CN104776908A - EMD generalized energy-based wheeltrack vibration signal fault feature extraction method - Google Patents

Abstract

The invention discloses an EMD generalized energy-based wheeltrack vibration signal fault feature extraction method which comprises the following steps: collecting a vibration acceleration signal of a real-time running train, integrating the train speed to determine the starting and stopping moments corresponding to one revolution of the wheel, and intercepting the acceleration signal of corresponding time history by using the starting and stopping moments; carrying out wavelet decomposition, threshold processing of each layer of wavelet coefficient and wavelet reconstruction on the collected vibration acceleration signal to realize wavelet denoising; carrying out empirical mode decomposition on the obtained axle box vibration acceleration signal to obtain a series of intrinsic mode functions; finally determining the energy weight coefficient by combining the vibration acceleration signal under fault excitation simulated by a vehicle track coupling kinetic model, calculating the empirical mode decomposition generalized energy and determining the fault feature according to the value. The EMD generalized energy-based wheeltrack vibration signal fault feature extraction method has the advantages of being low in cost, and high in feature extraction resolution ratio and real-time performance.

Description

Based on the Wheel Rail Vibration signal fault feature extracting method of EMD generalized energy

Technical field

The present invention relates to city railway train monitoring in transit and safe early warning technical field, particularly a kind of Wheel Rail Vibration signal fault feature extracting method based on empirical mode decomposition (EMD) generalized energy.

Background technology

According to Chinese city track traffic association statistics, " 12 " period urban track traffic will build up 2500 km that put into operation, average annual 500 km, and to the year two thousand twenty end, urban track traffic total kilometrage is built up in the whole nation will reach 7000 km.Urban track traffic, towards aspect development such as high speed, high density, student with skills complexity, operation system linkage height, proposes more and more higher requirement to vehicle driving control, fault diagnosis and detection.

The traveling system of urban rail transit vehicles is one of critical system of vehicle, and it not only bears car body weight, also transmits the driving force between rail and vehicle and damping force.As one of the kernel component of traveling system, urban rail transit vehicles wheel, to the coupling part being train and track, carries the weight of whole train and ensures train operation in orbit.Flat wheel fault is one of great driving accident hidden danger of urban rail transit vehicles, the flat wheel fault of vehicle can produce periodic noise and wheel-rail impact power when vehicle travels, this noise has not only had a strong impact on passenger and to have ridden comfort level, brings interference to circuit surrounding enviroment; And the impact energy of wheel track is transmitted to roadbed internal layer by railway roadbed, it is one of major reason causing concrete sleeper and rail fracture, and this kind of impact is also the cold cut of vehicle axles fatigue, the major reason of bearing damage,, load high at car speed weighs and scratch deepens, this high-strength impact can cause more serious destruction.

Although current urban track traffic operation department has formulated the turnaround plan of all kinds of different cycles to Railway wheelset, but this Static Detection not only takies vehicle active time but also bring a large amount of cost of labor, cannot the flat wheel fault of Real-Time Monitoring car wheel-set, more and more can not meet urban track traffic operation security coefficient and operating service quality requirements.

Summary of the invention

The object of the present invention is to provide the Wheel Rail Vibration signal fault feature extracting method based on EMD generalized energy that a kind of cost is low, engineering construction is good, by gathering the signals such as axle box vibration, framework vibration and body oscillating, and calculating EMD generalized energy, real time on-line monitoring wheel is to flat wheel fault.

The technical solution realizing the object of the invention is: a kind of Wheel Rail Vibration signal fault feature extracting method based on EMD generalized energy, comprises the following steps:

1st step, the vibration acceleration signal of Real-time Collection running train also encloses corresponding start/stop time to speed of a motor vehicle integration determination rotation of wheel one, removes with this start/stop time the acceleration signal intercepting corresponding time history;

2nd step, intercepts to the 1st step the vibration acceleration signal obtained and carries out wavelet decomposition, the threshold process of each layer wavelet coefficient and wavelet reconstruction successively, realize Wavelet Denoising Method;

3rd step, carries out empirical mode decomposition to the vibration acceleration signal after the 2nd step Wavelet Denoising Method, obtains a series of intrinsic mode function IMF _n;

4th step, determines intrinsic mode function IMF _nenergy weight coefficient, and calculate EMD generalized energy, according to this EMD generalized energy determination fault signature.

Compared with prior art, its remarkable advantage is in the present invention: (1) cost is low, and the hardware system involved by the method only comprises vibration transducer and data processing host; (2) from the intrinsic mode function of signal, introduce the IMF based on signal local characteristics, process wheel track flat wheel vibration signal that is non-linear, non-stationary in time and frequency with high resolution, ask for energy feature; (3) the difference determination energy weight coefficient of the response that the dynamic response utilizing fault to encourage and non-fault encourage; (4) EMD generalized energy calculated amount is little, can realize on-line real time monitoring, flat wheel state change that is that happened suddenly by the threshold decision Timeliness coverage of EMD generalized energy and long-term accumulated, thus provides and safeguard early warning timely.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the Wheel Rail Vibration signal fault feature extracting method that the present invention is based on EMD generalized energy.

Fig. 2 is vehicle track coupling dynamics realistic model figure.

Fig. 3 is that to equal wheel fault be the time-domain diagram that the axle box vibration signal of 7mm carries out signal before and after wavelet noise in the present invention, and wherein (a) is the time-domain diagram of wavelet noise front signal, and (b) is the time-domain diagram of signal after wavelet noise.

Fig. 4 is that to equal wheel fault be the frequency domain figure that the axle box vibration signal of 7mm carries out signal before and after wavelet noise in the present invention, and wherein (a) is the frequency domain figure of wavelet noise front signal, and (b) is the frequency domain figure of signal after wavelet noise.

Fig. 5 is that the trouble-free axle box vibration signal of the present invention carries out EMD and decomposes 8 the IMF components and 1 residual components that obtain.

Fig. 6 is that to equal wheel fault be that the axle box vibration signal of 7mm carries out EMD and decomposes 8 the IMF components and 1 residual components that obtain in the present invention.

The axle box vibration signal of Fig. 7 to be flat wheel fault be 7mm carry out EMD decompose after each component energy decompose rear each component energy figure with normal signal EMD, wherein (a) is without flat wheel fault energy proper vector, and (b) is 7mm flat wheel the feature parameter vectors.

Embodiment

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

Composition graphs 1, the present invention is based on the Wheel Rail Vibration signal fault feature extracting method of EMD generalized energy, first gather the vibration acceleration signal of real time execution train and corresponding start/stop time is enclosed to speed of a motor vehicle integration determination rotation of wheel one, removing with this start/stop time the acceleration signal intercepting corresponding time history; Secondly wavelet decomposition, the threshold process of each layer wavelet coefficient and wavelet reconstruction are carried out to the vibration acceleration signal collected, realize Wavelet Denoising Method; Then empirical mode decomposition is carried out to the axle box vibration acceleration signal obtained, obtain a series of intrinsic mode function IMF _n; Finally combine the existence obtained by vehicle track coupling dynamics model emulation and put down the lower vibration acceleration signal determination energy weight coefficient of wheel fault excitation, calculating EMD generalized energy, according to this value determination fault signature.Comprise the following steps:

1st step, the vibration acceleration signal of Real-time Collection running train also encloses corresponding start/stop time to speed of a motor vehicle integration determination rotation of wheel one, removes with this start/stop time the acceleration signal intercepting corresponding time history;

The vibration acceleration signal of described train is designated as x _i(t), i=1,2 ..., m, subscript i represent the traveling based parts such as corresponding axle box, framework and car body, and m represents traveling based part sum.

2nd step, intercepts to the 1st step the vibration acceleration signal obtained and carries out wavelet decomposition, the threshold process of each layer wavelet coefficient and wavelet reconstruction successively, realize Wavelet Denoising Method;

Wavelet Denoising Method is carried out to the vibration acceleration signal collected.One dimension Noise signal can be expressed as

x(t)＝f(t)+σe(t),t＝0,1,…，n-1

In formula, f (t) represents actual signal, and e (t) represents noise, and x (t) represents containing noisy signal.In practical engineering application, useful signal is different with the wavelet conversion coefficient characteristic of noise, when Noise signal carries out wavelet decomposition, obtain the wavelet coefficient under different scale, by retaining the wavelet coefficient of actual signal and the wavelet coefficient of attenuate acoustic noise, then signal de-noising can be realized through signal reconstruction.Concrete steps are:

(2.1) wavelet decomposition of signal: select suitable little basis function ripple and determine wavelet decomposition number of plies N, N layer wavelet decomposition is carried out to signals and associated noises.

(2.2) threshold process of each layer wavelet coefficient: according to thresholding functions (hard-threshold or soft-threshold etc.), threshold process is carried out to each layer wavelet coefficient that signal decomposition obtains, obtain new wavelet coefficient.

(2.3) signal reconstruction: be reconstructed the wavelet coefficient processed, obtains the signal after denoising.

3rd step, carries out empirical mode decomposition to the vibration acceleration signal after the 2nd step Wavelet Denoising Method, obtains a series of intrinsic mode function IMF _n; Concrete steps are as follows:

(3.1) set original signal as x (t), determine Local Extremum all in the whole time domain of signal;

(3.2) cubic spline function is adopted to carry out to all maximum point of signal x (t) and minimum point the coenvelope u that interpolation fitting obtains signal x (t) respectively ₀(t) and lower envelope v ₀t (), then by u ₀(t) and v ₀t () obtains the average envelope m of signal ₀(t):

$m_0\left(t\right)=\frac{1}{2}(u_0\left(t\right)+v_0\left(t\right))$

(3.3) average envelope m is deducted with original signal x (t) ₀t (), obtains remainder, be designated as h ₁(t):

h ₁(t)＝x(t)-m ₀(t)

Step (3.1) can think once the process of " sieve " to step (3.3), and original signal x (t) becomes h through the process of once " sieve " ₁(t), under normal circumstances h ₁t () is not the intrinsic mode function satisfied condition, need to decompose further.Now by h ₁t () is used as new original signal, repeat step (3.1) ~ step (3.3), supposes to repeat k time, until obtain h _kt () meets the condition of intrinsic mode function, process is as follows:

$\begin{array}{c}{m}_1\left(t\right)=\frac{1}{2}(u_1\left(t\right)+v_1\left(t\right))\\ h_2\left(t\right)=h_1\left(y\right)-m_1\left(t\right)\\ .\\ .\\ .\\ m_{k-1}\left(t\right)=\frac{1}{2}(u_{k-1}\left(t\right)+v_{k-1}\left(t\right))\\ h_k\left(t\right)=h_{k-1}\left(y\right)-m_{k-1}\left(t\right)\end{array}$

Now h _kt () is first intrinsic mode function of original signal x (t), be designated as c ₁t (), it comprises the highest component of the frequency of original signal x (t).

(3.4) c is deducted with original signal x (t) ₁t () obtains remainder and is designated as r ₁(t):

r ₁(t)＝x(t)-c ₁(t)

To residual signal r ₁t () repeats above-mentioned steps (3.1) ~ step (3.4), then can obtain second intrinsic mode function c ₂(t), repeat n decomposition and obtain each intrinsic mode function, its process is as follows:

$\begin{array}{c}{r}_1\left(t\right)-c_2\left(t\right)=r_2\left(t\right)\\ .\\ .\\ .\\ r_{n-1}\left(t\right)-c_n\left(t\right)=r_n\left(t\right)\end{array}$

(3.5) as residual components r _nwhen () meets given stop criterion t, then stop whole signal decomposition process, obtain last intrinsic mode function c _n(t) and residual components r _n(t), now original signal x (t) is expressed as multiple intrinsic mode function and residual components sum:

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{c}_i\left(t\right){+r}_n\left(t\right)$

C in formula _it () represents i-th natural mode of vibration component, c _it () represents the component of original signal different frequency section, r _nthe residual components of steady composition in (t) representation signal.

4th step, determines intrinsic mode function IMF _nenergy weight coefficient, and calculate EMD generalized energy, according to this EMD generalized energy determination fault signature;

The expression formula of EMD generalized energy is:

$Q=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\sqrt{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\left(f_j\right)E_i\left({\mathrm{\η}}_j\right)}$

In formula: Q is EMD generalized energy index; I=1,2 ..., m, i represent traveling based part, and m represents traveling based part sum; J=1,2 ..., n, j are the label obtaining each intrinsic mode functions after EMD decomposes, and n is intrinsic mode functions sum; η _jfor the signal that jth item intrinsic mode functions is extracted, length is the vibration acceleration that rotation of wheel one encloses that corresponding start/stop time intercepts corresponding time history; λ _i(f _j) be the energy weight coefficient of the jth item intrinsic mode functions that i-th vibration signal is corresponding; E _i(η _j) be the energy of the jth item intrinsic mode functions that i-th vibration signal is corresponding, ENERGY E _irepresent with following formula:

$E_i={\∫}_0^x{G}_i\left(f\right)\mathrm{dx}={\mathrm{\ψ}}_i^2$

In formula: G _ifor track power spectral density function; F is frequency; ψ _i ²for mean square value, and mean square value ψ _i ²calculating formula is

${\mathrm{\ψ}}_i^2=\frac{1}{x}{\∫}_0^x{\mathrm{\η}}^2\left(x\right)\mathrm{dx}\≈\frac{1}{m}\underset{\mathrm{\μ}=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\η}}_{\mathrm{\μ}}^2$

Energy coefficient λ (f _j) following dimension normalization condition need be met:

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\λ}\left(f_j\right)=1$

Different intrinsic mode functions has different energy coefficienies, and the vibration signal IMF of the frequency band that the larger expression of energy coefficient is corresponding is with it larger to track quality influence.

Adopt feature energy method to calculate energy coefficient, first set up vehicle track coupling dynamics model, the vibration acceleration signal x under emulation obtains failure-free operation and there is fault excitation _r(t) and x _f(t); Secondly to x _r(t) and x _ft EMD that () carries out the 3rd step decomposes, and obtains the IMF mode function under each wave band; Again calculate x _r(t) and x _fthe ENERGY E of the intrinsic mode functions under each wave band of (t) _rjand E _fj; Then by x _f(t) each IMF ENERGY E _fjdeduct x _r(t) each IMF ENERGY E _rjobtain E _rfj; Finally by each IMF ENERGY E _rfiwith the ratio of the gross energy E proper vector as energy coefficient, namely $\mathrm{\λ}\left(f_j\right)=E_{\mathrm{rfj}}/\underset{j=}{\overset{n}{\mathrm{\Σ}}}{E}_{\mathrm{rfj}}.$ Concrete steps are:

(4.1) Zhai Wan bright method establishment vehicle track coupling dynamics model is adopted.Vehicle-track vertical coupled model, as Fig. 2, comprises vehicle subsystem, Orbit subsystem and Wheel-rail contact model.Vehicle subsystem is two frameworks, four groups of multiple degrees of freedom Rigid-body Systems of taking turns composition, has 10 degree of freedom, and wherein car body and framework consider sink-float and both direction degree of freedom of nodding, and takes turns only considering sink-float direction degree of freedom; Orbit subsystem is reduced to rail, sleeper, railway roadbed and roadbed, and rail, sleeper and railway roadbed only consider sink-float direction degree of freedom; Wheel-rail contact model application Hertz contact theory.

Stock rail coupled system dynamics equation can be write as matrix form according to D ' Alembert principle:

$M\stackrel{..}{x}+C\stackrel{.}{x}+\mathrm{Kx}=P$

In formula, M, C, K represent quality, damping, stiffness matrix respectively; P represents load vector; displacement vector, velocity, the acceleration vector of associated freedom is represented respectively with x.Under track irregularity incentive action, apply quick explicit integration schemes and can carry out numerical integration, solve the response of kinetic model, specifically see document (Zhai Wanming work. car track coupling dynamics (third edition). Science Press .2007).

(4.2) the vibration acceleration signal x under obtaining failure-free operation and there is the flat bar excitation of wheel _r(t) and x _f(t), and add white noise.To x _r(t) and x _ft () repeats the 3rd step, acquire a series of intrinsic mode function IMF _n.

(4.3) according to formula:

$E_j={\mathrm{\ψ}}_j^2=\frac{1}{x}{\∫}_0^x{\mathrm{\η}}^2\left(x\right)\mathrm{dx}$

Calculate x _r(t) and x _fthe ENERGY E of the intrinsic mode functions under each wave band of (t) _rjand E _fj;

By x _f(t) each IMF ENERGY E _fjdeduct x _r(t) each IMF ENERGY E _rjobtain E _rfj, that is:

E _rfj＝E _fj-E _rj

Above formula can because E _fjbe less than E _rjbe the situation of negative at specific f wave band, in actual computation, if there is negative, then directly define E _rfjbe zero.Its physical significance to represent in fault-signal almost not to should the trouble unit of wavelength, also not to should the energy of wavelength in the output of system.

By each IMF ENERGY E _rfiwith gross energy ratio as the proper vector of energy coefficient, that is:

$\mathrm{\λ}\left(f_j\right)=E_{\mathrm{rfj}}/\underset{j=}{\overset{n}{\mathrm{\Σ}}}{E}_{\mathrm{rfj}}$

Embodiment 1

The present embodiment obtains the wheel of putting down under wheel fault and track irregularity superposition excitation at wheel based on Dynamics Simulation Model and responds vibration signal.The parameter of the Vehicular system of realistic model is express locomotive, and the parameter of rail system is China high-speed line HST60 basic motive parameter.Train running speed v=20m/s is set respectively, iteration spatial mesh size Δ s=1mm in simulation process.Wheel flat wheel fault model is expressed as in formula, x represents the displacement of scratch length direction, and z (x) represents the vertical irregularity of track that scratch is corresponding, and L represents scratch length, D _f=L ²/ 16R represents and effectively abrades the degree of depth.Definition L=0,1,2 ..., the wheel flat of 7mm length is excited data, and applying quick explicit integration schemes can carry out numerical integration, solves the response of kinetic model.Experiment gathers axle box vibration acceleration signal, and sample frequency is 20000Hz, and the duration is 0.1s.

Composition graphs 3 ~ 4, choosing flat wheel fault is the time and frequency domain analysis that the axle box vibration signal of 7mm carries out signal before and after wavelet noise.Wavelet basis function is chosen as sym8 small echo, and scaling sequence length is 256, and visible wheel-rail impact signal main frequency is within 1000Hz, and shock duration is about 16 milliseconds, time-domain diagram impacts forming several plots peak.By comparing time-frequency figure before and after denoising and time-frequency amplitude figure, visible wavelet threshold denoising eliminates most of noise in signal, and the time-frequency characteristics of impact signal is retained well, demonstrates the validity of Wheel Rail Vibration signal wavelet threshold denoising.

Composition graphs 5 ~ 6, choosing non-fault peace wheel fault is that the axle box vibration signal of 7mm carries out EMD decomposition, and Wheel Rail Vibration signal decomposition obtains 8 IMF components and 1 residual components, and in figure, signal is original signal, imf1-imf8 is 8 IMF components, and res is residual components.As can be seen from Figure 5, the signal in each modal components is all linear without significantly impacting, and signal is stationarity, therefore without flat wheel fault signature.As can be seen from Figure 6, without obviously wheel is to impact signal in imf5, imf6, imf7 and imf8, should be original signal high-frequency noises, imf2 and imf3 is the component of amplitude maximum, be the main concentrated area of flat wheel fault signature composition, therefore choose front 5 components and carry out energy spectrometer.

Composition graphs 7, flat wheel fault is that after the axle box vibration signal of 7mm carries out EMD decomposition, each component energy and normal signal EMD decompose rear each component energy.Visible, each component energy of relative normal signal, imf1 and imf2 is the component of amplitude maximum, is the main concentrated area of flat wheel fault signature composition.Flat wheel fault is that each component energy of the vibration signal of 7mm and each component energy of normal signal subtract each other and obtain E _rfj, that is: E _rfj=E _fj-E _rj.Basis further determine that energy weight coefficient is, λ _{(1 ~ 5)}=[0.16030.68000.12980.02820.0016].

The vibration signal that all the other flat wheel fault levels are gathered according to carry out the calculating of EMD generalized energy, calculate λ simultaneously _{(1 ~ 5)}broad sense gross energy in=1/5 situation, contrasts with EMD generalized energy.Experiment only gathers axle box vibration signal, i.e. m=1; Front 5 components that have chosen after EMD decomposition carry out energy spectrometer, i.e. n=5.

Associative list 1, broad sense total energy value take turns fault level present linear increment relation with flat, and when distinguishing 3rd level and the 4th grade of flat wheel fault, due to the interference that track irregularity superposition encourages, the broad sense gross energy of vibration signal is respectively 4.25 × 10 ³with 3.93 × 10 ³, specifically cannot distinguish fault level.EMD generalized energy amplitude has the increase of certain amplitude compared with total energy value, same and flatly take turns fault level and present linear relationship.Owing to introducing the energy coefficient of each wave band, make the contribution of energy to EMD generalized energy of the specific IMF wave band caused by flat wheel fault larger, therefore avoid when distinguishing 3rd level and the 4th grade of flat wheel fault, what the interference due to track irregularity superposition excitation caused is difficult to distinguish fault level.

Table 1 gross energy and the contrast of EMD generalized energy

In sum, the present invention compared with prior art, can extract the Wheel Rail Vibration signal characteristic that flat wheel fault causes in real time, accurately, realizes flat wheel On-line Fault Real-Time Monitoring.

Claims (5)

1., based on a Wheel Rail Vibration signal fault feature extracting method for EMD generalized energy, it is characterized in that, comprise the following steps:

1st step, the vibration acceleration signal of Real-time Collection running train also encloses corresponding start/stop time to speed of a motor vehicle integration determination rotation of wheel one, removes with this start/stop time the acceleration signal intercepting corresponding time history;

2nd step, intercepts to the 1st step the vibration acceleration signal obtained and carries out wavelet decomposition, the threshold process of each layer wavelet coefficient and wavelet reconstruction successively, realize Wavelet Denoising Method;

3rd step, carries out empirical mode decomposition to the vibration acceleration signal after the 2nd step Wavelet Denoising Method, obtains a series of intrinsic mode function IMF _n;

4th step, determines intrinsic mode function IMF _nenergy weight coefficient, and calculate EMD generalized energy, according to this EMD generalized energy determination fault signature.

2. the Wheel Rail Vibration signal fault feature extracting method based on EMD generalized energy according to claim 1, it is characterized in that, described in the 1st step, the vibration acceleration signal of train is designated as x _i(t), i=1,2 ..., m, subscript i represent corresponding traveling based part, and m represents traveling based part sum.

3. the Wheel Rail Vibration signal fault feature extracting method based on EMD generalized energy according to claim 1, it is characterized in that, described in the 2nd step, the concrete steps of Wavelet Denoising Method are:

(2.1) wavelet decomposition of signal: select little basis function ripple and determine wavelet decomposition number of plies N, carries out N layer wavelet decomposition to signals and associated noises;

(2.2) threshold process of each layer wavelet coefficient: according to thresholding functions, threshold process is carried out to each layer wavelet coefficient that signal decomposition obtains, obtain new wavelet coefficient;

(2.3) wavelet reconstruction: be reconstructed new wavelet coefficient, obtains the signal after denoising.

4. the Wheel Rail Vibration signal fault feature extracting method based on EMD generalized energy according to claim 1, is characterized in that, carry out empirical mode decomposition described in the 3rd step to the vibration acceleration signal after Wavelet Denoising Method, obtain a series of intrinsic mode function IMF _n, concrete steps are as follows:

(3.1) set original signal as x (t), determine Local Extremum all in the whole time domain of signal;

(3.2) cubic spline function is adopted to carry out to all maximum point of signal x (t) and minimum point the coenvelope u that interpolation fitting obtains signal x (t) respectively ₀(t) and lower envelope v ₀t (), then by u ₀(t) and v ₀t () obtains the average envelope m of signal ₀(t):

$m_0\left(t\right)=\frac{1}{2}(u_0\left(t\right)+v_0\left(t\right))$

(3.3) average envelope m is deducted with original signal x (t) ₀t (), obtains remainder, be designated as h ₁(t):

h ₁(t)＝x(t)-m ₀(t)

Further decomposition, by h ₁t () is used as new original signal, repeat step (3.1) ~ step (3.3), supposes to repeat k time, until obtain h _kt () meets the condition of intrinsic mode function, process is as follows:

$\begin{array}{c}{m}_1\left(t\right)=\frac{1}{2}(u_1\left(t\right)+v_1\left(t\right))\\ h_2\left(t\right)=h_1\left(y\right)-m_1\left(t\right)\\ .\\ .\\ .\\ m_{k-1}\left(t\right)=\frac{1}{2}(u_{k-1}\left(t\right)+v_{k-1}\left(t\right))\\ h_k\left(t\right)=h_{k-1}\left(y\right)-m_{k-1}\left(t\right)\end{array}$

Now h _kt () is first intrinsic mode function of original signal x (t), be designated as c ₁(t), c ₁t () comprises the highest component of the frequency of original signal x (t);

(3.4) c is deducted with original signal x (t) ₁t () obtains residual signal and is designated as r ₁(t):

r ₁(t)＝x(t)-c ₁(t)

To residual signal r ₁t () repeats above-mentioned steps (3.1) ~ (3.4), then obtain second intrinsic mode function c ₂(t), repeat n decomposition and obtain each intrinsic mode function, its process is as follows:

$\begin{array}{c}{r}_1\left(t\right)-c_2\left(t\right)=r_2\left(t\right)\\ .\\ .\\ .\\ r_{n-1}\left(t\right)-c_n\left(t\right)=r_n\left(t\right)\end{array}$

(3.5) as residual components r _nwhen () meets given stop criterion t, then stop whole signal decomposition process, obtain last intrinsic mode function c _n(t) and residual components r _n(t), now original signal x (t) is expressed as multiple intrinsic mode function and residual components sum:

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{c}_i\left(t\right)+r_n\left(t\right)$

C in formula _it () represents i-th natural mode of vibration component, c _it () represents the component of original signal different frequency section, r _nthe residual components of steady composition in (t) representation signal.

5. the Wheel Rail Vibration signal fault feature extracting method based on EMD generalized energy according to claim 1, is characterized in that, determine intrinsic mode function IMF described in the 4th step _nenergy weight coefficient, and calculate EMD generalized energy, according to this EMD generalized energy determination fault signature, specific as follows:

The expression formula of EMD generalized energy is:

$Q=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\sqrt{\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\left(f_j\right)E_i\left({\mathrm{\η}}_j\right)}$

In formula: Q is EMD generalized energy index; I=1,2 ..., m, i represent traveling based part, and m represents traveling based part sum; J=1,2 ..., n, j are the label obtaining each intrinsic mode functions after EMD decomposes, and n is intrinsic mode functions sum; η _jfor the signal that jth item intrinsic mode functions is extracted, length is the vibration acceleration that rotation of wheel one encloses that corresponding start/stop time intercepts corresponding time history; λ _i(f _j) be the energy weight coefficient of the jth item intrinsic mode functions that i-th vibration signal is corresponding; E _i(η _j) be the energy of the jth item intrinsic mode functions that i-th vibration signal is corresponding, ENERGY E _irepresent with following formula:

$E_i={\∫}_0^x{G}_i\left(f\right)\mathrm{dx}={\mathrm{\ψ}}_i^2$

In formula: G _ifor track power spectral density function; F is frequency; for mean square value, and mean square value calculating formula is

${\mathrm{\ψ}}_i^2=\frac{1}{x}{\∫}_0^x{\mathrm{\η}}^2\left(x\right)\mathrm{dx}\≈\frac{1}{m}\underset{\mathrm{\μ}=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\η}}_{\mathrm{\μ}}^2$

Energy coefficient λ (f _j) following dimension normalization condition need be met:

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\λ}\left(f_j\right)=1$

Different intrinsic mode functions has different energy coefficienies, and the vibration signal IMF of the frequency band that the larger expression of energy coefficient is corresponding is with it larger to track quality influence;

Adopt feature energy method determination intrinsic mode function IMF _nenergy weight coefficient, concrete steps are:

(4.1) adopt Zhai Wan bright method establishment vehicle track coupling dynamics model, stock rail coupled system dynamics equation is write as matrix form according to D ' Alembert principle:

$M\stackrel{\·\·}{x}+C\stackrel{\·}{x}+\mathrm{Kx}=P$

In formula, M, C, K represent quality, damping, stiffness matrix respectively; P represents load vector; displacement vector, velocity, the acceleration vector of associated freedom is represented respectively with x;

(4.2) the vibration acceleration signal x of failure-free operation is obtained _r(t) and the vibration acceleration signal x under there is the flat bar excitation of wheel _f(t), and add white noise, to x _r(t) and x _ft () repeats the 3rd step, obtain a series of intrinsic mode function IMF _n;

(4.3) x is calculated according to the following formula _rthe ENERGY E of the intrinsic mode functions under (t) each wave band _rjand x _fthe ENERGY E of the intrinsic mode functions under (t) each wave band _fj:

$E_j={\mathrm{\ψ}}_j^2=\frac{1}{x}{\∫}_0^x{\mathrm{\η}}^2\left(x\right)\mathrm{dx}$

By x _ft () each IMF ENERGY E fj deducts each IMF ENERGY E rj of xr (t) and obtains Erfj, that is:

E _rfj＝E _fj-E _rj

By each IMF ENERGY E rfi and gross energy ratio as the proper vector λ (f of energy coefficient _j), that is:

$\mathrm{\λ}\left(f_j\right)=E_{\mathrm{rfj}}/\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{E}_{\mathrm{rfj}}.$