CN105844060B - It is a kind of can the non-probability decision degree of evaluation structure safety coefficient design method - Google Patents
It is a kind of can the non-probability decision degree of evaluation structure safety coefficient design method Download PDFInfo
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Abstract
The invention discloses it is a kind of can the non-probability decision degree of evaluation structure safety coefficient design method, first with the finite sample data of structural parameters, the non-probability nature of uncertain parameter is rationally characterized using non-statistical measure；The uncertain distribution character of the determining structural stress such as approximate solution, Monte Carlo simulation methods, intensity；The non-Making by Probability Sets Interference Model of stress intensity of structure is built, proposes corresponding non-Making by Probability Sets theory Reliability assessment formula；With reference to non-Making by Probability Sets theory Reliability assessment formula, the analytical expression of the relevant safety coefficient such as foundation and non-Making by Probability Sets theory reliability, strength variable coefficient and the stress coefficient of variation；For engineering structure, corresponding safety coefficient is calculated according to the requirement of corresponding reliability, safety coefficient structure design is carried out, obtains the Optimal Design of Structure scheme for meeting certain reliability.The present invention has taken into account design safety itself and economy, and it is simple to remain conventional security factor design method concept, the characteristics of easily implementation.
Description
Technical field
The present invention relates to the design optimizings containing non-probability Structure with uncertain parameters, more particularly to consider non-probability set
It rationally discusses during reliability, the uncertain stress coefficient of variation, strength variable coefficient and Central safety factor combine and feels at ease
Overall coefficient quantitatively characterizing and the design margin evaluation design based on non-probability decision degree, to obtain the knot for meeting certain reliability
Structure optimization design scheme.
Background technology
In terms of structure design, traditional safety coefficient design method is extensive due to the advantages that concept is simple, easy to use
Applied to engineering field.On the other hand, reliability design approach is required due to that can ensure that structure meets specific reliability, and
Gathering around structure, there are one more rational designs.However, both methods has a degree of shortcoming.It is wherein traditional
Method of safety coefficients due to various parameters as definite value, without the random variation characteristic of analytical parameters, and only with one with warp
It tests or summarizes determining coefficient broadly to count and various uncertain factors, the structure for having certain subjectivity random, designed
The waste of material can inevitably be caused or can not ensure safety.In addition determining safety coefficient there is no with quantitative structural reliability
It is required that therefore traditional safety coefficient cannot representative structure completely reliability.And although structural reliability design method will not
Determine that parameter is considered as the stochastic variable obeyed and be centainly distributed, and carries out structure design by selecting a suitable reliability,
But since it requires designer that must have the relevant knowledges such as certain reliability and mathematical statistics, its extensive use by
Certain restrictions.
In order to which the reasonability of the being easily understood property of safety coefficient design method and reliability design approach is effectively combined
Come, the development trend of structure design is that safety coefficient is gradually made to establish mathematical relationship with reliability at present, with reliance security system
Number replaces conventional security coefficient to ensure the probability of success of structure, is then designed according to a conventional method again.This is a kind of realization
A kind of i.e. easy and effective method of structural reliability design.
However it is to be noted that the determining of safety coefficient is built upon probabilistic reliability reason under current reliability meaning
By under, probability Stress-Strength Interference Model, it needs a large amount of uncertain data or information to obtain accurate probability density
Function, coefficient of variation equal distribution characteristic, this is generally difficult to what is realized in practice in engineering.And ginseng is not known in most cases
Several boundaries is more easy to obtain, and Multidisciplinary systems theory is come into being.And then safety coefficient is really under Multidisciplinary systems theory
The research of fixed and corresponding safety coefficient construction design method has important theory significance and engineering practical value.For reality
Finite sample data in the engineering of border establish the accurate Efficient Characterization technology, no of uncertain variables based on non-probability theory
Determine response assessment technology, the safety coefficient solution technique based on non-probability decision degree and the safety based on non-probability decision degree
The complete structure design method of coefficient design optimizing has significant realistic meaning.
Invention content
Present invention solves the technical problem that it is：Overcome conventional security Y-factor method Y subjectivity blindness and reliability design approach
Property complex and difficult to understand, effective and reasonable by the simple and convenient and reliability design approach of method of safety coefficients fully combine, needle
Characterize the finite sample data of uncertain parameter in practice to engineering, provide it is a kind of can the non-probability decision degree of evaluation structure safety
Factor design method.
The present invention fully considers the uncertain factor of engineering structure generally existing, for the feelings of finite sample data
Condition can carry out conventional safety coefficient design, gained based on the safety coefficient of the non-probability decision degree of evaluation structure by proposition
To structure design result can not only meet the requirement of a degree of reliability, but also convenience of calculation, convenient for engineering design people
Member understands and receives, and is more in line with truth, engineering adaptability is stronger.The technical solution adopted by the present invention realizes step such as
Under：
The first step：By structural parameters, include the limited sample of load, elastic properties of materials constant, intensity index and structure size
Notebook data is write as raw data matrixWherein x1(1),x1(2),…xm(n) it is derived from
Experiment or the initial data of equal precision measurement, m are the total number of structural parameters, and n is the number of each parameter sample data；It utilizes
Grey topology degree, information entropy theory, smallest interval collection theory non-statistical measure finite sample data are screened and are commented
Estimate, gross error and invalid data in Rejection of samples data, the quasi- uncertainty evaluation of rower of going forward side by side, and then obtain structural parameters
Reasonable indeterminacy section characterization vectorThat is interval vectorWherein haveFor efficiency test result or the average value vector of measurement data, s is not true based on gray scale theoretical evaluation
The extension uncertain variables that quantitative estimated value or information entropy theory determines, k are corresponding Dynamic gene, and m is structural parameters
Number,For the section characterization of p-th of structural parameters, I represents section, T representing matrix transposition.
For the efficiency test result of i-th structural parameters or the average value vector of measurement data.
Second step：Vector is characterized using the section that the first step obtainsRationally characterization finite sample number
According to load, elastic properties of materials constant, intensity index and structure size uncertain information, including load, elastic properties of materials constant,
The Lower and upper bounds of intensity index and structure size and central value, the relational expression of section radius, have：
Wherein XUFor the upper bound expression of structural parameters, XLFor the lower bound expression of structural parameters, XcFor in structural parameters
Center value expression formula, XrSection expression formula for structural parameters；Subscript U represents the value upper bound of variable, and subscript L represents taking for variable
It is worth lower bound；Subscript c represents section central value, and subscript r represents section radius；
Third walks：The uncertain information X for the structural parameters that second step is obtainedU、XL、XcAnd XrIt is introduced into work structuring
Calculation expression S (the x of stress S and intensity R1,x2,…,xm) and R (x1,x2,…,xm) in；And then it introduces non-probability and does not know to pass
Theoretical and method is broadcast, it is theoretical based on interval arithmetic rule and interval extension, utilize uncertain variables comprehensive calculation method, vertex
Method, Taylor series expansions approximate solution, Monte Carlo analogue simulations etc. determine the uncertain region of structural stress S, intensity R
BetweenWithAnd uncertain distribution character Sc,SrAnd Rc,Rr.Wherein have：
WhereinThe respectively lower bound of structural stress S and intensity R；The respectively upper bound of structural stress S and intensity R
Sc,RcThe respectively central value of structural stress S and intensity R, Sr,RrRespectively structural stress, intensity section radius；
4th step：Structural stress S, the uncertain distribution character of intensity R walked according to third, including central value Sc,Rc
With section radius Sr,Rr, using non-Making by Probability Sets theoretical stress-Strength Interference Model, establish the power function of non-probability decision degree
Equation：
M (R, S)=R-S
Wherein work as M=R-S>Structure is in a safe condition when 0, otherwise works as M=R-S<Structure is in failure state when 0；It is right
Structural stress S, intensity R, which carry out standard interval mapping, to be had：
R=Rc+RrδR, S=Sc+SrδS
Wherein δR∈ [- 1,1], δS∈ [- 1,1] is the intensity of standardization, stress interval variable.Obtain standardized variable sky
Between under limit state equation be：
M(δR,δS)=Rc-Sc+RrδR-SrδS=0
Finally obtain non-Making by Probability Sets theory reliability RSet, i.e. the ratio between safety zone and basic variable overall area is：
5th step：Structural stress S, the uncertain distribution character of intensity R walked according to third, including central value Sc,Rc
With section radius Sr,Rr, the Central safety factor n under interval of definition theorymFor the ratio between the central value of structural strength R, stress S, i.e.,
nm=Rc/Sc；Define strength variable coefficient CRWith stress coefficient of variation CSRespectively：
Then have：
Rr=CR×Rc,Sr=CS×Sc
R∈RI=[Rc(1-CR),Rc(1+CR)]
S∈SI=[Sc(1-CS),Sc(1+CS)]
Based on four formulas above, the Central safety factor n under interval theory is obtainedm, strength variable coefficient CR, stress
Coefficient of variation CSAnd non-Making by Probability Sets theory reliability RSetRelational expression：
Wherein have
6th step：Suitable reliability R is selected for engineering structureSet；Utilize obtained strength variable coefficient CR, stress
Coefficient of variation CS, solve and non-Making by Probability Sets theory reliability RSetCorresponding Central safety factor nm, and carry out safety coefficient knot
Structure designs, and obtains the optimization design scheme for meeting certain reliability.Wherein Optimized model is as follows：
find:d
min f(d)
Here, d represents m dimension design variables；F (d) is optimization aim, such as construction weight or size；It is design variable
The feasible zone of d；giI-th and the relevant certainty constraints of structural response, such as stress, rigidity, frequency are represented,For phase
Answer allowable value；L is the number of certainty constraint；For the corresponding Central safety factor of non-probability decision degree.
The advantages of the present invention over the prior art are that：The present invention is carried for engineering containing Structure with uncertain parameters in practice
A kind of new approaches of Optimal Structure Designing have been supplied, have been compensated for existing for conventional security factor design method and reliability design approach
Deficiency effectively combines the advantage of the two.The safety coefficient of constructed non-probability decision degree, is applicable not only to limited sample
The situation of notebook data (by being no more than 10) can also establish the correspondence with non-probability decision degree, meter and the coefficient of variation
Influence to safety coefficient.To structure optimizes existing for uncertain parameter when, can fully consider uncertain point
The influence of the safety coefficients such as cloth characteristic, reliability can substantially reduce structure under the premise of ensuring that structure meets certain reliability
Weight while improving performance, reduces design cycle and financial cost.
Description of the drawings
Fig. 1 be the present invention for can the non-probability decision degree of evaluation structure safety coefficient design method flow chart；
Fig. 2 is the Stress-Strength Interference Model schematic diagram of the non-Making by Probability Sets theory in the present invention；
Fig. 3 is the flat normalization transformation schematic diagram that fails under the interval theory in the present invention；
Fig. 4 is the rectangular section cantilever beam structure geometrical model schematic diagram that the present invention is directed to the parameter containing uncertain structure；
Fig. 5 is the rectangular section cantilever beam structure optimum results comparison curves that the present invention is directed to the parameter containing uncertain structure；
Fig. 6 is the rectangular section cantilever beam structure Optimization Design of Reliability iteration that the present invention is directed to the parameter containing uncertain structure
Course curve.
Specific embodiment
As shown in Figure 1, the present invention propose a kind of safety coefficient design method for assessing non-probability decision degree, including with
Lower step：
(1) by carrying out experimental study or equal precision measurement to structure parameter, structural parameters are obtained, including load, material
Expect the raw data matrix of the finite sample data of elastic constant, intensity index and structure sizeWherein x1(1),x1(2),…xm(n) be derived from experiment or equal precision measurement it is original
Data, m are the total number of structural parameters, and n is the number of each parameter sample data；Utilize grey topology degree, information entropy theory, most
The non-statistical measure of minizone collection theory is screened and is assessed to finite sample data, coarse in Rejection of samples data
Error and invalid data, the quasi- uncertainty evaluation of rower of going forward side by side；
Wherein grey topology degree is by effective measurement data sequence { xj(i), i=1,2 ..., n } it is arranged in new sequence from small to largeAnd the new sequence after one-accumulate generates：
Definition
Wherein, c is grey constant factor, it is considered that is 2.5.S is the estimated value of the Uncertainty based on grey evaluation.
IfSo sectionIt is considered as the estimation interval of actual value.
(2) vector is characterized using the section obtained using the first stepRationally characterization finite sample
The uncertain information of load, elastic properties of materials constant, intensity index and structure size under data qualification, including structural parameters
Lower and upper bounds and central value, section radius, here xiRepresent load, elastic properties of materials constant, intensity index and structure size not
It determines parameter, then has：
XI=[XL,XU]=[Xc-Xr,Xc+Xr]=Xc+Xr[-1,1]
Wherein XUFor the upper bound expression of structural parameters, XLFor the lower bound expression of structural parameters, XcFor in structural parameters
Center value expression formula, XrSection expression formula for structural parameters；Subscript U represents the value upper bound of variable, and subscript L represents taking for variable
It is worth lower bound；Subscript c represents section central value, and subscript r represents section radius.It should be noted that above-mentioned uncertain parameter into
During row uncertainty evaluation, the correlation between structural parameters is not considered, i.e., mutual uncertainty.
(3) the uncertain parameters information and distribution character X obtained second stepU、XL、XcAnd XrIt is introduced into work knot
Calculation expression S (the x of structure stress S and intensity R1,x2,…,xm) and R (x1,x2,…,xm) in, it introduces non-probability and does not know to propagate
Theoretical and method, it is theoretical based on interval arithmetic rule and interval extension, using uncertain variables comprehensive calculation method, vertex scheme,
Taylor series expansions approximate solution, Monte Carlo analogue simulations etc. determine the indeterminacy section of structural stress S, intensity RWithAnd uncertain distribution character Sc,SrAnd Rc,Rr.Have：
WhereinThe respectively lower bound of structural stress S and intensity R；The respectively upper bound of structural stress S and intensity R,
Sc,RcThe respectively central value of structural stress S and intensity R, Sr,RrRespectively structural stress, intensity section radius；Wherein area
Between arithmetic be：
And single order Taylor series expansions are utilized, it can obtain：
Interval extension operation is carried out to above formula：
(4) structural stress S, the uncertain distribution character of intensity R walked according to third, including central value Sc,RcAnd area
Between radius Sr,Rr, using non-Making by Probability Sets theoretical stress-Strength Interference Model, establish the power function equation of non-probability decision degree
For：
M (R, S)=R-S
And then to stress S ∈ SI, intensity R ∈ RICarry out standard interval mapping has：
δS=(S-Sc)/Sr,δR=(R-Rc)/Rr
R=Rc+RrδR, S=Sc+SrδS
Wherein SI、RIFor stress and the uncertain distributed area of intensity；Limit state equation is substituted into, standardization is obtained and becomes
The failure plane in limit state equation, that is, standardized variable space under quantity space is：
M(δR,δS)=Rc-Sc+RrδR-SrδS=0
Wherein δR∈ [- 1,1], δS∈ [- 1,1] is the intensity of standardization, stress interval variable.The reliability of definition structure
It is more than the possibility of working stress, i.e. η (M (δ for structural strengthR,δR)>0).Finally obtain non-Making by Probability Sets theory reliability
RSet, i.e. the ratio between safety zone and basic variable overall area is：
When stress and intensity interval do not interfere, when possible maximum working stress (the i.e. upper bound) less than possible
Minimum strength (i.e. lower bound) when, it at this moment fails for impossible event, i.e. RSet=1；Conversely, when possible minimum working stress
(i.e. lower bound) more than possible maximum intensity (the i.e. upper bound) when, it is at this moment safe for impossible event, i.e. RSet=0.
(5) structural stress S, the uncertain distribution character of intensity R walked according to third, including central value Sc,RcAnd area
Between radius Sr,Rr, the Central safety factor n under interval of definition theorymFor the ratio between the central value of structural strength R, stress S, i.e. nm=
Rc/Sc；Define strength variable coefficient CRWith stress coefficient of variation CSRespectively：
Then have：
Rr=CR×Rc,Sr=CS×Sc
R∈RI=[Rc(1-CR),Rc(1+CR)]
S∈SI=[Sc(1-CS),Sc(1+CS)]
Based on four formulas above, the Central safety factor n under interval theory is obtainedm, strength variable coefficient CR, stress
Coefficient of variation CSAnd non-Making by Probability Sets theory reliability RSetRelational expression：
ByThat is Sc+Sr>Rc-Rr, can obtain：
Finally determining non-Making by Probability Sets theory reliability safety coefficient should meet
Relational expression, which solve, to be had：
It enables
The safety coefficient of non-Making by Probability Sets theory reliability can be weighed by, which solving, is：
(6)：Suitable reliability R is selected for engineering structureSet；Utilize obtained strength variable coefficient CR, stress variation
Coefficient CS, solve and non-Making by Probability Sets theory reliability RSetCorresponding Central safety factor nm, and carry out safety coefficient structure and set
Meter obtains the optimization design scheme for meeting certain reliability.Wherein Optimized model is as follows：
find:d
min f(d)
Here, d represents m dimension design variables；F (d) is optimization aim；It is the feasible zone of design variable d；giRepresent i-th
It is a with the relevant certainty constraints of structural response, representative constraints may include structural stress, strain, frequency, just
The force models response indexs such as degree；For corresponding allowable value；L is constraint number；For the corresponding Central Security of non-probability decision degree
Coefficient.
Embodiment：
The characteristics of in order to more fully understand the invention and its applicability to engineering reality, the present invention are directed to such as Fig. 4 institutes
The rectangular section cantilever beam structure of the parameters such as load containing uncertain structure, the material property shown pacified based on non-probability decision degree
Overall coefficient designs.The cantilever beam structure is in position b1=2.0m and b2Concentrfated load P is respectively subjected to at=5.0m1And P2Effect.Its
China and foreign countries' load p1And P2It is uncertain variables, distribution character is determined by a series of experiments data point in table.The limit of cantilever beam is strong
It spends for indeterminacy section variable, distributed area is R ∈ [380- β × 380,380+ β × 380], wherein β=0.06.By material power
It gains knowledge it is found that the limit state equation of the cantilever beam is：
Here, mmaxFor section maximal bending moment, b=h.The coefficient of variation of intensity R is C as from the foregoingR=β=0.06；And it asks
The premise of the coefficient of variation of solution stress S is to obtain load p1And P2Distribution character.Using grey topology degree to load test data into
Row processing, obtains load p1And P2Distribution character be：
P1∈[4560,5460],P2∈[1780,2240]
And then the coefficient of variation that can obtain stress S is CS=0.10.According to different reliability requirements, corresponding peace can obtain
Overall coefficient is to carry out Optimal Structure Designing.
Table 1
The embodiment carries out cantilever beam structure Optimal Section Design using the RELIABILITY DESIGN requirement of four kinds of different levels, i.e.,
RSetRespectively 0.9999,0.999,0.99 and 0.9.Fig. 5 gives safety coefficient design based on non-probability decision degree and non-general
The optimum results of rate Optimization Design of Reliability；(a)-(d) in Fig. 6 gives object function under four kinds of different level reliabilitys
Iteration course curve.It can be seen that：Compared to initial designs, weight loss effect is apparent；With the raising of level of reliability, structure becomes
In safety, weight increased.Further, it can be seen that safety coefficient design and non-probability decision degree based on non-probability decision degree
Optimum results it is consistent.The simpler convenience of right optimization process, and be capable of providing corresponding to project planner one
Safety coefficient, engineering adaptability are stronger.
In conclusion the present invention proposes a kind of safety system of non-probability decision degree assessed containing Structure with uncertain parameters
Number design method.First, it according to the finite sample data of the uncertain parameters such as available structural loads, material property, utilizes
Non-statistical measure carries out effective and reasonable accurate Characterization to uncertain parameter, provide uncertain parameter the section upper bound, under
Boundary, section central value and radius equal distribution feature；Secondly, with reference to section knowwhy and the related solution side of uncertain propagation
Method provides distribution and the coefficient of variation that structural stress, intensity etc. form the parameter of limit state equation；Based on non-probability
Gather Stress-Strength Interference Model, member center safety coefficient, stress/strength variable coefficient, non-probability decision degree function close
System, and then obtain and the corresponding safety coefficient analytical expression of reliability；Finally, with acquisition based on non-probability decision degree
Safety coefficient is constraint, using loss of weight as target, completes the Optimal Structure Designing of different level reliability.
It the above is only the specific steps of the present invention, protection scope of the present invention be not limited in any way；All use is equal
Transformation or equivalence replacement and the technical solution that is formed, all fall within rights protection scope of the present invention.
Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.
Claims (4)
1. it is a kind of can the non-probability decision degree of evaluation structure safety coefficient design method, it is characterised in that realize step it is as follows：
The first step：By structural parameters, include the finite sample number of load, elastic properties of materials constant, intensity index and structure size
According to being write as raw data matrixWherein x1(1),x1(2),…xm(n) be derived from experiment or
The initial data of equal precision measurement, m are the total number of structural parameters, and n is the number of each parameter sample data；Utilize non-statistical
Measure is screened and is assessed to finite sample data, obtains the reasonable indeterminacy section characterization vector of structural parametersWhereinFor the section characterization of p-th of structural parameters, I represents section, T representing matrix transposition；
Second step：Vector is characterized using the section that the first step obtainsInterval arithmetic is carried out, is tied
The uncertain information of structure parameter includes Lower and upper bounds and the center of load, elastic properties of materials constant, intensity index and structure size
Value, the relational expression of section radius, have：
Wherein XUFor the upper bound expression of structural parameters, XLFor the lower bound expression of structural parameters, subscript U represents the value of variable
The upper bound, subscript L represent the value lower bound of variable；Subscript c represents section central value, and subscript r represents section radius；
Third walks：The uncertain information for the structural parameters that second step is obtained is introduced into the calculating of engineering structure stress S and intensity R
Expression formula S (x1,x2,…,xm) and R (x1,x2,…,xm) in, it introduces non-probability and does not know communication theory and method, determine structure
The indeterminacy section of stress S, intensity RWithAnd uncertain distribution character Sc,SrAnd Rc,Rr, have：
WhereinS,RThe respectively lower bound of structural stress S and intensity R；The respectively upper bound of structural stress S and intensity R, Sc,Rc
The respectively central value of structural stress S and intensity R, Sr,RrRespectively structural stress, intensity section radius；Above-mentioned non-probability
Uncertain communication theory and method include being suitable for the uncertain variables comprehensive calculation method of simple two dimension or three-dimensional situation,
Taylor series expansion approximate solution methods and suitable for challenge and the Monte Carlo methods of multidimensional number, wherein,
Taylor series expansion approximation algorithms are specific as follows：
Interval extension operation is carried out to upper formula to obtain：
4th step：Structural stress S, the uncertain distribution character of intensity R walked according to third, including central value Sc,RcAnd area
Between radius Sr,Rr, establish the power function equation of non-probability decision degree：
M (R, S)=R-S
Standard interval mapping is carried out to structural stress S, intensity R, the limit state equation obtained under standardized variable space is：
M(δR,δS)=Rc-Sc+RrδR-SrδS=0
Wherein δR∈ [- 1,1], δS∈ [- 1,1] is the intensity R of standardization, stress S interval variables；
Using the non-Making by Probability Sets Interference Model of stress-intensity, non-Making by Probability Sets theory reliability R is obtainedSet：
The non-Making by Probability Sets Interference Model of the stress-intensity refer to basic variable region by limit state equation be divided into failure domain and
Security domain, wherein failure domain is M (R, S)<0, security domain is M (R, S)>0；Non- Making by Probability Sets theory reliability RSetIt is defined as pacifying
The ratio between universe and basic variable overall area, i.e.,：
5th step：Structural stress S, the uncertain distribution character of intensity R walked according to third, including central value Sc,RcAnd area
Between radius Sr,Rr, the Central safety factor n under interval of definition theorymFor the ratio between the central value of structural strength R, stress S, i.e. nm=
Rc/Sc；Define strength variable coefficient CRWith stress coefficient of variation CSRespectively：
Obtain the Central safety factor n under interval theorym, strength variable coefficient CR, stress coefficient of variation CSAnd non-probability set is reasonable
By reliability RSetRelational expression：
The non-Making by Probability Sets theory reliability RSetExpression formula beUnder obtain, that is, haveI.e.
Sc+Sr>Rc-Rr, and then：
And the Central safety factor n under interval theorymIt should meet
6th step：Suitable reliability R is selected for engineering structureSet；Utilize obtained strength variable coefficient CR, stress variation lines
Number CS, solve and non-Making by Probability Sets theory reliability RSetCorresponding Central safety factor nm, and safety coefficient structure design is carried out,
Obtain the optimization design scheme for meeting certain reliability.
2. it is according to claim 1 it is a kind of can the non-probability decision degree of evaluation structure safety coefficient design method, feature
It is：It is theoretical that non-statistical measure described in step 1 includes grey topology degree, information entropy theory, smallest interval collection；It is limited
The screening of sample data includes rejecting gross error and invalid data, validation verification with assessment.
3. it is according to claim 1 it is a kind of can the non-probability decision degree of evaluation structure safety coefficient design method, feature
It is：The Optimized model that optimization design scheme described in step 6 uses is as follows：
find:d
min f(d)
Here, d represents m dimension design variables；F (d) is optimization aim；It is the feasible zone of design variable d；giRepresent i-th with
The relevant certainty constraints of structural response,For corresponding allowable value；L is constraint number；It is corresponded to for non-probability decision degree
Central safety factor.
4. it is according to claim 3 it is a kind of can the non-probability decision degree of evaluation structure safety coefficient design method, feature
It is：Non- Making by Probability Sets theory reliability R described in step 6SetValue be respectively 0.9,0.99,0.999 and 0.9999, institute
State giThe constraints of representative, the constraints include force model response index, and the force model response index includes structure
Stress, strain, frequency, rigidity.
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| CN106777492B (en) * | 2016-11-16 | 2020-06-02 | 北京航空航天大学 | Non-probability reliability optimization design method for structural system |
| CN106650147B (en) * | 2016-12-30 | 2018-07-13 | 北京航空航天大学 | A kind of non-probability Topology Optimization Method of Continuum Structure based on uncertain but bounded |
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