CN114199489B - Method and device for adjusting natural seismic wave fitting response spectrum based on digital filtering - Google Patents

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

Method and device for adjusting natural seismic wave fitting response spectrum based on digital filtering

technical field

The invention relates to a structure anti-seismic design and analysis method, in particular to a method for adjusting natural seismic wave fitting response spectrum.

Background technique

In seismic codes and standards, it is often required to carry out dynamic time-history response analysis for important engineering structures, and dynamic time-history response analysis requires appropriate design ground motion input. There are three commonly used methods to adjust and generate design ground motions: the first is to perform amplitude modulation on historically recorded ground motions as input ground motions, the second is to use purely artificially synthesized ground motions as ground motion input, and the third is to It uses the numerical method to adjust the natural ground motion to match the design response spectrum as the ground motion input. Due to the limited number and geographical distribution of strong earthquakes recorded in history, there are few original seismic records that can be used for construction sites in actual engineering; purely artificially synthesized ground motions are difficult to truly simulate the effect of ground motions because they fully use artificial spectrum to represent seismic waves; therefore, using It is a more reasonable method to adjust the natural ground motion to make it fully match or envelop the design response spectrum and meet the engineering characteristics of the code, and this method is also the focus of theoretical research in the field of earthquake engineering and an urgent problem to be solved. However, the existing technology often has problems such as long calculation time and low fitting accuracy, which cannot meet the requirements of seismic design and analysis of engineering structures.

Contents of the invention

Purpose of the invention: Aiming at the defects of the prior art, the purpose of the present invention is to provide a method for adjusting the response spectrum of natural seismic waves based on digital filtering, which can fully retain the characteristics of natural ground motion records and have higher calculation efficiency and precision.

Another object of the present invention is to provide a corresponding device for adjusting the fitting response spectrum of natural seismic waves based on digital filtering.

Technical solution: In the first aspect, a method for adjusting natural seismic wave fitting response spectrum based on digital filtering, comprising the following steps:

(1) Based on the attributes of the target response spectrum, select the natural earthquake time history A(t), the duration of which is T, that is, t∈[0,T], and the time interval is dt;

确定其M个频率计算点分别为{f₁；f₂；...；f_M}，确定频带数目为M-1，频率区间分别为(-∞，f₂],[f₂,f₃]...,[f_M-2,f_M-1],[f_M-1,+∞)；(2) Based on target response spectrum

Determine its M frequency calculation points as {f ₁ ; f ₂ ;...; f _M }, determine the number of frequency bands as M-1, and the frequency intervals are (-∞, f ₂ ], [f ₂ , f ₃ ]...,[f _M-2 ,f _M-1 ],[f _M-1 ,+∞);

(3) Utilize digital filter technology to take the upper and lower limits of the 2nd to M-2 frequency intervals as the cut-off frequency, and perform band-pass filtering on the time history of natural ground motions, and perform low-pass filtering on the first frequency band with f ₂ as the cut-off frequency, and the M-th The -1 frequency band is high-pass filtered with f _M-1 as the cut-off frequency, and the natural earthquake time history is decomposed to obtain M-1 basis functions g _n (t), n=1,2,...,M-1, where The frequency range contained in the basis function covers the frequency range of the original natural earthquake;

重构得到初始时程

且初始时程A⁽⁰⁾(t)的反应谱为S⁽⁰⁾；(4) Determine the amplitude coefficients that make up the time-history basis function of natural ground motions

Refactoring to get the initial schedule

And the response spectrum of the initial time course A ⁽⁰⁾ (t) is S ⁽⁰⁾ ;

(5) The initial time history is iteratively calculated using the influence matrix method until the fitting accuracy of the time history response spectrum and the target response spectrum meets the requirements, so as to obtain the ground motion time history fitted with the target response spectrum.

Further, in the step (1), the natural ground motion time history corresponding to the target response spectrum is selected according to the site type, source characteristics and response spectrum shape.

Further, a Kaiser window-based FIR digital filter is used for digital filtering in the step (3).

为第m频率点处时程反应谱的极性，通过迭代逐步调整各基函数的幅值系数，直至时程反应谱S⁽⁰⁾与目标反应谱S^T的匹配精度满足要求为止。Further, in the step (4), the iterative operation of the initial time course using the influence matrix method includes: based on the initial time course A ⁽⁰⁾ (t), calculating the nth basis function g _n (t) for the mth The contribution of the response spectrum value at the frequency point f _m is recorded as the impact factor I _mn , and the influence matrix is constructed according to I _mn

is the polarity of the time-history response spectrum at the mth frequency point, and the amplitude coefficients of each basis function are adjusted step by step through iteration until the matching accuracy of the time-history response spectrum S ⁽⁰⁾ and the target response spectrum S ^T meets the requirements.

Further, the impact factor _Imn is calculated as follows:

Among them, ω _m is the circular frequency ω _m =2πf _m corresponding to the mth frequency point; h _m (t) is the unit pulse function; τ _m is the occurrence time of the mth frequency single-degree-of-freedom acceleration peak response.

In the second aspect, a device for adjusting the fitting response spectrum of natural seismic waves based on digital filtering is provided, including:

The natural earthquake time history selection module is used to select the natural earthquake time history A(t) based on the attributes of the target response spectrum. The duration of the time history is T, that is, t∈[0,T], and the time interval is dt ;

确定其M个频率计算点分别为{f₁；f₂；...；f_M}，确定频带数目为M-1，频率区间分别为(-∞，f₂],[f₂,f₃]...,[f_M-2,f_M-1],[f_M-1,+∞)；The target response spectrum frequency band determination module is used for based on the target response spectrum

Determine its M frequency calculation points as {f ₁ ; f ₂ ;...; f _M }, determine the number of frequency bands as M-1, and the frequency intervals are (-∞, f ₂ ], [f ₂ , f ₃ ]...,[f _M-2 ,f _M-1 ],[f _M-1 ,+∞);

The digital filter decomposition module is used to use the digital filter technology to perform band-pass filtering on the natural earthquake time history with the upper and lower limits of the second to M-2 frequency intervals as the cut-off frequency, and to perform low-pass filtering on the first frequency band with _f2 as the cut-off frequency Filtering, the M-1th frequency band is high-pass filtered with f _M-1 as the cut-off frequency, and the natural earthquake time history is decomposed to obtain M-1 basis functions g _n (t), n=1,2,...,M -1, where the frequency range contained in the basis function covers the frequency range possessed by the original natural earthquake;

重构得到初始时程

且初始时程A⁽⁰⁾(t)的反应谱为S⁽⁰⁾；The initial time history reconstruction module is used to determine the amplitude coefficients that make up the time history basis functions of natural ground motions

Refactoring to get the initial schedule

And the response spectrum of the initial time course A ⁽⁰⁾ (t) is S ⁽⁰⁾ ;

The iterative fitting module is used to perform iterative calculations using the influence matrix method according to the initial time history until the fitting accuracy of the time history response spectrum and the target response spectrum meets the requirements, so as to obtain the ground motion time history fitted with the target response spectrum.

In a third aspect, a computer device is provided, including:

one or more processors;

storage; and

One or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the In one aspect, the steps of the method for adjusting natural seismic wave fitting response spectrum based on digital filtering.

Beneficial effects: compared with the prior art, the present invention has technical changes. The present invention introduces digital filtering technology to filter and decompose the basis functions obtained by filtering and decomposing the natural recorded earthquake time history, and reconstructs to obtain the initial earthquake time history; then iteratively calculates the earthquake time history response spectrum and the target response spectrum according to the influence matrix method to meet the accuracy requirements required by specifications or specific projects. The invention has high calculation efficiency, and compared with the prior art, while the matching accuracy is higher, the natural ground motion characteristics of the earthquake time history are preserved as much as possible.

Description of drawings

Fig. 1 is the general flowchart of the method for adjusting natural seismic wave fitting response spectrum based on digital filtering according to an embodiment of the present invention;

Fig. 2 is an example of initial iterative time course response spectrum and target response spectrum of the embodiment of the present invention;

Fig. 3 is an example of an intermediate result and a final result obtained by iteration in an embodiment of the present invention.

Detailed ways

The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.

In one embodiment, the R.G.1.60 design spectrum is selected as the target response spectrum, and the method of the present invention is used to generate an input time history of ground motion matching the target response spectrum. As shown in Figure 1, a filter-based design ground motion generation method includes the following steps:

(1) Select the natural ground motion time history whose site type and source characteristics are the same as the target site, and whose response spectrum frequency component distribution is similar to the target response spectrum.

Response spectra have similar shapes. For example, if the target spectrum is higher in the middle and lower at both ends, then the ground motion time-history response spectrum should also be selected with a higher middle and lower ends. In this embodiment, the acceleration time history of the Mammoth Lake earthquake recorded by the Long Valley station is selected as the original natural ground motion time history, and the comparison between the initial time history and the target response spectrum is shown in Fig. 2 . The duration of the time course is T=30s, and the time interval is dt=0.005s. The maximum frequency and the minimum frequency involved in the RG1.60 design spectrum are f _min =0.1 Hz and f _max =100 Hz respectively, that is, the target response spectrum calculation frequency range is [0.1, 100] Hz.

(2) Determine the number of frequency bands and the frequency range contained in each frequency band according to the frequency points of the target response spectrum.

The number of frequency points in the target response spectrum RG1.60 design spectrum is M=301, and each frequency point in the frequency range [0.1,100]Hz is evenly distributed in logarithmic coordinates, that is, f ₁ =0.1000, f ₂ =0.1023,.. ., f ₃₀₀ =97.7237, f ₃₀₁ =100.0000. Therefore, 300 frequency band intervals can be determined as (-∞,f ₂ ],...,[f ₂₉₉ ,f ₃₀₀ ],[f ₃₀₀ ,+∞).

(3) Using digital filtering technology to decompose the natural ground motion into wavelets containing each frequency band, and reconstruct the initial time history required for iteration.

In this embodiment, the finite impulse response filter of the 900-order Kaiser window function is used to filter and decompose the historical seismic acceleration in the divided 300 frequency bands, wherein the 2nd to 299th frequency bands are respectively made with the upper and lower limits of the interval as the cut-off frequency. band-pass filtering to obtain the basis functions g ₂ (t), g ₂ (t),...,g ₂₉₉ (t) respectively, and perform low-pass filtering on the first frequency band with f ₂ as the cut-off frequency to obtain the basis functions g ₁ ( t), the 300th frequency band is high-pass filtered with f ₃₀₀ as the cut-off frequency to obtain the basis function g ₃₀₀ (t), and finally obtain the filtering time history g _n (t) covering 300 frequency band intervals, n=1,2,. ...,300.

重构时程记为

重构时程的反应谱为S⁽⁰⁾。Using the generalized minimum residual method to solve the problem, the amplitude coefficients of the original natural ground motions reconstructed using 300 basis functions obtained by filtering

The refactoring schedule is recorded as

The response spectrum of the reconstructed time course is S ⁽⁰⁾ .

(5) The influence matrix method is used to iteratively fit the target response spectrum.

Assuming that the relative error between the required time history response spectrum and the target spectrum at each frequency point is not greater than η = 15%, use the influence matrix method to adjust the amplitudes of all basis functions in the [0.1, 100] Hz frequency range in each iteration coefficient, so that the time-course response spectrum obtained by each iteration gradually fits to the target response spectrum, and the iteration stops when the maximum relative error between the time-course response spectrum and the target spectrum is not greater than the threshold η.

(6) Output the time history when the relative error meets the threshold requirement.

The intermediate and final results of the iterative process are shown in Figure 3. The obtained time-history acceleration response spectrum and the target response spectrum meet the required matching accuracy, and it can be seen from the matching process that this method makes the time-history response spectrum evenly and consistently toward the target The response spectrum is close.

Based on the same technical idea of the above-mentioned method embodiments, in another embodiment, a device for adjusting natural seismic wave fitting response spectrum based on digital filtering is provided, including:

The natural earthquake time history selection module is used to select the natural earthquake time history A(t) based on the attributes of the target response spectrum. The duration of the time history is T, that is, t∈[0,T], and the time interval is dt ;

确定其M个频率计算点分别为{f₁；f₂；...；f_M}，确定频带数目为M-1，频率区间分别为(-∞,f₂],[f₂,f₃],...,[f_M-2,f_M-1],[f_M-1,+∞)；The target response spectrum frequency band determination module is used for based on the target response spectrum

Determine its M frequency calculation points as {f ₁ ; f ₂ ;...; f _M }, determine the number of frequency bands as M-1, and determine the frequency intervals as (-∞, f ₂ ], [f ₂ , f ₃ ],...,[f _M-2 ,f _M-1 ],[f _M-1 ,+∞);

The digital filter decomposition module is used to use the digital filter technology to perform band-pass filtering on the time history of natural earthquakes with the upper and lower limits of the 2nd to M-2 frequency intervals as the cut-off frequency, and to perform low-pass filtering on the first frequency band with _f2 as the cut-off frequency Filtering, the M-1th frequency band is high-pass filtered with f _M-1 as the cut-off frequency, and the natural earthquake time history is decomposed to obtain M-1 basis functions g _n (t), n=1,2,...,M -1, where the frequency range contained in the basis function covers the frequency range possessed by the original natural earthquake;

重构得到初始时程

且初始时程A⁽⁰⁾(t)的反应谱为S⁽⁰⁾；The initial time history reconstruction module is used to determine the amplitude coefficients that make up the time history basis functions of natural ground motions

Refactoring to get the initial schedule

And the response spectrum of the initial time course A ⁽⁰⁾ (t) is S ⁽⁰⁾ ;

The iterative fitting module is used to perform iterative calculations using the influence matrix method according to the initial time history until the fitting accuracy of the time history response spectrum and the target response spectrum meets the requirements, so as to obtain the ground motion time history fitted with the target response spectrum.

Among them, the natural ground motion time history selection module selects the natural ground motion time history corresponding to the target response spectrum according to the site type, source characteristics and response spectrum shape.

In this embodiment, the digital filter decomposition module uses a Kaiser window-based finite impulse response FIR digital filter.

As a preferred implementation, the iterative fitting module includes:

为第m频率点处时程反应谱的极性；The influence matrix construction unit is used to calculate the contribution of the n-th basis function g _n (t) to the response spectrum value at the m-th frequency point f _m based on the initial time history A ⁽⁰⁾ (t), which is recorded as the impact factor I _mn , construct the influence matrix according to I _mn

is the polarity of the time history response spectrum at the mth frequency point;

The iterative calculation unit is used to gradually adjust the amplitude coefficients of each basis function through iterations until the matching accuracy of the time-course response spectrum S ⁽⁰⁾ and the target response spectrum S ^T meets the requirements; and

The time history output unit is used to calculate the corresponding velocity time history and displacement time history through the amplitude coefficient of the acceleration time history that meets the matching accuracy, and output the acceleration, velocity and displacement time history data that meet the requirements.

The impact factor I _mn is calculated according to the following formula:

Among them, ω _m is the circular frequency ω _m =2πf _m corresponding to the mth frequency point; h _m (t) is the unit pulse function; τ _m is the occurrence time of the mth frequency single-degree-of-freedom acceleration peak response.

It should be understood that the device for adjusting natural seismic wave fitting response spectrum based on digital filtering provided in this embodiment can realize all the technical solutions in the above-mentioned method embodiments, and the functions of each functional module can be specifically realized according to the methods in the above-mentioned method embodiments For specific implementation processes that are not described in detail in this embodiment, reference may be made to relevant descriptions in the foregoing embodiments.

Those skilled in the art should understand that the embodiments of the present invention may be provided as methods, apparatuses, systems, or computer program products. Accordingly, the present invention can 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, etc.) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatuses, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the present invention can still be Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall fall within the protection scope of the claims of the present invention.

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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