CN103940905A - Beam structural damage detection method based on stable wavelet transform and fractal analysis - Google Patents

Abstract

The invention relates to a beam structural damage detection method based on stable wavelet transform and fractal analysis, and the method is particularly applicable to situation that weak damage to a beam structure is detected based on a modal vibration shape or a working vibration shape of the beam in a noise environment (on-site engineering environment). The method comprises the following steps: measuring the modal vibration shape or the working vibration shape of the beam, enabling the number of sampling points of the testing vibration shape to meet the requirements on the stable wavelet transform, performing stable wavelet transform hierarchy decomposition on the testing vibration shape so as to obtain detail transform coefficients of different scales after the decomposition, performing Katz fractal analysis on each detail transform coefficient under a set window so as to obtain fractal dimensional trace of different scales, respectively calculating the information entropy of the fractal dimensional trace of different scales so as to obtain an information entropy-spectrum, and judging according to the scale fractal dimensional trace of a layer (scale) enabling the values in the information entropy-spectrum to be suddenly reduced, wherein high jumping of the scale fractal dimensional trace indicates happening of damage, and the position of the damage is pointed out.

Description

Girder construction damage detecting method based on Stationary Wavelet Transform and fractals

Technical field

The present invention relates to a kind of girder construction damage detecting method based on Stationary Wavelet Transform and fractals.

Background technology

Works is carried out to health monitoring, to structure earlier damage is keeped in repair, not only can significantly reduce maintenance cost, and can ensure structural behaviour, the extending structure life-span.Beam structure, as the typical members of works, damages identification to it, particularly does structure Non-Destructive Testing and has obtained domestic and international broad research.

Structural damage detection method based on theory of oscillation is at present domestic and international broad research and large class methods that obtained Preliminary Applications.But these method ubiquities: insensitive to small and weak damage, noise immunity is low, rely on the deficiencies such as harmless benchmark architecture.To the damage check of works, often under noise circumstance (engineering site environment), to the detection of the small and weak damage of structure, and generally lack the original mechanics parameter information of works.Research shows that structure microlesion only has remarkable response on some or several power yardsticks of total, and insensitive to other yardstick.Based on Stationary Wavelet Transform, the vibration shape is carried out to multiple dimensioned layering decomposition, and the research that combination utilizes the advantage of Fractal Dimension Analysis technology in announcement Signal Singularity to carry out the small and weak damage check of girder construction under noise circumstance have not been reported.

Summary of the invention

For overcoming the problems referred to above, the invention provides a kind of girder construction damage detecting method based on Stationary Wavelet Transform and fractals.Be specially adapted to the detection to the small and weak damage of girder construction under noise circumstance.

The method is carried out multiple dimensioned layering decomposition based on Stationary Wavelet Transform to the vibration shape, and in conjunction with utilizing Fractal Dimension Analysis technology to carry out structural damage detection in the advantage disclosing in Signal Singularity.Than existing method, that the present invention has is responsive to small and weak damage, anti-noise ability by force, does not rely on the advantages such as harmless benchmark architecture.Can be used for the small and weak damage of girder construction under noise circumstance to detect.The invention solves in addition in multi-scale Wavelet Analysis and select which (a bit) yardstick to carry out a difficult problem for damage check, the Structure Damage Identification to other based on multiscale analysis has inspiration and reference function.

For reaching above object, the technical solution adopted in the present invention is:

A girder construction damage detecting method based on Stationary Wavelet Transform and fractals, comprises the following steps: A, based on modern measurement equipment, as laser scanning vialog, obtains Mode Shape or the work vibration shape shape signal W of girder construction;

B, vibration shape multiscale analysis;

If vibration shape shape signal W data length does not meet the needs of Stationary Wavelet Transform (stationary wavelet transform, SWT), Data of Mode is carried out to linear interpolation, obtaining number is 2 ⁿthe new signal W of multiple ^*, to meet the needs that the vibration shape carried out to Stationary Wavelet Transform; N is the number of plies of the vibration shape being carried out to Stationary Wavelet Transform predecomposition, gets 4 or 5; If W data length meets the needs of SWT, W is carried out to Stationary Wavelet Transform, obtain yardstick mode factor.

To W or W ^*carry out Stationary Wavelet Transform, obtain vibration shape Scale Decomposition coefficient as the formula (1):

W (or W ^*)=A _n+ D _n+ D _n-1+ ... D _i+ ... + D ₂+ D ₁(1)

In formula, A _nand D _ifor vibration shape Scale Decomposition coefficient, i=1,2 ..., N; N is the number of plies of predecomposition, and N gets 4 or 5.Wherein A _nfor yardstick 2 ⁿon approximation coefficient, D _ifor yardstick 2 ⁱon detail coefficients; In operation, can utilize ' swt ' order in MATLAB software to realize the multiscale analysis of formula (1) to the vibration shape;

C, obtain the scale fractal dimension trace (scale fractal dimension trajectory, SFDT) of each detail coefficients: given one comprises the moving window that number of samples is n, and n=4,6 or 8, makes sliding window along detail coefficients D _isquiggle constantly move forward, each mobile sliding window all calculates Katz fractal dimension (the Katz's fractal dimension of contained segment of curve in window, KFD) and as the fractal dimension of this sliding window central sample point, along with sliding window traversal whole piece squiggle, just obtain corresponding to D _iscale fractal dimension trace (SFDT-D _i); Wherein KFD is calculated as follows:

$\mathrm{KFD}=\frac{{\log }_{10}\left(n\right)}{{\log }_{10}\left(n\right)+{\log }_{10}(d/L)}---\left(2\right)$

In formula: d is the maximal value of the air line distance of any two sampled points on the interior squiggle of window; L is squiggle total length in window;

D, calculating SFDT-D _iinformation entropy (information entropy, IE), composition information entropy-spectrum: calculate each SFDT-D by formula (3) _iinformation entropy,

$H_{{\mathrm{SFDT}-D}_i}=-\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{p}_{\mathrm{ik}}\log p_{\mathrm{ik}}---\left(3\right)$

In formula: N _isFDT-D _isample points, Probability p _ikcalculated by formula (4),

$p_{\mathrm{ik}}=(c_{\mathrm{ik}}^{\′}-\min \left(c_{\mathrm{ik}}^{\′}\right))/\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}(c_{\mathrm{ik}}^{\′}-\min \left(c_{\mathrm{ik}}^{\′}\right))---\left(4\right)$

C ' in formula _ikthe SFDT-D through threshold value correction _icoefficient, the coefficient settings that is not more than threshold value is zero, and the coefficient that is greater than threshold value remains unchanged; Threshold value is defined as average and the standard deviation sum of SFDT-Di original coefficient; Min represents to get minimum value.

By each SFDT-D _iinformation entropy composition information entropy-spectrum in information entropy-spectrum, diminish the suddenly layer at place of numerical value is defined as structural damage detection yardstick used.Damage identification by the SFDT under this yardstick: in SFDT, high takeofing indicating the generation of damage, and indicated the position of damage.

Beneficial effect of the present invention shows:

1. whether the present invention can be used for the various damages of beam structure, as the detection of crackle, hole, layering, corrosion etc., can disclose damage to occur, and can determine the exact position of damage.

2. the present invention is by decomposing (formula (1)) and further Fractal Dimension Analysis (formula (2)) to the layering of the vibration shape, make this law possess the ability of identifying small and weak damage under noise circumstance, be particularly suitable for the detection of the small and weak damage of beam structure under engineering site environment.

3. the present invention utilizes the vibration shape scale fractal dimension trace information entropy (formula (3)) of definition to determine that damage information accounts for the layer at leading vibration shape scale coefficient place, has solved a difficult problem for How to choose yardstick in the girder construction damage check based on multi-scale Wavelet Analysis.

Brief description of the drawings

In order to be illustrated more clearly in the embodiment of the present application or technical scheme of the prior art, to the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below, apparently, the accompanying drawing the following describes is only some embodiment that record in the application, for those of ordinary skill in the art, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing;

Fig. 1 method schematic diagram;

The actual measurement vibration shape of Fig. 2 girder construction under 3950Hz frequency excitation;

In Fig. 2, testing sampling number is 297.

Fig. 3 girder construction is the vibration shape after data expansion under 3950Hz frequency excitation;

Fig. 3 explanation: by linear interpolation, sampling number is expanded to 320, to meet the needs of Stationary Wavelet Transform.This example is decomposed number of plies N=4, and 320 is 2 ⁴20 times.

The each detail coefficients figure of Fig. 4 vibration shape Stationary Wavelet Transform;

Fig. 4 has shown the multiscale analysis effect to the vibration shape.

Scale fractal dimension trace diagram in Fig. 5 vibration shape SWT detail coefficients.

Fig. 5 explanation: at SFDT-D ₃on can detect the generation of damage, and can accurately determine its position.

Embodiment

The correlation technique content of not addressing below all can adopt or use for reference prior art.

In order to make those skilled in the art person understand better the technical scheme in the application, below in conjunction with the accompanying drawing in the embodiment of the present application, technical scheme in the embodiment of the present application is clearly and completely described, obviously, described embodiment is only some embodiments of the present application, instead of whole embodiment.Based on the embodiment in the application, those of ordinary skill in the art are not making the every other embodiment obtaining under creative work prerequisite, all should belong to the scope of the application's protection.

Embodiment

The semi-girder that the present embodiment selects one 6061 aluminium alloys to make, beam length 543mm, wide 30mm, high 8mm, at the beam back side apart from stiff end 293mm place, opens a wide 1mm, and deeply 1mm runs through the crack of beam width direction.

With modality vibration exciter as power driver at the beam back side, near applying sinusoidal excitation with natural frequency near free end, measure the vibration in beam front as sensor with laser vibration measurer simultaneously, obtain the vibration shape signal of beam under excitation frequency; The vibration shape of the present embodiment is drawn by 297 sampled points that are spacedly distributed on beam.

In the present embodiment, laser sensor is the PSV-400 laser scanning vialog that German Polytec company produces; Power driver is 4890 modality vibration exciters that B & K company of Denmark produces.Multiscale analysis to the vibration shape in analysis and obtaining of scale fractal dimension trace all utilize MATLAB software programming to realize.

Taking girder construction, the test result under 3950Hz frequency excitation is carried out the detailed description of this method as example below, can certainly select the test result under other excitation frequencies to carry out damage check.

A. obtain the vibration shape of girder construction under 3950Hz frequency excitation by actual measurement, as shown in Figure 2.

B. by linear interpolation, by Data of Mode continuation to 320 point, (this example is decomposed number of plies N=4, and 320 is 2 ⁴20 times), obtain the vibration shape after data expansions, as shown in Figure 3.The vibration shape after data expansion is carried out to Stationary Wavelet Transform layering decomposition, and decomposing the number of plies is 4, and N=4 in formula (1), obtains each detail coefficients D thus ₁, D ₂, D ₃, D ₄, as shown in Figure 4.In operation, can utilize ' swt ' order in MATLAB software to realize the Stationary Wavelet Transform layering decomposition to the expansion vibration shape.

C. given one to comprise number of samples be 6 moving window, sliding window is constantly moved forward along the squiggle of each detail coefficients, each mobile sliding window all calculates the Katz fractal dimension of contained segment of curve in window the fractal dimension as this sliding window central sample point by formula (2), along with sliding window traversal whole piece squiggle, just obtain corresponding scale fractal dimension trace.Each scale fractal dimension trace SFDT-D ₁, SFDT-D ₂, SFDT-D ₃, SFDT-D ₄as shown in Figure 5.

D. the information entropy of calculating each scale fractal dimension trace by formula (3), the information entropy obtaining under each yardstick is $\left[\begin{array}{cccc}{H}_{{\mathrm{SFDT}-D}_1}& H_{{\mathrm{SFDT}-D}_2}& H_{{\mathrm{SFDT}-D}_3}& H_{{\mathrm{SFDT}-D}_4}\end{array}\right]=\left[\begin{array}{cccc}4.9274& 5.2167& 3.2657& 5.4217\end{array}\right].$ Visible yardstick information entropy-spectrum, the 3rd layer of sudden change that existence diminishes, represents that this layer (yardstick) can be used as the yardstick of damage check.

As seen from Figure 5, diminish suddenly in the information entropy-spectrum SFDT-D of place layer correspondence ₃(the 3rd layer of scale fractal that detail coefficients is corresponding dimension trace of the vibration shape) has unique high takeofing, and the transverse axis position (about 290mm) that this peak value is corresponding is the damage position detecting, (circled positions in figure) conforms to actual damage position.Confirm thus the validity of the present invention to girder construction damage check; Meanwhile, this test contains neighbourhood noise and degree of injury is less, and the adaptability of this method to the small and weak structural damage detection of girder construction under noise circumstance has been described.

The above is only the application's preferred implementation, makes those skilled in the art can understand or realize the application.To be apparent to one skilled in the art to the multiple amendment of these embodiment, General Principle as defined herein can, in the case of not departing from the application's spirit or scope, realize in other embodiments.Therefore, the application will can not be restricted to these embodiment shown in this article, but will meet the widest scope consistent with principle disclosed herein and features of novelty.

Claims (1)

1. the girder construction damage detecting method based on Stationary Wavelet Transform and fractals, is characterized in that comprising the following steps:

A, the Mode Shape of obtaining girder construction or work vibration shape shape signal W;

B, vibration shape multiscale analysis;

If vibration shape shape signal W data length does not meet the needs of Stationary Wavelet Transform SWT, Data of Mode is carried out to linear interpolation, obtaining number is 2 ⁿthe new signal W of multiple ^*, to meet the needs that the vibration shape carried out to Stationary Wavelet Transform; N is the number of plies of the vibration shape being carried out to Stationary Wavelet Transform predecomposition, gets 4 or 5; If W data length meets the needs of SWT, W is carried out to Stationary Wavelet Transform, obtain yardstick mode factor;

To W or W ^*carry out Stationary Wavelet Transform, obtain vibration shape Scale Decomposition coefficient as the formula (1):

W(W ^*)=A _N+D _N+D _N-1+…D _i+…+D ₂+D ₁ （1）

In formula, A _nand D _ifor vibration shape Scale Decomposition coefficient, wherein A _nfor yardstick 2 ⁿon approximation coefficient, D _ifor yardstick 2 ⁱon detail coefficients; In operation, utilize ' swt ' order in MATLAB software to realize the multiscale analysis of formula (1) to the vibration shape;

C, obtain the scale fractal dimension trace SFDT of each detail coefficients: given one comprises the moving window that number of samples is n, and n=4,6 or 8, makes sliding window along detail coefficients D _isquiggle constantly move forward, each mobile sliding window all calculates the Katz fractal dimension KFD of contained segment of curve in window the fractal dimension as this sliding window central sample point, along with sliding window travels through whole piece squiggle, just obtains corresponding to D _iscale fractal dimension trace (SFDT-D _i); Wherein KFD is calculated as follows:

$\mathrm{KFD}=\frac{{\log }_{10}\left(n\right)}{{\log }_{10}\left(n\right)+{\log }_{10}(d/L)}---\left(2\right)$

In formula: d is the maximal value of the air line distance of any two sampled points on the interior squiggle of window; L is squiggle total length in window;

D, calculating SFDT-D _iinformation entropy IE, composition information entropy-spectrum: calculate each SFDT-D by formula (3) _iinformation entropy,

$H_{{\mathrm{SFDT}-D}_i}=-\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{p}_{\mathrm{ik}}\log p_{\mathrm{ik}}---\left(3\right)$

In formula: N _isFDT-D _isample points, Probability p _ikcalculated by formula (4),

$p_{\mathrm{ik}}=(c_{\mathrm{ik}}^{\′}-\min \left(c_{\mathrm{ik}}^{\′}\right))/\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}(c_{\mathrm{ik}}^{\′}-\min \left(c_{\mathrm{ik}}^{\′}\right))---\left(4\right)$

C ' in formula _ikthe SFDT-D through threshold value correction _icoefficient, is not more than the SFDT-D of threshold value _icoefficient settings is zero, and is greater than the SFDT-D of threshold value _icoefficient remains unchanged; Threshold value is defined as SFDT-D _ithe average of original coefficient and standard deviation sum; Min represents to get minimum value;

By each SFDT-D _iinformation entropy composition information entropy-spectrum in information entropy-spectrum, diminish the suddenly layer at place of numerical value is defined as structural damage detection yardstick used; Damage identification by the SFDT under this yardstick: in SFDT, high takeofing indicating the generation of damage, and indicated the position of damage;

Described i=1,2 ..., N, described N is the number of plies of predecomposition, gets 4 or 5.