CN104794332B - A kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model - Google Patents

Abstract

A kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model, first, the Foundation pressure time course data for specifying building scaled model is obtained by the wind tunnel test of high frequency balance and converts base data to prototype；Then, this batch of substrate time course data is applied into different theoretical analysis models carries out specifying respectively the wind-excited responese of building to analyze；At the same time, it is applied to specify the benchmark model of building to carry out dynamic response analysis as input condition with a collection of substrate time course data, the structural response that calculating is obtained is responded as benchmark；Finally, from the principle of the Bayesian model method of average, set up the probability expression of structural response and carry out model selection and response prediction analysis of uncertainty applied to different analysis models；Bayesian Factor is defined, the uncertainty of different analysis models is assessed, and therefrom finds one group of " optimal " model.

Description

A kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model

Technical field

High frequency balance wind-tunnel is based on the invention belongs to high building structure Wind resistant analysis and design field, more particularly to one kind The Uncertainty Analysis Method of the skyscraper wind-excited responese analysis model of experimental technique.

Background technology

With the high speed development of China's economic construction, skyscraper and tall and slender structure are largely newly-built in various regions.Due to such Building structure has flexible high, the low dynamic characteristics of damping so that Dynamic Wind Loads effect turns into influence high building structure peace One of principal element of full property and usability.High frequency balance wind-tunnel technique is present analysis and determines skyscraper power wind The effective means of load effect, has the advantages that modelling is simple, it is convenient, time saving economical to test, so extensive in recent years In wind- tunnel investigation applied to high-rise and tall and slender structure.

For the rule building with linear normal modes feature, the wind tunnel test of high frequency balance passes through direct measurement model bottom Portion's charming appearance and behaviour shearing, moment of flexure and moment of torsion, can be very good to estimate the mode wind-force of prototype structure on the basis of linear mode assumption, Wind-induced vibration analysis work is conveniently completed.However, the three-dimensional coupling nonlinear of modern high-rise building The feature of mode, the applicability to high frequency balance wind-tunnel technique proposes test.In order to adapt to skyscraper three-dimensional coupling The dynamic characteristics of nonlinear analog-circuit, many scholars carry respectively from high frequency balance wind-tunnel technique according to different hypothesis Different theoretical analysis models are gone out.Wherein, representative method have mode updating (MSC) method (J.D.Holmes, A.Rofail and L.Aurelius,High frequency base balance methodologies for tall buildings with torsional and coupled resonant modes,In:11th International Conference on Wind Engineering.Texas Tech University,Lubbock,Tx,pp.2381-2388, 2003.), linear normal modes (ALMS) method (M.F.Huang, K.T.Tse, C.M.Chan, et al., An integrated design technique of advanced linear-mode-shape method and serviceability drift optimization for tall buildings with lateral-torsional modes, Eng.Struct., 32,2146-56,2010.), Yip-Flay methods (D.Y.N.Yip, R.G.J.Flay, A new force balance data analysis method for wind response predictions of tall buildings, J.Wind Eng.Ind.Aerodyn., 54-55,457-71,1995.) and Xie-Irwin methods (J.Xie and P.A.Irwin, Application of the force balance technique to a building complex,J.Wind Eng.Ind.Aerodyn.,77-78,579-590,1998.).These methods inevitably introduce 3 kinds during analysis Uncertainty, i.e. model choose uncertain, and parameter uncertainty and response prediction are uncertain.

In Structural Wind Engineering field, the research on analysis of uncertainty focuses primarily upon parameter uncertainty this side Face, and it is comparatively fewer to choose the probabilistic research of uncertain and response prediction for model.In general, it is right In the building of geometrical rule, same a collection of wind tunnel test data application carries out wind-excited responese in different analysis models and calculated The structural response value arrived is basically identical, and the major limitation of existing theoretical analysis model comes from parameter uncertainty, i.e. wind load The uncertainty of distribution form.However, for the Tall Buildings especially asymmetric buildings of facade perforate, same A collection of wind tunnel test data application is not larger in the structural response value difference that different analysis model progress wind-excited responese calculating is obtained, That is, model chooses and the uncertain of response prediction can also produce not during such building wind-excited responese analysis Negligible influence.Benchmark sound is obtained therefore, it is necessary to obtain actual measurement response by measurement method or calculated by benchmark model Should be worth to examine the applicability of existing analysis model, and find out one group can most represent the optimal models of true model so as to such Building carries out subsequent fine Study on thinning.

The content of the invention

It is an object of the invention to provide a kind of skyscraper wind-excited responese point based on high frequency balance wind-tunnel technique The uncertain program of numerical calculation of model is analysed, the existing analysis model for Tall Buildings is solved on numerical algorithm The problem of there is larger error between true model, by probability measure aspect the optimal models found out of quantitative comparison can More accurately reflect the response for specifying building structure under wind environment effect, be that follow-up equivalent static wind load becomes more meticulous and ground Study carefully the Uncertainty Analysis Method for the skyscraper wind-excited responese analysis model laid a good foundation.

The technical solution adopted by the present invention is：

A kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model, its analytical procedure is as follows：

Step 1, obtained by the wind tunnel test of high frequency balance and specify the Foundation pressure time course data of building scaled model and incite somebody to action Base data is converted to architecture archetype by building scaled model；

Step 2, by the Foundation pressure time course data obtained in step 1 be applied to theoretical analysis model 1,2 ..., in n respectively Specify the wind-excited responese analysis of building；

Step 3, the Foundation pressure time course data obtained in step 1 is applied to specify to the benchmark of building as input condition Model carries out dynamic response analysis, and the structural response that calculating is obtained is responded as benchmark；

Step 4, from the principle of the Bayesian model method of average, the probability expression of model is set up, computation model 1, 2nd ..., n response density function, that is, determine that response prediction is uncertain；

Step 5, posterior model probability is updated, that is, determines that model is chosen uncertain；

Step 6, Bayesian Factor is defined, the uncertainty of different analysis models is assessed, and therefrom finds one group " optimal " Model.

Further, the probabilistic analytical procedure of the response prediction of step 4 is as follows：

The uncertainty of high-rise tall and slender structure wind-excited responese analysis model can be largely classified into 3 classes：Model is chosen uncertain Property, parameter uncertainty and response prediction be uncertain, can be represented by the formula：

In formula：z_ijRepresent by analysis modelAnd one group of input variable x_jCalculate obtained structure physical responses corresponding Actual value；δ_ijRepresent by model i and variable x_jCalculate obtained structure physical responses and actual value z_ijDifference, represent ring Answer uncertainty in traffic；Choose different analysis modelsCaused uncertainty is considered as model and chooses uncertain, and defeated Enter variable x_jUncertain be then referred to as parameter uncertainty；

According to the principle of the Bayesian model method of average, conditional probabilityThe response of N number of model can be expressed as Density functionWith posterior model probability Pr (M_i|z_ij) sum of products, it is shown below：

Due to not considering the parameter uncertainty that structure or aerodynamic parameter are brought, so each analysis model is all assumed to be really Fixed, model M_iResponse density function assume Normal Distribution, be shown below：

In formula：VarianceIt can be obtained by Maximum Likelihood Estimation, it is assumed that true response z_ijIn element it is mutual It is independent, then model M_iCorresponding true response prediction probability P r (z_ij|M_i) following formula can be expressed as：

Wherein posterior density Pr (z_ij|σ_i) Normal Distribution, expression formula is as follows：

Formula (5) is substituted into formula (4), model M can be obtained_iCorresponding true response prediction probability P r (z_ij|M_i)：

Then by Pr (z in formula (6)_ij|M_i) expression formula take the logarithm differential, and make it be equal to 0, just can obtain variance Maximum likelihood value：

Further, the model selection analysis of uncertainty step in step 5 is as follows：

The Bayesian model method of average usually assumes that each model possesses identical prior probability, i.e.,：

In given true response z_ijIn the case of, model M_iPosterior probability Pr (M_i|z_ij) can be managed by Bayes Obtained by calculating, calculating formula is as follows：

According to the Bayesian formula of formula (9) and utilize z_ijIn each element, model M_iPosterior probability carry out repeat more Newly.

Further, " optimal " model finding step of step 6 is as follows：

Compare influence of the different models to output response for convenience, for each model M_iDefine Bayesian Factor B_i, expression formula is as follows：

The Bayesian Factor B defined by formula (10)_i, can rapidly assess based on high frequency balance wind-tunnel technique The uncertainty of different analysis models, and can therefrom find one group of " optimal " model (i.e. B_i=1) cause by the model Obtained response is calculated closest to actual value.

Further, in analysis and time domain of the charming appearance and behaviour structural response analysis in step 2 including mode wind-force or in frequency domain Response analysis.Due to the simply model Foundation pressure time course data that rigid model high frequency balance test is obtained, and wind load edge is built The spatial and temporal distributions form for building height is unknown.Therefore, the estimation of mode wind-force is the analysis model based on high frequency balance test Key technology point.On the basis of linear mode assumption, the wind tunnel test of high frequency balance passes through direct measurement model bottom charming appearance and behaviour Shearing, moment of flexure and moment of torsion, can accurately estimate the mode wind-force of prototype structure.However, the three-dimensional coupling of modern high-rise building The feature of nonlinear analog-circuit, the applicability to high frequency balance wind-tunnel technique proposes test.In order to adapt to skyscraper three The dynamic characteristics of coupling nonlinear mode is tieed up, many scholars are from high frequency balance wind-tunnel technique, according to different hypothesis Different theoretical analysis models is proposed respectively to estimate mode wind-force.

Further, benchmark model in step 3 is become more meticulous model from the finite element for specifying building.Present invention selection is specified The finite element of the building model that becomes more meticulous examines the applicabilities of different theoretical analysis models as benchmark model.But need note Meaning, benchmark model is not limited to finite element and become more meticulous model, and building is obtained under identical wind environment by measurement method Actual measurement response can also be responded as benchmark.

Beneficial effects of the present invention：Different analysis models are quantitatively compared by probability measure aspect, and found out most Excellent model can more accurately reflect response of the specified building structure under wind environment effect, and the anti-of engineering structure is carried out accordingly Wind design and research, will obtain more accurate reliable result, and this method computational efficiency is high, extends to Other Engineering field The analysis of uncertainty of analysis model.

Brief description of the drawings

Fig. 1 is techniqueflow chart of the invention.

Fig. 2 a are that certain skyscraper finite element becomes more meticulous model.

Fig. 2 b are certain skyscraper lumped mass simplified model.

Fig. 3 a are certain rank Mode Shape of skyscraper the 1st.

Fig. 3 b are certain rank Mode Shape of skyscraper the 2nd.

Fig. 3 c are certain rank Mode Shape of skyscraper the 3rd.

Fig. 4 is certain skyscraper rigid model wind tunnel test and the definition of incident wind angle.

The 1st rank generalized displacement σ that Fig. 5 a obtain for analysis model under each wind angle_qThe broad sense obtained with basic benchmark model DisplacementThe ratio between.

The 2nd rank generalized displacement σ that Fig. 5 b obtain for analysis model under each wind angle_qThe broad sense obtained with basic benchmark model DisplacementThe ratio between.

The 3rd rank generalized displacement σ that Fig. 5 c obtain for analysis model under each wind angle_qThe broad sense obtained with basic benchmark model DisplacementThe ratio between.

Embodiment

The present invention is further described with reference to specific embodiment, but does not limit the invention to these tools Body embodiment.One skilled in the art would recognize that present invention encompasses potentially included in Claims scope All alternatives, improvement project and equivalents.

Reference picture 1, a kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model, its analytical procedure is such as Under：

Step 1, obtained by the wind tunnel test of high frequency balance and specify the Foundation pressure time course data of building scaled model and incite somebody to action Base data is converted to architecture archetype by building scaled model；Its concrete operations：For specifying skyscraper, rigid reduced scale is made Model, debugs Flow Field in Wind Tunnel, carries out high frequency balance wind tunnel test, obtains the component (F of Foundation pressure 5 of building scaled model_x,F_y, M_xx,M_yy,M_θθ) time course data, and data are converted to architecture archetype by scaled model；

Step 2, by the Foundation pressure time course data obtained in step 1 be applied to theoretical analysis model 1,2 ..., in n respectively Specify the wind-excited responese analysis of building；Charming appearance and behaviour structural response analysis in the present embodiment step 2 includes point of mode wind-force Response analysis in analysis and time domain or in frequency domain.Due to rigid model high frequency balance test obtain simply model Foundation pressure when Number of passes evidence, and spatial and temporal distributions form of the wind load along building height is unknown.Therefore, the estimation of mode wind-force is to be based on high frequency The key technology point of the analysis model of balance test.On the basis of linear mode assumption, high frequency balance wind tunnel test passes through straight Measurement model bottom charming appearance and behaviour shearing, moment of flexure and moment of torsion are connect, the mode wind-force of prototype structure can be accurately estimated.However, modern The feature of the three-dimensional coupling nonlinear mode of skyscraper, the applicability to high frequency balance wind-tunnel technique proposes test. In order to adapt to the dynamic characteristics of the three-dimensional coupling nonlinear mode of skyscraper, many scholars go out from high frequency balance wind-tunnel technique Hair, proposes different theoretical analysis models to estimate mode wind-force respectively according to different hypothesis.

Step 3, the Foundation pressure time course data obtained in step 1 is applied to specify to the benchmark of building as input condition Model carries out dynamic response analysis, and the structural response that calculating is obtained is responded as benchmark；Benchmark mould in the present embodiment step 3 Type is become more meticulous model from specifying the finite element of building.Present invention selection specifies the finite element of building to become more meticulous model as base Quasi-mode type examines the applicability of different theoretical analysis models.It is however noted that, benchmark model has been not limited to Primordial essence refined model is limited, obtaining actual measurement response of the building under identical wind environment by measurement method can also respond as benchmark.

Step 4, from the principle of the Bayesian model method of average, the probability expression of model is set up, computation model 1, 2nd ..., n response density function, that is, determine that response prediction is uncertain；

Step 5, posterior model probability is updated, that is, determines that model is chosen uncertain；

Step 6, Bayesian Factor is defined, the uncertainty of different analysis models is assessed, and therefrom finds one group " optimal " Model.

The probabilistic analytical procedure of response prediction of the present embodiment step 4 is specific as follows：

The uncertainty of high-rise tall and slender structure wind-excited responese analysis model can be largely classified into 3 classes：Model is chosen uncertain Property, parameter uncertainty and response prediction be uncertain, can be represented by the formula：

In formula：z_ijRepresent by analysis modelAnd one group of input variable x_jCalculate obtained structure physical responses corresponding Actual value；δ_ijRepresent by model i and variable x_jCalculate obtained structure physical responses and actual value z_ijDifference, represent response Uncertainty in traffic；Choose different analysis modelsCaused uncertainty is considered as model and chooses uncertain, and inputs Variable x_jUncertain be then referred to as parameter uncertainty；

According to the principle of the Bayesian model method of average, conditional probabilityThe response of N number of model can be expressed as Density functionWith posterior model probability Pr (M_i|z_ij) sum of products, it is shown below：

Due to not considering the parameter uncertainty that structure or aerodynamic parameter are brought, so each analysis model is all assumed to be really Fixed, model M_iResponse density function assume Normal Distribution, be shown below：

In formula：VarianceIt can be obtained by Maximum Likelihood Estimation, it is assumed that true response z_ijIn element it is mutual It is independent, then model M_iCorresponding true response prediction probability P r (z_ij|M_i) following formula can be expressed as：

Wherein posterior density Pr (z_ij|σ_i) Normal Distribution, expression formula is as follows：

Formula (5) is substituted into formula (4), model M can be obtained_iCorresponding true response prediction probability P_r(z_ij|M_i)：

Then by Pr (z in formula (6)_ij|M_i) expression formula take the logarithm differential, and make it be equal to 0, just can obtain variance Maximum likelihood value：

It is specific as follows that model in the present embodiment step 5 chooses analysis of uncertainty step：

The Bayesian model method of average usually assumes that each model possesses identical prior probability, i.e.,：

In given true response z_ijIn the case of, model M_iPosterior probability Pr (M_i|z_ij) can be managed by Bayes Obtained by calculating, calculating formula is as follows：

According to the Bayesian formula of formula (9) and utilize z_ijIn each element, model M_iPosterior probability carry out repeat more Newly.

" optimal " model finding step of the present embodiment step 6 is specific as follows：

Compare influence of the different models to output response for convenience, for each model M_iDefine Bayesian Factor B_i, expression formula is as follows：

The Bayesian Factor B defined by formula (10)_i, can rapidly assess based on high frequency balance wind-tunnel technique The uncertainty of different analysis models, and can therefrom find one group of " optimal " model (i.e. B_i=1) cause by the model Obtained response is calculated closest to actual value.

In order to more clearly from illustrate above-mentioned steps, now this patent is introduced by taking the Wind resistant analysis of certain skyscraper as an example Embodiment, it is specific as follows：

Certain is high 194 meters, the long and narrow bombyx Botryticatus of 163 meters of long hem width, wide 37 meters of short side be used for the present invention based on high frequency The wind-excited responese analysis of balance wind tunnel technique, its FEM model is as shown in Figure 2 a.According to rigid floor slab, per Stall Flaggy can be simulated by a lumped mass system containing three degree of freedom, and the lumped-mass model of the building is as schemed Shown in 2b.Fig. 3 is the three dimension mode bending vibation mode picture of 3 ranks before the building, due to the long and narrow build of building so that along x to (i.e. along short side Direction) the vibration shape leading role is accounted in preceding two ranks mode, the 3rd rank mode is based on the vibration shape along y to (i.e. along long side direction). Simultaneously as the irregular facade perforate of the building causes its dynamic characteristics similar to the multitower high building with vestibule, i.e., three-dimensional mould Complicated variation tendency is presented in the state vibration shape.

Synchronous multipoint pressure measure wind tunnel test is carried out to the scaled model of the building, Fig. 4 is with showing consideration periphery landform The definition of the model in wind tunnel of looks and incident wind angle, Flow Field in Wind Tunnel is B class landforms atmospheric boundary layer air-flows, and ground is coarse α=0.16 is spent, experiment takes a wind angle in the range of 0 °~360 ° every 10 °, totally 36 wind angles, adopted under each wind angle Sample length is 8200 data points, and sample duration 27.33s, and sample frequency is 300Hz.

By synchronous multipoint pressure measure wind tunnel test, the blast time course data of the building surface can be measured, then to wind Pressure time-histories, which is integrated processing, can export the component time-histories of substrate 5.The component time-histories of substrate 5 is tried as the high frequency balance of " virtual " Test data application in 4 kinds of high frequency balance analysis models response ratio compared with and analysis of uncertainty in so that between different models Response difference will not be caused by research technique or other factors, and only be caused in itself by analysis model.On the other hand, it is The analysis of uncertainty of 4 kinds of high frequency balance analysis models is carried out, the embodiment of the present invention defines two kinds of benchmark models, the first It is benchmark model based on wind-excited responese analysis model in the frequency domain based on synchronous multipoint pressure measure wind tunnel test, abbreviation；And it is another Plant and be then referred to as the benchmark model that becomes more meticulous, i.e., floor layer wind-force time-histories is obtained by synchronous multipoint pressure measure wind tunnel test and made Finite element is applied to for input source to become more meticulous model, so as to obtain corresponding structural response value.

Fig. 5 show first three rank generalized displacement and basic benchmark mould that different analysis models are obtained under each wind angle of the building The ratio between corresponding exponent number generalized displacement that type is obtainedBecause the x that the building second-order accounts for leading role is high to vibration shape edge Spend variation abnormality and even the reverse vibration shape (as shown in Figure 3 b) occur, therefore compare the curve of the rank of first three in Fig. 5 and can be found that by not The deviation for calculating the generalized displacement that obtained second-order generalized displacement is obtained with benchmark model with model be significantly greater than the first rank and 3rd rank, and notable fluctuation occurs for the change at second-order ratio box haul angle.As shown in Figure 5 b, calculated with basic benchmark model Obtained generalized displacement is made comparisons it can be found that calculating obtained second-order generalized displacement in each wind angle by MSC methods, ALMS methods Under it is relatively conservative to some extent, and it is then relatively inclined that obtained generalized displacement is calculated by Yip-Flay methods, Xie-Irwin methods It is small.

Table 1 list under each wind angle calculated based on high frequency balance wind-excited responese analysis model obtain before 3 rank broad sense positions Shifting and basic benchmark model calculate the mean error and root-mean-square error between obtained generalized displacement.As can be seen from Table 1 by The error that Yip-Flay methods are calculated between the generalized displacement that obtained preceding 3 rank generalized displacement and basic benchmark model calculating are obtained is equal Root is minimum, and it is possible thereby to preliminarily qualitatively judging Yip-Flay analysis models calculates the closest basic benchmark of obtained response Model calculates obtained " true " response.

Analysis model calculates being averaged between obtained preceding 3 rank generalized displacement and basic benchmark model under each wind angle of table 1 Error and root-mean-square error

In order to which 4 kinds of wind-excited responese analysis models based on high frequency balance are carried out with the not true of model selection and response prediction Qualitative quantization is assessed, it is necessary first to which, it is determined that representing the benchmark model of " true " response, the embodiment of the present invention defines two kinds of benchmark Model, i.e., basic benchmark model and the benchmark model that becomes more meticulous.Determine after benchmark model, it is necessary to provide each analysis model Prior probability.The Bayesian model method of average assumes that each model possesses identical prior probability, so 4 kinds of this paper are based on high frequency The prior probability of the wind-excited responese analysis model of balance is all taken as 0.25.Then, model probability renewal process just can be along wind 36 repetitions are carried out to the change at angle to update.

Table 2 and table 3 are used as actual value to calculate obtained response using basic benchmark model and the benchmark model that becomes more meticulous respectively Model posterior probability and Bayesian Factor.By two tables it is clear that calculating what is obtained using the model method of average The model posterior probability of Yip-Flay methods is maximum, i.e. B_i=1, the significantly larger than posterior probability of other three models.Thus just It can quantitatively judge that Yip-Flay analysis models calculate obtained response and obtained " true " is calculated closest to two kinds of benchmark models Response.

The model probability of table 2 and Bayesian Factor (basic benchmark model is calculated to obtained response and is used as actual value)

The model probability of table 3 and Bayesian Factor (benchmark model that becomes more meticulous is calculated to obtained response and is used as actual value)

Claims (6)

1. a kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model, its analytical procedure is as follows：

Step 1, obtained by the wind tunnel test of high frequency balance and specify the Foundation pressure time course data of building scaled model and by substrate Data are converted to architecture archetype by building scaled model；

Step 2, by the Foundation pressure time course data obtained in step 1 be applied to theoretical analysis model 1,2 ..., carry out respectively in n Specify the wind-excited responese analysis of building；

Step 3, the Foundation pressure time course data obtained in step 1 is applied to specify to the benchmark model of building as input condition Dynamic response analysis is carried out, the structural response that calculating is obtained is responded as benchmark；

Step 4, from the principle of the Bayesian model method of average, set up the probability expression of model, computation model 1,2 ..., n Response density function, that is, determine that response prediction is uncertain；

Step 5, posterior model probability is updated, that is, determines that model is chosen uncertain；

Step 6, Bayesian Factor is defined, the uncertainty of different analysis models is assessed, and therefrom finds one group of " optimal " model.

2. a kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model as claimed in claim 1, its feature It is：The probabilistic analytical procedure of response prediction of step 4 is as follows：

The uncertainty of high-rise tall and slender structure wind-excited responese analysis model can be divided into 3 classes：Model chooses uncertain, and parameter is not Certainty and response prediction are uncertain, can be represented by the formula：

$z_{ij}={\tilde{f}}_i\left(x_j\right)+{\mathrm{\δ}}_{ij}---\left(1\right)$

In formula：z_ijRepresent by analysis modelAnd one group of input variable x_jCalculate obtained structure physical responses corresponding true Value；δ_ijRepresent by model i and variable x_jCalculate obtained structure physical responses and actual value z_ijDifference, represent response prediction It is uncertain；Choose different analysis modelsCaused uncertainty is considered as model and chooses uncertain, and input variable x_j Uncertain be then referred to as parameter uncertainty；

According to the principle of the Bayesian model method of average, conditional probabilityThe response density of N number of model can be expressed as FunctionWith posterior model probability Pr (M_i|z_ij) sum of products, it is shown below：

$\mathrm{Pr}\left({\tilde{f}}_i\right(x_j\left)\right|z_{ij})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{Pr}\left({\tilde{f}}_i\right(x_j\left)\right|M_i,z_{ij})\×\mathrm{Pr}\left(M_i\right|z_{ij})---\left(2\right)$

Due to not considering the parameter uncertainty that structure or aerodynamic parameter are brought, so each analysis model all assumes to be to determine , model M_iResponse density function assume Normal Distribution, be shown below：

$\mathrm{Pr}\left({\tilde{f}}_i\right(x_j\left)\right|M_i,z_{ij})=Norm\left({\tilde{f}}_i\right(x_j),{\mathrm{\σ}}_i^2)---\left(3\right)$

In formula：VarianceIt can be obtained by Maximum Likelihood Estimation, it is assumed that true response z_ijIn element it is independent mutually, Then model M_iCorresponding true response prediction probability P r (z_ij|M_i) following formula can be expressed as：

$\mathrm{Pr}\left(z_{ij}\right|M_i)=\mathrm{Pr}(z_{i1},z_{i2},...,z_{ij},...,z_{im}|{\mathrm{\σ}}_i)={\mathrm{\Π}}_{j=1}^m\mathrm{Pr}\left(z_{ij}\right|{\mathrm{\σ}}_i)---\left(4\right)$

Wherein posterior density Pr (z_ij|σ_i) Normal Distribution, expression formula is as follows：

$\mathrm{Pr}\left(z_{ij}\right|{\mathrm{\σ}}_i)=\frac{1}{\sqrt{2{\mathrm{\π\σ}}_i^2}}\exp (-\frac{{(z_{ij}-{\tilde{f}}_i(x_j\left)\right)}^2}{2{\mathrm{\σ}}_i^2})---\left(5\right)$

Formula (5) is substituted into formula (4), model M can be obtained_iCorresponding true response prediction probability P r (z_ij|M_i)：

$\mathrm{Pr}\left(z_{ij}|M_i\right)={\left(\frac{1}{\sqrt{2{\mathrm{\π\σ}}_i^2}}\right)}^m\exp \left(-\frac{{\mathrm{\Σ}}_{j=1}^m{\left(z_{ij}-{\tilde{f}}_i\left(x_j\right)\right)}^2}{2{\mathrm{\σ}}_i^2}\right)---\left(6\right)$

Then by Pr (z in formula (6)_ij|M_i) expression formula take the logarithm differential, and make it be equal to 0, just can obtain varianceIt is very big Likelihood value：

${\mathrm{\σ}}_i^2=\frac{{\mathrm{\Σ}}_{j=1}^m{(z_{ij}-{\tilde{f}}_i(x_j\left)\right)}^2}{m}---\left(7\right).$

3. a kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model as claimed in claim 1, its feature It is：It is as follows that model in step 5 chooses analysis of uncertainty step：

The Bayesian model method of average usually assumes that each model possesses identical prior probability, i.e.,：

$\mathrm{Pr}\left(M_i\right)=\frac{1}{N}---\left(8\right)$

In given true response z_ijIn the case of, model M_iPosterior probability Pr (M_i|z_ij) bayesian theory meter can be passed through Obtain, calculating formula is as follows：

$\mathrm{Pr}\left(M_i|z_{ij}\right)=\frac{\mathrm{Pr}\left(M_i\right)\×\mathrm{Pr}\left(z_{ij}|M_i\right)}{{\mathrm{\Σ}}_{ii=1}^n\mathrm{Pr}\left(M_{ii}\right)\×\mathrm{Pr}\left(z_{ij}|M_{ii}\right)}---\left(9\right)$

According to the Bayesian formula of formula (9) and utilize z_ijIn each element, model M_iPosterior probability carry out repeat renewal.

4. a kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model as claimed in claim 1, its feature It is：" optimal " model finding step of step 6 is as follows：

Compare influence of the different models to output response for convenience, for each model M_iDefine Bayesian Factor B_i, table It is as follows up to formula：

$B_i=\frac{max\{\mathrm{Pr}\left(M_1\right|z_{1j}),\mathrm{Pr}\left(M_2\right|z_{2j}),...,\mathrm{Pr}\left(M_n\right|z_{nj})\}}{\mathrm{Pr}\left(M_i\right|z_{ij})}---\left(10\right)$

The Bayesian Factor B defined by formula (10)_i, can rapidly assess the difference based on high frequency balance wind-tunnel technique The uncertainty of analysis model, and can therefrom find one group of i.e. B of " optimal " model_i=1 to calculate by the model The response arrived is closest to actual value.

5. a kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model as claimed in claim 1, its feature It is：Response analysis in analysis and time domain of the charming appearance and behaviour structural response analysis including mode wind-force in step 2 or in frequency domain.

6. a kind of Uncertainty Analysis Method of skyscraper wind-excited responese analysis model as described in one of Claims 1 to 5, It is characterized in that：Benchmark model in step 3 is become more meticulous model from the finite element for specifying building.