CN103776901A - Visco-elastic interlayer structure aging state identification method based on vibration response message - Google Patents

Abstract

The invention discloses a visco-elastic interlayer structure aging state identification method based on a vibration response message. The identification method comprises the following steps: firstly, obtaining the vibration response message of the structure through a random excitation experiment; then constructing a self-adapted second-generation wavelet based on signal waveform characteristics, and further providing a self-adapted redundancy second generation wavelet packet transform method for pre-processing a vibration response signal; extracting frequency domain statistical characteristics of each frequency band signal Hilbert spectrum envelope to form an original characteristic set; then, selecting a small quantity of sensitive characteristics from a large amount of original characteristic sets based on a distance estimation technology; finally, constructing a multi-wavelet kernel function based on a multi-wavelet theory and providing a multi-wavelet support vector machine method by combining a support vector machine; and achieving the automatic identification of a visco-elastic interlayer structure aging state by using the selected sensitive characteristics as inputs of the multi-wavelet support vector machine.

Description

Viscoelastic sandwich construction ageing state recognition methods based on vibratory response information

Technical field

The present invention relates to the recognition methods of physical construction health status, particularly a kind of recognition methods of viscoelastic sandwich construction ageing state.

Background technology

Viscoelastic sandwich construction has the performances such as good sealing, vibration damping, noise reduction, extensive in application in machine equipments.In long-term use procedure, owing to being subject to the impact of the environmental factors such as temperature, humidity, vibration and variation thereof, the catabiosis such as viscoelastic material will inevitably relax, hardens, embrittlement, change the dynamic perfromance of viscoelastic sandwich construction, and then affect the usability of structure.Therefore, identification viscoelastic sandwich construction ageing state, to improving structural reliability, improve structure practicality and have great importance.Meanwhile, be also Efficient Evaluation Whole Equipment usefulness in the urgent need to, for extension device serviceable life, guarantee that its safety in utilization has important engineering use value.

Conventional structure ageing state recognition methods at present mainly contains the method based on model and the method based on vibratory response.But, the constituent complexity of viscoelastic sandwich construction, the dynamics of viscoelastic material is non-constant, and the difficulty that this has all increased model solution has restricted the accuracy rate of model solution.The vibratory response information recognition structure characteristic that method based on vibratory response utilizes structure to produce under external drive, for identification viscoelastic sandwich construction ageing state provides convenience, effective approach.In the time that in various degree aging appears in viscoelastic sandwich construction, the dynamics of structure, as rigidity, damping etc. can change, shows as the variation of structural vibration response information under external drive.Therefore, analyzing the otherness of vibratory response information under the different ageing states of viscoelastic sandwich construction, extract and select effectively to describe the characteristic index of this otherness, is a kind of effectively technological approaches based on the automatic recognition structure ageing state of intelligent classification algorithm.

Summary of the invention

The object of this invention is to provide a kind of vibratory response information of utilizing external drive to produce and identify the method for viscoelastic sandwich construction ageing state.The method precision is high, cost is low, simple and reliable, be convenient to be applied in engineering reality.

For reaching above object, the present invention takes following technical scheme to be achieved:

A viscoelastic sandwich construction ageing state recognition methods based on vibratory response information, is characterized in that, comprises following steps:

(1) obtaining of vibratory response information

By shaking table and control system thereof, viscoelastic sandwich construction is applied to arbitrary excitation, after vibration is stable, gather vibratory response information;

(2) feature extraction based on self-adaptive redundant Second Generation Wavelets packet transform

First, based on the adaptive Second Generation Wavelets of signal waveform latent structure, vibration response signal x is carried out to 1 layer of Second Generation Wavelet Transformation, take the Hilbert envelope spectrum entropy index of detail signal d as objective function, utilize genetic algorithm for solving to make its minimum fallout predictor P _opt; Suppose detail signal { d _ihilbert envelope spectrum be { f _i, calculate the distribution probability density p of its spectrum value in whole spectrum _i, the objective function of fallout predictor is defined as:

$E_f=-\stackrel{n}{\mathrm{\Σ}}{p}_i\ln p_i$

In order to make approximation signal s can more accurately characterize the original feature except detail signal in No. i of believing, with reconstructed error J _uas the criterion of renovator, solve and make J _uminimum renovator U _opt, J _ube defined as:

$J_U=E\left\{{({\hat{s}}^{\left(0\right)}-s^{\left(0\right)})}^2\right\}+E\left\{{({\hat{d}}^{\left(0\right)}-d^{\left(0\right)})}^2\right\}$

Wherein,

with

be respectively reconstruction signal in the time of detail signal d=0 even sequence sample and odd sequence sample; E{} represents mathematical expectation;

Secondly, according to the adaptive predictor P of structure _optwith adaptive updates device U _opt, utilize the method for interpolation zero padding to obtain the redundancy fallout predictor of l layer with redundancy renovator

propose self-adaptive redundant second generation wavelet packet transform method, it decomposes and restructuring procedure is shown below respectively:

$\left\{\begin{array}{c}{c}_{l+\mathrm{1,2}}=c_{l,1}-P_{\mathrm{opt}}^{(l+1)}\left(c_{l,1}\right)\\ c_{l+\mathrm{1,1}}=C_{l,1}+U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)\\ ...\\ c_{{l+\mathrm{1,2}}^{l+1}}=c_{{\mathrm{1,2}}^l}-P_{\mathrm{opt}}^{(l+1)}\left(c_{{l,2}^t}\right)\\ c_{l+1,2^{l+1}-1}=c_{{\mathrm{1,2}}^l}+U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)\end{array}\right.$

$\left\{\begin{array}{c}{c}_{l,1}=\frac{1}{2}(c_{l+\mathrm{1,1}}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)+c_{l+\mathrm{1,2}}+P_{\mathrm{opt}}^{(l+1)}(c_{l+\mathrm{1,1}}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)))\\ ...\\ c_{{l,2}^l}=\frac{1}{2}(c_{l+1,2^{l+1}-1}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)+c_{l+1,2^{l+1}}+P_{\mathrm{opt}}^{(l+1)}(c_{l+1,2^{l+1}-1}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)))\end{array}\right.$

Finally, the self-adaptive redundant Second Generation Wavelets packet transform based on proposing carries out feature extraction, and vibration response signal is carried out at least three layers of WAVELET PACKET DECOMPOSITION, extracts respectively the frequency domain statistical nature composition primitive character collection of each band signal Hilbert envelope spectrum;

(3) select based on the sensitive features apart from assessment technology

By the evaluation factor of j feature, be defined as:

${\mathrm{\α}}_j=d_j^{\left(b\right)}/d_j^{\left(w\right)}$

Wherein,

represent the mean value of the between class distance of a j feature C class;

represent the mean value of the inter-object distance of a j feature C class, α _jsize reflected j the complexity that feature is classified to C class, α _jj feature of larger expression is more responsive, more easily C class is classified, and selects α _jcorresponding feature forms sensitive features collection;

(4) Classification and Identification based on many wavelet support vector machines

First, construct many Wavelet Kernel Functions according to support vector machine kernel function condition and many wavelet transformation theory, adopt the many small echos of GHM, many Wavelet Kernel Functions of structure are defined as follows:

$K_1(x,x^{\′})=\underset{i=1}{\overset{d}{\mathrm{\Π}}}\mathrm{COR}\left({\mathrm{\ψ}}_1\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)+\underset{i=1}{\overset{d}{\mathrm{\Π}}}\mathrm{COR}\left({\mathrm{\ψ}}_2\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)$

$K_2(x,x^{\′})=\underset{i=1}{\overset{d}{\mathrm{\Π}}}(\mathrm{COR}\left({\mathrm{\ψ}}_1\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)\×\mathrm{COR}\left({\mathrm{\ψ}}_2\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right))$

Wherein: K represents kernel function; D represents sample dimension; ψ _k(), k=1,2 represent two many wavelet functions of GHM; $\mathrm{COR}\left({\mathrm{\ψ}}_k\right)={\∫}_{-\∞}^{\∞}{\mathrm{\ψ}}_k\left(v\right){\mathrm{\ψ}}_k(t+v)\mathrm{d\; v}$ Represent the auto-correlation of many wavelet functions,

Secondly, many Wavelet Kernel Functions of structure are combined with support vector machine, realize the Classification and Identification of many wavelet support vector machines;

Finally, many wavelet support vector machines are exported the categorised decision function of following form:

$f\left(x\right)=\mathrm{sign}[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i{K}_k(x,x_i)+b]$

Wherein: x represents unknown sample; N represents training sample number; K=1 or 2, represents respectively the Wavelet Kernel Function more than two of structure can automatically identify the ageing state of the corresponding viscoelastic sandwich construction of unknown sample according to this categorised decision function.

In said method, described evaluation factor α _jselection is greater than a threshold value, the mean value that this Threshold is all evaluation factors.

The present invention has realized modern signal processing, sensitive features is selected and the mixing of many wavelet support vector machines Classification and Identification on algorithm.Its advantage is, utilize vibratory response information identification viscoelastic sandwich construction ageing state, have simply, reliably, easily go, cost is low, the feature such as real-time, is applicable to the ageing state of on-the-spot Real time identification viscoelastic sandwich construction, is conducive to improve reliability of structure and security, for the identification of small sample structure ageing state provides new approaches and new method, there is important engineering practical value.

Accompanying drawing explanation

Below in conjunction with the drawings and the specific embodiments, the present invention is described in further detail.

Fig. 1 is viscoelastic sandwich construction ageing state identification process figure of the present invention.

Fig. 2 is the decomposition and reconstruction schematic diagram of the self-adaptive redundant Second Generation Wavelets packet transform that proposes in Fig. 1.In figure, x represents original signal;

represent reconstruction signal;

with represent respectively the l layer redundancy fallout predictor and the redundancy renovator that utilize interpolation zero padding method to obtain.

Fig. 3 is many Wavelet Kernel Functions figure of structure.Wherein, Fig. 3 (a) represents the figure of many Wavelet Kernel Functions 1 of structure; Fig. 3 (b) represents the figure of many Wavelet Kernel Functions 2 of structure.

Fig. 4 is the structure diagram of the viscoelastic sandwich construction that designs and produces.As shown in FIG., this viscoelastic sandwich construction is mainly made up of metal material and viscoelastic material (rubber), by coupling bolt, metal level and rubber layer is compressed, for measuring bolt snap-in force, at pressure transducer of nut arranged beneath.

Fig. 5 is shaking table applies arbitrary excitation power spectrum density to viscoelastic sandwich construction, and excitation frequency scope is 10-2000Hz.Within the scope of 50-1000Hz, excitation energy maintains 0.005g ²/ Hz.In figure, horizontal ordinate represents frequency, and unit is hertz (Hz); Ordinate represents power spectrum density, and unit is g ²/ Hz.

Fig. 6 is the time-domain diagram of the different ageing states of viscoelastic sandwich construction vibration response signal under outside arbitrary excitation.Wherein, Fig. 6 (a)～(m) be respectively time domain waveform figure of structure vibration response signal in the time of 1～13 kind of ageing state.In figure, horizontal ordinate represents the time, and unit is s; Ordinate represents amplitude, and unit is g.

Fig. 7 is the sensitive features selection figure based on apart from assessment technology.In figure, horizontal ordinate represents sample, ordinate representation feature evaluation factor.

Fig. 8 is the viscoelastic sandwich construction ageing state recognition result that adopts the inventive method.Wherein, Fig. 8 (a) is for using support vector machine (brief note the is MSVM1) recognition result of many Wavelet Kernel Functions 1; Fig. 8 (b) is for using support vector machine (brief note the is MSVM2) recognition result of many Wavelet Kernel Functions 2.In figure, horizontal ordinate represents the test sample book of 13 kinds of ageing states, and ordinate represents the class label of each test sample book.

Its embodiment

Shown in Fig. 1, be viscoelastic sandwich construction ageing state identification process figure, test the vibratory response information that obtains viscoelastic sandwich construction by arbitrary excitation; Based on the adaptive Second Generation Wavelets of signal waveform latent structure, and then proposition self-adaptive redundant second generation wavelet packet transform method, and for the pre-service of vibration response signal, then extract respectively the frequency domain statistical nature composition primitive character collection of each band signal Hilbert envelope spectrum; Based on concentrating and select minority sensitive features from a large amount of primitive characters apart from assessment technology; Construct many Wavelet Kernel Functions based on many wavelet theories, and many wavelet support vector machines of proposition method that combines with support vector machine, the input using sensitive features as many wavelet support vector machines, realizes the automatic identification of viscoelastic sandwich construction ageing state.

The present invention utilizes vibratory response information identification viscoelastic sandwich construction ageing state to implement by following concrete steps:

(1) obtaining of vibratory response information

Viscoelastic sandwich construction is arranged on shaking table, by shaking table and control system thereof, structure is applied to arbitrary excitation, after vibration is stable, gather the vibratory response information of structure.

(2) feature extraction based on self-adaptive redundant Second Generation Wavelets packet transform

With reference to figure 2, first, based on the adaptive Second Generation Wavelets of signal waveform latent structure.Vibration response signal x is carried out to 1 layer of Second Generation Wavelet Transformation, take the Hilbert envelope spectrum entropy index of detail signal d as objective function, utilize genetic algorithm for solving to make its minimum fallout predictor P _opt.Suppose detail signal { d _ihilbert envelope spectrum be _fi}, calculates the distribution probability density p of its spectrum value in whole spectrum _i, the objective function of fallout predictor is defined as:

$E_f=-\underset{i}{\overset{n}{\mathrm{\Σ}}}{p}_i\ln p_i$

In order to make approximation signal s can more accurately characterize the feature except detail signal in original signal, with reconstructed error J _uas the criterion of renovator, solve and make J _uminimum renovator U _opt, J _ube defined as:

$J_U=E\left\{{({\hat{s}}^{\left(0\right)}-s^{\left(0\right)})}^2\right\}+E\left\{{({\hat{d}}^{\left(0\right)}-d^{\left(0\right)})}^2\right\}$

Wherein, with

be respectively reconstruction signal in the time of detail signal d=0 even sequence sample and odd sequence sample; E{} represents mathematical expectation.

Secondly, according to the adaptive predictor P of structure _optwith adaptive updates device U _opt, utilize the method for interpolation zero padding to obtain the redundancy fallout predictor of l layer

with redundancy renovator

propose self-adaptive redundant second generation wavelet packet transform method, it decomposes and restructuring procedure is shown below respectively:

$\left\{\begin{array}{c}{c}_{l+\mathrm{1,2}}=c_{l,1}-P_{\mathrm{opt}}^{(l+1)}\left(c_{l,1}\right)\\ c_{l+\mathrm{1,1}}=C_{l,1}+U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)\\ ...\\ c_{{l+\mathrm{1,2}}^{l+1}}=c_{{\mathrm{1,2}}^l}-P_{\mathrm{opt}}^{(l+1)}\left(c_{{l,2}^t}\right)\\ c_{l+1,2^{l+1}-1}=c_{{\mathrm{1,2}}^l}+U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)\end{array}\right.$

$\left\{\begin{array}{c}{c}_{l,1}=\frac{1}{2}(c_{l+\mathrm{1,1}}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)+c_{l+\mathrm{1,2}}+P_{\mathrm{opt}}^{(l+1)}(c_{l+\mathrm{1,1}}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)))\\ ...\\ c_{{l,2}^l}=\frac{1}{2}(c_{l+1,2^{l+1}-1}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)+c_{l+1,2^{l+1}}+P_{\mathrm{opt}}^{(l+1)}(c_{l+1,2^{l+1}-1}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)))\end{array}\right.$

Finally, the self-adaptive redundant Second Generation Wavelets packet transform based on proposing carries out feature extraction.Vibration response signal is carried out to 3 layers of WAVELET PACKET DECOMPOSITION, extract respectively the frequency domain statistical nature composition primitive character collection of each band signal Hilbert envelope spectrum.

(3) select based on the sensitive features apart from assessment technology

The of a sort inter-object distance of a certain feature is less, and inhomogeneous between class distance is larger, and this feature is more responsive.The evaluation factor of j feature, is defined as:

${\mathrm{\α}}_j=d_j^{\left(b\right)}/d_j^{\left(w\right)}$

Wherein,

represent the mean value of the between class distance of a j feature C class;

represent the mean value of the inter-object distance of a j feature C class

α _jsize reflected j the complexity that feature is classified to C class.α _jj feature of larger expression is more responsive, more easily C class is classified.Selection is greater than the α of certain threshold value _jcorresponding feature forms sensitive features collection, the mean value that wherein this Threshold is all evaluation factors.

(4) Classification and Identification based on many wavelet support vector machines

First, construct many Wavelet Kernel Functions according to support vector machine kernel function condition and many wavelet transformation theory.In the present invention, many small echos are elected the many small echos of the most frequently used GHM as, and many Wavelet Kernel Functions of structure are defined as follows:

$K_1(x,x^{\′})=\underset{i=1}{\overset{d}{\mathrm{\Π}}}\mathrm{COR}\left({\mathrm{\ψ}}_1\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)+\underset{i=1}{\overset{d}{\mathrm{\Π}}}\mathrm{COR}\left({\mathrm{\ψ}}_2\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)$ $K_2(x,x^{\′})=\underset{i=1}{\overset{d}{\mathrm{\Π}}}(\mathrm{COR}\left({\mathrm{\ψ}}_1\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)\×\mathrm{COR}\left({\mathrm{\ψ}}_2\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right))$

Wherein: K represents kernel function; D represents sample dimension; ψ _k(), k=1,2 represent wavelet function more than two;

represent the auto-correlation of many wavelet functions.The Wavelet Kernel Function more than two constructing as shown in Figure 3.

Secondly, many Wavelet Kernel Functions of structure are combined with support vector machine, realize the Classification and Identification of many wavelet support vector machines.The structure of many wavelet support vector machines and traditional support vector machine is basic identical, and difference is the kernel function difference that they use.

Finally, many wavelet support vector machines are exported the categorised decision function of following form:

$f\left(x\right)=\mathrm{sign}[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i{K}_k(x,x_i)+b]$

Wherein: x represents unknown sample; N represents training sample number; K=1 or 2, represents respectively the Wavelet Kernel Function more than two of constructing.

Can automatically identify the ageing state of the corresponding viscoelastic sandwich construction of unknown sample according to the test output of many wavelet support vector machines.

Below provide a concrete application example process, simultaneous verification the validity of the present invention in engineering application.

Design and produce a kind of typical viscoelastic sandwich construction, as shown in Figure 4, this structure is mainly made up of metal material and viscoelastic material (rubber), and viscoelastic material is clipped in the middle of metal material, by coupling bolt, structure is packed together to a structural entity.First, viscoelastic material is put into a senile experiment case and carry out senile experiment, when experiment, temperature is 110 ℃, and air circulation mode is forced-air blast.Common mode has been intended 13 kinds of ageing states, and the days of ageing that every kind of state is corresponding is as shown in table 1.Therefrom can find out, from ageing state 1 to ageing state 13, the degree of aging of viscoelastic sandwich construction is deepened successively.

Table 1 viscoelastic sandwich construction ageing state and mark

Secondly, viscoelastic sandwich construction is arranged on shaking table and carries out arbitrary excitation experiment, the pretightning force of viscoelastic sandwich construction is consistent: 7500N.The power spectrum density of exciting force as shown in Figure 5.By acceleration transducer and data acquisition equipment collection and store the vibratory response information of structure under 13 kinds of ageing states.Under 13 kinds of ageing states of viscoelastic sandwich construction, the time domain waveform of vibration response signal as shown in Figure 6.As can be seen from Figure 6, under 13 kinds of states, the time domain waveform of structure dynamic response signal there are differences, but there is no regular difference, fails intuitively to reflect the ageing state of structure.

Utilize the method for the invention, first, based on the adaptive Second Generation Wavelets of signal waveform latent structure, adopt self-adaptive redundant Second Generation Wavelets packet transform to carry out 3 layers of decomposition to vibration response signal, extract respectively the frequency domain statistical nature composition primitive character collection of each band signal Hilbert envelope spectrum; Then, based on concentrating and select minority sensitive features from a large amount of primitive characters apart from assessment technology, as shown in Figure 7; Finally, the input using the sensitive features of selecting as the many wavelet support vector machines that propose, realizes the automatic identification of viscoelastic sandwich construction ageing state.Wherein, the penalty factor of many wavelet support vector machines is set as 100, and kernel functional parameter adopts cross-validation method search optimal value in [0.25,0.5,1～16].Recognition result is as shown in Fig. 8 and table 2, and wherein using the support vector machine brief note of many Wavelet Kernel Functions 1 is MSVM1, and using the support vector machine brief note of many Wavelet Kernel Functions 2 is MSVM2.Can find out from Fig. 8 and table 2, MSVM1 and MSVM2 have shown same good ageing state recognition result, 5 wrong increments in 390 test sample books of 13 kinds of states, are only there are originally, recognition accuracy has reached 98.72%, thereby has verified the validity of the present invention aspect identification viscoelastic sandwich construction ageing state.

Table 2 viscoelastic sandwich construction ageing state recognition accuracy (%)

Claims (2)

1. the viscoelastic sandwich construction ageing state recognition methods based on vibratory response information, is characterized in that, comprises following steps:

(1) obtaining of vibratory response information

By shaking table and control system thereof, viscoelastic sandwich construction is applied to arbitrary excitation, after vibration is stable, gather vibratory response information;

(2) feature extraction based on self-adaptive redundant Second Generation Wavelets packet transform

First, based on the adaptive Second Generation Wavelets of signal waveform latent structure, vibration response signal x is carried out to 1 layer of Second Generation Wavelet Transformation, take the Hilbert envelope spectrum entropy index of detail signal d as objective function, utilize genetic algorithm for solving to make its minimum fallout predictor P _opt; Suppose detail signal { d _ihilbert envelope spectrum be { f _i, calculate the distribution probability density p of its spectrum value in whole spectrum _i, the objective function of fallout predictor is defined as:

$E_f=-\stackrel{n}{\mathrm{\Σ}}{p}_i\ln p_i$

In order to make approximation signal s can more accurately characterize the original feature except detail signal in No. i of believing, with reconstructed error J _uas the criterion of renovator, solve and make J _uminimum renovator U _opt, J _ube defined as:

$J_U=E\left\{{({\hat{s}}^{\left(0\right)}-s^{\left(0\right)})}^2\right\}+E\left\{{({\hat{d}}^{\left(0\right)}-d^{\left(0\right)})}^2\right\}$

Wherein,

with

be respectively reconstruction signal in the time of detail signal d=0

even sequence sample and odd sequence sample; E{} represents mathematical expectation;

Secondly, according to the adaptive predictor P of structure _optwith adaptive updates device U _opt, utilize the method for interpolation zero padding to obtain the redundancy fallout predictor of l layer

with redundancy renovator

propose self-adaptive redundant second generation wavelet packet transform method, it decomposes and restructuring procedure is shown below respectively:

$\left\{\begin{array}{c}{c}_{l+\mathrm{1,2}}=c_{l,1}-P_{\mathrm{opt}}^{(l+1)}\left(c_{l,1}\right)\\ c_{l+\mathrm{1,1}}=C_{l,1}+U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)\\ ...\\ c_{{l+\mathrm{1,2}}^{l+1}}=c_{{\mathrm{1,2}}^l}-P_{\mathrm{opt}}^{(l+1)}\left(c_{{l,2}^t}\right)\\ c_{l+1,2^{l+1}-1}=c_{{\mathrm{1,2}}^l}+U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)\end{array}\right.$

$\left\{\begin{array}{c}{c}_{l,1}=\frac{1}{2}(c_{l+\mathrm{1,1}}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)+c_{l+\mathrm{1,2}}+P_{\mathrm{opt}}^{(l+1)}(c_{l+\mathrm{1,1}}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+\mathrm{1,2}}\right)))\\ ...\\ c_{{l,2}^l}=\frac{1}{2}\left(c_{l+1,2^{l+1}-1}\right)-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right)+c_{l+1,2^{l+1}}+P_{\mathrm{opt}}^{(l+1)}(c_{l+1,2^{l+1}-1}-U_{\mathrm{opt}}^{(l+1)}\left(c_{l+1,2^{l+1}}\right))\end{array}\right.$

Finally, the self-adaptive redundant Second Generation Wavelets packet transform based on proposing carries out feature extraction, and vibration response signal is carried out at least three layers of WAVELET PACKET DECOMPOSITION, extracts respectively the frequency domain statistical nature composition primitive character collection of each band signal Hilbert envelope spectrum;

(3) select based on the sensitive features apart from assessment technology

By the evaluation factor of j feature, be defined as:

${\mathrm{\α}}_j=d_j^{\left(b\right)}/d_j^{\left(w\right)}$

Wherein,

represent the mean value of the between class distance of a j feature C class;

represent the mean value of the inter-object distance of a j feature C class, α _jsize reflected j the complexity that feature is classified to C class, α _jj feature of larger expression is more responsive, more easily C class is classified, and selects to be greater than the α of certain threshold value _jcorresponding feature forms sensitive features collection;

(4) Classification and Identification based on many wavelet support vector machines

First, construct many Wavelet Kernel Functions according to support vector machine kernel function condition and many wavelet transformation theory, adopt the many small echos of GHM, many Wavelet Kernel Functions of structure are defined as follows:

$K_1(x,x^{\′})=\underset{i=1}{\overset{d}{\mathrm{\Π}}}\mathrm{COR}\left({\mathrm{\ψ}}_1\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)+\underset{i=1}{\overset{d}{\mathrm{\Π}}}\mathrm{COR}\left({\mathrm{\ψ}}_2\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)$

$K_2(x,x^{\′})=\underset{i=1}{\overset{d}{\mathrm{\Π}}}(\mathrm{COR}\left({\mathrm{\ψ}}_1\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right)\×\mathrm{COR}\left({\mathrm{\ψ}}_2\left(\frac{x_i-{x_i}^{\′}}{a}\right)\right))$

Wherein: K represents kernel function; D represents sample dimension; ψ _k(), k=1,2 represent two many wavelet functions of GHM; $\mathrm{COR}\left({\mathrm{\ψ}}_k\right)={\∫}_{-\∞}^{\∞}{\mathrm{\ψ}}_k\left(v\right){\mathrm{\ψ}}_k(t+v)\mathrm{d\; v}$ Represent the auto-correlation of many wavelet functions,

Secondly, many Wavelet Kernel Functions of structure are combined with support vector machine, realize the Classification and Identification of many wavelet support vector machines;

Finally, many wavelet support vector machines are exported the categorised decision function of following form:

$f\left(x\right)=\mathrm{sign}[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i{K}_k(x,x_i)+b]$

Wherein: x represents unknown sample; N represents training sample number; K=1 or 2, represents respectively the Wavelet Kernel Function more than two of structure can automatically identify the ageing state of the corresponding viscoelastic sandwich construction of unknown sample according to this categorised decision function.

2. the viscoelastic sandwich construction ageing state recognition methods based on vibratory response information as claimed in claim 1, is characterized in that described evaluation factor α _jselection is greater than a threshold value, the mean value that this Threshold is all evaluation factors.

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