CN107194036A - A kind of large-span roof structure non-gaussian Numerical Simulation Methods of Wind Load - Google Patents
A kind of large-span roof structure non-gaussian Numerical Simulation Methods of Wind Load Download PDFInfo
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Abstract
The present invention provides a kind of large-span roof structure non-gaussian Numerical Simulation Methods of Wind Load.Method provided by the present invention improves traditional single-point non-gaussian blast simulation algorithm, and traditional single-point non-gaussian blast simulation is decomposed with Proper Orthogonal(POD)Technology, Hermite matrixes are combined, and the blast field data as obtained by POD technologies by wind tunnel test is decomposed into the combination of principal coordinate and eigenvector, before selection energy contribution rate is largerNThe corresponding principal coordinate time-histories of rank POD eigenvectors is simulated, and levies vectorial combine to form simulated wind pressure with script.On the one hand, the present invention not only maintains correlation of the wind-pressure field in the time and space by POD technologies, and substantially reduces analog matrix exponent number, so as to reduce amount of calculation, improves computational efficiency;On the other hand, nongausian process is converted into Gaussian process by the present invention using Hermite matrixes, and introduces three simulation error evaluating amendment analog results, more conforms to the characteristic that actual long-span roof fluctuating wind is had a meeting, an audience, etc. well under one's control.
Description
Technical field
The invention belongs to large-span roof structure wind force proofing design field, it is related to a kind of analogy method of random pulse wind-pressure field,
More particularly to a kind of large-span roof structure non-gaussian Numerical Simulation Methods of Wind Load.
Background technology
Wind load is the important load of control structure safety, especially for the larger longspan structure of flexibility and towering knot
Structure, even serves conclusive sometimes.Considering the local important area of separation stream effect, wind load often shows strong
Pulsation and non-Gaussian feature.Compared with Gaussian process, in the case of identical average and variance, the peak value of non-gaussian random process
It is bigger, more unfavorable effect can be produced to structure, thus it is significant to the research of non-gaussian wind load.For stadium
The large span architecture such as shop and indoor coal storage yard, the geometrical non-linearity degree of structure is higher, and compared to frequency domain method, time domain method can contemplate structure
Non-linear factor, can relatively accurately reflect the wind shake coupling condition of structure.However, due to the influence of various factors, greatly across room
The wind load time-history data that the experiment of lid structure wind tunnel pressure measuring is provided all are limited, it is difficult to meet research non-gaussian wind load and knot
The requirement of structure power wind scorpion.Although traditional harmony superposition can be used for blast simulation, but with the increase of measuring point quantity,
Amount of calculation can be greatly increased, and can not simulate nongausian process.Therefore, obtained using numerical simulation and meet specified conditions
It is very important when long away from non-gaussian wind load.
The content of the invention
It is an object of the invention to provide a kind of new non-gaussian wind-pressure field analogy method, it is provided in particular in a kind of big across room
Lid structure non-gaussian Numerical Simulation Methods of Wind Load, this method decomposes (POD) technology using Proper Orthogonal and is obtained wind tunnel test
The target zero-mean wind-pressure field taken be decomposed into the time of relying only on principal coordinate and only with spatial variations eigenvector combination, root
According to each rank eigenvector characteristic value size, the principal coordinate time-histories before choosing corresponding to N rank POD eigenvectors is simulated, by preceding N
Rank POD principal coordinates time-histories is converted into Gaussian process with Hermite matrixes, is simulated and is corrected with harmony superposition (WAWS), then with
Originally levy vector combination and form simulation zero-mean wind-pressure field.Calculate obtained measuring point simulation pulsating wind pressure time-histories and maintain wind-pressure field
Correlation in the time and space, more conforms to the characteristic that actual long-span roof fluctuating wind is had a meeting, an audience, etc. well under one's control, extends to other roof systems
Structural wind resistance design.
Therefore, the above-mentioned purpose of the present invention is achieved through the following technical solutions:
The present invention provides a kind of large-span roof structure non-gaussian Numerical Simulation Methods of Wind Load, and this method includes following step
Suddenly:
The first step:Tested by wind tunnel pressure measuring, obtain wind-pressure field:
P (x, y, t)={ p1(t)、p2(t)...pn(t) each measuring point blast average }, is calculated:
Obtain target zero-mean wind-pressure field P*(x, y, t)={ p1 *(t);p2 *(t)...pn *(t)};
Second step:Carry out Proper Orthogonal decomposition (POD), target zero-mean wind-pressure field P*(x, y, t) can be expanded into:
In formula:For the i-th rank POD principal coordinate time-histories,For the i-th rank eigenvector, corresponding characteristic value is then remembered
For
3rd step:According to the characteristic value size of each rank eigenvector, the preceding N ranks POD principal coordinate time-histories of simulation is chosen And corresponding eigenvector
4th step:Preceding N ranks POD principal coordinate time-histories after selection is simulated, simulation algorithm is as follows:
(1) the i-th rank POD principal coordinate time-histories is calculatedThe power spectrum of target nongausian process, skewness and kurtosis, respectively
It is designated as:
(2) according to Hermite square transformation relations, the i-th rank POD principal coordinate time-histories auto-correlation functions are derivedCorresponding Gaussian process auto-correlation function
(3) it is rightThe power spectrum of primary simulation Gaussian process is obtained as Fast Fourier Transform (FFT)Using harmonic superposition
Method obtains the Gaussian process of jth time simulationIts power spectrum is calculated, is designated as
(4) Hermite square transform methods are used, jth time simulation nongausian process is obtainedCalculate its power spectrum,
Skewness and kurtosis, is designated as respectively:
(5) jth time simulation error evaluating is introduced
For target nongausian process power spectral density functionThe nongausian process power obtained with jth time simulation
Spectral density functionBetween relative error, fnFor discrete Frequency point,For target high-order statistic
With simulating obtained nongausian process high-order statisticBetween error;
(6) ifOrOrWherein, target errorWithThen in (3)
Simulate Gaussian process power spectrumIt is modified, method is as follows:
In formula:β is amendment constant, and value 1.3, are back to (2) after amendment here, carries out next step iterative calculation;
IfAndAndWherein, target errorWithOr iterative steps
More than 50000 steps, stop iteration, obtained simulation nongausian process is the i-th rank POD principal coordinate time precise integration results, is designated asAnd be back to (1), simulate i+1 rank POD principal coordinate time-histories;
(7) above-mentioned (1) is repeated to (6), until N rank POD principal coordinate time precise integrations before completing, simulation principal coordinate time-histories difference
For:
5th step:Obtained principal coordinate time-histories will be simulated and combine formation simulation zero-mean wind-pressure field with levying vector originally:
Harmony superposition (WAWS) and Proper Orthogonal are decomposed (POD) technology, Hermite squares by method provided by the present invention
Battle array is combined, and the blast field data as obtained by POD technologies by wind tunnel test is decomposed into the combination of principal coordinate and eigenvector, choosing
The corresponding principal coordinate time-histories of preceding N ranks POD eigenvectors for taking energy contribution rate larger is simulated, and levies vectorial combination with script
Form simulated wind pressure.On the one hand, the present invention not only maintains correlation of the wind-pressure field in the time and space by POD technologies
Property, and analog matrix exponent number is substantially reduced, so as to reduce amount of calculation, improve computational efficiency;On the other hand, the present invention is used
Nongausian process is converted into Gaussian process by Hermite matrixes, and introduces three simulation error evaluatingsRepair
Positive analog result, more conforms to actual conditions.Method provided by the present invention can be generalized to other field of roof structure design.
Brief description of the drawings
Fig. 1 is flow chart of the invention.
Fig. 2 is model in wind tunnel point layout figure.
Fig. 3 is first five rank eigenvector isopleth cloud atlas.
Fig. 4 is first five rank simulation principal coordinate time-histories and target time-histories power spectral density comparison diagram.
Fig. 5 is the power spectral density comparison diagram of the representative measuring point pulsating wind pressure analogue value and desired value.
Embodiment
The invention will be further described with reference to the accompanying drawings and examples.
The present invention provides a kind of large-span roof structure non-gaussian Numerical Simulation Methods of Wind Load, its flow as shown in figure 1, should
Method comprises the following steps:
The first step:Tested by wind tunnel pressure measuring, obtain wind-pressure field:
P (x, y, t)={ p1(t)、p2(t)...pn(t) each measuring point blast average }, is calculated:
Obtain target zero-mean wind-pressure field P*(x, y, t)={ p1 *(t);p2 *(t)...pn *(t)};
Second step:Carry out Proper Orthogonal decomposition, target zero-mean wind-pressure field P*(x, y, t) can be expanded into:
In formula:For the i-th rank POD principal coordinate time-histories,For the i-th rank eigenvector, corresponding characteristic value is then
It is designated as
3rd step:According to the characteristic value size of each rank eigenvector, the preceding N ranks POD principal coordinate time-histories of simulation is chosen And corresponding eigenvector
4th step:Preceding N ranks POD principal coordinate time-histories after selection is simulated, simulation algorithm is as follows:
(1) the i-th rank POD principal coordinate time-histories is calculatedThe power spectrum of target nongausian process, skewness and kurtosis, respectively
It is designated as:
(2) according to Hermite square transformation relations, the i-th rank POD principal coordinate time-histories auto-correlation functions are derivedCorresponding Gaussian process auto-correlation function
(3) it is rightThe power spectrum of primary simulation Gaussian process is obtained as Fast Fourier Transform (FFT)Using harmonic superposition
Method obtains the Gaussian process of jth time simulationIts power spectrum is calculated, is designated as
(4) Hermite square transform methods are used, jth time simulation nongausian process is obtainedCalculate its power spectrum,
Skewness and kurtosis, is designated as respectively:
(5) jth time simulation error evaluating is introduced
For target nongausian process power spectral density functionThe nongausian process power obtained with jth time simulation
Spectral density functionBetween relative error, fnFor discrete Frequency point,For target high-order statistic
With simulating obtained nongausian process high-order statisticBetween error;
(6) ifOrOrWherein, target errorWithThen in (3)
Simulate Gaussian process power spectrumIt is modified, method is as follows:
In formula:β is amendment constant, and value 1.3, are back to (2) after amendment here, carries out next step iterative calculation;
IfAndAndWherein, target errorWithOr iteration step
Number is more than 50000 steps, stops iteration, obtained simulation nongausian process is the i-th rank POD principal coordinate time precise integration results, note
ForAnd be back to (1), simulate i+1 rank POD principal coordinate time-histories;
(7) above-mentioned (1) is repeated to (6), until N rank POD principal coordinate time precise integrations before completing, simulation principal coordinate time-histories difference
For:
5th step:Obtained principal coordinate time-histories will be simulated and combine formation simulation zero-mean wind-pressure field with levying vector originally:
One embodiment is enumerated below:
The first step:Fig. 2 is Cangnan power plant indoor coal storage yard rack model in wind tunnel point layout figure, according to the wind tunnel test
Data, choose 0 ° of representative (no dump operating mode) load and carry out non-gaussian blast field stimulation.30 seconds time-histories in the middle of interception,
Each measuring point blast average is subtracted, each measuring point target zero-mean blast field data is obtained.
Second step:Proper Orthogonal decomposition is carried out to gained target zero-mean wind-pressure field, each rank principal coordinate time-histories and this is obtained
Levy vector.
3rd step:According to the corresponding characteristic value size of each rank eigenvector, choose simulation preceding 100 rank principal coordinate time-histories and
Corresponding eigenvector, first five rank eigenvector isopleth cloud atlas is as shown in Figure 3.
4th step:100 rank principal coordinate time-histories before after selection are simulated:
(1) the i-th rank principal coordinate time-histories is calculatedTarget nongausian process power spectrum, skewness and kurtosis, preceding 5 rank is main to sit
Mark skewness and kurtosis as shown in table 1;
Table 1
(2) the i-th rank principal coordinate time-histories auto-correlation function is derived according to Hermite square transformation relations;
(3) it is rightPrimary simulation Gaussian process power spectrum is obtained as Fast Fourier Transform (FFT)Using harmony superposition
Obtain a simulation Gaussian processCalculate its power spectrum;
(4) Hermite square transform methods are used, obtain simulating nongausian processCalculate its power spectrum, the degree of bias and
Kurtosis;
(5) jth time simulation error evaluating is introduced
(6) ifOrOrThen to simulation Gaussian process power spectrum in (3)It is modified, returns
It is back to (2), carries out next step iterative calculation;
IfAndAndOr iterative steps are more than 50000 steps, stop iteration, obtained simulation
Nongausian process is the i-th rank principal coordinate time precise integration result;It is back to (1), simulates i+1 rank principal coordinate time-histories;
(7) above-mentioned (1) is repeated to (6), until preceding 100 rank principal coordinate time precise integration is completed, during first five rank simulation principal coordinate
Journey and the contrast of target time-histories are as shown in Figure 4.
5th step:The principal coordinate time-histories that simulation is obtained levies vector with original and combines formation simulation zero-mean wind-pressure field.Arteries and veins wind
Press the power spectral density pair of the larger representative measuring point G3 of coefficient root-mean-square value (shown in being marked in Fig. 2) analogues value and desired value
Than as shown in Figure 5.
As described above, although the present invention has been represented and described with reference to specific preferred embodiment, it must not be explained
For to the limitation of itself of the invention., can be right under the premise of the spirit and scope of the present invention that appended claims are defined are not departed from
Various changes can be made in the form and details for it.
Claims (1)
1. a kind of large-span roof structure non-gaussian Numerical Simulation Methods of Wind Load, it is characterised in that this method comprises the following steps:
The first step:Tested by roof system rigid model wind tunnel pressure measuring, obtain wind-pressure field data sample:
P (x, y, t)={ p1(t)、p2(t)...pn(t) each measuring point blast average }, is calculated:Obtain
Target zero-mean wind-pressure field P*(x, y, t)={ p1 *(t);p2 *(t)...pn *(t)};
Second step:Carry out Proper Orthogonal decomposition, target zero-mean wind-pressure field P*(x, y, t) can be expanded into:
In formula:For the i-th rank POD principal coordinate time-histories,For the i-th rank eigenvector, corresponding characteristic value is then designated as
3rd step:According to the characteristic value size of each rank eigenvector, the preceding N ranks POD principal coordinate time-histories of simulation is chosen And corresponding eigenvector
4th step:Preceding N ranks POD principal coordinate time-histories after selection is simulated, simulation algorithm is as follows:
(1) the i-th rank POD principal coordinate time-histories is calculatedThe power spectrum of target nongausian process, skewness and kurtosis, remember respectively
For:
(2) according to Hermite square transformation relations, the i-th rank POD principal coordinate time-histories auto-correlation functions are derivedCorresponding Gaussian process auto-correlation function
(3) it is rightThe power spectrum of primary simulation Gaussian process is obtained as Fast Fourier Transform (FFT)Obtained using harmony superposition
To the Gaussian process data of jth time simulationIts power spectrum is calculated, is designated as
(4) Hermite square transform methods are used, jth time simulation obtains nongausian process dataCalculate its power spectrum,
Skewness and kurtosis, is designated as respectively:
(5) the error assessment parameter to jth time analog result is introduced
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In formula:β is amendment constant, and value 1.3, are back to (2) after amendment here, carries out next step iterative calculation;
IfAndAndWherein, target errorWithOr iterative steps are big
In 50000 steps, stop iteration, obtained nongausian process data are the i-th rank POD principal coordinate time precise integration results, are designated asAnd be back to (1), simulate i+1 rank POD principal coordinate time-histories;
(7) above-mentioned (1) is repeated to (6), until the work of N rank POD principal coordinates time precise integration is completed before completing, simulates obtained main seat
Marking time course data is respectively:
5th step:The principal coordinate time-histories that simulation is obtained combines the simulation for obtaining zero-mean wind-pressure field with former wind-pressure field eigenvector
As a result:
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CN111027261A (en) * | 2019-11-15 | 2020-04-17 | 四川大学 | Hybrid simulation test method for researching structural wind excitation response |
CN112131638A (en) * | 2020-09-09 | 2020-12-25 | 石家庄铁道大学 | Wind-induced dynamic characteristic type determination method of large-span roof structure and terminal equipment |
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CN108804838A (en) * | 2018-06-15 | 2018-11-13 | 辽宁工程技术大学 | A kind of Wind-resistant design method of Pressures On Complex Large-span degree hyperbolic roof system |
CN111027261A (en) * | 2019-11-15 | 2020-04-17 | 四川大学 | Hybrid simulation test method for researching structural wind excitation response |
CN111027261B (en) * | 2019-11-15 | 2023-09-26 | 四川大学 | Hybrid simulation test method for researching structural wind excitation response |
CN112131638A (en) * | 2020-09-09 | 2020-12-25 | 石家庄铁道大学 | Wind-induced dynamic characteristic type determination method of large-span roof structure and terminal equipment |
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