CN107967240A - Shatter-proof time-histories acceleration optimization algorithm based on artificial ground shaking generating process - Google Patents
Shatter-proof time-histories acceleration optimization algorithm based on artificial ground shaking generating process Download PDFInfo
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Abstract
The invention belongs to earthquake motion optimization algorithmic technique field, propose a kind of shatter-proof time-histories acceleration optimization algorithm based on artificial ground shaking generating process, and improve the precision initially shaken, it can solve in hydro-structure numerical computations, under seismic loading, nonlinear dynamical damage calculates that the time is long, slow-footed problem.This algorithm is with NB35047 2015《Hydroelectric project hydraulic structure earthquake resistant design code》Standard design response spectrum is composed for target, using the shatter-proof time-histories acceleration function of MATLAB Software Creates.Beneficial effects of the present invention：1. introducing earthquake motion efficiently produces algorithm；2. initially vibrations have preferable fitting precision；3. reduce the time of nonlinear dynamical damage, easy to analyze.
Description
Technical field
The invention belongs to earthquake motion optimization algorithmic technique field, it is proposed that a kind of based on the resistance to of artificial ground shaking generating process
Time-histories acceleration optimization algorithm is shaken, and improves the precision initially shaken, can be solved in hydro-structure numerical computations, it is non-thread
Property Dynamic time history analysis calculate that the time is long, slow-footed problem.
Background technology
In recent years, China has built large quantities of world-class high concrete dams in west area, its height of dam it is more 200 meters with
On, the west area in China is the more hair bands of earthquake, and in the event of earthquake, the possibility of dam body damage will greatly increase, therefore,
It is very necessary, the health monitoring of high concrete dam and peace to analyze degree of impairment of the concrete dam under different earthquake fatigue resistance
Full evaluation is also widely paid close attention to.
However, in traditional non-linear dynamic time-histories, analyzing the response under different earthquake fatigue resistance needs substantial amounts of adjust
Width calculates, so generation increases over time, the ever-increasing shatter-proof time-histories acceleration function of Earthquake Intensity is one and relatively attaches most importance to
The work wanted, gradually increases it is crucial that how to generate one with time increase Earthquake Intensity, and the reaction of different time course
The spectrum function good with target spectrum fitting degree.On the basis of conventional artificial's earthquake motion, there is provided one kind optimization algorithm and plan
Conjunction works well.
The present invention has both sides purpose：One there is provided a kind of earthquake motion efficiently produce algorithm and improve initially shake
The fitting precision of response spectrum；Second, in nonlinear dynamical damage, the sound under different earthquake fatigue resistance can be once calculated
Situation is answered, compared with traditional Incremental Dynamic Analysis, reduces the time calculated after amplitude modulation, while the post processing of response is also carried
Facility is supplied.
The content of the invention
The present invention provides a kind of shatter-proof time-histories acceleration based on artificial ground shaking generating process to optimize algorithm, in tradition
On the basis of synthesizing artificial ground shaking, the precision initially shaken is improved, its response spectrum is closed with the fitting of standard design response spectrum
System is good, recycles MATLAB unconstrained optimizations to obtain target earthquake motion time history to its further fitting.This algorithm can synthesize
Meet the shatter-proof time-histories acceleration function of acceleration response spectrum fitting precision requirement under different time course, can ensure in hydro-structure
It is used for input earthquake in engineering, so as to calculate the response condition under different earthquake fatigue resistance, assessment dam body is in geological process
Under damaged degree and failure probability, shorten the Nonlinear time-history analysis time, traditional Incremental Dynamic Analysis can be replaced, it is right
Hydro-structure numerical simulation has far-reaching influence.
Technical scheme：
Shatter-proof time-histories acceleration optimization algorithm based on artificial ground shaking generating process, step are as follows：
This algorithm is with NB35047-2015《Hydroelectric project hydraulic structure earthquake resistant design code》Standard design response spectrum is
Target is composed, and using the shatter-proof time-histories acceleration function of MATLAB Software Creates, flow chart is as shown in Figure 1, be further illustrated below resistance to
The detailed process of time-histories acceleration function generation is shaken, step is as follows：
(1) generation initially shaken
1) steady earthquake motion time history
By response spectrum and the approximation relation of power spectrum, according to standard design response spectrum, it is calculated in power spectrum and Fu
Leaf amplitude spectrum, formula such as (1), (2), (3), standard design response spectrum are as shown in Figure 2；
In formula：S (ω) is power spectrum；
Sa(ω) is the standard design response spectrum on frequency domain；
ξ is damping ratio；
ω is circular frequency；
P is probability coefficent, generally takes p >=0.85；
T is Strong Ground Motion Duration length；
A (i ω) is Fourier's amplitude spectrum；
Δ ω is frequency interval；
fsFor sample frequency；
Nfft counts for Fourier transformation；
Generate phase spectrum at random in [0,2 π], Fourier's amplitude spectrum is multiplied with phase spectrum, positive and negative circular frequency is combined into
One vector, after inverse Fourier transform, it is the steady earthquake ground motion acceleration time-histories x in time domain to take real part, specific formula
It is as follows：
In formula：X is the steady earthquake ground motion acceleration time-histories in time domain；
G (ω) is phase spectrum；
2) earthquake motion time history x is generated after filtering0
Using filter function, the high-frequency content of the steady earthquake motion time history x (i ω) on frequency domain is filtered out, filter function is such as
Under：
In formula, ω1、ξ1For the first filtering parameter；
ω2、ξ2For the second filtering parameter；
H1(i ω) is the first filter function；
H2(i ω) is the second filter function；
Steady earthquake ground motion acceleration time-histories x in time domain is changed to obtain Acceleration time course x on frequency domain by Fourier
(i ω), is multiplied to obtain filtered amplitude spectrum A with filter function0(i ω), then obtain by inverse Fourier transform filtered
Earthquake ground motion acceleration time-histories x0, specific formula is as follows：
X (i ω)=fft (x) (7)
A0(i ω)=x (i ω) × H1(iω)×H2(iω) (8)
x0=f-1[A0(iω)eig(ω)] (9)
In formula, x (i ω) is the Acceleration time course on frequency domain；
A0(i ω) is filtered amplitude spectrum；
x0For filtered earthquake ground motion acceleration time-histories；
3) iterative process is corrected
Filtered earthquake ground motion acceleration time-histories x0Generation calculates spectrum, and width is corrected with calculating the ratio of spectrum using response spectrum
Value spectrum, formula are as follows：
In formula, A ' (i ω) is revised amplitude spectrum；
Sa1(ω) composes to calculate；
Using revised amplitude spectrum A ' (i ω) as the initial value of next iteration, by formula (9) and (10) constantly into
Row iteration, until to calculate spectrum and Response Spectrum fitting relation good for earthquake motion, otherwise iteration always, it is good to have finally obtained fit correlation
Good initially vibrations xg′.Fig. 3 is earthquake motion xg' response spectrum and standard design response spectrum fit solution.
4) linear function
Since shatter-proof time-histories acceleration function has under different time course, target spectrum is with calculating spectrum Sac(T,tdiff) have well
The property of fitting precision, therefore for different time course tdiff, target spectrum has into the relation of multiple with standard design response spectrum, specifically
Relational expression is as follows：
In formula, Sa(T) it is the standard design response spectrum in time domain；
ttargetFor the object time；
SaT(T,tdiff) composed for target；
tdiffTo be fitted the time of response spectrum；
The target that can be calculated by formula (11) under different time course is composed.Due to the calculating spectrum and mesh under different time course
Mark spectrum needs to meet fitting precision, therefore initially shakes xg' need to multiply linear strain-hardening function f (t), during the purpose is to make different
Response spectrum under journey, into multiple proportion, has good fit correlation even if calculating and composing with standard design response spectrum with target spectrum, public
Formula such as (12), (13)：
xnew'=f (t) × xg' (13)
In formula, ttFor the total time-histories elapsed time of earthquake motion；
F (t) is linear function；
xg' it is initially to shake；
xnew' it is the earthquake motion increased with time Earthquake Intensity；
Calculate fitting degree such as Fig. 4 of spectrum and target spectrum, the earthquake motion x increased with time Earthquake Intensitynew' such as Fig. 5 institutes
Show.
(2) unconstrained optimization
Above procedure, which has calculated, initially shakes xnew', spectrum is calculated as seen from Figure 4 composes the plan under long period with target
It is general to close effect, it is therefore desirable to which further optimization calculates.Algorithm proposes Unconstrained Optimization Algorithms, further makes calculating spectrum and mesh
Mark spectrum meets required precision, and unconstrained optimization includes following three parts：
1) standard design response spectrum algorithm
Algorithm with MATLAB softwares and《Hydroelectric project hydraulic structure earthquake resistant design code》In standard design response spectrum
Show that target composes algorithm under different cycles, i.e., according to (11) formula, obtain the target spectrum S under different cyclesaT(T,tdiff)。
2) earthquake motion reaction of formation spectrum algorithm
Step (1) generation earthquake motion xnew' after, linear acceleration method step_by_step integration is carried out to it, obtains the meter under different time course
Calculate spectrum Sac(T,tdiff)。
3) algorithm is optimized
It is iterated optimization to calculating spectrum and target spectrum using least square method and calculates, even if calculates the difference composed with response spectrum
Value reaches minimum.In the calculation, it is necessary to which Reusability standard design response spectrum algorithm, earthquake motion reaction of formation compose algorithm, therefore
Needing largely to calculate the time, initial acceleration Function Fitting precision will produce Optimized Iterative below certain influence,
So x of generationnew' earthquake motion is very crucial.
Optimization is needed differently to shake the acceleration function under elapsed time in the process, therefore computationally intensive, optimization
Formula is as follows：
In formula, Tmax is the cycle maximum of standard design response spectrum；
tmaxEarthquake motion always lasts；
Sac(T,tdiff) composed for the calculating under different cycles.
According to formula (14) optimisation criteria design response spectrum algorithm and earthquake motion reaction of formation spectrum algorithm, make two kinds of differences composed
Value reaches minimum value, and then adjusts earthquake motion time history, draws shatter-proof time-histories acceleration function.Reaction after unconstrained optimization
Spectrum fitting degree is shown in Fig. 7.As seen in Figure 7, fitting precision is good, calculate spectrum target compose around fluctuation less, have compared with
Good fitting character.Fig. 8 is the shatter-proof time-histories acceleration function of generation.
Beneficial effects of the present invention：
1. introducing earthquake motion efficiently produces algorithm
Traditional earthquake motion has ascent stage, steady section and descending branch three parts, and shatter-proof time-histories acceleration function introduces filter
Wave function and earthquake motion efficiently produce algorithm, meet the requirements the response spectrum under any time-histories, shatter-proof time-histories acceleration function
Generation equivalent to the peak accelerator of many earthquake motions, different Earthquake Intensities can be represented, there is deep physical significance.
2. initially vibrations have preferable fitting precision
Algorithm synthesizes 4 5s earthquake ground motion acceleration time-histories, is composed 20s earthquake motions, under identical iterations, calculates
Method compares two methods of 4 5s earthquake motion time histories, the earthquake motion of 20s earthquake motion time histories synthesis, by two kinds of response spectrums not
With the comparison under time-histories, such as Fig. 4, Fig. 6, it can be seen that 4 5s earthquake motion time histories fit within the initial journey being fitted under different time course
Spend, therefore, algorithm is used as using the 20s earthquake motions of 4 5s synthesis initially shakes xnew', improve the essence initially shaken
Degree, has preferable effect.
3. reduce the time of nonlinear dynamical damage, easy to analyze
For arch dam, the free degree is more, and loading characteristic is complicated, and site topography, complex geologic conditions, utilize software numerical value
Simulation, when carrying out Nonlinear time-history analysis, it is possible to reduce a large amount of calculating times under different amplitude modulation, and can be very good to find out
The degree of impairment of dam body under different earthquake fatigue resistance, describes the pass between different earthquake fatigue resistance and degree of injury on a macro scale
System, easily sets up the relation between each response, easy to reprocessing analysis.
Brief description of the drawings
Fig. 1 is shatter-proof time-histories acceleration function generating process flow chart.
Fig. 2 is standard design response spectrum schematic diagram.
Fig. 3 is earthquake motion xg' calculate spectrum and standard design response spectrum fitting schematic diagram.
Fig. 4 is x under different time coursenew' calculate spectrum and target spectrum fitting schematic diagram.
Fig. 5 is the earthquake motion x with time increase Earthquake Intensity increasenew' schematic diagram.
Fig. 6 is 20s earthquake motions xgCalculate spectrum and target spectrum fitting schematic diagram.
Fig. 7 is shatter-proof time-histories acceleration function xETACalculate spectrum and target spectrum fitting schematic diagram.
Fig. 8 is shatter-proof time-histories acceleration function xETASchematic diagram.
In figure：A is the cycle (s)；B is acceleration response spectrum (g)；C is Strong Ground Motion Duration (s)；D is acceleration magnitude
(g)；A is water conservancy project specification Plays design response spectrum curve；B is the response spectrum curve of 20s earthquake motions generation；C is 0-5s targets
Response spectrum curve；D is 0-10s goal response spectral curves；E is 0-15s goal response spectral curves；F sets a song to music for 0-20s goal responses
Line；G calculates spectral curve for 0-5s；H calculates spectral curve for 0-10s；I calculates spectral curve for 0-15s；J is calculated for 0-20s and set a song to music
Line；K is earthquake ground motion acceleration time-histories.
Embodiment
Below in conjunction with attached drawing and technical solution, the embodiment of this further explanation.
A kind of earthquake motion based on MATLAB softwares efficiently produces algorithm, including MATLAB software process qualities initially shake and
Unconstrained optimization problem two parts：
1. the generation initially shaken
Composed using standard design response spectrum as target, set parameter value according to specification, obtain the response spectrum such as Fig. 2
Figure.
Set the design parameter that generation initially shakes：Sample frequency fs, Strong Ground Motion Duration length t, earthquake motion
Total time-histories elapsed time tt, it is fitted the time t of response spectrumdiff.Algorithm takes 4 5s earthquake motions synthesis 20s earthquake motions xg', in life
Into earthquake motion xg' when, it is necessary to iterate, after reaching certain iterations, can generate preferably bent with Response Spectrum fitting relation
Line.According to explanation and the specific formula of (1) step is combined, has been synthesized using 0.01s as time interval, the initially vibrations of 20s
xnew', this part simply generates the acceleration function good substantially with target spectrum fitting degree, and Fig. 4 is 20s earthquake motions xnew’
Calculate spectrum and the fit correlation of standard design response spectrum.As seen from Figure 4, for long period part, vibration is more obvious, therefore
Also need to further iteration optimization.
2. unconstrained optimization iterative algorithm
Obtain based on the initially vibrations x initially shaken under generating algorithmnew' afterwards, it is necessary to its further analysis, adopt
The iteration of earthquake motion is carried out with MATLAB unconstrained optimizations, further adjusts shatter-proof time-histories acceleration function.Algorithm has been fitted 4
Response spectrum curve under time-histories, i.e. tdiffTake 5s, 10s, 15s, 20s；ttargetValue is 10s, therefore, according to formula (11), 5s
Target spectrum be 0.5 times of standard design response spectrum, 10s response spectrums are standard design response spectrum, and so on.
The design parameter of unconstrained optimization is set：The cycle maximum of T max of standard design response spectrum, earthquake motion always last
tmax, response spectrum elapsed time T；With xnew' as initially shock value, the calculating spectrum under different time course is calculated, utilizes
Formula (14) makes it minimum with goal response spectral difference value, and MATLAB unconstrained optimizations are iterated it optimization.According to formula
(14), it is necessary to x when can be seen that each suboptimizationnew' each point of earthquake motion optimizes calculating, i.e., need herein
2000 points are fitted, it is met the required precision of 4 targets spectrum, calculate it is very big, it is necessary to the plenty of time, therefore just
Beginning earthquake motion fitting degree is better, more favourable to unconstrained optimization.Shatter-proof time-histories acceleration function after fitting as shown in figure 8,
Calculate spectrum and target spectrum fit solution is as shown in Figure 7.
Claims (1)
1. it is a kind of based on artificial ground shaking generating process shatter-proof time-histories acceleration optimization algorithm, it is characterised in that this algorithm with
NB35047-2015《Hydroelectric project hydraulic structure earthquake resistant design code》Standard design response spectrum is composed for target, using MATLAB
Software Create is shatter-proof time-histories acceleration function, step are as follows：
(1) generation initially shaken
1) steady earthquake motion time history
By response spectrum and the approximation relation of power spectrum, according to standard design response spectrum, power spectrum and Fourier's width is calculated
Value spectrum, formula such as (1), (2), (3)：
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In formula：S (ω) is power spectrum；
Sa(ω) is the standard design response spectrum on frequency domain；
ξ is damping ratio；
ω is circular frequency；
P is probability coefficent, takes p >=0.85；
T is Strong Ground Motion Duration length；
A (i ω) is Fourier's amplitude spectrum；
Δ ω is frequency interval；
fsFor sample frequency；
Nfft counts for Fourier transformation；
Generate phase spectrum at random in [0,2 π], Fourier's amplitude spectrum is multiplied with phase spectrum, positive and negative circular frequency is combined into one
Vector, after inverse Fourier transform, it is the steady earthquake ground motion acceleration time-histories x in time domain to take real part, and specific formula is as follows：
X=f-1[A(iω)eig(ω)] (4)
In formula：X is the steady earthquake ground motion acceleration time-histories in time domain；
G (ω) is phase spectrum；
2) earthquake motion time history x is generated after filtering0
Using filter function, the high-frequency content of the steady earthquake motion time history x (i ω) on frequency domain is filtered out, filter function is as follows：
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H2(i ω) is the second filter function；
Steady earthquake ground motion acceleration time-histories x in time domain is changed to obtain Acceleration time course x (i on frequency domain by Fourier
ω), it is multiplied to obtain filtered amplitude spectrum A with filter function0(i ω), then obtain by inverse Fourier transform filtered
Oscillatory acceleration time-histories x0, specific formula is as follows：
X (i ω)=fft (x) (7)
A0(i ω)=x (i ω) × H1(iω)×H2(iω) (8)
x0=f-1[A0(iω)eig(ω)] (9)
In formula, x (i ω) is the Acceleration time course on frequency domain；
A0(i ω) is filtered amplitude spectrum；
x0For filtered earthquake ground motion acceleration time-histories；
3) iterative process is corrected
Filtered earthquake ground motion acceleration time-histories x0Generation calculates spectrum, and amplitude spectrum is corrected with calculating the ratio of spectrum using response spectrum,
Formula is as follows：
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Generation, until to calculate spectrum and Response Spectrum fitting relation good for earthquake motion, otherwise iteration always, finally obtain fit correlation well at the beginning of
Beginning earthquake motion xg′；
4) linear function
Since shatter-proof time-histories acceleration function has under different time course, target spectrum is with calculating spectrum Sac(T,tdiff) have it is good fit
The property of precision, therefore for different time course tdiff, target spectrum has into the relation of multiple, physical relationship with standard design response spectrum
Formula is as follows：
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<mi>arg</mi>
<mi>e</mi>
<mi>t</mi>
</mrow>
</msub>
</mfrac>
<mo>&times;</mo>
<msub>
<mi>S</mi>
<mi>a</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>T</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, Sa(T) it is the standard design response spectrum in time domain；
ttargetFor the object time；
SaT(T,tdiff) composed for target；
tdiffTo be fitted the time of response spectrum；
The target being calculated by formula (11) under different time course is composed；Since the calculating spectrum under different time course and target spectrum need
Meet fitting precision, therefore initially shake xg' need to multiply linear strain-hardening function f (t), it is anti-under different time course the purpose is to make
It should compose with standard design response spectrum into multiple proportion, even if calculating spectrum and target spectrum has good fit correlation, formula such as (12)
(13)：
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>t</mi>
<mi>t</mi>
</msub>
<msub>
<mi>t</mi>
<mrow>
<mi>t</mi>
<mi>arg</mi>
<mi>e</mi>
<mi>t</mi>
</mrow>
</msub>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
xnew'=f (t) × xg' (13)
In formula, ttFor the total time-histories elapsed time of earthquake motion；
F (t) is linear function；
xg' it is initially to shake；
xnew' it is the earthquake motion increased with time Earthquake Intensity；
(2) unconstrained optimization
This algorithm proposes Unconstrained Optimization Algorithms, calculating spectrum is composed with target and meets required precision, unconstrained optimization bag
Containing following three parts：
1) standard design response spectrum algorithm
This algorithm with MATLAB softwares and《Hydroelectric project hydraulic structure earthquake resistant design code》In standard design response spectrum obtain
Go out target under different cycles and compose algorithm, i.e., according to (11) formula, obtain the target spectrum S under different cyclesaT(T,tdiff), generation
Target is composed；
2) earthquake motion reaction of formation spectrum algorithm
Step (1) generation earthquake motion xnew' after, linear acceleration method step_by_step integration is carried out to it, obtains the calculating spectrum under different time course
Value Sac(T,tdiff), the calculating spectrum of generation；
3) algorithm is optimized
Calculated using least square method calculating to compose to be iterated to optimize with target spectrum, even if calculating spectrum and the difference of response spectrum reach
To minimum；In the calculation, Reusability standard design response spectrum algorithm, earthquake motion reaction of formation spectrum algorithm, it is therefore desirable to a large amount of
The calculating time, initial acceleration Function Fitting precision produces certain influence to Optimized Iterative below, so generation
xnew' earthquake motion is very crucial；
Optimization is needed differently to shake the acceleration function under elapsed time in the process, thus it is computationally intensive, optimize formula
It is as follows：
<mrow>
<mi>min</mi>
<mi>F</mi>
<mrow>
<mo>(</mo>
<msup>
<msub>
<mi>x</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>w</mi>
</mrow>
</msub>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Integral;</mo>
<mn>0</mn>
<msub>
<mi>T</mi>
<mi>max</mi>
</msub>
</munderover>
<munderover>
<mo>&Integral;</mo>
<mn>0</mn>
<msub>
<mi>t</mi>
<mi>max</mi>
</msub>
</munderover>
<mo>&lsqb;</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>a</mi>
<mi>T</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>,</mo>
<msub>
<mi>t</mi>
<mrow>
<mi>d</mi>
<mi>i</mi>
<mi>f</mi>
<mi>f</mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
<mo>-</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>,</mo>
<msub>
<mi>t</mi>
<mrow>
<mi>d</mi>
<mi>i</mi>
<mi>f</mi>
<mi>f</mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mi>d</mi>
<mi>t</mi>
<mi>d</mi>
<mi>T</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, Tmax is the cycle maximum of standard design response spectrum；
tmaxEarthquake motion always lasts；
Sac(T,tdiff) composed for the calculating under different cycles；
According to formula (14) optimisation criteria design response spectrum algorithm and earthquake motion reaction of formation spectrum algorithm, reach the difference of two kinds of spectrums
To minimum value, and then earthquake motion time history is adjusted, draw shatter-proof time-histories acceleration function.
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