CN105787655B - Method for identifying modal parameters of super high-rise structure - Google Patents

Method for identifying modal parameters of super high-rise structure Download PDF

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CN105787655B
CN105787655B CN201610101215.1A CN201610101215A CN105787655B CN 105787655 B CN105787655 B CN 105787655B CN 201610101215 A CN201610101215 A CN 201610101215A CN 105787655 B CN105787655 B CN 105787655B
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李志军
埃德里霍贾特
朴孝善
李高宏
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Xian Technological University
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Abstract

The invention discloses a method for identifying modal parameters of a super high-rise structure, which is used for effectively analyzing non-stationary, nonlinear and strong noise signals based on discrete synchronous extrusion wavelet transform transduction, accurately reconstructing the characteristics of modal components of complex synthetic signals in the form of resonance components, and effectively analyzing the resonance components by combining Hilbert Transform (HT) to obtain the characteristics of instantaneous amplitude and frequency, so that the purpose of identifying the main frequency and damping ratio of the super high-rise structure is achieved, and in order to ensure the accuracy of identifying the modal parameters, a least square linear fitting method (linear least-square fit, LL ST) is introduced to smooth and predict results.

Description

Method for identifying modal parameters of super high-rise structure
Technical Field
The invention belongs to the field of structural health monitoring, and particularly relates to a modal parameter identification method for a super high-rise structure.
Background
Structural health monitoring is the process of assessing structural health status, identifying structural damage sites and damage levels. Health monitoring of the super high-rise building structure is a key step for prolonging the service life of the structure, and in view of the importance of the super high-rise structure, the health monitoring work aiming at the structure has great social benefit and economic benefit. One important issue that needs to be addressed by structural health monitoring is structural modal parameter identification based on vibration signals. The existing Wavelet Transform (WT) and Empirical Mode Decoupling (EMD) methods have the problems that the modal parameters of similar frequencies cannot be identified and the basic modal parameters of the structure cannot be effectively identified from low-amplitude and high-noise measurement vibration signals.
The synchronous extrusion wavelet transform transducer effectively analyzes non-stationary, nonlinear and strong noise signals, and accurately reconstructs modal components of complex composite signals in the form of resonance components, wherein the signals are very common in actual building structures, such as earthquake motion and wind load.
Disclosure of Invention
In view of the above, the present invention is directed to a method for identifying modal parameters of a super high-rise structure.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
a method for identifying modal parameters of a super high-rise structure is characterized by comprising the following steps:
step 1: screening acceleration measurement signals of different structural layers, and selecting measurement signals containing main fundamental frequencies of the structure
Figure GDA0002053822170000011
And analyzing, i is 1,2, …, n is the corresponding layer number of the structure, removing the noise of the measurement signal according to the synchronous extrusion wavelet transform, and then decomposing and reconstructing the main modal component of the structure based on the de-noised measurement signal, wherein the measurement signal is expressed as:
Figure GDA0002053822170000021
in the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000022
the first m main modal components of the acceleration measurement signal of the ith layer reconstructed after the synchronous extrusion wavelet decomposition; fi(t) noise and higher-order modal components filtered out of the i-th layer acceleration measurement signal;
step 2: constructing an analysis signal according to Hilbert transform, then obtaining a corresponding instantaneous phase angle and amplitude according to the analysis signal, and then preliminarily identifying the main frequency and the damping ratio of the structure by the derivative of the natural logarithm of the corresponding instantaneous phase angle and amplitude to time;
and step 3: and performing smooth prediction on the primary frequency and the damping ratio of the primary identification according to a least square linear fitting method to obtain an accurate identification result.
The step 1 specifically comprises the following steps:
step 101: screening the measurement signals, the number of sampling points satisfying 2 to ensure the accuracy of the calculationnWherein n is a positive integer, n is 10 or 11, i.e. the number of points used is 1024 or 2048, and a measurement signal containing the structural primary fundamental frequency is selected for analysis;
step 102: for discrete wavelet transform of screened measuring signal, firstly defining measuring signal
Figure GDA0002053822170000023
Continuous Wavelet Transform (CWT), Wf(a,. is) is
Figure GDA0002053822170000024
Where ψ is a selected base wavelet function; a is a proportionality coefficient; "+" indicates convolution;
in the frequency domain space, wavelet transform Wf(a,. cndot.) is represented by
Figure GDA0002053822170000025
For an arbitrary position (a)j,tk) Here tkIs a scaling factor of any discrete time point and corresponding discrete time form
Figure GDA0002053822170000026
L is a non-negative integer, nvTo influence the parameters of the scaling factor, usually 32 or 64, we calculate the Discrete Wavelet Transform (DWT) using the following formula
Figure GDA0002053822170000027
In the formula (I), the compound is shown in the specification,nand
Figure GDA0002053822170000031
is the standard discrete Fourier Transform (Fourier Transform) and its inverse; "·" denotes a point multiplication;
Figure GDA0002053822170000032
is the sampling interval of the frequency domain space;
step 103: based on continuous wavelet transform coefficients, Wf(a,. cndot.) the corresponding real-valued frequency is obtained by the following equation
Figure GDA0002053822170000033
In the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000034
for effective noise filtering, a hard threshold parameter (gamma) is selected as
Figure GDA0002053822170000035
The MAD is a discrete wavelet coefficient of the matrix,
Figure GDA0002053822170000036
average absolute deviation of (d); blThe method is an augmentation factor related to the MAD, and the suggested value is 1.2-1.7;
Figure GDA0002053822170000037
is the magnitude of the discrete wavelet coefficient;
from equation (6), the point where the amplitude of the discrete wavelet transform coefficient is smaller than γ is discarded to effectively filter the noise effect, and based on equation (5), the real-valued frequency based on the discrete wavelet transform is obtained as
Figure GDA0002053822170000038
In the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000039
and is
Figure GDA00020538221700000310
Step 104: based on the results obtained from equations (4) and (7)
Figure GDA00020538221700000311
And
Figure GDA00020538221700000312
defining de-noised acceleration signals
Figure GDA00020538221700000313
Discrete simultaneous extrusion wavelet transform
Figure GDA00020538221700000314
In the formula, the frequency of two divisions omegalSatisfies the conditions
Figure GDA00020538221700000315
Step 105: setting corresponding m band-pass filters, then carrying out inverse discrete synchronous extrusion wavelet transform, and denoising acceleration signals
Figure GDA00020538221700000316
Can be reconstructed as
Figure GDA00020538221700000317
In the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000041
is a normalization constant.
The step 2 specifically comprises the following steps:
step 201: for each modal component reconstructed by discrete synchronous wavelet transform, namely the modal component obtained by the formula (9), firstly, the analysis signal form of the corresponding j-th order modal component is obtained based on Hilbert transform
Figure GDA0002053822170000042
In the formula, Aij(t) is related to the frequency ωjThe amplitude of the corresponding reconstructed modal component at time t; thetaij(t) is the phase angle at the respective time instant;
step 202: based on equation (10), the transient frequency and damping ratio of the structure are obtained from the following equations
Figure GDA0002053822170000043
Figure GDA0002053822170000044
In the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000045
the damping system modal frequency is the j-th order mode.
The step 3 specifically comprises the following steps:
step 301: at a phase angle thetaij(t) in the time t-dependent change diagram, obtaining a corresponding average straight line according to a least square linear fitting method to approximately represent the phase angle thetaij(t) the relation of the change along with the time t, and the predicted modal frequency omega of the damping system can be obtained by the slope of the fitting straight linedjNamely, obtained by using formula (11);
step 302: natural logarithm at amplitude lnAij(t) in the time t-dependent graph, selecting a corresponding time interval, and obtaining a corresponding average straight line by using a least square linear fitting method to approximately represent lnA in the time intervalij(t) as a function of t, the slope of the fitted line can be used to derive ξ in equation (12)jωjA value of (d);
step 303: according to the result obtained in the first two stepsOmega ofdjAnd ξjωjAnd using a known relationship
Figure GDA0002053822170000046
The predicted structural modal frequency value and damping ratio value can be obtained.
Compared with the prior art, the invention has the beneficial effects that:
the invention can effectively identify the structural fundamental modal frequency and the corresponding damping ratio from the vibration measurement signals with low amplitude, strong noise and similar frequency characteristics measured by the state reaction sensor of the super high-rise structure. Therefore, the defects of the traditional wavelet analysis method and the empirical mode decoupling method are overcome.
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FIG. 1 is a flow chart of an embodiment of the present invention;
fig. 2 is a specific super high-rise building of an embodiment of the present invention-korea seoul le world tower (L otte worldpower, &lttt translation = L "&gtt L &/t &gtt WT);
FIG. 3(a) is a diagram showing the position of the acceleration sensor along the height of the heaven world tower according to the embodiment of the present invention;
fig. 3(b) is a diagram showing the arrangement of the position and orientation of the acceleration sensor along the floor according to the embodiment of the present invention;
FIG. 4(a) shows the signals measured by the acceleration sensor in the x direction at the north side of 72 layers according to an embodiment of the present invention;
FIG. 4(b) shows the analysis signal of the screening according to the embodiment of the present invention;
FIG. 5 is a time-frequency distribution diagram of signals according to an embodiment of the present invention;
FIG. 6 is a modal component reconstruction of an embodiment of the present invention;
FIG. 7 shows a phase angle θ according to an embodiment of the present inventionij(t) graph of the variation with time t and least squares linear fit straight line. Wherein, the graph (a) is a first modal response; panel (b) is a second modal response; panel (c) is a third modal response;
FIG. 8 is a graph of the natural logarithm of magnitude lnA for an embodiment of the inventionij(t) graph of the variation with time t and least squares linear fit straight line. Wherein, the graph (a) is a first modal response; FIG. (b) shows a second moldCarrying out state reaction; graph (c) shows the third modal response.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention 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 invention and are not intended to limit the invention.
The invention can effectively analyze non-stationary, nonlinear and strong noise signals based on the DSWT (discrete synchronous squeezed wavelet transform), accurately reconstruct the characteristics of modal components of complex synthetic signals in the form of resonance components, and effectively analyze the resonance components by combining the Hilbert Transform (HT) to obtain the characteristics of instantaneous amplitude and frequency, thereby achieving the purpose of identifying the main frequency and damping ratio of the super high-rise structure.
The embodiment of the invention provides a modal parameter identification method of a super high-rise structure, which is realized by the following steps:
step 1: screening acceleration measurement signals of different structural layers, and selecting measurement signals containing main fundamental frequencies (generally, the first 9 orders) of the structure
Figure GDA0002053822170000061
(i ═ 1,2, …, n is the number of layers corresponding to the structure) to remove the noise of the measurement signal according to the synchronous squeeze wavelet transform, and then decompose and reconstruct the main modal components of the structure (filter out the higher-order modal components with less influence) based on the de-noised measurement signal, so that the measurement signal is expressed as:
Figure GDA0002053822170000062
in the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000063
is the same as the meridianStep one, squeezing the first m main modal components of the reconstructed acceleration measurement signal of the ith layer after wavelet decomposition; fi(t) noise and higher-order modal components filtered out of the i-th layer acceleration measurement signal;
specifically, the step 1 specifically includes the following steps:
step 101: screening the measurement signals, the number of sampling points satisfying 2 to ensure the accuracy of the calculationnWherein n is a positive integer, n is 10 or 11, i.e. the number of points is 1024 or 2048, and the most abundant part of the structural fundamental frequency component in the measurement signal is selected for analysis (mainly the first 9 order frequency);
step 102: for discrete wavelet transform of screened measuring signal, firstly defining measuring signal
Figure GDA0002053822170000064
Continuous Wavelet Transform (CWT), Wf(a,. is) is
Figure GDA0002053822170000065
Where ψ is a selected base wavelet function; a is a proportionality coefficient; "+" indicates convolution;
in the frequency domain space, wavelet transform Wf(a,. cndot.) is represented by
Figure GDA0002053822170000066
For an arbitrary position (a)j,tk) Here tkIs a scaling factor of any discrete time point and corresponding discrete time form
Figure GDA0002053822170000071
(L is a non-negative integer, nvTo influence the parameters of the scaling factor, usually 32 or 64), we calculate the Discrete Wavelet Transform (DWT) using the following formula
Figure GDA0002053822170000072
In the formula (I), the compound is shown in the specification,nand
Figure GDA0002053822170000073
is the standard discrete Fourier Transform (Fourier Transform) and its inverse; "·" denotes a point multiplication;
Figure GDA0002053822170000074
is the sampling interval of the frequency domain space;
step 103: based on continuous wavelet transform coefficients, Wf(a,. cndot.) the corresponding real-valued frequency is obtained by the following equation
Figure GDA0002053822170000075
In the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000076
for effective noise filtering, a hard threshold parameter (gamma) is selected as
Figure GDA0002053822170000077
The MAD is a discrete wavelet coefficient of the matrix,
Figure GDA0002053822170000078
average absolute deviation of (d); blThe method is an augmentation factor related to the MAD, and the suggested value is 1.2-1.7;
Figure GDA0002053822170000079
is the magnitude of the discrete wavelet coefficient;
from equation (6), the point where the amplitude of the discrete wavelet transform coefficient is smaller than γ is discarded to effectively filter the noise effect, and based on equation (5), the real-valued frequency based on the discrete wavelet transform is obtained as
Figure GDA00020538221700000710
In the formula (I), the compound is shown in the specification,
Figure GDA00020538221700000711
and is
Figure GDA00020538221700000712
Step 104: based on the results obtained from equations (4) and (7)
Figure GDA00020538221700000713
And
Figure GDA00020538221700000714
defining de-noised acceleration signals
Figure GDA00020538221700000715
Discrete simultaneous extrusion wavelet transform
Figure GDA00020538221700000716
In the formula, the frequency of two divisions omegalSatisfies the conditions
Figure GDA0002053822170000081
Step 105: setting corresponding m band-pass filters, then carrying out inverse discrete synchronous extrusion wavelet transform, and denoising acceleration signals
Figure GDA0002053822170000082
Can be reconstructed as
Figure GDA0002053822170000083
In the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000084
is a normalization constant.
Step 2: constructing an analysis signal according to Hilbert transform, then obtaining an instantaneous phase angle and an amplitude according to the analysis signal, and then preliminarily identifying the main frequency and the damping ratio of the structure by the derivative of the natural logarithm of the corresponding instantaneous phase angle and amplitude to time;
specifically, the step 2 specifically includes the following steps:
step 201: for each modal component reconstructed by discrete synchronous wavelet transform, namely the modal component obtained by the formula (9), firstly, the analysis signal form of the corresponding j-th order modal component is obtained based on Hilbert transform
Figure GDA0002053822170000085
In the formula, Aij(t) is related to the frequency ωjThe amplitude of the corresponding reconstructed modal component at time t; thetaij(t) is the phase angle at the respective time instant;
step 202: based on equation (10), the transient frequency and damping ratio of the structure are obtained from the following equations
Figure GDA0002053822170000086
Figure GDA0002053822170000087
In the formula (I), the compound is shown in the specification,
Figure GDA0002053822170000088
the damping system modal frequency is the j-th order mode.
And step 3: and performing smooth prediction on the primary frequency and the damping ratio of the primary identification according to a least square linear fitting method to obtain an accurate identification result.
Specifically, the step 3 specifically includes the following steps:
step 301: at a phase angle thetaij(t) in the time t-dependent change diagram, obtaining a corresponding average straight line according to a least square linear fitting methodTo approximately represent the phase angle thetaij(t) the relation of the change along with the time t, and the predicted modal frequency omega of the damping system can be obtained by the slope of the fitting straight linedjNamely, obtained by using formula (11);
step 302: natural logarithm at amplitude lnAij(t) in the time t-dependent graph, selecting a corresponding time interval, and obtaining a corresponding average straight line by using a least square linear fitting method to approximately represent lnA in the time intervalij(t) as a function of t, the slope of the fitted line can be used to derive ξ in equation (12)jωjA value of (d);
step 303: according to ω obtained from the first two stepsdjAnd ξjωjAnd using a known relationship
Figure GDA0002053822170000091
The predicted structural modal frequency value and damping ratio value can be obtained.
Example (b):
the specific implementation flow of the invention is shown in figure 1. In fig. 1, the external excitation may be in the form of wind load, seismic load, explosive load, or the like. An example of the choice is an ultra-high skyscraper, the happy world tower, located in seoul, korea, as shown in fig. 2. The total height of the building is 555 meters, 123 layers above the ground and 6 layers below the ground, the construction is currently carried out, and the completion is expected in 2016. The acceleration sensors are respectively arranged on the 6 th underground layer, the 1 st, 24 th, 39 th, 64 th and 72 th above ground layers, and 34 sensors are arranged in total, and the specific positions are shown in detail in figure 3. In fig. 3 (b): (1) specific placement positions of the sensors are shown, South (South), North (North) and middle (Center), respectively; (2) the specific placement orientations of the sensors are shown, in the x, y and z directions, respectively. At 9-10 nights, 4-2-4-2015, acceleration signals are recorded, the sampling period is 0.005 (second), the maximum wind speed is 14 m/s, and the wind direction is southwest.
Step 1: and reconstructing the front 3-order modal component in the x direction by utilizing discrete synchronous extrusion wavelet transform. The concrete implementation steps are as follows:
(1) by screening signals of all layers, test data of the acceleration sensor arranged in the x direction at the north side position of 72 layers is selected, namely, the graph (a) in FIG. 4. If the number of sampling points is 2048, the signal segmentation duration is 2048 × 0.005 — 10.24 (seconds), and the last 10.24 (seconds) of the signal data measured by the position sensor is used as the analysis signal period for parameter identification, that is, fig. 4 (b).
(2) The time-frequency band relationship of the measurement signal after filtering noise using the discrete simultaneous wavelet transform is shown in fig. 5. Parameter n in a transformationvTaking 32; the hard threshold parameter gamma is taken to be 1.48.
(3) According to fig. 5, 3 bandpass filters are provided, each at 0.1Hz ═ ω1L<ω1<ω1U＝0.17Hz,0.3Hz＝ω1L<ω1<ω1U0.75Hz and 0.75Hz ω1L<ω1<ω1UAfter 1.7Hz and inverse discrete simultaneous extrusion wavelet transform, the first 3 rd order reconstructed mode components along the x-direction can be obtained, as shown in fig. 6.
Step 2: obtaining the phase angle theta by using Hilbert transformij(t) a time t-dependent relationship and a natural logarithm of magnitude lnAij(t) varies with time t. The concrete implementation steps are as follows:
(1) using equation (10), the analysis signal form of the corresponding reconstructed modal component is obtained.
(2) Obtaining a phase angle theta according to the corresponding analysis signalij(t) is plotted against time t, i.e. the corresponding dashed line in fig. 7.
(3) From the corresponding analysis signal, the natural logarithm of the amplitude lnA is obtainedij(t) is plotted against time t, i.e. the corresponding dashed line in fig. 8.
And step 3: and accurately predicting the 3 rd order modal frequency and the damping ratio of the super high-rise structure along the x direction based on a least square linear fitting method. The concrete implementation steps are as follows:
(1) predicting the phase angle theta by using the least square linear fitting method to obtain a corresponding average straight lineij(t) as a function of time t, i.e. the straight line shown by the corresponding solid line in FIG. 7, from the slope of which the predicted modal frequency ω of the damping system can be obtaineddjNamely, the application of the formula (11).
(2) Similarly, selecting corresponding time interval, and predicting lnA in the time interval by using a least square linear fitting method to obtain a corresponding average straight lineij(t) as a function of t, i.e., the straight line shown by the corresponding solid line in FIG. 8, from which the slope of the fitted straight line ξ in equation (12) can be derivedjωjThe value of (c).
(3) According to ω obtained from the first two stepsdjAnd ξjωjAnd using a known relationship
Figure GDA0002053822170000101
The predicted structural modal frequency value and damping ratio can be obtained, and in the actual engineering, the expression form of the natural vibration period is more accepted by engineers, so that the structural modal frequency value is converted into the natural vibration period value, and the specific numerical value is shown in table 1. In table 1, the self-oscillation period value identified by the present invention is compared with the value obtained by the finite element model to show the effectiveness of the method of the present invention. It should be noted that the period value of the natural vibration obtained by the proposed finite element model does not take the construction factors into consideration, and therefore, the adjustment of the corresponding stage is not performed.
TABLE 1
Figure GDA0002053822170000111
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.

Claims (2)

1. A method for identifying modal parameters of a super high-rise structure is characterized by comprising the following steps:
step 1: screening acceleration measurement signals of different structural layers, and selecting measurement signals containing main fundamental frequencies of the structure
Figure FDA0002548682590000011
Analysis was carried out with p ═ 1,2, …, nsRemoving the measurement signal according to the synchronous squeeze wavelet transform for the corresponding number of layers of the structureThen, based on the denoised measurement signal, the main modal components of the structure are decomposed and reconstructed, and then the measurement signal is expressed as:
Figure FDA0002548682590000012
wherein g is 1,2, …, ms，
Figure FDA0002548682590000013
Is the g-th main modal component, F, of the p-th layer acceleration measurement signal reconstructed after the synchronous extrusion wavelet decompositionp(t) is the noise and higher-order modal components filtered out of the p-th layer acceleration measurement signal;
step 2: constructing an analysis signal according to Hilbert transform, then obtaining a corresponding instantaneous phase angle and amplitude according to the analysis signal, and then preliminarily identifying the main frequency and the damping ratio of the structure by the derivative of the natural logarithm of the corresponding instantaneous phase angle and amplitude to time;
and step 3: performing smooth prediction on the primary frequency and the damping ratio of the primary identification according to a least square linear fitting method to obtain an accurate identification result;
the step 1 specifically comprises the following steps:
step 101: screening the measurement signals, the number of sampling points satisfying 2 to ensure the accuracy of the calculationnSelecting a measurement signal containing the main fundamental frequency of the structure for analysis;
step 102: for discrete wavelet transform of screened measuring signal, firstly defining measuring signal
Figure FDA0002548682590000014
Continuous Wavelet Transform (CWT), Wf(a,. is) is
Figure FDA0002548682590000015
Where ψ is a selected base wavelet function; a is a proportionality coefficient; "+" indicates convolution;
in the frequency domain space, wavelet transform Wf(a,. cndot.) is represented by
Figure FDA0002548682590000016
For an arbitrary position (a)j,tk) Here tkIs a scaling factor of any discrete time point and corresponding discrete time form
Figure FDA0002548682590000021
j＝1,2,…,LnvL is a non-negative integer, nvTo influence the parameters of the scaling factor, a Discrete Wavelet Transform (DWT) is calculated using the following formula, usually 32 or 64
Figure FDA0002548682590000022
In the formula (I), the compound is shown in the specification,nand
Figure FDA0002548682590000023
is the standard discrete Fourier Transform (Fourier Transform) and its inverse; "·" denotes a point multiplication;
Figure FDA0002548682590000024
λk2 pi k/n, k 0, …, n-1 being the sampling interval of the frequency domain space;
step 103: based on continuous wavelet transform coefficients, Wf(a,. cndot.) the corresponding real-valued frequency is obtained by the following equation
Figure FDA0002548682590000025
In the formula (I), the compound is shown in the specification,
Figure FDA0002548682590000026
for effective noise filtering, a hard threshold parameter (gamma) is selected as
Figure FDA0002548682590000027
The MAD is a discrete wavelet coefficient of the matrix,
Figure FDA0002548682590000028
average absolute deviation of (d); blThe coefficient of increase related to the MAD is 1.2-1.7;
Figure FDA0002548682590000029
is the magnitude of the discrete wavelet coefficient;
from equation (6), the point where the amplitude of the discrete wavelet transform coefficient is smaller than γ is discarded to effectively filter the noise effect, and based on equation (5), the real-valued frequency based on the discrete wavelet transform is obtained as
Figure FDA00025486825900000210
In the formula (I), the compound is shown in the specification,
Figure FDA00025486825900000211
and is
Figure FDA00025486825900000212
k＝0,…,n-1；
Step 104: based on the results obtained from equations (4) and (7)
Figure FDA00025486825900000213
And
Figure FDA00025486825900000214
defining de-noised acceleration signals
Figure FDA00025486825900000215
Discrete synchronous extrusion ofWavelet transform
Figure FDA00025486825900000216
In the formula, the frequency of two divisions omegalSatisfies the conditions
Figure FDA0002548682590000031
Step 105: set corresponding msThe acceleration signal is denoised by a band-pass filter and then a discrete synchronous extrusion wavelet inverse transformation
Figure FDA0002548682590000032
Can be reconstructed as
Figure FDA0002548682590000033
In the formula (I), the compound is shown in the specification,
Figure FDA0002548682590000034
is a normalization constant;
the step 2 specifically comprises the following steps:
step 201: for each modal component reconstructed by discrete simultaneous wavelet transform, i.e. the modal component obtained by equation (9), the analytical signal form of the corresponding g-th order modal component is obtained based on Hilbert transform
Figure FDA0002548682590000035
In the formula, Apg(t) is related to the frequency ωgThe amplitude of the corresponding reconstructed modal component at time t; thetapg(t) is the phase angle at the respective time instant;
step 202: based on equation (10), the transient frequency and damping ratio of the structure are obtained from the following equations
Figure FDA0002548682590000036
Figure FDA0002548682590000037
In the formula (I), the compound is shown in the specification,
Figure FDA0002548682590000038
the damping system modal frequency is a g-order modal;
the step 3 specifically comprises the following steps:
step 301: at a phase angle thetapg(t) in the time t-dependent change diagram, obtaining a corresponding average straight line according to a least square linear fitting method to approximately represent the phase angle thetapg(t) the relation of the change along with the time t, and the predicted modal frequency omega of the damping system can be obtained by the slope of the fitting straight linedgNamely, obtained by using formula (11);
step 302: natural logarithm at amplitude lnApg(t) in the time t-dependent graph, selecting a corresponding time interval, and obtaining a corresponding average straight line by using a least square linear fitting method to approximately represent lnA in the time intervalpg(t) as a function of t, the slope of the fitted line can be used to derive ξ in equation (12)gωgA value of (d);
step 303: according to ω obtained from the first two stepsdgAnd ξgωgAnd using a known relationship
Figure FDA0002548682590000041
The predicted structural modal frequency value and damping ratio value can be obtained.
2. The method for identifying modal parameters of super high-rise structure according to claim 1, wherein n is a positive integer and n is 10 or 11, i.e. the number of points used is 1024 or 2048.
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