CN107144643A - A kind of damnification recognition method of Lamb wave monitoring signals statistical parameter - Google Patents
A kind of damnification recognition method of Lamb wave monitoring signals statistical parameter Download PDFInfo
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Abstract
The invention discloses a kind of damnification recognition method of Lamb wave monitoring signals statistical parameter, this method step is as follows：Excitation/sensor array of line style is arranged on geodesic structure is treated；Sense channel is set up, the Lamb wave structural response signal of all excitation/sensory paths is gathered；Lamb wave structural response signal to collection carries out multiple statistical nature parameter extractions, constitutive characteristic sample set；Dimension-reduction treatment is carried out to feature samples collection using principal component analytical method；The training sample of different type of impairments is respectively trained, structural damage identification model is drawn；By in test sample data input structural damage identification model, the type of damage is judged.The inventive method employs multiple specific statistical nature parameters, possesses the advantage that multi-angle reflects different damage informations, realizes the purpose to structural damage type identification.
Description
Technical field
The present invention relates to a kind of damnification recognition method of Lamb wave monitoring signals statistical parameter, and in particular to a kind of plate shell class
The Lamb wave monitoring damnification recognition method of multiple statistical nature parameters, belongs to Damage Assessment Method technical field in engineering structure.
Background technology
Various damages, the existing sound hair of structure damage monitoring technology easily occur in use for engineering structure
Penetrate technology, Shearography technology, ultrasonic technology etc., but acoustic emission is present that signal is weaker, decay is fast, also to overcome
The problems such as noise；Shearography technology is influenceed by factors such as shearing displacement, actuation duration, energisation modes, in damage
Quantitative aspect not yet forms unified standard；Ultrasonic technology can detect body structure surface and the shallow defect under coating, only
Ask conduct ultrasound and can need transmitting medium by geodesic structure, therefore application is relatively broad, and Lamb wave is supervised in ultrasonic technology
Survey technology is using relatively broad.
In recent years, the application of Lamb wave structural health monitoring technology from aerospace field expand to ship, railway,
The field such as civil engineering and automatic industrial, is played in terms of structural health safety reducing personnel and property loss and ensureing
Very important effect.Lamb wave has the characteristics of decay is slow, propagation distance is remote, and very quick to the microlesion of structure
Sense.During Lamb wave is free boundary solid panel, the stress wave for the special shape that shear wave and compressional wave are coupled to form, it is special to there is frequency dispersion in it
Property and multi-mode phenomenon.Under multimodal scenario, according to different mode different defects are reflected with the mechanism of different characteristic, is extracted
Go out multiple statistical nature parameters of Lamb wave structural response signal, response condition of the reflection different mode to different damages.According to
Response condition, so as to identify damage.It is, therefore, desirable to provide a kind of damage that effectively can be judged type of impairment is known
Other method.
The content of the invention
The technical problems to be solved by the invention are：A kind of non-destructive tests side of Lamb wave monitoring signals statistical parameter is provided
Method, according to the difference of the Lamb wave mechanism of different damages, extracts multiple statistical nature parameters, according to the difference of different damages
Lamb wave structural response signal feature, non-destructive tests are carried out using identification model, are realized and are recognized what is assessed to unknown type of impairment
Purpose.
The present invention uses following technical scheme to solve above-mentioned technical problem：
A kind of damnification recognition method of Lamb wave monitoring signals statistical parameter, comprises the following steps：
Step 1, on geodesic structure is treated, according to the size of detection zone, multiple pressure sensor composition excitation/sensings are arranged
Linear array；Select a sensor as excitation in excitation/sensing linear array, another sensor is used as sensing, group
Build the Lamb wave response signal of all sense channels under sense channel, collection structural health conditions；
Step 2, different types of damage is arranged on the sense channel that step 1 is set up, for each type of impairment, collection should
The Lamb wave response signal of the corresponding sense channel of type of impairment；
Step 3, statistical nature parameter extraction is carried out respectively to the Lamb wave response signal that step 1 and step 2 are obtained, extracted
Go out six Statistical Parameters, including：Root mean square, variance, degree of skewness, coefficient of kurtosis, peak-to-peak value and K factor, obtain healthy shape
Characteristic data set and the corresponding characteristic data set of each type of impairment under state；
Step 4, using principal component analytical method to the characteristic data set under health status and the corresponding spy of each type of impairment
Levy data set and carry out dimension-reduction treatment, obtain the corresponding new feature number of new feature data set and each type of impairment under health status
According to collection；
Step 5, the new feature data set under health status is classified according to type of impairment, obtains each type of impairment pair
The feature samples for the health status answered, the feature samples of the corresponding health status of each type of impairment are respectively trained using EM algorithms,
Obtain the gauss hybrid models parameter of each type of impairment health status；
Step 6, for each type of impairment, the new feature data set of each type of impairment is divided into training sample and test specimens
This, trains the type of impairment gauss hybrid models hybrid parameter, so as to obtain each damage using EM algorithms from training sample
The gauss hybrid models of type；Wherein, the initial parameter of EM algorithms is joined for the gauss hybrid models of the type of impairment health status
Number；
Step 7, test sample is inputted in the gauss hybrid models of each type of impairment respectively, the likelihood function of computation model
Value, and the likelihood function value size of relatively more each model, the maximum type of impairment of model likelihood function value is ranged by test sample
In.
As a preferred embodiment of the present invention, root mean square expression formula is described in step 3：
Wherein, RMS is root mean square, xiFor i-th of Lamb wave response signal, n is the number of all Lamb wave response signals.
As a preferred embodiment of the present invention, variance expression formula is described in step 3：
Wherein, Variance is variance, xiFor i-th of Lamb wave response signal, n is the individual of all Lamb wave response signals
Number,For xiAverage value.
As a preferred embodiment of the present invention, degree of skewness expression formula is described in step 3：
Wherein, Skewness is degree of skewness,xiFor i-th of Lamb wave response signal, n is
The number of all Lamb wave response signals,For xiAverage value.
As a preferred embodiment of the present invention, coefficient of kurtosis expression formula is described in step 3：
Wherein, Kurtosis is coefficient of kurtosis, xiFor i-th of Lamb wave response signal, n is all Lamb wave response signals
Number,For xiAverage value.
As a preferred embodiment of the present invention, peak-to-peak value expression formula is described in step 3：
PPK=max (xi)-min(xi)
Wherein, PPK is peak-to-peak value, max (xi)、min(xi) it is respectively xiMaximum, minimum value, xiFor i-th of Lamb wave
Response signal.
As a preferred embodiment of the present invention, K factor expression formula is described in step 3：
K-factor=max (xi)×RMS
Wherein, K-factor is K factor, max (xi) it is xiMaximum, xiFor i-th of Lamb wave response signal, RMS is
Root mean square.
As a preferred embodiment of the present invention, step 4 detailed process is：With the characteristic data set under health status
Exemplified by：
(41) correlation matrix of d × p characteristic data sets under health status is calculated：
Wherein, d is the number of times of collection Lamb wave response signal, and p is the number of all statistical nature parameters, and R is real symmetrical
Matrix, rab=rba, a, b=1,2 ..., p, rabFor xaWith xbBetween coefficient correlation, xa,xbThe either rank of data set is characterized,
Expression formula is as follows：
Wherein,For xaAverage value,For xbAverage value, xcaFor xaC-th of element, xcbFor xbC-th yuan
Element；
(42) correlation matrix R eigenvalue λ is calculateda, and arranged according to order from big to small；
(43) the corresponding characteristic vector of each characteristic value after sequence is calculated；
(44) the corresponding principal component Z of each characteristic value after sequence is calculatedaAccumulation contribution rate：
(45) choose accumulation contribution rate characteristic vector corresponding more than 85% characteristic value and build new feature data set：
A '=A × Ml×m
Wherein, A ' expressions new feature data set, A represents characteristic data set, Ml×mRepresent spy of the contribution rate of accumulative total more than 85%
The matrix that characteristic vector corresponding to value indicative is constituted, m represents the number of characteristic value of the contribution rate of accumulative total more than 85%, and l is characterized
The line number of vector.
The present invention uses above technical scheme compared with prior art, with following technique effect：
1st, Lamb wave of the present invention spreads all over each point of structure in the communication process of structure, with propagation distance farther out, decline
The advantages of subtracting relatively slow, more sensitive to microlesion.Lamb wave has frequency dispersion effect and multi-mode phenomenon.According to different patterns
Under, the different mechanism of reflection feature of different defects, by extracting multiple statistical nature parameters of Lamb wave signal, reflects
Response condition of the different mode to different damages.According to response condition, damage is identified.
2nd, effectively structural damage type can be identified by the present invention, according to multiple statistical natures of different damages
Amount, training draws the identification model of all kinds of damages, and its information reflected can intuitively identify the type of damage, be conducive to work
The maintenance and reparation in journey structure later stage.
Brief description of the drawings
Fig. 1 is the schematic layout pattern of test specimen structure and sensing/excitation array in the embodiment of the present invention.
Fig. 2 is the flow chart of damnification recognition method of the present invention.
Fig. 3 (a) is tri- characterization factors of RMS, Variance, Skewness of structural health conditions.
Fig. 3 (b) is tri- characterization factors of Kurtosis, PPK, K-factor of structural health conditions.
Fig. 3 (c) is tri- characterization factors of RMS, Variance, Skewness of structure circular hole damage.
Fig. 3 (d) is tri- characterization factors of Kurtosis, PPK, K-factor of structure circular hole damage.
Fig. 3 (e) is tri- characterization factors of RMS, Variance, Skewness of structure erosion damage.
Fig. 3 (f) is tri- characterization factors of Kurtosis, PPK, K-factor of structure erosion damage.
Fig. 4 is the structural representation for the gauss hybrid models that the present invention is used.
Fig. 5 (a) is the likelihood function value size of the different damage gauss hybrid models of circular hole test sample input.
Fig. 5 (b) is the likelihood function value size of the different damage gauss hybrid models of corrosion test sample input.
Embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the drawings.Below by
The embodiment being described with reference to the drawings is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
The present invention provides a kind of damnification recognition method of Lamb wave monitoring signals statistical parameter, and its general principle is：Utilize
Active Lamb Wave-based Monitoring gathers Lamb wave structural response signal, extracts multiple statistical natures ginseng of structural response signal
Amount.Because the dimension of statistical nature parameter is numerous, dimension-reduction treatment is carried out to sample characteristics collection using principal component analytical method.Build
The identification model of difference damage, completes non-destructive tests.In the present embodiment, identification model uses gauss hybrid models, can basis
The likelihood angle value of gauss hybrid models judges the affiliated type of damage, realizes the purpose of type of impairment identification.
A kind of damnification recognition method of Lamb wave monitoring signals statistical parameter of the present invention, is comprised the following steps that：
(1) on geodesic structure is treated, according to detection zone size, multigroup piezoelectric transducer composition excitation/sensing line style is arranged
Array；
(2) in one group of excitation/sensor array, one piezoelectric transducer of selection is used as driver, another piezoelectric sensing
Device sets up the Lamb wave response letter of all excitation/sensing passages under sense channel, collection structure current state as sensor
Number；
(3) the Lamb wave structural response signal to collection carries out statistical nature parameter extraction, extracts six Time-domain Statistics
Characterization factor：RMS, Variance, Skewness, Kurtosis, PPK and K-factor；Skewness describes collection letter
Number be distributed symmetrically character condition, whether Kurtosis describes the distribution peaks that collection signal constitutes lofty or flat；
(4) dimension-reduction treatment is carried out to feature samples using principal component analytical method, obtains feature samples collection；
(5) training sample of different type of impairments is respectively trained out to the identification model parameter of each damage, all kinds of damages are obtained
The identification model of wound；
(6) by test sample data input identification model, the output valve of computation model compares the defeated of all kinds of damage models
Go out and be worth size, be worth it is bigger, then illustrate test sample belong to the category probability it is bigger, judge damage type.
Wherein, principal component analytical method is multiple initial data can be selected into a few by linear transformation to integrate
The Multielement statistical analysis method of index, its detailed step is：
(1) correlation matrix of d × p feature samples collection is calculated, expression formula is as follows：
Wherein, R is real symmetric matrix (i.e. rab=rba), a, b=1,2 ..., p, p is the individual of all statistical nature parameters
P=6, r in number, the present inventionabFor xaWith xbBetween coefficient correlation, expression formula is as follows：
(42) correlation matrix R eigenvalue λ is calculateda, characteristic equation is generally solved using Jacobi method (Jacobi) | λ
I-R |=0, obtain eigenvalue λa, and arranged according to order from big to small, i.e. λ1≥λ2≥…≥λp≥0；
(43) the corresponding characteristic vector of each characteristic value after sequence is calculated, eigenvalue λ is obtained respectivelyaCorresponding characteristic vector
ea, require here | | ea| |=1, i.e.,Wherein eabRepresent vector eaB-th of component；
(44) expression formula of principal component contributor rate and accumulation contribution rate is as follows：
Principal component ZaContribution rate be：
Accumulation contribution rate is：
Under normal circumstances, eigenvalue λ of the contribution rate of accumulative total more than 85% is chosen1,λ2,…,λmCorresponding first,
2nd ..., m (m≤p) individual principal component.
(45) choose accumulation contribution rate characteristic vector corresponding more than 85% characteristic value and build new feature data set：
A '=A × Ml×m
Wherein, A ' expressions new feature data set, A represents characteristic data set, Ml×mRepresent spy of the contribution rate of accumulative total more than 85%
The matrix that characteristic vector corresponding to value indicative is constituted, m represents the number of characteristic value of the contribution rate of accumulative total more than 85%, and l is characterized
The line number of vector.
Gauss hybrid models (GMM) are used for describing the distribution of hybrid density, and its probability density function is shown below：
Wherein, x is the feature samples for gathering signal, and k is the dimension of gauss hybrid models mixing member, and D is feature samples
Dimension, αq、μqAnd ΣqHybrid weight, mean vector and the covariance matrix of each Gaussian Mixture member in GMM are represented respectively.
The training process of gauss hybrid models is actually the process of parameter Estimation.Training is first using being needed before EM algorithms
Beginning parameter, parameter value of the K-means algorithms after initialization is ensure that on the premise of calculating is simple and convenient can more preferably EM calculations
The execution of method is prepared, and the selection of initial parameter uses K-means algorithms.If updating obtained Gauss under structural health conditions to mix
The hybrid weight of matched moulds type, mean vector, covariance matrix is respectively αq(0)、μq(0)、Σq(0)；Under On Damage State
Feature samples collection training during, use hybrid weight αq(0), mean vector μq(0), covariance matrix Σq(0) as EM
The initial parameter of algorithm；Hybrid weight, mean vector, the covariance matrix of each Gaussian component of damage probability model after renewal
It is expressed as αq(w)、μq(w)、Σq(w), w is >=1 positive integer.
The EM parameter estimation algorithms of gaussian probability model are divided into E steps and walked with M：
E walks the expectation for obtaining complete likelihood function：
Wherein, θ=(μ1, μ2..., μk, Σ1, Σ2..., Σk), it is Gaussian Mixture distributed constant.θ is represented after updating
Value, θt-1Represent parameter current estimate.
M steps are tried to achieve as Q=(θ, θt-1) be maximum when each parameter expression formula：
The revaluation formula of hybrid weight：
The revaluation formula of mean vector：
The revaluation formula of covariance matrix：
Below with reference to drawings and the specific embodiments, the present invention is described in detail：
(1) test specimen of one embodiment of the present invention is epoxy resin structural composite panel, and its size is
1000mm × 500mm × 3mm, as shown in figure 1, wherein open circles casement intends the pilot hole in engineering structure.By 28 pieces of pressures
Electric transducer is evenly arranged according to the spacing every 150mm, and vertical direction arranges 4 pieces, altogether 7 group.In Fig. 1 shade circular hole with
Shade irregular figure represents circular hole damage and corrosion damage respectively.According to order from left to right, first group and second group of pressure
Electric transducer horizontal direction has 4 groups of circular hole damages；3rd group has 4 groups of corrosion damages with the 4th group of piezoelectric transducer horizontal direction；
First group to the 5th group the 3rd, have 5 groups of circular holes damages between the 4th piece of piezoelectric transducer；6th group and the of the 7th group
3rd, having between the 4th piece of piezoelectric transducer between 2 groups of corrosion damages, first, second piece of piezoelectric transducer has 2 groups of corrosion damages；
There is 1 group of corrosion damage between 4th group of first, second piece of piezoelectric transducer.9 groups of circular hole damages, 9 groups of corrosion damages altogether.
(2) flow chart of the invention is as shown in Fig. 2 the data of progress structural health conditions and On Damage State first are adopted
Collection.
The first step：Gather the response signal of structural health conditions.
1. select a sensor as driver in sensing/excitation linear array, another sensor is used as sensing
Device simultaneously gathers structural response signal.
Step is repeated in the path of 18 groups of damages shown in Fig. 1 1. four times, obtains 144 groups of structural health response letters
Number (every group path obtain 2 groups of structural response signals).
Second step：The structural response signal of circular hole damage and corrosion damage in structure is gathered respectively.
2. according to order from left to right, first group with 4 groups of paths of second group of piezoelectric transducer horizontal direction, first group
The 3rd to the 5th group, 5 groups of paths between the 4th piece of piezoelectric transducer are repeated in step 1. four times, obtain 72 groups of circular holes and damage
The structural response signal of wound.
3. according to order from left to right, the 3rd group with 4 groups of paths of the 4th group of piezoelectric transducer horizontal direction, the 6th group
With the 7th group the 3rd, between the 4th piece of piezoelectric transducer and between first, second piece of piezoelectric transducer amount to 4 groups of paths,
1 group of path between 4th group of first, second piece of piezoelectric transducer is repeated in step 1. four times, obtains 72 groups of corrosion damages
Structural response signal.
3rd step：The extraction of multiple statistical nature parameters, the statistics extracted are carried out to the structural response signal collected
Characterization factor is respectively RMS, Variance, Skewness, Kurtosis, PPK and K-factor.The statistical nature of extraction because
It is sub as shown in Figure 3.System when Fig. 3 (a) to Fig. 3 (f) is respectively structural health conditions, the damage of structure circular hole, structure erosion damage
Count characterization factor.Principal component analysis, dimensionality reduction to three-dimensional data are carried out to feature samples collection.
4th step：By the feature samples collection of different damages be divided into training sample and test sample, the present embodiment circular hole and
The training sample and test sample of corrosion damage are respectively 36 groups.The feature samples collection of structural health conditions is corresponding in turn to all the way
The damage sample set in footpath.
5th step：The identification model selected in the present embodiment is gauss hybrid models, and its structural representation is as shown in figure 4, x
For input, that is, gather the feature samples of signal；P (x | θ) it is output, i.e. likelihood function value.The training process of gauss hybrid models
Actually the process of parameter Estimation, estimates model parameter used here as EM algorithms.Circle is respectively trained using EM algorithms
Hole and the feature samples of the corresponding health status of corrosion, the initial parameter before EM algorithm uses uses K-means algorithms, wherein high
The number k of this component is set to 2.Obtain the health status gauss hybrid models parameter alpha of circular holeq(0)Circular hole、μq(0)Circular hole、Σq(0)Circular hole；
The health status gauss hybrid models parameter alpha of corrosionq(0)Corrosion、μq(0)Corrosion、Σq(0)Corrosion。
6th step：Mixed respectively using the gauss hybrid models of the damage of EM Algorithm for Training circular hole and corrosion damage training sample
Parameter, the number k of Gaussian component is set to 2, and the wherein initial parameter before the use of EM algorithms is the corresponding health status Gauss of damage
Mixed model parameter.Draw circular hole damage and the gauss hybrid models of corrosion damage.
7th step：Test sample data are inputted into circular hole damage with corrosion damage gauss hybrid models, calculating mould respectively
The likelihood function value of type, the likelihood function value size of relatively more all kinds of damage models, value is bigger, then illustrates that test sample belongs to such
Other probability is bigger, judges the type of damage.Likelihood function value size in the embodiment is more as shown in Figure 5.Fig. 5 (a)
The likelihood function value size of different damage gauss hybrid models is inputted for circular hole test sample, Fig. 5 (b) is that corrosion test sample is defeated
Enter the likelihood function value size of different damage gauss hybrid models.Following table compares for classification results, and as a result show to extract is more
Individual characteristic quantity, which is used for Damage Assessment Method, has preferable classifying quality.
The technological thought of above example only to illustrate the invention, it is impossible to which protection scope of the present invention is limited with this, it is every
According to technological thought proposed by the present invention, any change done on the basis of technical scheme each falls within the scope of the present invention
Within.
Claims (8)
1. a kind of damnification recognition method of Lamb wave monitoring signals statistical parameter, it is characterised in that comprise the following steps：
Step 1, on geodesic structure is treated, according to the size of detection zone, multiple pressure sensor composition excitation/sensing line styles are arranged
Array；Select a sensor as excitation in excitation/sensing linear array, another sensor sets up inspection as sensing
Survey the Lamb wave response signal of all sense channels under passage, collection structural health conditions；
Step 2, different types of damage is arranged on the sense channel that step 1 is set up, for each type of impairment, gathers the damage
The Lamb wave response signal of the corresponding sense channel of type；
Step 3, statistical nature parameter extraction is carried out respectively to the Lamb wave response signal that step 1 and step 2 are obtained, extracts six
Individual Statistical Parameters, including：Root mean square, variance, degree of skewness, coefficient of kurtosis, peak-to-peak value and K factor, are obtained under health status
Characteristic data set and the corresponding characteristic data set of each type of impairment；
Step 4, using principal component analytical method to the characteristic data set under health status and the corresponding characteristic of each type of impairment
Dimension-reduction treatment is carried out according to collection, the corresponding new feature data of new feature data set and each type of impairment under health status are obtained
Collection；
Step 5, the new feature data set under health status is classified according to type of impairment, obtains each type of impairment corresponding
The feature samples of health status, the feature samples of the corresponding health status of each type of impairment are respectively trained using EM algorithms, are obtained
The gauss hybrid models parameter of each type of impairment health status；
Step 6, for each type of impairment, the new feature data set of each type of impairment is divided into training sample and test sample, profit
The type of impairment gauss hybrid models hybrid parameter is trained from training sample with EM algorithms, so as to obtain each type of impairment
Gauss hybrid models；Wherein, the initial parameter of EM algorithms is the gauss hybrid models parameter of the type of impairment health status；
Step 7, test sample is inputted in the gauss hybrid models of each type of impairment respectively, the likelihood function value of computation model,
And the likelihood function value size of relatively more each model, test sample is ranged in the maximum type of impairment of model likelihood function value.
2. the damnification recognition method of Lamb wave monitoring signals statistical parameter according to claim 1, it is characterised in that step 3
The root mean square expression formula is：
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<mi>S</mi>
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Wherein, RMS is root mean square, xiFor i-th of Lamb wave response signal, n is the number of all Lamb wave response signals.
3. the damnification recognition method of Lamb wave monitoring signals statistical parameter according to claim 1, it is characterised in that step 3
The variance expression formula is：
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Wherein, Variance is variance, xiFor i-th of Lamb wave response signal, n is the number of all Lamb wave response signals,
For xiAverage value.
4. the damnification recognition method of Lamb wave monitoring signals statistical parameter according to claim 1, it is characterised in that step 3
The degree of skewness expression formula is：
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Wherein, Skewness is degree of skewness,xiFor i-th of Lamb wave response signal, n is all
The number of Lamb wave response signal,For xiAverage value.
5. the damnification recognition method of Lamb wave monitoring signals statistical parameter according to claim 1, it is characterised in that step 3
The coefficient of kurtosis expression formula is：
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<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mo>)</mo>
</mrow>
<mn>4</mn>
</msup>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
</mrow>
Wherein, Kurtosis is coefficient of kurtosis, xiFor i-th of Lamb wave response signal, n is the individual of all Lamb wave response signals
Number,For xiAverage value.
6. the damnification recognition method of Lamb wave monitoring signals statistical parameter according to claim 1, it is characterised in that step 3
The peak-to-peak value expression formula is：
PPK=max (xi)-min(xi)
Wherein, PPK is peak-to-peak value, max (xi)、min(xi) it is respectively xiMaximum, minimum value, xiFor i-th of Lamb wave response letter
Number.
7. the damnification recognition method of Lamb wave monitoring signals statistical parameter according to claim 1, it is characterised in that step 3
The K factor expression formula is：
K-factor=max (xi)×RMS
Wherein, K-factor is K factor, max (xi) it is xiMaximum, xiFor i-th of Lamb wave response signal, RMS is square
Root.
8. the damnification recognition method of Lamb wave monitoring signals statistical parameter according to claim 1, it is characterised in that the step
Rapid 4 detailed process is：By taking the characteristic data set under health status as an example：
(41) correlation matrix of d × p characteristic data sets under health status is calculated：
<mrow>
<mi>R</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>r</mi>
<mn>11</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>12</mn>
</msub>
</mtd>
<mtd>
<mn>...</mn>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mrow>
<mn>1</mn>
<mi>p</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>r</mi>
<mn>21</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>22</mn>
</msub>
</mtd>
<mtd>
<mn>...</mn>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>r</mi>
<mrow>
<mi>p</mi>
<mn>1</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mrow>
<mi>p</mi>
<mn>2</mn>
</mrow>
</msub>
</mtd>
<mtd>
<mn>...</mn>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mrow>
<mi>p</mi>
<mi>p</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein, d is the number of times of collection Lamb wave response signal, and p is the number of all statistical nature parameters, and R is real symmetric matrix,
rab=rba, a, b=1,2 ..., p, rabFor xaWith xbBetween coefficient correlation, xa,xbThe either rank of data set is characterized, is expressed
Formula is as follows：
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>d</mi>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>c</mi>
<mi>b</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>d</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>d</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>c</mi>
<mi>b</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
Wherein,For xaAverage value,For xbAverage value, xcaFor xaC-th of element, xcbFor xbC-th of element；
(42) correlation matrix R eigenvalue λ is calculateda, and arranged according to order from big to small；
(43) the corresponding characteristic vector of each characteristic value after sequence is calculated；
(44) the corresponding principal component Z of each characteristic value after sequence is calculatedaAccumulation contribution rate：
<mrow>
<mfrac>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>a</mi>
</munderover>
<msub>
<mi>&lambda;</mi>
<mi>h</mi>
</msub>
</mrow>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>g</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>p</mi>
</munderover>
<msub>
<mi>&lambda;</mi>
<mi>g</mi>
</msub>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</mrow>
(45) choose accumulation contribution rate characteristic vector corresponding more than 85% characteristic value and build new feature data set：
A '=A × Ml×m
Wherein, A ' expressions new feature data set, A represents characteristic data set, Ml×mRepresent characteristic value of the contribution rate of accumulative total more than 85%
The matrix that corresponding characteristic vector is constituted, m represents the number of characteristic value of the contribution rate of accumulative total more than 85%, and l is characterized vector
Line number.
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| CN113960160A (en) * | 2021-06-29 | 2022-01-21 | 北京交通大学 | Damage detection method and device based on ultrasonic Lamb wave compact array |
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| CN108536971B (en) * | 2018-04-13 | 2022-04-26 | 广州市建筑科学研究院有限公司 | Bayesian model-based structural damage identification method |
| US10983095B2 (en) | 2018-05-16 | 2021-04-20 | University Of South Carolina | Combined global-local structural health monitoring |
| CN112881167A (en) * | 2020-09-10 | 2021-06-01 | 北京理工大学 | Fretting fatigue crack initiation position determination method |
| CN112858473A (en) * | 2020-12-25 | 2021-05-28 | 杭州浙达精益机电技术股份有限公司 | Turnout switch blade damage state monitoring method based on feature fusion |
| CN112903953A (en) * | 2021-01-21 | 2021-06-04 | 北京航空航天大学 | Metal plate structure damage type identification system and method |
| CN112903953B (en) * | 2021-01-21 | 2022-03-15 | 北京航空航天大学 | Metal plate structure damage type identification system and method |
| CN113884567A (en) * | 2021-06-29 | 2022-01-04 | 北京交通大学 | Steel rail weld damage detection method and device based on ultrasonic Lamb waves |
| CN113960160A (en) * | 2021-06-29 | 2022-01-21 | 北京交通大学 | Damage detection method and device based on ultrasonic Lamb wave compact array |
| CN113884567B (en) * | 2021-06-29 | 2023-12-08 | 北京交通大学 | Rail weld damage detection method and device based on ultrasonic Lamb wave |
| CN113960160B (en) * | 2021-06-29 | 2023-12-08 | 北京交通大学 | Damage detection method and device based on ultrasonic Lamb wave compact array |
| CN113933387A (en) * | 2021-09-08 | 2022-01-14 | 南京邮电大学 | Composite material structure damage monitoring method and system |
| CN113933387B (en) * | 2021-09-08 | 2024-05-14 | 南京邮电大学 | Method and system for monitoring damage of composite material structure |
| CN114692302A (en) * | 2022-03-28 | 2022-07-01 | 中南大学 | Fatigue crack detection method and system based on Gaussian mixture model |
| CN114692302B (en) * | 2022-03-28 | 2023-08-25 | 中南大学 | Fatigue crack detection method and system based on Gaussian mixture model |
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