CN106548031A - A kind of Identification of Modal Parameter - Google Patents

Abstract

The invention belongs to structural health detection field, more particularly, to a kind of Identification of Modal Parameter.The characteristic decomposed according to the time scale of data itself using Empirical mode decomposition by Identification of Modal Parameter provided by the present invention, vibration signal is resolved into into the intrinsic mode function with different frequency composition by different frequency range, specific basic function need not be chosen non-stationary, nonlinear data are adaptive to than data processing methods such as Fourier transform, wavelet transformations.Therefore, improved Fast Bayesian FFT methods can preferably process non-stationary process, identify the optimal estimation value and uncertainty of modal parameters under non-stationary ecitation.Meanwhile, improved Fast Bayesian FFT methods are applied to the Modal Parameter Identification of close frequency structure and Low SNR signal simultaneously so as to the situation for no longer being limited and can preferably suitable for low signal-to-noise ratio by wideband structure.

Description

A kind of Identification of Modal Parameter

Technical field

The invention belongs to structural health detection field, more particularly, to a kind of Identification of Modal Parameter.

Background technology

Modal parameters identification refer to by build output in response to determining that in structure physical parameter, such as self-vibration frequency The parameters such as rate, structural damping, the vibration shape.During building structure health detection, the measure error due to testing sensor is extraneous Noise etc. affects, and contains substantial amounts of uncertain factor in distinguishing structural mode.In existing modal idenlification theory, Zhi Nengshi Do not go out the estimation of modal parameters, and the statistical property of analytical structure parameter and the uncertainty of quantization parameter cannot be specified.

Bayesian FFT methods strictly observe the physical model of statistical error, it is assumed that the acceleration responsive signal sample of actual measurement Originally actual value and measure error sum be can be expressed as.Using bayesian theory, posterior probability is calculated according to actual observation record close Degree function, can not only effectively recognize the optimal estimation value of modal parameter, moreover it is possible to according to the Hessian squares of log-likelihood function Battle array solves its modal parameter posteriority covariance, calculates the coefficient of variation of modal parameter, quantifies the uncertainty of recognition result.For The fast method that the single mode of a certain resonance bands is proposed, Fast Bayesian FFT methods also substantially increase the method Computational efficiency, the method for enabling effectively applied.

Fast Bayesian FFT methods employ in the calculation stationary signal it is assumed that only be suitable for stationary random process, And actual high wind load and earthquake load mostly are non-stationary process, corresponding structural response is also significant non-stationary process, Therefore the modal parameters having under this kind of actual hazardous condition of the method None- identified under the excitation of notable non-stationary property.

For a certain resonance bands show the method can only the structure-oriented natural frequency of vibration there is the version of significant difference, Between different modalities, nothing is significantly obscured, the interior control action by single mode of single frequency band.And the high level being widely used at present is built Mostly close frequency structure is built, the natural frequency of vibration is sufficiently close under the structure difference vibration shape, it is difficult to select suitable resonance bands to be separated.

Rapid design method in Fast Bayesian FFT methods then in employ high s/n ratio it is assumed that in environmental noise Substantially, in the case that measure error is significantly or structural response is weaker, signal to noise ratio is difficult to meet and requires.

The content of the invention

It is an object of the present invention to for the problem with present on, there is provided a kind of Identification of Modal Parameter.

For this purpose, the above-mentioned purpose of the present invention is achieved through the following technical solutions：

A kind of Identification of Modal Parameter, it is characterised in that methods described in turn includes the following steps：

(1) the structural response TIME HISTORY SIGNAL obtained under environmental excitation is recorded by structural health detecting systemTo this TIME HISTORY SIGNAL power spectral transformation, extracts respective frequencies at each peak value, as the approximation of natural frequency of structures；

(2) centered on respective frequencies at each peak value extracted in step (1), using bandpass filter to measurement signalPretreatment, extracts the TIME HISTORY SIGNAL of mode corresponding to the centre frequency；

(3) filtered signal is decomposed using Empirical mode decomposition, it is containing different frequency to be broken down into Intrinsic mode function, and time frequency analysis or power spectrumanalysis are carried out, determine the main frequency of each intrinsic mode function, i.e. time-histories letter After number being fourier transformed, its frequency corresponding to amplitude higher position；

(4) approximation according to natural frequency of structures, chooses the component of the intrinsic mode function of respective frequencies band

(5) using Fast Bayesian FFT methods recognize single mode under modal parameters optimal estimation value and its Corresponding posteriority is uncertain；

(6) repeat step (3) to (5), until the result of mode needed for identification is completed all.

Preferably, time frequency analysis are carried out using Hilbert conversion in step (3)：

In formula：It is right to representMake Hilbert conversion, instantaneous amplitude Phase angleLinear fit is carried out to which and can obtain θ (t)=ω t+ φ₀；

Structure instantaneous frequency is obtained by following formula (2), is determined by the excursion of structure instantaneous frequency ω (t)Master Want frequency,

Preferably, in step (5) optimal estimation value by following formula (3) do maximum estimate obtain, posteriority uncertainty under The Hessian matrix inversions of formula (3) are calculated,

F in formula, ξ, S, σ², Φ respectively structure frequency, damping, power spectral density of mode force, measure error root mean square and the vibration shape.N is Measurement channel number, F_kWith G_kForJing after FFT, frequency is f_kThe real part and imaginary part of place's transformed value, k is respective frequencies point sequence Number, N_fFor Frequency point sum.D_kWith A to calculate intermediate variable, can be calculated by formula (4) and formula (5) respectively.

Fast Bayesian FFT methods are improved using Empirical mode decomposition (EMD), which are expanded in modal idenlification field The scope of application, improve parameter identification precision and method robustness.

There is N for one_dThe system of the individual free degree, the structure acceleration response under external load excitation can be designated as：

Structure acceleration response can be decomposed as the following formula using EMD：

WhereinTo decompose the jth rank modal response for obtaining, c_iT () is the i-th rank intrinsic mode function, r (t) is remaining Amount.

Fourier transformation can be calculated as follows：

Meanwhile,Can be expressed from the next：

WhereinFor correlation function.

For positive damping system,For subtraction function.Therefore work as N → ∞,The limit be intended to 0, show F_jkWith F_jlIt is approximate independent.According to central-limit theorem, the augmented matrix Z of definition_jk=[F_jk G_jk]^TMeet Joint Gaussian distribution, therefore, Inherent parameter can be recognized using Bayesian FFT methods.

Identification of Modal Parameter provided by the present invention using Empirical mode decomposition according to data itself when Between the characteristic decomposed of yardstick, vibration signal is resolved into into the intrinsic mode function with different frequency composition by different frequency range (IMF), it is not necessary to choose specific basic function be adaptive to than data processing methods such as Fourier transform, wavelet transformations it is non-flat Surely, nonlinear data.Therefore, improved Fast Bayesian FFT methods can preferably process non-stationary process, identify non- The optimal estimation value and uncertainty of modal parameters under steady excitation.Meanwhile, improved Fast Bayesian FFT sides Method is simultaneously applied to the Modal Parameter Identification of close frequency structure and Low SNR signal, method itself comprising the denoising to signal and Filtering, further meets former method to high s/n ratio it is assumed that making only to contain single mode in process signal so as to no longer receive The restriction of wideband structure and situation that can preferably suitable for low signal-to-noise ratio.

Description of the drawings

Acceleration time course figures of the Fig. 1 for Wenchuan earthquake ripple.

Fig. 2 be X under the conditions of 1% damping value provided by the present invention to Y-direction Acceleration time course figure.

Fig. 3 is front 5 rank IMF component time-history curves provided by the present invention.

Fig. 4 is front 5 rank IMF component time frequency analysis figures provided by the present invention.

Fig. 5 is front 5 rank IMF component power spectrum density curves provided by the present invention.

Fig. 6 a are using Fast Bayesian FFT methods X using improved Fast Bayesian FFT methods with directly Direction frequency identification error contrast.

Fig. 6 b are using Fast Bayesian FFT methods X using improved Fast Bayesian FFT methods with directly Direction damping identification error contrast.

Fig. 7 a are using Fast Bayesian FFT methods Y using improved Fast Bayesian FFT methods with directly Direction frequency identification error contrast.

Fig. 7 b are using Fast Bayesian FFT methods Y using improved Fast Bayesian FFT methods with directly Direction damping identification error contrast.

Specific embodiment

The present invention is described in further detail with specific embodiment referring to the drawings.

Computation model：Certain skyscraper is reduced to by single-degree-of-freedom system using Mode Decomposition, and takes front two order modes state Carry out calculating analysis.Under earthquake load, the structure forced vibration differential equation is：

Wherein ζ be structural damping, ω_jFor structure inherent circular frequency,

Using the shared Wenchuan earthquake ripple of CENC (CENC), the time is 12 days 06 May in 2008 to load: 28, sample frequency is 50Hz, and total time is 500s, and Acceleration time course is shown in Fig. 1.

Before structure, the two rank natural frequencies of vibration are respectively adopted 0.2051Hz and 0.3467Hz according to object is simplified, structural damping from 1% increases to 5% step by step with 0.5% difference, altogether 9 different damping systems, calculates the acceleration of different damping system Respond for modal idenlification.Fig. 2 be X under the conditions of 1% damping value to Y-direction Acceleration time course.

Select bandpass filter to signal filtering, X is selected to filter bandwidht [0.17 according to original signal power spectral density plot 0.24] Hz, Y-direction are [0.31 0.38] Hz.Then empirical mode decomposition is adopted filtered signal to be further decomposed into for difference The intrinsic mode function of frequency content, wherein X decompose first five rank IMF component time-histories figures to EMD and see Fig. 3.Subsequently to each IMF components Time frequency analysis and power spectrumanalysis are carried out, the corresponding major frequency components of each IMF, frequency division when Fig. 4 is front 5 rank IMF components is determined Analysis result, wherein abscissa are the time, and ordinate is the frequency at correspondence moment, and Fig. 5 is that front 5 rank IMF component powers spectrum density is bent Line.From Fig. 4 and Fig. 5, in IMF1, energy is distributed mainly on 0.2Hz or so, with X to single order natural frequency of vibration 0.2051Hz pair Should, the first rank IMF is selected as modal response.

Through processing, the consistent level of signal compared with original signal, is improve, increase signal to noise ratio, while wherein only containing Single mode, is reducing disturbing factor when calculating modal parameter using Fast Bayesian FFT methods.

Interpretation of result：

Fig. 6 and Fig. 7 is using Fast Bayesian FFT using improved Fast Bayesian FFT methods with directly The contrast of square recognition result.In figure abscissa for default damping parameter, ordinate be frequency with damping recognition result with The ratio of setting value.

Frequency identification error increases with the increase of setting damping value, directly adopts FBFFT methods (Fast Bayesian FFT methods) X is 3.27% to the maximum to error, and Y-direction worst error is -1.98%；And adopt EMD-FBFFT methods (improved Fast Bayesian FFT methods) X to worst error be 2.61%, Y-direction worst error be -1.80.Improved Fast Bayesian FFT methods can preferably recognize frequency resultant.

Damping recognition result error is relatively large.30%, and stability are all higher than using FBFFT method identification errors directly Poor, Y-direction result is greatly enlarged with the increase of setting damping value；And adopt EMD-FBFFT method recognition results more steady Fixed, as the increase of setting damping, X are stable 10% to error, Y-direction error is also less than 30%.Improved Fast Bayesian FFT methods can preferably recognize frequency resultant.Compare, using improved Fast Bayesian FFT methods Identification error is less, more preferable to the stability of different damping system identification.

Above-mentioned specific embodiment is used for illustrating the present invention, only the preferred embodiments of the present invention, rather than Limit the invention, in the protection domain of spirit and claims of the present invention, any modification that the present invention is made, Equivalent, improvement etc., both fall within protection scope of the present invention.

Claims (3)

1. a kind of Identification of Modal Parameter, it is characterised in that methods described in turn includes the following steps：

(1) the structural response TIME HISTORY SIGNAL obtained under environmental excitation is recorded by structural health detecting systemThe time-histories is believed Number power spectral transformation, extracts respective frequencies at each peak value, as the approximation of natural frequency of structures；

(2) centered on respective frequencies at each peak value extracted in step (1), using bandpass filter to measurement signal Pretreatment, extracts the TIME HISTORY SIGNAL of mode corresponding to the centre frequency；

(3) filtered signal is decomposed using Empirical mode decomposition, it is containing different frequency composition to be broken down into Intrinsic mode function, and time frequency analysis or power spectrumanalysis are carried out, determine the main frequency of each intrinsic mode function；

(4) approximation according to natural frequency of structures, chooses the component of the intrinsic mode function of respective frequencies band

(5) the optimal estimation value and its correspondence of modal parameters under single mode are recognized using Fast Bayesian FFT methods Posteriority it is uncertain；

(6) repeat step (3) to (5), until the result of mode needed for identification is completed all.

2. Identification of Modal Parameter according to claim 1, it is characterised in that step adopts Hilbert in (3) Conversion carries out time frequency analysis,

$Z\left(t\right)={\stackrel{\·\·}{x}}_j\left(t\right)+iHT\[{\stackrel{\·\·}{x}}_j\left(t\right)\]=a\left(t\right)e^{i\mathrm{\θ}\left(t\right)}---\left(1\right)$

In formula：It is right to representMake Hilbert conversion, instantaneous amplitudePhase place AngleLinear fit is carried out to which and can obtain θ (t)=ω t+ φ₀；

Structure instantaneous frequency is obtained by following formula (2), is determined by the excursion of structure instantaneous frequency ω (t)Main frequency Rate,

$\mathrm{\ω}\left(t\right)=\frac{d\mathrm{\θ}\left(t\right)}{dt}---\left(2\right).$

3. Identification of Modal Parameter according to claim 1, it is characterised in that optimal estimation value in step (5) Maximum is done by following formula (3) to estimate to obtain, the uncertain Hessian matrix inversions to following formula (3) of posteriority are calculated,

$\begin{array}{c}L(f,\mathrm{\ξ},S,{\mathrm{\σ}}^2,\mathrm{\Φ})=-{\mathrm{nN}}_f\ln 2+(n-1)N_f{\mathrm{ln\σ}}^2+\underset{k}{\Σ}\ln ({\mathrm{SD}}_k+{\mathrm{\σ}}^2)+\\ {\mathrm{\σ}}^{-2}\left(\underset{k}{\Σ}\right(F_k^T{F}_k+G_k^T{G}_k)-{\mathrm{\Φ}}^{T}A\mathrm{\Φ})\end{array}---\left(3\right)$

F in formula, ξ, S, σ², Φ respectively structure frequency, damping, power spectral density of mode force, measure error root mean square and the vibration shape；N is logical for measurement Road number, F_kWith G_kForJing after FFT, frequency is f_kPlace transformed value real part and imaginary part, k be respective frequencies point sequence number, N_f For Frequency point sum, D_kWith A to calculate intermediate variable, it is calculated by formula (4) and formula (5) respectively,

$D_k={\[{(f^2/f_k^2-1)}^2+{(2\mathrm{\ξ}f/f_k)}^2\]}^{-1}---\left(4\right)$

$A=\underset{k}{\Σ}{(1+{\mathrm{\σ}}^2/{\mathrm{SD}}_k)}^{-1}(F_k{F}_k^T+G_k{G}_k^T)---\left(5\right).$