CN114199489B - Method and device for adjusting natural seismic wave fitting reaction spectrum based on digital filtering - Google Patents
Method and device for adjusting natural seismic wave fitting reaction spectrum based on digital filtering Download PDFInfo
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Abstract
The invention discloses a method and a device for adjusting natural seismic wave fitting reaction spectrum based on digital filtering, wherein the method comprises the following steps: determining the frequency band number and the frequency range contained in each frequency band by taking the frequency point of the target reaction spectrum as a node, decomposing the natural earthquake motion record into wavelets with different frequency bands by utilizing a digital filtering technology, and reconstructing each wavelet to obtain an initial time interval required by iteration; and for the initial time course, iteratively and gradually adjusting the wavelet amplitude coefficients by utilizing an influence matrix method until the fitting precision of the corresponding time course response spectrum and the target response spectrum meets the requirement. The invention solves the problem of insufficient reservation of natural characteristics of earthquake motion in the current reaction spectrum fitting technology, has high iterative calculation efficiency and higher matching precision, and is beneficial to improving the dynamic time-course response analysis efficiency of engineering structures and obtaining higher-reliability analysis results.
Description
Technical Field
The invention relates to a structural earthquake-resistant design and analysis method, in particular to a method for adjusting natural earthquake wave fitting reaction spectrum.
Background
In seismic codes and standards, it is often required to develop dynamic time-course response analysis for important engineering structures, which requires proper design of seismic inputs. There are three methods of adjusting and generating the designed earthquake motion that are currently in common use: the first is to make amplitude modulation on the earthquake motion recorded in the history as the input earthquake motion, the second is to make purely artificial earthquake motion as the earthquake motion input, and the third is to make the natural earthquake motion match with the designed response spectrum by using a numerical method and then make the natural earthquake motion as the earthquake motion input. Because the number and the regional distribution of strong earthquakes of the history records are limited, the original earthquake records which can be used for constructing a site in actual engineering are fewer; purely artificial synthetic earthquake motion is difficult to truly simulate the action effect of the earthquake motion because the artificial spectrum is fully utilized to represent earthquake waves; therefore, the numerical method is more reasonable to adjust the natural earthquake motion so as to fully match or envelop the design response spectrum and meet the standard requirements on the earthquake motion engineering characteristics, and the method is also a key attention of theoretical research in the current earthquake engineering field and a problem to be solved urgently. However, the problems of long calculation time consumption, low fitting precision and the like often exist in the prior art, and the requirements of engineering structure anti-seismic design and analysis cannot be met.
Disclosure of Invention
The invention aims to: aiming at the defects of the prior art, the invention aims to provide a method for adjusting the natural seismic wave fitting reaction spectrum based on digital filtering, which not only can fully reserve the characteristic of natural seismic wave recording, but also has higher calculation efficiency and accuracy.
It is another object of the present invention to provide a corresponding device for adjusting the natural seismic wave fit response spectrum based on digital filtering.
The technical scheme is as follows: in a first aspect, a method for adjusting a natural seismic wave fit response spectrum based on digital filtering includes the steps of:
(1) Selecting a natural earthquake motion time course A (T) based on the attribute of the target reaction spectrum, wherein the duration time of the time course is T, namely T epsilon [0, T ], and the time interval is dt;
(2) Based on target reaction profile
Determining M frequency calculation points as { f }, respectively 1 ；f 2 ；...；f M Determines the number of frequency bands to be M-1, frequency intervals respectively is (- +++, f (f) 2 ],[f 2 ,f 3 ]...,[f M-2 ,f M-1 ],[f M-1 ,+∞)；
(3) Band-pass filtering the natural earthquake motion time by using the digital filtering technique and using the upper and lower limits of the frequency range from 2 nd to M-2 nd as cut-off frequencies, the 1 st frequency band is f 2 For low-pass filtering of cut-off frequency, the M-1 band is f M-1 The cut-off frequency is subjected to high-pass filtering, and the natural earthquake motion time course is decomposed to obtain M-1 basis functions g n (t), n=1, 2,..m-1, wherein the frequency range contained by the basis function covers the frequency range possessed by the original natural vibration;
(4) Determining the amplitude coefficient of a time-course basis function of natural earthquake motion
Reconstruction gives the initial time course->
And initial time course A (0) (t) the reaction spectrum is S (0) ；
(5) And (3) carrying out iterative operation on the initial time course by using an influence matrix method until the fitting precision of the time course reaction spectrum and the target reaction spectrum meets the requirement, thereby obtaining the earthquake motion time course fitted with the target reaction spectrum.
Further, in the step (1), a natural earthquake motion time course corresponding to the target reaction spectrum is selected according to the field type, the earthquake source characteristics and the reaction spectrum shape.
Further, the step (3) uses a finite impulse response FIR digital filter based on a Kaiser window when performing digital filtering.
Further, in the step (4), performing an iterative operation on the initial time course by using an influence matrix method includes: based on initial time course A (0) (t) calculating an nth basis function g n (t) for the mth frequency point f m The contribution of the reaction spectrum value is recorded as an influence factor I mn According to I mn Construction of an influence matrix
For the polarity of the time-course reaction spectrum at the mth frequency point, the amplitude coefficient of each basis function is adjusted step by iteration until the time-course reaction spectrum S (0) Reaction spectrum S with target T Until the matching accuracy of the (c) meets the requirement.
Further, the influence factor I mn Calculated as follows:
wherein omega m Circle frequency omega corresponding to mth frequency point m ＝2πf m ；h m (t) is a unit pulse function; τ m The m-th frequency single degree of freedom acceleration peak response occurs.
In a second aspect, there is provided an apparatus for adjusting a natural seismic wave fit reaction spectrum based on digital filtering, comprising:
the natural earthquake motion time course selection module is used for selecting a natural earthquake motion time course A (T) based on the attribute of the target reaction spectrum, wherein the duration time length of the time course is T, namely T is E [0, T ], and the time interval is dt;
a target reaction spectrum band determining module for determining a target reaction spectrum
Determining M frequency calculation points as { f }, respectively 1 ；f 2 ；...；f M Determines the number of frequency bands to be M-1, frequency intervals respectively is (- +++, f (f) 2 ],[f 2 ,f 3 ]...,[f M-2 ,f M-1 ],[f M-1 ,+∞)；
The digital filtering and decomposing module is used for carrying out band-pass filtering on the natural earthquake motion time course by using the digital filtering technology and taking the upper limit and the lower limit of the frequency interval from the 2 nd frequency to the M-2 nd frequency as the cut-off frequency, and the 1 st frequency band is f 2 For low-pass filtering of cut-off frequency, the M-1 band is f M-1 The cut-off frequency is subjected to high-pass filtering, and the natural earthquake motion time course is decomposed to obtain M-1 basis functions g n (t), n=1, 2,..m-1, wherein the frequency range contained by the basis function covers the frequency range possessed by the original natural vibration;
an initial time interval reconstruction module for determining amplitude coefficients constituting a natural earthquake motion time interval basis function
Reconstruction gives the initial time course->
And initial time course A (0) (t) the reaction spectrum is S (0) ；
And the iterative fitting module is used for carrying out iterative operation by utilizing an influence matrix method according to the initial time interval until the fitting precision of the time interval response spectrum and the target response spectrum meets the requirement, so as to obtain the earthquake motion time interval fitted with the target response spectrum.
In a third aspect, there is provided a computer device comprising:
one or more processors;
a memory; and
one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, which when executed by the processors implement the steps of the method of adapting a natural seismic wave fit reaction spectrum based on digital filtering according to the first aspect of the invention.
The beneficial effects are that: compared with the prior art, the invention has technical change. The invention introduces a digital filtering technology to filter and decompose the natural recorded earthquake motion time course to obtain a basis function, and the original earthquake motion time course is obtained by reconstruction; and then, carrying out iterative computation according to an influence matrix method to gradually fit the earthquake time course reaction spectrum with the target reaction spectrum so as to meet the accuracy requirements required by the standard or specific engineering. Compared with the prior art, the invention has high calculation efficiency, and the matching precision is higher, and meanwhile, the natural earthquake motion characteristic of the earthquake time course is reserved as much as possible.
Drawings
FIG. 1 is a general flow chart of a method for adjusting a natural seismic wave fit response spectrum based on digital filtering in accordance with an embodiment of the invention;
FIG. 2 is an example of an initial iterative time course reaction spectrum and a target reaction spectrum of an embodiment of the invention;
fig. 3 is an example of intermediate results and final results obtained by iteration in an embodiment of the invention.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
In one embodiment, the r.g.1.60 design spectrum is selected as the target reaction spectrum, and the method of the present invention is used to generate a seismic input time course that matches the target reaction spectrum. As shown in fig. 1, a method for generating a design earthquake motion based on a filtering technique includes the steps of:
(1) The field type and the source characteristics are selected to be the same as those of the target field, and the frequency component distribution of the reaction spectrum is similar to the natural earthquake motion time course of the target reaction spectrum.
The shape of the response spectrum is similar, for example, the middle of the target spectrum is higher, and the two ends of the target spectrum are lower, so that the earthquake motion time course response spectrum is also selected to be higher at the middle and lower at the two ends. In this embodiment, the acceleration time course of the Mammoth Lake earthquake recorded by the Long Valley station is selected as the original natural earthquake motion time course, and the initial time course and the target response spectrumAs shown in figure 2. The duration of the time interval is t=30s and the time interval is dt=0.005 s. The maximum frequency and the minimum frequency related to the R.G.1.60 design spectrum are f respectively min ＝0.1Hz，f max =100 Hz, i.e. the target reaction spectrum has a calculated frequency range of [0.1,100]]Hz。
(2) And determining the number of frequency bands and the frequency range contained in each frequency band according to the target reaction spectrum frequency points.
The frequency point number of the target reaction spectrum R.G.1.60 design spectrum is M=301, and the frequency range is [0.1,100]]Each frequency point in Hz is evenly distributed in logarithmic scale, i.e. f 1 ＝0.1000,f 2 ＝0.1023,...,f 300 ＝97.7237,f 301 = 100.0000. Thus, 300 band intervals can be determined to be (- ≡f 2 ],...,[f 299 ,f 300 ],[f 300 ,+∞)。
(3) The natural vibration is decomposed into wavelets containing each frequency band by using a digital filtering technology, and the initial time course required by iteration is obtained by reconstruction.
In this embodiment, a finite impulse response filter of a Kaiser window function of 900 th order is adopted to filter and decompose the historical record seismic acceleration in 300 frequency bands, wherein the 2 nd to 299 th frequency bands respectively use the upper and lower limits of the interval as cut-off frequencies to carry out band-pass filtering to respectively obtain a base function g 2 (t),g 2 (t),...,g 299 (t), 1 st frequency band f 2 Low-pass filtering the cut-off frequency to obtain a base function g 1 (t), 300 th band at f 300 The cut-off frequency is subjected to high-pass filtering to obtain a base function g 300 (t) finally obtaining the filtering time periods g respectively covering 300 frequency band intervals n (t),n＝1,2,...,300。
Solving by generalized minimum residual method to obtain 300 basis function reconstructed original natural earthquake motion amplitude coefficient
The reconstruction schedule is recorded as->
The reaction spectrum of the reconstruction time interval is S (0) 。
(5) And performing iterative fitting on the target reaction spectrum by using an influence matrix method.
Assuming that the relative error of the time-course reaction spectrum and the target spectrum at each frequency point is not more than eta=15%, and using an influence matrix method, adjusting the amplitude coefficients of all the basis functions in the frequency range of [0.1,100] Hz in each iteration, so that the time-course reaction spectrum obtained in each iteration is gradually fitted to the target reaction spectrum until the maximum relative error of the time-course reaction spectrum and the target spectrum is not more than a threshold eta.
(6) And outputting a time course that the relative error meets the threshold requirement.
The intermediate result and the final result of the iterative process are shown in fig. 3, the acceleration response spectrum and the target response spectrum of the obtained time course meet the required matching precision, and as can be seen from the matching process, the method enables the time course response spectrum to be uniformly and consistently close to the target response spectrum.
Based on the same technical concept as the above method embodiment, in another embodiment, an apparatus for adjusting a natural seismic wave fitting reaction spectrum based on digital filtering is provided, including:
the natural earthquake motion time course selection module is used for selecting a natural earthquake motion time course A (T) based on the attribute of the target reaction spectrum, wherein the duration time length of the time course is T, namely T is E [0, T ], and the time interval is dt;
a target reaction spectrum band determining module for determining a target reaction spectrum
Determining M frequency calculation points as { f }, respectively 1 ；f 2 ；...；f M Determines the number of frequency bands to be M-1, frequency intervals respectively is (- +++, f (f) 2 ],[f 2 ,f 3 ],...,[f M-2 ,f M-1 ],[f M-1 ,+∞)；
The digital filtering and decomposing module is used for carrying out band-pass filtering on the natural earthquake motion time course by using the digital filtering technology and taking the upper limit and the lower limit of the frequency interval from the 2 nd frequency to the M-2 nd frequency as the cut-off frequency, and the 1 st frequency band is f 2 For low-pass filtering of cut-off frequency, the M-1 band is f M-1 The cut-off frequency is subjected to high-pass filtering, and the natural earthquake motion time course is decomposed to obtain M-1 basis functions g n (t), n=1, 2,..m-1, wherein the frequency range contained by the basis function covers the frequency range possessed by the original natural vibration;
an initial time interval reconstruction module for determining amplitude coefficients constituting a natural earthquake motion time interval basis function
Reconstruction gives the initial time course->
And initial time course A (0) (t) the reaction spectrum is S (0) ；
And the iterative fitting module is used for carrying out iterative operation by utilizing an influence matrix method according to the initial time interval until the fitting precision of the time interval response spectrum and the target response spectrum meets the requirement, so as to obtain the earthquake motion time interval fitted with the target response spectrum.
The natural earthquake motion time course selection module selects a natural earthquake motion time course corresponding to the target reaction spectrum according to the field type, the earthquake source characteristics and the reaction spectrum shape.
In this embodiment, the digital filter decomposition module uses a finite impulse response FIR digital filter based on a Kaiser window.
As a preferred embodiment, the iterative fitting module comprises:
an influence matrix construction unit for constructing a matrix based on the initial time course A (0) (t) calculating an nth basis function g n (t) for the mth frequency point f m The contribution of the reaction spectrum value is recorded as an influence factor I mn According to I mn Construction of an influence matrix
The polarity of the time course reaction spectrum at the mth frequency point;
an iterative calculation unit for adjusting the amplitude coefficient of each basis function step by iteration until the time-course response spectrum S (0) Reaction spectrum S with target T Is to satisfy matching accuracyObtaining; and
and the time interval output unit is used for calculating corresponding speed time interval and displacement time interval through the amplitude coefficient of the acceleration time interval meeting the matching precision and outputting acceleration, speed and displacement time interval data meeting the requirements.
Wherein influencing factor I mn Calculated as follows:
wherein omega m Circle frequency omega corresponding to mth frequency point m ＝2πf m ；h m (t) is a unit pulse function; τ m The m-th frequency single degree of freedom acceleration peak response occurs.
It should be understood that the device for adjusting the natural seismic wave fitting reaction spectrum based on digital filtering provided in this embodiment may implement all the technical solutions in the above method embodiments, and the functions of each functional module may be specifically implemented according to the method in the above method embodiments, and the specific implementation process that is not described in detail in this embodiment may refer to the related description in the above embodiments.
It will be apparent to those skilled in the art that embodiments of the present invention may be provided as a method, apparatus, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus, devices (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.
Claims (6)
1. A method for adjusting natural seismic wave fitting reaction spectrum based on digital filtering is characterized by comprising the following steps:
(1) Selecting a natural earthquake motion time course A (T) based on the attribute of the target reaction spectrum, specifically selecting a natural earthquake motion time course corresponding to the target reaction spectrum according to the field type, the earthquake source characteristic and the reaction spectrum shape, wherein the duration time of the time course is T, namely T epsilon [0, T ], and the time interval is dt;
(2) Based on target reaction profile
Determining M frequency calculation points as { f }, respectively 1 ；f 2 ；...；f M Determines the number of frequency bands to be M-1, frequency intervals respectively is (- +++, f (f) 2 ],[f 2 ,f 3 ]...,[f M-2 ,f M-1 ],[f M-1 ,+∞)；
(3) The finite impulse response FIR digital filter based on Kaiser window is utilized, the upper and lower limits of the 2 nd to M-2 nd frequency intervals are used as cut-off frequencies, the band-pass filtering is carried out on the natural earthquake motion time course, and the 1 st frequency band is f 2 For low-pass filtering of cut-off frequency, the M-1 band is f M-1 The cut-off frequency is subjected to high-pass filtering, and the natural earthquake motion time course is decomposed to obtain M-1 basis functions g n (t), n=1, 2,..m-1, wherein the frequency range contained by the basis function covers the frequency range possessed by the original natural vibration;
(4) Determining the amplitude coefficient of a time-course basis function of natural earthquake motion
Reconstruction gives the initial time course->
And initial time course A (0) (t) the reaction spectrum is S (0) ；
(5) And (3) carrying out iterative operation on the initial time course by using an influence matrix method until the fitting precision of the time course reaction spectrum and the target reaction spectrum meets the requirement, thereby obtaining the earthquake motion time course fitted with the target reaction spectrum.
2. The method for adjusting natural seismic wave fitting reaction spectrum based on digital filtering according to claim 1, wherein: the step (4) of performing iterative operation on the initial time course by using an influence matrix method comprises the following steps of: based on initial time course A (0) (t) calculating an nth basis function g n (t) for the mth frequency point f m The contribution of the reaction spectrum value is recorded as an influence factor I mn According to I mn Construction of an influence matrix
For the polarity of the time-course reaction spectrum at the mth frequency point, the amplitude coefficient of each basis function is adjusted step by iteration until the time-course reaction spectrum S (0) Reaction spectrum S with target T Until the matching accuracy of the (c) meets the requirement.
3. The method for adjusting natural seismic wave fitting reaction spectrum based on digital filtering according to claim 2, wherein: the influencing factor I mn Calculated as follows:
wherein omega m Circle frequency omega corresponding to mth frequency point m ＝2πf m ；h m (t) is a unit pulse function; τ m The m-th frequency single degree of freedom acceleration peak response occurs.
4. A device for adjusting a natural seismic wave fitting response spectrum based on digital filtering, comprising:
the natural earthquake motion time course selection module is used for selecting a natural earthquake motion time course A (T) based on the attribute of the target reaction spectrum, wherein the duration time length of the time course is T, namely T is E [0, T ], and the time interval is dt; the natural earthquake motion time course selection module selects a natural earthquake motion time course corresponding to the target reaction spectrum according to the field type, the earthquake source characteristics and the reaction spectrum shape;
a target reaction spectrum band determining module for determining a target reaction spectrum
Determining M frequency calculation points as { f }, respectively 1 ；f 2 ；...；f M Determines the number of frequency bands to be M-1, frequency intervals respectively is (- +++, f (f) 2 ],[f 2 ,f 3 ]...,[f M-2 ,f M-1 ],[f M-1 ,+∞)；
The digital filtering and decomposing module is used for carrying out band-pass filtering on the natural earthquake motion time course by using a Kaiser window-based finite impulse response FIR digital filter and taking the upper limit and the lower limit of the 2 nd to M-2 nd frequency intervals as cut-off frequencies, wherein the 1 st frequency band is f 2 For low-pass filtering of cut-off frequency, the M-1 band is f M-1 The cut-off frequency is subjected to high-pass filtering, and the natural earthquake motion time course is decomposed to obtain M-1 basis functions g n (t), n=1, 2,..m-1, wherein the frequency range of the basis function covers the frequency range of the original natural vibration;
an initial time interval reconstruction module for determining amplitude coefficients constituting a natural earthquake motion time interval basis function
Reconstruction gives the initial time course->
And initial time course A (0) (t) the reaction spectrum is S (0) ；
And the iterative fitting module is used for carrying out iterative operation by utilizing an influence matrix method according to the initial time interval until the fitting precision of the time interval response spectrum and the target response spectrum meets the requirement, so as to obtain the earthquake motion time interval fitted with the target response spectrum.
5. The device for adjusting natural seismic wave fit reaction spectrum based on digital filtering according to claim 4, wherein: the iterative fitting module comprises:
an influence matrix construction unit for constructing a matrix based on the initial time course A (0) (t) calculating an nth basis function g n (t) for the mth frequency point f m The contribution of the reaction spectrum value is recorded as an influence factor I mn According to I mn Construction shadowSound matrix
The polarity of the time course reaction spectrum at the mth frequency point;
an iterative calculation unit for adjusting the amplitude coefficient of each basis function step by iteration until the time-course response spectrum S (0) Reaction spectrum S with target T Until the matching precision of the number of the matching points meets the requirement;
and the time interval output unit is used for calculating corresponding speed time interval and displacement time interval through the amplitude coefficient of the acceleration time interval meeting the matching precision and outputting acceleration, speed and displacement time interval data meeting the requirements.
6. A computer device, comprising:
one or more processors;
a memory; and
one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, which when executed by the processors implement the steps of the method of adjusting a natural seismic wave fit reaction spectrum based on digital filtering as claimed in any one of claims 1 to 3.
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