CN110110369A - A kind of truss structure reliability optimization method based on general generating function - Google Patents
A kind of truss structure reliability optimization method based on general generating function Download PDFInfo
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- CN110110369A CN110110369A CN201910268951.XA CN201910268951A CN110110369A CN 110110369 A CN110110369 A CN 110110369A CN 201910268951 A CN201910268951 A CN 201910268951A CN 110110369 A CN110110369 A CN 110110369A
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Abstract
The invention discloses a kind of truss structure reliability optimization methods based on general generating function.It replaces traditional double-loop method to calculate the reliability of truss structure using general generating, the judgement of limit of bearing capacity failure criteria is reached by structure, truss structure dominant failure mode is scanned for and identified；Establish the general generating function model of truss structure reliability；It is handled with K-means clustering algorithm, general generating is subjected to the compound operation of data and generates a large amount of Discrete Stochastic data clusters and merges, to reduce amount of calculation；The mathematical model of reliability optimization is finally established, with the minimum target of the quality of structure, is met certain requirements with reliability index as constraint condition, carries out structural optimization based on reliability design.
Description
Technical field
The present invention relates to a kind of structural optimization based on reliability method, be related in truss structure fail-safe analysis based on logical
With the reliability optimization of generating function.
Background technique
With the continuous development of science and technology, engineering structure also becomes increasingly complex, and reliability of structure design is nowadays adult
Most concerned problem.For the structure of some complexity, such as aircraft, steamer, submarine, any one internal part is lost
Effect, all will cause substantial spoilage to it, lose national wealth, or even threaten people's life.It can be seen that in structure
Structuralreliability theory has great importance in design.In traditional structure engineering design, engineer is in order to have structure
There is higher safety, increases superfluous constraint in the structure usually to improve reliability of structure.Although this method makes structure
With very high safety, but extra constraint makes the manufacturing cost for increasing engineering, wastes resource.For traditional structure
Reliability optimization can have enough safeties in the case where construction weight is most light.But traditional Model of Structural Reliability
Optimization efficiency it is low.Optimizing a large-scale labyrinth using conventional method, the most of the time is all wasted in calculating
On.Therefore, it is extremely urgent to develop a kind of efficient reliability optimization algorithm.
Summary of the invention
1, the purpose of the present invention
In order to solve the problems, such as that calculation amount constraint condition is more, calculation amount is excessive, the invention proposes one kind to be based on general life
At the structural optimization based on reliability method of function.
2, the technical solution adopted in the present invention
Truss structure reliability optimization method proposed by the present invention based on general generating function, in accordance with the following steps into
Row:
Step 1: based on the plastic limit analysis of structure, obtaining the shape of plastic hinge to the failure mode of truss structure
At and position；
Step 2: integrity problem is described, using truss structure as research object, it is assumed that the model of institute's research structure
Power function isg(X), definition structure reliability is A；
Step 3: the general generating function model of discrete random variable is established, if the possibility implementation value of discrete random variable X is
(x1,x2,……,xN), corresponding probability is (p1,p2,……pN).The then general generating function mould of discrete random variable X
Type is defined as:
Step 4: being handled with K-means clustering algorithm, substantially reduce workload, improves computational efficiency；
Step 5: the mathematical model of reliability optimization is established, it is full with reliability index with the minimum target of the quality of structure
Foot is certain to be required to be constraint condition, establishes optimized mathematical model are as follows:
The first step specifically:
1.1) with a plastic hinge as failure member, when plastic hinge develops to certain amount, make structure formation mechanism,
Bearing capacity is lost, these failure members just constitute an out-of-service sequence of structure, if with EijIt indicates in i-th of out-of-service sequence
J failure event (formation that failing path develops to j-th of plastic hinge), miIndicate the failure member number of i-th of out-of-service sequence, then
I-th of out-of-service sequence can be expressed as:
1.2) multiple out-of-service sequences can lead to the same failure mode (the same mechanism).In the failure probability of computing system
When, usually only consider the i.e. significant out-of-service sequence of the biggish out-of-service sequence of those failure probabilities, the following criterion of significant out-of-service sequence
Identification:
P(E1∩…∩EMs)≥VPref (4)
V is truncation (branch) parameter in formula, and Ms is the failure event number of this out-of-service sequence, PrefProbability value is referred to for truncation.
1.3) dominant failure mode for having destroyed control action to structure just constitutes the base of structural system fail-safe analysis
Plinth.The failure domain of i-th of dominant failure mode can be expressed as:
R in formulajIt is plastic limit bending moment, PjIt is outer load, aij、bijIt is constant related with construction geometry property, NrIt is
Form plastic hinge number, NpIt is outer load number.
The second step specifically:
2.1) stochastic inputs variable x=[x is defined1,x2,……xN]TWith joint probability density function f (x)；
2.2) according to the dominant failure mode of truss structure, constructing function functiong(X), the failure for providing truss structure is general
Rate pFCarry out fail-safe analysis.
4th step specifically:
4.1) it is randomly assigned k cluster centre (m1,m2,…,mk), carry out initialization value；
4.2) to each sample xi, the cluster centre nearest from it is found, and assign it to such；
4.3) each brand new center is recalculated；NiIt is the current sample number of the i-th cluster；
4.4) deviation is calculated,
4.5) convergence judgement is carried out, if E value restrains, returns (m1,m2,…,mk), algorithm terminates；Otherwise, turn 4.2.
3, beneficial effect of the present invention
(1) present invention establishes the general generating function model of discrete type by third step, compared to traditional first-order reliability method
The analysis method for reliability such as method, substantially increase computational accuracy.
(2) present invention is used uniformly general generating and replaces the reliable of traditional double-loop method calculating truss structure
Property, the judgement of limit of bearing capacity failure criteria is reached by structure, truss structure dominant failure mode is scanned for and identified；
Establish the general generating function model of truss structure reliability；With K-means clustering algorithm handle, by general generating into
The compound operation of row data and generate a large amount of Discrete Stochastic data clusters and merge, to reduce amount of calculation；Finally establish
The mathematical model of reliability optimization is met certain requirements with reliability index with the minimum target of the quality of structure to constrain item
Part carries out structural optimization based on reliability design.
(3) present invention is compared to existing analysis method for reliability, the present invention for labyrinth reliability optimization, both
Guarantee accuracy, can also be improved working efficiency.
(4) for the present invention compared to existing analysis method for reliability, the present invention is not strong for the dependence of initial point, has
Certain engineering adaptability.
Attached drawing 1 is the logic diagram of the method for the present invention；
Attached drawing 2 is the matlab main program figure of the method for the present invention；
Attached drawing 3 is the matlab pair programme diagram of the method for the present invention；
Attached drawing 4 is the optimum results figure of the method for the present invention；
Attached drawing 5 is the flow chart of k-means clustering algorithm.
Specific embodiment
As shown in Figure 1-3, the structural optimization based on reliability method of the invention based on general generating function, in accordance with the following steps
It carries out:
Step 1: based on the plastic limit analysis of structure, obtaining the shape of plastic hinge to the failure mode of truss structure
At and position；
With a plastic hinge as a failure member.When plastic hinge develops to certain amount, make structure formation mechanism, loses
Bearing capacity, these failure members just constitute an out-of-service sequence of structure.One out-of-service sequence is some failure by structure
Path is formed by different developing stage, and multiple out-of-service sequences can lead to the same failure mode (the same mechanism).?
When the failure probability of computing system, the i.e. significant out-of-service sequence of the biggish out-of-service sequence of those failure probabilities is usually only considered, due to
Multiple out-of-service sequences can lead to the same failure mode, and the dominant failure mode for having destroyed control action to structure is just constituted
The basis of structure system reliability analysis.
Step 2: integrity problem is described, using truss structure as research object, it is assumed that the model of institute's research structure
Power function is g (X), and definition structure reliability is A；
Definition limit state function is g (x)=x1 2+x2 2-x1x2-1.5(x1+x2)+1.5, wherein stochastic variable x1And x2Phase
It is mutually independent, stochastic variable x1And x2Logarithm normal distribution and weibull distribution are obeyed respectively.
Step 3: the general generating function model of discrete random variable is established, if the possibility implementation value of discrete random variable X is
(x1,x2,……,xN), corresponding probability is (p1,p2,……pN).The then general generating function mould of discrete random variable X
Type is defined as:
According to the specific column of second step relatively Monte Carlo method, the area of general generating and first-order second moment method
Not.It is as shown in the table:
| Monte Carlo method | General generating | First-order second moment method | |
| Reliability | 0.9999 | 0.99989 | 0.99854 |
| Calculate the time | 180s | 2s | 2s |
| Error | 0.01% | 0.136% |
General generating function technical ability guarantees accuracy as can be seen from the table, also can greatly shorten and calculate the time, improves
Working efficiency.
Step 4: being handled with K-means clustering algorithm, substantially reduce workload, improves computational efficiency；
Cluster is realized by continuous iteration, is just terminated iterative process when algorithmic statement is to termination condition, is obtained poly-
Class result.Means clustering algorithm is using cluster sum of squared errors function E as clustering criteria function, whereinxijIt is j-th of sample of the i-th class, miIt is the cluster centre or mass center of the i-th class, niIt is the i-th class sample
Number.K- means clustering algorithm is substantially exactly to find k optimal cluster centres by iterating, by all n sample points
It is assigned to the cluster centre nearest from it, making cluster error sum of squares E minimum, detailed process is as follows:
4.1) it is randomly assigned k cluster centre (m1,m2,…,mk), carry out initialization value；
4.2) to each sample xi, the cluster centre nearest from it is found, and assign it to such；
4.3) each brand new center is recalculated；NiIt is the current sample number of the i-th cluster；
4.4) deviation is calculated,
4.5) convergence judgement is carried out, if E value restrains, returns (m1,m2,…,mk), algorithm terminates；Otherwise, turn 4.2.
If Fig. 5 is the flow chart of k-means clustering algorithm；
Step 5: the mathematical model of reliability optimization is established, it is full with reliability index with the minimum target of the quality of structure
Foot is certain to be required to be constraint condition, establishes optimized mathematical model are as follows:
As shown in figure 4, carrying out the optimization that iterates using reliability index as constraint condition, it is poly- to find optimal K- mean value
Class interval, it can be seen that, the present invention has more accurate accuracy, method high reliablity, and it is big to seek the time used
Big reduction, is more suitable for the actual conditions of reality, and obvious technical effects are prominent.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (4)
1. a kind of truss structure reliability optimization method based on general generating function, it is characterised in that include the following steps:
Step 1: to the failure mode of truss structure, based on the plastic limit analysis of structure, obtain plastic hinge formation and
Position；
Step 2: integrity problem is described, using truss structure as research object, it is assumed that the model function of institute's research structure
Function isg(X), definition structure reliability is A；
Step 3: the general generating function model of discrete random variable is established, if the possibility implementation value of discrete random variable X is (x1,
x2,……,xN), corresponding probability is (p1,p2,……pN)；Then the general generating function model of discrete random variable X is fixed
Justice are as follows:
And
Step 4: being handled with K-means clustering algorithm；
Step 5: establishing optimized mathematical model are as follows:
MinW=W (x) (2)
W (X) represents the quality of truss structure in formula；Represent reliability allowable, βs(x) reliability of truss structure is represented.
2. the structural optimization based on reliability method according to claim 1 based on general generating function, it is characterised in that described
The first step specifically:
1.1) with a plastic hinge as failure member, when plastic hinge develops to certain amount, make structure formation mechanism, lose
Bearing capacity, these failure members just constitute an out-of-service sequence of structure, if with EijIndicate that failing path develops to j-th of modeling
Property hinge i-th of out-of-service sequence of formation in j-th of failure event, miIndicate the failure member number of i-th of out-of-service sequence, then i-th
Out-of-service sequence can be expressed as:
1.2) multiple out-of-service sequences can lead to the same failure mode, in the failure probability of computing system, only consider those mistakes
The biggish out-of-service sequence of probability, that is, significant out-of-service sequence is imitated, significant out-of-service sequence is identified with following criterion:
P(E1∩…∩EMs)≥VPref (4)
V is Truncation Parameters in formula, and Ms is the failure event number of this out-of-service sequence, PrefProbability value is referred to for truncation；
1.3) dominant failure mode for having destroyed control action to structure just constitutes the basis of structural system fail-safe analysis, the
The failure domain of i dominant failure mode can be expressed as:
R in formulajIt is plastic limit bending moment, PjIt is outer load, aij、bijIt is constant related with construction geometry property, NrIt is to have formed modeling
Property hinge number, NpIt is outer load number.
3. the structural optimization based on reliability method according to claim 1 based on general generating function, it is characterised in that: described
Second step specifically:
2.1) stochastic inputs variable x=[x is defined1,x2,……xN]TWith joint probability density function f (x)；
2.2) according to the dominant failure mode of truss structure, constructing function function g (X) provides the failure probability p of truss structureFInto
Row fail-safe analysis
4. the structural optimization based on reliability method according to claim 1 based on general generating function, it is characterised in that: described
4th step specifically:
4.1) it is randomly assigned k cluster centre (m1,m2,…,mk), carry out initialization value；
4.2) to each sample xi, the cluster centre nearest from it is found, and assign it to such；
4.3) each brand new center is recalculated；NiIt is the current sample number of the i-th cluster；
4.4) deviation is calculated,
4.5) convergence judgement is carried out, if E value restrains, returns (m1,m2,…,mk), algorithm terminates；Otherwise, turn 4.2.
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| CN111143970A (en) * | 2019-12-04 | 2020-05-12 | 西北工业大学 | Optimal design method for interlocking device of ejection system |
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Cited By (2)
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