CN113029569A - Train bearing autonomous fault identification method based on cyclic strength index - Google Patents

Train bearing autonomous fault identification method based on cyclic strength index Download PDF

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CN113029569A
CN113029569A CN202110264292.XA CN202110264292A CN113029569A CN 113029569 A CN113029569 A CN 113029569A CN 202110264292 A CN202110264292 A CN 202110264292A CN 113029569 A CN113029569 A CN 113029569A
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frequency
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CN113029569B (en
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辛格
钟槭畑
李哲
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Beijing Jiaotong University
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Beijing Jiaotong University
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    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention provides a train bearing autonomous fault identification method based on a cycle intensity index. The method comprises the following steps: acquiring a vibration signal of a train bearing through an acceleration sensor; calculating the spectral coherence of the vibration signal, and calculating a cycle intensity index according to the spectral coherence of the vibration signal; integrating the normalized circulating intensity index on the optimal frequency band to obtain an enhanced circulating index, calculating the fault probability value of each subharmonic according to the enhanced circulating index, and calculating the weighted fault index of each part; and calculating the median of the peak values of all the enhanced cyclic indexes exceeding the fault judgment threshold to obtain the judgment threshold of the binary hypothesis model, comparing the weighted fault indexes of all the parts with the judgment threshold of the binary hypothesis model, and determining whether faults exist in all the parts of the bearing according to the comparison result. The invention can automatically output the fault position and fault probability of the bearing according to the acquired original vibration signal, and is convenient for application of industrial production.

Description

Train bearing autonomous fault identification method based on cyclic strength index
Technical Field
The invention relates to the technical field of train rolling bearing fault diagnosis, in particular to a train bearing autonomous fault identification method based on a cyclic intensity index.
Background
The rolling bearing is one of the most widely used components in the train, and is also a fault-prone component of the train, and the reliable intelligent fault diagnosis method applied to bearing fault diagnosis can remarkably reduce the workload of related maintenance departments while ensuring the safe operation of the train. With the continuous development of diagnostic techniques.
A method of diagnosing the state of health of a rolling bearing in the prior art includes: the bearing fault diagnosis method based on the vibration signal comprises fast Fourier transform, short-time Fourier transform, wavelet transform, empirical mode decomposition and the like. The disadvantages of this method are: the final diagnosis result needs to be obtained through artificial analysis, so that the requirement and the workload of the professional level of workers are increased, the intelligent degree is not high enough, and the deployment in industrial production activities is not facilitated.
Another prior art method of diagnosing the state of health of a rolling bearing comprises: machine learning such as K-means clustering, SVM and the like and deep learning method based on neural network. The disadvantages of this method are: although intelligent diagnosis can be realized, a large amount of data samples are needed for model training, and the quality of acquired data is required, because it is very difficult to acquire real and high-quality data due to problems of industry confidentiality and the like. Meanwhile, the method has poor interpretability, has high requirements on hardware, data transmission level and the like, and is difficult to implement when falling to the ground.
Disclosure of Invention
The embodiment of the invention provides a train bearing autonomous fault identification method based on a cyclic strength index, so as to effectively and autonomously diagnose the fault of a train bearing.
In order to achieve the purpose, the invention adopts the following technical scheme.
A train bearing autonomous fault identification method based on a cyclic strength index comprises the following steps:
step S1: acquiring a vibration signal of a train bearing through an acceleration sensor;
step S2, calculating the spectrum coherence of the vibration signal, calculating a cycle intensity index according to the spectrum coherence of the vibration signal, and normalizing the corresponding cycle intensity index according to the distribution characteristic of the spectrum frequency of the vibration signal;
step S3: setting a significance level according to a hypothesis testing principle, and establishing a binary hypothesis model;
step S4: integrating the normalized circulation intensity index on the optimal frequency band to obtain an enhanced circulation index, and calculating a fault judgment threshold according to a histogram of the enhanced circulation index;
step S5: calculating fault characteristic frequency of each part of a train bearing and a frequency doubling narrow band of the fault characteristic frequency;
step S6: calculating the fault probability value of each subharmonic according to the enhanced circulation index and the frequency doubling narrow band of the fault characteristic frequency of each part of the train bearing, and calculating the weighted fault index of each part according to the fault probability value of each subharmonic;
step S7: and calculating the median of the peak values of all the enhanced cyclic indexes exceeding the fault judgment threshold to obtain the judgment threshold of the binary hypothesis model, comparing the weighted fault indexes of all the parts with the judgment threshold of the binary hypothesis model, and determining whether faults exist in all the parts of the bearing according to the comparison result.
Preferably, the step S2 specifically includes:
s21: setting a vibration signal at time t acquired by using an acceleration sensor as x (t), and calculating an autocorrelation function R of the vibration signal x (t) under the time t and a time delay taux(t,τ)：
Rx(t,τ)＝E{x(t)x(t-τ)*}
Wherein E represents a mathematical expectation operation and denotes a complex conjugate operation;
s22: calculating an autocorrelation function R of the vibration signal x (t)x(t, τ) spectrum corresponding to time delay τ:
Figure BDA0002971430110000021
wherein f iskRepresenting discretized spectral frequencies, fkK Δ f, Δ f being the spectral frequency resolution, FT representing the fourier transform;
s23, calculating the spectral dependence of the vibration signal x (t):
Figure BDA0002971430110000031
wherein, alpha is cycle frequency, T is time range, and j is imaginary unit;
s24, calculating the spectrum coherence of the vibration signal x (t):
Figure BDA0002971430110000032
s25 calculation of the frequency corresponding to the spectrum fkCyclic strength index C ofx(α；fk)：
Figure BDA0002971430110000033
S26: to cyclic strength index Cx(α；fk) Discretizing and according to the spectral frequency fkThe corresponding circulating intensity index is normalized:
Figure BDA0002971430110000034
wherein alpha isi＝iΔα，i＝0,1,2,…,αimax，αimaxFor the upper limit of the cycle frequency, Δ α is the cycle frequency resolution, MED (C)x(αi；fk) Is representative of corresponding to spectral frequency fkMoving median of the circulating intensity index of (A), MAD (C)x(αi；fk) Represents corresponds to a spectral frequency fkThe absolute deviation of the moving median of the cyclic intensity index.
Preferably, the step S3 specifically includes: according to the hypothesis testing principle, the following binary hypothesis model is established:
Figure BDA0002971430110000035
under the condition that the significance level is p, the designed statistic amount does not exceed 100 percent of histogram (1-p)The values of the sites are considered to accept H in the bivariate hypothesis model0Assume that values above 100% quantile in histogram (1-p) are considered to accept H in the bivariate hypothesis model1It is assumed.
Preferably, the S4 step includes:
s41: integrating the normalized circulating intensity index in the optimal frequency range to obtain an enhanced circulating index which obeys stable distribution:
Figure BDA0002971430110000041
where l, h correspond to the lower and upper limits of the summation of the optimum spectral frequencies, respectively.
S42: calculating CS (. alpha.) (j) The histogram of (1-p) is taken as a threshold t of 100% quantiles1-p。
Preferably, the S5 step includes:
s51: according to the characteristics of the train bearing, a narrow-band definition mode for calculating the fault characteristic frequency of the train bearing is as follows:
outer ring fault characteristic frequency doubling narrow band OBjComprises the following steps:
Figure BDA0002971430110000042
side frequency IB of inner ring fault characteristic frequencyjAnd narrow band where frequency multiplication is performed
Figure BDA0002971430110000043
And
Figure BDA0002971430110000044
comprises the following steps:
Figure BDA0002971430110000045
Figure BDA0002971430110000046
Figure BDA0002971430110000047
side frequency RB _ S of rolling element unilateral fault characteristic frequencyjAnd narrow band where frequency multiplication is performed
Figure BDA0002971430110000048
And
Figure BDA0002971430110000049
comprises the following steps:
Figure BDA00029714301100000410
Figure BDA00029714301100000411
Figure BDA0002971430110000051
side frequency RB _ D of rolling element bilateral fault characteristic frequencyjAnd narrow band where frequency multiplication is performed
Figure BDA0002971430110000052
And
Figure BDA0002971430110000053
comprises the following steps:
Figure BDA0002971430110000054
Figure BDA0002971430110000055
Figure BDA0002971430110000056
narrow band CB _ I where frequency multiplication of fault characteristic frequency of retainer inner collision ring is locatedjComprises the following steps:
Figure BDA0002971430110000057
narrow band CB _ O where frequency multiplication of fault characteristic frequency of retainer touch outer ring is locatedjComprises the following steps:
Figure BDA0002971430110000058
wherein j is the narrow band where the jth frequency multiplication is located, n is the number of calculated frequency multiplication, and alphaBPFO、αBPFI、αBSF_S、αBSF_D、αFTFIAnd alphaFTFOThe frequency is the fault characteristic frequency of an outer ring, an inner ring, a single end of a rolling body, double ends of the rolling body, an inner ring contacted by a retainer and an outer ring contacted by the retainer, a subscript 1 represents the frequency of a maximum value in a first narrow band, the frequency is used as a later harmonic calculation reference, and mu is an error coefficient and represents the deviation ratio of a real value and a theoretical value of the fault characteristic frequency of a bearing;
s52: the manner of calculating the failure characteristic frequency in the step S51 is as follows:
outer ring fault characteristic frequency:
Figure BDA0002971430110000059
inner ring fault characteristic frequency:
Figure BDA00029714301100000510
characteristic frequency of single-side fault of rolling body:
Figure BDA0002971430110000061
characteristic frequency of double-side fault of rolling body:
Figure BDA0002971430110000062
characteristic frequency of cage collision inner ring failure:
Figure BDA0002971430110000063
characteristic frequency of cage touch outer ring failure:
Figure BDA0002971430110000064
wherein n is the number of the rolling bodies, D is the diameter of the rolling bodies, D is the pitch diameter of the bearing, theta is the contact angle of the rolling bodies, frThe measured axis is frequency-converted.
Preferably, the S6 step includes:
s61: calculating the maximum amplitude of the ith harmonic corresponding to each part of the train bearing in the narrow band:
Figure BDA0002971430110000065
wherein max {. is the maximum value in the set, BjCalculating the narrow band corresponding to the fault characteristic frequency of each part in S51;
s62: calculating the fault probability value of the ith harmonic corresponding to each part of the train bearing:
Figure BDA0002971430110000066
wherein arctan (·) is an arctangent function.
S63: calculating the weighted fault index of each part of the train bearing:
outer ring:
Figure BDA0002971430110000067
inner ring:
Figure BDA0002971430110000071
one-sided failure of the rolling body:
Figure BDA0002971430110000072
double-side failure of the rolling body:
Figure BDA0002971430110000073
the retainer touches the inner ring:
Figure BDA0002971430110000074
the retainer touches the outer ring:
Figure BDA0002971430110000075
wherein the content of the first and second substances,
Figure BDA0002971430110000076
FPjand
Figure BDA0002971430110000077
and calculating the failure probability values of the left frequency band, the main frequency band and the right frequency band respectively, wherein n is the number of calculated harmonics.
Preferably, the S7 step includes:
s71: calculating all exceeding thresholds t1-pPeak median of enhancement cycle index of (2):
MD＝median{CS(αi)},if[CS(αi)＞t1-p]
wherein if [ CS (alpha) ]i)＞t1-p]Indicating that the threshold t is exceeded1-pSelecting if the current value is greater than the preset value, or else, not selecting, wherein medium {. is the median in the set;
s72: calculating a judgment threshold T of the binary hypothesis model:
T＝2arctan(MD-t1-p)/π
and S73, judging according to the weighted fault indexes of the parts calculated in the step S6: when the weighted fault index FP of a certain position is larger than or equal to T, H is rejected0Suppose that H is accepted1Supposing that the vibration signal x (t) contains fault information, the part in the train bearing is in fault, and the fault probability value FP of the part is outputj: when the weighted failure index FP < T of all the positions, H is accepted0If the vibration signal x (t) does not contain fault information, the train bearing is not in fault. According to the technical scheme provided by the embodiment of the invention, the method provided by the embodiment of the invention can automatically diagnose the fault identification of the train rolling bearing without human participation in analysis, and is beneficial to improving the industrial deployment efficiency and reducing the operation and maintenance cost.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a processing flow chart of a train bearing autonomous failure identification method based on a cyclic strength index according to an embodiment of the present invention;
FIG. 2 is a time-domain vibration signal (inner ring fault) of a train axle box bearing collected by an acceleration sensor according to an embodiment;
FIG. 3 is a graph of an enhanced cyclic index indicating a fault threshold and a narrow band of fault signature frequencies according to one embodiment;
FIG. 4 is a time-domain vibration signal (outer ring fault) of a train axle box bearing collected by an acceleration sensor according to the second embodiment;
FIG. 5(a) is a histogram of the non-normalized circulating intensity index of example two;
FIG. 5(b) is a histogram of the normalized circulating intensity index of example two;
FIG. 6(a) is an enhanced cyclic index obtained by summing the unnormalized cyclic intensity indices of example two on the frequency axis;
FIG. 6(b) is an enhanced cyclic index obtained by summing the normalized cyclic intensity indexes of example two on the frequency axis;
fig. 7 is an enhanced cyclic index graph with the failure threshold and the failure characteristic frequency narrowband marked according to the second embodiment.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
Example one
In order to verify the feasibility of the invention, the experimental platform data of the axle box bearing of the train is adopted in the embodiment, and the fault characteristics of the axle box bearing are analyzed. The sampling frequency of the data is 32768Hz, the sampling time duration of the data is 10s, the frequency conversion of the bearing is 8.32Hz, and the early bearing inner ring fault data is taken as an example.
The processing flow of the train bearing autonomous fault identification method based on the cyclic strength index provided by the embodiment of the invention is shown in fig. 1, and comprises the following processing steps:
step S1: acquiring a vibration signal of a train bearing through an acceleration sensor;
step S2, calculating the spectrum coherence of the vibration signal, further calculating a circulation intensity index, and standardizing the corresponding circulation intensity index according to the distribution characteristic of spectrum frequency;
step S3: establishing a binary hypothesis model according to a hypothesis testing principle;
step S4: integrating the normalized circulating intensity index on the optimal frequency band to obtain an enhanced circulating index, setting a significance level, and calculating a threshold value according to a histogram of the enhanced circulating index;
step S5: calculating fault characteristic frequency of a train bearing and a frequency doubling narrow band of the fault characteristic frequency;
step S6: calculating the fault probability value of each subharmonic according to the enhanced cycle index, and calculating the weighted fault index of each part;
step S7: and calculating the median of all peak values exceeding the threshold value, obtaining a binary hypothesis model judgment threshold value, and making judgment according to the weighted fault index of each part calculated in the step S6, namely determining whether each part of the bearing has faults and the probability of the faults.
In the step S1, the vibration signal x (t) at the time t is acquired by using the acceleration sensor, the sampling frequency of the signal is 32768Hz, the data sampling time length is 10S, and the acquired vibration signal is shown in fig. 2, so that the visible fault characteristic is obvious;
the step of S2 includes:
s21: calculating the autocorrelation function of the vibration signal at time t and time delay tau:
Rx(t,τ)＝E{x(t)x(t-τ)*}
wherein E represents a mathematical expectation operation and denotes a complex conjugate operation;
s22: calculating the frequency spectrum of the autocorrelation function of the vibration signal x (t) corresponding to the time delay τ:
Figure BDA0002971430110000111
wherein f iskRepresenting discretized spectral frequencies, fkK Δ f, Δ f being the spectral frequency resolution, FT representing the fourier transform;
s23, calculating the spectral dependence of the vibration signal x (t):
Figure BDA0002971430110000112
wherein, alpha is cycle frequency, T is time range, and j is imaginary unit;
s24, calculating the spectrum coherence of the vibration signal x (t):
Figure BDA0002971430110000113
s25 calculation of the frequency corresponding to the spectrum fkCyclic strength index C ofx(α；fk)：
Figure BDA0002971430110000114
S26: to cyclic strength index Cx(α；fk) Discretizing and according to the spectral frequency fkThe corresponding circulating intensity index is normalized to have a stable distribution:
Figure BDA0002971430110000115
wherein alpha isi＝iΔα，i＝0,1,2,…,αimax，αimaxFor the upper limit of the cycle frequency, Δ α is the cycle frequency resolution, MED (C)x(αi；fk) Is representative of corresponding to spectral frequency fkMoving median of the circulating intensity index of (A), MAD (C)x(αi；fk) Represents corresponds to a spectral frequency fkThe absolute deviation of the moving median of the cyclic intensity index.
In this example, take alphaimaxWhen the moving median is found, the window size is taken to be 71 (reference range 51-91) 600.
Further, in the step S3, according to the hypothesis testing principle, a binary hypothesis model is established:
Figure BDA0002971430110000121
at a significance level of p, values in the designed statistics that do not exceed 100% of the quantiles in the histogram (1-p) are considered to accept H0Assume that values above 100% quantile in histogram (1-p) are considered to reject H0Suppose that H is accepted1It is assumed.
For significance level, where p is 0.01 in this example, it is interpreted as the value of the designed statistic that does not exceed 99% of the quantiles in the histogram would be considered acceptable for H with a probability of 0.01 of making an error0Assume that values above 99% quantile of the histogram reject H0Suppose, accept H1It is assumed.
Further, the step of S4 includes:
s41: integrating the normalized circulating intensity index in the optimal frequency range to obtain the enhanced circulating index CS (alpha) which is subject to stable distributioni)：
Figure BDA0002971430110000122
Where l, h correspond to the lower and upper limits of the summation of the optimum spectral frequencies, respectively.
The optimal frequency range is obtained according to train bearing fault diagnosis experience, in this example, the full-band range of the spectrum frequency is integrated, i.e., l is 0, and h is Fs/(2 Δ f) 16384.
S42: calculating CS (. alpha.) (j) The histogram of (1-p) 100% quantile points is taken as a fault judgment threshold value t1-p。
In this example, p is 0.01, and it is explained that the threshold calculated from the bigram is considered to be reliable under the condition that the probability of making an error is 0.01, and the t is calculated by taking 99% quantile point of the histogram as the threshold0.99＝0.1543
Further, the step of S5 includes:
s51: according to the train bearing characteristics, the narrow-band definition mode for calculating the fault characteristic frequency is as follows:
outer ring fault characteristic frequency and frequency doubling narrow band:
Figure BDA0002971430110000131
inner ring fault characteristic frequency, side frequency and narrow band where frequency multiplication is carried out:
Figure BDA0002971430110000132
Figure BDA0002971430110000133
Figure BDA0002971430110000134
the characteristic frequency of the fault on one side of the rolling body, the side frequency and the narrow band where the frequency multiplication is carried out are as follows:
Figure BDA0002971430110000135
Figure BDA0002971430110000136
Figure BDA0002971430110000137
the characteristic frequency and the side frequency of the fault at two sides of the rolling body and the narrow band where the frequency multiplication is carried out are as follows:
Figure BDA0002971430110000138
Figure BDA0002971430110000139
Figure BDA00029714301100001310
the characteristic frequency of the fault of the inner ring collision of the retainer and the narrow band of the frequency multiplication thereof are as follows:
Figure BDA00029714301100001311
the characteristic frequency of the fault of the retainer touching the outer ring and the narrow band of the frequency multiplication are as follows:
Figure BDA00029714301100001312
wherein j is the narrow band where the jth frequency multiplication is located, n is the number of calculated frequency multiplication, and alphaBPFO、αBPFI、αBSF_S、αBSF_D、αFTFIAnd alphaFTFOThe calculated failure characteristic frequency of the outer ring, the inner ring, the single end of the rolling body, the double ends of the rolling body, the inner ring contacted by the retainer and the outer ring contacted by the retainer is shown, a subscript 1 represents the frequency of a maximum value in a first narrow band, the frequency is used as a calculation reference of later harmonic waves, and mu is an error coefficient and represents the deviation ratio of a real value and a theoretical value of the failure characteristic frequency of the bearing.
In this example, μ is 0.02 and n is 3, i.e., the number of frequency multipliers is 3.
S52: the manner of calculating the failure characteristic frequency in the step S51 is as follows:
outer ring fault characteristic frequency:
Figure BDA0002971430110000141
inner ring fault characteristic frequency:
Figure BDA0002971430110000142
characteristic frequency of single-side fault of rolling body:
Figure BDA0002971430110000143
characteristic frequency of double-side fault of rolling body:
Figure BDA0002971430110000144
characteristic frequency of cage collision inner ring failure:
Figure BDA0002971430110000145
characteristic frequency of cage touch outer ring failure:
Figure BDA0002971430110000146
wherein n is the number of the rolling bodies, D is the diameter of the rolling bodies, D is the pitch diameter of the bearing, theta is the contact angle of the rolling bodies, frThe measured axis is frequency-converted.
In this example, the number of rolling elements is 18, the diameter of the rolling elements is 26mm, the pitch diameter of the bearing is 170mm, and the rotation frequency of the measured shaft is 8.32 Hz. Alpha is obtained by calculation according to the formula in S52BPFO＝63.39，αBPFI＝102.27，αBSF_S＝26.55，αBSF_D＝53.10，αFTFI＝4.79，αFTFO3.52. The effect graph of inner ring fault characteristic frequency and frequency multiplication narrow band, threshold and enhanced cycle index obtained according to calculation is shown in fig. 3, wherein a longitudinal black dotted line in the graph represents outer ring fault characteristic and narrow band range of side frequency thereof, narrow bands at other positions are also calculated according to a similar mode, a transverse black dotted line represents the threshold obtained based on binary hypothesis model calculation, it can be seen from the graph that spectral lines of inner ring fault characteristic and side frequency are obviously higher, and spectral lines of frequency conversion characteristic are also obvious due to modulation relation.
Further, the step of S6 includes:
s61: calculating the maximum amplitude of the ith harmonic corresponding to each part of the train bearing in the narrow band:
Figure BDA0002971430110000151
wherein max {. is the maximum value in the set, BjThe narrow band corresponding to the failure characteristic frequency of each site in S51 is calculated for each site.
S62: calculating the fault probability value of the ith harmonic corresponding to each part of the train bearing:
Figure BDA0002971430110000152
wherein arctan (·) is an arctangent function.
S63: calculating the weighted fault index of each part:
outer ring:
Figure BDA0002971430110000153
inner ring:
Figure BDA0002971430110000154
one-sided failure of the rolling body:
Figure BDA0002971430110000155
double-side failure of the rolling body:
Figure BDA0002971430110000156
the retainer touches the inner ring:
Figure BDA0002971430110000161
the retainer touches the outer ring:
Figure BDA0002971430110000162
wherein the content of the first and second substances,
Figure BDA0002971430110000163
FPjand
Figure BDA0002971430110000164
and calculating the failure probability values of the left frequency band, the main frequency band and the right frequency band respectively, wherein n is the number of calculated harmonics.
The calculation effect of the narrow band of the inner ring fault characteristic frequency is shown in fig. 3, the fault probability of each other part is calculated according to the similar manner, and the fault probability of each part is calculated according to the formula in S6 and is shown in table 1:
TABLE 1
Type of failure FPouter FPinner FProll_S FProll_D FPcage_I FPcage_O
Probability of failure 0.1616 0.7158 0.059 0.0842 0 0.0153
Further, the step of S7 includes:
s71: calculating all exceeding thresholds t1-pMedian peak value of (d):
MD＝median{CS(αi)},if[CS(αi)＞t1-p]
wherein if [ CS (alpha) ]i)＞t1-p]Indicating that the threshold t is exceeded1-pSelecting if the median is selected, or else, not selecting, wherein the median is the median in the set.
S72: calculating a binary hypothesis model judgment threshold value:
T＝2arctan(MD-t1-p)/π
in this example, T is 0.1965 calculated from the above equation.
And S73, judging according to the weighted fault indexes of the parts calculated in the step S6: when the weighted fault index FP of a certain position is more than or equal to T, H is rejected0Suppose that H is accepted1Supposing that the representative vibration signal x (t) contains fault information, the part in the train bearing is in fault, and the fault probability value FP of the part is outputj(ii) a When the weighted failure index FP < T of all the positions, H is accepted0It is assumed that the representative vibration signal x (t) does not contain fault information and the train bearings are not faulty.
According to the comparison of the data in table 1 with the judgment probability threshold T, only the inner ring failure probability exceeds the threshold, so that H is rejected under the condition that the significance level p is 0.010Suppose, H1Let it be assumed thatThe dynamic signal x (t) includes failure information, and the output result is shown in table 2.
TABLE 2
Bearing condition Fault of
Location of failure Inner ring
Probability of failure 0.7158
The fault identification result is consistent with the type of bearing fault, and this example illustrates the contents of the present invention in detail.
Example two
The first example is an early inner ring fault bearing, the fault characteristics are very obvious, the detailed implementation process is explained, the second example is to further prove the superiority of the invention through a vibration signal example with strong pulse noise interference and weak fault characteristics, and the early outer ring fault data of the bearing is taken as an example.
The invention is further described in detail by taking the fault data of the outer ring of the bearing as an example and combining the attached drawings.
According to the flow shown in FIG. 1, the implementation steps of the present invention are as follows:
and step S1, acquiring vibration signals x (t) of the train bearing through a vibration acceleration sensor, wherein the sampling frequency is 32768Hz, the data sampling time is 10S, the acquired time domain vibration signal data is shown in figure 4, and the visible signals contain strong pulse noise and weak fault pulses.
Step S2: calculating the spectral coherence of the vibration signal x (t), further calculating the cyclic intensity index, and normalizing the corresponding cyclic intensity index according to the distribution characteristic of the spectral frequency:
step S21: calculating the autocorrelation function of the vibration signal at time t and time delay tau:
Rx(t,τ)＝E{x(t)x(t-τ)*}
wherein, E represents the mathematical expectation operation,*represents a complex conjugate operation;
step S22: calculating the frequency spectrum of the autocorrelation function of the vibration signal x (t):
Figure BDA0002971430110000181
wherein f iskRepresenting discretized spectral frequencies, fkΔ f is the spectral frequency resolution, in this example Δ f is Fs/N is 1/t is 0.1, FT represents the fourier transform;
step S23, calculating the spectral dependence of the vibration signal x (t):
Figure BDA0002971430110000182
wherein, alpha is cycle frequency, T is time range, and j is imaginary unit;
step S24, calculating the spectral coherence of the vibration signal x (t):
Figure BDA0002971430110000183
step S25 of calculating the frequency f corresponding to the spectrumkCyclic strength index C ofx(α；fk)：
Figure BDA0002971430110000184
Step S26: discretizing the circulating intensity index, and then normalizing:
Figure BDA0002971430110000185
wherein alpha isi＝iΔα，i＝0,1,2,…,αimax，αimaxFor the upper limit of the cycle frequency, Δ α is the cycle frequency resolution, MED (C)x(α；fk) Is a spectral frequency fkMoving median, MAD (C), of the corresponding circulating intensity indexx(α；fk) Is a spectral frequency fkAbsolute deviation of the moving median of the corresponding cyclic intensity index.
In this example, take alphaimaxWhen the moving median is obtained, the window size is 71 as 600. Fig. 5(a) is a histogram of data distribution of the circulating intensity index before normalization, and fig. 5(b) is a histogram of data distribution of the circulating intensity index after normalization, and it is apparent that the data distribution after normalization is closer to a normal distribution, and the circulating intensity index after normalization has a stronger statistical significance.
Step S3: according to a hypothesis testing principle, a binary hypothesis model is established:
Figure BDA0002971430110000191
wherein, at a significance level of p, values in the designed statistics that do not exceed 100% of the quantiles of the histogram (1-p) are considered to accept H0Assume that values above 100% quantile in histogram (1-p) are considered to reject H0Suppose that H is accepted1It is assumed.
In this example, where the significance level p is 0.01, the values in the statistics that do not exceed 99% of the quantiles in the histogram are considered to be acceptable for H0Assume that values above 99% quantile of the histogram reject H0Suppose, accept H1It is assumed.
Step S4: integrating the normalized circulating intensity index on the optimal frequency band to obtain an enhanced circulating index, setting a significance level, and calculating a threshold value according to a histogram of the enhanced circulating index:
step S41: according to the normalized circulating intensity index, integrating in a selected frequency range to obtain an enhanced circulating index which obeys stable distribution:
Figure BDA0002971430110000192
wherein l and h are respectively the lower limit and the upper limit of the selected and summed spectrum frequency. In this example, the whole band range of the spectrum frequency is integrated, i.e., l is 0, and h is Fs/(2 × Δ f) is 16384. Fig. 6(a) is an enhanced cyclic index obtained by summing unnormalized cyclic intensity indexes, and fig. 6(b) is an enhanced cyclic index obtained by summing normalized cyclic intensity indexes, it is obvious that the enhanced cyclic index obtained by integrating the normalized cyclic intensity indexes is clearer and has less interference compared with the spectral line of the enhanced cyclic index without performing the normalization operation, which shows that the normalization operation can make the statistical significance of the model stronger on one hand, and can more prominently enhance the spectral line representing the fault feature in the cyclic index on the other hand, and reduce the interference of some noises.
Step S42: calculating the enhanced circulation index CS (. alpha.)j) The histogram of (1-p) is taken as a fault determination threshold t1-p。
For the significance level, general values are 0.05, 0.01, 0.005, 0.001, etc., in this example, p is 0.01, and the explanation is that the threshold calculated according to the binary model is considered to be reliable under the condition that the probability of making an error is 0.01, 99% of quantiles of the histogram are taken as a fault judgment threshold, and t is calculated to obtain t0.99The significance of the failure determination threshold is that the portion of the boosted cyclic index below the threshold is divided into the portions considered to be accepted H, 0.25480It is assumed that, belonging to non-failure information, the part exceeding the threshold is considered as rejection H0Suppose, accept H1Presumably, it is considered a fault component.
Step S5: calculating the fault characteristic frequency of the train bearing and the frequency doubling narrow band:
step S51: according to the train bearing characteristics, the narrow-band definition mode for calculating the fault characteristic frequency is as follows:
outer ring fault characteristic frequency and frequency doubling narrow band:
Figure BDA0002971430110000201
inner ring fault characteristic frequency, side frequency and narrow band where frequency multiplication is carried out:
Figure BDA0002971430110000202
Figure BDA0002971430110000203
Figure BDA0002971430110000204
the characteristic frequency of the fault on one side of the rolling body, the side frequency and the narrow band where the frequency multiplication is carried out are as follows:
Figure BDA0002971430110000205
Figure BDA0002971430110000206
Figure BDA0002971430110000207
the characteristic frequency and the side frequency of the fault at two sides of the rolling body and the narrow band where the frequency multiplication is carried out are as follows:
Figure BDA0002971430110000208
Figure BDA0002971430110000209
Figure BDA0002971430110000211
the characteristic frequency of the fault of the inner ring collision of the retainer and the narrow band of the frequency multiplication thereof are as follows:
Figure BDA0002971430110000212
the characteristic frequency of the fault of the retainer touching the outer ring and the narrow band of the frequency multiplication are as follows:
Figure BDA0002971430110000213
wherein j is the narrow band where the jth frequency multiplication is located, n is the number of calculated frequency multiplication, and alphaBPFO、αBPFI、αBSF_S、αBSF_D、αFTFIAnd alphaFTFOThe calculated failure characteristic frequency of the outer ring, the inner ring, the single end of the rolling body, the double ends of the rolling body, the inner ring contacted by the retainer and the outer ring contacted by the retainer is shown, a subscript 1 represents the frequency of a maximum value in a first narrow band, the frequency is used as a calculation reference of later harmonic waves, and mu is an error coefficient and represents the deviation ratio of a real value and a theoretical value of the failure characteristic frequency of the bearing.
In this example, μ is 0.02 and n is 3, i.e., the number of frequency multipliers is 3.
Step S52: the calculation method of each fault characteristic frequency in S51 is as follows:
outer ring fault characteristic frequency:
Figure BDA0002971430110000214
inner ring fault characteristic frequency:
Figure BDA0002971430110000215
single-end fault characteristic frequency of the rolling body:
Figure BDA0002971430110000216
single-end fault characteristic frequency of the rolling body:
Figure BDA0002971430110000217
characteristic frequency of cage collision inner ring failure:
Figure BDA0002971430110000221
characteristic frequency of cage touch outer ring failure:
Figure BDA0002971430110000222
wherein n is the number of the rolling bodies, D is the diameter of the rolling bodies, D is the pitch diameter of the bearing, theta is the contact angle of the rolling bodies, frThe measured axis is frequency-converted.
In this example, the number of rolling elements is 18, the diameter of the rolling elements is 26mm, the pitch diameter of the bearing is 170mm, and the rotation frequency of the measured shaft is 8.32 Hz. Alpha is obtained by calculation according to the formula in S52BPFO＝63.39，αBPFI＝102.27，αBSF_S＝26.55，αBSF_D＝53.10，αFTFI＝4.79，αFTFO3.52. FIG. 7 shows an effect diagram of the outer ring fault characteristic frequency and its frequency multiplication narrow band, threshold value, and enhanced cycle index obtained by calculation, and a longitudinal black dotted line in FIG. 7 represents an outer ring fault characteristic narrow band range OBiThe narrow bands of other parts are calculated in a similar manner, and the horizontal black dotted line represents the threshold value t calculated based on the bigram model0.99The black spectral line with the obvious periodic characteristic is the fault characteristic of the outer ring fault characteristic frequency and the frequency multiplication thereof, and the alpha appears in the signalBPFOAnd high-amplitude spectral lines at multiples thereof.
Step S6: calculating the fault probability value of each subharmonic according to the enhanced cycle index, and calculating the fault index of each part:
step S61: calculating the maximum amplitude value in the narrow band where the ith harmonic corresponding to each part of the train bearing is located as follows:
Figure BDA0002971430110000223
wherein max {. is the maximum value in the set, BjThe narrow band corresponding to the failure characteristic frequency of each site in S51 is calculated for each site.
Step S62: calculating the fault probability value of the ith harmonic corresponding to each part of the train bearing:
Figure BDA0002971430110000224
wherein arctan (·) is an arctangent function.
The arctan function is used in this step to normalize the calculated values and map them between [0,1 ].
Step S63: calculating the weighted fault index of each part:
outer ring:
Figure BDA0002971430110000231
inner ring:
Figure BDA0002971430110000232
one-sided failure of the rolling body:
Figure BDA0002971430110000233
double-side failure of the rolling body:
Figure BDA0002971430110000234
the retainer touches the inner ring:
Figure BDA0002971430110000235
the retainer touches the outer ring:
Figure BDA0002971430110000236
wherein the content of the first and second substances,
Figure BDA0002971430110000237
FPjand
Figure BDA0002971430110000238
and calculating the failure probability values of the left frequency band, the main frequency band and the right frequency band respectively, wherein n is the number of calculated harmonics.
The calculation effect of the outer ring fault characteristic frequency narrow band shown in fig. 5 is that, as can be seen from the figure, the outer ring fault characteristic frequency has 5 clear harmonic amplitudes, in this example, the calculation frequency multiplication number is selected to be 3, the fault probabilities of other parts are calculated according to this similar manner, and the fault probabilities of the parts calculated according to the formula in S6 are shown in table 1:
TABLE 1
Type of failure FPouter FPinner FProll_S FProll_D FPcage_I FPcage_O
Probability of failure 0.6451 0.0434 0 0 0 0.0771
The step in S7 includes:
s71: calculating the median of all peaks of enhancement cycle index that exceed the threshold:
Figure BDA0002971430110000241
wherein if [ CS (alpha) ]i)＞t1-p]Selecting when the representation exceeds a threshold value, otherwise, not selecting, wherein medium {. is the median in the solved set;
s72: calculating a final judgment value:
T＝2arctan(MD-t1-p)/π
in this example, T is 0.2443 calculated from the above equation.
In this example, the maximum calculation length α of the enhancement cycle index is setimax600, the harmonic calculation number n is 3 and the significance level p is 0.01And executing the following operations according to the calculation result:
making a judgment based on the weighted failure index for each part calculated in step S6: when the weighted fault index FP of a certain position is more than or equal to T, H is rejected0Suppose that H is accepted1Supposing that the representative vibration signal x (t) contains fault information, the part in the train bearing is in fault, and the fault probability value FP of the part is outputj(ii) a When the weighted failure index FP < T of all the positions, H is accepted0It is assumed that the representative vibration signal x (t) does not contain fault information and the train bearings are not faulty.
According to the comparison of the data in table 1 with the judgment probability threshold T, only the outer ring failure probability exceeds the threshold, so that H is rejected under the condition that the significance level p is 0.010Suppose, H1It is assumed that the vibration signal x (t) includes failure information, and the output result is shown in table 2.
TABLE 2
Bearing condition Fault of
Location of failure Outer ring
Probability of failure 0.6451
The invention establishes the fault probability model of each part of the bearing based on the hypothesis test principle and the statistical characteristics of the circulating intensity index, and can effectively output the fault information of each part of the bearing in a probability manner in a quantitative manner. Compared with the existing method, the method has the advantages that the diagnosis result can automatically output the fault condition of the bearing part without artificial analysis, the method is more intelligent, the diagnosis result has interpretability in statistical sense, and the industrial production deployment is facilitated.
In summary, the embodiments of the present invention provide a train bearing autonomous fault identification method based on a cycle intensity index, which aims at the problem that the current vibration signal-based bearing fault diagnosis method still needs manual analysis and is not intelligent enough, and can calculate the cycle intensity index and an enhanced cycle index according to a vibration signal, calculate a weighted fault index of each part of a bearing from the enhanced cycle index based on a binary hypothesis model, compare the weighted fault index with a threshold, determine that a fault exists in a part exceeding the threshold, and automatically output a quantized value of the corresponding fault. The method can provide probability explanation for the diagnosis result without human participation in analysis, can be used as an autonomous diagnosis method to realize fault identification of the train rolling bearing, and is beneficial to improving industrial deployment efficiency and reducing operation and maintenance cost.
The method of the embodiment of the invention can automatically output the fault position and the fault probability of the bearing according to the acquired original vibration signal under the condition of setting the basic parameters of the bearing, and is convenient for the application of industrial production.
Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams in the figures are not necessarily required to practice the present invention.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (7)

1. A train bearing autonomous fault identification method based on a cyclic strength index is characterized by comprising the following steps:
step S1: acquiring a vibration signal of a train bearing through an acceleration sensor;
step S2, calculating the spectrum coherence of the vibration signal, calculating a cycle intensity index according to the spectrum coherence of the vibration signal, and normalizing the corresponding cycle intensity index according to the distribution characteristic of the spectrum frequency of the vibration signal;
step S3: setting a significance level according to a hypothesis testing principle, and establishing a binary hypothesis model;
step S4: integrating the normalized circulation intensity index on the optimal frequency band to obtain an enhanced circulation index, and calculating a fault judgment threshold according to a histogram of the enhanced circulation index;
step S5: calculating fault characteristic frequency of each part of a train bearing and a frequency doubling narrow band of the fault characteristic frequency;
step S6: calculating the fault probability value of each subharmonic according to the enhanced circulation index and the frequency doubling narrow band of the fault characteristic frequency of each part of the train bearing, and calculating the weighted fault index of each part according to the fault probability value of each subharmonic;
step S7: and calculating the median of the peak values of all the enhanced cyclic indexes exceeding the fault judgment threshold to obtain the judgment threshold of the binary hypothesis model, comparing the weighted fault indexes of all the parts with the judgment threshold of the binary hypothesis model, and determining whether faults exist in all the parts of the bearing according to the comparison result.
2. The method according to claim 1, wherein the step S2 specifically includes:
s21: setting a vibration signal at time t acquired by using an acceleration sensor as x (t), and calculating an autocorrelation function R of the vibration signal x (t) under the time t and a time delay taux(t,τ)：
Rx(t,τ)＝E{x(t)x(t-τ)*}
Wherein E represents a mathematical expectation operation and denotes a complex conjugate operation;
s22: calculating an autocorrelation function R of the vibration signal x (t)x(t, τ) spectrum corresponding to time delay τ:
Figure FDA0002971430100000011
wherein f iskRepresenting discretized spectral frequencies, fkK Δ f, Δ f being the spectral frequency resolution, FT representing the fourier transform;
s23, calculating the spectral dependence of the vibration signal x (t):
Figure FDA0002971430100000021
wherein, alpha is cycle frequency, T is time range, and j is imaginary unit;
s24, calculating the spectrum coherence of the vibration signal x (t):
Figure FDA0002971430100000022
s25 calculation of the frequency corresponding to the spectrum fkCyclic strength index C ofx(α；fk)：
Figure FDA0002971430100000023
S26: to cyclic strength index Cx(α；fk) Discretizing and according to the spectral frequency fkThe corresponding circulating intensity index is normalized:
Figure FDA0002971430100000024
wherein alpha isi＝iΔα，i＝0,1,2,…,αimax，αimaxFor the upper limit of the cycle frequency, Δ α is the cycle frequency resolution, MED (C)x(αi；fk) Is representative of corresponding to spectral frequency fkMoving median of the circulating intensity index of (A), MAD (C)x(αi；fk) Represents corresponds to a spectral frequency fkThe absolute deviation of the moving median of the cyclic intensity index.
3. The method according to claim 1, wherein the step S3 specifically includes: according to the hypothesis testing principle, the following binary hypothesis model is established:
Figure FDA0002971430100000025
at a significance level of p, values in the designed statistics that do not exceed 100% quantiles of histogram (1-p) are considered to accept H in the bivariate hypothesis model0Assume that values above 100% quantile in histogram (1-p) are considered to accept H in the bivariate hypothesis model1It is assumed.
4. The method of claim 1, wherein the step of S4 includes:
s41: integrating the normalized circulating intensity index in the optimal frequency range to obtain an enhanced circulating index which obeys stable distribution:
Figure FDA0002971430100000031
where l, h correspond to the lower and upper limits of the summation of the optimum spectral frequencies, respectively.
S42: calculating CS (. alpha.) (j) The histogram of (1-p) is taken as a threshold t of 100% quantiles1-p。
5. The method of claim 1, wherein the step of S5 includes:
s51: according to the characteristics of the train bearing, a narrow-band definition mode for calculating the fault characteristic frequency of the train bearing is as follows:
outer ring fault characteristic frequency doubling narrow band OBjComprises the following steps:
Figure FDA0002971430100000032
side frequency IB of inner ring fault characteristic frequencyjAnd narrow band where frequency multiplication is performed
Figure FDA0002971430100000033
And
Figure FDA0002971430100000034
comprises the following steps:
Figure FDA0002971430100000035
Figure FDA0002971430100000036
Figure FDA0002971430100000037
side frequency RB _ S of rolling element unilateral fault characteristic frequencyjAnd narrow band where frequency multiplication is performed
Figure FDA0002971430100000038
And
Figure FDA0002971430100000039
comprises the following steps:
Figure FDA00029714301000000310
Figure FDA00029714301000000311
Figure FDA0002971430100000041
side frequency RB _ D of rolling element bilateral fault characteristic frequencyjAnd narrow band where frequency multiplication is performed
Figure FDA0002971430100000042
And
Figure FDA0002971430100000043
comprises the following steps:
Figure FDA0002971430100000044
Figure FDA0002971430100000045
Figure FDA0002971430100000046
narrow band CB _ I where frequency multiplication of fault characteristic frequency of retainer inner collision ring is locatedjComprises the following steps:
Figure FDA0002971430100000047
narrow band CB _ O where frequency multiplication of fault characteristic frequency of retainer touch outer ring is locatedjComprises the following steps:
Figure FDA0002971430100000048
wherein j is the narrow band where the jth frequency multiplication is located, n is the number of calculated frequency multiplication, and alphaBPFO、αBPFI、αBSF_S、αBSF_D、αFTFIAnd alphaFTFOThe frequency is the fault characteristic frequency of an outer ring, an inner ring, a single end of a rolling body, double ends of the rolling body, an inner ring contacted by a retainer and an outer ring contacted by the retainer, a subscript 1 represents the frequency of a maximum value in a first narrow band, the frequency is used as a later harmonic calculation reference, and mu is an error coefficient and represents the deviation ratio of a real value and a theoretical value of the fault characteristic frequency of a bearing;
s52: the manner of calculating the failure characteristic frequency in the step S51 is as follows:
outer ring fault characteristic frequency:
Figure FDA0002971430100000049
inner ring fault characteristic frequency:
Figure FDA00029714301000000410
characteristic frequency of single-side fault of rolling body:
Figure FDA0002971430100000051
characteristic frequency of double-side fault of rolling body:
Figure FDA0002971430100000052
characteristic frequency of cage collision inner ring failure:
Figure FDA0002971430100000053
characteristic frequency of cage touch outer ring failure:
Figure FDA0002971430100000054
wherein n is the number of the rolling bodies, D is the diameter of the rolling bodies, D is the pitch diameter of the bearing, theta is the contact angle of the rolling bodies, frThe measured axis is frequency-converted.
6. The method of claim 1, wherein the step of S6 includes:
s61: calculating the maximum amplitude of the ith harmonic corresponding to each part of the train bearing in the narrow band:
Mj＝miax{CS(αi)},αi∈Bj
wherein max {. is the maximum value in the set, BjCalculating the narrow band corresponding to the fault characteristic frequency of each part in S51;
s62: calculating the fault probability value of the ith harmonic corresponding to each part of the train bearing:
Figure FDA0002971430100000055
wherein arctan (·) is an arctangent function.
S63: calculating the weighted fault index of each part of the train bearing:
outer ring:
Figure FDA0002971430100000056
inner ring:
Figure FDA0002971430100000061
one-sided failure of the rolling body:
Figure FDA0002971430100000062
double-side failure of the rolling body:
Figure FDA0002971430100000063
the retainer touches the inner ring:
Figure FDA0002971430100000064
the retainer touches the outer ring:
Figure FDA0002971430100000065
wherein the content of the first and second substances,
Figure FDA0002971430100000066
FPjand
Figure FDA0002971430100000067
and calculating the failure probability values of the left frequency band, the main frequency band and the right frequency band respectively, wherein n is the number of calculated harmonics.
7. The method of claim 1, wherein the step of S7 includes:
s71: calculating all exceeding thresholds t1-pPeak median of enhancement cycle index of (2):
MD＝median{CS(αi)},if[CS(αi)＞t1-p]
wherein if [ CS (alpha) ]i)＞t1-p]Indicating that the threshold t is exceeded1-pSelecting if the current value is greater than the preset value, or else, not selecting, wherein medium {. is the median in the set;
s72: calculating a judgment threshold T of the binary hypothesis model:
T＝2arctan(MD-t1-p)/π
and S73, judging according to the weighted fault indexes of the parts calculated in the step S6: when the weighted fault index FP of a certain position is larger than or equal to T, H is rejected0Suppose that H is accepted1Supposing that the vibration signal x (t) contains fault information, the part in the train bearing is in fault, and the fault probability value FP of the part is outputj: when the weighted failure index FP < T of all the positions, H is accepted0If the vibration signal x (t) does not contain fault information, the train bearing is not in fault.
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