CN115017965A - Snake classification method based on HHT energy and maximum Lyapunov exponent - Google Patents

Snake classification method based on HHT energy and maximum Lyapunov exponent Download PDF

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CN115017965A
CN115017965A CN202210946734.3A CN202210946734A CN115017965A CN 115017965 A CN115017965 A CN 115017965A CN 202210946734 A CN202210946734 A CN 202210946734A CN 115017965 A CN115017965 A CN 115017965A
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CN115017965B (en
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王敏
宁静
王铎颖
刘鑫
李艳萍
陈春俊
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Southwest Jiaotong University
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Abstract

The invention discloses a snake classification method based on HHT energy and a maximum Lyapunov exponent, which comprises the following steps: s1, performing frequency domain and periodicity analysis on the framework transverse acceleration signals obtained by simulation in different running states, and determining a snake classification threshold; s2, HHT energy calculation and maximum Lyapunov index analysis are carried out on the framework lateral acceleration signals collected in real time to obtain corresponding HHT energy values and maximum Lyapunov indexes, snake classification and snake degree determination are carried out on the signals according to snake classification thresholds, and current snake classification is completed. The method combines the HHT energy method with the maximum Lyapunov index to qualitatively identify different running states of the vehicle system and quantitatively analyze the magnitude of the snake movement, so as to realize specific monitoring of the snake movement.

Description

Snake classification method based on HHT energy and maximum Lyapunov exponent
Technical Field
The invention belongs to the technical field of high-speed train operation monitoring, and particularly relates to a snake movement classification method based on HHT energy and a maximum Lyapunov index.
Background
The snaking is one of the core problems of a vehicle dynamic system, and the vehicle running safety can be seriously influenced by slow convergence of small snaking or severe large snaking in the running process of the vehicle. Therefore, the method is very important for online monitoring of small-amplitude snaking and large-amplitude snaking of the vehicle.
The existing online monitoring of the hunting instability of the high-speed train has the following defects:
(1) the peak value of a transverse acceleration signal of a framework is continuously reached to 8m/S for 6 times by the conventional snaking monitoring standard 2 In practice, large vibration occurs even if the lateral acceleration of the frame does not meet the existing monitoring standard. In addition, the existing standard does not consider the influence degree of the hunting instability on the vehicle dynamics, only uses a fixed value to judge whether the hunting occurs, and has certain limitation.
(2) Some vehicles may be interfered by external sudden factors (rail irregularity, crosswind and the like), although obvious harmonic vibration occurs, the operation safety is not greatly influenced at very few moments in operation, and at the moment, the speed reduction measures are too strict for snake-running alarm.
Disclosure of Invention
In view of the above-mentioned deficiencies in the prior art, the present invention provides a snake classification method based on HHT energy and maximum lyapunov exponent, which addresses the problems in the background art described above.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: the snake classification method based on HHT energy and maximum Lyapunov exponent comprises the following steps:
s1, performing time domain, frequency domain and periodicity analysis on the framework transverse acceleration signals obtained by simulation in different running states, and determining a snake classification threshold;
s2, performing HHT energy calculation and maximum Lyapunov index analysis on the framework transverse acceleration signals acquired in real time to obtain corresponding HHT energy values and maximum Lyapunov indexes, and performing snake classification and snake degree determination on the HHT energy values and the maximum Lyapunov indexes according to snake classification thresholds to complete current snake classification;
the snaking classification result comprises normal operation, rapid snaking convergence, small snaking and large snaking, and the rapid snaking convergence is the operation behavior of harmonic vibration which does not affect the operation safety of the vehicle in the preset time.
Further, the step S1 is specifically:
s11, simulating to obtain framework transverse acceleration signals under different running states;
wherein the different running states include normal running, rapid snake convergence, small snake and large snake;
s12, preprocessing the transverse acceleration signal of the framework to obtain an analysis signal;
s13, performing EMD analysis on the analysis signal, and calculating a final marginal spectrum;
s14, calculating the HHT energy value according to the final marginal spectrum;
s15, determining a first crawling classification threshold value by using an SVM classification method based on the calculated HHT energy value;
the first snake movement classification threshold is used for distinguishing normal operation, small snake movement and large snake movement;
s16, analyzing the framework transverse acceleration signal by using the maximum lyapunov index to determine the maximum lyapunov index value;
s17, determining a second snake classification threshold value by using an SVM classification method based on the calculated maximum Lyapunov index value;
wherein the second snake classification threshold is used to distinguish between rapid snake convergence and snake instability, wherein snake instability comprises small snake rows and large snake rows.
Further, in step S1, the method for preprocessing the frame lateral acceleration signal specifically includes:
and performing band-pass filtering on the framework transverse acceleration signal at 0.5Hz-10Hz, and extracting the framework transverse acceleration signal with the time length of 4s as an analysis signal.
Further, the step S13 is specifically:
s13-1, performing EMD decomposition on the analysis signal in each operation state to obtainnImf component signals;
s13-2, carrying out Hilbert transformation on the Imf component signal to obtain a Hilbert spectrum of the Imf component signal, and carrying out time domain integration to obtain a marginal spectrum;
and S13-3, superposing the marginal spectrum with the main frequency above 2Hz in the marginal spectrum to obtain a final marginal spectrum.
Further, in the step S13-1, the signal is analyzedx(t) The formula for performing EMD decomposition is:
Figure 524482DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,c i is a component signal of the Imf frequency domain,r n as residual function, subscriptiIs the ordinal number of the Imf component signal,nimf component signal total;
in the step S13-2, the Imf component signal is processedc i The formula for performing the Hilbert transform is:
Figure 507482DEST_PATH_IMAGE002
in the formula (I), the compound is shown in the specification,G i (t) For the signal after the Hilbert transform,
Figure 355221DEST_PATH_IMAGE003
in order to extend the interval of time,
Figure 372856DEST_PATH_IMAGE004
for a prolonged interval of time of
Figure 663667DEST_PATH_IMAGE005
The Imf component signal at time, t being time,
Figure 116645DEST_PATH_IMAGE008
is the circumferential ratio;
the Imf component signalc i Hilbert spectrum of
Figure 554449DEST_PATH_IMAGE009
Comprises the following steps:
Figure 801890DEST_PATH_IMAGE011
in the formula (I), the compound is shown in the specification,
Figure 75877DEST_PATH_IMAGE012
as a function of the magnitude of the signal,
Figure 316234DEST_PATH_IMAGE013
in order to be a function of the phase,
Figure 624856DEST_PATH_IMAGE014
in order to be the frequency of the radio,RPto take the real part, j is the unit of imaginary number, e (.) Is an exponential function;
the marginal spectrum
Figure 558046DEST_PATH_IMAGE015
Comprises the following steps:
Figure 53749DEST_PATH_IMAGE017
wherein T is the analysis signal time length;
the final marginal spectrum in said step S13-3
Figure 379688DEST_PATH_IMAGE018
Comprises the following steps:
Figure 526505DEST_PATH_IMAGE020
in the formula (I), the compound is shown in the specification,
Figure 381328DEST_PATH_IMAGE021
is a marginal spectrum with dominant frequencies above 2Hz,k=1,2,…,l，kis the marginal spectral number with the dominant frequency above 2Hz,lthe total number of marginal spectra with dominant frequencies above 2 Hz.
Further, in the step S14, the HHT energy value
Figure 895486DEST_PATH_IMAGE023
The calculation formula of (2) is as follows:
Figure 743225DEST_PATH_IMAGE025
in the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE026
in order to be the final marginal spectrum,
Figure 964122DEST_PATH_IMAGE027
to analyze the signal frequency.
Further, the step S16 is specifically:
s16-1, analyzing signals in each operation statex(t) Structure of the deviceuDimensional spaceR u ：
Figure 521006DEST_PATH_IMAGE028
In the formula, T 1 In order to delay the time of the delay,
Figure 506148DEST_PATH_IMAGE029
，k 1 =1,2,…，
Figure 908310DEST_PATH_IMAGE030
is a time interval;
s16-2, inuDimensional spaceR u In (1), two adjacent tracks are takenL 1 AndL 2 starting points are respectivelyx 0 Andy 0 the distance between the two starting points isd 0 =y 0 -x 0 Elapsed time
Figure 780451DEST_PATH_IMAGE031
Then move respectively tox 0 Andy 0 at this time, the distance isd 1 =y 1 -x 1 Is circulated to pass through
Figure 491924DEST_PATH_IMAGE033
Then obtainmAnd j And further obtain the maximum Lyapunov exponent
Figure 715095DEST_PATH_IMAGE034
Comprises the following steps:
Figure 920949DEST_PATH_IMAGE036
in the formula (I), the compound is shown in the specification,j=1,2,…,m，min order to be able to perform the number of iterations,d j =y j -x j 。
further, the step S2 is specifically:
s21, calculating the HHT energy value of the frame transverse acceleration signal acquired in real time, and classifying the HHT energy value according to the first crawling classification threshold;
s22, judging whether the vehicle normally runs at present according to the crawling classification result;
if yes, finishing classification;
if not, go to step S23;
and S23, calculating the maximum Lyapunov index of the framework lateral acceleration signal acquired in real time, classifying the framework lateral acceleration signal according to a second snake classification threshold, and taking the currently calculated HHT energy value as the quantitative evaluation value of the snake degree of the current classification result.
The invention has the beneficial effects that:
the method combines the HHT energy method with the Lyapunov (Lyapunov) index to perform qualitative identification of different running states and quantitative analysis of the snaking degree of the vehicle system so as to realize specific monitoring of the snaking movement, and has the following specific advantages:
(1) considering that the existing snake monitoring standard only researches the time domain amplitude of each characterization quantity to have certain limitation and does not grasp the nature (frequency domain and periodicity) characteristics of snake, the energy method based on HHT provided by the invention judges whether snake exists (including small snake) or not from the aspects of the size of the main frequency of the signal frequency domain, the concentration of the frequency spectrum, the frequency value and the like, quantitatively analyzes the size of the snake degree, and quantitatively evaluates the snake degree of two snake motion states (small snake and large snake);
(2) the invention divides the vehicle running state into four types of normal running, small snaking, large snaking and rapid snaking convergence, and considers that the frame transverse acceleration signal may have the snaking characteristic of short time, large snaking or small snaking when the vehicle runs in the actual process, the adversary converges to the normal running, and the condition has less influence on the running safety of the vehicle system, therefore, the invention further analyzes the signal, considers the signal as the signal which does not influence the vehicle system safety, and is called as rapid snaking convergence and identifies the signal.
Drawings
Fig. 1 is a flow chart of the snake classification method based on HHT energy and maximum lyapunov exponent provided by the present invention.
FIG. 2 is a diagram of the branch type provided by the present invention.
Fig. 3 is a schematic diagram of the measured tread surface of S1002G with different driving mileage according to the present invention.
FIG. 4 is a schematic view of the damping characteristics of the anti-hunting shock absorber provided in accordance with the present invention.
Fig. 5 is a schematic diagram of a bifurcation of a vehicle model limit ring provided by the invention.
FIG. 6 is a schematic diagram of a lateral acceleration signal for a frame according to the present invention.
Fig. 7 is a schematic diagram of Hilbert margin spectrum of simulation data provided by the present invention.
Fig. 8 is a statistical diagram of HHT energy of three types of simulation data provided by the present invention.
Fig. 9 is a statistical diagram of HHT energy of four types of simulation data provided by the present invention.
FIG. 10 is a schematic diagram of the maximum Lyapunov exponent provided by the present invention.
FIG. 11 is a statistical diagram of the maximum Lyapunov exponent of the simulation data provided by the present invention.
FIG. 12 is a measured data frame lateral acceleration signal diagram provided by the present invention.
Fig. 13 is a graph of measured data HHT energy provided by the present invention.
Fig. 14 is a diagram of the Lyapunov index of the measured data provided by the present invention.
FIG. 15 is a HHT-lyapunov index map provided by the present invention.
Fig. 16 is a partial signal amplification analysis diagram provided by the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Example 1:
the embodiment of the invention provides a crawling classification method based on HHT energy and a maximum Lyapunov exponent, as shown in figure 1, comprising the following steps:
s1, performing time domain, frequency domain and periodicity analysis on the framework transverse acceleration signals obtained by simulation under different running states to determine a snake classification threshold;
s2, performing HHT energy calculation and maximum Lyapunov index analysis on the framework transverse acceleration signals acquired in real time to obtain corresponding HHT energy values and maximum Lyapunov indexes, and performing snake classification and snake degree determination on the signals according to snake classification thresholds to finish current snake classification;
the snaking classification result comprises normal operation, rapid snaking convergence, small snaking and large snaking, wherein the rapid snaking convergence is the operation behavior of harmonic vibration which does not affect the operation safety of the vehicle in a short time.
Step S1 of the embodiment of the present invention specifically includes:
s11, simulating to obtain framework transverse acceleration signals in different running states;
wherein the different running states include normal running, rapid snake convergence, small snake and large snake;
s12, preprocessing the transverse acceleration signal of the framework to obtain an analysis signal;
s13, performing EMD analysis on the analysis signal, and calculating a final marginal spectrum;
s14, calculating the HHT energy value according to the final marginal spectrum;
s15, determining a first crawling classification threshold value by using an SVM classification method based on the calculated HHT energy value;
the first snake movement classification threshold is used for distinguishing normal operation, small snake movement and large snake movement;
s16, analyzing the framework transverse acceleration signal by using the maximum lyapunov index to determine the maximum lyapunov index value;
s17, determining a second snake classification threshold value by using an SVM classification method based on the calculated maximum lyapunov index value;
wherein the second snake classification threshold is used to distinguish between rapid snake convergence and snake instability, wherein snake instability comprises small snake rows and large snake rows.
In step S1 of this embodiment, the method for preprocessing the frame lateral acceleration signal specifically includes:
and performing band-pass filtering on the framework transverse acceleration signal at 0.5Hz-10Hz, and extracting the framework transverse acceleration signal with the time length of 4s as an analysis signal.
In step S13 of this embodiment, EMD analysis is performed on a large amount of simulation data to obtain a frequency band of main frequency and energy of the crawling signal, which are substantially above 2Hz, and a marginal spectrum of each Imf classification signal is calculated in consideration of the fact that the frequency band of the crawling signal is substantially above 2Hz, and the marginal spectrums of the main frequency above 2Hz are summed to obtain a final marginal spectrum. Based on this, step S13 of this embodiment is specifically:
s13-1, performing EMD decomposition on the analysis signal in each operation state to obtainnImf component signals;
s13-2, carrying out Hilbert transformation on the Imf component signal to obtain a Hilbert spectrum of the Imf component signal, and carrying out time domain integration to obtain a marginal spectrum;
and S13-3, superposing the marginal spectrum with the main frequency above 2Hz in the marginal spectrum to obtain a final marginal spectrum.
In step S13-1, the present embodiment analyzes the signalx(t) The formula for performing EMD decomposition is:
Figure 896864DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,c i is a component signal of the Imf frequency domain,r n as residual function, subscriptiIs the ordinal number of the Imf component signal,nimf component signal total;
in the step S13-2, the Imf component signal is processedc i The formula for performing the Hilbert transform is:
Figure 795550DEST_PATH_IMAGE037
in the formula (I), the compound is shown in the specification,G i (t) For the signal after the Hilbert transform,
Figure 974858DEST_PATH_IMAGE005
in order to extend the interval of time,
Figure 984403DEST_PATH_IMAGE038
for a prolonged time interval of
Figure 80404DEST_PATH_IMAGE005
The Imf component signal at time, t being time,
Figure 884411DEST_PATH_IMAGE039
is the circumferential ratio;
structure analysis signalz i (t) Comprises the following steps:
Figure DEST_PATH_IMAGE041
obtaining an amplitude functiona i (t) Comprises the following steps:
Figure DEST_PATH_IMAGE043
phase function
Figure DEST_PATH_IMAGE045
Comprises the following steps:
Figure DEST_PATH_IMAGE047
instantaneous frequency
Figure DEST_PATH_IMAGE049
：
Figure DEST_PATH_IMAGE050
The Imf component signalc i Hilbert spectrum of
Figure DEST_PATH_IMAGE052
Comprises the following steps:
Figure DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE054
as a function of the magnitude of the signal,
Figure DEST_PATH_IMAGE055
in order to be a function of the phase,
Figure 190497DEST_PATH_IMAGE014
in order to be the frequency of the radio,RPto take the real part, j is the unit of imaginary number, e (.) Is an exponential function;
the marginal spectrum
Figure DEST_PATH_IMAGE056
Comprises the following steps:
Figure DEST_PATH_IMAGE057
wherein T is the analysis signal time length;
the final marginal spectrum in said step S13-3
Figure DEST_PATH_IMAGE058
Comprises the following steps:
Figure DEST_PATH_IMAGE059
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE060
is a marginal spectrum with dominant frequencies above 2Hz,k=1,2,…,l，kis the marginal spectral number with the dominant frequency above 2Hz,lthe total number of marginal spectra with dominant frequencies above 2 Hz.
The conventional snake monitoring standard only researches the amplitude characteristics of each characteristic quantity and has certain limitation, the embodiment of the invention starts from the essential (frequency domain and periodicity) characteristics of snake, considers the characteristics of the size of a dominant frequency, the concentration of a frequency spectrum, the frequency value and the like, and provides a method for researching snake movement by using an HHT energy methodThe size of the degree was evaluated quantitatively. In step S14 of the present embodiment, HHT energy value
Figure 250070DEST_PATH_IMAGE023
The calculation formula of (2) is as follows:
Figure DEST_PATH_IMAGE061
in the formula (I), the compound is shown in the specification,
Figure 872681DEST_PATH_IMAGE026
in order to be the final marginal spectrum,
Figure 582011DEST_PATH_IMAGE027
to analyze the signal frequency.
In step S16 of this embodiment, it is considered that some vehicles may be interfered by external burst factors, although significant harmonic vibration occurs, there is only a very small time during operation, and there is no great influence on the operation safety, and at this time, the hunting alarm is too strict to take speed reduction measures. The method for determining the maximum lyapunov exponent in step S16 of this embodiment specifically includes:
s16-1, analyzing signals in each operation statex(t) Structure of the deviceuDimensional spaceR u ：
Figure 1491DEST_PATH_IMAGE028
In the formula, T 1 In order to delay the time of the delay,
Figure 336526DEST_PATH_IMAGE029
，k 1 =1,2,…，
Figure 157852DEST_PATH_IMAGE030
is a time interval;
s16-2, inuDimensional spaceR u In (1), two adjacent tracks are takenL 1 AndL 2 starting points are respectivelyx 0 Andy 0 the distance between the two starting points isd 0 =y 0 -x 0 Elapsed time
Figure 569242DEST_PATH_IMAGE031
Then move respectively tox 0 Andy 0 at this time, the distance isd 1 =y 1 -x 1 Is circulated to pass through
Figure 476018DEST_PATH_IMAGE033
Then obtainmAnd j And further obtain the maximum Lyapunov exponent
Figure 614744DEST_PATH_IMAGE034
Comprises the following steps:
Figure DEST_PATH_IMAGE062
in the formula (I), the compound is shown in the specification,j=1,2,…,m，min order to be able to perform the number of iterations,d j =y j -x j 。
step S2 of the embodiment of the present invention specifically includes:
s21, calculating the HHT energy value of the frame transverse acceleration signal acquired in real time, and classifying the HHT energy value according to the first crawling classification threshold;
s22, judging whether the vehicle normally runs at present according to the crawling classification result;
if yes, finishing classification;
if not, go to step S23;
and S23, calculating the maximum Lyapunov index of the framework lateral acceleration signal acquired in real time, classifying the framework lateral acceleration signal according to a second snake classification threshold, and taking the currently calculated HHT energy value as the quantitative evaluation value of the snake degree of the current classification result.
In the embodiment of the invention, the HHT energy value is combined with the maximum Lyapunov (Lyapunov) index, so that the qualitative identification of normal operation, small-amplitude snaking, large-amplitude snaking and rapid snaking convergence and the quantitative analysis of the small-amplitude snaking and large-amplitude snaking degree of the vehicle system are carried out, and the classification of the snaking motion is refined.
Example 2:
the embodiment of the invention provides a specific example for analyzing a simulation data set formed by framework lateral acceleration signals obtained by simulation by using the method of the invention:
the first step is as follows: building high-speed train dynamics model
The SIMPACK software is used for establishing a complete vehicle dynamics model of a high-speed train of a certain type in China, and the basic parameters of the train are shown in Table 1. The vehicle comprises 1 vehicle body, 2 frameworks, 4 wheel pairs, 8 axle boxes, a primary suspension system (a primary steel spring, a primary vertical shock absorber and a rotating arm type axle box positioning device) and a secondary suspension system (an air spring, a secondary vertical shock absorber, a secondary transverse shock absorber, an anti-snaking shock absorber, an anti-rolling torsion bar, a traction pull rod and a transverse backstop). The car body, the frame and the wheel pair have 6 degrees of freedom (longitudinal, transverse, vertical, side rolling, nodding and shaking), and the axle box has only 1 nodding degree of freedom. Thus, the vehicle dynamics model has 50 degrees of freedom.
Table 1: high-speed train dynamics partial parameter table
Figure DEST_PATH_IMAGE063
The second step is that: establishing simulation working condition types
Railway vehicle nonlinear systems typically exhibit a typical limit cycle bifurcation as shown in figure 2. In the figure, the abscissa is the speed of the vehicle, the ordinate is the amplitude of the limit ring of any rigid body (wheel set, frame or vehicle body) vibration, and the limit ring branching form of the vehicle system is generally analyzed by using the wheel set transverse displacement as the ordinate. Where the solid line represents the stable limit cycle amplitude and the dashed line represents the unstable limit cycle amplitude.
Regarding the selection of the wheel set tread, because the tread shape has a great influence on the bifurcation result of the limit ring of the high-speed train system, in order to enable the bifurcation type of the high-speed train system to be supercritical bifurcation or subcritical bifurcation, simulate the small snaking state of the high-speed train and make the running state of the high-speed train more practical, the practical measured tread of S1002G with 3 different driving miles in one rotary repair cycle (2.5 × 105 km) is respectively selected in the embodiment. As shown in fig. 3, the tread surface 1 to the tread surface 3 have sequentially increased mileage and the tread surface has sequentially increased wear. Wherein, the tread 1 is an actually measured abrasion tread obtained by measuring the outline of the wheel set when the train runs for about 5 multiplied by 104 km; the tread 2 is an actually measured abrasion tread obtained by measuring the outline of the wheel set when the train runs for about 10 multiplied by 104 km; the tread 3 is an actual measurement abrasion tread obtained by measuring the outline of the wheel set when the train runs for about 15 multiplied by 104 km.
Regarding the parameter setting of the anti-snaking damper, the anti-snaking damper can effectively restrain the snaking motion of the high-speed train, and has great influence on the critical speed and the bifurcation type of the high-speed train system. In the actual operation process, along with the increase of the operation mileage, the damping characteristics of the anti-snaking shock absorber of the vehicle system can change, and in order to fully simulate different operation states of the high-speed train at the actual operation speed, 3 anti-snaking shock absorbers with different damping characteristics are used to limit the critical speed change of the vehicle system to the actual operation speed interval. This embodiment uses 3 types of anti-hunting shock absorbers with different damping characteristics. The damping characteristic curves of the 3 types of anti-hunting shock absorbers having different damping characteristics are shown in fig. 4, and the unloading force and the unloading speed corresponding to the anti-hunting shock absorber 1 to the anti-hunting shock absorber 3 are sequentially increased.
S1002G actual measurement tread with different driving mileage and anti-snaking vibration dampers with different damping characteristics are used for calculation, and 3 working conditions of a high-speed train (speed: 300-400 km/h) are simulated:
(1) working condition 1: simulating normal operation by using the tread 1 and the anti-snaking shock absorber 1;
(2) working condition 2: simulating small-amplitude snaking by using the tread 2 and the anti-snaking shock absorber 2;
(3) working condition 3: simulating by using the tread 3 and the anti-snaking vibration absorber 3, and simulating large-amplitude snaking by using the measured track irregularity and simulating rapid snaking convergence by using the simulated track irregularity;
and calculating to obtain a limit ring bifurcation diagram under each working condition according to the working conditions, wherein as shown in fig. 5, the dynamic model of the high-speed train under the working condition 1 follows supercritical distribution, and the vehicle is in a normal running state when the vehicle model runs in an interval of 300-400 km/h under the working condition. The dynamic model of the high-speed train is subjected to supercritical distribution under the working condition 2, the wheel pair of the vehicle is in a small-amplitude vibration state when the vehicle model runs in a range of 300-400 km/h under the working condition, the vehicle is in a small-amplitude periodic snaking state at the moment, and the transverse vibration amplitude is gradually increased along with the increase of the speed. Under the working condition 3, the dynamic model of the high-speed train obeys subcritical bifurcation, and under the working condition, when the vehicle model runs in an interval of 300-400 km/h, a vehicle system limit ring is in an unstable area, and disturbance fields influenced by external factors are located at different positions, and the vehicle is in different running states. And adding the actually measured rail irregularity to the working condition 1 and the working condition 2 to simulate the normal running and the small snaking state. The actual measurement rail irregularity is added to the working condition 3 type to simulate a large-amplitude snaking state, and the simulation rail irregularity is added to the working condition 3 type to simulate a rapid snaking convergence state as interference of external factors.
In the embodiment, different operating states of the vehicle system are defined according to the Hopf bifurcation theory of the vehicle system, and are defined as follows:
(1) and (4) normal operation: if the amplitude value (wheel pair transverse displacement) of the limit ring corresponding to the running speed of the vehicle is 0, the snaking motion generated by any disturbance of a vehicle system can be converged, and the running state of the vehicle is the normal running state at the moment;
(2) small snaking: if the running speed of the vehicle exceeds the critical speed, the amplitude (wheel pair transverse displacement) of a limit ring corresponding to the speed is larger than 0 but smaller than the wheel track gap, and the snaking motion of a vehicle system caused by any disturbance can form a stable limit ring, and the running state of the vehicle is a small snaking state at the moment;
(3) rapid snake convergence: when a vehicle system obeys subcritical bifurcation, when the running speed of a vehicle exceeds a nonlinear critical speed, the vehicle is influenced by a sudden change of excitation at a certain position, the vehicle quickly recovers to a normal running state after short snaking, and the running state of the vehicle is a quick snaking convergence state at the moment;
(4) greatly snaking: when a vehicle system obeys subcritical bifurcation, when the running speed of a vehicle exceeds a nonlinear critical speed and the excitation is large, the vehicle directly generates hunting instability, and the running state of the vehicle is a large-amplitude hunting state.
By establishing the working conditions, the simulation conditions of the four running states are determined. In order to construct a large number of simulation data sets, the running speed of the vehicle is divided into 6 speed levels (300 km/h, 320km/h, 340km/h, 360km/h, 380km/h and 400km/h), three amplitude value proportionality coefficients of 0.5, 1.0 and 2.0 are respectively set for the track irregularity, and the track irregularity data sets are expanded. Each running state corresponds to 6 speed levels, the track with 3 amplitude ratios is not smooth, 18 sets of simulation conditions are provided, and the four running states correspond to 72 sets of simulation conditions. And randomly taking 20 samples from the framework transverse acceleration signals obtained by each group of simulation, wherein the sampling time length of each sample segment is 4s, the sampling frequency is 250Hz, and the total number of simulation data sets of 1440 sample segments is obtained.
The third step: HHT energy analysis
The snake state is classified by the method, and the signal is subjected to EMD analysis, as shown in Table 2, the distribution of main frequency and energy frequency bands in normal operation is relatively uniform, the energy of Imf signal components with the main frequency of more than 2Hz accounts for 62%, and the energy of IMF signal components with the frequency of less than 2Hz accounts for 38%. As shown in tables 3 and 4, the energy occupancy ratio of Imf components with high main frequency of the snake signals (small amplitude snake and large amplitude snake) is high, the main frequency and the energy band of the snake signals are basically above 2Hz, and the energy occupancy ratio of the signal components is above 90%. As shown in table 5, since the fast crawling convergence signal includes crawling features, the percentage of Imf component main frequency over 2Hz is also as high as 80%, Imf component signals with main frequency over 2Hz are superimposed, Hilbert transform is performed on the reconstructed signal to obtain a Hilbert marginal spectrum, as shown in fig. 7, and then the Hilbert marginal spectrum is integrated in a frequency domain to obtain a final HHT energy value.
The HHT energy values of normal operation, small snaking, and large snaking class 3 data of the simulation dataset (1440 sample points) were analyzed and classification thresholds of 0.82 and 2.34, respectively, were calculated using the SVM method, as shown in fig. 8 (class 3). Signal HHT energy values less than 0.82 are considered normal operation, signal HHT energy values greater than 0.82 and less than 2.34 are considered small snaking, and signal HHT energy values greater than 2.34 are considered large snaking. The magnitude of the HHT energy value reflects the magnitude of the snaking degree, namely, the larger the HHT energy value is, the more violent the snaking degree is, and the smaller the HHT energy value is, the smaller the snaking degree is.
As shown in fig. 9, the fast meandering convergence data is added to the 3 kinds of data to find that the fast meandering convergence HHT energy value overlaps with the small meandering and large meandering HHT energy value, and the classification threshold value cannot be distinguished, so that it is necessary to distinguish them by supplementing a new index.
TABLE 2 Normal operation (66.1% energy over 2 Hz)
Figure DEST_PATH_IMAGE064
TABLE 3 Small snake rows (95.87% energy over 2 Hz)
Figure DEST_PATH_IMAGE065
TABLE 4 Large Snake rows (99.5% energy over 2 Hz)
Figure DEST_PATH_IMAGE066
TABLE 5 fast Snake convergence (82.9% energy over 2 Hz)
Figure DEST_PATH_IMAGE067
The fourth step: maximum Lyapunov (Lyapunov) analysis
FIG. 6 is a set of framework lateral acceleration signals in a simulation data set, and an exemplary analysis is performed on the set of different operating condition signals, as shown in FIG. 10, the maximum Lyapunov index values of large snake rows and small snake rows both converge below 10, the signal periodicity is strong, the maximum Lyapunov index values of normal operation and fast snake convergence both converge above 10, and the signal periodicity is weak. Therefore, the rapid snake convergence and normal operation can be classified into a type with weak periodicity through the maximum Lyapunov index value, and the small snake and the large snake can be classified into a type with strong periodicity.
Maximum lyapunov indexes of normal operation, small-amplitude snaking, large-amplitude snaking and rapid snaking convergence data of a simulation data set (1440 sample points) are analyzed, a classification threshold value of 10.26 is calculated by using an SVM method, when the maximum lyapunov index value is lower than 10.26 as shown in FIG. 11, the maximum lyapunov index value is considered to belong to the class of normal operation and rapid snaking convergence, and when the maximum lyapunov index value is higher than 10.26, the maximum lyapunov index value is considered to belong to the class of small-amplitude snaking and large-amplitude snaking.
The maximum Lyapunov exponent method and the HHT energy method are combined, and normal operation, small-amplitude snake movement, large-amplitude snake movement and rapid snake movement convergence are distinguished. Signal HHT energy value is considered to be normal operation when it is less than 0.82, small snaking when it is greater than 0.82 and less than 2.34 and the maximum lyapunov exponent value is less than 10.26, large snaking when it is greater than 2.34 and the maximum lyapunov exponent value is less than 10.26, and fast snaking convergence when it is greater than 0.82 and the maximum lyapunov exponent value is greater than 10.26. The method considers the periodic characteristic of snaking and the frequency domain characteristics of the snaking signal including the size of frequency dominant frequency, the concentration of frequency spectrum, the frequency value and the like, thereby being capable of qualitatively identifying different running states of a vehicle system and quantitatively representing the energy value of the snaking signal so as to reflect the size of the snaking degree.
The fifth step: verification of measured data
In order to verify the correctness of the method, the present embodiment uses the measured data to verify the correctness. As shown in FIG. 12, the measured lateral acceleration data of a part of measured frameworks obtained from a high-speed train at a speed of 300km/h-400km/h has a duration of 1220 seconds, a single sample data length of 4s and a total number of samples of 305.
The measured data were analyzed by the HHT-maximum Lyapunov exponent method, and the HHT energy value and the maximum Lyapunov exponent value of the data were obtained as shown in FIGS. 13 and 14, respectively. The distribution range of the HHT energy value is 0-6, and the distribution range of the maximum Lyapunov exponent value is 0-25.
As shown in fig. 15, a HHT energy value of less than 0.82 for a sample point is considered to be normal operation, a HHT energy value of greater than 0.82 and less than 2.34 for a sample point and a maximum Lyapunov exponent value of less than 10.26 is considered to be small amplitude hunting, and a HHT energy value of greater than 2.34 and a maximum Lyapunov exponent value of less than 10.26 is considered to be large amplitude hunting. HHT energy values greater than 0.82 and maximum Lyapunov exponent values greater than 10.26 are considered rapid snake convergence. The combination of the maximum Lyapunov exponent value threshold value of 10.26 and the HHT energy value threshold values of 0.82 and 2.34 is proved to be capable of distinguishing 4 running states of normal running, small snaking and rapid snaking convergence, and large snaking, and the magnitude of the snaking degree is reflected by the HHT energy value.
FIG. 16 is an enlarged view of a portion of signals, with a time interval of 696s to 716 s.
It can be observed from the recognition result of fig. 16 that the signal in the period of 704 seconds to 708 seconds is recognized as normal operation by the conventional method, and by observing that a significant periodicity occurs, the method provided in this embodiment recognizes the signal as a small snaking state, and the small snaking recognition can play a role of warning. The acceleration peak value of the signal in the period from 708 seconds to 712 seconds does not reach the snake alarm standard used at present (the acceleration peak value reaches 8m/s for 6 continuous periods) 2 Conventional methods would recognize this as normal operation. However, it can be seen by observation that the peak value of this signal is at 6m/s 2 ~8m/s 2 Inter) approaches the presently used snake alarm criteria and a significant periodicity occurs, which the method proposed in this example recognizes as a large snake condition,therefore, the recognition result is considered to be reasonable in this embodiment. The conventional method recognizes the signal as normal operation in the period from 712 seconds to 716 seconds, and the method of the present embodiment recognizes the signal as rapid hunting convergence, which indicates that the hunting tends to stabilize and returns to the normal operation state. The traditional method regards the three sections of signals as normal running states, but the method provided by the embodiment identifies the three states as small snaking, large snaking and rapid snaking convergence, accurately identifies different states of vehicle snaking, can take measures in time to prevent serious snaking of the train, and helps the safe running of the train. The method provided by the embodiment is verified to be feasible through actual data, and online monitoring can be realized in the vehicle running process.
Existing high speed train hunting criteria are directed to large amplitude hunting and are analyzed only from the perspective of the signal time domain. Therefore, the HHT energy value and the maximum Lyapunov index value are integrated, the time domain, the frequency domain and the periodicity characteristics of the signal are considered, and the time domain, the frequency domain and the periodicity characteristics are used as reference indexes for distinguishing different snaking states of the high-speed train. The method is not focused on determining an accurate threshold for distinguishing different snake running states. Due to the limitation of simulation data, the threshold standard established by the simulation data of the method has certain error. The accuracy of the threshold can be supplemented by means of bench tests or line actual measurements and the like, and the accuracy of the threshold in actual monitoring is improved by combining machine learning algorithms such as transfer learning and the like to be further improved.

Claims (8)

1. The snake classification method based on HHT energy and maximum Lyapunov exponent is characterized by comprising the following steps:
s1, performing time domain, frequency domain and periodicity analysis on the framework transverse acceleration signals obtained by simulation under different running states to determine a snake classification threshold;
s2, performing HHT energy calculation and maximum Lyapunov index analysis on the framework transverse acceleration signals acquired in real time to obtain corresponding HHT energy values and maximum Lyapunov indexes, and performing snake classification and snake degree determination on the signals according to snake classification thresholds to finish current snake classification;
the snaking classification result comprises normal operation, rapid snaking convergence, small snaking and large snaking, and the rapid snaking convergence is the operation behavior of harmonic vibration which does not affect the operation safety of the vehicle in the preset time.
2. The snake classification method based on HHT energy and maximum Lyapunov exponent according to claim 1, wherein the step S1 is specifically:
s11, simulating to obtain framework transverse acceleration signals under different running states;
wherein the different running states include normal running, rapid snake convergence, small snake and large snake;
s12, preprocessing the transverse acceleration signal of the framework to obtain an analysis signal;
s13, performing EMD analysis on the analysis signal, and calculating a final marginal spectrum;
s14, calculating the HHT energy value according to the final marginal spectrum;
s15, determining a first crawling classification threshold value by using an SVM classification method based on the calculated HHT energy value;
the first snake movement classification threshold is used for distinguishing normal operation, small snake movement and large snake movement;
s16, analyzing the framework transverse acceleration signal by using the maximum lyapunov index to determine the maximum lyapunov index value;
s17, determining a second snake classification threshold value by using an SVM classification method based on the calculated maximum Lyapunov index value;
wherein the second snake classification threshold is used to distinguish between rapid snake convergence and snake instability, wherein snake instability comprises small snake rows and large snake rows.
3. The snake classification method based on HHT energy and maximum Lyapunov exponent according to claim 2, wherein the preprocessing method for the frame lateral acceleration signal in step S1 is specifically as follows:
and performing band-pass filtering on the framework transverse acceleration signal at 0.5Hz-10Hz, and extracting the framework transverse acceleration signal with the time length of 4s as an analysis signal.
4. The snake classification method based on HHT energy and maximum Lyapunov exponent according to claim 2, wherein the step S13 is specifically:
s13-1, performing EMD decomposition on the analysis signal in each operation state to obtainnImf component signals;
s13-2, carrying out Hilbert transformation on the Imf component signal to obtain a Hilbert spectrum of the Imf component signal, and carrying out time domain integration to obtain a marginal spectrum;
and S13-3, superposing the marginal spectrum with the main frequency above 2Hz in the marginal spectrum to obtain a final marginal spectrum.
5. The snake classification method based on HHT energy and maximum Lyapunov exponent according to claim 2, wherein in step S13-1, the analysis signal is analyzedx(t) The formula for performing EMD decomposition is:
Figure 425442DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,c i is a component signal of the Imf frequency domain,r n as residual function, subscriptiIs the ordinal number of the Imf component signal,nimf component signal total;
in the step S13-2, the Imf component signal is processedc i The formula for performing the Hilbert transform is:
Figure 938344DEST_PATH_IMAGE002
in the formula (I), the compound is shown in the specification,G i (t) For the signal after the Hilbert transform,
Figure 989346DEST_PATH_IMAGE003
in order to extend the interval of time,
Figure 334876DEST_PATH_IMAGE004
for a prolonged time interval of
Figure 360601DEST_PATH_IMAGE003
The Imf component signal at time, t being time,
Figure 283427DEST_PATH_IMAGE005
is the circumferential ratio;
the Imf component signalc i Hilbert spectrum of
Figure 747906DEST_PATH_IMAGE006
Comprises the following steps:
Figure 823310DEST_PATH_IMAGE007
in the formula (I), the compound is shown in the specification,
Figure 347832DEST_PATH_IMAGE008
as a function of the magnitude of the signal,
Figure 554691DEST_PATH_IMAGE009
in order to be a function of the phase,
Figure 698228DEST_PATH_IMAGE010
in order to be the frequency of the radio,RPin order to obtain the solid part,jis an imaginary unit, e (.) Is an exponential function;
the marginal spectrum
Figure 487192DEST_PATH_IMAGE011
Comprises the following steps:
Figure 572829DEST_PATH_IMAGE012
wherein T is the analysis signal time length;
the final marginal spectrum in said step S13-3
Figure 345613DEST_PATH_IMAGE013
Comprises the following steps:
Figure 27261DEST_PATH_IMAGE014
in the formula (I), the compound is shown in the specification,
Figure 201890DEST_PATH_IMAGE015
is a marginal spectrum with dominant frequencies above 2Hz,k=1,2,…,l，kis the marginal spectral number with the dominant frequency above 2Hz,lthe total number of marginal spectra with dominant frequencies above 2 Hz.
6. The snake classification method based on HHT energy and maximum Lyapunov exponent according to claim 2, wherein the HHT energy value is determined in step S14
Figure 989586DEST_PATH_IMAGE017
The calculation formula of (2) is as follows:
Figure 125033DEST_PATH_IMAGE018
in the formula (I), the compound is shown in the specification,
Figure 469426DEST_PATH_IMAGE019
in order to be the final marginal spectrum,
Figure 623196DEST_PATH_IMAGE020
to analyze the signal frequency.
7. The snake classification method based on HHT energy and maximum Lyapunov exponent according to claim 3, wherein the step S16 is specifically:
s16-1, analyzing signals in each operation statex(t) Structure of the deviceuDimensional spaceR u ：
Figure 598105DEST_PATH_IMAGE021
In the formula, T 1 In order to delay the time of the delay,
Figure 814323DEST_PATH_IMAGE022
，k 1 =1,2,…n-1，
Figure 149358DEST_PATH_IMAGE023
is a time interval;
s16-2, inuDimensional spaceR u In (1), two adjacent tracks are takenL 1 AndL 2 starting points are respectivelyx 0 Andy 0 the distance between the two starting points isd 0 =y 0 -x 0 Elapsed time
Figure 908367DEST_PATH_IMAGE024
Then move respectively tox 0 Andy 0 at this time, the distance isd 1 =y 1 -x 1 Is circulated to pass through
Figure 116494DEST_PATH_IMAGE025
Then obtainmAnd j And further obtain the maximum Lyapunov exponent
Figure DEST_PATH_IMAGE026
Comprises the following steps:
Figure 413483DEST_PATH_IMAGE027
in the formula (I), the compound is shown in the specification,j=1,2,…,m，min order to be able to perform the number of iterations,d j =y j -x j , d j as adjacent tracksL 2 TojPoint to adjacent trackL 1 To go tojThe distance between the points.
8. The snake classification method based on HHT energy and maximum Lyapunov exponent according to claim 2, wherein the step S2 is specifically:
s21, calculating the HHT energy value of the frame transverse acceleration signal acquired in real time, and classifying the HHT energy value according to the first crawling classification threshold;
s22, judging whether the vehicle normally runs at present according to the crawling classification result;
if yes, finishing classification;
if not, go to step S23;
s23, calculating the maximum Lyapunov index of the frame transverse acceleration signal acquired in real time, classifying the frame transverse acceleration signal according to a second snake classification threshold, and taking the currently calculated HHT energy value as the quantitative evaluation value of the snake degree of the current classification result.
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