CN105092711A - Steel rail crack acoustic emission signal detecting and denoising method based on Kalman filtering - Google Patents

Abstract

The invention discloses a steel rail crack acoustic emission signal detecting and denoising method based on Kalman filtering. The method includes the following steps of firstly, establishing a wheel-rail contact noise linear time sequence AR model; secondly, establishing a wheel-rail contact noise Kalman filtering basic equation through corresponding parameters of the AR model; thirdly, estimating the wheel-rail contact noise through Kalman recursive filtering; fourthly, restraining the wheel-rail contact noise. Compared with the prior art, the method has the advantages that on the basis of a noise acoustic emission signal which can be directly measured, the AR model is established for the known part of a noise signal so that Kalman filtering can be conducted, estimation of the noise signal is achieved, and a steel rail crack signal can be detected without knowing the priori knowledge of the steel rail crack signal; by means of the denoising method, under the high-speed condition that the steel rail crack signal is completely submerged in the noise signal, the aims of restraining noise and detecting steel rail cracks can still be achieved.

Description

A kind of rail cracks acoustic emission signal based on Kalman filtering detects and denoising method

Technical field

The present invention relates to the denoising method of a kind of rail in high speed railway acoustic emission flaw detection, be specifically related to a kind of rail cracks acoustic emission signal based on Kalman filtering and detect and denoising method.

Background technology

Current China Express Railway is flourish, but when driving because rail is squeezed deformation and fatigue wear for a long time, Rail Surface can be made and inner crackle occurs, fracture or the hurt of other form, the rail fracture expanded by rail cracks is train derailment accident main cause, and the probability that the raising of high speed train speed makes it crack increases greatly.Existing large-scale inspection car and the hand propelled defectoscope road occupying time is long, operating efficiency is low, is not suitable for the rail examination of high-speed railway.Acoustic emission is different from traditional railway hurt detection technique (ultrasonic technique and electromagnetic induction technology), it is a kind of dynamic lossless detection method, there is the features such as real-time is good, susceptibility is strong, the crackle of Rail Surface can not only be detected, and can the generation of the inner hurt of perception rail, so acoustic emission is very suitable for the on-line checkingi of rail cracks.But acoustic emission is due to its susceptibility, be easily subject to the interference of outside noise, the simultaneous noise signal that effective Signal of Cracks detects.When train speed is larger, rail cracks signal floods by noise signal completely that produce, causes rail cracks signal to distinguish, is the subject matter of acoustic emission flaw detection application under obstruction high-speed case.So the key of rail in high speed railway acoustic emission flaw detection carries out denoising to the acoustic emission signal being subject to noise.

Summary of the invention

A kind of rail cracks acoustic emission signal based on Kalman filtering is the object of the present invention is to provide to detect and denoising method, can restraint speckle signal, detect the rail cracks signal under different rows vehicle speed, determine the generation moment of crackle acoustic emission source, for rail cracks hurt feature extraction and classifying provides further guidance.

The object of the invention is to be achieved through the following technical solutions:

Rail cracks acoustic emission signal based on Kalman filtering detects and a denoising method, comprises the following steps: transmit to pure sound and set up AR model, obtains linear session series model parameter; The Kalman filtering fundamental equation of noise signal is set up according to the corresponding relation of noise signal model; Kalman filtering recursive algorithm is adopted directly to obtain the estimation of noise signal to noise signal; Transmit with Noise and deduct the object that noise signal estimates to reach restraint speckle, detection rail cracks.As shown in Figure 1, concrete steps are as follows:

Step one: set up Wheel Rail Contact noise linearity Time Series AR model, process flow diagram as shown in Figure 2.

1) gather the wheel track motion acoustic emission signal S that the calibrate AE sensor under friction speed receives, intercepting length before rail cracks occurs is the data segment of N number of sampled point, as pure noise signal, is designated as { x (k) }, k=1,2 ..., N;

2) Yule-Walker method estimation model parameter sets up the AR model of noise signal sequence { x (k) }:

x(k)+a ₁x(k-1)+a ₂x(k-2)…+a _px(k-p)＝w(k)；

Above formula is the p rank AR model of noise signal sequence { x (k) }, a in formula ₁, a ₂..., a _pfor model parameter, model error w (k) is average, and to be zero variance be white Gaussian noise;

Definition auto-covariance matrix ${\mathrm{\Γ}}_n=\left[\begin{array}{cccc}{\mathrm{\γ}}_0& {\mathrm{\γ}}_1& \mathrm{...}& {\mathrm{\γ}}_{n-1}\\ {\mathrm{\γ}}_1& {\mathrm{\γ}}_0& \mathrm{...}& {\mathrm{\γ}}_{n-2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\γ}}_{n-1}& {\mathrm{\γ}}_{n-2}& \mathrm{...}& {\mathrm{\γ}}_0\end{array}\right]$ And vector ${\mathrm{\γ}}_n=\left[\begin{array}{c}{\mathrm{\γ}}_1\\ {\mathrm{\γ}}_2\\ .\\ .\\ .\\ {\mathrm{\γ}}_n\end{array}\right],$ Then Parameters of Autoregressive Models a ₁, a ₂..., a _pby the autocovariance γ of p rank AR model ₀, γ ₁... γ _pby Yule-Walker equation

$\left[\begin{array}{c}{\mathrm{\γ}}_1\\ {\mathrm{\γ}}_2\\ .\\ .\\ .\\ {\mathrm{\γ}}_p\end{array}\right]\left[\begin{array}{cccc}{\mathrm{\γ}}_0& {\mathrm{\γ}}_1& \mathrm{...}& {\mathrm{\γ}}_{p-1}\\ {\mathrm{\γ}}_1& {\mathrm{\γ}}_0& \mathrm{...}& {\mathrm{\γ}}_{p-2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\γ}}_{p-1}& {\mathrm{\γ}}_{p-2}& \mathrm{...}& {\mathrm{\γ}}_0\end{array}\right]\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_p\end{array}\right]$

Uniquely determine, white noise error variance uniquely determined by following formula:

${\mathrm{\σ}}_w^2={\mathrm{\γ}}_0-(a_1{\mathrm{\γ}}_1+a_2{\mathrm{\γ}}_2+...+a_p{\mathrm{\γ}}_p),$

Thus set up the AR model of noise signal;

3) wherein the determination of model order p adopts AIC value method:

$AIC\left(p\right)=ln\left({\mathrm{\σ}}_w^2\right)+2p/N;$

In formula, N is signal length, the p making AIC value obtain minimum value is optimization model exponent number, after Confirming model exponent number, namely available Yule-Walker method estimates model parameter and the model error variance of noise signal, and then obtains the AR model of noise signal under friction speed.

Step 2: set up Wheel Rail Contact noise Kalman filtering fundamental equation by AR model relevant parameter, process flow diagram as shown in Figure 3.

1) Kalman filtering fundamental equation is defined as follows:

State equation: X _k=Φ _{k, k-1}x _k-1+ Γ _{k, k-1}w _k-1;

Measure equation: Z _k=H _kx _k+ V _k;

State vector X wherein to be estimated _kby system noise sequence W _k-1drive, Φ _{k, k-1}for t _k-1moment is to t _kthe Matrix of shifting of a step in moment, Γ _{k, k-1}for system noise drives matrix, Z _kfor measuring amount, H _kfor calculation matrix, require system noise sequence W _kfor zero-mean variance matrix is Q _kwhite noise, measurement noises sequence V _kfor zero-mean variance matrix is R _kwhite noise, and the two is uncorrelated;

2) state vector X is formed by noise signal sequence { x (k) } _k:

According to noise signal p rank AR model-composing state vector X _k:

$X_k=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ .\\ .\\ .\\ x_{p-1}\left(k\right)\\ x_p\left(k\right)\end{array}\right]=\left[\begin{array}{c}x(k-p)\\ x(k-p+1)\\ .\\ .\\ .\\ x(k-2)\\ x(k-1)\end{array}\right];$

Wherein state vector X _kfor p dimension, p ties up state component following relation:

$\left\{\begin{array}{c}{x}_1\left(k\right)=x_2(k-1)\\ x_2\left(k\right)=x_3(k-1)\\ .\\ .\\ .\\ x_{p-1}\left(k\right)=x_p(k-1)\end{array}\right.;$

3) state equation of noise signal { x (k) } is set up:

According to the AR relationship model of noise signal in step one, obtain state equation:

Contrast with Kalman filtering state equation, obtain Matrix of shifting of a step:

System noise drives matrix:

${\mathrm{\Γ}}_{k,k-1}=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\\ 1\end{array}\right];$

Error sequence w (k) of model is system noise W _k, so system noise variance matrix then state equation X _k=Φ _{k, k-1}x _k-1+ Γ _{k, k-1}w _k-1known;

4) the measurement equation of noise signal { x (k) } is set up:

Actual measurement Noise transmits sequence for { z (k) }, makes Z _k=z (k), obtaining measurement equation is:

Z _k＝[00…01]X _k+V _k；

Calculation matrix:

H _k＝[00…01]；

If measurement noises V _kfor zero-mean white noise, measurement noises variance matrix then measure equation Z _k=H _kx _k+ V _kknown.

Step 3: Kalman's Recursive Filtering estimates Wheel Rail Contact noise.

The present invention starts with from known noise signal, when taking noise signal as quantity of state, directly can obtain the estimation of noise signal, Kalman filtering recursive algorithm through Kalman filtering:

State one-step prediction

${\hat{X}}_{k,k-1}={\mathrm{\Φ}}_{k,k-1}{\hat{X}}_{k-1};$

One-step prediction error covariance matrix P _{k, k-1}:

$P_{k,k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+{\mathrm{\Γ}}_{k,k-1}{Q}_{k-1}{\mathrm{\Γ}}_{k,k-1}^T;$

Kalman filtering gain K _k:

$K_k=P_{k,k-1}{H}_k^T{\[H_k{P}_{k,k-1}{H}_k^T+R_k\]}^{-1};$

State filtering is estimated

${\hat{X}}_k={\hat{X}}_{k,k-1}+K_k{\[Z_k-H_k{\hat{X}}_{k,k-1}\]}^{-1};$

Filtering error variance matrix P _k:

P _k＝[I-K _kH _k]P _k，k-1；

In formula, I is unit battle array, as long as given initial value and P ₀, just can according to measurement Z _krecurrence calculation obtains the estimation in k moment generally get initial value for state X ₀average, P ₀=var [X ₀] be state X ₀variance, obtain the estimation of noise signal after Kalman filtering.

Step 4: the suppression of Wheel Rail Contact noise.

For removing noise signal, deducting noise signal with original signals and associated noises S and estimating the effect of restraint speckle can be reached.When taking noise as the quantity of state of Kalman filter equation, think that rail cracks signal is measurement noises V _k, but due to Signal of Cracks be nonstationary random signal, and can not directly record pure Signal of Cracks, can not using its variance as measurement noises variance, so measurement noises V _kvariance R _kget the smaller value being greater than system noise error variance, now do not react the amplitude quantization situation of Signal of Cracks, so with original signals and associated noises deduct the noise signal after Kalman filtering estimate, obtain the projection P of rail cracks signal, in this approach as a kind of detection method of rail cracks signal.When the projection of this Signal of Cracks exists, then the generation of rail cracks can be detected.

Compared with prior art, tool has the following advantages in the present invention:

1) on the basis that the sound that can directly record transmits, AR model is set up to known noise signal portions and carries out Kalman filtering, obtain the estimation of noise signal, without the need to knowing that the priori of rail cracks signal can detect the generation of rail cracks signal;

2) denoising method proposed by the invention, under being submerged in the high-speed case of noise signal completely, still can reach restraint speckle at rail cracks signal, detects the object that rail cracks occurs.

Accompanying drawing explanation

Fig. 1 is for being block scheme of the present invention;

Fig. 2 is for setting up Wheel Rail Contact noise signal AR model flow figure;

Fig. 3 is for setting up Wheel Rail Contact noise signal Kalman filtering fundamental equation process flow diagram;

Fig. 4 is that Wheel Rail Contact noise signal intercepts schematic diagram;

Fig. 5 is that under 48km/h speed, Noise transmits;

Fig. 6 is the rail cracks signal projection obtained after detecting denoising under 48km/h speed;

Fig. 7 is acoustic emission signal raw data under 140km/h speed;

Fig. 8 is that the Noise under 140km/h speed transmits;

Fig. 9 is the rail cracks signal projection obtained after detecting denoising under 140km/h speed.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is further described; but be not limited thereto; everyly technical solution of the present invention modified or equivalent to replace, and not departing from the spirit and scope of technical solution of the present invention, all should be encompassed in protection scope of the present invention.

The invention provides a kind of rail cracks acoustic emission signal based on Kalman filtering to detect and denoising method, comprise the following steps: the AR model setting up noise signal under friction speed, take noise signal as quantity of state, set up Kalman filtering fundamental equation, estimated by Kalman filtering recurrence calculation noise signal, finally transmit with original Noise and deduct noise signal estimation, rail cracks signal can be detected.To record respectively at various speeds every 6km/h from 6km/h ~ 140km/h and organize experimental data more.

Perform step one: the noise signal of the acoustic emission signal before useful signal arrives all for this reason under speed, getting noise signal length is 10000 points, for 24km/h acoustic emission signal noise signal { x (k) } as shown in Figure 4.AIC value-exponent number curve is drawn to the noise signal under friction speed, obtain the optimum AR model order p under friction speed, estimate model parameter and the model error variance of noise signal again by Yule-Walker method, set up the noise signal AR model under respective optimum exponent number respectively.

Perform step 2: set up quantity of state X by noise signal _k, set up respective Kalman filtering state equation X by the noise signal AR model under friction speed _k=Φ _{k, k-1}x _k-1+ Γ _{k, k-1}w _k-1with measurement equation Z _k=H _kx _k+ V _k.

Perform step 3: Noise original under each speed is signaled and carries out Kalman filtering, obtain noise signal and estimate

Perform step 4: original Noise signalling S deducts noise signal and estimates, obtains rail cracks signal projection P.

Fig. 5 is Noise generation signal under 48km/h speed, and Fig. 6 is the rail cracks signal projection obtained after detecting denoising under 48km/h speed.48km/h is rail cracks signal is not flooded situation typical rate by noise, and before denoising, noise signal amplitude is at 20mV, and the amplitude of noisy rail cracks signal is 80mV, and noise signal amplitude accounts for greatly 25% of noisy rail cracks signal amplitude; And in useful signal after Fig. 6 denoising, noise signal amplitude is about 0.5mV, and the amplitude of rail cracks signal is about 10mV, and noise signal is about 5% with rail cracks signal amplitude ratio.Contrast before and after denoising, noise signal diminishes with rail cracks signal amplitude ratio, illustrates that the signal denoising detection method based on Kalman filtering can significantly noise decrease, strengthens useful signal, signal to noise ratio (S/N ratio) is increased.

Fig. 7 is acoustic emission signal raw data under 140km/h speed, signal segment is flooded completely as depicted in figure 8 comprising rail cracks signal, Fig. 9 obtains the projection of rail cracks signal after detecting denoising, and during 140km/h, rail cracks signal has been submerged in completely in noise signal and cannot have distinguished.In Fig. 8, during 140km/h, noise signal amplitude, at about 85mV, has a saturation signal point (amplitude is shown as 100mV) when the time is 4.06s.Rail cracks signal can be detected from the signal flooded by noise after denoising, noise is inhibited.Still containing noise in signal after testing after denoising, the amplitude of noise is 0.8mV, and useful signal amplitude is at about 3mV, and final noise signal is about 26.7% with rail cracks signal amplitude ratio.Compared with being submerged in situation, the detection denoising scheme based on Kalman filtering can reach restraint speckle, detects the object that rail cracks signal occurs.

The above-mentioned analysis of integrated embodiment, for the detection of rail cracks acoustic emission signal in rail in high speed railway flaw detection, the present invention adopts the rail cracks input denoising method based on Kalman filtering.AR model is set up to known noise signal, and set up Kalman filtering fundamental equation on this basis, after Kalman filtering, obtain noise signal estimate, then deduct noise estimation by original Noise generation signal, reach restraint speckle, detect the object of rail cracks signal.Due to the method that this method is based on noise signal, in this way not by the impact of rail cracks signal, no matter whether useful signal is submerged in noise signal, the generation of rail cracks acoustic emission signal can both be detected from noise signal.

Claims (3)

1. the rail cracks acoustic emission signal based on Kalman filtering detects and a denoising method, it is characterized in that described method step is as follows:

Step one, set up Wheel Rail Contact noise linearity Time Series AR model:

1) gather the wheel track motion acoustic emission signal S that the calibrate AE sensor under friction speed receives, intercepting length before rail cracks occurs is the data segment of N number of sampled point, as pure noise signal, is designated as { x (k) }, k=1,2 ..., N;

2) Yule-Walker method estimation model parameter sets up the AR model of noise signal sequence { x (k) }:

x(k)+a ₁x(k-1)+a ₂x(k-2)…+a _px(k-p)＝w(k)；

Above formula is the p rank AR model of noise signal sequence { x (k) }, a in formula ₁, a ₂..., a _pfor model parameter, model error w (k) is average, and to be zero variance be white Gaussian noise;

Definition auto-covariance matrix ${\mathrm{\Γ}}_n=\left[\begin{array}{cccc}{\mathrm{\γ}}_0& {\mathrm{\γ}}_1& \mathrm{...}& {\mathrm{\γ}}_{n-1}\\ {\mathrm{\γ}}_1& {\mathrm{\γ}}_0& \mathrm{...}& {\mathrm{\γ}}_{n-2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\γ}}_{n-1}& {\mathrm{\γ}}_{n-2}& \mathrm{...}& {\mathrm{\γ}}_0\end{array}\right]$ And vector ${\mathrm{\γ}}_n=\left[\begin{array}{c}{\mathrm{\γ}}_1\\ {\mathrm{\γ}}_2\\ .\\ .\\ .\\ {\mathrm{\γ}}_n\end{array}\right],$ Then Parameters of Autoregressive Models a ₁, a ₂..., a _pby the autocovariance γ of p rank AR model ₀, γ ₁... γ _pby Yule-Walker equation

$\left[\begin{array}{c}{\mathrm{\γ}}_1\\ {\mathrm{\γ}}_2\\ .\\ .\\ .\\ {\mathrm{\γ}}_p\end{array}\right]\left[\begin{array}{cccc}{\mathrm{\γ}}_0& {\mathrm{\γ}}_1& \mathrm{...}& {\mathrm{\γ}}_{p-1}\\ {\mathrm{\γ}}_1& {\mathrm{\γ}}_0& \mathrm{...}& {\mathrm{\γ}}_{p-2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\γ}}_{p-1}& {\mathrm{\γ}}_{p-2}& \mathrm{...}& {\mathrm{\γ}}_0\end{array}\right]\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_p\end{array}\right]$

Uniquely determine, white noise error variance uniquely determined by following formula:

${\mathrm{\σ}}_w^2={\mathrm{\γ}}_0-(a_1{\mathrm{\γ}}_1+a_2{\mathrm{\γ}}_2+...+a_p{\mathrm{\γ}}_p),$

Thus set up the AR model of noise signal;

3) determination of model order p adopts AIC value method:

$AIC\left(p\right)=ln\left({\mathrm{\σ}}_w^2\right)+2p/N;$

In formula, N is signal length, the p making AIC value obtain minimum value is optimization model exponent number, after Confirming model exponent number, namely available Yule-Walker method estimates model parameter and the model error variance of noise signal, and then obtains the AR model of noise signal under friction speed;

Step 2, set up Wheel Rail Contact noise Kalman filtering fundamental equation by AR model relevant parameter:

1) Kalman filtering fundamental equation is defined as follows:

State equation: X _k=Φ _{k, k-1}x _k-1+ Γ _{k, k-1}w _k-1;

Measure equation: Z _k=H _kx _k+ V _k;

State vector X wherein to be estimated _kby system noise sequence W _k-1drive, Φ _{k, k-1}for t _k-1moment is to t _kthe Matrix of shifting of a step in moment, Γ _{k, k-1}for system noise drives matrix, Z _kfor measuring amount, H _kfor calculation matrix, require system noise sequence W _kfor zero-mean variance matrix is Q _kwhite noise, measurement noises sequence V _kfor zero-mean variance matrix is R _kwhite noise, and the two is uncorrelated;

2) state vector X is formed by noise signal sequence { x (k) } _k:

According to noise signal p rank AR model-composing state vector X _k:

$X_k=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ .\\ .\\ .\\ x_{p-1}\left(k\right)\\ x_p\left(k\right)\end{array}\right]=\left[\begin{array}{c}x(k-p)\\ x(k-p+1)\\ .\\ .\\ .\\ x(k-2)\\ x(k-1)\end{array}\right];$

Wherein state vector X _kfor p dimension, p ties up state component following relation:

$\left\{\begin{array}{c}{x}_1\left(k\right)=x_2(k-1)\\ x_2\left(k\right)=x_3(k-1)\\ .\\ .\\ .\\ x_{p-1}\left(k\right)=x_p(k-1)\end{array}\right.;$

3) state equation of noise signal { x (k) } is set up:

According to the AR relationship model of noise signal in step one, obtain state equation:

Contrast with Kalman filtering state equation, obtain Matrix of shifting of a step:

System noise drives matrix:

${\mathrm{\Γ}}_{k,k-1}=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\\ 1\end{array}\right];$

Error sequence w (k) of model is system noise W _k, so system noise variance matrix then state equation X _k=Φ _{k, k-1}x _k-1+ Γ _{k, k-1}w _k-1known;

4) the measurement equation of noise signal { x (k) } is set up:

Actual measurement Noise transmits sequence for { z (k) }, makes Z _k=z (k), obtaining measurement equation is:

Z _k＝[00…01]X _k+V _k；

Calculation matrix:

H _k＝[00…01]；

If measurement noises V _kfor zero-mean white noise, measurement noises variance matrix then measure equation Z _k=H _kx _k+ V _kknown;

Step 3, Kalman's Recursive Filtering estimate Wheel Rail Contact noise:

When taking noise signal as quantity of state, directly can obtain the estimation of noise signal through Kalman filtering, Kalman filtering recursive algorithm:

State one-step prediction

${\hat{X}}_{k,k-1}={\mathrm{\Φ}}_{k,k-1}{\hat{X}}_{k-1};$

One-step prediction error covariance matrix P _{k, k-1}:

$P_{k,k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+{\mathrm{\Γ}}_{k,k-1}{Q}_{k-1}{\mathrm{\Γ}}_{k,k-1}^T;$

Kalman filtering gain K _k:

$K_k=P_{k,k-1}{H}_k^T{\[H_k{P}_{k,k-1}{H}_k^T+R_k\]}^{-1};$

State filtering is estimated

${\hat{X}}_k={\hat{X}}_{k,k-1}+K_k{\[Z_k-H_k{\hat{X}}_{k,k-1}\]}^{-1};$

Filtering error variance matrix P _k:

P _k＝[I-K _kH _k]P _k，k-1；

In formula, I is unit battle array, as long as given initial value and P ₀, just can according to measurement Z _krecurrence calculation obtains the estimation in k moment the estimation of noise signal is obtained after Kalman filtering;

The suppression of step 4, Wheel Rail Contact noise:

For removing noise signal, deducting noise signal with original signals and associated noises S and estimating the effect of restraint speckle can be reached.

2. the rail cracks acoustic emission signal based on Kalman filtering according to claim 1 detects and denoising method, it is characterized in that described initial value for state X ₀average.

3. the rail cracks acoustic emission signal based on Kalman filtering according to claim 1 detects and denoising method, it is characterized in that described P ₀=var [X ₀] be state X ₀variance.