CN108304679A - A kind of adaptive reliability analysis method - Google Patents
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Abstract
The disclosure provides a kind of adaptive reliability analysis method, and this method includes：It is sampled in uncertainty probability space, chooses initial DoE, Kriging alternative models are built by initial DoE；It is sampled using importance sampling technique, obtains candidate samples；It screens the sample point in the candidate samples closest to the power function limit state surface and calculates its response；Judge whether the Kriging alternative models meet convergence criterion, if being unsatisfactory for convergence criterion, the sample point and response are added in the DoE, the Kriging alternative models are updated according to this, until meeting convergence criterion；Reliability assessment is carried out to the Kriging alternative models, if the Kriging alternative models are unsatisfactory for required precision, candidate samples amount is increased by the importance sampling technique, iteration updates according to this, until meeting required precision.The analysis method of the disclosure can effectively improve the efficiency and precision of Structural System Reliability Analysis in Practical Project.
Description
Technical field
The disclosure belongs to systems reliability analysis and structure-design technique field more particularly to a kind of adaptive reliability point
Analysis method.
Background technology
In structure engineering design, Design of Reliability Analysis has become an important field of research.Considering structure
In the case that the input of system is stochastic variable, it is to tie to find out and fall into sample and the ratio of entire sample space amount in failure domain
The failure probability of construction system can effectively reflect its reliability level, to carry out structure by the failure probability of structural system
Design of Reliability Analysis.
Currently, main analysis method for reliability is the method based on sampling techniques, such as Monte Carlo Analogue Method (MCS),
This method is widely used in the assessment of integrity problem.The advantages of this method is can to solve commenting for various integrity problems
Estimate, but also have the shortcomings that be difficult to cover, such as needs to carry out bulk sampling calculating when solving the problems, such as small failure probability.In order to carry
Computationally efficient, researcher proposes a series of methods for reducing variance, such as importance sampling technique, subset simulation selective sampling
Method, important sampling method etc..However these methods are when solving the failure probability of structural system, precision and selected design point
Directly related, therefore, when to complicated structural system Probability Evaluation, precision is unsatisfactory with efficiency.Another method is
Moment Methods are divided into single order Moment Methods (FORM) and second moment method (SORM).In fail-safe analysis, by being set in stochastic variable
Taylor linear expansion is carried out to limit state function at enumeration (MPP), is then calculated by the power function of fewer number
To evaluate the failure probability of structural system, but larger error is will produce when solving high dimensional nonlinear integrity problem.
In addition, in complex mechanical system fail-safe analysis, power function is often one " flight data recorder ", researcher
It is only capable of providing limited model measurement data and simulation times.At this point, being solved by the alternative model combination methods of sampling this kind of
The reliability assessment of black box problem is comparatively ideal method.Currently, common alternative model has support vector machines (support
Vector machine), artificial intelligence neural networks (artificial neural network), chaos multinomial expansion
(polynomial chaos expansion), Quadratic response method (quadratic response surface), it is related to
Amount machine (relevance vector machine) and Kriging model (Kriging) etc. are combined by alternative model and are sampled
With smaller calculation amount when method is used for the reliability of evaluation structure system, but also shows alternative model approximate error and be difficult to
Control the disadvantage in ideal threshold range.
Therefore, it is necessary to propose a kind of adaptive reliability analysis method to solve the above problems.
It should be noted that information is only used for reinforcing the reason to the background of the disclosure disclosed in above-mentioned background technology part
Solution, therefore may include the information not constituted to the prior art known to persons of ordinary skill in the art.
Invention content
The disclosure is designed to provide a kind of adaptive reliability analysis method, and then overcomes at least to a certain extent
One or more problem caused by the limitation and defect of the relevant technologies.
Other characteristics and advantages of the disclosure will be apparent from by the following detailed description, or partially by the disclosure
Practice and acquistion.
According to one aspect of the disclosure, a kind of adaptive reliability analysis method is provided, including：
It is sampled in uncertainty probability space, chooses input sample point, and the input is calculated according to mapping relations
The output sample point of sample point builds Kriging alternative models by the input sample point and output sample point；
It finds out and converges on the input sample point of power function limit state surface in the input sample point as selective sampling
Density center is sampled acquisition candidate samples using importance sampling technique；
The sample point closest to the power function limit state surface in the candidate samples is screened, and calculates its response
Value；
Judge whether the Kriging alternative models meet convergence criterion, if being unsatisfactory for convergence criterion, by the sample
Point and response are added in the input sample point and output sample point, update the Kriging alternative models according to this, until
Meet convergence criterion；
Reliability assessment is carried out to the Kriging alternative models, if the Kriging alternative models are unsatisfactory for precision and want
It asks, then candidate samples amount is increased by the importance sampling technique, iteration updates according to this, until meeting required precision.
It in a kind of exemplary embodiment of the disclosure, is sampled in uncertainty probability space, chooses input sample point,
Including：
A point x is selected in failure domain0As markovian beginning sample point；
It is simulated by Metropolis rules and generates NMA Markov Chain sample xM, wherein including NsA Markov shape
State point and NrA Markov refuses point, the NMA Markov Chain sample xMThe as described input sample point.
In a kind of exemplary embodiment of the disclosure, the input sample point for converging on power function limit state surface is
The Markov state point.
It is described that acquisition candidate samples are sampled using importance sampling technique in a kind of exemplary embodiment of the disclosure, it wraps
It includes：
With NsA Markov Chain state point xsAs selective sampling density center；
In each sampling center xsSimulation generates N respectively at placeIA sample xΙ, that is, generate NΩ=NI×NsA candidate samples xΩ。
In a kind of exemplary embodiment of the disclosure, closest to the power function limit state surface in the candidate samples
Sample point by the Kriging alternative models and learning function screening obtain.
In a kind of exemplary embodiment of the disclosure, the learning function is：
Wherein,Indicate the Kriging predicated responses of sample x,Indicate the Kriging variances of response, φ ()
It is respectively the probability density function and cumulative distribution function of standardized normal distribution with Φ ().
In a kind of exemplary embodiment of the disclosure, closest to the power function limit state surface in the candidate samples
Sample point be the candidate samples in make E (R (x)) be the sample point corresponding to maximum value.
It is described to judge whether the Kriging alternative models meet convergence standard in a kind of exemplary embodiment of the disclosure
Then, including：
Convergence criterion is set, expression formula isWherein,For mean value, εETo prevent
Denominator tends to 0 positive value in expression formula；
If SERF≤10-4, judge that the Kriging alternative models meet convergence criterion, conversely, being then unsatisfactory for convergence criterion.
It is described that reliability assessment, packet are carried out to the Kriging alternative models in a kind of exemplary embodiment of the disclosure
It includes：
Calculate the failure probability of the Kriging alternative modelsWith failure probability coefficient of variation
If describedValue be less than 5%, the Kriging alternative models meet accuracy requirement, conversely, being then discontented with
Sufficient accuracy requirement.
In a kind of exemplary embodiment of the disclosure, the failure probabilityIt is derived from based on weighting importance sampling technique,
The weighting importance sampling technique is for quantifying each described initial input sample point to the failure probabilityInfluence, to carry
The precision of the high analysis method for reliability.
The adaptive reliability analysis method that disclosure illustrative embodiments are provided can be used for solving having height non-
Linearly, the fail-safe analysis problem of high n-dimensional random variable n, small failure probability and sophisticated functions function, can effectively improve Practical Project
The efficiency and precision of middle Structural System Reliability Analysis.
It should be understood that above general description and following detailed description is only exemplary and explanatory, not
The disclosure can be limited.
Description of the drawings
The drawings herein are incorporated into the specification and forms part of this specification, and shows the implementation for meeting the disclosure
Example, and together with specification for explaining the principles of this disclosure.It should be evident that the accompanying drawings in the following description is only the disclosure
Some embodiments for those of ordinary skill in the art without creative efforts, can also basis
These attached drawings obtain other attached drawings.
Fig. 1 schematically shows adaptive reliability analysis method flow chart in one exemplary embodiment of the disclosure；
Fig. 2 schematically shows adaptive reliability analysis method flow chart in disclosure another exemplary embodiment；
Fig. 3 schematically shows the generation method flow chart of random three-dimensional porous media in disclosure exemplary embodiment；
The random three-dimensional that the generation method of random three-dimensional porous media is generated during Fig. 4 is schematically shown according to fig. 2 is porous
The structural schematic diagram of medium.
Specific implementation mode
Example embodiment is described more fully with reference to the drawings.However, example embodiment can be with a variety of shapes
Formula is implemented, and is not understood as limited to example set forth herein；On the contrary, thesing embodiments are provided so that the disclosure will more
Fully and completely, and by the design of example embodiment comprehensively it is communicated to those skilled in the art.Described feature, knot
Structure or characteristic can be in any suitable manner incorporated in one or more embodiments.
In addition, attached drawing is only the schematic illustrations of the disclosure, it is not necessarily drawn to scale.Identical attached drawing mark in figure
Note indicates same or similar part, thus will omit repetition thereof.Some block diagrams shown in attached drawing are work(
Energy entity, not necessarily must be corresponding with physically or logically independent entity.Software form may be used to realize these work(
Energy entity, or these functional entitys are realized in one or more hardware modules or integrated circuit, or at heterogeneous networks and/or place
These functional entitys are realized in reason device device and/or microcontroller device.
This example embodiment provides a kind of adaptive reliability analysis method, as shown in Figure 1, the analysis method for reliability
May include：
S1, it is sampled in uncertainty probability space, chooses input sample point, and described defeated according to mapping relations calculating
The output sample point for entering sample point builds Kriging alternative models by the input sample point and output sample point；
S2, it finds out and converges on the input sample point of power function limit state surface in the input sample point as important pumping
Sample density center is sampled acquisition candidate samples using importance sampling technique；
Closest to the sample point of the power function limit state surface in S3, the screening candidate samples, and calculate its sound
It should be worth；
S4, judge whether the Kriging alternative models meet convergence criterion, it, will be described if being unsatisfactory for convergence criterion
Sample point and response are added in the input sample point and output sample point, update the Kriging alternative models according to this,
Until meeting convergence criterion；
S5, reliability assessment is carried out to the Kriging alternative models, if the Kriging alternative models are unsatisfactory for essence
Degree requires, then increases candidate samples amount by the importance sampling technique, and iteration updates according to this, until meeting required precision.
The adaptive reliability analysis method that disclosure illustrative embodiments are provided can be used for solving having height non-
Linearly, the fail-safe analysis problem of high n-dimensional random variable n, small failure probability and sophisticated functions function, can effectively improve Practical Project
The efficiency and precision of middle Structural System Reliability Analysis.
The adaptive reliability analysis method provided below in conjunction with the accompanying drawings this example embodiment carries out specifically
It is bright.
In step sl, it is sampled in uncertainty probability space, chooses input sample point, and according to mapping relations meter
The output sample point for calculating the input sample point builds Kriging by the input sample point and output sample point and substitutes mould
Type.It may include following steps：
S11, it can be selected a little as markovian beginning sample point in failure domain；
S12, generation N can be simulated by Metropolis rulesMA Markov Chain sample xM, wherein including NsA Ma Er
Section's husband's state point and NrA Markov refuses point：NM=Ns+Nr.X can be calculated by numerical simulation model or test modelM
Response be denoted as G (xM), then initial DoE passes through (xM,G(xM)) constitute.Research shows that markovian length need not be long,
Generally according to the difference of studied power function complexity, length can be met the requirements between taking 50 to 100.In addition, horse
Influence of the front end start-up portion of Er Kefu chains to structural realism is far smaller than subsequent part, and therefore, this example is implemented
Mode can reject the sample of Markov Chain front end 20%.
S13, Kriging alternative models can be constructed by initial DoE.Experience have shown that the quantity of initial DoE generally take 30 to
80 can meet demand.The Kriging models in this example embodiment can carry out structure by the DACE kits of MTALAB
It makes, Gauss model may be selected in correlation model, and constant may be selected in regression model.
In step s 2, the input sample point work that power function limit state surface is converged in the input sample point is found out
For important sampling density center, acquisition candidate samples are sampled using importance sampling technique.It may include following steps：
S21, can be with NsA Markov Chain state point xsCenter as selective sampling density；
S22, candidate samples can be obtained by importance sampling technique and is denoted as xΩ。
It, can be with N in this example embodimentsA Markov Chain state point xsCenter as selective sampling density.The sample
It is generated with probability min { 1, r } in Markov Chain simulation process, falls area on limit state surface or near limit state surface
Domain shows that these samples are affected to structural realism.Therefore, N can be passed through in important areasA sample is in sampling
The heart, Fast simulation obtains one group of significant samples, to improve sampling efficiency.This example embodiment can be obtained by importance sampling technique
Candidate samples are denoted as xΩ。xΩIt indicates in each sampling center xsSimulation generates N respectively at placeIA sample xΙI.e.：NΩ=NI×Ns, wherein
NIDesirable 2000.Sample x in this stepΩResponse can need not calculate, candidate samples point and optimal sample point will be in samples
xΩMiddle generation.
Closest to the sample point of the power function limit state surface in S3, the screening candidate samples, and calculate its sound
It should be worth.
In step s3, the sample point in candidate samples closest to the power function limit state surface can be by described
Kriging alternative models and learning function screening obtain.First, the prediction of unknown point can be obtained by Kriging alternative models
Value and variance.Then, learning function can be passed through
Whereinφ () and Φ () is respectively the probability density function and iterated integral of standardized normal distribution
Cloth function.Indicate the Kriging predicated responses of sample x,Indicate the Kriging variances of response.Find out candidate samples
xΩSample point corresponding to middle E (R (x)) maximum value is denoted as x*, calculate its response G (x*), and by this group of data (x*,G(x*))
It is added in DoE.Finally, Kriging alternative models are reconfigured by updating DoE, prediction result precision can be made to be improved, walked
Rapid S3 is active learning process.
S4, judge whether the Kriging alternative models meet convergence criterion, it, will be described if being unsatisfactory for convergence criterion
Sample point and response are added in the input sample point and output sample point, update the Kriging alternative models according to this,
Until meeting convergence criterion.
In step s 4, in order to make the symbol of Kriging alternative models Accurate Prediction power function at unknown sample,
One suitable convergence criterion of setting, expression formula are needed during Active Learning to be
WhereinIndicate mean value, denominator tends to 0 in the formula in order to prevent, to εESelect a smaller positive value such as 10-6, i.e. εE=10-6。
If meeting SERF≤10-4When, show that Kriging alternative models meet power function approximate requirements, end step S4 is entered step
Otherwise S5 updates DoE, reconfigure Kriging alternative models, return to step S3.
S5 carries out reliability assessment, if the Kriging alternative models are unsatisfactory for essence to the Kriging alternative models
Degree requires, then increases candidate samples amount by the importance sampling technique, and iteration updates according to this, until meeting required precision.It can wrap
Include following steps：
S51, the failure probability for calculating Kriging alternative modelsWith failure probability coefficient of variation
If S52,Value be less than 5%, then it is believed that Kriging alternative models meet accuracy requirement, otherwise pass through
Step S3 increases xΩSample size, and increase sample xICapacity.Experience have shown that NIValue range between 2000-2800
Meet the analysis demand of structural realism.
S53, whenAfter 5%, flow stops, and can assess structural realism.
In step s 51, failure probabilityIt can be based on weighting importance sampling technique to be derived from, the weighting importance sampling technique
For quantifying each described initial input sample point to the failure probabilityInfluence, to improve the fail-safe analysis side
The precision of method.
Such as Fig. 2, the analysis method shown in the disclosure is based on improved Markov chain combination Active Learning Kriging moulds
Type and weighting importance sampling technique (WIS), constitute a Two-way Cycle analysis method for reliability, for efficiently, accurately and adaptively
The failure probability of evaluation structure system.
In Analysis of structural reliability, it usually needs obtain analog sample, Ma Erke by arbitrary probability density function
Husband's chain is then that a kind of effective algorithm is used for completing this work.In Metropolis algorithms, sample passes through arbitrary Ma Er
Section's husband's chain generates, wherein markovian limiting condition Stationary Distribution is equal to target distribution.It will be apparent that the probability density of sample
Function is exactly Markov Chain state point, as markovian increase converges on destination probability density function.Therefore, pass through
Stationary Distribution sample can adaptively fall into important area, which is by optimum density function representation：f(x
| F)=IF(x)f(x)/Pf, wherein f (x | F) indicate optimum density function, IF(x) it is indicator function, f (x) is probability density letter
Number, PjFor failure probability.
It is recommended that distribution f*(ε|xj) (j=1,2 ..., m) so that ε is in xjCentered in the range of, probability density function
It chooses about ε and xjIt is symmetrical so that Markov Chain generates new state point on the basis of current state.It is usually high
This probability density function and uniform probability density function are two kinds of main alternative distribution patterns.When selection n dimensions are uniformly divided
When cloth probability density function is as distribution is suggested, the gengon length of side can generate large effect to markovian algorithm,
And when selecting n dimension Gaussian probability-density functions as distribution is suggested, Markov Chain can be made to tend to be steady state, therefore,
It is open to select Gaussian Profile as the probability density function for suggesting distribution.N ties up two significant in value features of Gauss normal distribution
Respectively mean value xji(i=1,2 ..., n) and standard deviation sigmai(i=1,2 ..., n), suggestion distribution can be expressed as：
Wherein variable ε is with xjCentered on be distributed, distribution distance and parameter σiIt is related.
The disclosure proposes that a kind of relatively stable auto-adaptive parameter method is used for determining parameter σi.In the initial rank of Markov Chain
Section passes through a larger σiValue can rapidly search for the important area of object function, and in the Markov Chain the latter half
Smaller σiValue can obtain more samples in the region of interest.Therefore auto-adaptive parameter σiIt is expressed as：
Wherein N indicates markovian step number, σ0Indicate initial standard deviation, value range 1.5-4.5.
A sample point x is selected in the domain F that fails0As markovian initial point.Pass through Metropolis-
Hastings algorithms and suggestion distribution f*(ε|xj) it is based on markovian preceding state xjObtain+1 state point of jth
xj+1.Candidate point ε is distributed f by suggestion*(ε|xj) generate, then calculate f (ε | F) and f (xj| F) ratio.Wherein, f (ε |
F the conditional probability density function of candidate point ε, f (x) are indicatedj| F) indicate Markov Chain preceding state conditional probability density
Function.The ratio is expressed as：
By Metropolis-Hastings criterion it is found that as r ＞ 1, then it is+1 shape of markovian jth to receive ε
State is：xj+1=ε conversely, ε is received with probability r as+1 state of markovian jth, and receives x with remaining probability 1-rj
It is as+1 state of jth：xj+1=xj, the Markov Chain that can be met the requirements repeatedly.Repeating above step can be with
Obtain m Markov Chain state point i.e.：xm={ x1,x2,…,xm}。
In fail-safe analysis, the influence of the most probable failure point (MPP) of structure to failure probability be it is distinguishing, in order to
The higher failure probability of precision is obtained as a result, the disclosure can be used adaptive weighted Importance Sampling Method (WIS) quantification each
Influence of a MPP points to structural realism, then efficiently and accurately calculates the failure probability of structure.
It is assumed that m advance samples are used for the failure probability of evaluation structure as the center of selective sampling density function, as above
Described, m sample can describe the different contributions of structure by following adaptive weighted expression formula, and expression formula can be with table
It is shown as：
Wherein βjThe RELIABILITY INDEX for indicating j-th of sample in m sample, can be asked by AFORM or other optimization methods
.Adaptive strategy can be used to remove assessment β for the disclosurej, acquired at sampling center by importance sampling techniqueThen it finds out reliable
Spend index
Therefore, selective sampling probability density function hx(x) it is derived as H (x) again, wherein H (x) is adaptive important pumping
Sample density function, expression formula are as follows：
Wherein, hj(x)=f*(x|xj) indicate j-th of selective sampling density function, γjIt is j-th of selective sampling center
Weighting coefficient, andIt is probability density function to meet H (x).
By above-mentioned derivation, the failure probability expression formula based on weighting importance sampling technique can be expressed as：
WhereinIndicate j-th of selective sampling probability density function hj(x) expectation.Assuming that NjA sample is according to important
Sampling density function hj(x) center simulation of sampling at j-th generates, and kth group sample passes through probability density function hk(x) (k=
1,2,…Nj) simulation generation, therefore, failure probability expression formula can be expressed as：
The expectation of formula (6) and variance can be derived from respectively, wherein it is expected to be expressed as：
It can be obtained by formula (7),It is failure probability PfUnbiased esti-mator, therefore, failure probability can pass throughIt acquires.
Failure probabilityVariance can be obtained by approximate calculation：
In addition, failure probabilityCoefficient of variation (Cov) can be expressed as：
Kriging models are made of two parts：A part is determining point progress minimum dispersion linear unbiased estimator, another part
Then it is made of random process.Therefore, Kriging models can be indicated by following formula：
G (x)=f (x)Tβ+z(x) (10)
Wherein f (x)Tβ indicates the approximate mean value of response, f (x)T=(f1(x),f2(x),…,fk(x)) basic function, β are indicated
=(β1,β2,…,βk) it is regression coefficient matrix.The f (x) of usual Kriging modelsTβ is a constant, i.e. f (x)Tβ=β.With
Under all formula be all based on Kriging models and derived, z (x) is that stable Gaussian random process its mean value is
0, variance σ2, covariance can be expressed as：
Cov(z(xi),z(xj))=σ2Rθ(xi,xj) i, j=1,2 ..., k (11)
Wherein, Rθ(xi,xj) it is the x generated by parameter θiAnd xjBetween correlation function.Rθ(xi,xj) usually may be selected
One anisotropic Gauss model, expression formula are：
Wherein, xi,rAnd xj,rIt is r-th of sample, θ in sample coordinate systemrIt is the relevant parameter of model of fit.
Usual one group of DoE may be used to determine the relevant parameter of Kriging models, then can obtain target by agent model
The unknown sample of function.Usual one group of DoE is desirableCorresponding output responseThen relevant parameter is calculated：
Wherein,It is the correlation matrix of every group of sample in DoE, k 1 is filled in 1 matrix.
In addition,Pass through matrix R with βθIn θ acquire, θ can be calculated by maximum Likelihood：
Show to respond belowIn the predicted value of unknown sample point, expression formula is：
Wherein r (x)=Rθ(x,x(i)), i=1,2 ..., q.
Kriging variancesBy finding outIt can be obtained with the Minimum Mean Square Error (MSC) of G (x), therefore it
Expression formula is：
Wherein
Kriging models are mainly characterized by unknown point progress precise interpolation calculating, and therefore, response is in experimental design
It is at known point the result is that it is accurate i.e.：Its Kriging variance is 0.In addition, passing through Kriging variances
Local approximation can be carried out in zone of ignorance to object function acquire response.
Such as Fig. 3, the disclosure tests institute's extracting method of the present invention by the dynamic response problem of a nonlinear oscillator
Card, power function expression formula are as follows：
Wherein x=(c1,c2,m,r,t1,F1),The distribution characteristics of stochastic variable such as 1 institute of table in formula
Show.
The stochastic variable of 1 nonlinear oscillator of table is distributed
Analysis is carried out to non-linear oscillator problem by different reliability methods and calculates to obtain its result of calculation such as 2 institute of table
Show.
The distinct methods of 2 nonlinear oscillator of table analyze acquired results
The carried adaptive reliability analysis method (ALK-WIS) of the disclosure, importance sampling technique (IS), Echard are proposed
The NAIS methods that AK-SS and Balesdent that AK-MCS methods, Huang et al. are proposed et al. are proposed are reliable to structural system
Property assessment when compared, comparison index include power function call number Ncall, candidate samples point quantity NΩAnd failure
Probability percent error εPf.Its N for tri- kinds of methods of AK-MCS, AK-SS and ALK-WIScallBy initial DoE and Active Learning
Additional DoE two parts that process generates are constituted.This example uses sample size 7 × 10 by monte carlo method7When calculate gained
Failure probability Pf=2.834 × 10-2, and solved using the value as the reference of other methods.
During ALK-WIS carries out the fail-safe analysis of nonlinear oscillator, DoE is as shown in Figure 4.In initial DoE
Great amount of samples is located on limit state surface or is located at limit state surface neighbouring position, shows improved Markov through the invention
Chain obtains the preferable Markov Chain analog sample of effect in important area.It is substituted by the initial Kriging of the sample architecture
Then model enriches Kriging alternative models by Active Learning function, constructed as shown in Figure 4 by 9 repetitive exercises
Meet the Kriging alternative models of required precision.After Kriging alternative models are successfully constructed, added based on the model
Weigh the reliability of selective sampling assessment system.
As shown in Table 2, the failure probability of same order its N is obtained by different reliability methodscallIt is different, and
The number of institute's extracting method invoking performance function of the present invention is only at least 68 times, show ALK-WIS with other methods compared with compared with
High computational efficiency.By comparing each methodAs a result it is recognized that while failure probability precision highest required by AK-SS methods, but
This method is compared with institute's extracting method of the present invention, is removedHave other than smaller advantage in index, in NcallWithTwo kinds
The upper of index has apparent disadvantage.In summary, institute's extracting method of the present invention is when carrying out structural system reliability assessment no matter
Still there is apparent advantage compared with other methods in efficiency in precision.
It should be noted that although describing each step of method in the disclosure with particular order in the accompanying drawings, this is simultaneously
Undesired or hint must execute these steps according to the particular order, or have to carry out the step ability shown in whole
Realize desired result.Additional or alternative, it is convenient to omit multiple steps are merged into a step and executed by certain steps,
And/or a step is decomposed into execution of multiple steps etc..
Those skilled in the art after considering the specification and implementing the invention disclosed here, will readily occur to its of the disclosure
His embodiment.This application is intended to cover any variations, uses, or adaptations of the disclosure, these modifications, purposes or
Adaptive change follow the general principles of this disclosure and include the undocumented common knowledge in the art of the disclosure or
Conventional techniques.The description and examples are only to be considered as illustrative, and the true scope and spirit of the disclosure are by claim
It points out.
It should be understood that the present disclosure is not limited to the precise structures that have been described above and shown in the drawings, and
And various modifications and changes may be made without departing from the scope thereof.The scope of the present disclosure is only limited by the attached claims.
Claims (10)
1. a kind of adaptive reliability analysis method, which is characterized in that including：
It is sampled in uncertainty probability space, chooses input sample point, and the input sample is calculated according to mapping relations
The output sample point of point builds Kriging alternative models by the input sample point and output sample point；
It finds out and converges on the input sample point of power function limit state surface in the input sample point as selective sampling density
Center is sampled acquisition candidate samples using importance sampling technique；
The sample point closest to the power function limit state surface in the candidate samples is screened, and calculates its response；
Judge whether the Kriging alternative models meet convergence criterion, if being unsatisfactory for convergence criterion, by the sample point and
Response is added in the input sample point and output sample point, updates the Kriging alternative models according to this, until meeting
Convergence criterion；
Reliability assessment is carried out to the Kriging alternative models, if the Kriging alternative models are unsatisfactory for required precision,
Candidate samples amount is then increased by the importance sampling technique, iteration updates according to this, until meeting required precision.
2. analysis method according to claim 1, which is characterized in that be sampled, choose in uncertainty probability space
Input sample point, including：
A point x is selected in failure domain0As markovian beginning sample point；
It is simulated by Metropolis rules and generates NMA Markov Chain sample xM, wherein including NsA Markov state point
And NrA Markov refuses point, the NMA Markov Chain sample xMThe as described input sample point.
3. analysis method according to claim 2, which is characterized in that described to converge on the defeated of power function limit state surface
It is the Markov state point to enter sample point.
4. analysis method according to claim 3, which is characterized in that described be sampled using importance sampling technique is waited
Sampling sheet, including：
With NsA Markov Chain state point xsAs selective sampling density center；
In each sampling center xsSimulation generates N respectively at placeIA sample xΙ, that is, generate NΩ=NI×NsA candidate samples xΩ。
5. according to Claims 1 to 4 any one of them analysis method, which is characterized in that closest to institute in the candidate samples
The sample point for stating power function limit state surface is obtained by the Kriging alternative models and learning function screening.
6. analysis method according to claim 5, which is characterized in that the learning function is：
Wherein,Indicate the Kriging predicated responses of sample x,Indicate the Kriging variances of response, φ () and Φ
() is respectively the probability density function and cumulative distribution function of standardized normal distribution.
7. analysis method according to claim 6, which is characterized in that closest to the power function in the candidate samples
The sample point of limit state surface is to make E (R (x)) be the sample point corresponding to maximum value in the candidate samples.
8. analysis method according to claim 7, which is characterized in that described whether to judge the Kriging alternative models
Meet convergence criterion, including：
Convergence criterion is set, expression formula isWherein,For mean value, εETo prevent from expressing
Denominator tends to 0 positive value in formula；
If SERF≤10-4, judge that the Kriging alternative models meet convergence criterion, conversely, being then unsatisfactory for convergence criterion.
9. according to Claims 1 to 4 any one of them analysis method, which is characterized in that described to substitute mould to the Kriging
Type carries out reliability assessment, including：
Calculate the failure probability of the Kriging alternative modelsWith failure probability coefficient of variation
If describedValue be less than 5%, the Kriging alternative models meet accuracy requirement, conversely, being then unsatisfactory for precision
Demand.
10. analysis method according to claim 9, which is characterized in that the failure probabilityBased on weighting selective sampling
Method is derived from, and the weighting importance sampling technique is for quantifying each described initial input sample point to the failure probability
Influence, to improve the precision of the analysis method for reliability.
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