CN117851812A - VMD-KF-based turnout railhead damage vibration feature extraction method - Google Patents
VMD-KF-based turnout railhead damage vibration feature extraction method Download PDFInfo
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Abstract
The invention relates to the technical field of nondestructive testing, in particular to a switch rail head damage vibration characteristic extraction method based on VMD-KF, which comprises the following steps: the method comprises the steps of initially selecting a signal section with a plurality of impacts for analysis by means of impacts at joints of rail heads and turnouts; obtaining a stabilized eigenmode function (IMF) component of impact vibration based on the VMD, extracting wheel set information from the low-order IMF component to determine the train speed, and estimating the distribution range of the damage signal; extracting vibration signals caused by damage from high-order IMF components containing impact vibration based on KF; finally, the characteristics of the damage vibration signal are extracted based on the Hilbert yellow transform HTT. The invention is used for monitoring and analyzing the vibration characteristics of the turnout section, and has important significance for ensuring the structural integrity of the wheel set and the turnout; the method solves the problem that the conventional method is difficult to extract and analyze when processing the non-stationary vibration signals.
Description
Technical Field
The invention relates to the technical field of nondestructive testing, in particular to a switch rail head damage vibration characteristic extraction method based on VMD-KF.
Background
The turnout is an important component in railway infrastructure, is a connecting device for enabling a train to change track, and is also a key infrastructure for affecting stable and safe running of the train. The complex contact relationship between the braking and starting actions of the train and the track between turnouts can lead to larger contact stress, and when the contact stress exceeds the yield strength limit of turnout materials, the phenomena of fatigue crack or flaking off of the track head can be generated. Under the condition of high-speed running of the train, the contact state between the wheel set and the rail head damage is changed from rolling friction to unsteady contact to generate an impact effect. The impact vibration indexes can be several times of the conventional rolling friction, and meanwhile, the impact acceleration of the turnout is accompanied by larger turnout, so that the structural integrity of the turnout railhead and the wheelset is seriously threatened. In addition, the problems of weak signal and non-stable characteristics of the impact vibration signals of the turnout section wheel set and the rail head damage exist, so that the damage characteristics are difficult to characterize by the traditional signal processing and analyzing method. Therefore, the method for extracting the vibration characteristics of the switch rail head damage is provided for monitoring and analyzing the switch damage and the impact vibration characteristics, and has important significance for guaranteeing the structural integrity of the wheel set and the switch.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a VMD-KF-based switch rail head damage vibration characteristic extraction method which is used for monitoring and analyzing switch interval vibration characteristics and has important significance for guaranteeing the structural integrity of wheel sets and switches.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method for extracting vibration characteristics of turnout railhead damage based on VMD-KF comprises the following specific steps:
step S1, preliminary selecting an original signal: the method comprises the steps of initially selecting signals for analysis by means of impact at joints of rail heads and turnouts;
step S2, VMD decomposition: acquiring accurate speed of a train and components containing damage vibration from each order of IMF based on VMD decomposition;
step S3, signal enhancement: extracting a damage vibration signal from a high-order IMF component containing impact vibration based on KF;
step S4, feature extraction: the characteristics of the impairment vibration signal are extracted based on HTT.
Preferably, in step S1, the method specifically includes:
s101, obtaining an original vibration signal of a train passing through a turnout by vertically pasting acceleration sensor response to the bottom of the turnout rail;
step S102, a signal section with a plurality of shocks is preliminarily selected from the original signals for analysis in consideration of the fact that large shocks are generated when the train passes through the joint of the railhead and the turnout.
Preferably, in step S2, the method specifically includes:
step S201, VMD decomposition is carried out on the selected signals, and an initial decomposition layer number, a penalty factor alpha and a bandwidth parameter tau are set;
step S202, solving the center frequency of each IMF of VMD decomposition;
step S203, obtaining a single-side spectrum of the mode through hilbert yellow transformation:
wherein delta (t) is a dilichlet function, which is a convolution operation, u k Is a component of each decomposition modality;
step S204, by adding an index typeAdjusting the spectrum of the modal component to baseband:
wherein delta (t) is a Dirichlet function, u k Is a component of each decomposition modality;
step S205, solving the formula step S204 to shift the square L of the gradient of the frequency signal 2 The norm obtains the bandwidth of each mode, and an optimal variation model is established according to constraint conditions：
Wherein K is the number of modal components, w k For each decomposition modal component u k Delta (t) is the dirichlet function;
step S206, a Lagrange multiplier and a secondary penalty factor are introduced to solve the model of the step S205, wherein in order to ensure the signal reconstruction accuracy under the Gaussian noise background, alpha is a sufficiently large positive number, and the expression of the Lagrange multiplier is as follows:
wherein u is k Is the component of each decomposition mode, lambda (t), f (t) are the input signals, w k For each decomposition modal component u k Is a center frequency of (a);
step S207, based on the alternate direction multiplier algorithm, alternately updating { u } k (t)}、{w k Solving the expanded lagrangian expression "saddle point" with λ (t) until the stop condition of the iteration is satisfied; at this time, the variational model obtains an optimal solution, and the input signal f (t) is decomposed into K limited bandwidth IMF components;
and step S208, extracting and analyzing the wave crest characteristics of the impact signals with larger amplitude from the low-order IMF components, extracting wheel set information to determine the train speed, and further reducing the distribution range of the damaged vibration signals.
Preferably, in step S3, the method specifically includes:
step S301, filtering and weak signal enhancement are carried out on the high-frequency IMF4 component containing noise and vibration by adopting a KF method, so that a pure damage vibration signal can be obtained;
step S302, assuming that y (n) is an IMF component including noise and impact vibration, S (n) is a clean impact vibration signal, and d (n) is a noise signal, the relationship between the three can be expressed as:
y(n)＝s(n)+d(n),0≤n≤N-1
wherein N is the number of data points, and N is the frame length;
step S303, performing Fourier transform on two sides of the step S302 to obtain:
Y(ω)＝S(ω)+D(ω)
step S304, assuming that S (n) and D (n) are mutually independent signals, S (ω) and D (ω) are mutually independent signals, it can be deduced that:
E||S(ω)| 2 |＝E||Y(ω)| 2 |-E||D(ω)| 2 |
wherein Y (ω), S (ω), and D (ω) are the short-time power spectra of Y (n), S (n), and D (n), respectively;
step S305, for a short-time smoothing process of IMF component in a certain frame, includes:
|S(ω)| 2 ＝|Y(ω)| 2 -λ d (ω)
wherein lambda is d (omega) is |D (omega) | 2 Statistical averages over silence periods;
the amplitude of the impact vibration signal after KF method in step S306 can be expressed as:
preferably, in step S4, specifically includes:
step S401, carrying out Hilbert transformation on each IMF component obtained by KF decomposition one by one:
where Re represents a constant, i represents a sum operation value, j is an imaginary unit, and φ i (t) is the phase, alpha i (t) is amplitude, ω i (t) is frequency; phi (phi) i (t)、α i (t) and ω i (t) are all functions of time;
in step S402, the Hilbert amplitude spectrum of x (t) in the formula S401 is:
the boundary spectrum of step S403, x (t) is:
h(ω)＝∫ ω H(ω,t)
step S404, the instantaneous energy density is:
IE(t)＝∫ ω H(ω,t)2dω
step S405, utilizeThe time-frequency characteristics of the signal can be obtained.
Preferably, in step S101, the direction of the acceleration signal collected by the acceleration sensor is perpendicular to the attaching position.
Preferably, in step S208, the wheel set information is a center distance between wheels.
By adopting the technical scheme: the invention discloses a turnout rail head damage vibration characteristic extraction method based on variable modal decomposition (Variational mode decomposition, VMD) -Kalman Filter (KF), which mainly comprises the following steps: the method comprises the steps of initially selecting a signal section with a plurality of impacts for analysis by means of impacts at joints of rail heads and turnouts; obtaining a stabilized eigenmode function (Intrinsic Mode Function, IMF) component of impact vibration based on the VMD, extracting wheel set information from the low-order IMF component to determine the train speed, and estimating the distribution range of the damage signal; extracting vibration signals caused by damage from high-order IMF components containing impact vibration based on KF; finally, the characteristics of the impairment vibration signal are extracted based on Hilbert yellow transform (HTT). Aiming at the problem that the non-stationary characteristic of the impact vibration signal of the turnout section wheel set and the rail head damage is difficult to characterize damage, the invention provides a turnout impact vibration signal extraction method based on VMD-KF, and solves the problem that the non-stationary vibration signal is difficult to extract and analyze in the conventional method.
Compared with the prior art, the invention has the following beneficial effects:
the invention is used for monitoring and analyzing the vibration characteristics of the turnout section, and has important significance for ensuring the structural integrity of the wheel set and the turnout.
Drawings
FIG. 1 is a flow chart of signal feature extraction according to the present invention;
FIG. 2 is a diagram of the original signal of the switch vibration in the present invention;
FIG. 3 is a 4-layer VMD exploded view of the original vibration signal of the present invention;
FIG. 4 is a Kalman filter diagram of the present invention;
FIG. 5 is a graph of the impact vibration signal of a lesion in the present invention;
fig. 6 is a diagram showing the result of hubert yellow transformation of the impact vibration signal according to the present invention.
Detailed Description
The following technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, and thus the protection scope of the present invention is more clearly defined. The described embodiments of the present invention are intended to be only a few, but not all embodiments of the present invention, and all other embodiments that may be made by one of ordinary skill in the art without inventive faculty are intended to be within the scope of the present invention.
As shown in fig. 1, the method for extracting the vibration characteristics of the switch head damage based on the VMD-KF comprises the following steps:
the experimental conditions of the examples are as follows:
taking the vibration signal of the train passing through the turnout section at a low speed of about 18km/h as an example, there is a turnout rail head damage at a distance of 0.3m from the turnout to the common rail joint.
Step S1, preliminary selecting an original signal: the method comprises the steps of initially selecting signals for analysis by means of impact at joints of rail heads and turnouts;
step S2, VMD decomposition: acquiring accurate speed of a train and components containing damage vibration from each order of IMF based on VMD decomposition;
step S3, signal enhancement: extracting a damage vibration signal from an IMF component containing impact vibration based on KF;
step S4, feature extraction: the characteristics of the impairment vibration signal are extracted based on HTT.
Specifically, step S1 specifically includes:
step S101, acquiring an original vibration signal of a train passing through a turnout by vertically pasting an acceleration sensor response to the bottom of the turnout;
step S102, considering that a large impact is generated when the train passes through the joint of the railhead and the turnout, a signal section with a plurality of impacts is preliminarily selected from the original signals for analysis. In particular, since the number of wheels per bogie is fixed, it can be used to initially determine the moment at which a wheel set passes over the joint. Then signals at the time near the large vibration signal are intercepted, and the intercepted original signals are shown in fig. 2. From fig. 2, a preliminary selection of pulse signals containing multiple pulses is found, which is indicative of multiple impacts of wheel sets with switch joints, injuries, etc.
Specifically, step S2 specifically includes:
step S201, VMD decomposition is carried out on the selected signals, the initial decomposition layer number is set to be 2, and the penalty factor alpha and the bandwidth parameter tau are set to be default parameters 200 and 0;
step S202, solving the center frequency of each IMF of VMD decomposition;
step S203, obtaining a unilateral spectrum of the mode through hilbert yellow transformation:
wherein delta (t) is a dilichlet function, which is a convolution operation, u k Is a component of each decomposition modality;
step S204, by adding an index typeAdjusting the spectrum of the modal component to baseband:
wherein delta (t) is a Dirichlet function, u k Is a component of each decomposition modality;
step S205, solving the formula step S204 to shift the square L of the gradient of the frequency signal 2 The norm obtains the bandwidth of each mode, and an optimal variation model is established according to constraint conditions:
wherein K is the number of modal components, w k For each decomposition modal component u k Delta (t) is the dirichlet function;
step S206, a Lagrange multiplier and a secondary penalty factor are introduced to solve the model of step S205. In order to ensure the signal reconstruction accuracy in the gaussian noise background, α needs to be a sufficiently large positive number. The Lagrange multiplier has the expression:
wherein u is k Is the component of each decomposition mode, lambda (t), f (t) are the input signals, w k For each decomposition modal component u k Is a center frequency of (a);
step S207, based on the alternate direction multiplier algorithm, alternately updating { u } k (t)}、{w k And λ (t) to solve the extended lagrangian expression "saddle point" until the stop condition of the iteration is satisfied. At this time, the variational model obtains an optimal solution, and the input signal f (t) is decomposed into K limited bandwidth IMF components;
and step S208, extracting and analyzing the wave crest characteristics of the impact signals with larger amplitude from the low-order IMF components, extracting wheel set information to determine the train speed, and further reducing the distribution range of the damaged vibration signals. Specifically, the number of decomposition layers was finally determined to be 4 in the present embodiment, and the decomposition result is shown in fig. 3. Wheel information can be found from the low frequency IMF1 layer, thereby determining that the true wave speed is 18km/h. From the high frequency IMF4 layer, a small pulse may be found before the wheel information, possibly as a damage signal, but the amplitude of the damage signal is low and the signal-to-noise ratio of the signal is low.
Specifically, step S3 specifically includes:
step S301, filtering and weak signal enhancement are carried out on the high-frequency IMF4 component containing noise and vibration by adopting a KF method, so that a pure damage vibration signal can be obtained;
in step S302, assuming that y (n) is an IMF component including noise and impact vibration, S (n) is a clean impact vibration signal, and d (n) is a noise signal, the relationship between the three can be expressed as:
y(n)＝s(n)+d(n),0≤n≤N-1
wherein N is the number of data points, and N is the frame length;
step S303, performing Fourier transform on two sides of the step S302 to obtain:
Y(ω)＝S(ω)+D(ω)
in step S304, assuming that S (n) and D (n) are mutually independent signals, S (ω) and D (ω) are mutually independent signals, it can be deduced that:
E||S(ω)| 2 |＝E||Y(ω)| 2 |-E||D(ω)| 2 |
wherein Y (ω), S (ω), and D (ω) are the short-time power spectra of Y (n), S (n), and D (n), respectively;
step S305, for a short-time stationary process of IMF component in a certain frame, includes:
|S(ω)| 2 ＝|Y(ω)| 2 -λ d (ω)
wherein lambda is d (omega) is |D (omega) | 2 Statistical averages over silence periods;
step S306, therefore, the amplitude of the impact vibration signal after KF method can be expressed as:
in this embodiment, the kalman filter chart is shown in fig. 4, and the pulse signal caused by the damage can be observed significantly. By extracting the impact vibration signal of the lesion, the signal is shown in fig. 5.
Specifically, step S4 specifically includes:
step S401, carrying out Hilbert transformation on each IMF component obtained by KF decomposition one by one:
where Re represents a constant, i represents a sum operation value, j is an imaginary unit, and φ i (t) is the phase, alpha i (t) is amplitude, ω i (t) is frequency; alpha i (t), ai (t) and ω i (t) are all functions of time;
in step S402, the Hilbert amplitude spectrum of x (t) in the formula S401 is:
the boundary spectrum of step S403, x (t) is:
h(ω)＝∫ ω H(ω,t)
in step S404, the instantaneous energy density is:
IE(t)＝∫ ω H(ω,t)2dω
step S405, utilizeThe time-frequency characteristics of the signal can be obtained.
In this example, the result of the hilbert yellow transform of the impact vibration signal of the damage is shown in fig. 6, from which the impact effect of the wheel on the damage can be found many times, and the frequency of the impact is distributed at 3500-5000Hz. By extracting and analyzing the impact signals, the method has important significance for monitoring the state of the turnout.
The description and practice of the invention disclosed herein will be readily apparent to those skilled in the art, and may be modified and adapted in several ways without departing from the principles of the invention. Accordingly, modifications or improvements may be made without departing from the spirit of the invention and are also to be considered within the scope of the invention.
Claims (7)
1. A method for extracting vibration characteristics of turnout railhead damage based on VMD-KF is characterized by comprising the following specific steps:
step S1, preliminary selecting an original signal: the method comprises the steps of initially selecting signals for analysis by means of impact at joints of rail heads and turnouts;
step S2, VMD decomposition: acquiring accurate speed of a train and components containing damage vibration from each order of IMF based on VMD decomposition;
step S3, signal enhancement: extracting a damage vibration signal from a high-order IMF component containing impact vibration based on KF;
step S4, feature extraction: the characteristics of the impairment vibration signal are extracted based on HTT.
2. The method for extracting vibration characteristics of a switch head damage based on VMD-KF according to claim 1, wherein in step S1, specifically comprising:
s101, obtaining an original vibration signal of a train passing through a turnout by vertically pasting acceleration sensor response to the bottom of the turnout rail;
step S102, a signal section with a plurality of shocks is preliminarily selected from the original signals for analysis in consideration of the fact that large shocks are generated when the train passes through the joint of the railhead and the turnout.
3. The method for extracting vibration characteristics of a switch head damage based on VMD-KF according to claim 2, wherein in step S2, specifically comprising:
step S201, VMD decomposition is carried out on the selected signals, and an initial decomposition layer number, a penalty factor alpha and a bandwidth parameter tau are set;
step S202, solving the center frequency of each IMF of VMD decomposition;
step S203, obtaining a single-side spectrum of the mode through hilbert yellow transformation:
wherein delta (t) is a dilichlet function, which is a convolution operation, u k Is a component of each decomposition modality;
step S204, by adding an index typeAdjusting the spectrum of the modal component to baseband:
wherein delta (t) is a Dirichlet function, u k Is a component of each decomposition modality;
step S205, solving the formula step S204 to shift the square L of the gradient of the frequency signal 2 The norm obtains the bandwidth of each mode, and an optimal variation model is established according to constraint conditions:
wherein K is the number of modal components, w k For each decomposition modal component u k Delta (t) is the dirichlet function;
step S206, a Lagrange multiplier and a secondary penalty factor are introduced to solve the model of the step S205, wherein in order to ensure the signal reconstruction accuracy under the Gaussian noise background, alpha is a sufficiently large positive number, and the expression of the Lagrange multiplier is as follows:
wherein u is k Is the component of each decomposition mode, lambda (t), f (t) are the input signals，w k For each decomposition modal component u k Is a center frequency of (a);
step S207, based on the alternate direction multiplier algorithm, alternately updating { u } k (t)}、{w k Solving the expanded lagrangian expression "saddle point" with λ (t) until the stop condition of the iteration is satisfied; at this time, the variational model obtains an optimal solution, and the input signal f (t) is decomposed into K limited bandwidth IMF components;
and step S208, extracting and analyzing the wave crest characteristics of the impact signals with larger amplitude from the low-order IMF components, extracting wheel set information to determine the train speed, and further reducing the distribution range of the damaged vibration signals.
4. The method for extracting vibration characteristics of a switch head damage based on VMD-KF according to claim 3, wherein in step S3, specifically comprising:
step S301, filtering and weak signal enhancement are carried out on the high-frequency IMF4 component containing noise and vibration by adopting a KF method, so that a pure damage vibration signal can be obtained;
step S302, assuming that y (n) is an IMF component including noise and impact vibration, S (n) is a clean impact vibration signal, and d (n) is a noise signal, the relationship between the three can be expressed as:
y(n)＝s(n)+d(n),0≤n≤N-1
wherein N is the number of data points, and N is the frame length;
step S303, performing Fourier transform on two sides of the step S302 to obtain:
Y(ω)＝S(ω)+D(ω)
step S304, assuming that S (n) and D (n) are mutually independent signals, S (ω) and D (ω) are mutually independent signals, it can be deduced that:
E||S(ω)| 2 |＝E||Y(ω)| 2 |-E||D(ω)| 2 |
wherein Y (ω), S (ω), and D (ω) are the short-time power spectra of Y (n), S (n), and D (n), respectively;
step S305, for a short-time smoothing process of IMF component in a certain frame, includes:
|S(ω)| 2 ＝|Y(ω)| 2 -λ d (ω)
wherein lambda is d (omega) is |D (omega) | 2 Statistical averages over silence periods;
the amplitude of the impact vibration signal after KF method in step S306 can be expressed as:
5. the method for extracting vibration characteristics of a switch head damage based on VMD-KF according to claim 4, wherein in step S4, specifically comprising:
step S401, carrying out Hilbert transformation on each IMF component obtained by KF decomposition one by one:
where Re represents a constant, i represents a sum operation value, j is an imaginary unit, and φ i (t) is the phase, alpha i (t) is amplitude, ω i (t) is frequency; phi (phi) i (t)、α i (t) and ω i (t) are all functions of time;
in step S402, the Hilbert amplitude spectrum of x (t) in the formula S401 is:
the boundary spectrum of step S403, x (t) is:
h(ω)＝∫ ω H(ω,t)
step S404, the instantaneous energy density is:
IE(t)＝∫ ω H(ω,t)2dω
step S405, utilizeThe time-frequency characteristics of the signal can be obtained.
6. The method for extracting vibration characteristics of a switch head damage based on VMD-KF according to claim 2, wherein in step S101, the direction of the acceleration signal collected by the acceleration sensor is perpendicular to the pasting position.
7. The method for extracting vibration characteristics of a switch head injury based on VMD-KF according to claim 3, wherein in step S208, the wheel set information is a center distance between wheels.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111679328A (en) * | 2020-04-08 | 2020-09-18 | 太原理工大学 | Transient electromagnetic detection signal noise reduction method based on variational modal decomposition |
| WO2021139331A1 (en) * | 2020-01-08 | 2021-07-15 | 重庆交通大学 | Bearing fault diagnosis method based on instantaneous frequency optimization vmd |
| CN115855419A (en) * | 2022-11-07 | 2023-03-28 | 中国铁道科学研究院集团有限公司 | Turnout vibration time delay analysis method and device |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2021139331A1 (en) * | 2020-01-08 | 2021-07-15 | 重庆交通大学 | Bearing fault diagnosis method based on instantaneous frequency optimization vmd |
| CN111679328A (en) * | 2020-04-08 | 2020-09-18 | 太原理工大学 | Transient electromagnetic detection signal noise reduction method based on variational modal decomposition |
| CN115855419A (en) * | 2022-11-07 | 2023-03-28 | 中国铁道科学研究院集团有限公司 | Turnout vibration time delay analysis method and device |
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