CN107328868A - A kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type - Google Patents

A kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type Download PDF

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CN107328868A
CN107328868A CN201710500277.4A CN201710500277A CN107328868A CN 107328868 A CN107328868 A CN 107328868A CN 201710500277 A CN201710500277 A CN 201710500277A CN 107328868 A CN107328868 A CN 107328868A
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李强
乔星
陈精杰
何柯
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Abstract

The present invention relates to a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type.The acoustical signal produced first during collection coating test, extract signal characteristic parameter, clustering is carried out to acoustic emission signal, then the signal chosen near each cluster centre carries out wavelet transformation to it, and energy spectrum coefficient is extracted as the characteristic parameter of pattern-recognition, coating damage type is identified according to Energy distribution.The acoustie emission event number of all kinds of damages is finally counted, the data obtained is combined with plus load displacement curve, the critical load and corresponding signal frequency of coating failure process is obtained, failure procedure of the ceramic coating under plus load effect is fully understanded.The present invention provides direct foundation for the failure Mechanism of ceramic coating, and the life prediction to coating normal service is significant.

Description

A kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type
Technical field
The present invention relates to a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type.
Background technology
Ceramic coating refers to sprayed coating of the coating material for ceramics, has been widely used in high-temperature superconductor, electronics industry, aviation The every field such as space flight.It can effectively reduce influence of the working environment to base material, so that the performance of optimization component. At present, the mechanical property and its damage development of ceramic coating are an important research topics.
Acoustic emission testing technology is as a kind of Dynamic Non-Destruction Measurement method, and it has been widely applied to various types of section bar In the damage check of material.Although the damage mode of ceramic coating and damage process are sufficiently complex, during damage all Acoustic emission signal can be produced, therefore ceramic coating failure procedure is monitored in real time by acoustic emission, is research coating The effective means of damage development and failure mechanism.The processing and analysis of acoustic emission signal are the keys of acoustic emission, how to be done The qualitative and quantitative information of acoustic emission source is obtained for research material to effective identification of acoustic emission signal, and from these signals Failure mechanism there is important influence.
As a kind of Dynamic Monitoring, research of the sound emission to coating failure is significant, meanwhile, follow-up letter Number analysis with processing it is also extremely important.Chinese patent (application number:CN200810031180.4 a kind of thermal barrier coating) is disclosed to damage The Acoustic Emission Real-Time Monitoring method of its failure procedure is injured, by carrying out wavelet transformation to thermal barrier coating acoustic emission signal, is extracted Wavelet Energy Spectrum coefficient identifies two kinds of failure moulds of thermal barrier coating surface vertical crack and Interface Crack as signal characteristic parameter Formula.But, this method needs to carry out wavelet transformation to each damage acoustic emission signal and energy spectrum coefficient is calculated, and then takes people Work knows method for distinguishing and carries out pattern-recognition to signal one by one.Due to often producing a large amount of acoustical signals in process of the test, therefore Need to put into substantial amounts of time and efforts during analysis.Chinese patent (application number:CN201310341961.4 one) is disclosed Thermal barrier coating acoustic emission signal automatic identifying method is planted, is characterized in carrying out wavelet package transforms to collected acoustical signal and extracts Energy spectrum coefficient, then builds BP artificial neural networks, and finally identify the corresponding damage of acoustic emission signal by repeatedly training Type, this method improve efficiently the problem of workload is big on the basis of previous patent, but still need to each Individual signal waveform does the extraction of wavelet transformation and energy spectrum coefficient, and process is complex.
The content of the invention
It is an object of the invention to solve above-mentioned to there is problem there is provided a kind of sound of quick identification ceramic coating failure type Transmission signal analysis method, this method can simplify existing signal analysis method on the basis of distortionless, improve signal analysis Efficiency.
To achieve the above object, the technical scheme is that:A kind of sound hair of quick identification ceramic coating failure type Penetrate signal analysis method,
The acoustic emission signal of S1, collection ceramic coating in damage failure procedure;
S2, extraction FEATURE PARAMETERS OF ACOUSTIC EMISSION are simultaneously normalized;
S3, the signal characteristic parameter to being obtained in step S2, carry out clustering, obtain sorted signal and corresponding Cluster centre;
Several nearest signals of S4, each cluster centre of selection carry out wavelet transformation, extract Wavelet Energy Spectrum coefficient conduct The FEATURE PARAMETERS OF ACOUSTIC EMISSION of ceramic coating damage mode is recognized, coating damage type is identified.
In an embodiment of the present invention, it is the method progress by using average variance criterion in the step S2 The normalized of FEATURE PARAMETERS OF ACOUSTIC EMISSION, its principle is to transform data to average for 0, standard deviation for 1 standard just State distribution transformation, is implemented as follows,
For the sample with n acoustic emission signal, the calculation formula of average variance criterion is:
Wherein, xiFor primary signal parameter, xi' it is signal parameter after standardization;For the average of primary signal parameter, σ is Standard deviation.
In an embodiment of the present invention, the FEATURE PARAMETERS OF ACOUSTIC EMISSION includes the duration of acoustic emission signal, shaken The characteristic parameter of width, signal intensity.
In an embodiment of the present invention, the step S3 to implement process as follows,
Euclidean distance conduct is chosen as the input vector of pattern-recognition according to the signal characteristic parameter obtained in step S2 Similarity measure between acoustic emission signal, the corresponding profile value of different value of K is calculated using formula (2), institute is determined according to profile value Choosing classification number,
Wherein, a (l) represent l-th point with its in similar other point between average distance, b (l, k) be one to Amount, represents the average distance of and different classes of middle each point at l-th point;It is that can determine that cluster is effective that s values, which are met more than predetermined threshold value,;
According to the classification number of determination, it is that can obtain sorted signal and corresponding cluster centre to carry out clustering.
In an embodiment of the present invention, the predetermined threshold value of the s values is 0.6.
In an embodiment of the present invention, to implement process as follows by the step S4,
The cluster centre obtained according to step S3, choose several nearest signals of each cluster centre according to formula (3)- (6) calculate and extract Wavelet Energy Spectrum coefficient as the FEATURE PARAMETERS OF ACOUSTIC EMISSION of identification ceramic coating damage mode,
Acoustical signal available waveforms function f (t) is represented:
F (t)=f0(t)+f1(t)+...+fn(t) (3)
Wherein, f0(t),f1(t),...,fn(t) it is the at different levels of decomposed signal;Energy at different levels is:
Gross energy calculation formula is:
Energy coefficient solution formula at different levels is under wavelet scale:
R(i)(t)=E(i)(t)/E(T)(t) (6)
Each frequency range Wavelet Energy Spectrum coefficient is drawn according to above formula, the wherein wavelet scale corresponding to maximum is the feature of signal Yardstick, corresponding frequency range is the characteristic spectra of acoustical signal.
In an embodiment of the present invention, also need to carry out wavelet decomposition scales before the calculating for carrying out extraction Wavelet Energy Spectrum coefficient Calculating, formula is:
Wherein, fsFor sample frequency, LfFor filter length, N is sampling length.
Compared to prior art, the invention has the advantages that:The present invention is the failure Mechanism of ceramic coating There is provided direct foundation, simplify existing signal analysis method on the basis of distortionless, improve the efficiency of signal analysis to applying The life prediction of layer normal service is significant.
Brief description of the drawings
Fig. 1 is analysis method schematic flow sheet of the present invention.
Fig. 2 is the graph of a relation between profile value s in the present invention and cluster classification number k.
Fig. 3 is distribution map of the three class acoustic emission signals in different parameters space.
Fig. 4 is five layers of wavelet decomposition schematic diagram of signal.
Fig. 5 is the wavelets and scaling function function graft of db8 small echos.
Fig. 6 is the ceramic coating damage typical feature energy spectrum diagram of three kinds of acoustic emission signal in the present invention:(a) coating elastoplasticity Deform (b) synusia crackle (c) Interface Crack.
Fig. 7 is the Ring-down count of different failure modes and compression distance in ceramic coating impression failure procedure in the present invention Relation schematic diagram.
Embodiment
1-7, technical scheme is specifically described below in conjunction with the accompanying drawings.
A kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type of the present invention,
The acoustic emission signal of S1, collection ceramic coating in damage failure procedure;
S2, extract FEATURE PARAMETERS OF ACOUSTIC EMISSION (including the spy such as duration, amplitude, the signal intensity of acoustic emission signal Levy parameter) and be normalized;
S3, the signal characteristic parameter to being obtained in step S2, carry out clustering, obtain sorted signal and corresponding Cluster centre;
Several nearest signals of S4, each cluster centre of selection carry out wavelet transformation, extract Wavelet Energy Spectrum coefficient conduct The FEATURE PARAMETERS OF ACOUSTIC EMISSION of ceramic coating damage mode is recognized, coating damage type is identified.
It is that FEATURE PARAMETERS OF ACOUSTIC EMISSION is carried out by using the method for average variance criterion in the step S2 Normalized, its principle is to transform data to average for 0, and standard deviation converts for 1 standardized normal distribution, implement as Under,
For the sample with n acoustic emission signal, the calculation formula of average variance criterion is:
Wherein, xiFor primary signal parameter, xi' it is signal parameter after standardization;For the average of primary signal parameter, σ is Standard deviation.
The step S3 to implement process as follows,
Euclidean distance conduct is chosen as the input vector of pattern-recognition according to the signal characteristic parameter obtained in step S2 Similarity measure between acoustic emission signal, the corresponding profile value of different value of K is calculated using formula (2), institute is determined according to profile value Choosing classification number,
Wherein, a (l) represent l-th point with its in similar other point between average distance, b (l, k) be one to Amount, represents the average distance of and different classes of middle each point at l-th point;It is that can determine that cluster is effective that s values, which are met more than predetermined threshold value,; The predetermined threshold value of the s values is 0.6;
According to the classification number of determination, it is that can obtain sorted signal and corresponding cluster centre to carry out clustering.
It is as follows that the step S4 implements process,
The cluster centre obtained according to step S3, choose several nearest signals of each cluster centre according to formula (3)- (6) calculate and extract Wavelet Energy Spectrum coefficient as the FEATURE PARAMETERS OF ACOUSTIC EMISSION of identification ceramic coating damage mode,
Acoustical signal available waveforms function f (t) is represented:
F (t)=f0(t)+f1(t)+...+fn(t) (3)
Wherein, f0(t),f1(t),...,fn(t) it is the at different levels of decomposed signal;Energy at different levels is:
Gross energy calculation formula is:
Energy coefficient solution formula at different levels is under wavelet scale:
R(i)(t)=E(i)(t)/E(T)(t) (6)
Each frequency range Wavelet Energy Spectrum coefficient is drawn according to above formula, the wherein wavelet scale corresponding to maximum is the feature of signal Yardstick, corresponding frequency range is the characteristic spectra of acoustical signal.
The calculating of progress wavelet decomposition scales is also needed before the calculating for carrying out extraction Wavelet Energy Spectrum coefficient, formula is:
Wherein, fsFor sample frequency, LfFor filter length, N is sampling length.
It is below the specific implementation process of the present invention.
A kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type of the present invention, realizes step such as Under:
(1) acoustic emission signal of the collection ceramic coating in damage failure procedure;
(2) characteristic parameter such as duration, amplitude, signal intensity of acoustic emission signal collected in extraction step (1), And normalized is done to parameters using the method for average variance criterion;
(3) Euclidean distance conduct is chosen as the input vector of pattern-recognition according to the signal parameter obtained in step (2) Similarity measure between acoustic emission signal, the corresponding profile value of different value of K is calculated using formula (2), institute is determined according to profile value Choosing classification number;
(4) the k values determined according to step (3) obtain sorted signal and correspondingly to acoustic emission signal progress clustering Cluster centre;
(5) the nearest several signals of each cluster centre are chosen and carry out wavelet transformation, are counted according to the formula (3)~(6) Calculate and extract Wavelet Energy Spectrum coefficient as the FEATURE PARAMETERS OF ACOUSTIC EMISSION of identification ceramic coating damage mode, wherein selected Wavelet decomposition scales are drawn by formula (7).
The principle of clustering is as follows in the present invention:
Acoustic emission signal clustering method based on unsupervised pattern-recognition, be in damage mode and each signal classification all In the case of unknown, by choosing suitable signal characteristic parameter, according to a certain specific method for measuring similarity between parameter The similar acoustic emission signal of classification is divided into a class with clustering algorithm.Its basic step is:
1) selected acoustic emission signal parameter is normalized and all parameters is converted between [0,1] Number;
2) classification number k is pre-defined, and k sample is chosen according to certain rule and is used as initial cluster centre;
3) distance of each input vector and cluster centre is calculated, input vector is distributed to and its cluster centre distance A minimum class, draws an initial classification schemes, and recalculate cluster centre according to average of all categories;
4) sample is reclassified according to new cluster centre;
5) iterative cycles this 3), 4) process, when cluster centre convergence, cluster terminates.
Wherein, the method that normalized uses average variance criterion, its principle is to transform data to average to be 0, standard deviation converts for 1 standardized normal distribution.
For the sample with n acoustic emission signal, the calculation formula of average variance criterion is:
Wherein, xiFor primary signal parameter, xi' it is signal parameter after standardization;For the average of primary signal parameter, σ is Standard deviation
Classification number k values are determined that k-means clusters the determination of k value profile value by its respective profile value:
Wherein, a (l) represent l-th point with its in similar other point between average distance, b (l, k) be one to Amount, represents the average distance of and different classes of middle each point at l-th point.
Get between the bigger explanation class of s values and class and more open, Clustering Effect is better.Generally, when s value is more than 0.6 It is assured that cluster is effective.
The principle of wavelet analysis is as follows in the present invention:
Wavelet analysis is a kind of new time frequency analysis, transform method, the feature with multiresolution, in time domain and frequency domain all With good resolution ratio, the principle of wavelet transformation is that data are decomposed into a series of Wavelet Component, i.e., small wave scale.It is each small Wave energy level is due to its specific frequency range.
Generally, acoustical signal available waveforms function f (t) is represented:
F (t)=f0(t)+f1(t)+...+fn(t) (3)
Wherein, f0(t),f1(t),...,fn(t) it is the at different levels of decomposed signal;Energy at different levels is:
Gross energy calculation formula is:
Energy coefficient solution formula at different levels is under wavelet scale:
R(i)(t)=E(i)(t)/E(T)(t) (6)
Each frequency range Wavelet Energy Spectrum coefficient is drawn according to above formula, the wherein wavelet scale corresponding to maximum is the feature of signal Yardstick, corresponding frequency range is the characteristic spectra of acoustical signal.
The calculating of progress wavelet decomposition scales is also needed before the calculating for carrying out extraction Wavelet Energy Spectrum coefficient, formula is:
Wherein, fsFor sample frequency, LfFor filter length, N is sampling length.
Embodiment:
Pattern-recognition is carried out to coating failure process by taking 8YSZ thermal barrier coating indentation tests as an example:
Thermal barrier coating sample is prepared using air plasma spraying method, and matrix is Inconel718 high temperature alloys, is glued Knot layer is NiCoCrAlY, and ceramic layer is 8YSZ, and tack coat and ceramic layer thickness are respectively 100 μm and 300 μm.
Fig. 1 is the acoustic emission signal of sample damage in signal analysis flow chart, collection Indentation Process, extracts signal characteristic ginseng Simultaneously it is normalized according to formula (1) for number, then chooses Euclidean distance and is used as similarity measure between acoustic emission signal And clustering is carried out to acoustical signal.The corresponding profile value of different value of K can be obtained according to formula (2) in this example, Fig. 2 is required wheel Relation between exterior feature value s and cluster classification number k.As k=3, s=0.6736, therefore signal can be broadly divided into three classes.Fig. 3 For distribution map of the three class signals in different parameters space after signal clustering.The small of signal can be tried to achieve according to formula (7) Wave Decomposition yardstick is 5 grades, and three nearest class signals of selected distance cluster centre carry out five to it respectively in cluster analysis result Layer wavelet decomposition (shown in Fig. 4), and each frequency band Wavelet Energy Spectrum coefficient is calculated using formula (3)~(6), know as pattern Another characteristic parameter, identifies coating damage type.Wherein first kind signal waveform amplitude is relatively low, and main band is A5 energy Level, its corresponding energy coefficient is 0.5519;Equations of The Second Kind basic frequency of signal band is D5 energy levels, and its corresponding energy coefficient is 0.5017;3rd class basic frequency of signal band is D4 energy levels, and its corresponding energy coefficient is 0.4201.Fig. 5 is this example in signal waveform Selected wavelet basis function --- the wavelets and scaling function functional arrangement of db8 small echos in analysis.Fig. 6 is thermal barrier coating in this example Three kinds of typical sound emission signal characteristic energy spectrum diagrams under indentation load effect, main band is respectively A5 (0-156.25kHz), D5 (156.25-312.5kHz) and D4 (312.5-625kHz), correspondence coating elastic-plastic deformation, synusia cracking and Interface Cracking.Fig. 7 Acoustic emission signal event number and compression distance for each damage mode in thermal barrier coating impression failure procedure in the present invention Graph of a relation, with the increase of loading of pressing in, elastic-plastic deformation first occurs for coat inside, synusia crackle then occurs and interface is split Line.
The present invention uses the technical scheme of the above, with advantages below:Effectively analyze being done to signal waveform and handle it Before (extraction for including wavelet transformation and energy spectrum coefficient) clustering first is done to signal, all signals have been done one clearly point Class.Then the nearest several signals of chosen distance cluster centre do waveform processing, and letter is effectively simplified under the conditions of distortionless Number waveform processing procedures, reduce the workload of signal analysis, improve the analysis efficiency of signal.The chief value of the present invention exists In:A kind of simple and quick signal analysis method is proposed, is provided for the failure Mechanism and life prediction of ceramic coating Direct foundation.
Above is presently preferred embodiments of the present invention, all changes made according to technical solution of the present invention, produced function is made During with scope without departing from technical solution of the present invention, protection scope of the present invention is belonged to.

Claims (7)

1. a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type, it is characterised in that:
The acoustic emission signal of S1, collection ceramic coating in damage failure procedure;
S2, extraction FEATURE PARAMETERS OF ACOUSTIC EMISSION are simultaneously normalized;
S3, the signal characteristic parameter to being obtained in step S2, carry out clustering, obtain sorted signal and corresponding cluster Center;
Several nearest signals of S4, each cluster centre of selection carry out wavelet transformation, extract Wavelet Energy Spectrum coefficient and are used as identification The FEATURE PARAMETERS OF ACOUSTIC EMISSION of ceramic coating damage mode, identifies coating damage type.
2. a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type according to claim 1, its It is characterised by:It is that FEATURE PARAMETERS OF ACOUSTIC EMISSION is carried out by using the method for average variance criterion in the step S2 Normalized, its principle is to transform data to average for 0, and standard deviation converts for 1 standardized normal distribution, implements It is as follows,
For the sample with n acoustic emission signal, the calculation formula of average variance criterion is:
<mrow> <msubsup> <mi>x</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> <mi>&amp;sigma;</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein, xiFor primary signal parameter, x 'iFor signal parameter after standardization;For the average of primary signal parameter, σ is standard Difference.
3. a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type according to claim 1 or 2, It is characterized in that:Duration of the FEATURE PARAMETERS OF ACOUSTIC EMISSION including acoustic emission signal, amplitude, the feature of signal intensity Parameter.
4. a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type according to claim 1, its It is characterised by:The step S3 to implement process as follows,
Euclidean distance is chosen according to the signal characteristic parameter obtained in step S2 as the input vector of pattern-recognition to send out as sound Similarity measure between signal is penetrated, the corresponding profile value of different value of K is calculated using formula (2), is divided according to selected by being determined profile value Class number,
<mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mn>1</mn> <mi>n</mi> </munderover> <mfrac> <mrow> <mo>&amp;lsqb;</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>(</mo> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mi>a</mi> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>max</mi> <mo>&amp;lsqb;</mo> <mi>a</mi> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>min</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>(</mo> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein, a (l) represents the average distance between l-th point of other points with its in similar, and b (l, k) is a vector, table Show the average distance of and different classes of middle each point at l-th point;It is that can determine that cluster is effective that s values, which are met more than predetermined threshold value,;
According to the classification number of determination, it is that can obtain sorted signal and corresponding cluster centre to carry out clustering.
5. a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type according to claim 1, its It is characterised by:The predetermined threshold value of the s values is 0.6.
6. a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type according to claim 1, its It is characterised by:It is as follows that the step S4 implements process,
The cluster centre obtained according to step S3, chooses several nearest signals of each cluster centre according to formula (3)-(6) Calculate and extract Wavelet Energy Spectrum coefficient as the FEATURE PARAMETERS OF ACOUSTIC EMISSION of identification ceramic coating damage mode,
Acoustical signal available waveforms function f (t) is represented:
F (t)=f0(t)+f1(t)+...+fn(t) (3)
Wherein, f0(t),f1(t),...,fn(t) it is the at different levels of decomposed signal;Energy at different levels is:
<mrow> <msup> <mi>E</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>&amp;tau;</mi> <mo>=</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> </mrow> <mi>t</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msup> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Gross energy calculation formula is:
<mrow> <msup> <mi>E</mi> <mrow> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </msubsup> <msup> <mi>E</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Energy coefficient solution formula at different levels is under wavelet scale:
R(i)(t)=E(i)(t)/E(T)(t) (6)
Each frequency range Wavelet Energy Spectrum coefficient is drawn according to above formula, the wherein wavelet scale corresponding to maximum is the feature chi of signal Degree, corresponding frequency range is the characteristic spectra of acoustical signal.
7. a kind of Analysis of Acoustic Emission Signal method of quick identification ceramic coating failure type according to claim 6, its It is characterised by:The calculating of progress wavelet decomposition scales is also needed before the calculating for carrying out extraction Wavelet Energy Spectrum coefficient, formula is:
<mrow> <msub> <mi>J</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>&amp;lsqb;</mo> <mi>int</mi> <mrow> <mo>(</mo> <msub> <mi>log</mi> <mn>2</mn> </msub> <mfrac> <msub> <mi>f</mi> <mi>s</mi> </msub> <mn>20</mn> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mi>int</mi> <mrow> <mo>(</mo> <msub> <mi>log</mi> <mn>2</mn> </msub> <mfrac> <mi>N</mi> <msub> <mi>L</mi> <mi>f</mi> </msub> </mfrac> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Wherein, fsFor sample frequency, LfFor filter length, N is sampling length.
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