normalized extreme state equation to obtain a composite sample, the ratio of the volume of the security domain to the total volume of the basic variable domain can be conveniently obtained, a data basis is provided for the subsequent calculation module to measure the set interference reliability, and the high-efficiency and accurate measurement of the set interference reliability is facilitated;
the method of the measuring system of the invention has strict theory, ensures the uniform distribution of the sampling samples of the (super) ellipsoid convex set with any dimension on the basis of the standardized extreme state equation, overcomes the theoretical defects of the traditional sampling method, ensures the accuracy and credibility of the reliability simulation result, effectively solves the measuring problem of the set interference reliability containing the (super) ellipsoid convex set model, is suitable for convex set models with different conditions, thereby measuring the reliability of different types of structures, and ensures the accuracy and credibility of the reliability calculation result.
According to another aspect of the present invention, there is provided another apparatus for aggregate interferometric reliability measurement, comprising a processor, a memory and a computer program stored in the memory and executable on the processor, wherein the computer program is operable to implement the steps of a method for aggregate interferometric reliability measurement according to the present invention.
The invention has the beneficial effects that: the measuring device for the set interference type reliability is realized by a computer program stored on a memory and running on a processor, the method is rigorous in theory, the uniform distribution of any dimension (super) ellipsoid convex set sampling samples is ensured on the basis of a standardized extreme state equation, the theoretical defect of the traditional sampling method is overcome, the accuracy and the credibility of a reliability simulation result are ensured, the measuring problem of the set interference reliability containing a (super) ellipsoid convex set model is effectively solved, and the measuring device is suitable for convex set models under different conditions, so that the reliability of different types of structures can be measured, the accuracy and the credibility of a reliability calculation result are ensured, the method is simple, convenient and practical, the operability is strong, the calculation efficiency and the accuracy of the set interference reliability of a large-scale complex structure are effectively improved, and the measuring device can be widely applied to the field of structure reliability measurement.
In accordance with another aspect of the present invention, there is provided a computer storage medium comprising: at least one instruction which, when executed, performs a step in a method for aggregate interferometric reliability measurement of the present invention.
The beneficial effects of the invention are: the method is rigorous in theory, ensures the uniform distribution of any dimension (super) ellipsoid convex set sampling samples on the basis of a standardized extreme state equation, overcomes the theoretical defects of the traditional sampling method, ensures the accuracy and the credibility of a reliability simulation result, effectively solves the measurement problem of the set interference reliability of a (super) ellipsoid convex set model, is suitable for convex set models under different conditions, can measure the reliability of different types of structures, ensures the accuracy and the credibility of a reliability calculation result, is simple, convenient and practical, has strong operability, effectively improves the calculation efficiency and the accuracy of the set interference reliability of a large-scale complex structure, and can be widely applied to the field of structure reliability measurement.
Drawings
FIG. 1 is a first flowchart illustrating a method for measuring reliability of integrated interference type according to a first embodiment of the present invention;
FIG. 2 is a cross-sectional view of a middle annular rib reinforced cylindrical shell according to an embodiment of the present invention;
FIG. 3 is a top view of a middle annular rib reinforced cylindrical shell according to an embodiment of the present invention;
FIG. 4 is a flowchart illustrating a second method for measuring reliability of integrated interference type according to a first embodiment of the present invention;
FIG. 5 is a diagram illustrating a structure of a metrology system for integrated interferometric reliability in a second embodiment of the present invention.
In the drawings, the components represented by the respective reference numerals are listed below:
1. shell, 2, ribs.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth to illustrate, but are not to be construed to limit the scope of the invention.
The present invention will be described with reference to the accompanying drawings.
In a first embodiment, as shown in fig. 1, a method for measuring reliability of an integrated interferometric type includes the following steps:
s1: establishing a convex set model for describing structural uncertainty, and dividing the convex set model into an interval model and a hyper-ellipsoid model;
s2: respectively carrying out standardized transformation on the interval model and the hyperellipsoid model to obtain a standardized interval model and a unit hypersphere model, and obtaining a standardized limit state equation according to the standardized interval model and the unit hypersphere model;
s3: respectively and uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized extreme state equation to respectively obtain an interval model sample and a hypersphere model sample;
s4: and obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the set interference type reliability of the structure according to the standardized extreme state equation and the composite sample.
The measurement method of the embodiment is rigorous in theory, ensures the uniform distribution of any dimension (super) ellipsoid convex set sampling sample on the basis of a standardized extreme state equation, overcomes the theoretical defects of the traditional sampling method, ensures the accuracy and credibility of a reliability simulation result, effectively solves the measurement problem of the set interference reliability of the (super) ellipsoid convex set model, is suitable for convex set models under different conditions, can measure the reliability of different types of structures, ensures the accuracy and credibility of a reliability calculation result, is simple, convenient and practical, has strong operability, effectively improves the calculation efficiency and precision of the set interference reliability of large-scale complex structures, and can be widely applied to the field of structural reliability measurement.
The structure in this embodiment is a circular rib reinforced cylindrical shell, and for the measurement of the reliability of the integrated interference of the circular rib reinforced cylindrical shell, the instability reliability of the circular rib reinforced cylindrical shell is mainly analyzed and calculated, where the structure of the circular rib reinforced cylindrical shell is respectively shown in fig. 2 and 3, and includes a shell 1 and ribs 2 uniformly distributed at intervals inside the shell 1.
Preferably, as shown in fig. 4, S1 specifically includes the following steps:
s11: establishing an original extreme state equation of the structure according to the uncertainty parameter variable of the structure, and obtaining the convex set model according to the original extreme state equation;
the original extreme state equation is:
M＝G(X)＝G(x 1 ,x 2 ,...,x n )＝0；
where M is the original extreme state equation, G (X) is the original extreme state function, and X = (X) 1 ,x 2 ,...,x n ) Is the uncertainty parameter variable, n is the total number of the uncertainty parameter variable;
s12: dividing the convex set model into a p-dimensional interval model and m hyper-ellipsoid models;
the interval model is as follows: x I ＝(x 1 ,x 2 ,...,x p )；
Wherein, X I Interval variable vector, x, of the interval model in p dimension 1 、x 2 …x p All are interval uncertainty parameter variables;
the hyper-ellipsoid model is as follows:
wherein, X i A hyperellipsoid variable vector of the ith said hyperellipsoid model, E i (X i ,θ i ) For the ith set of said hyperellipsoid variable vectors,
is the central point vector, omega, of the ith hyper-ellipsoid model i Is the ith positive definite matrix, theta i Is the scale parameter of the ith super ellipsoid model.
In order to obtain a basic variable domain and a safety domain of a structure, when a convex set model is established, firstly, an uncertain parameter variable of the structure is determined, an original extreme state equation of the convex set model is established according to the uncertain parameter variable, and due to the difference of complex structures, the types of the convex set models established by different structures are different.
Specifically, the critical pressure p for buckling of the plate shell between adjacent ribs in FIG. 2 of this embodiment cr Calculated as p cr ＝C g C s p E Wherein p is E For destabilizing the Euler pressure, C g First model correction factor, C, for accounting for the effects of initial geometric defects on the calculation itself and shell out-of-roundness s The second model correction factor for the calculation itself and the influence of plasticity and residual stress is taken into account.
P when the Poisson coefficient of the material is 0.3 E Is calculated by the formula
Wherein E is the elastic modulus of the material, h is the thickness of the shell, r is the radius of the shell, u is a dimensionless parameter, and->
Where l is the rib spacing.
According to the method of step 11 of this embodiment, the original extreme state equation for destabilization of the shell structure of the annular rib reinforced cylindrical shell is set to G sh (p,p cr )＝p cr -p =0, wherein p is the actual bearing pressure of the shell;
the actual bearing pressure p of the shell, the radius r of the shell, the thickness h of the shell, the elastic modulus E of the material, the interval l of the ribs and the correction coefficient C of a first model g And a second model correction coefficient C s As uncertainty parameter variables, establishing a convex set model according to the uncertainty parameter vectors; the above original extreme state equation can be further rewritten:
specifically, in this embodiment, the actual bearing pressure p of the casing is an interval variable, which constitutes a one-dimensional interval model, X i ＝(r,h,E,l,C s ,C g ) T For the hyperellipsoid variables, a six-dimensional hyperellipsoid model is constructed and i =1, described by the hyperellipsoid model:
wherein, in this embodiment, θ is known 1 =1, and knows the following vector:
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 fig. 4, S2 specifically includes the following steps:
s21: converting the interval variable according to an interval standard conversion formula to obtain a standard interval model;
the interval standardization transformation formula is as follows:
wherein the content of the first and second substances,
is the interval variable X I Of the central value vector, Δ X I Is the interval variable X I Of the dispersion vector, delta I Is a normalized interval variable of dimension p and delta I ∈[-1,1] p ；
S22: transforming the m hyper-ellipsoid models according to a hyper-ellipsoid standardized transformation formula to obtain m unit hyper-spheroid models;
the normalized transformation formula of the hyperellipsoid is as follows:
the unit hypersphere model is: Δ u i ∈{Δu i :Δu i T Δu i ≤1},(i＝1,2,…,m)；
Wherein Q is i Is the (i) th orthogonal matrix and,
as a transpose of the ith said orthogonal matrix, D i For the ith diagonal matrix, Δ u i Normalized hypersphere variable, Δ u, for the ith said unit hypersphere model i T Transposed vector, u, for the ith said normalized hypersphere variable i For the introduction vector of the i-th said unit hypersphere model, <>
Is the center point vector of the ith said unit hypersphere model, and &>
I i Is the ith identity matrix;
s23: obtaining the standardized extreme state equation according to the original extreme 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 ,…,Δu m )＝0；
wherein M' is the normalized extreme state equation, δ is the normalized variable and δ = (δ) 1 ,Δu 1 ,Δu 2 ,…,Δu m ) G' (delta) is a normalized limit state function, Δ u 1 、Δu 2 …Δu m Are all the normalized hypersphere variables.
In the embodiment, a standardized interval variable and a unit hyper-sphere model are obtained through standardized transformation, so that a standardized extreme state equation of the whole convex set model is conveniently obtained, the interval model and the hyper-ellipsoid model are respectively uniformly sampled according to the standardized extreme state equation, a theoretical basis is laid for measuring the reliability of the set interference type according to the ratio of the volume of a security domain to the total volume of a basic variable domain obtained by combining compound samples obtained after uniform sampling, and the reliability of the set interference type is more accurate and efficient.
Specifically, the interval model of this embodiment is a one-dimensional interval model, the hyper-ellipsoid model is a six-dimensional hyper-ellipsoid model, and the hyper-ellipsoid model and the interval model are subjected to standardized transformation, respectively, and the obtained standardized extreme state equation is:
wherein r is 1 、h 1 、E 1 、l 1 、C s1 And C g1 Respectively, a normalized hypersphere variable, p, after normalized transformation 1 To normalize the transformed normalized interval variable, r 1 、h 1 、E 1 、l 1 、C s1 And C g1 Form a six-dimensional unitHypersphere model, p 1 Form a one-dimensional normalized interval variable and p 1 ∈[-1,1]。
Preferably, as shown in fig. 4, in S3, the specific step of obtaining the interval model sample includes:
s31: and acquiring a first random number of the standardized interval model in a first preset sampling range, and uniformly sampling the standardized interval model according to the first random number and the standardized limit state equation to obtain the interval model sample.
Because the possibility that the standardized interval variable takes each value in the interval is the same, the p-dimensional standardized interval variable in the invention is uniformly distributed in the first preset sampling range, so that the first random number of the p-dimensional standardized interval variable in the first preset sampling range is obtained, the uniform sampling of the standardized interval variable can be realized, and the accuracy of the interference reliability of the subsequent measurement set is improved conveniently.
Specifically, the embodiment first extracts the normalized interval variable at [0,1 ] using the rand command in MATLAB] p (first predetermined sampling range) due to the first predetermined sampling range and the aforementioned normalized interval variable p 1 The normalized interval variable is converted to: p is a radical of 1 ＝2p Δ -1 and p Δ ∈[0,1]Realizing the normalized interval variable p in the present embodiment 1 And (4) extracting a sample.
Preferably, as shown in fig. 4, in S3, the specific step of obtaining the hypersphere model sample includes:
s32: acquiring a radial probability density function of a radial distance component of the unit hyper-sphere model in a spherical coordinate system, acquiring a second random number of an elevation angle component of the unit hyper-sphere model in the spherical coordinate system in a second preset sampling range, and acquiring a third random number of a direction angle component of the unit hyper-sphere model in the spherical coordinate system in a third preset sampling range;
s33: uniformly sampling the elevation component according to the second random number to obtain an elevation component sample; uniformly sampling the direction angle component according to the third random number to obtain a direction angle component sample; based on a Metropolis sampling method, sampling the radial distance component according to the radial probability density function to obtain a radial distance component sample;
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 direction angle component sample and the radial distance component sample;
step 35: converting the initial hyper-sphere model sample according to a conversion formula of a spherical coordinate system and an orthogonal coordinate system to obtain the hyper-sphere model sample of the unit hyper-sphere model in the orthogonal coordinate system;
the conversion formula of the spherical coordinate system and the orthogonal coordinate system is as follows:
wherein n is i Dimension of the ith said unitary hyper-sphere model, deltau i,1 Is the 1 st dimensional coordinate component, delauu, of the ith unit hyper-sphere model in the orthogonal coordinate system i,2 Is the 2 nd dimension coordinate component of the unit hyper-sphere model in the orthogonal coordinate system,
for the ith said unit hyper-sphere model in said orthogonal coordinate system i -a 1-dimensional coordinate component, -a->
For the ith said unit hyper-sphere model in said orthogonal coordinate system i Component of dimensional coordinate, r i For the radial distance component of the ith unit hypersphere model in the spherical coordinate system, < >>
Are all as followsThe elevation component of i of the unit hypersphere models in the spherical coordinate system, and +>
For the direction angle component of the ith unit hyper-sphere model in the spherical coordinate system, and->
Wherein, for the formula of omitting part in the conversion formula of the spherical coordinate system and the orthogonal coordinate system, when h is more than or equal to 2 and less than or equal to n i In case of-1, the formula of the omitted portion is Δ u i,h ＝r i sinβ 1 sinβ 2 …sinβ h-1 cosβ h ，Δu i,h Is the h-dimension coordinate component of the ith unit hyper-sphere model in the orthogonal coordinate system.
By the sampling method, the radial distance component in the spherical coordinate system and the components (namely the elevation angle component and the direction angle component) in the other spherical coordinate systems can be respectively sampled, and then the hypersphere model sample which accords with the uniform distribution of the hypersphere model of the unit hypersphere model is obtained through coordinate transformation, so that the accuracy of the interference reliability of the subsequent measurement set is improved conveniently.
Specifically, the present embodiment samples the elevation angle component and the direction angle component due to n of the present embodiment i =6, so the elevation component β 1 ～β 4 ∈[0,π]Sample extraction of (2) first extract the interval [0,1 ] using the rand command in MATLAB]Multiplying the random number by pi to obtain the random number; angular component of direction beta 5 ∈[0,2π]The sample extraction of (2) is performed by first extracting the interval [0,1 ] in MATLAB by using the rand command]And then multiplying the random number by 2 pi.
Preferably, in S32, the specific step of obtaining the radial probability density function includes:
s321: respectively calculating the volume and the surface area of the unit hypersphere model under the spherical coordinate system;
the volume is:
wherein the content of the first and second substances,
is n i The volume, R, of the unit hyper-sphere model of dimensions i Is n i A radius of the unit hyper-sphere model of dimensions;
Γ (-) is a gamma function, and when n i In the case of an even number, the number of the first,
when n is i In the case of an odd number of the groups,
is given a constant, and->
The surface area is:
wherein, the first and the second end of the pipe are connected with each other,
is n of the unit hyper-sphere model i -said surface area of a 1-dimensional sphere;
s322: obtaining the radial probability density function according to the volume and the surface area;
the radial probability density function is:
wherein, f (r) i ) The radial probability density function for the ith said unit hyper-sphere model.
Through the radial probability density function, the radial distance component is convenient to sample, and the unit hyper-sphere model is ensured to be obtained to obey uniformly distributed hyper-sphere model samples under an orthogonal coordinate system.
Specifically, the radial probability density function of the six-dimensional unit hyper-sphere model of the present embodiment is:
the process of adopting the Metropolis sampling method comprises the following steps: when t =0, selecting an initial value r 0 And f (r) 0 ) Not less than 0; at t +1 iterations, the distribution q (r) is distributed by suggestion 1 |r t ) Extracting a candidate value r c And the distribution is proposed to be symmetrical, such as normal distribution or interval uniform distribution; and let α = min [ f (r) c )/f(r t ),1]And the transition probability of alpha satisfies r t+1 ＝r c The transition probability of 1-alpha satisfies r t+1 ＝r t (ii) a The distribution f (r) is obtained by the above sampling 1 ) And f (r) is obtained from the Markov chain (Markov chain) 1 ) The radial distance component is sampled according to the fourth random number.
Preferably, as shown in fig. 2, in S4, the specific step of calculating the set interference type reliability of the structure is:
calculating the set interference type reliability according to the standardized extreme state equation, the composite sample and a set interference type reliability calculation formula;
the set interference type reliability calculation formula is as follows:
wherein R is set Is the said setCombined interference type reliability, q all For the total number of sample points in the composite sample, q s The number of sample points in the composite sample that satisfy G' (δ) > 0.
The total number of sample points in the composite sample can be equivalent to the total volume of the structural basic domain, and according to the standardized extreme state equation G '(delta) =0 of S23, the number of sample points satisfying G' (delta) > 0 in the composite sample can be equivalent to the volume of a safety domain, so that the set interference reliability calculation formula can efficiently and accurately measure the set interference reliability of the structure; the sampling technology has strict mathematical theory support, ensures the rigor and effectiveness of sampling, ensures the accuracy and credibility of the reliability calculation result, has simple, convenient and practical method and strong operability, effectively improves the calculation efficiency and precision of the interference reliability of the large complex structure set, and can be widely applied to the field of structural reliability measurement.
Specifically, the total number of sample points in the composite sample obtained in this embodiment is 1000 ten thousand times, and the aggregate interference reliability of the annular rib reinforced cylindrical shell calculated according to the aggregate interference reliability calculation formula is 0.9985185, and in addition, this embodiment also adopts a conventional measurement method, that is, the radial distance component of the spherical coordinate system is also sampled in uniform distribution, and the obtained reliability result is 0.9997206 under the same total number of sample points, so that, in the conventional sampling strategy, due to a method defect, the obtained composite sample is gathered in the middle of the unit hyper-sphere model, that is, a density non-uniformity phenomenon is present, which directly results in a larger measurement result of the structural reliability, that is, more samples fall in a safety domain, and such an error is difficult to predict, which results in distortion and loss of reliability results.
In a second embodiment, as shown in fig. 5, a system for measuring reliability of an ensemble interference type includes a modeling module, a normalization transformation module, a sampling module, and a calculation module;
the modeling module is used for establishing a convex set model for describing structural uncertainty and dividing the convex set model into an interval model and a hyper-ellipsoid model;
the standardized transformation module is used for respectively carrying out standardized transformation on the interval model and the hyperellipsoid model to obtain a standardized interval model and a unit hypersphere model, and obtaining a standardized extreme state equation according to the standardized interval model and the unit hypersphere model;
the sampling module is used for respectively and uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized extreme state equation to respectively obtain an interval model sample and a hypersphere model sample;
and the calculation module is used for obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the set interference type reliability of the structure according to the standardized extreme state equation and the composite sample.
A convex set model is established through a modeling module and is divided into an interval model and a hyper-ellipsoid model, so that the structural uncertainty of the coexistence condition of hyper-ellipsoid variables and interval variables can be conveniently described; because the ratio of the volume of the structural security domain to the total volume of the basic variable domain is taken as the structural set interference type reliability in the set interference model, the normalized transformation module is used for respectively performing normalized transformation on the interval model and the hyperellipsoid model to obtain a normalized extreme state equation, so that the subsequent sampling module can perform uniform sampling according to the normalized extreme state equation to obtain a composite sample, the ratio of the volume of the security domain to the total volume of the basic variable domain can be conveniently obtained, a data basis is provided for the subsequent calculation module to measure the set interference reliability, and the high-efficiency and accurate measurement of the set interference reliability is facilitated;
the measurement system of the embodiment has strict theory, ensures the uniform distribution of any dimension (super) ellipsoid convex set sampling samples on the basis of a standardized extreme state equation, overcomes the theoretical defects of the traditional sampling method, ensures the accuracy and credibility of a reliability simulation result, effectively solves the measurement problem of the set interference reliability of a (super) ellipsoid convex set model, is suitable for convex set models in different conditions, can measure the reliability of different types of structures, ensures the accuracy and credibility of a reliability calculation result, is simple, convenient and practical, has strong operability, effectively improves the calculation efficiency and precision of the set interference reliability of large-scale complex structures, and can be widely applied to the field of structural reliability measurement.
Third embodiment, based on the first embodiment and the second embodiment, the present embodiment further discloses a measurement apparatus for measuring reliability of an aggregate interference type, including a processor, a memory, and a computer program stored in the memory and executable on the processor, where the computer program implements the following steps as shown in fig. 1 when running:
s1: establishing a convex set model for describing structural uncertainty, and dividing the convex set model into an interval model and a hyper-ellipsoid model;
s2: respectively carrying out standardized transformation on the interval model and the hyper-ellipsoid model 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: respectively and uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized extreme state equation to respectively obtain an interval model sample and a hypersphere model sample;
s4: and obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and calculating the set interference type reliability of the structure according to the standardized extreme state equation and the composite sample.
The measuring device for the set interference type reliability is realized by a computer program stored on a memory and running on a processor, the method is rigorous in theory, the uniform distribution of any dimension (super) ellipsoid convex set sampling samples is ensured on the basis of a standardized extreme state equation, the theoretical defect of the traditional sampling method is overcome, the accuracy and the credibility of a reliability simulation result are ensured, the measuring problem of the set interference reliability containing a (super) ellipsoid convex set model is effectively solved, and the measuring device is suitable for convex set models under different conditions, so that the reliability of different types of structures can be measured, the accuracy and the credibility of a reliability calculation result are ensured, the method is simple, convenient and practical, the operability is strong, the calculation efficiency and the accuracy of the set interference reliability of a large-scale complex structure are effectively improved, and the measuring device can be widely applied to the field of structure reliability measurement.
The present embodiment also provides a computer storage medium, where at least one instruction is stored on the computer storage medium, and when executed, the instruction implements the specific steps of S1 to S4.
The method is rigorous in theory, ensures the uniform distribution of any dimension (super) ellipsoid convex set sampling samples on the basis of a standardized extreme state equation, overcomes the theoretical defects of the traditional sampling method, ensures the accuracy and the credibility of a reliability simulation result, effectively solves the measurement problem of the set interference reliability of a (super) ellipsoid convex set model, is suitable for convex set models under different conditions, can measure the reliability of different types of structures, ensures the accuracy and the credibility of a reliability calculation result, is simple, convenient and practical, has strong operability, effectively improves the calculation efficiency and the accuracy of the set interference reliability of a large-scale complex structure, and can be widely applied to the field of structure reliability measurement.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (9)
1. A method for measuring reliability of the collective interference type, comprising the steps of:
step 1: establishing a convex set model for describing structural uncertainty, and dividing the convex set model into an interval model and a hyper-ellipsoid model;
and 2, step: respectively carrying out standardized transformation on the interval model and the hyperellipsoid model to obtain a standardized interval model and a unit hypersphere model, and obtaining a standardized limit state equation according to the standardized interval model and the unit hypersphere model;
and 3, step 3: respectively and uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized extreme state equation to respectively obtain an interval model sample and a hypersphere model sample;
and 4, 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 set interference type reliability of the structure according to the standardized extreme state equation and the composite sample;
in the step 3, the specific steps of obtaining the hypersphere model sample include:
step 32: acquiring a radial probability density function of a radial distance component of the unit hyper-sphere model in a spherical coordinate system, acquiring a second random number of an elevation angle component of the unit hyper-sphere model in the spherical coordinate system in a second preset sampling range, and acquiring a third random number of a direction angle component of the unit hyper-sphere model in the spherical coordinate system in a third preset sampling range;
step 33: uniformly sampling the elevation component according to the second random number to obtain an elevation component sample; uniformly sampling the direction angle component according to the third random number to obtain a direction angle component sample; based on a Metropolis sampling method, sampling the radial distance component according to the radial probability density function to obtain a radial distance component sample;
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 direction angle component sample and the radial distance component sample;
step 35: converting the initial hyper-sphere model sample according to a conversion formula of a spherical coordinate system and an orthogonal coordinate system to obtain the hyper-sphere model sample of the unit hyper-sphere model in the orthogonal coordinate system;
the conversion formula of the spherical coordinate system and the orthogonal coordinate system is as follows:
wherein n is i Dimension of the ith said unitary hyper-sphere model, deltau i,1 Is the 1 st dimensional coordinate component, delauu, of the ith unit hyper-sphere model in the orthogonal coordinate system i,2 Is the 2 nd dimension coordinate component of the unit hyper-sphere model in the orthogonal coordinate system,
for the ith said unit hyper-sphere model in said orthogonal coordinate system i -a 1-dimensional coordinate component, based on the measured value of the sensor>
For the ith said unit hyper-sphere model in said orthogonal coordinate system i Component of dimensional coordinate, r i For said radial distance component, β, of the ith said unit hyper-sphere model in said spherical coordinate system 1 ～/>
Said elevation component, in said spherical coordinate system, of each of said ith said unit hypersphere model>
Is the direction angle component of the ith unit hyper-sphere model in the spherical coordinate system, and beta 1 ～/>
，/>
2. The method for collective interferometric reliability measurement according to claim 1, wherein the step 1 comprises the following steps:
step 11: establishing an original extreme state equation of the structure according to the uncertainty parameter variable of the structure, and obtaining the convex set model according to the original extreme state equation;
the original extreme state equation is:
M＝G(X)＝G(x 1 ,x 2 ,...,x n )＝0；
wherein M is the original extreme state equation, G (X) is the original extreme state function, and X = (X) 1 ,x 2 ,...,x n ) Is the uncertainty parameter variable, n is the total number of the uncertainty parameter variable;
step 12: dividing the convex set model into a p-dimensional interval model and m hyper-ellipsoid models;
the interval model is as follows: x I ＝(x 1 ,x 2 ,...,x p )；
Wherein X I Interval variable, x, of the interval model in p dimension 1 、x 2 …x p All are interval uncertainty parameter variables;
the hyperellipsoid model is as follows:
wherein X i A hyper-ellipsoid variable of the i-th said hyper-ellipsoid model, E i (X i ,θ i ) For the ith set of the hyper-ellipsoid variables,
is the central point vector, omega, of the ith hyper-ellipsoid model i Is the ith positive definite matrix, theta i Is the scale parameter of the ith super ellipsoid model.
3. The method for measuring the reliability of the collective interference type according to claim 2, wherein the step 2 comprises the following steps:
step 21: converting the interval variable according to an interval standard conversion formula to obtain a standard interval model;
the interval standardization transformation formula is as follows:
wherein the content of the first and second substances,
is the interval variable X I Of central value vector, Δ X I Is the interval variable X I Of the dispersion vector, delta I Is a normalized interval variable of dimension p and delta I ∈[-1,1] p ；
Step 22: transforming the m hyper-ellipsoid models according to a hyper-ellipsoid standardized transformation formula to obtain m unit hyper-spheroid models;
the normalized transformation formula of the hyperellipsoid is as follows:
the unit hypersphere model is: Δ u i ∈{Δu i :Δu i T Δu i ≤1},i＝1,2,…,m；
Wherein Q is i Is the (i) th orthogonal matrix and,
as a transpose of the ith said orthogonal matrix, D i For the ith diagonal matrix, Δ u i Normalized hypersphere variable, Δ u, for the ith said unit hypersphere model i T As the transposed vector, u, of the ith said normalized hypersphere variable i An import vector for the ith said unit hypersphere model>
Is the vector of the center point of the ith unit hyper-sphere model, and is Delta u i ＝u i -u i 0 ，/>
I i Is the ith identity matrix;
step 23: obtaining the standardized extreme state equation according to the original extreme 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 ,…,Δu m )＝0；
where M' is the normalized extreme state equation, δ is the normalized variable and δ = (δ) 1 ,Δu 1 ,Δu 2 ,…,Δu m ) G' (delta) is a normalized limit state function, Δ u 1 、Δu 2 …Δu m Are all the normalized hypersphere variables.
4. The method for measuring the reliability of the collective interference type according to claim 3, wherein in the step 3, the step of obtaining the interval model samples comprises:
step 31: and acquiring a first random number of the standardized interval model in a first preset sampling range, and uniformly sampling 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 collective interferometric reliability measurement according to claim 3, wherein the step 32 of obtaining the radial probability density function comprises:
step 321: respectively calculating the volume and the surface area of the unit hypersphere model under the spherical coordinate system;
the volume is:
wherein the content of the first and second substances,
is n i The volume, R, of the unit hyper-sphere model of dimensions i Is n i A radius of the unit hyper-sphere model of dimensions;
Γ (-) is a gamma function, and when n i In the case of an even number, the number of the bits is,
when n is i In the case of an odd number of the groups,
is given a constant, and->
The surface area is:
wherein, the first and the second end of the pipe are connected with each other,
is n of the unit hyper-sphere model i -said surface area of a 1-dimensional sphere;
step 322: obtaining the radial probability density function according to the volume and the surface area;
the radial probability density function is:
wherein, f (r) i ) The radial probability density function for the ith said unit hyper-sphere model.
6. The method for collective interferometric reliability according to claim 4, wherein in the step 4, the specific step of calculating the collective interferometric reliability of the structure is:
calculating the set interference type reliability according to the standardized extreme state equation, the composite sample and a set interference type reliability calculation formula;
the set interference type reliability calculation formula is as follows:
wherein R is set For said collective interferometric type reliability, q all For the total number of sample points in the composite sample, q s The number of sample points in the composite sample that satisfy G' (δ) > 0.
7. A measurement system of the reliability of the set interference type is characterized by comprising a modeling module, a standardized transformation module, a sampling module and a calculation module;
the modeling module is used for establishing a convex set model for describing structural uncertainty and dividing the convex set model into an interval model and a hyper-ellipsoid model;
the standardized transformation module is used for respectively carrying out standardized transformation on the interval model and the hyperellipsoid model to obtain a standardized interval model and a unit hypersphere model, and obtaining a standardized extreme state equation according to the standardized interval model and the unit hypersphere model;
the sampling module is used for respectively and uniformly sampling the standardized interval model and the unit hypersphere model according to the standardized limit state equation to respectively obtain an interval model sample and a hypersphere model sample;
the computing module is used for obtaining a composite sample of the convex set model according to the interval model sample and the hypersphere model sample, and computing the set interference type reliability of the structure according to the standardized extreme state equation and the composite sample;
the sampling module is specifically configured to:
acquiring a radial probability density function of a radial distance component of the unit hyper-sphere model in a spherical coordinate system, acquiring a second random number of an elevation angle component of the unit hyper-sphere model in the spherical coordinate system in a second preset sampling range, and acquiring a third random number of a direction angle component of the unit hyper-sphere model in the spherical coordinate system in a third preset sampling range;
uniformly sampling the elevation component according to the second random number to obtain an elevation component sample; uniformly sampling the direction angle component according to the third random number to obtain a direction angle component sample; based on a Metropol is sampling method, sampling the radial distance component according to the radial probability density function to obtain a radial distance component sample;
obtaining an initial hypersphere model sample of the unit hypersphere model in the spherical coordinate system according to the elevation component sample, the direction angle component sample and the radial distance component sample;
converting the initial hypersphere model sample according to a conversion formula of a spherical coordinate system and an orthogonal coordinate system to obtain a hypersphere model sample of the unit hypersphere model in the orthogonal coordinate system;
the conversion formula of the spherical coordinate system and the orthogonal coordinate system is as follows:
wherein n is i Dimension of the ith said unitary hyper-sphere model, deltau i,1 Is the 1 st dimensional coordinate component, delauu, of the ith unit hyper-sphere model in the orthogonal coordinate system i,2 Is the 2 nd dimension coordinate component of the unit hyper-sphere model under the orthogonal coordinate system,
for the ith said unit hyper-sphere model in said orthogonal coordinate system i -a 1-dimensional coordinate component, -a->
For the ith said unit hyper-sphere model in said orthogonal coordinate system i Component of dimensional coordinate, r i For the radial distance component of the ith unit hypersphere model in the spherical coordinate system, < >>
The elevation component, in the spherical coordinate system, of each ith unit hyper-sphere model is greater than or equal to>
For the direction angle component of the ith unit hyper-sphere model in the spherical coordinate system, and->
8. An apparatus for aggregate interferometric reliability comprising a processor, a memory and a computer program stored in the memory and executable on the processor, the computer program when executed implementing the method steps of any one of claims 1 to 6.
9. A computer storage medium, the computer storage medium comprising: at least one instruction which when executed performs the method steps of any one of claims 1-6.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106021772A (en) * | 2016-05-31 | 2016-10-12 | 北京航空航天大学 | Existing structure static equivalent reliability evaluation method based on interval set envelope function |
| CN108536962A (en) * | 2018-04-10 | 2018-09-14 | 太原科技大学 | A kind of non-probability time-variant reliability assessment method of cantilever crane structure |
| CN108875233A (en) * | 2018-06-28 | 2018-11-23 | 电子科技大学 | Based on the structural reliability method of changeable weight response surface under Hybrid parameter matrix |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7003509B2 (en) * | 2003-07-21 | 2006-02-21 | Leonid Andreev | High-dimensional data clustering with the use of hybrid similarity matrices |
| US20160292248A1 (en) * | 2013-11-22 | 2016-10-06 | Cambridge Social Science Decision Lab Inc. | Methods, systems, and articles of manufacture for the management and identification of causal knowledge |
-
2019
- 2019-01-16 CN CN201910039746.6A patent/CN109885879B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106021772A (en) * | 2016-05-31 | 2016-10-12 | 北京航空航天大学 | Existing structure static equivalent reliability evaluation method based on interval set envelope function |
| CN108536962A (en) * | 2018-04-10 | 2018-09-14 | 太原科技大学 | A kind of non-probability time-variant reliability assessment method of cantilever crane structure |
| CN108875233A (en) * | 2018-06-28 | 2018-11-23 | 电子科技大学 | Based on the structural reliability method of changeable weight response surface under Hybrid parameter matrix |
Non-Patent Citations (5)
| Title |
|---|
| Non-probabilistic reliability-based topology optimization with multidimensional parallelepiped convex model;Zheng J 等;《Structural & Multidisciplinary Optimization》;20181231;第2205-2221页 * |
| 基于区间不确定性的涡轮盘强度可靠性优化设计;方鹏亚等;《推进技术》;20130715(第07期);第105-111页 * |
| 混合不确定信息航天机构可靠性综合分析方法;彭文胜等;《宇航学报》;20150530(第05期);第16-21页 * |
| 结构非概率可靠性模型在断裂力学分析中的应用研究;孙文彩 等;《应用基础与工程科学学报》;20100531;第816-822页 * |
| 超椭球凸集合可靠性综合指标定义及求解方法;周凌等;《航空学报》;20110726(第11期);第2025-2034页 * |
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