CN109284574A - A non-probabilistic reliability analysis method for series truss structure system - Google Patents

A non-probabilistic reliability analysis method for series truss structure system Download PDF

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CN109284574A
CN109284574A CN201811247772.XA CN201811247772A CN109284574A CN 109284574 A CN109284574 A CN 109284574A CN 201811247772 A CN201811247772 A CN 201811247772A CN 109284574 A CN109284574 A CN 109284574A
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truss structure
structure system
failure
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CN109284574B (en
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乔心州
王兵
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Xian University of Science and Technology
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Abstract

The invention discloses a kind of series connection truss structure system Multidisciplinary systems analysis methods, comprising steps of the power function of one, determining series connection each failure mode of truss structure system；Two, the multidimensional ellipsoidal model for describing uncertain variable is established；Three, the multidimensional for obtaining uncertain variable normalizes ellipsoidal model of equal value；Four, the hyper-sphere model of uncertain variable is obtained；Five, the volume of unit of account hyper-sphere model；Six, the wide boundary of the failure domain total volume of series connection truss structure system is obtained；Seven, the narrow boundary of the failure domain total volume of series connection truss structure system is obtained；Eight, the value range of the non-probability failure degree of series connection truss structure system is calculated；Nine, the value range of the non-probability decision degree of series connection truss structure system is calculated.The present invention considerably reduces the workload solved in the non-probability decision degree of series connection truss structure system by the width boundary interval estimation of the failure domain total volume of series connection truss structure system, provides relatively accurate reasonable estimated value.

Description

A kind of series connection truss structure system Multidisciplinary systems analysis method
Technical field
The invention belongs to truss Multidisciplinary systems analysis technical fields, and in particular to a kind of series connection truss structure system is non- Probability and reliability analysis method.
Background technique
The truss structure that truss is made of many rod pieces is evenly distributed with its internal force, reduces material consumption and structure certainly The advantages that heavy and light and be widely used in the fields such as mechanical, building, building and aerospace.In Truss Design and manufacturing process, Often there is uncertain informations relevant to load, material property, geometric dimension and boundary condition etc., need giving for science Consider.Analysis method for reliability is one of the effective way for handling above-mentioned uncertain information, therefore probabilistic reliability method obtains It is widely applied.However, in many engineering practical structures problems, for determining the distribution parameter or probability of probabilistic reliability model What the sample information of density function was usually a lack of, in this context, it is only necessary to know boundary or the variation model of uncertain parameter The Multidisciplinary systems analysis method of security evaluation can be carried out to it by, which enclosing, is gradually proposed.Existing structure Multidisciplinary systems It is for single failure mode that analysis is mostly, and such as Once approximate method and quadratic approximation, and truss structure is a typical tandem junction Structure multi-invalidation mode system, in theory, Monte Carlo can provide the Multidisciplinary systems point of series connection truss structure system The accurate solution of analysis, but it causes solution efficiency lower because amount of calculation is huge, therefore nowadays lacks a kind of effective string Copula frame structural body system Multidisciplinary systems analysis method.
Summary of the invention
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing a kind of series connection truss Structural system Multidisciplinary systems analysis method passes through the width boundary section of the failure domain total volume of series connection truss structure system Estimation considerably reduces the workload solved in the non-probability decision degree of series connection truss structure system, and it is relatively accurate reasonable to provide Estimated value, give the structural system Multidisciplinary systems analysis for more meeting actual requirement of engineering as a result, widely applicable and answer It is extensive with prospect, convenient for promoting the use of.
In order to solve the above technical problems, the technical solution adopted by the present invention is that: a kind of non-probability of series connection truss structure system Analysis method for reliability, which is characterized in that method includes the following steps:
Step 1: determining the power function of series connection each failure mode of truss structure system: using truss structure failure criteria Determine the power function g of series connection each failure mode of truss structure systemi(X), wherein i is the number of structural system failure mode And i=1,2 ..., I, I are the number of structural system failure mode, X is uncertain variable vector and X=(X1,X2,..., Xm)T, m is the dimension that uncertain variable number and m are equal to the uncertain variable vector X, XlFor first of uncertain variable, l is that the value range of positive integer and l are 1~m,Indicate first of uncertain variable Xl The section of value,Xl For uncertain variable XlLower bound,For uncertain variable XlThe upper bound；
Step 2: establishing the multidimensional ellipsoidal model for describing uncertain variable: being become using data processor to uncertainty Amount establishes multidimensional ellipsoidal model, obtains multidimensional ellipsoidal model Wherein, vector X0For multidimensional ellipsoid do not know domain central point vector and It is not true for first Qualitative variable XlValue interval midpoint, ΩxFor for determining the eigenmatrix of the shape of multidimensional ellipsoid and the multidimensional ellipsoid in direction AndZllFirst of uncertainty when to determine multidimensional ellipsoidal model according to NATAF method Variable XlWith first of uncertain variable XlCovariance, RmFor the real number field of m dimension；
Step 3: the multidimensional for obtaining uncertain variable normalizes ellipsoidal model of equal value, process is as follows:
The normalized of step 301, uncertain variable vector: according to formulaIt obtains uncertain The uncertain variable normalized vector U of property variable vector X, wherein U=(U1,U2,...,Um)T, UlFor first of uncertainty Variable XlCorresponding normalization variable,For first of uncertain variable XlSection radius and
Step 302, the multidimensional for constructing uncertain variable normalize ellipsoidal model of equal value: using data processor to uncertain Property variable normalized vector U construct the multidimensional of uncertain variable and normalize ellipsoidal model of equal value ΩuFor uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid eigenmatrix and For withDiagonal matrix is tieed up for the m of diagonal element；
Step 4: obtaining the hyper-sphere model of uncertain variable, process is as follows:
Step 401, to uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid spy Levy matrix ΩuCholeskey decomposition is carried out, i.e.,Wherein, L0Lower three angular moment decomposed for Choleskey Battle array；
Step 402 is normalized ellipsoidal model of equal value and converts to obtain uncertain variable and exists using data processor to multidimensional Unit hyper-sphere model E in the space normed space δδ=δ | δTδ≤1,δ∈Rm, wherein δ be uncertain variable normalize to Measure U the space normed space δ standardized vector and The dimension in the space normed space δ is m, δlTo normalize variable UlStandardized variable in the space normed space δ；
Obtain the relationship between the standardized vector δ in uncertain variable vector X and the space normed space δ:
To the power function g of series connection each failure mode of truss structure systemi(X) it is deformed in the space normed space δ Processing, obtains the Structural functional equation g of the failure mode in the space normed space δi(δ)；
Step 5: according to formulaUnit of account hyper-sphere model EδVolume VAlways, wherein Γ () is Gamma function；
Step 6: obtaining the wide boundary of the failure domain total volume of series connection truss structure system: in normed space, when i-th The Structural functional equation g of a failure modeiThe curved surface and unit hyper-sphere model E that (δ) is constitutedδIt is empty using normed space δ when intersection Between failure mode Structural functional equation giPoint and unit hyper-sphere model E on the curved surface that (δ) is constitutedδThe distance between origin is most Small value calculates the Structural functional equation g of the failure mode in the space normed space δi(δ) corresponding failure domain volume Vi；
According to wide bound method formulaThe failure domain for calculating series connection truss structure system is overall Product VF, alwaysWide boundary, wherein
Step 7: obtaining the narrow boundary of the failure domain total volume of series connection truss structure system: to failure domain volume ViMiddle I The corresponding failure domain volume of failure mode carries out sorting from large to small adjustment, the failure domain volume W=(W after being adjusted1, W2,...,WI)T, wherein W1~WIFor V1~VIIt is sorting from large to small as a result, i.e. W1>W2>...>WI, W1=max (Vi), WI= min(Vi)；
According to narrow bound method formula Calculate the failure domain total volume V of series connection truss structure systemF, alwaysNarrow boundary,It fails for the i-th failure mode and jth The total failure domain of mode；
Step 8: calculating series connection truss structure system according to the narrow boundary of the failure domain total volume of series connection truss structure system Non- probability failure degree value range ηs,F, wherein
Step 9: according to formula ηs,R=1- ηs,F, calculate the value model of the non-probability decision degree of series connection truss structure system Enclose ηs,R。
Above-mentioned a kind of series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: described uncertain Property variable number m be not less than 2；
As m=2, unit hyper-sphere model EδFor unit circle, the Structural functional equation of the failure mode in the space normed space δ giThe two-dimentional arch surface that the curved surface and unit circle that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the area of two-dimentional arch surfaceIt indicates, wherein h is the height of two-dimentional arch surface；
As m=3, unit hyper-sphere model EδFor unit sphere, the structure function letter of the failure mode in the space normed space δ Number giThe three-dimensional segment that the curved surface and unit sphere that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the volume of three-dimensional segmentIt indicates, wherein h' is the height of three-dimensional segment；
As m >=4, unit hyper-sphere model EδHypersphere, the structure function letter of the failure mode in the space normed space δ are tieed up for m Number giThe m dimension hypersphere that curved surface and m the dimension hypersphere that (δ) is constituted are crossed to form lacks, and fail domain volume V at this timeiWith the scarce body of m dimension hypersphere ProductIt indicates, wherein h " is that m ties up what hypersphere lacked It is high.
A kind of above-mentioned series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: the series connection purlin The power function g of each failure mode of frame structural body systemi(X)=0 it is known as failure critical surface, when series connection truss structure system respectively fails The power function g of modei(X) < 0 when, series connection truss structure system failure；When the function of series connection each failure mode of truss structure system It can function gi(X) >=0 when, series connection truss structure system safety.
Above-mentioned a kind of series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: described uncertain Property variable includes dead load, dynamic loading, length, width, elasticity modulus.
A kind of above-mentioned series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: i-th failure The total failure domain of mode and jth failure modeIt is acquired by numerical integration.
Compared with the prior art, the present invention has the following advantages:
1, the present invention is normalized by the multidimensional ellipsoidal model to uncertain variable, obtains uncertain change The multidimensional of amount normalizes ellipsoidal model of equal value, solves when the magnitude difference in uncertain variable vector between each variable is larger When, there is the problem of serious morbid state in the eigenmatrix of multidimensional ellipsoidal model, guarantees the essence of calculated result in numerical procedure It is all having the same to guarantee that the multidimensional after normalized normalizes all elements in the eigenmatrix of ellipsoidal model of equal value for degree Magnitude, convenient for promoting the use of.
2, the width boundary interval estimation that the present invention passes through the failure domain total volume of series connection truss structure system, wherein string The wide boundary interval estimation of the failure domain total volume of copula frame structural body system fails domain volume by single failure mode to estimate to lose Domain is imitated, then further consideration multi-mode fails domain the narrow boundary interval estimation of the failure domain total volume for truss structure system of connecting altogether Narrower interval estimation range is given, corresponding Multidisciplinary systems Measure Indexes, reliable and stable, using effect are defined It is good.
3, the method for the present invention step is simple, has fully considered engineering actual demand, has given and more meet actual requirement of engineering The analysis of structural system Multidisciplinary systems as a result, widely applicable and application prospect is extensive, greatly simplifie series connection truss knot The workload that structure system failure domain volume calculates effectively compensates for the prior art and is only capable of carrying out the structure under single failure mode The deficiency of Multidisciplinary systems analysis, has expanded the range of structure Multidisciplinary systems analysis method, to the reliable of structural system Property analysis have very important significance, convenient for promote the use of.
In conclusion width boundary interval estimation of the present invention by the failure domain total volume of series connection truss structure system, The workload solved in the non-probability decision degree of series connection truss structure system is considerably reduced, relatively accurate reasonable estimation is provided Value gives the structural system Multidisciplinary systems analysis for more meeting actual requirement of engineering as a result, widely applicable and application prospect Extensively, convenient for popularization and use.
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
Detailed description of the invention
Fig. 1 is method flow block diagram of the invention.
Fig. 2 is the structural schematic diagram of series connection truss structure system in the present embodiment.
Fig. 3 is the Structural functional equation g of the failure mode in the present embodiment Plays space space δi(δ) constitute curved surface with Unit hyper-sphere model EδIntersect schematic diagram.
Specific embodiment
As shown in Figure 1 to Figure 3, a kind of series connection truss structure system Multidisciplinary systems analysis method of the invention, including Following steps:
Step 1: determining the power function of series connection each failure mode of truss structure system: using truss structure failure criteria Determine the power function g of series connection each failure mode of truss structure systemi(X), wherein i is the number of structural system failure mode And i=1,2 ..., I, I are the number of structural system failure mode, X is uncertain variable vector and X=(X1,X2,..., Xm)T, m is the dimension that uncertain variable number and m are equal to the uncertain variable vector X, XlFor first of uncertain variable, l is that the value range of positive integer and l are 1~m,Indicate first of uncertain variable Xl The section of value,Xl For uncertain variable XlLower bound,For uncertain variable XlThe upper bound；
In the present embodiment, the uncertainty variable includes dead load, dynamic loading, length, width, elasticity modulus.
In the present embodiment, the power function g of series connection each failure mode of truss structure systemi(X)=0 it is known as failure to face Interface, as the power function g of series connection each failure mode of truss structure systemi(X) < 0 when, series connection truss structure system failure；When The power function g for each failure mode of truss structure system of connectingi(X) >=0 when, series connection truss structure system safety.
Step 2: establishing the multidimensional ellipsoidal model for describing uncertain variable: being become using data processor to uncertainty Amount establishes multidimensional ellipsoidal model, obtains multidimensional ellipsoidal model Wherein, vector X0For multidimensional ellipsoid do not know domain central point vector and It is not true for first Qualitative variable XlValue interval midpoint, ΩxFor for determining the eigenmatrix of the shape of multidimensional ellipsoid and the multidimensional ellipsoid in direction AndZllFirst of uncertainty when to determine multidimensional ellipsoidal model according to NATAF method Variable XlWith first of uncertain variable XlCovariance, RmFor the real number field of m dimension；
Step 3: the multidimensional for obtaining uncertain variable normalizes ellipsoidal model of equal value, process is as follows:
The normalized of step 301, uncertain variable vector: according to formulaIt obtains uncertain The uncertain variable normalized vector U of property variable vector X, wherein U=(U1,U2,...,Um)T, UlFor first of uncertainty Variable XlCorresponding normalization variable,For first of uncertain variable XlSection radius and
Step 302, the multidimensional for constructing uncertain variable normalize ellipsoidal model of equal value: using data processor to uncertain Property variable normalized vector U construct the multidimensional of uncertain variable and normalize ellipsoidal model of equal value ΩuFor uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid eigenmatrix and For withDiagonal matrix is tieed up for the m of diagonal element；
It should be noted that being normalized by the multidimensional ellipsoidal model to uncertain variable, obtain not really The multidimensional of qualitative variable normalizes ellipsoidal model of equal value, solves when the magnitude difference in uncertain variable vector between each variable When larger, there is the problem of serious morbid state in the eigenmatrix of multidimensional ellipsoidal model, guarantees calculated result in numerical procedure Precision, guarantee that the multidimensional after normalized normalizes all elements in the eigenmatrix of ellipsoidal model of equal value and all has phase Same magnitude, convenient for promoting the use of.
Step 4: obtaining the hyper-sphere model of uncertain variable, process is as follows:
Step 401, to uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid spy Levy matrix ΩuCholeskey decomposition is carried out, i.e.,Wherein, L0Lower three angular moment decomposed for Choleskey Battle array；
Step 402 is normalized ellipsoidal model of equal value and converts to obtain uncertain variable and exists using data processor to multidimensional Unit hyper-sphere model E in the space normed space δδ=δ | δTδ≤1,δ∈Rm, wherein δ be uncertain variable normalize to Measure U the space normed space δ standardized vector and The dimension in the space normed space δ is m, δlTo normalize variable UlStandardized variable in the space normed space δ；
Obtain the relationship between the standardized vector δ in uncertain variable vector X and the space normed space δ:
To the power function g of series connection each failure mode of truss structure systemi(X) it is deformed in the space normed space δ Processing, obtains the Structural functional equation g of the failure mode in the space normed space δi(δ)；
Step 5: according to formulaUnit of account hyper-sphere model EδVolume VAlways, wherein Γ () is Gamma function；
Step 6: obtaining the wide boundary of the failure domain total volume of series connection truss structure system: in normed space, when i-th The Structural functional equation g of a failure modeiThe curved surface and unit hyper-sphere model E that (δ) is constitutedδIt is empty using normed space δ when intersection Between failure mode Structural functional equation giPoint and unit hyper-sphere model E on the curved surface that (δ) is constitutedδThe distance between origin is most Small value calculates the Structural functional equation g of the failure mode in the space normed space δi(δ) corresponding failure domain volume Vi；
According to wide bound method formulaThe failure domain for calculating series connection truss structure system is overall Product VF, alwaysWide boundary, wherein
In the present embodiment, the uncertainty variable number m is not less than 2；
As m=2, unit hyper-sphere model EδFor unit circle, the Structural functional equation of the failure mode in the space normed space δ giThe two-dimentional arch surface that the curved surface and unit circle that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the area of two-dimentional arch surfaceIt indicates, wherein h is the height of two-dimentional arch surface；
As m=3, unit hyper-sphere model EδFor unit sphere, the structure function letter of the failure mode in the space normed space δ Number giThe three-dimensional segment that the curved surface and unit sphere that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the volume of three-dimensional segmentIt indicates, wherein h' is the height of three-dimensional segment；
As m >=4, unit hyper-sphere model EδHypersphere, the structure function letter of the failure mode in the space normed space δ are tieed up for m Number giThe m dimension hypersphere that curved surface and m the dimension hypersphere that (δ) is constituted are crossed to form lacks, and fail domain volume V at this timeiWith the scarce body of m dimension hypersphere ProductIt indicates, wherein h " is that m ties up what hypersphere lacked It is high.
Step 7: obtaining the narrow boundary of the failure domain total volume of series connection truss structure system: to failure domain volume ViMiddle I The corresponding failure domain volume of failure mode carries out sorting from large to small adjustment, the failure domain volume W=(W after being adjusted1, W2,...,WI)T, wherein W1~WIFor V1~VIIt is sorting from large to small as a result, i.e. W1>W2>...>WI, W1=max (Vi), WI= min(Vi)；
According to narrow bound method formula Calculate the failure domain total volume V of series connection truss structure systemF, alwaysNarrow boundary,It fails for the i-th failure mode and jth The total failure domain of mode；
In the present embodiment, the total failure domain of i-th failure mode and jth failure modePass through numerical integration It acquires.
It should be noted that the width boundary interval estimation of the failure domain total volume by series connection truss structure system, In, the wide boundary interval estimation of the failure domain total volume for truss structure system of connecting fails domain volume by single failure mode to estimate Meter failure domain, the narrow boundary interval estimation of the failure domain total volume for truss structure system of connecting then further consider that multi-mode is lost altogether Effect domain gives narrower interval estimation range, defines corresponding Multidisciplinary systems Measure Indexes, reliable and stable, uses effect Fruit is good.
Step 8: calculating series connection truss structure system according to the narrow boundary of the failure domain total volume of series connection truss structure system Non- probability failure degree value range ηs,F, wherein
Step 9: according to formula ηs,R=1- ηs,F, calculate the value model of the non-probability decision degree of series connection truss structure system Enclose ηs,R。
As shown in Fig. 2, in the present embodiment, it is not true there are three in 5 bar truss structures by taking plane 5 rods truss structure as an example Determine variable X1、X2And X3, three uncertain variables X1、X2And X3It is load, the allowable stress of No. 1 bar is 240kN, No. 2 bars Allowable stress is 200kN, and the allowable stress of No. 3 bars is 280kN, and the allowable stress of No. 4 bars is 280kN, the allowable stress of No. 5 bars For 180kN, three uncertain variables X1、X2And X3Related coefficientWith0.2 is taken, three uncertain Variable X1、X2And X3Value table it is as shown in table 1.
Table 1
The power function g of the failure mode of 5 bars is determined in MATLAB using truss structure failure criteriai(X), wherein
The power function of the failure mode of No. 1 bar
The power function of the failure mode of No. 2 bars
The power function of the failure mode of No. 3 bars
The power function of the failure mode of No. 4 bars
The power function of the failure mode of No. 5 bars
The eigenmatrix of the multidimensional ellipsoid of uncertain variable vector X is determined according to NATAF method
Then multidimensional ellipsoidal model
In order to effectively overcome interference caused by eigenmatrix pathosis, multidimensional ellipsoidal model is normalized, is obtainedTo uncertain variable normalized vector U normalization space u in feature Matrix ΩuCholeskey decomposition is carried out, i.e., Matrix after decomposition is substituted into multidimensional to normalize in ellipsoidal model of equal value, is obtained
Then, unit hyper-sphere model of the uncertain variable in the space normed space δ is represented by
Deformation process is carried out in the space normed space δ to uncertain variable normalized vector U, is obtained
To the power function g of series connection each failure mode of truss structure systemi(X) it is deformed in the space normed space δ Processing, obtains the Structural functional equation of the failure mode of No. 1 bar in the space normed space δ
The bar of the space normed space δ 2 The Structural functional equation of failure modeNormed space The Structural functional equation of the failure mode of No. 3 bars in the space δ
Standard null Between No. 4 bars in the space δ failure mode Structural functional equation
Standard null Between No. 5 bars in the space δ failure mode Structural functional equation
Unit hyper-sphere model EδVolume
M takes 3 in the present embodiment, unit hyper-sphere model EδFor unit sphere, the structure of the failure mode in the space normed space δ Power function giThe three-dimensional segment that the plane and unit sphere that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith three-dimensional segment VolumeIt indicates, wherein h' is the height of three-dimensional segment；
By the Structural functional equation g of the failure mode in the space normed space δiThe curved surface and unit hyper-sphere model E that (δ) is constitutedδ Intersected, utilizes the Structural functional equation g of the failure mode in the space normed space δiPoint and unit are super on the curved surface that (δ) is constituted Spherical model EδThe distance between origin minimum value calculates the Structural functional equation g of the failure mode in the space normed space δi(δ) is corresponding Failure domain volume Vi, ginseng is shown in Table 2.
Table 2
Failure mode Segment radius r The high h' of segment Fail domain volume
gδ1 1 0.1458 0.0635
gδ2 1 0.2648 0.2007
gδ3 1 0.5254 0.7150
gδ4 1 0.3893 0.4143
gδ5 1 0.3656 0.3686
According to wide bound method formulaThe failure domain for calculating series connection truss structure system is overall Product VF, alwaysWide boundaryMust fail domain total volume VF, alwaysWide boundary are as follows: 0.7150≤VF, always≤ 1.7621。
To failure domain volume ViThe corresponding failure domain volume of middle I failure mode carries out sorting from large to small adjustment, obtains Failure domain volume W=(W adjusted1,W2,...,WI)T=(0.7150,0.4143,0.3686,0.2007,0.0635)T, root According to narrow bound method formulaCalculate series connection purlin The failure domain total volume V of frame structural body systemF, alwaysNarrow boundary, must fail domain total volume VF, alwaysNarrow boundary are as follows: 0.8654≤VF, always ≤0.9115。
The non-general of series connection truss structure system is calculated according to the narrow boundary of the failure domain total volume of series connection truss structure system The value range of rate failure degreeObtain 19.35%≤ηs,F≤ 20.38%, therefore, in the present embodiment, truss of connecting The value range η of the non-probability decision degree of structural systems,RAre as follows: 79.62%≤ηs,R≤ 80.65%.
The present invention gives the structural body for more meeting actual requirement of engineering in use, fully considered engineering actual demand It is Multidisciplinary systems analysis as a result, widely applicable and application prospect is extensive, greatly simplifies series connection truss structure system and lose The workload that domain volume calculates is imitated, effectively compensating for that the prior art is only capable of carrying out non-probability to the structure under single failure mode can By the deficiency of property analysis, the range of structure Multidisciplinary systems analysis method has been expanded, has been had to the fail-safe analysis of structural system There is very important meaning, convenient for promoting the use of.
The above is only presently preferred embodiments of the present invention, is not intended to limit the invention in any way, it is all according to the present invention Technical spirit any simple modification to the above embodiments, change and equivalent structural changes, still fall within skill of the present invention In the protection scope of art scheme.

Claims (5)

1.一种串联桁架结构体系非概率可靠性分析方法，其特征在于，该方法包括以下步骤：1. a non-probabilistic reliability analysis method of a series truss structure system, is characterized in that, this method comprises the following steps: 步骤一、确定串联桁架结构体系各失效模式的功能函数：采用桁架结构失效准则确定串联桁架结构体系各失效模式的功能函数gi(X)，其中，i为结构体系失效模式的编号且i＝1,2,...,I，I为结构体系失效模式的个数，X为不确定性变量向量且X＝(X1,X2,...,Xm)T，m为不确定性变量编号且m等于所述不确定性变量向量X的维数，Xl为第l个不确定性变量，l为正整数且l的取值范围为1～m，表示第l个不确定性变量Xl取值的区间，Xl 为不确定性变量Xl的下界，为不确定性变量Xl的上界；Step 1. Determine the function function of each failure mode of the series truss structure system: use the truss structure failure criterion to determine the function function g i (X) of each failure mode of the series truss structure system, where i is the number of the failure mode of the structure system and i= 1,2,...,I, I is the number of failure modes of the structural system, X is the uncertainty variable vector and X=(X 1 , X 2 ,...,X m ) T , m is the uncertainty variable number and m is equal to the dimension of the uncertainty variable vector X, X l is the lth uncertainty variable, l is a positive integer and the value range of l is 1～m, represents the interval of the value of the l-th uncertainty variable X l , where X l is the lower bound of the uncertainty variable X l , is the upper bound of the uncertainty variable X l ; 步骤二、建立描述不确定性变量的多维椭球模型：采用数据处理器对不确定性变量建立多维椭球模型，得到多维椭球模型其中，向量X0为多维椭球不确定域中心点向量且 为第l个不确定性变量Xl的取值区间中点，Ωx为用于确定多维椭球的形状和方向的多维椭球的特征矩阵且Zll为按照NATAF方法确定多维椭球模型时第l个不确定性变量Xl和第l个不确定性变量Xl的协方差，Rm为m维的实数域；Step 2: Establish a multi-dimensional ellipsoid model for describing uncertain variables: use a data processor to establish a multi-dimensional ellipsoid model for the uncertain variables, and obtain a multi-dimensional ellipsoid model Among them, the vector X 0 is the center point vector of the multidimensional ellipsoid uncertainty domain and is the midpoint of the value interval of the l-th uncertainty variable X l , Ω x is the characteristic matrix of the multi-dimensional ellipsoid used to determine the shape and direction of the multi-dimensional ellipsoid and Z11 is the covariance of the lth uncertainty variable X1 and the lth uncertainty variable X1 when the multidimensional ellipsoid model is determined according to the NATAF method, and Rm is the m -dimensional real number field; 步骤三、获取不确定性变量的多维归一化等价椭球模型，过程如下：Step 3: Obtain the multi-dimensional normalized equivalent ellipsoid model of the uncertainty variable, the process is as follows: 步骤301、不确定性变量向量的归一化处理：根据公式获取不确定性变量向量X的不确定性变量归一化向量U，其中，U＝(U1,U2,...,Um)T，Ul为第l个不确定性变量Xl对应的归一化变量，为第l个不确定性变量Xl的区间半径且 Step 301, the normalization of the uncertainty variable vector: according to the formula Obtain the uncertainty variable normalization vector U of the uncertainty variable vector X, where U=(U 1 , U 2 ,...,U m ) T , U l is the lth uncertainty variable X l The corresponding normalized variable, is the interval radius of the l-th uncertainty variable X l and 步骤302、构建不确定性变量的多维归一化等价椭球模型：采用数据处理器对不确定性变量归一化向量U构建不确定性变量的多维归一化等价椭球模型Ωu为不确定性变量归一化向量U在归一化空间u中确定的多维椭球的特征矩阵且 为以为对角元素的m维对角阵；Step 302 , constructing a multi-dimensional normalized equivalent ellipsoid model of the uncertainty variable: using a data processor to normalize the uncertainty variable vector U to construct a multi-dimensional normalized equivalent ellipsoid model of the uncertainty variable Ω u is the eigenmatrix of the multidimensional ellipsoid determined by the uncertainty variable normalization vector U in the normalized space u and for is an m-dimensional diagonal matrix of diagonal elements; 步骤四、获取不确定性变量的超球模型，过程如下：Step 4: Obtain the hypersphere model of the uncertainty variable, the process is as follows: 步骤401、对不确定性变量归一化向量U在的归一化空间u中确定的多维椭球的特征矩阵Ωu进行Choleskey分解，即其中，L0为Choleskey分解得到的下三角矩阵；Step 401 , perform Choleskey decomposition on the characteristic matrix Ω u of the multi-dimensional ellipsoid determined in the normalized space u of the uncertainty variable normalization vector U, that is, Among them, L 0 is the lower triangular matrix obtained by Choleskey decomposition; 步骤402、采用数据处理器对多维归一化等价椭球模型转化得到不确定性变量在标准空间δ空间中的单位超球模型Eδ＝{δ|δTδ≤1,δ∈Rm}，其中，δ为不确定性变量归一化向量U在标准空间δ空间的标准化向量且标准空间δ空间的维数为m，δl为归一化变量Ul在标准空间δ空间中的标准化变量；Step 402: Using a data processor to transform the multi-dimensional normalized equivalent ellipsoid model to obtain a unit hypersphere model of uncertainty variables in the standard space δ space E δ ={δ|δ T δ≤1,δ∈R m }, where δ is the normalized vector of the uncertainty variable normalized vector U in the standard space δ space and The dimension of the standard space δ space is m, and δ l is the standardized variable of the normalized variable U l in the standard space δ space; 得不确定性变量向量X与标准空间δ空间中的标准化向量δ之间的关系：The relationship between the uncertainty variable vector X and the standardized vector δ in the standard space δ space is obtained: 对串联桁架结构体系各失效模式的功能函数gi(X)在标准空间δ空间中进行变形处理，得到标准空间δ空间的失效模式的结构功能函数gi(δ)；The functional function g i (X) of each failure mode of the series truss structure system is deformed in the standard space δ space, and the structural function function g i (δ) of the failure mode in the standard space δ space is obtained; 步骤五、根据公式计算单位超球模型Eδ的体积V总，其中，Γ(·)为Gamma函数；Step 5. According to the formula Calculate the volume V total of the unit hypersphere model E δ , where Γ( ) is the Gamma function; 步骤六、获取串联桁架结构体系的失效域总体积的宽界限：在标准空间中，当第i个失效模式的结构功能函数gi(δ)构成的曲面与单位超球模型Eδ相交时，利用标准空间δ空间的失效模式的结构功能函数gi(δ)构成的曲面上点与单位超球模型Eδ原点之间的距离最小值计算标准空间δ空间的失效模式的结构功能函数gi(δ)对应的失效域体积Vi；Step 6. Obtain the wide limit of the total volume of the failure domain of the series truss structure system: in the standard space, when the surface formed by the structural function function g i (δ) of the ith failure mode intersects with the unit hypersphere model E δ , The structural function function g i of the failure mode in the standard space δ space is calculated by using the minimum distance between the point on the surface formed by the structural function function g i (δ) of the failure mode in the standard space δ space and the origin of the unit hypersphere model E δ (δ) corresponding failure domain volume V i ; 根据宽界限法公式计算串联桁架结构体系的失效域总体积VF,总的宽界限，其中， According to the broad bound method formula Calculate the total failure domain volume V F of the tandem truss structural system, the total width limit, where, 步骤七、获取串联桁架结构体系的失效域总体积的窄界限：对失效域体积Vi中I个失效模式对应的失效域体积进行从大到小排序调整，得到调整后的失效域体积W＝(W1,W2,...,WI)T，其中，W1～WI为V1～VI从大到小排序的结果，即W1&gt;W2&gt;...&gt;WI，W1＝max(Vi)，WI＝min(Vi)；Step 7: Obtain the narrow limit of the total volume of the failure domain of the tandem truss structure system: sort and adjust the failure domain volumes corresponding to I failure modes in the failure domain volume V i from large to small, and obtain the adjusted failure domain volume W= (W 1 ,W 2 ,...,W I ) T , where W 1 ˜W I are the results of sorting V 1 ˜V I from large to small, that is, W 1 &gt;W 2 &gt;...&gt ; W I , W 1 =max(V i ), W I =min(V i ); 根据窄界限法公式计算串联桁架结构体系的失效域总体积VF,总的窄界限，为第i失效模式和第j失效模式的共失效域；According to the narrow bound method formula Calculate the total failure domain volume V F of the tandem truss structural system, the total narrow bound, is the common failure domain of the i-th failure mode and the j-th failure mode; 步骤八、根据串联桁架结构体系的失效域总体积的窄界限计算串联桁架结构体系的非概率失效度的取值范围ηs,F，其中， Step 8: Calculate the value range η s,F of the non-probabilistic failure degree of the series truss structure system according to the narrow limit of the total volume of the failure domain of the series truss structure system, where, 步骤九、根据公式ηs,R＝1-ηs,F，计算串联桁架结构体系的非概率可靠度的取值范围ηs,R。Step 9. According to the formula η s,R =1-η s,F , calculate the value range η s,R of the non-probabilistic reliability of the series truss structure system. 2.按照权利要求1所述的一种串联桁架结构体系非概率可靠性分析方法，其特征在于：所述不确定性变量编号m不小于2；2. The non-probabilistic reliability analysis method for a series truss structure system according to claim 1, wherein the uncertainty variable number m is not less than 2; 当m＝2时，单位超球模型Eδ为单位圆，标准空间δ空间的失效模式的结构功能函数gi(δ)构成的曲面与单位圆相交形成的二维弓形面，此时失效域体积Vi用二维弓形面的面积表示，其中，h为二维弓形面的高；When m=2, the unit hypersphere model E δ is the unit circle, the two-dimensional arcuate surface formed by the intersection of the surface formed by the structural function function g i (δ) of the failure mode of the standard space δ space and the unit circle, the failure domain The volume V i uses the area of the two-dimensional arcuate surface represents, where h is the height of the two-dimensional arcuate surface; 当m＝3时，单位超球模型Eδ为单位球体，标准空间δ空间的失效模式的结构功能函数gi(δ)构成的曲面与单位球体相交形成的三维球缺，此时失效域体积Vi用三维球缺的体积表示，其中，h'为三维球缺的高；When m=3, the unit hypersphere model E δ is a unit sphere, and the three-dimensional spherical defect formed by the intersection of the surface formed by the structural function function g i (δ) of the failure mode of the standard space δ space with the unit sphere, the failure domain volume V i uses the volume of the three-dimensional spheroid represents, among them, h' is the height of the three-dimensional spherical gap; 当m≥4时，单位超球模型Eδ为m维超球，标准空间δ空间的失效模式的结构功能函数gi(δ)构成的曲面与m维超球相交形成的m维超球缺，此时失效域体积Vi用m维超球缺的体积表示，其中，h”为m维超球缺的高。When m≥4, the unit hypersphere model E δ is an m-dimensional hypersphere, and the m-dimensional hypersphere formed by the intersection of the surface formed by the structural function function g i (δ) of the failure mode of the standard space δ space and the m-dimensional hypersphere is missing. , at this time, the failure domain volume V i is the volume of the m-dimensional hypersphere defect represents, where h” is the height of the m-dimensional hypersphere. 3.按照权利要求1所述的一种串联桁架结构体系非概率可靠性分析方法，其特征在于：所述串联桁架结构体系各失效模式的功能函数gi(X)＝0称为失效临界面，当串联桁架结构体系各失效模式的功能函数gi(X)&lt;0时，串联桁架结构体系失效；当串联桁架结构体系各失效模式的功能函数gi(X)≥0时，串联桁架结构体系安全。3. A non-probabilistic reliability analysis method for a series truss structure system according to claim 1, characterized in that: the functional function g i (X)=0 of each failure mode of the series truss structure system is called a failure critical surface , when the function function g i (X) of each failure mode of the series truss structure system is &lt; 0, the series truss structure system fails; when the function function g i (X) of each failure mode of the series truss structure system is ≥ 0, the series truss structure system fails. Structural system security. 4.按照权利要求1所述的一种串联桁架结构体系非概率可靠性分析方法，其特征在于：所述不确定性变量包括静载荷、动载荷、长度、宽度、弹性模量。4 . The non-probabilistic reliability analysis method of a series truss structure system according to claim 1 , wherein the uncertain variables include static load, dynamic load, length, width, and elastic modulus. 5 . 5.按照权利要求1所述的一种串联桁架结构体系非概率可靠性分析方法，其特征在于：所述第i失效模式和第j失效模式的共失效域通过数值积分求得。5. A non-probabilistic reliability analysis method for a series truss structure system according to claim 1, characterized in that: a common failure domain of the i-th failure mode and the j-th failure mode Obtained by numerical integration.
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