CN109753633A - A kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model - Google Patents
A kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model Download PDFInfo
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Abstract
The invention discloses a kind of structures under wind Failure risk evaluation methods based on non-stationary GEV distributed model, the characteristic that the method for the present invention is changed over time by defining different parameters, construct the GEV model of multiple non-stationaries, the estimation that parameter is carried out using Maximal Generalized possibility predication (GML) method carries out the preferred of model according to AIC criterion.Structures under wind Failure risk evaluation is carried out by preferred non-stationary GEV model, wherein annual failure risk changes over time, has reacted the tendency of the variation tendency bring statistics achievement of non-stationary series.The method of the present invention can effectively solve the problems, such as the non-stationary of wind series of the nominal frequencies distributed model when coping with nonstationary time series estimation structures under wind failure risk, not only allow for the time trend of statistical series, uncertain human factor of the conventional treatment method when non-stationary wind series are converted to steady wind series is also avoided, it is ensured that the economy of optimizing structure design while engineering wind resistance reliability.
Description
Technical field
The present invention relates to structures under wind technical fields, and in particular to a kind of structure based on non-stationary GEV distributed model is anti-
Wind Failure risk evaluation method.
Background technique
In structures under wind system, the assessment of wind resistance failure risk is extremely important, and important parameter therein ---
The analytical calculation of design wind speed has very important influence.Existing design wind speed obtaining value method mainly uses Gumbel frequency
Distributed model (extreme I type), the model carry out frequency analysis calculating to nearly 25 years maximum 10min mean wind speed sequences over the years, should
Stationarity of the frequency statistics model based on statistical series it is assumed that however wind speed time series have sometimes it is non-stationary, it is difficult to accord with
This is closed it is assumed that making the model not applicable, because Gumbel frequency distribution model directly has ignored the non-stationary of statistical series
Property, the assessment achievement of the design wind speed value, wind resistance failure risk that obtain based on this model can generate gross differences.
When handling nonstationary time series, a series of trend that transform methods eliminate statistical variable is generally gone through at present
Nonstationary time series is modified to after weakly stationary state and is carried out using Stationary Distribution model by the non-stationary characteristics such as line, periodicity
Statistical analysis；Or search out the inflection point of unstable condition, it is assumed that the sequence before and after inflection point is mutually indepedent, with multiple frequency distribution
Model carries out piecewise analysis, however since the inflection point that distinct methods are found is not often identical, analysis result presents different degrees of
Difference so that production practices person usually generates puzzlement when determining design wind speed.
The processing mode of above-mentioned technical problem so that there are many risks for the wind force proofing design of building structure, or influences to build
The wind resistance reliability of object is built, or influences the economy of wind resisting structure design.
Summary of the invention
Art methods when it is an object of the invention to overcome the shortcomings of to handle non-stationary wind series propose reliability
The higher stronger structures under wind Failure risk evaluation method of economy solves GEV (Generalized Extreme Value) point
Use problem of the cloth model in non-stationary wind series estimation structures under wind risk.
In order to solve the above technical problems, the invention adopts the following technical scheme:
A kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model is provided,
It comprises the steps of:
Step 1 introduces time variable t to form parameter κ, location parameter μ and scale parameter α respectively, is joined according to shape
Number κ, location parameter μ, scale parameter α and the maximum wind velocity sequence (Y obtained in advancet, x) and construct at least one non-stationary
GEV model, and parameter estimation is carried out to the GEV model of the non-stationary；
The GEV model of step 2, all non-stationaries preferably constructed according to AIC criterion, and pass through the non-stationary after preferably
GEV model carries out structures under wind Failure risk evaluation.
Further, step 1 includes:
Time variable t is introduced in steady generalized extreme value distribution model (GEV), to describe original form parameter κ, position
The tendency that parameter μ, scale parameter α are changed over time, non-stationary generalized extreme value distribution model (GEVt) it is expressed as follows formula:
Wherein κtFor form parameter, μtFor location parameter, αtScale parameter, x are maximum 10min mean wind speed value over the years, t
For the time.It is corresponding when form parameter value difference as no time variable t for steady generalized extreme value distribution model (GEV)
Three kinds of distributional patterns: it as μ+α/κ≤x <+∞ and κ < 0, is distributed for Frechet；As-∞ < x <+∞ and κ=0, it is
Gumbel；As-∞ < x≤μ+α/κ and κ > 0, it is distributed for Weibull.
Further, the pass of time variable t and time are introduced respectively according to form parameter κ, location parameter μ, scale parameter α
System, non-stationary generalized extreme value distribution model can be there are many forms of expression, it is preferable that can be expressed as but be not limited to: GEV1
(μt=μ1+μ2Yt,α,κ)、GEV2(μt=μ1+μ2Yt+μ3Yt 2, α, κ) or GEV11(μt=μ1+μ2Yt,αt=exp (α1+α2Yt),
κ), Y thereintFor time statistical variable, the corresponding required estimation parameter of model is respectively μ1, μ2, α, κ；μ1, μ2, μ3, α, κ；
μ1, μ2, α1, α2, κ.
Preferably, parameter estimation is carried out using Maximal Generalized Likelihood estimation.
Further, the preferred of multiple models is carried out using AIC criterion, expression formula is as follows.
Wherein k is model parameter number,For the maximum likelihood index of model M.
Further, by preferably after non-stationary GEV model carry out structures under wind Failure risk evaluation method packet
It includes:
In the calculating such as following formula of 1 year wind resistance failure risk:
The calculating that wind resistance failure risk occurs in n sees below formula:
In formula, V0For design wind speed, pnFor 1 year failure risk.
Compared with prior art, the beneficial effects obtained by the present invention are as follows being: the method for the present invention can effectively solve nominal frequencies
Distributed model calculates the non-stationary problem of design wind speed sequence in reply nonstationary time series, not only allows for statistical series
Tendency has also avoided the uncertain human factor when non-stationary wind series are converted to steady wind series；The present invention
Time t can be introduced respectively to parameter, the performance shape of then non-stationary GEV model is flexibly selected according to each parameter and the relationship of time
Formula keeps the method for the present invention relevance grade wider more flexible.
Detailed description of the invention
Fig. 1 is specific embodiment of the invention history maximum 10min mean wind speed change curve；
Fig. 2 is change curve of the design wind speed of each distributed model of the specific embodiment of the invention within the statistics phase,
In:
Fig. 2 (a) is the change of 30 year one meeting design wind speed of each distributed model of the specific embodiment of the invention within the statistics phase
Change curve graph,
Fig. 2 (b) is the change of 50 year one meeting design wind speed of each distributed model of the specific embodiment of the invention within the statistics phase
Change curve graph,
Fig. 2 (c) is the change of 100 year one meeting design wind speed of each distributed model of the specific embodiment of the invention within the statistics phase
Change curve graph；
Fig. 3 is the change curve of annual design wind speed in each distributed model service life of the specific embodiment of the invention,
Wherein:
Fig. 3 (a) is annual 30 years one chance design wind speeds in each distributed model service life of the specific embodiment of the invention
Change curve,
Fig. 3 (b) is annual 50 years one chance design wind speeds in each distributed model service life of the specific embodiment of the invention
Change curve,
Fig. 3 (c) is annual 100 years one chance design wind speeds in each distributed model service life of the specific embodiment of the invention
Change curve；
Fig. 4 is wind resistance failure risk variation annual in each non-stationary distributed model statistics phase of the specific embodiment of the invention
Curve graph, in which:
It is every in statistics phase when each non-stationary distributed model design wind speed of Fig. 4 (a) specific embodiment of the invention is 31m/s
Year wind resistance failure risk,
It is every in statistics phase when each non-stationary distributed model design wind speed of Fig. 4 (b) specific embodiment of the invention is 32m/s
Year wind resistance failure risk,
It is every in statistics phase when each non-stationary distributed model design wind speed of Fig. 4 (c) specific embodiment of the invention is 34m/s
Year wind resistance failure risk；
Fig. 5 is the specific embodiment of the invention based on wind resistance failure risk in each non-stationary distributed model engineering service life
Change curve, in which:
Fig. 5 (a) be the specific embodiment of the invention each non-stationary distributed model design wind speed be 31m/s when engineering use
Phase wind resistance failure risk,
Fig. 5 (b) be the specific embodiment of the invention each non-stationary distributed model design wind speed be 32m/s when engineering use
Phase wind resistance failure risk,
Fig. 5 (c) be the specific embodiment of the invention each non-stationary distributed model design wind speed be 34m/s when engineering use
Phase wind resistance failure risk；
Fig. 6 is the Stationary Distribution model and GEV of the specific embodiment of the invention1The wind resistance risk of distributed model compares signal
Figure；
Fig. 7 is specific embodiment of the invention method flow diagram.
Specific embodiment
With reference to the accompanying drawing, the invention will be further described for example.Following embodiment is only used for clearly illustrating
Technical solution of the present invention, and not intended to limit the protection scope of the present invention.
The present invention has chosen certain island weather station, and for observing environment not by Effects of Urbanization, actual measurement air speed data is nature
Environmental change objectively responds.The weather station is established in nineteen fifty-nine, and it is maximum to survey within 1960~2013 years liftoff 10m high over the years
10min mean wind speed is as shown in Figure 1, survey liftoff 10m high maximum 10min mean wind speed in apparent downward trend, presentation is non-
Stationary nature, the frequency statistics model not being accordant to the old routine assume the stationarity of time series.
Liftoff 10m high maximum 10min mean wind speed building sequence (Y is surveyed within 1960~2013 years over the years by collectingt, x),
Wherein YtFor the time, x is liftoff 10m high maximum 10min mean wind speed over the years.
Present invention assumes that form parameter, location parameter, scale parameter change with time, characteristic can construct the non-stationary time
The generalized extreme value distribution model of sequence；Model is there are many form of expression, the Primary Reference form such as following table institute that lists in embodiment
Show, and unlisted whole forms.
The generalized extreme value distribution form of the main nonstationary time series of table 1
GEV in table0Form parameter, location parameter, scale parameter in (μ, α, κ) model not Y at any timetVariation, as often
The distributed model of the stationary time series of rule；GEV1(μt=μ1+μ2Yt, α, κ) only location parameter μ in modeltBecome linearly over time
Change, other two parameters do not change over time；GEV2(μt=μ1+μ2Yt+μ3Yt 2, α, κ) only location parameter μ in modeltAt any time
Variation, and the relationship with time presentation quadratic function；GEV11(μt=μ1+μ2Yt,αt=exp (α1+α2Yt), κ) position in model
Parameter μt, scale parameter αtIt changes over time, wherein location parameter changes linearly over time, and e index variation is presented in scale parameter.
The method for solving GEV model parameter is main linear away from method (L-Moment), maximum-likelihood method (ML), probability right
Estimate (PWM), Bayesian Estimation method (Bayesian) etc..Maximum-likelihood method (ML) is to develop relatively early, and more commonly used side
Method.Many scholars have developed Reactor (GML) on the basis of ML, the distribution form of preferential fixed form parameter
(such as fixed value, linear character etc.), then solve other distribution parameters.The present invention uses GML method, it is assumed that position, size ginseng
Number containing on the basis of time response, estimate the distribution parameter of non-stationary GEV model, use R language by fixed form parameter
ExtRemes program bag calculates, and is the prior art, this will not be detailed here.
When wind resisting structure designs, design wind speed mainly uses 30 years one chances, 50 years chances, 100 year return period met.It is right
In stationary random time's sequence, GEV0The design wind speed that distributed model obtains is fixed value, and statistical result is as shown in table 2.And it is right
In non-stationary Random time sequence, the corresponding design wind speed of non-stationary GEV distributed model presents apparent time response, and is
Linear decrease feature (see Fig. 2, table 2).The statistics phase is 1960~2013 years, is set what statistics non-stationary early period distributed model obtained
Meter wind speed value is all larger than Stationary Distribution model, and on the contrary in the statistics later period.Non-stationary distributed model is compared with Stationary Distribution model
Design value variation range be [- 4.24%, 3.02%], difference is within ± 5%.Compared each other by non-stationary model
It is found that GEV1With GEV2The design value difference of distributed model is very small, reflects difference small between two distributed models.
In non-stationary GEV model, GEV is presented in contemporary designs value respectively1≥GEV2>GEV11Rule.
Each distributed model nineteen sixty~2013 year of table 2 design wind speed value unit over the years: m/s
The general service life of engineering is 50 years, predicts engineering service life using non-stationary GEV distributed model herein
Interior design wind speed changes (being shown in Table 3, Fig. 3).The design value that each non-stationary distributed model obtains is small compared with stationary model by 3.28%~
11.20%, GEV1With GEV2The corresponding design value of distributed model is minimum.Design value shows rule respectively in two class model of GEV
Rule: GEV11>GEV1>GEV2。
Design wind speed value unit in each non-stationary distributed model service life of table 3: m/s
AIC criterion (AIC information criterion, that is, Akaike information criterion) can comprehensively consider the suitable of model
With property and complexity, it is often used to the preferred of multiple models.It is expressed from the next, wherein k is model parameter number,For mould
The maximum likelihood index of type M.AIC value is smaller, illustrates that the applicability of model and complexity are better, and required model parameter is reflected in side
Reliability.
By calculating GEV0、GEV1、GEV11、GEV2The maximum likelihood index of model be respectively -131.9, -129.8, -
129.8, -129.8, corresponding AIC value is respectively 269.84,267.61,269.60,269.60, it is seen that GEV1Model is wherein
Optimal, and it is better than stationary model GEV0.After optimization model, using GEV1The assessment of wind resistance failure risk is carried out, while to say
The bright difference with conventional stationary model, analysis simultaneously is based on GEV in embodiment0、GEV11、GEV2The wind resistance failure risk of model.
Assuming that the risk (probability) for surmounting a certain design wind speed for certain year is pt=ft(x > V0), V herein0To design wind
Speed is defined as wind resistance failure if the event occurs.It is then following formula in the risk of failure in 1 year.
For stationary random time's sequence, the risk to fail every year is definite value, i.e. ft(x > V0)=p then occurs in n anti-
The risk of wind failure sees below formula.
And for non-stationary Random time sequence, the risk to fail every year changes over time, then wind resistance failure occurs in n
Risk it is as follows.In ptThe accurate calculation risk of ability on the basis of calculating, and ptCalculating need to be divided at random based on non-stationary
The estimation of cloth model parameter.
For feature of the analysis non-stationary distributed model in risk analysis, the value of basic wind speed is using current specifications requirement
Method, meeting within 30 years one, meet within 50 years one, meeting basic wind speed difference value within 100 years one is 31m/s, 32m/s, 34m/s.Non-stationary
Distributed model can provide the statistics phase, any one year wind resistance failure risk in engineering validity period (time span of forecast), as shown in Figure 4.From
The wind resistance failure risk of statistics phase simulates explanation, and within the statistics phase, the corresponding failure risk of basic wind speed reduces with the time；System
The failure risk in the meter end of term is respectively less than the failure risk of Stationary Distribution model.
The calculating of arbitrary year wind resistance failure risk calculates engineering wind resistance failure risk for non-stationary distributed model and provides
Basis.According to formula (1-1~1-4), analysis project builds up the wind resistance failure risk in rear different service lives, engineering validity period
(time span of forecast) annual failure risk is as shown in figure 5, failure risk such as Fig. 6 in engineering validity period (time span of forecast).Pass through wind resistance
Failure risk comparison, in same service life, the risk size that non-stationary GEV distributed model obtains is regular: GEV11>GEV1>
GEV2。
For Stationary Distribution model GEV0, the wind resistance failure risk of engineering only has with the return period (occurrence frequency) of design value
It closes, is not influenced by distributed model.Rather than Stationary Distribution model calculates wind resistance failure risk and the selection of model is closely related, no matter
It is value-at-risk or the morphological feature (such as Fig. 5, Fig. 6, table 4) that wind resistance failure risk changes over time.Non-stationary distributed model meter
Obtained wind resistance failure risk is significantly less than Stationary Distribution model (being shown in Table 4), GEV1Compared with GEV0Lower about 49.85%~
69.38%.The return period of design value is bigger, and non-stationary distributed model is got over compared with the wind resistance failure risk difference of Stationary Distribution model
Greatly, it has been even up to about 70%.
4 stationary model GEV of table0With GEV1Failure risk in the engineering service life (50 years) of calculating compares unit: m/s
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the application
Apply the form of example.Moreover, it wherein includes the computer of computer usable program code that the application, which can be used in one or more,
The computer program implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.) produces
The form of product.
The application is referring to method, the process of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that every one stream in flowchart and/or the block diagram can be realized by computer program instructions
The combination of process and/or box in journey and/or box and flowchart and/or the block diagram.It can provide these computer programs
Instruct the processor of general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute for real
The device for the function of being specified in present one or more flows of the flowchart and/or one or more blocks of the block diagram.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
Enable the manufacture of device, the command device realize in one box of one or more flows of the flowchart and/or block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one or more flows of the flowchart and/or block diagram one
The step of function of being specified in a box or multiple boxes.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvements and modifications, these improvements and modifications can also be made
Also it should be regarded as protection scope of the present invention.
Claims (9)
1. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model, which is characterized in that comprising following
Step:
Step 1 introduces time variable t to form parameter κ, location parameter μ and scale parameter α respectively, according to form parameter κ,
Location parameter μ, scale parameter α and the maximum wind velocity sequence (Y obtained in advancet, x) and construct the GEV mould of at least one non-stationary
Type, and parameter estimation is carried out to the GEV model of the non-stationary；
The GEV model of step 2, all non-stationaries preferably constructed according to AIC criterion, and by preferably after non-stationary GEV
Model carries out structures under wind Failure risk evaluation.
2. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 1,
It is characterized in that, step 1 includes:
Time variable t is introduced in steady generalized extreme value distribution model GEV constructs non-stationary generalized extreme value distribution model GEVt, institute
State non-stationary generalized extreme value distribution model GEVtBe expressed as follows formula:
Wherein κtFor form parameter, μtFor location parameter, αtScale parameter, x is maximum 10min mean wind speed value over the years, when t is
Between.
3. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 1,
It is characterized in that, according to form parameter κ, location parameter μ, scale parameter α respectively with the relationship of time variable, the non-stationary of building
Generalized extreme value distribution model GEVtThere are many forms of expression.
4. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 3,
It is characterized in that, according to the relationship of form parameter κ, location parameter μ, scale parameter α and time t, non-stationary generalized extreme value distribution
Model GEVtIt indicates are as follows: GEV1(μt=μ1+μ2Yt,α,κ)、GEV2(μt=μ1+μ2Yt+μ3Yt 2, α, κ) or GEV11(μt=μ1+μ2Yt,αt=exp (α1+α2Yt), κ), Y thereintFor time statistical variable, the corresponding required estimation parameter of model is respectively μ1,
μ2, α, κ；μ1, μ2, μ3, α, κ；μ1, μ2, α1, α2, κ.
5. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 1,
It is characterized in that, carrying out parameter estimation using Maximal Generalized Likelihood estimation.
6. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 1,
It is characterized in that, carrying out the preferred of multiple models using AIC criterion, expression formula is as follows:
Wherein k is model parameter number,For the maximum likelihood index of model M.
7. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 1,
It is characterized in that, by preferably after non-stationary GEV model carry out structures under wind Failure risk evaluation method include:
In the calculating such as following formula of 1 year wind resistance failure risk:
In formula, V0For design wind speed, pnFor 1 year failure risk.
8. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 1,
It is characterized in that, by preferably after non-stationary GEV model carry out structures under wind Failure risk evaluation method include:
The calculating that wind resistance failure risk occurs in n sees below formula:
In formula, V0For design wind speed, pnFor 1 year failure risk.
9. a kind of structures under wind Failure risk evaluation method based on non-stationary GEV distributed model according to claim 1,
It is characterized in that, including the liftoff 10m high maximum 10min average wind of actual measurement over the years by weather station near engineering before step 1
Speed building sequence (Yt, x), wherein YtFor the time, x is liftoff 10m high maximum 10min mean wind speed over the years.
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|---|---|---|---|---|
| CN110400608A (en) * | 2019-06-13 | 2019-11-01 | 浙江大学建筑设计研究院有限公司 | The assessment method that cement-based material intensity changes with age |
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Application publication date: 20190514 |