CN110530509B - High-speed motor train unit axle box vibration dominant frequency prediction method based on maximum entropy spectrum analysis - Google Patents

High-speed motor train unit axle box vibration dominant frequency prediction method based on maximum entropy spectrum analysis Download PDF

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CN110530509B
CN110530509B CN201910834777.0A CN201910834777A CN110530509B CN 110530509 B CN110530509 B CN 110530509B CN 201910834777 A CN201910834777 A CN 201910834777A CN 110530509 B CN110530509 B CN 110530509B
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干锋
戴焕云
曾京
邬平波
黄彩虹
魏来
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Southwest Jiaotong University
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Abstract

The invention discloses a high-speed motor train unit axle box vibration main frequency prediction method based on maximum entropy spectrum analysis. According to the change rule of the vibration main frequency along with the vehicle running speed, compared with the traditional short-time FFT method, the velocity frequency graph obtained by the maximum entropy spectrum method can more clearly and accurately display the linear relation of the vibration main frequency along with the vehicle running speed, and can accurately predict the development trend of the vibration main frequency along with the speed. According to the linear relation between the vibration dominant frequency and the vehicle speed, the out-of-round order of the vehicle and the rail corrugation wavelength can be accurately judged, and whether the vibration dominant frequency is close to the vibration mode of the vehicle component to cause resonance or not is predicted by combining the modal information of the vehicle component.

Description

High-speed motor train unit axle box vibration dominant frequency prediction method based on maximum entropy spectrum analysis
Technical Field
The invention belongs to the technical field of high-speed motor train unit axle box vibration spectrum analysis, and particularly relates to a high-speed motor train unit axle box vibration dominant frequency prediction method based on maximum entropy spectrum analysis.
Background
Entropy is a quantity in information theory that reflects a measure of information. The larger the randomness of a random event, that is, the higher the uncertainty, the larger the entropy value, and the larger the amount of information carried, the maximum entropy spectrum estimation is a modern power spectrum calculation method proposed by Burg in 1967, which obtains its power spectral density estimation by extrapolating the autocorrelation function of an unknown delay point according to the maximum entropy criterion, that is, obtaining a signal spectrum estimation by extrapolating the unknown autocorrelation function from the known autocorrelation function according to the criterion of the maximum entropy, that is, it can ensure that the known information amount is unchanged, and obtain the maximum estimated information amount. The method is a nonlinear spectrum estimation method capable of obtaining high resolution, is particularly suitable for spectrum estimation of short data sequences, and obtains obvious effect.
For stationary random signals, the power spectral density of which is the fourier transform of the autocorrelation function, the autocorrelation function is infinite because the stationary random sequence is infinitely long, while in practice the data collected is always finite and the power spectrum of the signal can only be estimated from the finite data collected. In the traditional power spectrum estimation, data except the acquired limited data is assumed to be 0, which is equivalent to adding a window function to the data, an autocorrelation function is estimated through the acquired data, and then a power spectrum is obtained through FFT (fast Fourier transform), so that errors are inevitably generated, and the problems of low resolution, side frequency, spectral line leakage and the like exist. The basic idea of maximum entropy spectrum estimation is to make no deterministic assumption for data other than measured limited data, and to extrapolate the data other than the known limited data autocorrelation sequence under the premise that the entropy is maximum, and estimate the power spectral density of the signal to be detected.
In the process of high-speed running of a motor train unit train, due to the influences of line conditions, rail disturbance, wheel non-circularity, rail corrugation, bogie and train body vibration, the axle box vibrates violently, the vibration acceleration amplitude is large, the frequency is high, and the frequency components are complex. Particularly, the side frequency and the frequency multiplication which are related to the wheel out-of-round order and the rail corrugation wavelength and are in equal proportion to the vehicle speed easily occur under the impact of periodic wheel out-of-round and rail corrugation.
When the FFT method is adopted for carrying out axle box vibration acceleration frequency spectrum analysis, the side frequency and the frequency multiplication which are in equal proportion to the vehicle speed easily cause misunderstanding, which is caused by the frequency aliasing generated by the high-order non-circular order of the wheels and the rail corrugation wavelength and the low-order non-circular (such as first-order eccentricity or second-order non-circular) of the wheels, and the frequency corresponding to the side frequency and the frequency multiplication in the actual vibration signal may not exist. In order to eliminate the side frequency and frequency multiplication influence of the frequency spectrum, a more accurate and precise frequency analysis method needs to be selected.
Disclosure of Invention
Aiming at the defects in the prior art, the method for predicting the main frequency of the axle box vibration of the high-speed motor train unit based on the maximum entropy spectrum analysis solves the problem that the main frequency of the vibration cannot be predicted accurately because the influence of frequency spectrum side frequency and frequency doubling is not eliminated when the traditional FFT method is used for predicting the main frequency of the vibration.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: the method for predicting the main frequency of the axle box vibration of the high-speed motor train unit based on the maximum entropy spectrum analysis comprises the following steps:
s1, acquiring vibration acceleration data of the axle box of the high-speed motor train unit, and dividing the vibration acceleration data into acceleration data of a plurality of time slices;
s2, sequentially calculating the maximum entropy power spectrum of the acceleration data in each time slice, and performing secondary open operation on the maximum entropy power spectrum to obtain a corresponding maximum entropy amplitude spectrum;
s3, drawing a three-dimensional frequency spectrum distribution graph according to the maximum entropy amplitude spectrum of each time slice;
and S4, predicting the vibration dominant frequency according to the drawn three-dimensional frequency spectrum distribution diagram.
Further, the step S1 is specifically:
s11, calculating the total number N of the acquired acceleration data corresponding to the time slices;
s12, determining the starting time of each time slice according to the total number of the time slices;
and S13, dividing the acceleration data into acceleration data in a plurality of time slices according to the determined time slice starting time and the determined time length.
Further, in step S11, the total number N of time slices is:
Figure BDA0002191809890000031
in the formula, T is the total duration of the obtained acceleration data;
t0a set single time slice duration;
tsthe overlapping duration of adjacent time slices;
in the step S12, the start time t of each time slicenComprises the following steps:
tn＝(n-1)*(t0-ts)
in the formula, subscript N is the number of each time slice, and N is more than or equal to 1 and less than or equal to N.
Further, in step S2, the method for calculating the maximum entropy power spectrum of the acceleration data in each time slice specifically includes:
a1, setting the maximum entropy power spectrum order as M, the allowed minimum power spectrum error as e and the order increasing gradient as M;
a2, setting the initial order to be 0, and calculating the initial value P of the prediction error power of the acceleration in the current nth time slice0Initial value f of forward prediction error0And an initial value g of backward prediction error0；
A3, increasing the current order by M, and judging whether the order increased by M is smaller than M;
if yes, go to step A7;
if not, go to step A4;
a4, calculating the reflection coefficient K of the acceleration data in the time slice of the current order according to the forward prediction error and the subsequent prediction error when the order m is increased last timemGo to step A5;
a5 according to reflection coefficient KmSeparately calculating the predicted error power P at the current ordermForward prediction error fmAnd backward prediction error gmGo to step A6;
a6, judging whether the difference value between the prediction error power of the current order and the prediction error power of the previous order is less than e;
if yes, go to step A7;
if not, returning to the step A3;
and A7, determining the maximum entropy power spectrum according to the reflection coefficient of the current order.
Further, in the step A2,
the initial value P of the prediction error power0Comprises the following steps:
Figure BDA0002191809890000041
in the formula, K is an acceleration data function in the nth time slice;
x (i) is an acceleration data function in the nth time slice;
the initial value f of the forward prediction error0Comprises the following steps:
f0(i)＝x(i)
in the formula (f)0(n) is the initial value of the forward prediction error of the ith acceleration data in the nth time slice, and i ∈ [1, K]；
The backward prediction error initial value g0Comprises the following steps:
g0(i)＝x(i)
in the formula, g0(n) is the initial value of backward prediction error of the ith acceleration data in the nth time slice, and i ∈ [1, K]。
Further, the m-th order reflection coefficient K in the step a4mComprises the following steps:
Figure BDA0002191809890000042
in the formula (f)m-1(i) Forward prediction error for the (i-1) th acceleration data point of the (m-1) th order;
gm-1(i-1) is the backward prediction error of the (i-1) th acceleration data point of the (m-1) th order.
Further, in the step A5,
prediction error power P at the current ordermComprises the following steps:
Figure BDA0002191809890000051
in the formula, Pm-1Increasing the corresponding prediction error power of the order m for the previous time;
the predicted error power f of the ith acceleration data point at the current orderm(i) Comprises the following steps:
fm(i)＝fm-1(i)+Kmgm-1(i-1)
in the formula (f)m-1(i) Forward prediction error is the ith acceleration data point of the (m-1) th order;
gm-1(i-1) backward prediction error of the (i-1) th acceleration data point of the (m-1) th order;
the backward prediction error g of the ith acceleration data point in the current orderm(i) Comprises the following steps:
gm(i)＝gm-1(i-1)+Kmfm-1(i)。
further, the maximum entropy power spectrum W in the step A7mComprises the following steps:
Wm＝FFT(am)
wherein, FFT (-) is Fourier transform function;
amfilter coefficients comprising forward filter coefficients and backward filter coefficients;
wherein, the jth forward filter coefficient a at the mth orderm(j) Comprises the following steps:
am(j)＝am-1(j)+Kmam-1(l-j-1)
in the formula, am-1(l-j-1) is the l-j-1 forward filter coefficient at the m-1 order;
coefficient a of the ith backward filter at mth orderm(l) Comprises the following steps:
am(l)＝Km。
further, when the three-dimensional spectrogram is drawn in the step S3, the maximum entropy amplitude spectrum is taken as a vertical coordinate, and the frequency is taken as a horizontal coordinate to draw the three-dimensional spectrogram;
the three-dimensional frequency spectrum distribution map comprises a three-dimensional time-frequency map and a three-dimensional speed-frequency map.
The invention has the beneficial effects that:
according to the method for predicting the main frequency of the high-speed motor train unit axle box vibration based on the maximum entropy spectrum analysis, the main frequency of vibration is more clearly changed in a three-dimensional time-frequency graph and a speed-frequency graph by a short-time maximum entropy spectrum method, and the trend of the displayed main frequency of vibration along with time is clearer due to the fact that the side frequency and the frequency multiplication of relevant factors such as the speed, the out-of-round order, the corrugation wavelength and the like are obviously reduced or eliminated. According to the change rule of the vibration main frequency along with the vehicle running speed, compared with the traditional short-time FFT method, the velocity frequency graph obtained by the maximum entropy spectrum method can more clearly and accurately display the linear relation of the vibration main frequency along with the vehicle running speed, and can accurately predict the development trend of the vibration main frequency along with the speed. According to the linear relation between the vibration dominant frequency and the vehicle speed, the out-of-round order of the vehicle and the rail corrugation wavelength can be accurately judged, and whether the vibration dominant frequency is close to the vibration mode of the vehicle component to cause resonance or not is predicted by combining the modal information of the vehicle component.
Drawings
FIG. 1 is a flow chart of a high-speed motor train unit axle box vibration dominant frequency prediction method based on maximum entropy spectrum analysis.
Fig. 2 is a flowchart of a maximum power spectrum calculation method provided by the present invention.
Fig. 3 is a diagram illustrating a maximum entropy spectrum comparison between a conventional FFT method and the method of the present invention according to an embodiment of the present invention.
FIG. 4 is a conventional short-term FFT time-frequency diagram in an embodiment of the present invention.
FIG. 5 is a short-term maximum entropy time-frequency diagram in an embodiment provided by the present invention.
Fig. 6 is a velocity-frequency diagram obtained by the conventional FFT method according to an embodiment of the present invention.
FIG. 7 is a short-term maximum entropy speedmap in an embodiment 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.
Because the wheels are in rigid direct contact with the steel rails, when the wheels are out of round or the steel rails are subjected to corrugation, the vibration acceleration on the vehicle box is the largest, and the vibration frequency is reflected most obviously. A high-frequency-response vibration sensor is mounted on an axle box of the high-speed motor train unit, and vibration acceleration time domain data of the axle box in the high-speed running process of the motor train unit are acquired through AD conversion of a data acquisition board. And carrying out short-time maximum entropy spectrum analysis on the acquired data to obtain the vibration instantaneous frequency spectrum change of the axle box at each moment, and drawing a time-frequency graph and a speed-frequency graph of the short-time maximum entropy spectrum by combining with the vehicle speed data acquired by the GPS. Because the transient vibration frequency of the axle box vibration is difficult to analyze and calculate, the change of the transient vibration frequency is replaced by the overlapped time slices with shorter time intervals. And according to the linear relation between the vehicle speed and the vibration dominant frequency, fitting to obtain a linear formula between the vibration dominant frequency and the vehicle speed to predict the development trend of the vibration dominant frequency.
Based on the principle, the invention provides a method for predicting the main frequency of the axle box vibration of the high-speed motor train unit based on the maximum entropy spectrum analysis, which is shown in figure 1, and comprises the following steps:
s1, acquiring vibration acceleration data of the axle box of the high-speed motor train unit, and dividing the vibration acceleration data into acceleration data of a plurality of time slices;
the divided time slices are overlapped time slices with equal time intervals;
s2, sequentially calculating the maximum entropy power spectrum of the acceleration data in each time slice, and performing secondary open operation on the maximum entropy power spectrum to obtain a corresponding maximum entropy amplitude spectrum;
s3, drawing a three-dimensional frequency spectrum distribution graph according to the maximum entropy amplitude spectrum of each time slice;
and S4, predicting the vibration dominant frequency according to the drawn three-dimensional frequency spectrum distribution diagram.
The step S1 is specifically:
s11, calculating the total number N of the acquired acceleration data corresponding to the time slices;
wherein, the total number N of the time slices is:
Figure BDA0002191809890000081
in the formula, T is the total duration of the obtained acceleration data;
t0a set single time slice duration;
tsthe overlapping duration of adjacent time slices;
s12, determining the starting time of each time slice according to the total number of the time slices;
wherein the start time t of each time slicenComprises the following steps:
tn＝(n-1)*(t0-ts)
in the formula, subscript N is the number of each time slice, and N is more than or equal to 1 and less than or equal to N.
And S13, dividing the acceleration data into acceleration data in a plurality of time slices according to the determined time slice starting time and the determined time length.
In the above time-slicing process, in order to make the frequency of the analyzed single-time-slice close to the instantaneous vibration frequency, the length of the single time-slice is t0The smaller the better. But for an AD sampling process with a limited sampling frequency, a single time slice length t0Inner frequency resolution df being 1/t0I.e. a single time slice length t0The smaller the frequency resolution df is. To synthesize a single time slice length t0And frequency resolution df, often using a single time slice length t for full range acceleration data0The frequency resolution df was obtained at 1Hz with analytical accuracy. To compensate for the disadvantage that a single time slice is too long to approach the instantaneous vibration frequency, it is permissible that adjacent time slices may overlap, e.g. assuming tsAt 0.9s, the start times of two adjacent time slices differ by 0.1s, and there is 0.9s of overlapping data.
As shown in fig. 2, in step S2, the method for calculating the maximum entropy power spectrum of the acceleration data in each time slice specifically includes:
a1, setting the maximum entropy power spectrum order as M, the allowed minimum power spectrum error as e and the order increasing gradient as M;
for maximum entropy spectrum analysis, the larger the order M, the smaller the allowed minimum power spectrum error e, and the higher the analysis accuracy. The order M also has a certain relation with the sampling frequency F, and the higher the sampling frequency is, the larger the order M needs to be iterated. In general, the maximum entropy power spectrum order M can be set to 100 or more, the error e is close to 0, and the order increasing gradient M is 1.
A2, setting the initial order to be 0, and calculating the initial value P of the prediction error power of the acceleration in the current nth time slice0Initial value f of forward prediction error0And an initial value g of backward prediction error0；
Wherein, the initial value P of the error power is predicted0Comprises the following steps:
Figure BDA0002191809890000091
in the formula, K is an acceleration data function in the nth time slice;
x (i) is an acceleration data function in the nth time slice;
initial value f of forward prediction error0Comprises the following steps:
f0(i)＝x(i)
in the formula (f)0(n) is the initial value of the forward prediction error of the ith acceleration data in the nth time slice, and i ∈ [1, K]；
Initial value g of backward prediction error0Comprises the following steps:
g0(i)＝x(i)
in the formula, g0(n) is the initial value of backward prediction error of the ith acceleration data in the nth time slice, and i ∈ [1, K]；
The above forward prediction error f0(i) And backward prediction error g0(i) The initial values of (a) are all x (i).
A3, increasing the current order by M, and judging whether the order after increasing M is less than M;
if yes, go to step A7;
if not, go to step A4;
a4, calculating the reflection coefficient K of the acceleration data in the time slice of the current order according to the forward prediction error and the subsequent prediction error when the order m is increased last timemGo to step A5;
wherein the m-th order reflection coefficient KmIs composed of
Figure BDA0002191809890000101
In the formula (f)m-1(i) Forward prediction error for the (i-1) th acceleration data point of the (m-1) th order;
gm-1(i-1) is the backward prediction error of the (i-1) th acceleration data point of the (m-1) th order.
A5 according to reflection coefficient KmSeparately calculating the predicted error power P at the current ordermForward prediction error fmAnd backward prediction error gmGo to step A6;
wherein the prediction error power P at the current ordermComprises the following steps:
Figure BDA0002191809890000102
in the formula, Pm-1Increasing the corresponding prediction error power of the order m for the previous time;
the predicted error power f of the ith acceleration data point at the current orderm(i) Comprises the following steps:
fm(i)＝fm-1(i)+Kmgm-1(i-1)
in the formula (f)m-1(i) Forward prediction error is the ith acceleration data point of the (m-1) th order;
gm-1(i-1) backward prediction error of the (i-1) th acceleration data point of the (m-1) th order;
the backward prediction error g of the ith acceleration data point in the current orderm(i) Comprises the following steps:
gm(n)＝gm-1(n-1)+Kmfm-1(n)
a6, judging whether the difference value between the prediction error power of the current order and the prediction error power of the previous order is less than e;
if yes, go to step A7;
if not, returning to the step A3;
a7, determining the maximum entropy power spectrum according to the reflection coefficient of the current orderam。
Wherein the maximum entropy power spectrum WmComprises the following steps:
wherein, FFT (-) is Fourier transform function;
amfilter coefficients comprising forward filter coefficients and backward filter coefficients;
wherein, the jth forward filter coefficient a at the mth orderm(j) Comprises the following steps:
am(j)＝am-1(j)+Kmam-1(l-j-1)
in the formula, am-1(l-j-1) is the l-j-1 forward filter coefficient at the m-1 order;
coefficient a of the ith backward filter at mth orderm(l) Comprises the following steps:
am(l)＝Km
when the three-dimensional spectrogram is drawn in step S3, the maximum entropy amplitude spectrum is taken as the ordinate, the frequency is taken as the abscissa, and the three-dimensional spectrogram is drawn, and the three-dimensional spectrogram distribution map includes a three-dimensional time-frequency map and a three-dimensional fast-frequency map. The three-dimensional time-frequency graph is characterized in that the x axis is time, the y axis is frequency, and the z axis is frequency spectrum amplitude, and reflects the change rule of the main frequency in the acceleration vibration spectrum along with time. In the three-dimensional speed-frequency diagram, the x axis is speed, the y axis is frequency, and the z axis is frequency spectrum amplitude, so that the change rule of the main frequency in the acceleration vibration spectrum along with the speed of the vehicle is reflected.
In the step S4, the prediction of the vibration dominant frequency is realized according to the development trend of the vibration dominant frequency in the drawn three-dimensional map.
In one embodiment of the present invention, a comparative example of the method of the present invention with a conventional FFT method is provided:
taking the vibration acceleration of the axle box of a certain high-speed motor train unit as an example, taking 10s as a time slice, calculating a spectrogram by adopting a traditional FFT method and a maximum entropy spectrogram pair obtained by the method disclosed by the invention as shown in FIG. 3, and as can be seen from FIG. 3, the maximum entropy spectrogram curve obtained by the method disclosed by the invention is smoother, and the identified frequency is more accurate.
The time-frequency diagram of the vibration acceleration of the 650s axle box is analyzed by respectively adopting the traditional short-time FFT method and the short-time maximum entropy spectrum method with 1s as the time length of a time slice as shown in figures 4-5. It can be seen that in the time-frequency diagram, the vibration main frequency change in the time-frequency diagram obtained by the short-time maximum entropy spectrum method is very clear, and the side frequency and the frequency multiplication generated by the relevant factors such as the vehicle speed, the out-of-round order, the corrugation wavelength and the like are obviously weakened or eliminated.
And similarly, obtaining the speed information corresponding to each time slice according to the acquired speed data. The axle box vibration acceleration rate frequency graphs are then plotted from small to large for each time slice as shown in FIGS. 6-7. It can be seen that in the velocity frequency diagram, the vibration main frequency change in the velocity frequency diagram obtained by the short-time maximum entropy spectrum method is clearer, and the side frequency and the frequency multiplication generated by the relevant factors such as the vehicle speed, the non-circular order, the corrugation wavelength and the like are obviously weakened or eliminated. According to the change rule of the vibration main frequency along with the running speed of the vehicle, the development trend of the vibration main frequency along with the speed can be well predicted by a speed frequency chart obtained by a maximum entropy spectrum method.
The invention has the beneficial effects that:
according to the method for predicting the main frequency of the high-speed motor train unit axle box vibration based on the maximum entropy spectrum analysis, the main frequency of vibration is more clearly changed in a three-dimensional time-frequency graph and a speed-frequency graph by a short-time maximum entropy spectrum method, and the trend of the displayed main frequency of vibration along with time is clearer due to the fact that the side frequency and the frequency multiplication of relevant factors such as the speed, the out-of-round order, the corrugation wavelength and the like are obviously reduced or eliminated. According to the change rule of the vibration main frequency along with the vehicle running speed, compared with the traditional short-time FFT method, the velocity frequency graph obtained by the maximum entropy spectrum method can more clearly and accurately display the linear relation of the vibration main frequency along with the vehicle running speed, and can accurately predict the development trend of the vibration main frequency along with the speed. According to the linear relation between the vibration dominant frequency and the vehicle speed, the out-of-round order of the vehicle and the rail corrugation wavelength can be accurately judged, and whether the vibration dominant frequency is close to the vibration mode of the vehicle component to cause resonance or not is predicted by combining the modal information of the vehicle component.

Claims (8)

1. The method for predicting the main frequency of the axle box vibration of the high-speed motor train unit based on the maximum entropy spectrum analysis is characterized by comprising the following steps of:
s1, acquiring vibration acceleration data of the axle box of the high-speed motor train unit, and dividing the vibration acceleration data into acceleration data of a plurality of time slices;
s2, sequentially calculating the maximum entropy power spectrum of the acceleration data in each time slice, and performing quadratic evolution operation on the maximum entropy power spectrum to obtain a corresponding maximum entropy amplitude spectrum;
s3, drawing a three-dimensional frequency spectrum distribution graph according to the maximum entropy amplitude spectrum of each time slice;
s4, predicting vibration dominant frequency according to the drawn three-dimensional frequency spectrum distribution map;
in step S2, the method for calculating the maximum entropy power spectrum of the acceleration data in each time slice specifically includes:
a1, setting the maximum entropy power spectrum order as M, the allowed minimum power spectrum error as e and the order increasing gradient as M;
a2, setting the initial order to be 0, and calculating the initial value P of the prediction error power of the acceleration in the current nth time slice0Initial value f of forward prediction error0And an initial value g of backward prediction error0；
A3, increasing the current order by M, and judging whether the order increased by M is smaller than M;
if yes, go to step A7;
if not, go to step A4;
a4, calculating the reflection coefficient K of the acceleration data in the time slice of the current order according to the forward prediction error and the subsequent prediction error when the order m is increased last timemGo to step A5;
a5 according to reflection coefficient KmSeparately calculating the predicted error power P at the current ordermForward prediction error fmAnd backward prediction error gmGo to step A6;
a6, judging whether the difference value between the prediction error power of the current order and the prediction error power of the previous order is less than e;
if yes, go to step A7;
if not, returning to the step A3;
and A7, determining the maximum entropy power spectrum according to the reflection coefficient of the current order.
2. The method for predicting the axle box vibration dominant frequency of the high-speed motor train unit based on the maximum entropy spectrum analysis according to claim 1, wherein the step S1 specifically comprises the following steps:
s11, calculating the total number N of the acquired acceleration data corresponding to the time slices;
s12, determining the starting time of each time slice according to the total number of the time slices;
and S13, dividing the acceleration data into acceleration data in a plurality of time slices according to the determined time slice starting time and the determined time length.
3. The method for predicting the axle box vibration dominant frequency of the high-speed motor train unit based on the maximum entropy spectrum analysis of claim 2, wherein the total number N of the time slices in the step S11 is as follows:
Figure FDA0002554716460000021
in the formula, T is the total duration of the obtained acceleration data;
t0a set single time slice duration;
tsthe overlapping duration of adjacent time slices;
in the step S12, the start time t of each time slicenComprises the following steps:
tn＝(n-1)*(t0-ts)
in the formula, subscript N is the number of each time slice, and N is more than or equal to 1 and less than or equal to N.
4. The method for predicting the axle box vibration dominant frequency of high-speed motor train unit based on maximum entropy spectrum analysis according to claim 1, wherein in the step A2,
the initial value P of the prediction error power0Comprises the following steps:
Figure FDA0002554716460000022
in the formula, K is the total number of the acceleration data in the nth time slice;
x (i) is an acceleration data function in the nth time slice;
the initial value f of the forward prediction error0Comprises the following steps:
f0(i)＝x(i)
in the formula (f)0(n) is the initial value of the forward prediction error of the ith acceleration data in the nth time slice, and i ∈ [1, K]；
The backward prediction error initial value g0Comprises the following steps:
g0(i)＝x(i)
in the formula, g0(n) is the initial value of backward prediction error of the ith acceleration data in the nth time slice, and i ∈ [1, K]。
5. The method for predicting the axle box vibration dominant frequency of the high-speed motor train unit based on the maximum entropy spectrum analysis of claim 4, wherein the reflection coefficient K of the m-th order in the step A4mComprises the following steps:
Figure FDA0002554716460000031
in the formula (f)m-1(i) Forward prediction error for the (i-1) th acceleration data point of the (m-1) th order;
gm-1(i-1) is the backward prediction error of the (i-1) th acceleration data point of the (m-1) th order.
6. The method for predicting the axle box vibration dominant frequency of high-speed motor train unit based on maximum entropy spectrum analysis of claim 5, wherein in the step A5,
prediction error power P at the current ordermComprises the following steps:
Figure FDA0002554716460000032
in the formula, Pm-1Increasing order for previous timeThe corresponding prediction error power of m;
forward prediction error f of ith acceleration data point at the current orderm(i) Comprises the following steps:
fm(i)＝fm-1(i)+Kmgm-1(i-1)
in the formula (f)m-1(i) Forward prediction error for the ith acceleration data point of order m-1;
gm-1(i-1) backward prediction error of the (i-1) th acceleration data point of the (m-1) th order;
the backward prediction error g of the ith acceleration data point in the current orderm(i) Comprises the following steps:
gm(i)＝gm-1(i-1)+Kmfm-1(i)。
7. the method for predicting the axle box vibration dominant frequency of the high-speed motor train unit based on the maximum entropy spectrum analysis of claim 6, wherein the maximum entropy power spectrum W in the step A7mComprises the following steps:
Wm＝FFT(am)
wherein, FFT (-) is Fourier transform function;
amfilter coefficients comprising forward filter coefficients and backward filter coefficients;
wherein, the jth forward filter coefficient a at the mth orderm(j) Comprises the following steps:
am(j)＝am-1(j)+Kmam-1(l-j-1)
in the formula, am-1(l-j-1) is the l-j-1 forward filter coefficient at the m-1 order;
coefficient a of the ith backward filter at mth orderm(l) Comprises the following steps:
am(l)＝Km。
8. the method for predicting the axle box vibration dominant frequency of the high-speed motor train unit based on the maximum entropy spectrum analysis according to claim 1, wherein the maximum entropy amplitude spectrum is used as a vertical coordinate and the frequency is used as a horizontal coordinate to draw the three-dimensional frequency spectrum when the three-dimensional frequency spectrum is drawn in the step S3;
the three-dimensional frequency spectrum distribution map comprises a three-dimensional time-frequency map and a three-dimensional speed-frequency map.
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