CN105787655A - Superhigh-layer structure modal parameter identification method - Google Patents

Abstract

The invention discloses a superhigh-layer structure modal parameter identification method. Based on the feature that discretized synchrosqueezed wavelet transform (DSWT) can help to effectively analyze non-stationary, non-linear and high-noise signals and accurately reconstruct modal components of complex synthetic signals in the form of resonance components, and through combination with the feature that Hilbert transform (HT) can help to effectively analyze the resonance components and obtain instantaneous amplitude and frequencies, the purpose of identifying major frequencies and a damping ratio of a superhigh-layer structure is realized. In order to ensure identification accuracy of modal parameters, a linear least-square fit method (LLST) is introduced for smoothing a prediction result.

Description

Super high rise structure Modal Parameters Identification Modal Parameters Identification

Technical field

The invention belongs to monitoring structural health conditions field, be specifically related to a kind of super high rise structure Modal Parameters Identification mode Parameter identification method.

Background technology

Monitoring structural health conditions is evaluation structure health status, identifies structural damage position and the process of degree of injury.Superelevation The health monitoring of layer building structure is a step of extending structure key in service life, in view of the importance of super high rise structure self, Making works for the health monitoring of this structure has great Social benefit and economic benefit.Monitoring structural health conditions needs to solve The modal parameters identification being namely based on vibration signal of a major issue.Current existing wavelet analysis method (wavelet transform, WT) and empirical modal decoupling method (empirical mode decomposition, EMD) are deposited At the modal parameter of None-identified close frequencies and cannot measure vibration signal effectively identify knot from low amplitude value, strong noise The problem of structure basic friction angle parameter.

Synchronize extruding wavelet transformation and can effectively analyze non-stationary, non-linear and very noisy signal, exactly with resonance The modal components of the Reconfiguration of form complexity composite signal of component, and this kind of signal is very universal in actual building structure, such as Earthquake motion, wind load.

Summary of the invention

In view of this, offer a kind of super high rise structure Modal Parameters Identification mode ginseng is provided Number recognition methods.

For reaching above-mentioned purpose, the technical scheme is that and be achieved in that:

A kind of super high rise structure Modal Parameters Identification Modal Parameters Identification, it is characterised in that the method is passed through Following steps realize:

Step 1: the acceleration analysis signal of screening different structure layer, chooses the measurement letter comprising the main fundamental frequency of structure NumberIt is analyzed, i=1,2 ..., n is the corresponding number of plies of structure, removes measurement signal according to synchronizing extruding wavelet transformation Noise, then based on the measurement signal after denoising, decomposes and the primary modal component of reconfigured geometry, then measures signal and be expressed as:

${\stackrel{\·\·}{Z}}_i\left(t\right)\≈\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\stackrel{\·\·}{X}}_{ij}\left(t\right)+F_i\left(t\right)---\left(1\right)$

In formula,It is that i-th layer of acceleration of reconstruct after synchronized extruding wavelet decomposition is surveyed Front m main modal components of amount signal；F_iT () is the noise and high-order mode filtered out in i-th layer of acceleration analysis signal State component；

Step 2: according to Hilbert transform creation analysis signal, afterwards, obtains the most instantaneous according to described analysis signal Phase angle and amplitude, then tentatively identified structure main frequency by the natural logrithm of corresponding instantaneous phase angle and amplitude to the derivative of time And damping ratio；

Step 3: main frequency and the damping ratio of described preliminary identification is carried out according to least square linear fit method Smoothing prediction obtains recognition result accurately.

2, super high rise structure Modal Parameters Identification according to claim 1, it is characterised in that described step 1 Specifically include following steps:

Step 101: signal is measured in screening, for ensureing the precision calculated, the quantity of sampled point meets 2ⁿRequirement, wherein n Being a positive integer, it is proposed that n is 10 or 11, i.e. using quantity a little is 1024 or 2048, chooses and comprises the main fundamental frequency of structure Measurement signal be analyzed；

Step 102: the measurement signal for screening carries out wavelet transform, first definition measurement signalContinuous Wavelet transformation (continuous wavelet transform, CWT), W_f(a) is

$W_f(a,\·)=a^{-1/2}\stackrel{\‾}{\mathrm{\ψ}}(-\·/a)*{\stackrel{\·\·}{Z}}_i\left(t\right)---\left(2\right)$

In formula, ψ is the mother wavelet function selected；A is proportionality coefficient；" * " represents convolution；

At domain space, wavelet transformation W_f(a) is expressed as

${\hat{W}}_f(a,\mathrm{\λ})=a^{-1/2}{\widehat{\stackrel{\·\·}{Z}}}_i\left(\mathrm{\λ}\right)\widehat{\mathrm{\ψ}}\left(a\mathrm{\λ}\right)---\left(3\right)$

Then for optional position (a_j,t_k), t here_kIt is arbitrary discrete time point, the ratio of corresponding discrete-time version Example coefficientJ=1,2 ..., Ln_v, L is a nonnegative integer, n_vFor affecting the parameter of proportionality coefficient, generally take 32 or 64, we calculate wavelet transform (discrete wavelet transform, DWT) by equation below

${\tilde{W}}_{\tilde{f}}(a_j,\·)={\mathrm{\Γ}}_n^{-1}\[\left(r_n\tilde{f}\right)\·{\stackrel{\‾}{\widehat{\mathrm{\ψ}}}}_j\]---\left(4\right)$

In formula, Γ_nWithIt is standard off dissipating Fourier transformation (Fourier Transform) and its inverse transformation； " " represents dot product； ${\left({\widehat{\mathrm{\ψ}}}_j\right)}_k=a_j^{1/2}{\widehat{\mathrm{\ψ}}}_j\left(a_j{\mathrm{\λ}}_k\right);{\mathrm{\λ}}_k=2\mathrm{\π}k/n,(k=0,...,n-1)$ It is between the sampling of domain space Every；

Step 103: based on Continuous Wavelet Transform Coefficients, W_f(a), is obtained corresponding real-valued frequency by equation below

${\mathrm{\ω}}_f(a,b)=\frac{-i}{2\mathrm{\π}}\left(W_f{\left(a,b\right)}^{-1}\right){\∂}_b{W}_f(a,b)---\left(5\right)$

In formula, $i=\sqrt{-1};$

Cross noise filtering in order to effective, select hard critical parameter (the hard threshold parameter) γ to be

$\mathrm{\γ}=b_l\sqrt{2\log n}\·MAD\left({\left|{\tilde{W}}_{\tilde{f}}\right|}_{1:n_v}\right)---\left(6\right)$

MAD is discrete wavelet coefficient,Mean absolute deviation；b_lIt is the enhancement coefficient relevant to MAD, it is proposed that value is 1.2～1.7；It it is the amplitude of discrete wavelet coefficient；

From formula (6), the amplitude of the discrete wavelet transform coefficients point less than γ is rejected, thus effectively crosses noise filtering Impact, based on formula (5), then obtaining real-valued frequency based on wavelet transform is

${\widetilde{\mathrm{\ω}}}_{\tilde{f}}(a_j,t_k)=\frac{-i}{2\mathrm{\π}}\left({\tilde{W}}_{\tilde{f}}{\left(a_j,t_k\right)}^{-1}{\∂}_b{\tilde{W}}_{\tilde{f}}\right(a_j,t_k)---\left(7\right)$

In formula, ${\∂}_b{\hat{W}}_{\tilde{f}}(a_j,\·)={\mathrm{\Γ}}_n^{-1}\left(\right({\mathrm{\Γ}}_n\tilde{f})\·\∂{\widehat{\mathrm{\ψ}}}_j),$ And ${(\∂{\widehat{\mathrm{\ψ}}}_j)}_k=2{\mathrm{\πia}}_j^{1/2}{\mathrm{\λ}}_k\widehat{\mathrm{\ψ}}\left(a_j{\mathrm{\λ}}_k\right)/\mathrm{\Δ}t,(k=0,...,n-1).$

Step 104: based on by formula (4) and (7) gainedWithDefinition denoising acceleration signalDiscrete Synchronizing extruding wavelet transformation is

$T_f(\mathrm{\ω},b)=\underset{a_j:{\mathrm{\ω}}_f(a,b)\∈W_l,|W_f(a,b)>\mathrm{\γ}|}{\mathrm{\Σ}}{\tilde{W}}_{\tilde{f}}(a_j,b)a_j^{-1/2}(\log 2/n_v)---\left(8\right)$

In formula, two divided-frequency rate ω_lMeet condition $\{{\mathrm{\&omega;}}^{\&prime;}\&Element;R:|{\mathrm{\&omega;}}^{\&prime;}-{\mathrm{\&omega;}}_l|<|{\mathrm{\&omega;}}^{\&prime;}-{\mathrm{\&omega;}}_{l^{\&prime;}}|\&ForAll;l^{\&prime;}\&NotEqual;l\};$

Step 105: arrange corresponding m band filter, then carries out discrete synchronization and extrudes wavelet inverse transformation, then denoising adds Rate signalEach modal components can be reconfigured as

${\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t_k\right)=2R_{\mathrm{\&psi;}}^{-1}\mathrm{Re}\&lsqb;\underset{l\&Element;L_j\left(t_k\right)}{\mathrm{\&Sigma;}}{\tilde{T}}_{\tilde{f}}(w_l,t_k)\&rsqb;,(i=1,2,...,n),(j=1,2,...,m)---\left(9\right)$

In formula,It it is a generalized constant.

3, super high rise structure Modal Parameters Identification Modal Parameters Identification according to claim 1 and 2, its Being characterised by, described step 2 specifically includes following steps:

Step 201: the modal components obtained is reconstructed, i.e. by formula (9) by the discrete extruding wavelet transformation that synchronizes for each The modal components obtained, is primarily based on Hilbert transform and obtains the analysis signal form of corresponding jth rank modal components and be

$s_{aij}\left(t\right)={\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t\right)+i{\widetilde{\stackrel{\&CenterDot;\&CenterDot;}{X}}}_{ij}\left(t\right)=A_{ij}\left(t\right)e^{{\mathrm{i\&theta;}}_{ij}\left(t\right)}---\left(10\right)$

In formula, A_ijT () is and frequencies omega_jCorresponding reconstruct modal components is in the amplitude of t；θ_ijT () is the corresponding moment Phase angle；

Step 202: based on formula (10), instantaneous frequency and the damping ratio of structure are obtained by equation below

${\mathrm{\&omega;}}_j\left(t\right)=\frac{d\&lsqb;{\mathrm{\&theta;}}_{ij}\left(t\right)\&rsqb;}{dt}={\mathrm{\&omega;}}_{dj}---\left(11\right)$

${\mathrm{\&xi;}}_j\left(t\right)=\frac{d\&lsqb;{\mathrm{lnA}}_{ij}\left(t\right)\&rsqb;}{{\mathrm{\&omega;}}_{j}dt}---\left(12\right)$

In formula,Damping system model frequency for jth order mode state.

4, super high rise structure Modal Parameters Identification Modal Parameters Identification according to claim 3, it is special Levying and be, described step 3 specifically includes following steps:

Step 301: in phase angle theta_ijIn (t) t variation diagram in time, obtain accordingly according to least square linear fit method Article one, mean linear carrys out approximate representation phase angle theta_ijT the relation of () t in time change, then can be predicted by the slope of this fitting a straight line Damping system model frequency ω_dj, i.e. utilize formula (11) gained；

Step 302: in natural logrithm lnA of amplitude_ijIn (t) t variation diagram in time, choose utilization of corresponding period minimum Two take advantage of linear fit method to obtain a corresponding mean linear carrys out lnA in this period of approximate representation_ijT relation that () changes with t, Then can be obtained ξ in formula (12) by the slope of this fitting a straight line_jω_jValue；

Step 303: according to by the ω of gained in first two steps_djAnd ξ_jω_jValue, and utilize known relation formulaThe structural modal frequency value then can predicted and damping ratio.

Compared with prior art, beneficial effects of the present invention:

Low amplitude value, very noisy that the present invention can be surveyed from the state response sensor of super high rise structure and have close The vibration measuring signal of frequecy characteristic efficiently identifies fundamental mode of structures frequency and corresponding damping ratio.Thus overcome biography The defect that system wavelet analysis method and empirical modal decoupling method exist.

Accompanying drawing explanation

Fig. 1 is the implementing procedure of the embodiment of the present invention；

Fig. 2 is carefree world tower (the Lotte World of the concrete high-rise building-South Korea Seoul of the embodiment of the present invention Tower,LWT)；

Fig. 3 (a) is the acceleration transducer location arrangements figure along height of the embodiment of the present invention carefree world tower；

Fig. 3 (b) is embodiment of the present invention acceleration transducer along the position of floor and orientation layout drawing；

Fig. 4 (a) is 72 layers of north side acceleration transducer measured signal in the x-direction that the embodiment of the present invention selects；

Fig. 4 (b) is the analysis signal of embodiment of the present invention screening；

Fig. 5 is the time frequency distribution map of embodiment of the present invention signal；

Fig. 6 is the modal components reconstruct of the embodiment of the present invention；

Fig. 7 is the phase angle theta of the embodiment of the present invention_ij(t) t variation diagram in time and least square linear fit straight line.Wherein, Figure (a) is first mode reaction；Figure (b) is second mode reaction；Figure (c) is the 3rd mode reaction；

Fig. 8 is natural logrithm lnA of the amplitude of the embodiment of the present invention_ijT () t variation diagram in time and least square linear are intended Close straight line.Wherein, figure (a) is first mode reaction；Figure (b) is second mode reaction；Figure (c) is the 3rd mode reaction.

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, right The present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, and It is not used in the restriction present invention.

The present invention synchronizes extruding wavelet transformation (discretized synchrosqueezed wavelet based on discrete Transform, DSWT) can effectively analyze non-stationary, non-linear and very noisy signal, exactly with the form of harmonic components The feature of the modal components of the complicated composite signal of reconstruct, and combine Hilbert transform (Hilbert transform, HT) and can have Effect analyzes harmonic components, obtains the feature of instantaneous amplitude and frequency, thus reaches to identify super high rise structure main frequency and damping The purpose of ratio.In order to ensure to identify the accuracy of modal parameter, introduce least square linear fit method (linear least- Square fit, LLST) carry out the result of smoothing prediction.

The embodiment of the present invention provides a kind of super high rise structure Modal Parameters Identification Modal Parameters Identification, the method Realized by following steps:

Step 1: the acceleration analysis signal of screening different structure layer, chooses and comprises the main fundamental frequency of structure and (typically select Select front 9 rank) measurement signalN is the corresponding number of plies of structure) it is analyzed, according to synchronizing extruding Wavelet transformation removes the noise measuring signal, then based on the measurement signal after denoising, decomposes and the primary modal of reconfigured geometry Component (filters the higher-order modal components that impact is less), then measure signal and be expressed as:

${\stackrel{\&CenterDot;\&CenterDot;}{Z}}_i\left(t\right)\&ap;\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t\right)+F_i\left(t\right)---\left(1\right)$

In formula,It is that i-th layer of acceleration of reconstruct after synchronized extruding wavelet decomposition is surveyed Front m main modal components of amount signal；F_iT () is the noise and high-order mode filtered out in i-th layer of acceleration analysis signal State component；

Specifically, described step 1 specifically includes following steps:

Step 101: signal is measured in screening, for ensureing the precision calculated, the quantity of sampled point meets 2ⁿRequirement, wherein n Being a positive integer, it is proposed that n is 10 or 11, i.e. using quantity a little is 1024 or 2048, chooses the basic frequency of structure in measurement signal The part that rate composition enriches the most is analyzed (the most front 9 order frequencies)；

Step 102: the measurement signal for screening carries out wavelet transform, first definition measurement signalContinuous Wavelet transformation (continuous wavelet transform, CWT), W_f(a) is

$W_f(a,\&CenterDot;)=a^{-1/2}\stackrel{\&OverBar;}{\mathrm{\&psi;}}(-\&CenterDot;/a)*{\stackrel{\&CenterDot;\&CenterDot;}{Z}}_i\left(t\right)---\left(2\right)$

In formula, ψ is the mother wavelet function selected；A is proportionality coefficient；" * " represents convolution；

At domain space, wavelet transformation W_f(a) is expressed as

${\hat{W}}_f(a,\mathrm{\&lambda;})=a^{-1/2}{\widehat{\stackrel{\&CenterDot;\&CenterDot;}{Z}}}_i\left(\mathrm{\&lambda;}\right)\widehat{\mathrm{\&psi;}}\left(a\mathrm{\&lambda;}\right)---\left(3\right)$

Then for optional position (a_j,t_k), t here_kIt is arbitrary discrete time point, the ratio of corresponding discrete-time version Example coefficientJ=1,2 ..., Ln_v(L is a nonnegative integer, n_vFor affecting the parameter of proportionality coefficient, generally take 32 or 64), we calculate wavelet transform (discrete wavelet transform, DWT) by equation below

${\tilde{W}}_{\tilde{f}}(a_j,\&CenterDot;)={\mathrm{\&Gamma;}}_n^{-1}\&lsqb;\left({\mathrm{\&Gamma;}}_n\tilde{f}\right)\&CenterDot;{\stackrel{\&OverBar;}{\widehat{\mathrm{\&psi;}}}}_j\&rsqb;---\left(4\right)$

In formula, Γ_nWithIt is standard off dissipating Fourier transformation (Fourier Transform) and its inverse transformation； " " represents dot product； ${\left({\widehat{\mathrm{\&psi;}}}_j\right)}_k=a_j^{1/2}{\widehat{\mathrm{\&psi;}}}_j\left(a_j{\mathrm{\&lambda;}}_k\right);{\mathrm{\&lambda;}}_k=2\mathrm{\&pi;}k/n,(k=0,...,n-1)$ It is between the sampling of domain space Every；

Step 103: based on Continuous Wavelet Transform Coefficients, W_f(a), is obtained corresponding real-valued frequency by equation below

${\mathrm{\&omega;}}_f(a,b)=\frac{-i}{2\mathrm{\&pi;}}\left(W_f{\left(a,b\right)}^{-1}\right){\&part;}_b{W}_f(a,b)---\left(5\right)$

In formula, $i=\sqrt{-1};$

Cross noise filtering in order to effective, select hard critical parameter (the hard threshold parameter) γ to be

$\mathrm{\&gamma;}=b_l\sqrt{2\log n}\&CenterDot;MAD\left({\left|{\tilde{W}}_{\tilde{f}}\right|}_{1:n_v}\right)---\left(6\right)$

MAD is discrete wavelet coefficient,Mean absolute deviation；b_lIt is the enhancement coefficient relevant to MAD, it is proposed that value is 1.2～1.7；It it is the amplitude of discrete wavelet coefficient；

From formula (6), the amplitude of the discrete wavelet transform coefficients point less than γ is rejected, thus effectively crosses noise filtering Impact, based on formula (5), then obtaining real-valued frequency based on wavelet transform is

${\widetilde{\mathrm{\&omega;}}}_{\tilde{f}}(a_j,t_k)=\frac{-i}{2\mathrm{\&pi;}}\left({\tilde{W}}_{\tilde{f}}{\left(a_j,t_k\right)}^{-1}{\&part;}_b{\tilde{W}}_{\tilde{f}}\right(a_j,t_k)---\left(7\right)$

In formula, ${\&part;}_b{\hat{W}}_{\tilde{f}}(a_j,\&CenterDot;)={\mathrm{\&Gamma;}}_n^{-1}\left(\right({\mathrm{\&Gamma;}}_n\tilde{f})\&CenterDot;\&part;{\widehat{\mathrm{\&psi;}}}_j),$ And ${(\&part;{\widehat{\mathrm{\&psi;}}}_j)}_k=2{\mathrm{\&pi;ia}}_j^{1/2}{\mathrm{\&lambda;}}_k\widehat{\mathrm{\&psi;}}\left(a_j{\mathrm{\&lambda;}}_k\right)/\mathrm{\&Delta;}t,(k=0,...,n-1).$

Step 104: based on by formula (4) and (7) gainedWithDefinition denoising acceleration signalDiscrete Synchronizing extruding wavelet transformation is

$T_f(\mathrm{\&omega;},b)=\underset{a_j:{\mathrm{\&omega;}}_f(a,b)\&Element;W_l,|W_f(a,b)>\mathrm{\&gamma;}|}{\mathrm{\&Sigma;}}{\tilde{W}}_{\tilde{f}}(a_j,b)a_j^{-1/2}(\log 2/n_v)---\left(8\right)$

In formula, two divided-frequency rate ω_lMeet condition $\{{\mathrm{\&omega;}}^{\&prime;}\&Element;R:|{\mathrm{\&omega;}}^{\&prime;}-{\mathrm{\&omega;}}_l|<|{\mathrm{\&omega;}}^{\&prime;}-{\mathrm{\&omega;}}_{l^{\&prime;}}|\&ForAll;l^{\&prime;}\&NotEqual;l\};$

Step 105: arrange corresponding m band filter, then carries out discrete synchronization and extrudes wavelet inverse transformation, then denoising adds Rate signalEach modal components can be reconfigured as

${\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t_k\right)=2R_{\mathrm{\&psi;}}^{-1}\mathrm{Re}\&lsqb;\underset{l\&Element;L_j\left(t_k\right)}{\mathrm{\&Sigma;}}{\tilde{T}}_{\tilde{f}}(w_l,t_k)\&rsqb;,(i=1,2,...,n),(j=1,2,...,m)---\left(9\right)$

In formula,It it is a generalized constant.

Step 2: according to Hilbert transform creation analysis signal, afterwards, obtains instantaneous phase angle according to described analysis signal And amplitude, then by the natural logrithm of corresponding instantaneous phase angle and amplitude, the derivative of time is tentatively identified structure main frequency and resistance Buddhist nun's ratio；

Specifically, described step 2 specifically includes following steps:

Step 201: the modal components obtained is reconstructed, i.e. by formula (9) by the discrete extruding wavelet transformation that synchronizes for each The modal components obtained, is primarily based on Hilbert transform and obtains the analysis signal form of corresponding jth rank modal components and be

$s_{aij}\left(t\right)={\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t\right)+i{\widetilde{\stackrel{\&CenterDot;\&CenterDot;}{X}}}_{ij}\left(t\right)=A_{ij}\left(t\right)e^{{\mathrm{i\&theta;}}_{ij}\left(t\right)}---\left(10\right)$

In formula, A_ijT () is and frequencies omega_jCorresponding reconstruct modal components is in the amplitude of t；θ_ijT () is the corresponding moment Phase angle；

Step 202: based on formula (10), instantaneous frequency and the damping ratio of structure are obtained by equation below

${\mathrm{\&omega;}}_j\left(t\right)=\frac{d\&lsqb;{\mathrm{\&theta;}}_{ij}\left(t\right)\&rsqb;}{dt}={\mathrm{\&omega;}}_{dj}---\left(11\right)$

${\mathrm{\&xi;}}_j\left(t\right)=\frac{d\&lsqb;{\mathrm{lnA}}_{ij}\left(t\right)\&rsqb;}{{\mathrm{\&omega;}}_{j}dt}---\left(12\right)$

In formula,Damping system model frequency for jth order mode state.

Step 3: main frequency and the damping ratio of described preliminary identification is carried out according to least square linear fit method Smoothing prediction obtains recognition result accurately.

Specifically, described step 3 specifically includes following steps:

Step 301: in phase angle theta_ijIn (t) t variation diagram in time, obtain accordingly according to least square linear fit method Article one, mean linear carrys out approximate representation phase angle theta_ijT the relation of () t in time change, then can be predicted by the slope of this fitting a straight line Damping system model frequency ω_dj, i.e. utilize formula (11) gained；

Step 302: in natural logrithm lnA of amplitude_ijIn (t) t variation diagram in time, choose utilization of corresponding period minimum Two take advantage of linear fit method to obtain a corresponding mean linear carrys out lnA in this period of approximate representation_ijT relation that () changes with t, Then can be obtained ξ in formula (12) by the slope of this fitting a straight line_jω_jValue；

Step 303: according to by the ω of gained in first two steps_djAnd ξ_jω_jValue, and utilize known relation formulaThe structural modal frequency value then can predicted and damping ratio.

Embodiment:

The present invention is embodied as flow process as shown in Figure 1.In FIG, the concrete form of external drive can be wind load, Shake load, explosive load etc..The instantiation selected is the Super High skyscraper being seated South Korea Seoul, the carefree world Tower, as shown in Figure 2.This building height overall 555 meters, 123 layers on the ground, 6 layers, underground, currently construct, it is contemplated that complete the end of the year 2016 Work.Acceleration transducer is arranged in the 6th layer, underground, on the ground the 1st layer, 24 layers, 39 layers, 64 layers and 72 layers, amounts to 34 biographies Sensor, particular location refers to Fig. 3.In Fig. 3 (b): (1) shows the concrete position of sensor, respectively southern side (South), north side (North) and middle part (Center)；(2) show sensor specifically arranges orientation, respectively x, y and Z to.In night 9 on April 2nd, 2015 up to 10 time, acceleration signal is recorded, and the sampling period was 0.005 (second), maximum wind velocity Being 14 meter per seconds, wind direction is southwest.

Step 1: utilize the discrete extruding wavelet transformation that synchronizes to reconstruct 3 rank modal components before x direction.Implementing step is:

(1) by sieving each layer signal, select position, 72 layers of north side along x to the number of the acceleration transducer test arranged According to, i.e. Fig. 4 (a).The quantity of sampled point takes 2048, then a length of 2048x0.005=10.24 (second) during the segmentation of signal, through point Analysis, select last 10.24 (second) sections of this position sensor measured signal data as the analysis signal of parameter identification time Section, i.e. Fig. 4 (b).

(2) discrete synchronization is utilized to extrude the T/F band relation such as Fig. 5 measuring signal after wavelet transformation crosses noise filtering Shown in.Parameter n in conversion_vTake 32；Hard critical parameter γ takes 1.48.

(3) according to Fig. 5, corresponding 3 band filters, respectively 0.1Hz=ω are set_1L<ω₁<ω_1U=0.17Hz, 0.3Hz=ω_1L<ω₁<ω_1U=0.75Hz and 0.75Hz=ω_1L<ω₁<ω_1U=1.7Hz, then carries out discrete synchronization and squeezes Pressure wavelet inverse transformation, then available front 3 rank reconstruct modal components in the x-direction, are specifically shown in Fig. 6.

Step 2: utilize Hilbert transform to obtain phase angle theta_ij(t) t variation relation in time and the natural logrithm of amplitude lnA_ij(t) t variation relation in time.Implementing step is:

(1) utilize formula (10), reconstructed the analysis signal form of modal components accordingly.

(2) according to analyzing signal accordingly, phase angle theta is obtained_ijCorresponding dotted line in (t) t variation relation figure, i.e. Fig. 7 in time Shown curve.

(3) according to analyzing signal accordingly, natural logrithm lnA of amplitude is obtained_ijT () t variation relation figure in time, i.e. schemes Curve shown in corresponding dotted line in 8.

Step 3: based on least square linear fit method, the most front 3 order mode state frequencies of this super high rise structure of Accurate Prediction Rate and damping ratio.Implementing step is:

(1) least square linear fit method is utilized to obtain a corresponding mean linear to predict phase angle theta_ijT () at any time Between t change relation, i.e. corresponding straight line shown in solid in Fig. 7, the slope of this fitting a straight line the damping system mould can predicted State frequencies omega_dj, i.e. the utilization of formula (11).

(2) in like manner, choosing the corresponding period utilizes least square linear fit method to obtain a corresponding mean linear LnA in predicting this period_ijCorresponding straight line shown in solid in t relation that () changes with t, i.e. Fig. 8, by the slope of this fitting a straight line ξ in formula (12) can be obtained_jω_jValue.

(3) according to by the ω of gained in first two steps_djAnd ξ_jω_jValue, and utilize known relation formulaThen The structural modal frequency value that can predict and damping ratio, in Practical Project, the expression-form of natural vibration period more engineer institute Accepting, thus transformation structure model frequency value is value natural vibration period, concrete numerical value is shown in Table 1.In Table 1, identification of the present invention from Periodic quantity of shaking has carried out corresponding contrast to FEM (finite element) model income value, to show the effectiveness of institute of the present invention extracting method.Need note Meaning, FEM (finite element) model gained value natural vibration period carried does not considers construction factor, thus does not carry out the tune of respective stage Whole.

Table 1

The above, only presently preferred embodiments of the present invention, it is not intended to limit protection scope of the present invention.

Claims (4)

1. a super high rise structure Modal Parameters Identification Modal Parameters Identification, it is characterised in that the method by with Lower step realizes:

Step 1: the acceleration analysis signal of screening different structure layer, chooses the measurement signal comprising the main fundamental frequency of structureIt is analyzed, i=1,2 ..., n is the corresponding number of plies of structure, removes making an uproar of measurement signal according to synchronizing extruding wavelet transformation Sound, then based on the measurement signal after denoising, decomposes and the primary modal component of reconfigured geometry, then measures signal and be expressed as:

${\stackrel{\&CenterDot;\&CenterDot;}{Z}}_i\left(t\right)\&ap;\underset{j=1}{\overset{m}{\&Sigma;}}{\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t\right)+F_i\left(t\right)---\left(1\right)$

In formula,It is i-th layer of acceleration analysis letter of reconstruct after synchronized extruding wavelet decomposition Number modal components main for front m；F_iT () is the noise filtered out in i-th layer of acceleration analysis signal and high order mode divides Amount；

Step 2: according to Hilbert transform creation analysis signal, afterwards, obtains corresponding instantaneous phase angle according to described analysis signal And amplitude, then by the natural logrithm of corresponding instantaneous phase angle and amplitude, the derivative of time is tentatively identified structure main frequency and resistance Buddhist nun's ratio；

Step 3: main frequency and the damping ratio of described preliminary identification is smoothed according to least square linear fit method Prediction obtains recognition result accurately.

Super high rise structure Modal Parameters Identification the most according to claim 1, it is characterised in that described step 1 is concrete Comprise the following steps:

Step 101: signal is measured in screening, for ensureing the precision calculated, the quantity of sampled point meets 2ⁿRequirement, wherein n is one just Integer, it is proposed that n is 10 or 11, i.e. using quantity a little is 1024 or 2048, chooses the measurement comprising the main fundamental frequency of structure Signal is analyzed；

Step 102: the measurement signal for screening carries out wavelet transform, first definition measurement signalContinuous wavelet Conversion (continuous wavelet transform, CWT), W_f(a) is

$W_f(a,\&CenterDot;)=a^{-1/2}\stackrel{-}{\mathrm{\&psi;}}(-\&CenterDot;/a)*\stackrel{..}{Z_i}\left(t\right)---\left(2\right)$

In formula, ψ is the mother wavelet function selected；A is proportionality coefficient；" * " represents convolution；

At domain space, wavelet transformation W_f(a) is expressed as

${\hat{W}}_f(a,\mathrm{\&lambda;})=a^{1/2}\stackrel{\widehat{..}}{Z_i}\left(\mathrm{\&lambda;}\right)\widehat{\mathrm{\&psi;}}\left(\mathrm{a\&lambda;}\right)---\left(3\right)$

Then for optional position (a_j,t_k), t here_kIt is arbitrary discrete time point, the ratio system of corresponding discrete-time version NumberJ=1,2 ..., Ln_v, L is a nonnegative integer, n_vFor affecting the parameter of proportionality coefficient, generally take 32 or 64, I Calculate wavelet transform (discrete wavelet transform, DWT) by equation below

${\tilde{W}}_{\tilde{f}}(a_j,\&CenterDot;)={\mathrm{\&Gamma;}}_n^{-1}\&lsqb;\left({\mathrm{\&Gamma;}}_n\tilde{f}\right)\&CenterDot;{\stackrel{\&OverBar;}{\widehat{\mathrm{\&psi;}}}}_j\&rsqb;---\left(4\right)$

In formula, Γ_nWithIt is standard off dissipating Fourier transformation (Fourier Transform) and its inverse transformation；“·” Represent dot product；λ_k=2 π k/n (k=0 ..., n-1) it is sampling interval of domain space；

Step 103: based on Continuous Wavelet Transform Coefficients, W_f(a), is obtained corresponding real-valued frequency by equation below

${\mathrm{\&omega;}}_f(a,b)=\frac{-i}{2\mathrm{\&pi;}}\left(W_f{\left(a,b\right)}^{-1}\right){\&part;}_b{W}_f(a,b)---\left(5\right)$

In formula, $i=\sqrt{-1};$

Cross noise filtering in order to effective, select hard critical parameter (the hard threshold parameter) γ to be

$\mathrm{\&gamma;}=b_l\sqrt{2\log n}\&CenterDot;MAD\left(\right|{\tilde{W}}_{\tilde{f}}{|}_{1:n_v})---\left(6\right)$

MAD is discrete wavelet coefficient,Mean absolute deviation；b_lIt is the enhancement coefficient relevant to MAD, it is proposed that value is 1.2 ～1.7；It it is the amplitude of discrete wavelet coefficient；

From formula (6), the amplitude of the discrete wavelet transform coefficients point less than γ is rejected, thus effectively crosses noise filtering shadow Ringing, based on formula (5), then obtaining real-valued frequency based on wavelet transform is

${\tilde{W}}_{\tilde{f}}(a_j,t_f)=\frac{-i}{2\mathrm{\&pi;}}\left(\widetilde{W_{\stackrel{~}{f}}}{(a,t_k)}^{-1}{\&PartialD;}_b\widetilde{W_{\stackrel{~}{f}}(a_j,t_k)}\right)---\left(7\right)$

In formula, ${\&part;}_b{\hat{W}}_{\tilde{f}}(a_j,\&CenterDot;)={\mathrm{\&Gamma;}}_n^{-1}\left(\right({\mathrm{\&Gamma;}}_n\tilde{f})\&CenterDot;\&part;{\widehat{\mathrm{\&psi;}}}_j),$ And ${(\&part;{\widehat{\mathrm{\&psi;}}}_j)}_k=2{\mathrm{\&pi;ia}}_j^{1/2}{\mathrm{\&lambda;}}_k\widehat{\mathrm{\&psi;}}\left(a_j{\mathrm{\&lambda;}}_k\right)/\mathrm{\&Delta;}t$ $(k=0,...,n-1).$

Step 104: based on by formula (4) and (7) gainedWithDefinition denoising acceleration signalDiscrete synchronization squeeze Pressure wavelet transformation is

$T_f\left(\mathrm{\&omega;},b\right)=\underset{a_j:{\mathrm{\&omega;}}_f\left(a,b\right)\&Element;W_l,\left|W_f\left(a,b\right)>\mathrm{\&gamma;}\right|}{\mathrm{\&Sigma;}}{\tilde{W}}_{\tilde{f}}\left(a_j,b\right)a_j^{-1/2}\left(\log 2/n_v\right)---\left(8\right)$

In formula, two divided-frequency rate ω_lMeet condition $\{{\mathrm{\&omega;}}^{\&prime;}\&Element;R:|{\mathrm{\&omega;}}^{\&prime;}-{\mathrm{\&omega;}}_l|<|{\mathrm{\&omega;}}^{\&prime;}-{\mathrm{\&omega;}}_{l^{\&prime;}}|\&ForAll;l^{\&prime;}\&NotEqual;l\};$

Step 105: arrange corresponding m band filter, then carries out discrete synchronization and extrudes wavelet inverse transformation, then denoising acceleration SignalEach modal components can be reconfigured as

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t_k\right)=2R_{\mathrm{\&psi;}}^{-1}\mathrm{Re}\&lsqb;\underset{l\&Element;L_j\left(t_k\right)}{\mathrm{\&Sigma;}}{\tilde{T}}_{\tilde{f}}\left(w_l,t_k\right)\&rsqb;,\left(i=1,2,\mathrm{...},n\right),(j=1,2,\mathrm{...},\\ m)---(9)\end{array}$

In formula,It it is a generalized constant.

Super high rise structure Modal Parameters Identification Modal Parameters Identification the most according to claim 1 and 2, its feature Being, described step 2 specifically includes following steps:

Step 201: by the discrete extruding wavelet transformation that synchronizes, the modal components obtained is reconstructed for each, is i.e. obtained by formula (9) Modal components, be primarily based on Hilbert transform and obtain the analysis signal form of corresponding jth rank modal components and be

$s_{aij}\left(t\right)={\stackrel{\&CenterDot;\&CenterDot;}{X}}_{ij}\left(t\right)+i{\widetilde{\stackrel{\&CenterDot;\&CenterDot;}{X}}}_{ij}\left(t\right)=A_{ij}\left(t\right)e^{{\mathrm{i\&theta;}}_{ij}\left(t\right)}---\left(10\right)$

In formula, A_ijT () is and frequencies omega_jCorresponding reconstruct modal components is in the amplitude of t；θ_ijT () is the phase in corresponding moment Angle；

Step 202: based on formula (10), instantaneous frequency and the damping ratio of structure are obtained by equation below

${\mathrm{\&omega;}}_j\left(t\right)=\frac{d\&lsqb;{\mathrm{\&theta;}}_{ij}\left(t\right)\&rsqb;}{dt}={\mathrm{\&omega;}}_{dj}---\left(11\right)$

${\mathrm{\&xi;}}_j\left(t\right)=\frac{d\&lsqb;{\mathrm{lnA}}_{ij}\left(t\right)\&rsqb;}{{\mathrm{\&omega;}}_{j}dt}---\left(12\right)$

In formula,Damping system model frequency for jth order mode state.

Super high rise structure Modal Parameters Identification Modal Parameters Identification the most according to claim 3, its feature exists Following steps are specifically included in, described step 3:

Step 301: in phase angle theta_ijIn (t) t variation diagram in time, obtain corresponding one according to least square linear fit method Mean linear carrys out approximate representation phase angle theta_ijThe relation of (t) t in time change, then the resistance can predicted by the slope of this fitting a straight line Buddhist nun system model frequency ω_dj, i.e. utilize formula (11) gained；

Step 302: in natural logrithm lnA of amplitude_ijT, in () t variation diagram in time, choosing the corresponding period utilizes least square Linear fit method obtains a corresponding mean linear and carrys out lnA in this period of approximate representation_ijT relation that () changes with t, then by The slope of this fitting a straight line can obtain ξ in formula (12)_jω_jValue；

Step 303: according to by the ω of gained in first two steps_djAnd ξ_jω_jValue, and utilize known relation formulaThen The structural modal frequency value that can predict and damping ratio.