CN103335617B - A kind of railway track geometric deformation detection method based on vibration signal - Google Patents

Abstract

The present invention relates to a kind of railway track geometric deformation detection method based on vibration signal, belong to train rail failure monitoring and diagnostic techniques field.Based on the vibration data of train diverse location geometric deformation kind, Short Time Fourier Transform is carried out to signal and obtains rumble spectrum; Extract spectrum signature, adopt principal component analysis (PCA) to the Feature Dimension Reduction extracted, obtain dominant frequency spectrum signature; For the support vector machine of each geometric deformation kind, set up the reliability computation model of each geometric deformation kind; During on-line checkingi, according to real-time measuring vibrations data, extract spectrum signature, and then obtain dominant frequency spectrum signature, the credit model of the geometric deformation kind adopting calculated off-line to obtain calculates the reliability being under the jurisdiction of every class, obtains diagnosis reliability vector according to reliability.This method can Precise Diagnosis locate the situation of geometric deformation kind.The bullet train being arranged on real time execution can carry out the on-line analysis of geometric deformation kind and the diagnosis of track.

Description

A kind of railway track geometric deformation detection method based on vibration signal

Technical field

The present invention relates to a kind of railway track geometric deformation detection method based on vibration signal, belong to train rail failure monitoring and diagnostic techniques field.

Background technology

Railway track is the basis of driving, and it directly bears the great force that train wheel transmits.Under the effect of these power, will there is various distortion in track, affect traffic safety.Along with the development of Line for Passenger Transportation, the contradiction of transport and track maintenance and repair.Static track irregularity can not reflect the state of track very well, and the track irregularity really had an impact to traffic safety, wheel-rail force, Vehicular vibration is dynamic track irregularity.Manual static checks that data can not adapt to the requirement of railway according to the permanent way maintenance method formulating maintenance plan, dynamic inspection car simultaneously for overhauling high-speed railway dynamic track irregularity needs to take service chart, cost is high, detects frequency low, is also difficult to the diagnostic requirements meeting circuit.

This geometric deformation detection method relies on a set of acceleration transducer hardware harvester, can be easily installed on passenger traffic bullet train, the vibration signal in Real-time Collection axle box, bogie and compartment etc. place interested, algorithm carries out Short Time Fourier Transform according to single-sensor signal, carry out extraction and the compression of feature, carry out diagnosing to preassigned geometric deformation kind and analyze, obtain corresponding reliability, then the result of multiple sensor diagnostic is merged, subsequently geometric deformation information and geographical location information are bound, be uploaded to monitoring center's process.

Summary of the invention

The object of the invention is the geometric deformation detection method proposing a kind of railway track based on vibration signal, gather the sensor vibration signal of multichannel in train travelling process, Short Time Fourier Transform is adopted to obtain rumble spectrum, extract spectrum signature, pivot analysis is adopted to obtain dominant frequency spectrum signature, off-line phase carries out the training of whole system parameter, the parameter that on-line stage utilizes calculated off-line to obtain according to the signal gathered carries out real-time calculating, obtain geometric deformation kind reliability corresponding with rail, realize the real-time online diagnosis of geometric deformation kind.

The present invention proposes a kind of railway track geometric deformation detection method based on vibration signal, comprises following steps:

(1) setting the set of train rail geometric deformation kind is Θ={ F ₁, F ₂, F ₃, F ₄, wherein, F _jrepresent the geometric deformation kind of the jth type in geometric deformation kind set Θ, j=1,2,3,4, the first geometric deformation is track centerline and the desirable track centerline vertical geometric position deviation along its length of rail reality, and the second geometric deformation is Rail Surface is corrugated shape wearing and tearing, the third geometric deformation is that Rail Surface regional area peels off, and the 4th kind of geometric deformation is that Rail Surface is without geometric deformation;

(2) vibration transducer s is set respectively at the axle box of train, bogie and car bottom _k, during train operation, the vibration signal of the corresponding site that three vibration transducers gather respectively, obtains three vibration signal sequence { x _k(m) }, k=1,2,3, the vibration signal sequence that axle box records is designated as { x ₁(m) }, the vibration signal sequence that bogie records is designated as { x ₂(m) }, the vibration signal sequence that car bottom records is designated as { x ₃(m) }, wherein, m is sampling instant, m=1 ..., M, M represent seasonal effect in time series length, carry out Short Time Fourier Transform respectively, obtain three rumble spectrums to above-mentioned three vibration signal sequences

$X_k^m\left(\mathrm{\ω}\right)=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}\stackrel{\‾}{\mathrm{\ω}}(n-m)x_k\left(n\right)e^{-\mathrm{j\ωn}}$

In above formula, n is calculating parameter, for Hamming window function, window function is:

$\stackrel{\‾}{\mathrm{\ω}}(n-m)=0.54-0.46\cos \left(\frac{\mathrm{\π}(n-m)}{100}\right),$ 0≤n-m≤200;

(3) from rumble spectrum in, extract 11 spectrum signatures, comprise the average energy of entropy, maximum amplitude, maximum amplitude angular frequency, average mean, root-mean-square value, variance, flexure, kurtosis, the average energy of the first frequency band, the average energy of the second frequency band and the 3rd frequency band, obtain spectrum signature the method extracting spectrum signature is as follows:

A () is by rumble spectrum frequency range be divided into 100 intervals, the probability density that each frequency separation occurs is l=1 ..., 100, then entropy $y_{k,1}^m=-p_{k,l}^m*\log \left(p_{k,l}^m\right);$

B () is from rumble spectrum in directly search out maximum amplitude and be i=1,2,3 ..., I, wherein X (ω _i) represent and angular frequency _icorresponding amplitude, I is the number of the discrete value of angular frequency, definition ω ₁for minimum angular frequency;

(c) and above-mentioned maximum amplitude corresponding angular frequency _ifor maximum amplitude angular frequency

(d) average mean for: $y_{k,4}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{X}_k^m\left({\mathrm{\ω}}_i\right);$

(e) root-mean-square value for: $y_{k,5}^m=\sqrt{\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{X}_k^m{\left({\mathrm{\ω}}_i\right)}^2};$

(f) variance for: $y_{k,6}^m=\frac{1}{I-1}\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(X_k^m\left({\mathrm{\ω}}_i\right)-y_{k,4}^m)}^2,$ for the average mean that (d) tries to achieve;

(g) flexure for: $y_{k,7}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{X}_k^m{\left({\mathrm{\ω}}_i\right)}^3;$

(h) kurtosis for: $y_{k,8}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{X}_k^m{\left({\mathrm{\ω}}_i\right)}^4;$

(i) the first frequency band average energy $y_{k,9}^m=\frac{1}{I_1}\underset{i=1}{\overset{I_1}{\mathrm{\Σ}}}{X}_k^m{\left({\mathrm{\ω}}_i\right)}^2,$ Wherein

(j) the second frequency band average energy $y_{k,10}^m=\frac{1}{I_2-I_1}\underset{i=I_1+1}{\overset{I_2}{\mathrm{\Σ}}}{X}_k^m{\left({\mathrm{\ω}}_i\right)}^2,$

(k) the 3rd frequency band average energy $y_{k,11}^m=\frac{1}{I-I_2}\underset{i=I_2+1}{\overset{I}{\mathrm{\Σ}}}{X}_k^m{\left({\mathrm{\ω}}_i\right)}^2,$

(4) centralization and normalized are carried out to above-mentioned spectrum signature:

Right in p tie up spectrum signature, extract and to form p after feature and tie up spectrum signature set and be wherein m is sampling instant, m=1 ..., M, M represent seasonal effect in time series length, tie up spectrum signature set to p carry out centralization and normalized step is:

Right equalization obtains: ${\stackrel{\‾}{y}}_{k,p}=\underset{m}{\mathrm{\Σ}}{y}_{k,p}^m$

Right centralization obtains:

Right normalization obtains:

Right $Y_k^m=[y_{k,1}^m,y_{k,2}^m,...,y_{k,11}^m]$ In often dimension spectrum signature carry out above-mentioned calculating, obtain ${\hat{Y}}_k^m=[{\hat{y}}_{k,1}^m,{\hat{y}}_{k,2}^m,...,{\hat{y}}_{k,11}^m];$

(5) sensor s _ktrain is measured, setting measurement be the geometric deformation F of a jth type _j, sampled point number is M _j, repeat step (2)-step (4), to measuring the vibration signal { x obtained _k(m _j) process, obtain spectrum signature wherein, m _j=1 ..., M _j, k=1,2,3, j=1,2,3,4, note is measured the whole vibration signals obtained and is $\left\{x_k\left(m^{\text{'}}\right)\right\}=\underset{j}{U}\left\{x_k\left(m_j\right)\right\},$ M'=1,2 ..., M', wherein, M' is total sampled point number $M^{\′}=\underset{j}{\mathrm{\Σ}}{M}_j,$ And the intermediate variable of recording step (4) ${\mathrm{\μ}}_{k,p}={\stackrel{\‾}{y}}_{k,p}^{m^{\′}}$ With

Calculate spectrum signature mean vector μ _j, ${\mathrm{\μ}}_j=\frac{1}{M_j}\underset{m_j=1}{\overset{M_j}{\mathrm{\Σ}}}{\hat{Y}}_{k,j}^{m_j},$

Calculate spectrum signature covariance matrix Σ _j, ${\mathrm{\Σ}}_j=\frac{1}{M_j}\underset{m_j=1}{\overset{M_j}{\mathrm{\Σ}}}{({\hat{Y}}_{k,j}^{m_j}-{\mathrm{\μ}}_j)}^T({\hat{Y}}_{k,j}^{m_j}-{\mathrm{\μ}}_j),$

Calculate spectrum signature total scatter matrix within class S,

(6) Eigenvalues Decomposition is carried out to above-mentioned total scatter matrix within class S, tries to achieve eigenvalue matrix Λ and the latent vector U of S:

S=UΛU ^-1

Wherein, U is the square formations of 11 × 11 dimensions, the i-th proper vector u being classified as total scatter matrix within class S in square formation _i, Λ is the diagonal matrix of 11 × 11 dimensions, and the element in diagonal matrix on diagonal line is proper vector u _icorresponding eigenwert is λ _i, i.e. Λ _ii=λ _i;

(7) to eigenvalue λ _isorting from big to small, from wherein selecting the individual maximum eigenwert of front q, obtaining the proper vector that the eigenwert maximum with front q is corresponding by q the transformation matrix B of composition 11 × q dimension _k, adopt transformation matrix to spectrum signature convert, obtain spectrum signature dominant frequency spectrum signature be:

$z_{k,j}^{m_j}={B_k}^T{\hat{Y}}_{k,j}^{m_j}$

Merging total dominant frequency spectrum signature is m'=1,2 ..., M', wherein, M' is total sampled point number $M^{\′}=\underset{j}{\mathrm{\Σ}}{M}_j,$ This method gets q=3;

(8) according to above-mentioned dominant frequency spectrum signature with the vectorial y of instruction _{k, j, m'}∈ {-1,1} mark geometric deformation kind F _jclassification, utilize the linear SVM model of belt sag item, solve this model, obtain discriminant vector coefficient w _k,jwith discrimination threshold b _k,j:

$\underset{w,b,\mathrm{\ξ}}{\min }\frac{1}{2}{w_{k,j}}^T{w}_{k,j}+\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\ξ}}_{k,j,m^{\′}}$

$\left\{\begin{array}{c}{y}_{k,j,m^{\′}}({w_{k,j}}^T{z}_k^{m^{\′}}+b_{k,j})\≥{1-\mathrm{\ξ}}_{k,j,m^{\′}}\\ {\mathrm{\ξ}}_{k,j,m^{\′}}\≥0,m^{\′}=1,...,M\end{array}\right.$

In above formula, ξ _{k, j, m'}for lax item, w _k,j ^trepresentation vector w _k,jtransposition;

(9) to sensor s _kat the train vibration signal that sampling instant n gathers, utilize the method for above-mentioned steps (2)-step (3) to process, obtain spectrum signature right in p tie up spectrum signature, extract and to form p after feature and tie up spectrum signature set and be utilize the μ that step (5) obtains _k,pand δ _k,pcarry out centralization and normalization to spectrum signature, transformation for mula is:

${\hat{y}}_{k,p}^n=\frac{y_{k,p}^n-{\mathrm{\μ}}_{k,p}}{{\mathrm{\δ}}_{k,p}}$

Right in often dimension spectrum signature carry out above-mentioned calculating, obtain spectrum signature utilize the transformation matrix B that step (7) obtains _kspectrum signature is converted, obtains sensor s _kin the dominant frequency spectrum signature of sampling instant n, be designated as following formula is utilized to calculate dominant frequency spectrum signature corresponding geometric deformation kind F _jinitial reliability

$p_{k,j}^n=\left\{\begin{array}{cc}1-\frac{a\&times;b^{-d_{k,j}^n}}{a+1}& d_{k,j}^n\&GreaterEqual;0\\ \frac{b^{d_{k,j}^n}}{a+1}& d_{k,j}^n<0\end{array}\right.$

Wherein, a=9, b=3, w _k,jfor discriminant vector coefficient, b _k,jfor discrimination threshold;

(10) the initial reliability of geometric deformation kind of above-mentioned steps (9) is utilized obtain dominant frequency spectrum signature initial reliability vector wherein with calculated by step (9), for the uncertain initial reliability of geometric deformation kind, account form is: above-mentioned initial reliability vector is normalized, obtains dominant frequency spectrum signature reliability vector be:

Note reliability vector is wherein, representative and dominant frequency spectrum signature corresponding geometric deformation kind F _jreliability, representative and dominant frequency spectrum signature the corresponding uncertain reliability of geometric deformation kind;

(11) use the discount factor matrix A of definition, discount process carried out, k=1 to the reliability that step (10) obtains ..., 3, j=1 ..., 4, adopt evidence theory to carry out the fusion of reliability vector, obtain the testing result of railway track geometric deformation, comprise the following steps:

(11-1) defining discount factor matrix is:

$A=\left[\begin{array}{cccc}{\mathrm{\&alpha;}}_{\mathrm{1,1}}& {\mathrm{\&alpha;}}_{\mathrm{1,2}}& {\mathrm{\&alpha;}}_{\mathrm{1,3}}& {\mathrm{\&alpha;}}_{\mathrm{1,4}}\\ {\mathrm{\&alpha;}}_{\mathrm{2,1}}& {\mathrm{\&alpha;}}_{\mathrm{2,2}}& {\mathrm{\&alpha;}}_{\mathrm{2,3}}& {\mathrm{\&alpha;}}_{\mathrm{2,4}}\\ {\mathrm{\&alpha;}}_{\mathrm{3,1}}& {\mathrm{\&alpha;}}_{\mathrm{3,2}}& {\mathrm{\&alpha;}}_{\mathrm{3,3}}& {\mathrm{\&alpha;}}_{\mathrm{3,4}}\end{array}\right]=\left[\begin{array}{cccc}0.2025& 0.0000& 0.0445& 0.1610\\ 0.2396& 0.1911& 0.0000& 0.0000\\ 0.0000& 0.1122& 0.2481& 0.0127\end{array}\right]$

(11-2) to geometric deformation kind F _jwhen detecting, j=1 ..., 4, Discount Formula is:

$m_{k,j}^n\left(F_r\right)=\left\{\begin{array}{cc}(1-{\mathrm{\&alpha;}}_{k,j})\&CenterDot;m_k^n\left(F_r\right)& F_r\&SubsetEqual;\mathrm{\&Theta;}\\ (1-{\mathrm{\&alpha;}}_{k,j})\&CenterDot;m_k^n\left(F_r\right)+{\mathrm{\&alpha;}}_{k,j}& F_r=\mathrm{\&Theta;}\end{array}\right.$

Fusion formula is:

Wherein, α _k,jfor discount factor, k=1 ..., 3, k'=1 ..., 3, F ₅for the complete or collected works of geometric deformation kind, F ₅=Θ, r=1 ..., 5, s=1 ..., 5;

According to above-mentioned fusion formula, obtain fusion results as geometric deformation kind F _jfinal reliability;

(11-3) travel through geometric deformation kind, repeat step (11-2), obtain final reliability vector after fusion is:

$m^n=[m_1^n\left(F_1\right),...,m_4^n\left(F_4\right),m_5^n\left(\mathrm{\&Theta;}\right)],$

Wherein, the uncertain final reliability of geometric deformation kind $m_5^n\left(\mathrm{\&Theta;}\right)=1-\underset{j=1,...,4}{\max }\left(m_j^n\left(F_j\right)\right)=m_5^n\left(F_5\right);$

(11-4) the final reliability vector of above-mentioned steps (11-3) is normalized:

Obtaining test reliability vector is:

(12) set a detection threshold t, according to the test reliability vector of above-mentioned steps (11), the geometric deformation kind of train rail is diagnosed, j=1,2,3: if m ⁿ(F _j) be greater than setting threshold value t, then judge geometric deformation F _joccur, if m ⁿ(F _j) be less than or equal to setting threshold value t, then judge geometric deformation F _jdo not occur, the span of t is 0.8≤t≤1.

The geometric deformation detection method of the railway track based on vibration signal that the present invention proposes, its advantage is, can detect preassigned geometric deformation kind.Based on the vibration data of the geometric deformation kind that train diverse location sensor gathers, adopt Short Time Fourier Transform to carry out the conversion of signal, obtain rumble spectrum; Extract the typical feature of frequency spectrum, adopt principal component analysis (PCA) to the Feature Dimension Reduction extracted, obtain dominant frequency spectrum signature; Then off-line structure is for the support vector machine of each geometric deformation kind, sets up the reliability computation model of each geometric deformation kind; During on-line checkingi, according to real-time measuring vibrations data, Short Time Fourier Transform is used to obtain rumble spectrum, extract spectrum signature, the principal component analysis adopting calculated off-line to obtain obtains dominant frequency spectrum signature, the credit model of the geometric deformation kind adopting calculated off-line to obtain calculates the reliability being under the jurisdiction of every class, is combined as initial reliability vector; Carry out discount by after the phase initial reliability vector normalization that different sensors collection calculates in the same time according to discount factor, then carry out fusion according to the evidence theory improved and after normalization, namely obtain diagnosis reliability vectorial.Under certain decision rule, carry out geometric deformation kind by diagnosis reliability vector and diagnose decision-making.The inventive method can Precise Diagnosis locate the situation of geometric deformation kind.Program according to the inventive method establishment can be run on microprocessor, supervisory control comuter, and the hardware such as combination sensor, data acquisition unit composition on-line monitoring system, the bullet train being arranged on real time execution can carry out the on-line analysis of geometric deformation kind and the diagnosis of track.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the inventive method.

Fig. 2 is rail geometric deformation kind diagnostic system simulation architecture figure in the embodiment of use the inventive method.

Fig. 3 is in the embodiment of the inventive method under the first deformation kind, the vibration data that axle box, bogie, compartment sensor collect.

Fig. 4 is in the embodiment of the inventive method under the second deformation kind, the vibration data that axle box, bogie, compartment sensor collect.

Fig. 5 is in the embodiment of the inventive method under the third deformation kind, the vibration data that axle box, bogie, compartment sensor collect.

Embodiment

The railway track geometric deformation detection method based on vibration signal that the present invention proposes, be divided into off-line training and on-line checkingi two parts, idiographic flow block diagram as shown in Figure 1, totally comprises following steps:

(1) setting the set of train rail geometric deformation kind is Θ={ F ₁, F ₂, F ₃, F ₄, wherein, F _jrepresent the geometric deformation kind of the jth type in geometric deformation kind set Θ, j=1,2,3,4, the first geometric deformation is track centerline and the desirable track centerline vertical geometric position deviation along its length of rail reality, and the second geometric deformation is Rail Surface is corrugated shape wearing and tearing, the third geometric deformation is that Rail Surface regional area peels off, and the 4th kind of geometric deformation is that Rail Surface is without geometric deformation;

(2) vibration transducer s is set respectively at the axle box of train, bogie and car bottom _k, during train operation, the vibration signal of the corresponding site that three vibration transducers gather respectively, obtains three vibration signal sequence { x _k(m) }, k=1,2,3, the vibration signal sequence that axle box records is designated as { x ₁(m) }, the vibration signal sequence that bogie records is designated as { x ₂(m) }, the vibration signal sequence that car bottom records is designated as { x ₃(m) }, wherein, m is sampling instant, m=1 ..., M, M represent seasonal effect in time series length, carry out Short Time Fourier Transform respectively, obtain three rumble spectrums to above-mentioned three vibration signal sequences

$X_k^m\left(\mathrm{\&omega;}\right)=\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{\mathrm{\&omega;}}(n-m)x_k\left(n\right)e^{-\mathrm{j\&omega;n}}$

In above formula, n is calculating parameter, for Hamming window function, window function is:

$\stackrel{\&OverBar;}{\mathrm{\&omega;}}(n-m)=0.54-0.46\cos \left(\frac{\mathrm{\&pi;}(n-m)}{100}\right),$ 0≤n-m≤200;

(3) from rumble spectrum in, extract 11 spectrum signatures, comprise the average energy of entropy, maximum amplitude, maximum amplitude angular frequency, average mean, root-mean-square value, variance, flexure, kurtosis, the average energy of the first frequency band, the average energy of the second frequency band and the 3rd frequency band, obtain spectrum signature the method extracting spectrum signature is as follows:

A () is by rumble spectrum frequency range be divided into 100 intervals, the probability density that each frequency separation occurs is l=1 ..., 100, then entropy $y_{k,1}^m=-p_{k,l}^m*\log \left(p_{k,l}^m\right);$

B () is from rumble spectrum in directly search out maximum amplitude and be i=1,2,3 ..., I, wherein X (ω _i) represent and angular frequency _icorresponding amplitude, I is the number of the discrete value of angular frequency, definition ω ₁for minimum angular frequency;

(c) and above-mentioned maximum amplitude corresponding angular frequency _ifor maximum amplitude angular frequency

(d) average mean for: $y_{k,4}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m\left({\mathrm{\&omega;}}_i\right);$

(e) root-mean-square value for: $y_{k,5}^m=\sqrt{\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2};$

(f) variance for: $y_{k,6}^m=\frac{1}{I-1}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{(X_k^m\left({\mathrm{\&omega;}}_i\right)-y_{k,4}^m)}^2,$ for the average mean that (d) tries to achieve;

(g) flexure for: $y_{k,7}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^3;$

(h) kurtosis for: $y_{k,8}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^4;$

(i) the first frequency band average energy $y_{k,9}^m=\frac{1}{I_1}\underset{i=1}{\overset{I_1}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2,$ Wherein

(j) the second frequency band average energy $y_{k,10}^m=\frac{1}{I_2-I_1}\underset{i=I_1+1}{\overset{I_2}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2,$

(k) the 3rd frequency band average energy $y_{k,11}^m=\frac{1}{I-I_2}\underset{i=I_2+1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2,$

(4) centralization and normalized are carried out to above-mentioned spectrum signature:

Right in p tie up spectrum signature, extract and to form p after feature and tie up spectrum signature set and be wherein m is sampling instant, m=1 ..., M, M represent seasonal effect in time series length, tie up spectrum signature set to p carry out centralization and normalized step is:

Right equalization obtains: ${\stackrel{\&OverBar;}{y}}_{k,p}=\underset{m}{\mathrm{\&Sigma;}}{y}_{k,p}^m$

Right centralization obtains:

Right normalization obtains:

Right $Y_k^m=[y_{k,1}^m,y_{k,2}^m,...,y_{k,11}^m]$ In often dimension spectrum signature carry out above-mentioned calculating, obtain ${\hat{Y}}_k^m=[{\hat{y}}_{k,1}^m,{\hat{y}}_{k,2}^m,...,{\hat{y}}_{k,11}^m];$

In order to deepen, to the understanding of spectrum signature, to illustrate here.Suppose to utilize certain sensor s _kthe data gathered, sampling time sequence length M=3, p tie up spectrum signature set be listed as follows:

Table 1 p ties up spectrum signature set

Table 2 equalization result

Table 3 centralization result

Table 4 normalization result

(5) sensor s _ktrain is measured, setting measurement be the geometric deformation F of a jth type _j, sampled point number is M _j, repeat step (2)-step (4), to measuring the vibration signal { x obtained _k(m _j) process, obtain spectrum signature wherein, m _j=1 ..., M _j, k=1,2,3, j=1,2,3,4, note is measured the whole vibration signals obtained and is m'=1,2 ..., M', wherein, M' is total sampled point number and the intermediate variable of recording step (4) ${\mathrm{\&mu;}}_{k,p}={\stackrel{\&OverBar;}{y}}_{k,p}^{m^{\&prime;}}$ With

Calculate spectrum signature mean vector μ _j, ${\mathrm{\&mu;}}_j=\frac{1}{M_j}\underset{m_j=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{\hat{Y}}_{k,j}^{m_j},$

Calculate spectrum signature covariance matrix Σ _j, ${\mathrm{\&Sigma;}}_j=\frac{1}{M_j}\underset{m_j=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{({\hat{Y}}_{k,j}^{m_j}-{\mathrm{\&mu;}}_j)}^T({\hat{Y}}_{k,j}^{m_j}-{\mathrm{\&mu;}}_j),$

Calculate spectrum signature total scatter matrix within class S, $S=\underset{j=1}{\overset{4}{\mathrm{\&Sigma;}}}\frac{1}{4}{\mathrm{\&Sigma;}}_j;$

(6) Eigenvalues Decomposition is carried out to above-mentioned total scatter matrix within class S, tries to achieve eigenvalue matrix Λ and the latent vector U of S:

S=UΛU ^-1

Wherein, U is the square formations of 11 × 11 dimensions, the i-th proper vector u being classified as total scatter matrix within class S in square formation _i, Λ is the diagonal matrix of 11 × 11 dimensions, and the element in diagonal matrix on diagonal line is proper vector u _icorresponding eigenwert is λ _i, i.e. Λ _ii=λ _i;

Here suppose that the total scatter matrix within class S obtained is:

$S=\left[\begin{array}{ccccccccccc}0.6& -0.5& -0.8& 0.8& 0.2& 0.4& 0.4& -0.7& -0.4& 0.8& 0.3\\ -0.9& 0& -0.5& 0.8& 0.7& 0& -0.7& -0.7& -0.1& -0.9& 0.1\\ 0.8& 0.2& -0.3& -0.3& 0.6& -0.1& 0.3& -0.2& -1& 0.5& 0.4\\ 0.4& 0.4& 0.4& 0.4& 0.2& -0.9& 0& 0.7& 1& -0.5& 0.3\\ -0.1& -1& -0.7& -0.6& -0.6& 0.4& 0.9& 0.6& -0.6& -0.2& -0.7\\ 0.2& 1& 0.4& -0.9& -0.5& -0.9& 0.3& -0.9& -0.8& 0.1& -0.7\\ -0.5& 1& -0.8& 0.5& 0.8& -0.9& 0.6& -0.2& -0.3& 0.9& 1\\ -0.1& -0.9& 0.3& 0& -0.9& 0& -0.1& 0.1& -0.6& -0.2& -0.6\\ 0.9& 0.8& -0.1& -0.1& -0.1& -0.8& -0.1& -0.2& -0.1& 1& -0.9\\ 0.1& 0.8& 0.6& 0.8& -0.6& 0.6& 0.7& 0.3& -0.3& -0.4& 0.1\\ 0.4& 0.6& 0.4& 0.2& 1& 0.6& -0.8& 0.3& 0.9& 0.4& 0.8\end{array}\right]$

Carry out SVD decomposition to above-mentioned formula, obtaining eigenvalue matrix Λ is:

$\mathrm{\&Lambda;}=\left[\begin{array}{ccccccccccc}3.458& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 3.125& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 2.634& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 2.115& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1.862& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1.647& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1.374& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0.997& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0.834& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0.653& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0.014\end{array}\right]$

The latent vector obtained is:

$U=\left[\begin{array}{ccccccccccc}-0.068& -0.181& -0.562& 0.272& 0.001& 0.279& 0.472& 0.081& 0.119& 0.448& 0.225\\ -0.178& 0.239& -0.269& -0.689& 0.160& 0.200& 0.185& 0.229& -0.407& -0.170& 0.133\\ -0.084& -0.368& -0.233& 0.214& 0.035& 0.100& -0.357& 0.704& -0.032& -0.291& -0.193\\ -0.246& 0.137& 0.408& 0.058& -0.212& -0.436& 0.381& 0.549& 0.009& 0.157& 0.212\\ 0.507& -0.007& -0.265& 0.175& -0.136& -0.408& -0.133& -0.014& -0.530& -0.027& 0.397\\ 0.159& -0.559& 0.350& -0.375& 0.041& 0.204& -0.233& 0.069& 0.045& 0.350& 0.416\\ -0.462& -0.382& -0.311& -0.231& -0.338& -0.422& -0.051& -0.282& 0.199& -0.234& 0.151\\ 0.405& 0.060& 0.001& -0.045& 0.032& 0.104& 0.254& 0.098& 0.529& -0.568& 0.377\\ -0.048& -0.501& 0.268& 0.177& 0.230& 0.048& 0.506& -0.188& -0.406& -0.343& -0.121\\ 0.025& 0.037& 0.123& 0.045& -0.837& 0.474& 0.040& -0.022& -0.194& -0.123& -0.023\\ -0.483& 0.206& 0.125& 0.378& 0.198& 0.241& -0.269& -0.120& -0.124& -0.167& 0.582\end{array}\right]$

(7) to eigenvalue λ _isorting from big to small, from wherein selecting the individual maximum eigenwert of front q, obtaining the proper vector that the eigenwert maximum with front q is corresponding by q the transformation matrix B of composition 11 × q dimension _k, adopt transformation matrix to spectrum signature convert, obtain spectrum signature dominant frequency spectrum signature be:

$z_{k,j}^{m_j}={B_k}^T{\hat{Y}}_{k,j}^{m_j}$

Merging total dominant frequency spectrum signature is m'=1,2 ..., M', wherein, M' is total sampled point number $M^{\&prime;}=\underset{j}{\mathrm{\&Sigma;}}{M}_j,$ This method gets q=3.

According to above-mentioned example, choosing three maximum proper vectors is:

λ ₁=3.458＞λ ₂=3.125＞λ ₃=2.634

Therefore the transformation matrix B obtained _kfor:

$B_k=\left[\begin{array}{ccc}{u}_1^{\&prime;}& u_2^{\&prime;}& u_3^{\&prime;}\end{array}\right]=\left[\begin{array}{ccc}-0.068& -0.181& -0.562\\ -0.178& 0.239& -0.269\\ -0.084& -0.368& -0.233\\ -0.246& 0.137& 0.408\\ 0.507& -0.007& -0.265\\ 0.159& -0.559& 0.350\\ -0.462& -0.382& -0.311\\ 0.405& 0.060& 0.001\\ -0.048& -0.501& 0.268\\ 0.025& 0.037& 0.123\\ -0.483& 0.206& 0.125\end{array}\right]$

(8) dominant frequency spectrum signature is utilized training Support Vector Machines, because sample is divided into 4 classes, therefore structure four two class support vector machines, for the jth class geometric deformation of rail, will the dominant frequency spectrum signature of same geometric deformation kind be belonged to as a class sample, the dominant frequency spectrum signature of same geometric deformation kind will do not belonged to as another kind of sample, train a support vector machine according to sample and geometric deformation kind, jth class geometric deformation is differentiated;

According to above-mentioned dominant frequency spectrum signature with the vectorial y of instruction _{k, j, m'}∈ {-1,1} mark geometric deformation kind F _jclassification, utilize the linear SVM model of belt sag item, solve this model, obtain discriminant vector coefficient w _k,jwith discrimination threshold b _k,j:

$\underset{w,b,\mathrm{\&xi;}}{\min }\frac{1}{2}{w_{k,j}}^T{w}_{k,j}+\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_{k,j,m^{\&prime;}}$

$\left\{\begin{array}{c}{y}_{k,j,m^{\&prime;}}({w_{k,j}}^T{z}_k^{m^{\&prime;}}+b_{k,j})\&GreaterEqual;{1-\mathrm{\&xi;}}_{k,j,m^{\&prime;}}\\ {\mathrm{\&xi;}}_{k,j,m^{\&prime;}}\&GreaterEqual;0,m^{\&prime;}=1,...,M\end{array}\right.$

In above formula, ξ _{k, j, m'}for lax item, w _k,j ^trepresentation vector w _k,jtransposition;

(9) to sensor s _kat the train vibration signal that sampling instant n gathers, utilize the method for above-mentioned steps (2)-step (3) to process, obtain spectrum signature right in p tie up spectrum signature, extract and to form p after feature and tie up spectrum signature set and be utilize the μ that step (5) obtains _k,pand δ _k,pcarry out centralization and normalization to spectrum signature, transformation for mula is:

${\hat{y}}_{k,p}^n=\frac{y_{k,p}^n-{\mathrm{\&mu;}}_{k,p}}{{\mathrm{\&delta;}}_{k,p}}$

Right in often dimension spectrum signature carry out above-mentioned calculating, obtain spectrum signature utilize the transformation matrix B that step (7) obtains _kspectrum signature is converted, obtains sensor s _kin the dominant frequency spectrum signature of sampling instant n, be designated as following formula is utilized to calculate dominant frequency spectrum signature corresponding geometric deformation kind F _jinitial reliability

$p_{k,j}^n=\left\{\begin{array}{cc}1-\frac{a\&times;b^{-d_{k,j}^n}}{a+1}& d_{k,j}^n\&GreaterEqual;0\\ \frac{b^{d_{k,j}^n}}{a+1}& d_{k,j}^n<0\end{array}\right.$

Wherein, a=9, b=3, w _k,jfor discriminant vector coefficient, b _k,jfor discrimination threshold;

Here sensor s is supposed _kask for and belong to geometric deformation kind F _jthe support vector machine parameter of reliability is w _k,j=[21-1] ^tand b _k,j=1, suppose the dominant frequency spectrum signature inputted with calculate belong to geometric deformation kind F _jinitial reliability be listed as follows shown in:

Table 5 input amendment intermediate parameters with belong to geometric deformation kind F _jinitial reliability

(10) the initial reliability of geometric deformation kind of above-mentioned steps (9) is utilized obtain dominant frequency spectrum signature initial reliability vector wherein with calculated by step (9), for the uncertain initial reliability of geometric deformation kind, account form is: above-mentioned initial reliability vector is normalized, obtains dominant frequency spectrum signature reliability vector be:

Note reliability vector is wherein, representative and dominant frequency spectrum signature corresponding geometric deformation kind F _jreliability, representative and dominant frequency spectrum signature the corresponding uncertain reliability of geometric deformation kind;

(11) use the discount factor matrix A of definition, discount process carried out, k=1 to the reliability that step (10) obtains ..., 3, j=1 ..., 4, adopt DS Evidence to carry out the fusion of reliability vector, obtain the testing result of railway track geometric deformation, comprise the following steps:

(11-1) defining discount factor matrix is:

$A=\left[\begin{array}{cccc}{\mathrm{\&alpha;}}_{\mathrm{1,1}}& {\mathrm{\&alpha;}}_{\mathrm{1,2}}& {\mathrm{\&alpha;}}_{\mathrm{1,3}}& {\mathrm{\&alpha;}}_{\mathrm{1,4}}\\ {\mathrm{\&alpha;}}_{\mathrm{2,1}}& {\mathrm{\&alpha;}}_{\mathrm{2,2}}& {\mathrm{\&alpha;}}_{\mathrm{2,3}}& {\mathrm{\&alpha;}}_{\mathrm{2,4}}\\ {\mathrm{\&alpha;}}_{\mathrm{3,1}}& {\mathrm{\&alpha;}}_{\mathrm{3,2}}& {\mathrm{\&alpha;}}_{\mathrm{3,3}}& {\mathrm{\&alpha;}}_{\mathrm{3,4}}\end{array}\right]=\left[\begin{array}{cccc}0.2025& 0.0000& 0.0445& 0.1610\\ 0.2396& 0.1911& 0.0000& 0.0000\\ 0.0000& 0.1122& 0.2481& 0.0127\end{array}\right]$

(11-2) to geometric deformation kind F _jwhen detecting, j=1 ..., 4, Discount Formula is:

$m_{k,j}^n\left(F_r\right)=\left\{\begin{array}{cc}(1-{\mathrm{\&alpha;}}_{k,j})\&CenterDot;m_k^n\left(F_r\right)& F_r\&SubsetEqual;\mathrm{\&Theta;}\\ (1-{\mathrm{\&alpha;}}_{k,j})\&CenterDot;m_k^n\left(F_r\right)+{\mathrm{\&alpha;}}_{k,j}& F_r=\mathrm{\&Theta;}\end{array}\right.$

Fusion formula is:

Wherein, α _k,jfor discount factor, k=1 ..., 3, k'=1 ..., 3, F ₅for the complete or collected works of geometric deformation kind, F ₅=Θ, r=1 ..., 5, s=1 ..., 5;

According to above-mentioned fusion formula, obtain fusion results as geometric deformation kind F _jfinal reliability; Owing to adopting discount factor α _k,j, k=1 ..., 3, be only concerned about geometric deformation kind F during fusion _jdiagnostic result, so only need calculate , without the need to calculating j'=1,2,3 and j' ≠ j.

Suppose to require the time point n moment, to geometric deformation kind F _jdiagnosis reliability fusion results, sensor s _k, k=1 ..., the reliability vector before 3 discounts obtained is as follows:

Table 6 sensor s _kthe reliability vector calculated

Carry out detection geometric deformation kind F ₁the fusion of reliability vector, ask for adopt the 1st row of discount factor matrix A, obtaining the reliability vector after discount is:

Table 7 sensor s _kdetect geometric deformation kind F ₁reliability vector after discount

According to fusion formula, the above results is merged, calculate

(11-3) travel through geometric deformation kind, repeat step (11-2), obtain j=1 ..., 4, the final reliability vector after fusion is:

$m^n=[m_1^n\left(F_1\right),...,m_4^n\left(F_4\right),m_5^n\left(\mathrm{\&Theta;}\right)],$

Wherein, the uncertain final reliability of geometric deformation kind $m_5^n\left(\mathrm{\&Theta;}\right)=1-\underset{j=1,...,4}{\max }\left(m_j^n\left(F_j\right)\right)=m_5^n\left(F_5\right);$

Adopt the data of step (11-2), adopt the 2nd, 3,4 of discount factor matrix A row to carry out discount successively, calculating result is: $m_2^n\left(F_2\right)=0.0899,$ $m_3^n\left(F_3\right)=0.1476,$ $m_4^n\left(F_4\right)=0.0752;$

Then calculate $m_5^n\left(\mathrm{\&Theta;}\right)=1-\underset{j=1,...,4}{\max }\left(m_j^n\left(F_j\right)\right)=0.2361\&CenterDot;$

(11-4) the final reliability vector of above-mentioned steps (11-3) is normalized:

Obtaining test reliability vector is:

This result is the diagnostic result after K sensor fusion, reliability m ⁿ(F _j) represent this time point n generation geometric deformation kind F _jprobability estimate, it is higher to there is the possibility of this geometric deformation kind in the larger i.e. representative of probability.

Adopt the data of (11-3), the result after finally being merged is:

m ⁿ=[m ⁿ(F ₁),...,m ⁿ(F ₄),m ⁿ(Θ)]＝[0.58190.06850.11240.05730.1799]

(12) set a detection threshold t, according to the test reliability vector of above-mentioned steps (11), the geometric deformation kind of train rail is diagnosed: the data analysis that time point n is collected, j=1,2,3, if m ⁿ(F _j) be greater than setting threshold value t, then judge geometric deformation F _joccur, if m ⁿ(F _j) be less than or equal to setting threshold value t, then judge geometric deformation F _jdo not occur, the span of t is 0.8≤t≤1.

Adopt the data of (8-4), due to all m ⁿ(F _j), j=1,2,3, be all less than setting threshold value, therefore geometric deformation kind F _jall do not occur.

Below in conjunction with accompanying drawing, introduce the embodiment of the inventive method in detail:

The FB(flow block) of the inventive method as shown in Figure 1, is mainly divided into off-line training and on-line checkingi two cores.Off-line training: the geometric deformation kind vibration data that the sensor based on train diverse location gathers, adopts Short Time Fourier Transform to obtain the frequency spectrum of signal; Extract 11 kinds of geometric deformation kind spectrum signatures, adopt principal component analytical method to obtain dominant frequency spectrum signature to spectrum signature dimensionality reduction; Then construct the support vector machine for each geometric deformation kind, set up reliability computation model; On-line checkingi: according to real-time measuring vibrations signal, uses Short Time Fourier Transform to obtain the frequency spectrum of signal, extracts spectrum signature, adopts the given principal component analysis (PCA) projecting direction compressive features of training to obtain dominant frequency spectrum signature; The credit model using calculated off-line to obtain calculates the reliability being under the jurisdiction of each geometric deformation kind, is combined as reliability vector; The reliability vector that different sensors collection calculates in the same time is mutually carried out discount according to discount factor, then merges according to the DS Evidence method improved, namely obtain final diagnosis reliability vector.Under certain decision rule, carry out geometric deformation kind by diagnosis reliability vector and diagnose decision-making.

Below in conjunction with the most preferred embodiment that the geometric deformation detection method of railway track in Fig. 2 emulates, introduce each step of the inventive method in detail, and can accurately be detected by simulation results show the present invention and locate geometric deformation kind occur situation.

1, track geometry deformation kind diagnostic system simulation example

Experiment uses SIMPACK dynamics simulation software to carry out modeling to bullet train rail cars, bogie, wheel to, rail, axle box, bogie and compartment arrange Vibration Condition that acceleration transducer detects vertical direction respectively, and the sampling rate of sensor is 1kHz.Adopt MATLAB to emulate the track excitation waveform of rail, the interface then provided by SIMPACK carries out changing rear input.

2, high-speed track geometric deformation kind is arranged and signals collecting

MATLAB is used to simulate the genre types of four kinds of high-speed track geometric deformations respectively, the first geometric deformation is track centerline and the desirable track centerline vertical geometric position deviation along its length of rail reality, and irregularity degree mainly to detect within the scope of 42m within the scope of height difference ± 3mm and 120m just difference ± 4mm two kinds of indexs; The second geometric deformation is Rail Surface is corrugated shape wearing and tearing, and the cycle of the degree of wear is 0.4m ~ 1.6m, and the degree of wear is 0.1mm; The third geometric deformation is that Rail Surface regional area peels off, and stochastic generation crackle and peeling conditions in 2m among a small circle, the 4th kind of geometric deformation is that Rail Surface is without geometric deformation.

Use the bullet train that speed per hour is 288km/h to run on the rail level of above-mentioned input, 3 sensors are recorded vibration signal data and is kept in local file.Under the first geometric deformation kind (within the scope of 100m ~ 220m, track projection 4mm), the data that axle box, bogie, compartment sensor collect are shown in Fig. 3; Under the second geometric deformation kind (within the scope of 300m ~ 332m, the cycle is 0.4m, rises and falls as ± 0.1mm), the data that axle box, bogie, compartment sensor collect are shown in Fig. 4; Under the third geometric deformation kind (within the scope of 300m ~ 302m, peeling off and crackle of random generation), the data that axle box, bogie, compartment sensor collect are shown in Fig. 5.

3, geometric deformation kind vibration signal asks for frequency spectrum, feature extraction and dimensionality reduction

Emulate each geometric deformation kind, the sensor that train is positioned at 3 kinds of diverse locations all will gather vibration signal.The each sensor of off-line phase will obtain 750 groups of vibration signals to each class kind.Short Time Fourier Transform is adopted to obtain rumble spectrum according to step (2) to vibration signal; Extract spectrum signature according to step (3), adopt principal component analysis (PCA) to obtain dominant frequency spectrum signature to the Feature Dimension Reduction extracted.

Extract spectrum signature according to step (3), under three kinds of sensors, each geometric deformation kind spectrum signature average is as shown in table 8-11:

The four class geometric deformation kind spectrum signature averages that table 8 axle box sensor records

The four class geometric deformation kind spectrum signature averages that table 9 bogie sensor records

The four class geometric deformation kind spectrum signature averages that table 10 compartment sensor records

Adopt step (5) (6) (7), carry out off-line training, the dominant frequency spectrum signature average of four kinds of geometric deformation kinds of trying to achieve is as shown in table 11-13:

The dominant frequency spectrum signature average of four kinds of geometric deformation kinds that table 11 axle box sensor transformation obtains

The dominant frequency spectrum signature average of four kinds of geometric deformation kinds that table 12 bogie sensor transformation obtains

Table 13 compartment sensor converts the dominant frequency spectrum signature average of the four kinds of geometric deformation kinds obtained

4, the calculating of support vector machine and credit model

Each sensor s _k750 groups of dominant frequency spectrum signatures are all obtained to each geometric deformation kind, when investigating jth kind, geometric deformation kind F will be belonged to _jsample as a class, sample size is 750, and all the other samples are as another kind of, and sample size is 2250, then train the linear SVM model of this belt sag item.

5, the on-line checkingi stage, asking for of each sensor reliability vector

Respectively use 768 groups of vibration signal data during each geometric deformation kind of each sensor measurement, therefore each sensor there are 3072 vibration signal data, has 9216 vibration signal data.Then ask for the reliability vector that each vibration signal is corresponding.

According to step (9), each sensor collection is converted to the dominant frequency spectrum signature obtained, adopt the reliability computation model of support vector machine to calculate and belong to geometric deformation kind F _jreliability.Be normalized according to the initial reliability of step (10) to all geometric deformation kinds, obtain reliability vector m _k=[m _k(F ₁) ..., m _k(F _n), m _k(Θ)].

Under three kinds of sensors, the average of each geometric deformation kind reliability vector is as shown in table 14-16:

The reliability vector that table 14 axle box sensor calculates under four class geometric deformation kind conditions

The reliability vector that table 15 bogie sensor calculates under four class geometric deformation kind conditions

The reliability vector that table 16 compartment sensor calculates under four class geometric deformation kind conditions

7, the on-line checkingi stage, the discount of reliability vector and fusion

According to step (11), the above results is used α _k,jcarry out discount, then use DS Evidence to carry out merging and namely obtain final diagnosis reliability vector.Because sample point and time point are one to one, therefore can realize the detection & localization of geometric deformation kind simultaneously.

According to step (12), get t=0.8, the Detection accuracy of the every class geometric deformation kind obtained is shown in table 17:

The Detection accuracy of the every class geometric deformation kind of table 17

Claims (1)

1., based on a railway track geometric deformation detection method for vibration signal, it is characterized in that the method comprises following steps:

(1) setting the set of train rail geometric deformation kind is Θ={ F ₁, F ₂, F ₃, F ₄, wherein, F _jrepresent the geometric deformation kind of the jth type in geometric deformation kind set Θ, j=1,2,3,4, the first geometric deformation is track centerline and the desirable track centerline vertical geometric position deviation along its length of rail reality, and the second geometric deformation is Rail Surface is corrugated shape wearing and tearing, the third geometric deformation is that Rail Surface regional area peels off, and the 4th kind of geometric deformation is that Rail Surface is without geometric deformation;

(2) vibration transducer s is set respectively at the axle box of train, bogie and car bottom _k, during train operation, the vibration signal of the corresponding site that three vibration transducers gather respectively, obtains three vibration signal sequence { x _k(m) }, k=1,2,3, the vibration signal sequence that axle box records is designated as { x ₁(m) }, the vibration signal sequence that bogie records is designated as { x ₂(m) }, the vibration signal sequence that car bottom records is designated as { x ₃(m) }, wherein, m is sampling instant, m=1 ..., M, M represent seasonal effect in time series length, carry out Short Time Fourier Transform respectively, obtain three rumble spectrums to above-mentioned three vibration signal sequences $\left\{X_k^m\left(\mathrm{\&omega;}\right)\right\}:$

$X_k^m\left(\mathrm{\&omega;}\right)=\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{\mathrm{\&omega;}}(n-m)x_k\left(n\right)e^{-\mathrm{j\&omega;n}}$

In above formula, n is calculating parameter, for window function, window function is:

$\stackrel{\&OverBar;}{\mathrm{\&omega;}}(n-m)=0.54-0.46\cos \left(\frac{\mathrm{\&pi;}(n-m)}{100}\right),0\&le;n-m\&le;200;$

(3) from rumble spectrum in, extract 11 spectrum signatures, comprise the average energy of entropy, maximum amplitude, maximum amplitude angular frequency, average mean, root-mean-square value, variance, flexure, kurtosis, the average energy of the first frequency band, the average energy of the second frequency band and the 3rd frequency band, obtain spectrum signature the method extracting spectrum signature is as follows:

A () is by rumble spectrum frequency range be divided into 100 intervals, the probability density that each frequency separation occurs is l=1 ..., 100, then entropy $y_{k,1}^m=-p_{k,l}^m*\log \left(p_{k,l}^m\right);$

B () is from rumble spectrum in directly search out maximum amplitude and be i=1,2,3 ..., I, wherein X (ω _i) represent and angular frequency _icorresponding amplitude, I is the number of the discrete value of angular frequency, definition ω ₁for minimum angular frequency;

(c) and above-mentioned maximum amplitude corresponding angular frequency _ifor maximum amplitude angular frequency

(d) average mean for: $y_{k,4}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m\left({\mathrm{\&omega;}}_i\right);$

(e) root-mean-square value for: $y_{k,5}^m=\sqrt{\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2};$

(f) variance for: $y_{k,6}^m=\frac{1}{I-1}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{(X_k^m\left({\mathrm{\&omega;}}_i\right)-y_{k,4}^m)}^2,$ for the average mean that (d) tries to achieve;

(g) flexure for: $y_{k,7}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2;$

(h) kurtosis for: $y_{k,8}^m=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^4;$

(i) the first frequency band average energy $y_{k,9}^m=\frac{1}{I_1}\underset{i=1}{\overset{I_1}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2;$ Wherein

(j) the second frequency band average energy $y_{k,10}^m=\frac{1}{I_2-I_1}\underset{i=I_1+1}{\overset{I_2}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2,$

(k) the 3rd frequency band average energy $y_{k,11}^m=\frac{1}{I-I_2}\underset{i=I_2+1}{\overset{I}{\mathrm{\&Sigma;}}}{X}_k^m{\left({\mathrm{\&omega;}}_i\right)}^2,$

(4) centralization and normalized are carried out to above-mentioned spectrum signature:

Right in p tie up spectrum signature, extract and to form p after feature and tie up spectrum signature set and be wherein m is sampling instant, m=1 ..., M, M represent seasonal effect in time series length, tie up spectrum signature set to p carry out centralization and normalized step is:

Right equalization obtains: ${\stackrel{\&OverBar;}{y}}_{k,p}=\underset{m}{\mathrm{\&Sigma;}}{y}_{k,p}^m$

Right centralization obtains: ${\tilde{y}}_{k,p}^m=y_{k,p}^m-{\stackrel{\&OverBar;}{y}}_{k,p}$

Right normalization obtains: ${\hat{y}}_{k,p}^m=\frac{{\tilde{y}}_{k,p}^m}{\underset{m}{\max }\left(\right|{\tilde{y}}_{k,p}^m\left|\right)};$

Right in often dimension spectrum signature carry out above-mentioned calculating, obtain

(5) sensor s _ktrain is measured, setting measurement be the geometric deformation F of a jth type _j, sampled point number is M _j, repeat step (2)-step (4), to measuring the vibration signal { x obtained _k(m _j) process, obtain spectrum signature wherein, m _j=1 ..., M _j, k=1,2,3, j=1,2,3,4, note is measured the whole vibration signals obtained and is m'=1,2 ..., M', wherein, M' is total sampled point number and the intermediate variable of recording step (4) ${\mathrm{\&mu;}}_{k,p}={\stackrel{\&OverBar;}{y}}_{k,p}^{m\&prime;}$ With ${\mathrm{\&delta;}}_{k,p}=\underset{m^{\&prime;}}{\max }\left(\right|{\tilde{y}}_{k,p}^{m^{\&prime;}}\left|\right),$

Calculate spectrum signature mean vector μ _j,

Calculate spectrum signature covariance matrix Σ _j, ${\mathrm{\&Sigma;}}_j=\frac{1}{M_j}\underset{m_j=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{({\hat{Y}}_{k,j}^{m_j}-{\mathrm{\&mu;}}_j)}^T({\hat{Y}}_{k,j}^{m_j}-{\mathrm{\&mu;}}_j),$

Calculate spectrum signature total scatter matrix within class S,

(6) Eigenvalues Decomposition is carried out to above-mentioned total scatter matrix within class S, tries to achieve eigenvalue matrix Λ and the latent vector U of S:

S＝UΛU ^-1

Wherein, U is the square formations of 11 × 11 dimensions, the i-th proper vector u being classified as total scatter matrix within class S in square formation _i, Λ is the diagonal matrix of 11 × 11 dimensions, and the element in diagonal matrix on diagonal line is proper vector u _icorresponding eigenwert is λ _i, i.e. Λ _ii=λ _i;

(7) to eigenvalue λ _isorting from big to small, from wherein selecting the individual maximum eigenwert of front q, obtaining the proper vector u that the eigenwert maximum with front q is corresponding _i', by q u _i' composition 11 × q dimension transformation matrix B _k, adopt transformation matrix to spectrum signature convert, obtain spectrum signature dominant frequency spectrum signature be:

$z_{k,j}^{m_j}={B_k}^T{\hat{Y}}_{k,j}^{m_j}$

Merging total dominant frequency spectrum signature is m'=1,2 ..., M', wherein, M' is total sampled point number $M^{\&prime;}=\underset{j}{\mathrm{\&Sigma;}}{M}_j,$ This method gets q=3;

(8) according to above-mentioned dominant frequency spectrum signature with the vectorial y of instruction _{k, j, m'}∈ {-1,1} mark geometric deformation kind F _jclassification, utilize the linear SVM model of belt sag item, solve this model, obtain discriminant vector coefficient w _k,jwith discrimination threshold b _k,j:

$\underset{w,b,\mathrm{\&xi;}}{\min }\frac{1}{2}{w_{k,j}}^T{w}_{k,j}+\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_{k,j,m\&prime;}$

$\left\{\begin{array}{c}{y}_{k,j,m\&prime;}({w_{k,j}}^T{z}_k^{m\&prime;}+b_{k,j})\&GreaterEqual;1-{\mathrm{\&xi;}}_{k,j,m\&prime;}\\ {\mathrm{\&xi;}}_{k,j,m\&prime;}\&GreaterEqual;0,m^{\&prime;}=1,...,M\end{array}\right.$

In above formula, ξ _{k, j, m'}for lax item, w _k,j ^trepresentation vector w _k,jtransposition;

(9) to sensor s _kat the train vibration signal that sampling instant n gathers, utilize the method for above-mentioned steps (2)-step (3) to process, obtain spectrum signature right in p tie up spectrum signature, extract and to form p after feature and tie up spectrum signature set and be utilize the μ that step (5) obtains _k,pand δ _k,pcarry out centralization and normalization to spectrum signature, transformation for mula is:

${\hat{y}}_{k,p}^n=\frac{y_{k,p}^u-{\mathrm{\&mu;}}_{k,p}}{{\mathrm{\&delta;}}_{k,p}}$

Right in often dimension spectrum signature carry out above-mentioned calculating, obtain spectrum signature utilize the transformation matrix B that step (7) obtains _kspectrum signature is converted, obtains sensor s _kin the dominant frequency spectrum signature of sampling instant n, be designated as following formula is utilized to calculate dominant frequency spectrum signature corresponding geometric deformation kind F _jinitial reliability

$p_{k,j}^n=\left\{\begin{array}{cc}1-\frac{a\&times;b^{-d_{k,j}^n}}{a+1}& d_{k,j}^n\&GreaterEqual;0\\ \frac{b^{d_{k,j}^n}}{a+1}& d_{k,j}^n<0\end{array}\right.$

Wherein, a=9, b=3, w _k,jfor discriminant vector coefficient, b _k,jfor discrimination threshold;

(10) the initial reliability of geometric deformation kind of above-mentioned steps (9) is utilized obtain dominant frequency spectrum signature initial reliability vector wherein with calculated by step (9), for the uncertain initial reliability of geometric deformation kind, account form is: above-mentioned initial reliability vector is normalized, obtains dominant frequency spectrum signature reliability vector be:

${\tilde{p}}_{k,j}^n=\frac{p_{k,j}^n}{\underset{j=1,...,5}{\mathrm{\&Sigma;}}{p}_{k,j}^n}$

Note reliability vector is $m_k^n=[m_k^n\left(F_1\right),...,m_k^n\left(F_4\right),m_k^n\left(\mathrm{\&Theta;}\right)]=[{\tilde{p}}_{k,1}^n,...,{\tilde{p}}_{k,4}^n,{\tilde{p}}_{k,5}^n],$ Wherein, representative and dominant frequency spectrum signature corresponding geometric deformation kind F _jreliability, representative and dominant frequency spectrum signature the corresponding uncertain reliability of geometric deformation kind;

(11) use the discount factor matrix A of definition, discount process carried out, k=1 to the reliability that step (10) obtains ..., 3, j=1 ..., 4, adopt evidence theory to carry out the fusion of reliability vector, obtain the testing result of railway track geometric deformation, comprise the following steps:

(11-1) defining discount factor matrix is:

$A=\left[\begin{array}{cccc}{\mathrm{\&alpha;}}_{\mathrm{1,1}}& {\mathrm{\&alpha;}}_{\mathrm{1,2}}& {\mathrm{\&alpha;}}_{\mathrm{1,3}}& {\mathrm{\&alpha;}}_{\mathrm{1,4}}\\ {\mathrm{\&alpha;}}_{\mathrm{2,1}}& {\mathrm{\&alpha;}}_{\mathrm{2,2}}& {\mathrm{\&alpha;}}_{\mathrm{2,3}}& {\mathrm{\&alpha;}}_{\mathrm{2,4}}\\ {\mathrm{\&alpha;}}_{\mathrm{3,1}}& {\mathrm{\&alpha;}}_{\mathrm{3,2}}& {\mathrm{\&alpha;}}_{\mathrm{3,3}}& {\mathrm{\&alpha;}}_{\mathrm{3,4}}\end{array}\right]=\left[\begin{array}{cccc}0.2025& 0.0000& 0.0445& 0.1610\\ 0.2396& 0.1911& 0.0000& 0.0000\\ 0.0000& 0.1122& 0.2481& 0.0127\end{array}\right]$

(11-2) to geometric deformation kind F _jwhen detecting, j=1 ..., 4, Discount Formula is:

$m_{k,j}^n\left(F_r\right)=\left\{\begin{array}{cc}(1-{\mathrm{\&alpha;}}_{k,j})\&CenterDot;m_k^n\left(F_r\right)& F_r\&SubsetEqual;\mathrm{\&Theta;}\\ (1-{\mathrm{\&alpha;}}_{k,j})\&CenterDot;m_k^n\left(F_r\right)+{\mathrm{\&alpha;}}_{k,j}& F_r=\mathrm{\&Theta;}\end{array}\right.$

Fusion formula is:

Wherein, α _k,jfor discount factor, k=1 ..., 3, k'=1 ..., 3, F _sfor the complete or collected works of geometric deformation kind, F _s=Θ, r=1 ..., 5, s=1 ..., 5;

According to above-mentioned fusion formula, obtain fusion results as geometric deformation kind F _jfinal reliability;

(11-3) travel through geometric deformation kind, repeat step (11-2), obtain j=1 ..., 4, the final reliability vector after fusion is:

$m^n=[m_1^n\left(F_1\right),...,m_4^n\left(F_4\right),m_5^n\left(\mathrm{\&Theta;}\right)],$

Wherein, the uncertain final reliability of geometric deformation kind

(11-4) the final reliability vector of above-mentioned steps (11-3) is normalized:

${\tilde{m}}_j^n\left(F_j\right)=\frac{m_j^n\left(F_j\right)}{\underset{j=1,...,5}{\mathrm{\&Sigma;}}{m}_j^n\left(F_j\right)}$

Obtaining test reliability vector is:

$m^n=[{\tilde{m}}_1^n\left(F_1\right),...,{\tilde{m}}_4^n\left(F_4\right),{\tilde{m}}_5^n\left(F_5\right)]=[m^n\left(F_1\right),...,m^n\left(F_4\right),m^n\left(\mathrm{\&Theta;}\right)],$

(12) set a detection threshold t, according to the test reliability vector of above-mentioned steps (11), the geometric deformation kind of train rail is diagnosed, j=1,2,3: if m ⁿ(F _j) be greater than setting threshold value t, then judge geometric deformation F _joccur, if m ⁿ(F _j) be less than or equal to setting threshold value t, then judge geometric deformation F _jdo not occur, the span of t is 0.8≤t≤1.