CN113777651A - Artificial earthquake motion synthesis method and device, electronic equipment and storage medium - Google Patents
Artificial earthquake motion synthesis method and device, electronic equipment and storage medium Download PDFInfo
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Abstract
The invention provides an artificial earthquake motion synthesis method, an artificial earthquake motion synthesis device, electronic equipment and a storage medium, wherein the artificial earthquake motion with double matching of spectrum energy is synthesized by matching an acceleration response spectrum and an Arias energy accumulation curve by adopting a frequency domain and time domain combined adjustment method; the method adopts an iteration method to match the target earthquake motion, successively corrects the power spectrum and the acceleration time range in each iteration to match the acceleration response spectrum and the Arias energy accumulation curve, and stops the iteration until the two are matched with the target earthquake motion at a higher degree to obtain the artificial earthquake motion with double matching of spectrum energy.
Description
Technical Field
The invention belongs to the technical field of seismic wave synthesis, and particularly relates to an artificial seismic motion synthesis method, an artificial seismic motion synthesis device, electronic equipment and a storage medium.
Background
The southwest area of China is located in the Himalayan volcanic seismic zone, and seismic activity is strong. The area has abundant water energy resources, and a large amount of hydraulic engineering such as high dam water and the like is built. Once the hydraulic engineering fails under the action of an earthquake, the life and property safety of the downstream people is threatened greatly, so that the earthquake-resistant safety analysis of the engineering structures is extremely important. When the anti-seismic design and reliability analysis are performed on the engineering structure, a large amount of strong seismic oscillation is needed. However, the existing strong earthquake records are very limited, and due to the difference of site conditions, the strong earthquake motion meeting the requirement of engineering earthquake-resistant design is much less and less. Therefore, the synthesis of seismic motion meeting engineering requirements by artificial methods has been an important research area of seismic engineering.
At present, the artificial earthquake motion synthesis method commonly used in engineering application is to superpose through triangular series with different frequencies and random phases and multiply by an intensity envelope line to perform non-stabilization. Firstly, calculating a response spectrum of target earthquake motion or selecting a standard response spectrum as a target response spectrum, and enabling the artificial earthquake motion response spectrum to approach the target response spectrum through iteration according to the conversion relation between the response spectrum and the power spectrum. However, although the earthquake motion generated by the method can be matched with the reaction spectrum of the target earthquake motion in the frequency domain, the synthetic earthquake motion energy accumulation process is far away from the target earthquake motion due to the fact that the control energy is not available. For seismic response of many structures, such as non-linear seismic response of dams and seismic response of liquefaction fields, the energy of seismic motion is a crucial influencing factor. Therefore, in artificially synthesizing the seismic motion, it is necessary to consider matching the control energy with the target seismic motion.
Disclosure of Invention
The present disclosure is directed to solving at least one of the technical problems of the prior art.
To this end, an embodiment of a first aspect of the present disclosure provides an artificial seismic motion synthesis method, including:
(1) calculating an Arias energy accumulation curve of the target seismic oscillation, and fitting according to the Arias energy accumulation curve to obtain an intensity envelope curve of the target seismic oscillation;
(2) calculating an acceleration response spectrum of the target earthquake motion, estimating a power spectrum of the target earthquake motion according to the acceleration response spectrum of the target earthquake motion, initializing a power spectrum of the artificial earthquake motion as the power spectrum of the target earthquake motion, and initializing a power spectrum correction factor of the artificial earthquake motion;
(3) correcting the power spectrum of the artificial earthquake motion by using the power spectrum correction factor of the artificial earthquake motion; calculating cosine waves at each frequency according to the power spectrum of the artificial seismic oscillation, superposing the cosine waves of all frequency components, and multiplying the superposed cosine waves by the intensity envelope curve of the target seismic oscillation so as to obtain the acceleration time course of the artificial seismic oscillation;
(4) calculating an Arias energy accumulation curve of the artificial seismic oscillation, and calculating an acceleration time-course correction factor of the artificial seismic oscillation according to the Arias energy accumulation curve of the artificial seismic oscillation and the Arias energy accumulation curve of the target seismic oscillation so as to correct the acceleration time-course of the artificial seismic oscillation and calculate an acceleration response spectrum of the corrected artificial seismic oscillation; calculating a power spectrum correction factor of the artificial earthquake motion according to the acceleration response spectrum of the target earthquake motion and the acceleration response spectrum of the artificial earthquake motion, and using the power spectrum correction factor to iteratively correct the power spectrum of the artificial earthquake motion next time;
(5) and (5) repeating the steps (3) to (4) until the acceleration response spectrum of the artificial earthquake motion and the Arias energy accumulation curve are matched with the target earthquake motion, so as to obtain the artificial earthquake motion with double matching of spectrum energy.
The artificial earthquake motion synthesis method provided by the embodiment of the first aspect of the disclosure has the following characteristics and beneficial effects:
in the method for synthesizing the artificial earthquake motion, the power spectrum is adjusted by comparing the acceleration response spectra of the artificial earthquake motion and the target earthquake motion in the frequency domain, the acceleration time course is generated by using the adjusted power spectrum, and then the acceleration time course is adjusted by comparing the Arias energy accumulation curves of the artificial earthquake motion and the target earthquake motion. After multiple iterations, the acceleration response spectrum and the Arias energy accumulation curve of the artificial seismic oscillation are matched with the target seismic oscillation. Compared with the prior art, the method can effectively control the energy of earthquake motion on the basis of ensuring the spectrum matching, so that the energy accumulation process is matched with the target earthquake motion. The generated spectrum can be matched with artificial earthquake motion in a double-matching mode, the characteristics of real earthquake motion can be reflected, and richer and more reliable earthquake motion data can be provided for engineering earthquake-proof design.
In some embodiments, in step (1), an Arias energy accumulation curve of the target seismic motion is calculated by:
in the formula, Htarget(t) is the Arias energy accumulation curve of the target seismic oscillation, which is a function of time t; g is the acceleration of gravity; a (tau) is the acceleration value of the target earthquake motion at the time of tau, tau is epsilon [0, t]；
And fitting to obtain an intensity envelope curve of the target earthquake motion by the following formula:
in the formula, q (t) is the intensity envelope curve of the target earthquake motion; a is1、a2And a3A first coefficient, a second coefficient and a third coefficient which are intensity envelope lines q (t) of the target earthquake motion respectively; t is t5And t95The Arias energy of the target earthquake motion is respectively corresponding time points of 5% and 95% of the total energy of the target earthquake motion; t'5And t'95At corresponding time points at 5% and 95% intensity, respectively, of the intensity envelope q (t) of the target seismic motion.
In some embodiments, in step (2), the power spectrum of the target seismic motion is estimated from the acceleration response spectrum of the target seismic motion by:
in the formula, delta omega is a discrete step length adopted for performing discrete processing on the circular frequency of the target seismic oscillation; omegaiAnd ωnI and n circle frequencies, G, respectively0(ωi) And G0(ωn) Respectively, i-th circle frequency ωiAnd nth circle frequency ωnA power spectrum of the corresponding target seismic oscillation; sa (Sa)target(ωn) For the nth circle frequency omeganThe acceleration response spectrum of the corresponding target earthquake motion; ζ is the damping ratio; eta is a reaction spectrum peak value factor, and the calculation formula is as follows:
in the formula, n0Is an intermediate variable, δ is a constant with respect to the damping ratio ζ.
In some embodiments, in step (3), the power spectrum of the artificial seismic motion is modified by:
in the formula, Gk-1(ωn) And Gk(ωn) The circle frequency omega at the k-1 th and k-th iterations respectivelynK is more than or equal to 2 in the corresponding power spectrum of the artificial earthquake motion;
for the k-th iteration circle frequency omeganA power spectrum correction factor of the corresponding artificial seismic oscillation;
synthesizing an acceleration time-course of the artificial seismic motion by:
in the formula, ak1(t) is the time course of the dynamic acceleration of the artificial earthquake phi before the kth iterative correctionnFor the nth circle frequency omeganThe initial phase angle of the cosine wave.
In some embodiments, in step (4), an acceleration time-course correction factor for the artificial seismic motion is calculated by:
ΔHtarget((j-1)td-jtd)＝Htarget(jtd)-Htarget((j-1)td)
ΔHk((j-1)td-jtd)＝Hk(jtd)-Hk((j-1)td)
in the formula, tdFor the whole acceleration time t of target seismic and artificial seismicNThe time periods adopted for discretization are all divided into
A segment; hk(jtd) And Hk((j-1)td) Arias energy accumulation curves, Δ H, for artificially shaking the jth time segment and the (j-1) th time segment in the kth iterative correction calculation, respectivelyk((j-1)td-jtd) Manually shaking the Arias energy increment of the jth time segment in the kth iterative correction calculation; htarget(jtd) And Htarget((j-1)td) Arias energy accumulation curves, Δ H, for the jth and (j-1) th time periods of target seismic oscillation, respectivelytarget((j-1)td-jtd) Moving the Arias energy increment of the j time period for the target earthquake;
artificially shaking an acceleration time course correction factor of a jth time period in the kth iterative correction calculation;
correcting the acceleration time course of the artificial seismic motion by:
in the formula, ak2((j-1)td-jtd) Correcting the calculated artificial seismic oscillation acceleration time course for the kth iteration;
calculating a power spectrum correction factor for the artificial seismic oscillation by:
in the formula (I), the compound is shown in the specification,
calculating the mid-circle frequency omega for the (k + 1) th iteration correctionnCorresponding power spectrum correction factor, Sa, of artificial seismic oscillationsk(ωn) Is the circle frequency omega in the k-th iteration correction calculationnAnd (3) corresponding acceleration response spectrum of the artificial earthquake motion.
In some embodiments, in step (4), the calculated acceleration time course a of the artificial seismic motion is corrected if the k-th iterationk2And (t) if the acceleration amplitude at a certain moment is larger than the acceleration peak value of the target earthquake motion, the acceleration amplitude at the certain moment is equal to the acceleration peak value of the target earthquake motion, and the sign of the acceleration amplitude at the certain moment is unchanged.
An embodiment of a second aspect of the present disclosure provides an artificial seismic motion synthesis apparatus, including:
the first calculation module is used for calculating an Arias energy accumulation curve of the target earthquake motion and fitting according to the Arias energy accumulation curve to obtain an intensity envelope curve of the target earthquake motion;
the second calculation module is used for calculating an acceleration response spectrum of the target earthquake motion, estimating a power spectrum of the target earthquake motion according to the acceleration response spectrum of the target earthquake motion, initializing the power spectrum of the artificial earthquake motion as the power spectrum of the target earthquake motion, and initializing a power spectrum correction factor of the artificial earthquake motion; and
the third calculation module is used for executing multiple iterative correction calculations until the acceleration response spectrum and the Arias energy accumulation curve of the artificial earthquake motion are respectively matched with the acceleration response spectrum and the Arias energy accumulation curve of the target earthquake motion; each iteration of correction comprises: correcting the power spectrum of the manual vibration by using the power spectrum correction factor of the manual vibration, calculating cosine waves at each frequency according to the power spectrum of the manual vibration, superposing the cosine waves of all frequency components, and multiplying the superposed cosine waves by the intensity envelope curve of the target vibration to obtain the acceleration time course of the manual vibration before iterative correction, calculating the acceleration time course correction factor of the manual vibration by using the Arias energy accumulation curve of the manual vibration and the Arias energy accumulation curve of the target vibration to correct the acceleration time course of the manual vibration, and calculating the acceleration response spectrum of the manual vibration after correction; and calculating a power spectrum correction factor of the artificial earthquake motion by using the acceleration response spectrum of the target earthquake motion and the acceleration response spectrum of the artificial earthquake motion, and using the power spectrum correction factor to iteratively correct the power spectrum of the artificial earthquake motion next time.
An embodiment of a third aspect of the present disclosure provides an electronic device, including:
at least one processor, and a memory communicatively coupled to the at least one processor;
wherein the memory stores instructions executable by the at least one processor, the instructions being configured to perform a method of artificial seismic motion synthesis provided in accordance with an embodiment of a first aspect of the disclosure.
A fourth aspect of the present disclosure provides a computer-readable storage medium storing computer instructions for causing a computer to execute an artificial seismic motion synthesis method provided according to an embodiment of the first aspect of the present disclosure.
Drawings
Fig. 1 is a flowchart of an artificial seismic motion synthesis method according to an embodiment of the first aspect of the disclosure.
Fig. 2a to 2c are an acceleration time course and an intensity envelope thereof, an acceleration response spectrum, and an Arias energy accumulation curve of the target seismic motion used in the embodiment of the first aspect of the present disclosure, respectively.
Fig. 3a to 3d are an initial power spectrum of the artificial seismic motion, an acceleration time interval of the artificial seismic motion, a comparison graph of an acceleration response spectrum of the artificial seismic motion and a target seismic motion, and a comparison graph of an Arias energy accumulation curve of the artificial seismic motion and the target seismic motion, respectively, which are set in the first iteration in the embodiment of the first aspect of the disclosure.
Fig. 4a to 4d are an initial power spectrum of the artificial earthquake motion, an acceleration time interval of the artificial earthquake motion, a comparison graph of an acceleration response spectrum of the artificial earthquake motion and a target earthquake motion, and a comparison graph of an Arias energy accumulation curve of the artificial earthquake motion and the target earthquake motion, respectively, after 3 iterations in the first aspect of the present disclosure.
Fig. 5 is a block diagram of an artificial seismic motion synthesis apparatus provided in an embodiment of a second aspect of the disclosure.
Fig. 6 is a schematic structural diagram of an artificial seismic synthetic electronic device according to an embodiment of the third aspect of the present disclosure.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
On the contrary, this application is intended to cover any alternatives, modifications, equivalents, and alternatives that may be included within the spirit and scope of the application as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present application. It will be apparent to one skilled in the art that the present application may be practiced without these specific details.
The method for synthesizing artificial earthquake motion provided by the embodiment of the first aspect of the disclosure has the overall flow with reference to fig. 1, and comprises the following steps:
(1) calculating an Arias energy accumulation curve of the target seismic oscillation, and fitting according to the Arias energy accumulation curve to obtain an intensity envelope curve of the target seismic oscillation;
(2) calculating an acceleration response spectrum of the target earthquake motion, estimating a power spectrum of the target earthquake motion according to the acceleration response spectrum of the target earthquake motion, initializing a power spectrum of the artificial earthquake motion as the power spectrum of the target earthquake motion, and initializing a power spectrum correction factor of the artificial earthquake motion;
(3) correcting the power spectrum of the manual vibration by using the power spectrum correction factor of the manual vibration; calculating cosine waves at each frequency according to the power spectrum of the artificial earthquake motion, superposing the cosine waves of all frequency components, and multiplying the superposed cosine waves by the intensity envelope curve of the target earthquake motion, thereby obtaining the acceleration time course of the artificial earthquake motion; the amplitude of the cosine wave at each frequency is determined by the power spectrum of the artificial vibration at the corresponding frequency, and the initial phase angle of the cosine wave is randomly generated;
(4) calculating an Arias energy accumulation curve of the artificial seismic oscillation, and calculating an acceleration time-course correction factor of the artificial seismic oscillation by using the Arias energy accumulation curve of the artificial seismic oscillation and the Arias energy accumulation curve of the target seismic oscillation so as to correct the acceleration time-course of the artificial seismic oscillation and calculate an acceleration response spectrum of the corrected artificial seismic oscillation; calculating a power spectrum correction factor of the artificial earthquake motion by using the acceleration response spectrum of the target earthquake motion and the acceleration response spectrum of the artificial earthquake motion, and using the power spectrum correction factor to iteratively correct the power spectrum of the artificial earthquake motion next time;
(5) and (5) repeating the steps (3) to (4) for iteration until the acceleration response spectrum and the Arias energy accumulation curve of the artificial earthquake motion are matched with the target earthquake motion, so as to obtain the artificial earthquake motion with double matching of spectral energy.
In some embodiments, in step (1), an Arias energy accumulation curve of the target seismic motion is calculated by:
in the formula, Htarget(t) is the Arias energy accumulation curve of the target seismic oscillation, which is a function of time t; g is the acceleration of gravity; a (tau) is the acceleration value of the target earthquake motion at the time of tau, tau is epsilon [0, t]。
In some embodiments, in step (1), an intensity envelope of the target seismic motion is obtained by fitting an Arias energy accumulation curve of the target seismic motion, and a specific calculation formula is as follows:
in the formula, q (t) is the intensity envelope curve of the target earthquake motion; a is1、a2And a3A first coefficient, a second coefficient and a third coefficient which are intensity envelope lines q (t) of the target earthquake motion respectively; t is t5And t95Arias energy of seismic motion of the target is the energyTime points at 5% and 95% of the total energy; t'5And t'95At corresponding time points at 5% and 95% intensity, respectively, of the intensity envelope q (t) of the target seismic motion.
In some embodiments, in step (2), the power spectrum of the target earthquake is calculated from the acceleration response spectrum of the target earthquake by:
in the formula, delta omega is a discrete step length adopted for performing discrete processing on the circular frequency of the target seismic oscillation; omegaiAnd ωnThe ith and nth circle frequencies, respectively; g0(ωi) And G0(ωn) Respectively, i-th circle frequency ωiAnd nth circle frequency ωnA power spectrum of the corresponding target seismic oscillation; sa (Sa)target(ωn) For the nth circle frequency omeganThe acceleration response spectrum of the corresponding target earthquake motion; zeta is damping ratio, generally 5%; eta is a reaction spectrum peak value factor, and the calculation formula is as follows:
in the formula, n0Is an intermediate variable, δ is a constant with respect to the damping ratio ζ.
In some embodiments, in step (2), for each frequency component, a power spectrum correction factor for the artificial seismic motion is initialized to 1, namely:
in the formula (I), the compound is shown in the specification,
for the nth circle frequency omeganAnd a power spectrum correction factor of the corresponding initial artificial seismic oscillation.
In some embodiments, in step (3), the power spectrum of the manual vibration is modified by:
in the formula, Gk-1(ωn) And Gk(ωn) The circle frequency omega at the k-1 th and k-th iterations respectivelynK is more than or equal to 2 in the corresponding power spectrum of the artificial earthquake motion;
for the k-th iteration circle frequency omeganAnd (3) a corresponding power spectrum correction factor of the artificial seismic oscillation.
In some embodiments, in step (3), the acceleration time-course of the artificial seismic motion is synthesized by:
in the formula, ak1(t) is the time course of the dynamic acceleration of the artificial earthquake phi before the kth iterative correctionnFor the nth circle frequency omeganThe initial phase angle of the cosine wave of (2) is obtained by random generation.
In some embodiments, in step (4), the Arias energy accumulation curve calculation method of target seismic motion is adopted, according to ak1(t) calculating an Arias energy accumulation curve H of the k iteration artificial seismic oscillationk(t); utilizing time interval t for whole acceleration time range of target earthquake motion and artificial earthquake motiondDiscretizing, and taking td(2 s is taken as a time period here), and the whole acceleration time ranges of the target earthquake motion and the artificial earthquake motion are respectively divided into
Segment, wherein tNThe total length of the acceleration time interval of the target earthquake motion or the artificial earthquake motion is equal to the total length of the acceleration time interval of the target earthquake motion and the artificial earthquake motion,
indicating rounding down on x. For each time segment
Respectively calculating the target earthquake motion and the k-th iteration artificial earthquake motion Arias energy increment according to the following formula:
ΔHtarget((j-1)td-jtd)＝Htarget(jtd)-Htarget((j-1)td)
ΔHk((j-1)td-jtd)＝Hk(jtd)-Hk((j-1)td) ⑦
in the formula,. DELTA.Htarget((j-1)td-jtd) Arias energy increment, H, for the j time period of seismic oscillation of the targettarget(jtd) And Htarget((j-1)td) Arias energy accumulation curves of a jth time period and a (j-1) th time period of target seismic oscillation respectively; Δ Hk((j-1)td-jtd) Artificially shaking the Arias energy increment, H, for the j time segment in the k iterationk(jtd) And Hk((j-1)td) The Arias energy accumulation curves for the j-th time segment and the (j-1) -th time segment are artificially shaken in the k-th iterative correction calculation, respectively. Calculating an acceleration time-course correction factor of the artificial seismic oscillation of the kth iteration according to the target seismic oscillation and the Arias energy increment of the artificial seismic oscillation of the kth iteration
In the formula (I), the compound is shown in the specification,
for shaking the jth segment manually in the kth iterative correction calculationAcceleration time course correction factor.
According to the acceleration time course correction factor of the artificial earthquake motion, the acceleration time course a of the artificial earthquake motion before the k-th iteration correctionk1(t) correcting to obtain the artificial seismic oscillation acceleration time course a after the kth iterative correction calculationk2((j-1)td-jtd)：
In some embodiments, the calculated acceleration time course a of the artificial seismic motion is corrected if the k-th iterationk2(t) there is an acceleration amplitude | a at a certain momentjIf | is greater than the acceleration peak value of the target earthquake motion, let | aj| is equal to the peak acceleration of the target seismic oscillation, ajThe sign of the earthquake motion is not changed, so that the acceleration peak value of the artificial earthquake motion does not exceed the target earthquake motion acceleration peak value.
In some embodiments, in step (4), the corrected acceleration time course a of the artificial seismic motion according to the k-th iterationk2(t) calculating the artificial seismic motion acceleration response spectrum of the kth iteration, and calculating the power spectrum correction factor of the artificial seismic motion of the next iteration (k + 1) th time according to the following formula:
in the formula (I), the compound is shown in the specification,
for the nth circle frequency omega in the (k + 1) th iteration correction calculationnCorresponding power spectrum correction factor, Sa, of artificial seismic oscillationsk(ωn) Is the nth circle frequency omega in the kth iterative correction calculationnAnd (3) corresponding acceleration response spectrum of the artificial earthquake motion.
The following is a specific embodiment of the disclosed method:
in the method, an actual Earthquake motion recorded by a north ridge Earthquake in 1994 in an NGA strong Earthquake database of the American Pacific Earthquake Engineering Center (PEER) is used as a target Earthquake motion, and an artificial Earthquake motion with an acceleration response spectrum and an Arias energy accumulation curve matched in a double mode is generated. Fig. 2a is an acceleration time course of the adopted target earthquake, and fig. 2b and fig. 2c are an acceleration response spectrum and an Arias energy accumulation curve of the adopted target earthquake respectively. The specific implementation steps are as follows:
(1) calculating an Arias energy accumulation curve of target seismic oscillation according to the formula I, and obtaining the intensity time points of 5% and 95% of the Arias energy accumulation curve as t5＝4.41s，t95Fig. 2a shows an intensity envelope of the target seismic motion obtained according to equation (14.60 s).
(2) And (3) obtaining an acceleration response spectrum of the target seismic motion with 5% damping ratio according to the acceleration time course of the target seismic motion, calculating a power spectrum of the target seismic motion by using the acceleration response spectrum of the target seismic motion according to a formula III and a formula IV, and initializing a power spectrum correction factor of the artificial seismic motion to be 1.
(3) Correcting the power spectrum of the artificial earthquake motion, and generating an acceleration time course of the artificial earthquake motion according to the corrected power spectrum of the artificial earthquake motion, wherein the method specifically comprises the following steps:
and (3-1) correcting the power spectrum of the artificial vibration by using a formula (v) according to the power spectrum correction factor of the artificial vibration.
(3-2) for each frequency component, randomly generating an initial phase angle of a cosine wave, generating an initial artificial seismic oscillation acceleration time course by using a formula (C), wherein the time course is shown in fig. 3b, and an acceleration response spectrum and an Arias energy accumulation curve of the artificial seismic oscillation are shown in fig. 3c and fig. 3 d. It can be seen that at this time, the acceleration response spectrum and the Arias energy accumulation curve of the artificial seismic oscillation are not matched with the target seismic oscillation.
(4) Correcting the acceleration time course of the artificial earthquake motion, and calculating a power spectrum correction factor of the artificial earthquake motion, wherein the method specifically comprises the following steps:
(4-1) calculating an acceleration time-course correction factor of the artificial seismic motion according to a formula (c) and a formula (b), and correcting the acceleration time-course of the artificial vibration by utilizing a formula (c) to enable an Arias energy accumulation curve to be matched with the target seismic motion; and the acceleration amplitude of the acceleration peak value of the earthquake motion of the target is exceeded in the acceleration time course of the artificial vibration, and the amplitude is made to be equal to the acceleration peak value of the earthquake motion of the target, so that the acceleration peak value of the artificial earthquake motion is not exceeded the acceleration peak value of the earthquake motion of the target.
(4-2) calculating the acceleration response spectrum of the corrected artificial seismic motion with 5% damping ratio, and calculating the power spectrum correction factor of the artificial seismic motion according to the formula (R < lambda > C) for correcting the power spectrum of the artificial seismic motion in the next iteration.
(5) Repeating the steps (3) - (4), obtaining a power spectrum for generating an artificial seismic acceleration time interval after 3 iterations in the embodiment as shown in fig. 4a, obtaining a generated artificial seismic acceleration time interval as shown in fig. 4b, and comparing the acceleration response spectrum and the Arias energy accumulation curve with the target seismic motion, such as fig. 4c and fig. 4 d. It can be seen that, at this time, the synthesized acceleration response spectrum of the artificial earthquake motion and the Arias energy accumulation curve almost coincide with the target earthquake motion, and the matching degree is very high, which indicates that the artificial earthquake motion and the target earthquake motion synthesized by the embodiment are matched in response spectrum and energy, and approach the actual measurement earthquake motion in spectral characteristics and energy characteristics, and is more suitable for engineering earthquake-resistant analysis.
The structure of the artificial seismic motion synthesis device provided by the embodiment of the second aspect of the disclosure is shown in fig. 5, and includes:
the first calculation module is used for calculating an Arias energy accumulation curve of the target earthquake motion and fitting according to the Arias energy accumulation curve to obtain an intensity envelope curve of the target earthquake motion;
the second calculation module is used for calculating an acceleration response spectrum of the target earthquake motion, estimating a power spectrum of the target earthquake motion according to the acceleration response spectrum of the target earthquake motion, initializing the power spectrum of the artificial earthquake motion as the power spectrum of the target earthquake motion, and initializing a power spectrum correction factor of the artificial earthquake motion; the third calculation module is used for executing multiple iterative correction calculations until the acceleration response spectrum and the Arias energy accumulation curve of the artificial earthquake motion are respectively matched with the acceleration response spectrum and the Arias energy accumulation curve of the target earthquake motion; each iteration of correction comprises: correcting the power spectrum of the manual vibration by using the power spectrum correction factor of the manual vibration, calculating cosine waves at each frequency according to the power spectrum of the manual vibration, superposing the cosine waves of all frequency components, and multiplying the superposed cosine waves by the intensity envelope curve of the target vibration to obtain the acceleration time course of the manual vibration before iterative correction, calculating the acceleration time course correction factor of the manual vibration by using the Arias energy accumulation curve of the manual vibration and the Arias energy accumulation curve of the target vibration so as to correct the acceleration time course of the manual vibration, and calculating the acceleration response spectrum of the manual vibration after correction; and calculating a power spectrum correction factor of the artificial earthquake motion by using the acceleration response spectrum of the target earthquake motion and the acceleration response spectrum of the artificial earthquake motion, and using the power spectrum correction factor to iteratively correct the power spectrum of the artificial earthquake motion next time.
In order to implement the above embodiments, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, where the computer program is executed by a processor, and is used to execute the artificial seismic motion synthesis method of the above embodiments.
Referring now to FIG. 5, a block diagram of an electronic device 900 suitable for use in implementing embodiments of the present disclosure is shown. It should be noted that the electronic device 900 includes an artificial seismic motion synthesis system therein, wherein the electronic device in the embodiment of the present disclosure may include, but is not limited to, a mobile terminal such as a mobile phone, a notebook computer, a digital broadcast receiver, a PDA (personal digital assistant), a PAD (tablet computer), a PMP (portable multimedia player), a vehicle terminal (e.g., a vehicle navigation terminal), and the like, and a fixed terminal such as a digital TV, a desktop computer, a server, and the like. The electronic device shown in fig. 5 is only an example, and should not bring any limitation to the functions and the scope of use of the embodiments of the present disclosure.
As shown in fig. 6, the electronic device 900 may include a processing means (e.g., a central processing unit, a graphics processor, etc.) 901 that may perform various appropriate actions and processes in accordance with a program stored in a Read Only Memory (ROM)902 or a program loaded from a storage means 908 into a Random Access Memory (RAM) 903. In the RAM 903, various programs and data necessary for the operation of the electronic apparatus 900 are also stored. The processing apparatus 901, the ROM 902, and the RAM 903 are connected to each other through a bus 904. An input/output (I/O) interface 905 is also connected to bus 904.
Generally, the following devices may be connected to the I/O interface 905: an input device 906 including, for example, a touch screen, a touch pad, a keyboard, a mouse, a camera, a microphone, and the like; an output device 907 including, for example, a Liquid Crystal Display (LCD), a speaker, a vibrator, and the like; storage 908 including, for example, magnetic tape, hard disk, etc.; and a communication device 909. The communication device 909 may allow the electronic apparatus 900 to perform wireless or wired communication with other apparatuses to exchange data. While fig. 5 illustrates an electronic device 900 having various means, it is to be understood that not all illustrated means are required to be implemented or provided. More or fewer devices may alternatively be implemented or provided.
In particular, according to an embodiment of the present disclosure, the processes described above with reference to the flowcharts may be implemented as computer software programs. For example, the present embodiments include a computer program product comprising a computer program embodied on a computer readable medium, the computer program comprising program code for performing the method illustrated in the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network through the communication device 909, or installed from the storage device 908, or installed from the ROM 902. The computer program performs the above-described functions defined in the methods of the embodiments of the present disclosure when executed by the processing apparatus 901.
It should be noted that the computer readable medium in the present disclosure can be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present disclosure, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In contrast, in the present disclosure, a computer readable signal medium may comprise a propagated data signal with computer readable program code embodied therein, either in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: electrical wires, optical cables, RF (radio frequency), etc., or any suitable combination of the foregoing.
The computer readable medium may be embodied in the electronic device; or may exist separately without being assembled into the electronic device.
The computer readable medium carries one or more programs which, when executed by the electronic device, cause the electronic device to: (1) calculating an Arias energy accumulation curve of the target seismic oscillation, and fitting according to the Arias energy accumulation curve of the target seismic oscillation to obtain an intensity envelope curve of the target seismic oscillation; (2) calculating an acceleration response spectrum of the target earthquake motion, estimating a power spectrum of the target earthquake motion according to the acceleration response spectrum of the target earthquake motion, initializing a power spectrum of the artificial earthquake motion as the power spectrum of the target earthquake motion, and initializing a power spectrum correction factor of the artificial earthquake motion; (3) correcting the power spectrum of the manual vibration by using the power spectrum correction factor of the manual vibration; calculating cosine waves at each frequency according to the power spectrum of the artificial earthquake motion, superposing the cosine waves of all frequency components, and multiplying the superposed cosine waves by the intensity envelope curve of the target earthquake motion, thereby obtaining the acceleration time course of the artificial earthquake motion; the amplitude of the cosine wave at each frequency is determined by the power spectrum of the artificial vibration at the corresponding frequency, and the initial phase angle of the cosine wave is randomly generated; (4) calculating an Arias energy accumulation curve of the artificial seismic oscillation, and calculating an acceleration time-course correction factor of the artificial seismic oscillation by using the Arias energy accumulation curve of the artificial seismic oscillation and the Arias energy accumulation curve of the target seismic oscillation so as to correct the acceleration time-course of the artificial seismic oscillation and calculate an acceleration response spectrum of the corrected artificial seismic oscillation; calculating a power spectrum correction factor of the artificial earthquake motion by using the acceleration response spectrum of the target earthquake motion and the acceleration response spectrum of the artificial earthquake motion, and using the power spectrum correction factor to iteratively correct the power spectrum of the artificial earthquake motion next time; (5) and (5) repeating the steps (3) to (4) for iteration until the acceleration response spectrum and the Arias energy accumulation curve of the artificial earthquake motion are matched with the target earthquake motion, so as to obtain the artificial earthquake motion with double matching of spectral energy.
Computer program code for carrying out operations for aspects of the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C + +, python, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by a program instructing associated hardware to complete, and the developed program may be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a separate product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
Claims (9)
1. An artificial seismic synthetic method, comprising:
(1) calculating an Arias energy accumulation curve of the target seismic oscillation, and fitting according to the Arias energy accumulation curve to obtain an intensity envelope curve of the target seismic oscillation;
(2) calculating an acceleration response spectrum of the target earthquake motion, estimating a power spectrum of the target earthquake motion according to the acceleration response spectrum of the target earthquake motion, initializing a power spectrum of the artificial earthquake motion as the power spectrum of the target earthquake motion, and initializing a power spectrum correction factor of the artificial earthquake motion;
(3) correcting the power spectrum of the artificial earthquake motion by using the power spectrum correction factor of the artificial earthquake motion; calculating cosine waves at each frequency according to the power spectrum of the artificial seismic oscillation, superposing the cosine waves of all frequency components, and multiplying the superposed cosine waves by the intensity envelope curve of the target seismic oscillation so as to obtain the acceleration time course of the artificial seismic oscillation;
(4) calculating an Arias energy accumulation curve of the artificial seismic oscillation, and calculating an acceleration time-course correction factor of the artificial seismic oscillation according to the Arias energy accumulation curve of the artificial seismic oscillation and the Arias energy accumulation curve of the target seismic oscillation so as to correct the acceleration time-course of the artificial seismic oscillation and calculate an acceleration response spectrum of the corrected artificial seismic oscillation; calculating a power spectrum correction factor of the artificial earthquake motion according to the acceleration response spectrum of the target earthquake motion and the acceleration response spectrum of the artificial earthquake motion, and using the power spectrum correction factor to iteratively correct the power spectrum of the artificial earthquake motion next time;
(5) and (5) repeating the steps (3) to (4) until the acceleration response spectrum of the artificial earthquake motion and the Arias energy accumulation curve are matched with the target earthquake motion, so as to obtain the artificial earthquake motion with double matching of spectrum energy.
2. The method for synthesizing artificial seismic motion according to claim 1, wherein in step (1), the Arias energy accumulation curve of the target seismic motion is calculated by the following formula:
in the formula, Htarget(t) is the Arias energy accumulation curve of the target seismic oscillation, which is a function of time t; g is the acceleration of gravity; a (tau) is the acceleration value of the target earthquake motion at the time of tau, tau is epsilon [0, t]；
And fitting to obtain an intensity envelope curve of the target earthquake motion by the following formula:
in the formula, q (t) is the intensity envelope curve of the target earthquake motion; a is1、a2And a3A first coefficient, a second coefficient and a third coefficient which are intensity envelope lines q (t) of the target earthquake motion respectively; t is t5And t95The Arias energy of the target earthquake motion is respectively corresponding time points of 5% and 95% of the total energy of the target earthquake motion; t'5And t'955% and 5% of the intensity envelope q (t) of the seismic motion of the target, respectivelyCorresponding time point at 95% intensity.
3. The artificial seismic synthesis method according to claim 2, wherein in step (2), the power spectrum of the target seismic is estimated from the acceleration response spectrum of the target seismic by the following formula:
in the formula, delta omega is a discrete step length adopted for performing discrete processing on the circular frequency of the target seismic oscillation; omegaiAnd ωnI and n circle frequencies, G, respectively0(ωi) And G0(ωn) Respectively, i-th circle frequency ωiAnd nth circle frequency ωnA power spectrum of the corresponding target seismic oscillation; sa (Sa)target(ωn) For the nth circle frequency omeganThe acceleration response spectrum of the corresponding target earthquake motion; ζ is the damping ratio; eta is a reaction spectrum peak value factor, and the calculation formula is as follows:
in the formula, n0Is an intermediate variable, δ is a constant with respect to the damping ratio ζ.
4. A method for synthesizing artificial seismic motion according to claim 3, wherein in step (3), the power spectrum of the artificial seismic motion is corrected by the following formula:
in the formula, Gk-1(ωn) And Gk(ωn) The circle frequency omega at the k-1 th and k-th iterations respectivelynK is more than or equal to 2 in the corresponding power spectrum of the artificial earthquake motion;
for the k-th iteration circle frequency omeganA power spectrum correction factor of the corresponding artificial seismic oscillation;
synthesizing an acceleration time-course of the artificial seismic motion by:
in the formula, ak1(t) is the time course of the dynamic acceleration of the artificial earthquake phi before the kth iterative correctionnFor the nth circle frequency omeganThe initial phase angle of the cosine wave.
5. The method according to claim 4, wherein in the step (4), the acceleration time-course correction factor of the artificial seismic motion is calculated by the following formula:
ΔHtarget((j-1)td-jtd)＝Htarget(jtd)-Htarget((j-1)td)
ΔHk((j-1)td-jtd)＝Hk(jtd)-Hk(j-1)td)
in the formula, tdFor the whole acceleration time t of target seismic and artificial seismicNThe time periods adopted for discretization are all divided into
A segment; hk(jtd) And Hk((j-1)td) Arias energy accumulation curves, Δ H, for artificially shaking the jth time segment and the (j-1) th time segment in the kth iterative correction calculation, respectivelyk((j-1)td-jtd) Manually shaking the Arias energy increment of the jth time segment in the kth iterative correction calculation; htarget(jtd) And Htarget((j-1)td) Arias energy accumulation curves, Δ H, for the jth and (j-1) th time periods of target seismic oscillation, respectivelytarget((j-1)td-jtd) Moving the Arias energy increment of the j time period for the target earthquake;
artificially shaking an acceleration time course correction factor of a jth time period in the kth iterative correction calculation;
correcting the acceleration time course of the artificial seismic motion by:
in the formula, ak2((j-1)td-jtd) Correcting the calculated artificial seismic oscillation acceleration time course for the kth iteration;
calculating a power spectrum correction factor for the artificial seismic oscillation by:
in the formula (I), the compound is shown in the specification,
calculating the mid-circle frequency omega for the (k + 1) th iteration correctionnCorresponding power spectrum correction factor, Sa, of artificial seismic oscillationsk(ωn) Is the circle frequency omega in the k-th iteration correction calculationnAnd (3) corresponding acceleration response spectrum of the artificial earthquake motion.
6. A method according to claim 5, wherein in step (4), the calculated acceleration time interval a of the artificial seismic motion is corrected if the kth iterationk2And (t) if the acceleration amplitude at a certain moment is larger than the acceleration peak value of the target earthquake motion, the acceleration amplitude at the certain moment is equal to the acceleration peak value of the target earthquake motion, and the sign of the acceleration amplitude at the certain moment is unchanged.
7. An artificial seismic synthesis apparatus, comprising:
the first calculation module is used for calculating an Arias energy accumulation curve of the target earthquake motion and fitting according to the Arias energy accumulation curve to obtain an intensity envelope curve of the target earthquake motion;
the second calculation module is used for calculating an acceleration response spectrum of the target earthquake motion, estimating a power spectrum of the target earthquake motion according to the acceleration response spectrum of the target earthquake motion, initializing the power spectrum of the artificial earthquake motion as the power spectrum of the target earthquake motion, and initializing a power spectrum correction factor of the artificial earthquake motion; and
the third calculation module is used for executing multiple iterative correction calculations until the acceleration response spectrum and the Arias energy accumulation curve of the artificial earthquake motion are respectively matched with the acceleration response spectrum and the Arias energy accumulation curve of the target earthquake motion; each iteration of correction comprises: correcting the power spectrum of the manual vibration by using the power spectrum correction factor of the manual vibration, calculating cosine waves at each frequency according to the power spectrum of the manual vibration, superposing the cosine waves of all frequency components, and multiplying the superposed cosine waves by the intensity envelope curve of the target vibration to obtain the acceleration time course of the manual vibration before iterative correction, calculating the acceleration time course correction factor of the manual vibration by using the Arias energy accumulation curve of the manual vibration and the Arias energy accumulation curve of the target vibration to correct the acceleration time course of the manual vibration, and calculating the acceleration response spectrum of the manual vibration after correction; and calculating a power spectrum correction factor of the artificial earthquake motion by using the acceleration response spectrum of the target earthquake motion and the acceleration response spectrum of the artificial earthquake motion, and using the power spectrum correction factor to iteratively correct the power spectrum of the artificial earthquake motion next time.
8. An electronic device, comprising:
at least one processor, and a memory communicatively coupled to the at least one processor;
wherein the memory stores instructions executable by the at least one processor and configured to perform the method of artificial seismic motion synthesis of any of the preceding claims 1-6.
9. A computer-readable storage medium storing computer instructions for causing a computer to perform the method of artificial seismic motion synthesis of any of claims 1-6.
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