CN103530275A - Structural damage warning method based on confidence of principle component of vibration transmissibility function - Google Patents

Abstract

The invention relates to the field of structural damage identification, in particular to a structural damage warning method based on confidence of the principle component of a vibration transmissibility function. The transmissibility function is constructed by using accelerated speed response, the transmissibility function is free of the influence of excitation amplitude, and the structural damage warning can be free of the influence of the excitation amplitude by taking the amplitude of the transmissibility function as analysis signals; the principle component of the vibration transmissibility function is extracted through the analysis of the principle component, correlation analysis is carried out on the principle component, the confidence of the principle component is computed according to the modal confidence criteria, evaluation is carried out on structural states by using the confidence of the principle component, and the influence of noise can be restrained or eliminated. The structural damage warning method based on the confidence of the principle component of the vibration transmissibility function is free of the influence of the excitation amplitude, capable of effectively restraining or eliminating the influence of noise, small in computing amount, extremely suitable for online monitoring, and strong in operability, and improves processing precision and warning accuracy.

Description

Structural damage method for early warning based on vibration transmissibility function major component degree of confidence

Technical field

The present invention relates to Damage Assessment Method field, particularly a kind of structural damage method for early warning based on vibration transmissibility function major component degree of confidence.

Background technology

Due to the effect of load and the impact of environment, civil engineering structure there will be damage in various degree in-service, if find not in time and take measures, by the consequence of bringing on a disaster property, is therefore necessary to carry out the Study on Damage Identification of structure.Damage Assessment Method is divided into four levels, damage alarming (differentiate structural damage whether exists), determine damage position, determine that degree of injury and structural life-time predicts, and damage alarming is the most key.

At present, people study and have proposed many structural damage method for early warning, wherein, the structural damage method for early warning based on Response Analysis, due to without measuring excitation, only utilizes structural response to assess configuration state, more approach actual conditions, therefore, be considered to a kind of method with wide application prospect, still, due to the impact of excitation amplitude and noise, easily there is misjudgment phenomenon in the structural damage method for early warning based on Response Analysis.

Summary of the invention

The present invention is directed to the impact that prior art is subject to excitation amplitude and noise, cause the phenomenon of prediction errors, a kind of structural damage method for early warning based on vibration transmissibility function major component degree of confidence is provided

The present invention utilizes acceleration responsive structure transport function, and the not impact of excited target amplitude of structural damage early warning is carried out in the not excited target amplitude impact of transport function using the amplitude of transport function as analytic signal; By principal component analysis (PCA), extract the major component of vibration transmissibility function, major component is carried out to correlation analysis, with reference to modal assurance criterion, calculate major component degree of confidence, utilize major component degree of confidence to assess configuration state, can suppress or eliminate the impact of noise.

Technical scheme of the present invention is: a kind of structural damage method for early warning based on vibration transmissibility function major component degree of confidence, and concrete steps are as follows:

Step 1: obtain the acceleration responsive signal of structural damage front and rear part measuring point, calculate vibration transmissibility function by Fourier transform:

$T_{\mathrm{ij}\left(\mathrm{\ω}\right)}=\frac{A_{i\left(\mathrm{\ω}\right)}}{A_{j\left(\mathrm{\ω}\right)}}---\left(1\right)$

In formula, A _i(ω), A _j(ω)be respectively a, the Fourier transform of b point response signal.

Step 2: principal component analysis (PCA) is a kind of data compression technique, has been widely used in the aspects such as data characteristics extraction, signal de-noising.Principal component analysis (PCA) is by the large minispread of data distribution variance, and first principal component variance is maximum, minimum affected by noise, and Second principal component, takes second place, the like.Therefore, raw data matrix is carried out to principal component analysis (PCA), whole features that all major components can characterization data, contrast the major component of each state of structure, successively than directly comparing evaluation structure state more reliable to raw data matrix.The variance of major component is larger, and because noise effect is less, the reliability of differentiating result will be larger.

Using the amplitude of vibration transmissibility function as analytic signal, be assumed to be stationary stochastic process, by s vibration transmissibility function T _ij(ω)be divided into the sample that p segment length is n, form the matrix X of the capable p row of n _s, the correlation matrix R of s vibration transmissibility function _swith major component Z _sfor:

$R_s=\frac{1}{n-1}{X}_s^T{X}_s---\left(2\right)$

（j=0，l，…，p，s=1，2，…，N _s)

In formula, Z _jsj the major component that represents s vibration transmissibility function,

for R _sj proper vector, p is that time-domain sampling is counted, N _squantity for vibration transmissibility function.

Step 3: the damage of structure can cause the variation of structural physical parameter, and be embodied in the dynamic response of structure, and the major component of the vibration transmissibility function of constructing by dynamic response also changes corresponding, therefore by the major component of contrast different conditions, can whether differentiate structural damage, thereby carry out damage alarming.Here with reference to modal assurance criterion, define s vibration transmissibility function j major component degree of confidence and be:

${\mathrm{ZXD}}_{\mathrm{js}}=\frac{{\left|\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_{\mathrm{ijs}}^r{z}_{\mathrm{ijs}}^t\right|}^2}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_{\mathrm{ijs}}^r{z}_{\mathrm{ijs}}^r\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_{\mathrm{ijs}}^t{z}_{\mathrm{ijs}}^t}---\left(4\right)$

（j=0，l，…，p，s=1，2，…，N _s）

In formula: z<sup TranNum="98">r</sup><sub TranNum="99">ijs</sub>, z<sup TranNum="100">t</sup><sub TranNum="101">ijs</sub>be respectively Z<sup TranNum="102">r</sup><sub TranNum="103">js</sub>, Z<sup TranNum="104">t</sup><sub TranNum="105">js</sub>i element, subscript r and t represent normal condition and test mode.If normal condition is consistent with the j major component of s vibration transmissibility function of test mode, ZXD<sub TranNum="106">js</sub>=1, on the contrary ZXD<sub TranNum="107">js</sub><1.

Step 4: definition damage alarming index is as follows:

$\mathrm{DI}=\frac{1}{N_{\mathrm{opt}}{N}_s}\underset{j=1}{\overset{N_{\mathrm{opt}}}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\mathrm{ZX}{D}_{\mathrm{js}}---\left(5\right)$

In formula, N _optquantity for selected major component.

Consider the impact of measuring noise, the major component confidence threshold value of definition structure health status and faulted condition is ε.

If DI≤ε, thinks that structure damages, otherwise not damaged.

The invention has the beneficial effects as follows:

The present invention is based on the structural damage method for early warning of vibration transmissibility function major component degree of confidence, using the amplitude of vibration transmissibility function as analytic signal, by principal component analysis (PCA), extract the major component of vibration transmissibility function, major component is carried out to correlation analysis, with reference to modal assurance criterion, calculate major component degree of confidence, utilize major component degree of confidence to assess configuration state.The method is the impact of excited target amplitude not, can effectively suppress or eliminate the impact of noise, and calculated amount is little, is very suitable for on-line monitoring, and the present invention is workable, has improved processing accuracy, has improved early warning accuracy.

Accompanying drawing explanation

The process flow diagram of Fig. 1 structural damage method for early warning of the present invention;

Seven layers of offshore platform structure numerical model of Fig. 2;

1 is post 1; 2 is post 2; 3 is post 3; 4 is post 4; 1. be damage rod member

The top plan view of seven layers of offshore platform structure numerical model of Fig. 3;

1 is post 1; 2 is post 2; 3 is post 3; 4 is post 4;

5 is X-direction face two; 6 is Y-direction face two; 7 is X-direction face one; 8 is Y-direction face one.

Embodiment

The specific embodiment of the present invention is as follows:

Embodiment 1:

A structural damage method for early warning for vibration transmissibility function major component degree of confidence, process flow diagram is shown in Fig. 1, concrete steps are as follows:

Step 1: obtain the acceleration responsive signal of structural damage front and rear part measuring point, calculate vibration transmissibility function by Fourier transform:

$T_{\mathrm{ij}\left(\mathrm{\&omega;}\right)}=\frac{A_{i\left(\mathrm{\&omega;}\right)}}{A_{j\left(\mathrm{\&omega;}\right)}}---\left(1\right)$

In formula, A _i(ω), A _j(ω)be respectively a, the Fourier transform of b point response signal.

Step 2: principal component analysis (PCA) is a kind of data compression technique, has been widely used in the aspects such as data characteristics extraction, signal de-noising.Principal component analysis (PCA) is by the large minispread of data distribution variance, and first principal component variance is maximum, minimum affected by noise, and Second principal component, takes second place, the like.Therefore, raw data matrix is carried out to principal component analysis (PCA), whole features that all major components can characterization data, contrast the major component of each state of structure, successively than directly comparing evaluation structure state more reliable to raw data matrix.The variance of major component is larger, and because noise effect is less, the reliability of differentiating result will be larger.

Using the amplitude of vibration transmissibility function as analytic signal, be assumed to be stationary stochastic process, by s vibration transmissibility function T _ij(ω)be divided into the sample that p segment length is n, form the matrix X of the capable p row of n _s, the correlation matrix R of s vibration transmissibility function _swith major component Z _sfor:

$R_s=\frac{1}{n-1}{X}_s^T{X}_s---\left(2\right)$

（j=0，l，…，p，s=1，2，…，N _s)

In formula, Z _jsj the major component that represents s vibration transmissibility function,

for R _sj proper vector, p is that time-domain sampling is counted, N _squantity for vibration transmissibility function.

Step 3: the damage of structure can cause the variation of structural physical parameter, and be embodied in the dynamic response of structure, and the major component of the vibration transmissibility function of constructing by dynamic response also changes corresponding, therefore by the major component of contrast different conditions, can whether differentiate structural damage, thereby carry out damage alarming.Here with reference to modal assurance criterion, define s vibration transmissibility function j major component degree of confidence and be:

${\mathrm{ZXD}}_{\mathrm{js}}=\frac{{\left|\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_{\mathrm{ijs}}^r{z}_{\mathrm{ijs}}^t\right|}^2}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_{\mathrm{ijs}}^r{z}_{\mathrm{ijs}}^r\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_{\mathrm{ijs}}^t{z}_{\mathrm{ijs}}^t}---\left(4\right)$

（j=0，l，…，p，s=1，2，…，N _s）

In formula: z<sup TranNum="157">r</sup><sub TranNum="158">ijs</sub>, z<sup TranNum="159">t</sup><sub TranNum="160">ijs</sub>be respectively Z<sup TranNum="161">r</sup><sub TranNum="162">js</sub>, Z<sup TranNum="163">t</sup><sub TranNum="164">js</sub>i element, subscript r and t represent normal condition and test mode.If normal condition is consistent with the j major component of s vibration transmissibility function of test mode, ZXD<sub TranNum="165">js</sub>=1, on the contrary ZXD<sub TranNum="166">js</sub><1.

Step 4: definition susceptibility to damage index is as follows:

$\mathrm{DI}=\frac{1}{N_{\mathrm{opt}}{N}_s}\underset{j=1}{\overset{N_{\mathrm{opt}}}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\mathrm{ZX}{D}_{\mathrm{js}}---\left(5\right)$

In formula, N _optquantity for selected major component.

Consider the impact of measuring noise, the major component confidence threshold value of definition structure health status and faulted condition is ε; If DI < ε, thinks that structure damages, otherwise not damaged.

Embodiment 2:

Employing ANSYS has set up the three-dimensional finite element model of seven layers of ocean platform, basic parameter: elastic modulus is E=2.07 * 10 ¹¹n/m ², density is 7800Kg/m ³, Poisson ratio μ=0.3.Post, crossbeam and support adopt BEAM4 unit, and top board adopts SHELL63 unit, pile up quality and adopt MASS21 unit to simulate on top board.This model is totally 44 nodes, 264 degree of freedom, and 92 BEAM4 unit, 1 SHELL3 unit, 4 MASS21 unit, cross section, 7 kinds of unit type, ocean platform is affixed with basis, directly by reducing the elastic modulus of rod member, carrys out the damage of model configuration.Model is as Fig. 2, shown in Fig. 3.During numerical simulation, getting its Y-direction face 26 analyzes.Be actuated to white Gaussian noise, its sample frequency is 1000Hz, while holding, is 49.152 seconds, puts on 14 points.Utilize the transient analysis module of ANSYS10.0, by time-history analysis, calculate respectively the acceleration (Y direction) of 15 and 19 dot structure damage front and back.According to formula (1), can obtain adjacent point-to-point transmission transport function.

Common mode has been intended four kinds of damage operating modes, as shown in table 1.

Table 1 MODEL DAMAGE operating mode

When excitation amplitude is 0.1, get transport function T ¹⁵ ₁₉front 512 spectral lines are analyzed.By T ¹⁵ ₁₉be divided into 8 segment length and be 64 sample, form the matrix X of 64 row 8 row _s; To X _scarry out principal component analysis (PCA), calculate its each rank major component, and obtain character pair value, and the contribution rate of each rank major component, as shown in table 2:

Front 8 rank eigenwert and the contribution rates of table 2

From table 2, can find, the contribution rate of first three rank major component surpasses 90%, can represent raw data overwhelming majority information, so get first three rank major component, calculates major component degree of confidence, and the damage criterion that utilizes formula (5) to try to achieve under different conditions is as shown in table 3:

Major component degree of confidence (excitation amplitude is 0.1) corresponding to table 3 different damage operating mode

When excitation amplitude is 0.3 and 0.5, major component degree of confidence is as shown in table 4, and in order to save space, its eigenwert and contribution rate are unlisted.

Major component degree of confidence (excitation amplitude is 0.3 and 0.5) corresponding to table 4 different damage operating mode

By table 3 and the visible DI < 0.9 of table 4, ε gets 0.9 here, so can infer that according to the damage alarming principle of major component degree of confidence damage has occurred structure.From table, can find the increasing along with degree of injury, DI constantly reduces, and the variation of excitation amplitude is little on the impact of damage alarming result.

For considering to measure the impact of noise, the random white noise of the normal distribution to a certain degree that superposeed in acceleration responsive, the simulation formula of noise is:

${\widetilde{\mathrm{\&gamma;}}}_i={\mathrm{\&gamma;}}_i(1+{\mathrm{\&epsiv;}}_i\mathrm{\&beta;})---\left(6\right)$

In formula, γ _iwith

be respectively noiseless and noisy node acceleration responsive, ε _ibe the random data of normal distribution, β is the size of institute's plus noise degree, and β gets respectively 0.01,0.03,0.05 and analyzes here.

Analytic process is identical during with noiseless, gets first three rank major component structure major component degree of confidence, and the major component degree of confidence of utilizing formula (5) to try to achieve under different conditions is as shown in table 5:

Major component degree of confidence corresponding to table 5 different damage operating mode

DI < 0.9 as seen from Table 5, according to the damage alarming principle of major component degree of confidence, can infer that damage has occurred structure, in the situation that having superposeed 5% noise, the method has successfully been judged all damage operating modes, illustrates that this method has certain noise resisting ability.

Seven layers of ocean platform numerical simulation result show, the damage alarming method based on vibration transmissibility function major component successfully supports damage to ocean platform and carried out early warning, and the not impact of excited target amplitude, has certain noise resisting ability simultaneously.

Claims (1)

1. the structural damage method for early warning based on vibration transmissibility function major component degree of confidence, is characterized in that, the concrete steps of described method for early warning are as follows:

Step 1: obtain the acceleration responsive signal of structural damage front and rear part measuring point, calculate vibration transmissibility function by Fourier transform:

$T_{\mathrm{ij}\left(\mathrm{\&omega;}\right)}=\frac{A_{i\left(\mathrm{\&omega;}\right)}}{A_{j\left(\mathrm{\&omega;}\right)}}---\left(1\right)$

In formula, A _i(ω), A _j(ω)fourier transform for response signal;

Step 2: using the amplitude of vibration transmissibility function as analytic signal, be assumed to be stationary stochastic process, by s vibration transmissibility function T _ij(ω)be divided into the sample that p segment length is n, form the matrix X of the capable p row of n _s, the correlation matrix R of s vibration transmissibility function _swith major component Z _sfor:

$R_s=\frac{1}{n-1}{X}_s^T{X}_s---\left(2\right)$

In formula, Z _jsj the major component that represents s vibration transmissibility function, j=0, l ..., p, s=1,2 ..., N _s;

for R _sj proper vector, p is that time-domain sampling is counted, N _squantity for vibration transmissibility function;

Step 3: by the major component of contrast different conditions, with reference to modal assurance criterion, define s vibration transmissibility function j major component degree of confidence and be:

${\mathrm{ZXD}}_{\mathrm{js}}=\frac{{\left|\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_{\mathrm{ijs}}^r{z}_{\mathrm{ijs}}^t\right|}^2}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_{\mathrm{ijs}}^r{z}_{\mathrm{ijs}}^r\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_{\mathrm{ijs}}^t{z}_{\mathrm{ijs}}^t}---\left(4\right)$

（j=0，l，…，p，s=1，2，…，N _s）

In formula: z<sup TranNum="244">r</sup><sub TranNum="245">ijs</sub>, z<sup TranNum="246">t</sup><sub TranNum="247">ijs</sub>be respectively Z<sup TranNum="248">r</sup><sub TranNum="249">js</sub>, Z<sup TranNum="250">t</sup><sub TranNum="251">js</sub>i element, subscript r and t represent normal condition and test mode; If normal condition is consistent with the j major component of s vibration transmissibility function of test mode, ZXD<sub TranNum="252">js</sub>=1, on the contrary ZXD<sub TranNum="253">js</sub><1;

Step 4: definition damage alarming index is as follows:

$\mathrm{DI}=\frac{1}{N_{\mathrm{opt}}{N}_s}\underset{j=1}{\overset{N_{\mathrm{opt}}}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\mathrm{ZX}{D}_{\mathrm{js}}---\left(5\right)$

In formula, N _optquantity for selected major component;

The major component confidence threshold value of definition structure health status and faulted condition is ε, if DI≤ε, structure is damaged, on the contrary not damaged.

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