阅读说明：本技术 一种基于包络谱故障特征识别的最优滤波频带选择方法 (Optimal filtering frequency band selection method based on envelope spectrum fault feature identification ) 是由 刘全利 康强 张元庆 于 2021-07-28 设计创作，主要内容包括：本发明提供了一种基于包络谱故障特征识别的最优滤波频带选择方法,包括以下步骤：步骤一：设定带宽Bw和步长Step；步骤二：频带划分,根据设定的Bw和Step对原始信号频带进行划分,得到N个子频带,在N个子频带上对信号进行滤波,得到N个子信号；步骤三：计算每一个子信号的包络谱,并使用故障特征识别方法对每一个包络谱进行分析,计算每一个包络谱的故障特征评价指标Val,选择Val值最大的包络谱对应子信号所在频带作为最优滤波频带。本发明通过对包络谱故障特征的识别,提出了一种基于包络谱故障特征识别的最优滤波频带选择方法,使其在信号中存在不同类型的噪声干扰时,依然能够选择正确的滤波频带。(The invention provides an optimal filtering frequency band selection method based on envelope spectrum fault feature identification, which comprises the following steps of: the method comprises the following steps: setting a bandwidth Bw and a Step length Step; step two: dividing the frequency band of an original signal according to set Bw and Step to obtain N sub-frequency bands, and filtering the signal on the N sub-frequency bands to obtain N sub-signals; step three: calculating the envelope spectrum of each sub-signal, analyzing each envelope spectrum by using a fault feature identification method, calculating a fault feature evaluation index Val of each envelope spectrum, and selecting the frequency band of the sub-signal corresponding to the envelope spectrum with the maximum Val value as an optimal filtering frequency band. The invention provides an optimal filtering frequency band selection method based on envelope spectrum fault feature identification through identification of envelope spectrum fault features, so that the correct filtering frequency band can be still selected when different types of noise interference exist in signals.)

1. An optimal filtering frequency band selection method based on envelope spectrum fault feature identification is characterized in that: the method comprises the following steps:

the method comprises the following steps: setting a bandwidth Bw and a Step length Step; wherein Bw is set as 3 to 5 times of fault characteristic frequency, Step needs to be larger than the frequency resolution of the signal and smaller than the set bandwidth Bw;

step two: dividing the frequency band of an original signal according to set Bw and Step to obtain N sub-frequency bands, and filtering the signal on the N sub-frequency bands to obtain N sub-signals;

step three: calculating the envelope spectrum of each sub-signal, analyzing each envelope spectrum by using a fault feature identification method, calculating a fault feature evaluation index Val of each envelope spectrum, and selecting the frequency band of the sub-signal corresponding to the envelope spectrum with the maximum Val value as an optimal filtering frequency band.

2. The optimal filtering band selection method based on envelope spectrum fault feature identification according to claim 1, wherein: the fault feature identification method comprises the following steps:

the method comprises the following steps: calculating a fault characteristic evaluation rate;

step two: initializing n to 1, Val to 0, and setting a search broadband and an error rate;

step three: the target frequency is equal to the fault characteristic frequency multiplied by n;

step four: searching a maximum value;

step five: judging whether the corresponding frequency is within an allowable error range; if yes, entering a sixth step; if not, directly outputting Val;

step six: searching the second largest value;

step seven: calculating the ratio Pn of the maximum value to the second maximum value;

step eight: judging whether P is larger than or equal to a critical value C, if so, entering a ninth step, and if not, directly outputting Val;

step nine: val is Val + Pn;

step ten: if n is 3, entering the step eleven; if not, returning to the step three after n is n + 1;

step eleven: and outputting the Val.

3. The optimal filtering band selection method based on envelope spectrum fault feature identification according to claim 2, wherein: and the target frequency in the third step is 1-3 frequency multiplication of the bearing fault characteristic frequency.

4. The optimal filtering band selection method based on envelope spectrum fault feature identification according to claim 2, wherein: the Val is used for evaluating the significance degree of fault features in the envelope spectrum;

Val＝P₁+P₂+P₃；

wherein P is₁、P₂、P₃Respectively representing the ratio of the amplitude at the first frequency multiplication, the second frequency multiplication and the third frequency multiplication of the bearing fault characteristic frequency to the second maximum value of the amplitude in a certain range of frequency bands nearby, i.e. P_i＝A_i1/A_i2，A_i1Amplitude at fault characteristic frequency or multiples thereof, A_i2The value is the second largest value of the amplitude in a certain range of frequency bands near the fault characteristic frequency or the frequency multiplication of the fault characteristic frequency, wherein i is 1, 2 and 3.

5. The optimal filtering band selection method based on envelope spectrum fault feature identification according to claim 4, wherein: in the process of A_i1And A_i2In the search of (3), in order to prevent the influence of a peak in the envelope spectrum, which is not related to the bearing failure characteristics, the search is not performed in the global range, but the search range is concentrated on the target frequency f_tarWithin a certain range nearby, the target frequency is the characteristic frequency f of the bearing fault_tault1 to 3 frequency doubling; defining W as the search bandwidth, setting the search bandwidth range to

6. The optimal filtering band selection method based on envelope spectrum fault feature identification according to claim 5, wherein: the search bandwidth is 50 Hz.

7. The optimal filtering band selection method based on envelope spectrum fault feature identification according to claim 5, wherein:

(1) when f is_tarSmaller, lower bound f of the search band may occur_tar-w/2 < 0, therefore, the size relationship between the lower search boundary and 0 needs to be determined during each search, and the lower search boundary is Max (0, f)_tar-w/2)；

(2) The search band cannot contain a multiple of the frequency of the fault signature, which may result in a second largest value A_i2Selecting amplitude at the fault frequency doubling position; therefore, the upper bound of the search range is taken asα is the error rate.

8. The optimal filtering band selection method based on envelope spectrum fault feature identification according to claim 5, wherein: after the search frequency band is determined, the spectral line with the maximum amplitude in the frequency band range is searched, and the amplitude corresponding to the spectral line is A_i1Assume that this line corresponds to a frequency ofWhen in useSatisfy the requirement ofWhen it is, the searched amplitude A is considered_i1The amplitude at the fault signature frequency is represented, where α is the allowable error rate and α is 0.05.

Technical Field

The invention relates to the field of fault diagnosis methods of rolling bearings, in particular to an optimal filtering frequency band selection method based on envelope spectrum fault feature identification in fault diagnosis of rolling bearings.

Background

The resonance demodulation is an effective method in the fault diagnosis of the rolling bearing, the key point is the determination of the parameters of the band-pass filter, the traditional method selects the filtering frequency band according to the experience and historical data of an operator, the efficiency is low, and the current engineering requirements cannot be met. For this reason, many band selection methods are proposed one after another and have a good effect in bearing failure diagnosis, among which fast spectral kurtosis (FK) and proturbram are the most classical two, but are susceptible to give erroneous band selection results when non-gaussian noise or cyclostationary noise unrelated to bearing failure characteristics is present in the signal.

FK takes the kurtosis value of the filtered time-domain signal as an evaluation index of the filtering effect, but the kurtosis value is easily affected by non-gaussian noise and impulsive noise in the signal, so that FK gives an incorrect filtering frequency band. The method is characterized in that an envelope spectrum kurtosis value of a filtered signal is used as an evaluation index of a filtering effect of the Protrugram, and the envelope spectrum kurtosis value reflects the strength of the signal cycle stability, so that the Protrugram is easily influenced by the cycle stability vibration noise irrelevant to the bearing fault characteristics in the signal. The bearings on the train are not usually used independently, but are integrated in mechanical systems such as a gear box, a motor or an axle box, and other cyclostationary vibrations can be included in the collected bearing vibration signals, and the cyclostationary vibrations which are not related to the bearing fault characteristics can cause FK and Protrugram to select wrong filter frequency bands to a certain extent, so that the bearing fault diagnosis is failed.

Disclosure of Invention

The invention aims to obtain better diagnosis effect in the fault diagnosis of the bearing of the train running part by using the resonance demodulation technology, and aims at two classical frequency band selection methods: the invention provides an optimal filtering frequency band selection method based on envelope spectrum fault feature identification through identifying envelope spectrum fault features, so that when different types of noise interference exist in signals, correct filtering frequency bands can still be selected.

In order to achieve the above purpose, the invention provides the following technical scheme:

an optimal filtering frequency band selection method based on envelope spectrum fault feature identification comprises the following steps:

the method comprises the following steps: setting a bandwidth Bw and a Step length Step; wherein Bw is set as 3 to 5 times of fault characteristic frequency, Step needs to be larger than the frequency resolution of the signal and smaller than the set bandwidth Bw;

step two: dividing the frequency band of an original signal according to set Bw and Step to obtain N sub-frequency bands, and filtering the signal on the N sub-frequency bands to obtain N sub-signals;

step three: calculating the envelope spectrum of each sub-signal, analyzing each envelope spectrum by using a fault feature identification method, calculating a fault feature evaluation index Val of each envelope spectrum, and selecting the frequency band of the sub-signal corresponding to the envelope spectrum with the maximum Val value as an optimal filtering frequency band.

Further, the fault feature identification method comprises the following steps:

the method comprises the following steps: calculating a fault characteristic evaluation rate; step two: initializing n to 1, Val to 0, and setting a search broadband and an error rate; step three: the target frequency is equal to the fault characteristic frequency multiplied by n; step four: searching a maximum value; step five: judging whether the corresponding frequency is within an allowable error range; if yes, entering a sixth step; if not, directly outputting Val; step six: searching the second largest value; step seven: calculating the ratio Pn of the maximum value to the second maximum value; step eight: judging whether P is larger than or equal to a critical value C, if so, entering a ninth step, and if not, directly outputting Val; step nine: val is Val + Pn; step ten: if n is 3, entering the step eleven; if not, returning to the step three after n is n + 1; step eleven: and outputting the Val.

Further, the target frequency in the third step is 1-3 frequency multiplication of the bearing fault characteristic frequency.

Further, the Val is used for evaluating the obvious range of fault characteristics in the envelope spectrumDegree; val ═ P₁+P₂+P₃(ii) a Wherein P is₁、P₂、P₃Respectively representing the ratio of the amplitude at the first frequency multiplication, the second frequency multiplication and the third frequency multiplication of the bearing fault characteristic frequency to the second maximum value of the amplitude in a certain range of frequency bands nearby, i.e. P_i＝A_i1/A_i2，A_i1Amplitude at fault characteristic frequency or multiples thereof, A_i2The value is the second largest value of the amplitude in a certain range of frequency bands near the fault characteristic frequency or the frequency multiplication of the fault characteristic frequency, wherein i is 1, 2 and 3.

Further, in carrying out A_i1And A_i2In the search of (3), in order to prevent the influence of a peak in the envelope spectrum, which is not related to the bearing failure characteristics, the search is not performed in the global range, but the search range is concentrated on the target frequency f_tarWithin a certain range nearby, the target frequency is the characteristic frequency f of the bearing fault_tault1 to 3 frequency doubling; defining W as the search bandwidth, setting the search bandwidth range to

Further, the search bandwidth is 50 Hz.

Further, (1) when f_tarSmaller, lower bound f of the search band may occur_tar-w/2 < 0, therefore, the size relationship between the lower search boundary and 0 needs to be determined during each search, and the lower search boundary is Max (0, f)_tar-w/2); (2) the search band cannot contain a multiple of the frequency of the fault signature, which may result in a second largest value A_i2Selecting amplitude at the fault frequency doubling position; therefore, the upper bound of the search range is taken asα is the error rate.

Further, after the search frequency band is determined, the spectral line with the maximum amplitude in the frequency band range is searched, and the amplitude corresponding to the spectral line is A_i1Assume that this line corresponds to a frequency ofWhen in useSatisfy the requirement ofWhen it is, the searched amplitude A is considered_i1The amplitude at the fault signature frequency is represented, where α is the allowable error rate and α is 0.05.

The invention has the beneficial effects that:

the frequency band division method can be divided into N sub-frequency bands, the envelope spectrum of the signal on each sub-frequency band is calculated, each envelope spectrum is analyzed by using a fault characteristic identification method, the envelope spectrum which displays the clearest fault characteristic of the bearing is found, and the frequency band of the sub-signal corresponding to the envelope spectrum is the optimal filtering frequency band. The pulse noise does not have the cycle stability, so that a spectrum peak is basically not generated in an envelope spectrum, the characteristic frequency of the cycle stability noise irrelevant to the bearing fault characteristic is different from the bearing fault characteristic frequency, and the position of the spectrum peak generated in the envelope spectrum is different from the position of the spectrum peak reflecting the bearing fault characteristic, so that the interference of the pulse noise in a signal and the cycle stability noise irrelevant to the bearing fault characteristic can be eliminated to the maximum extent by identifying the fault characteristic of the envelope spectrum.

Drawings

FIG. 1 is a block diagram of the band division method of the present invention;

FIG. 2 is a spectral plot of the characteristic frequency of a fault of the present invention;

FIG. 3 is an amplitude plot of the fault signature frequency of the present invention;

FIG. 4 is a graph of the amplitude of the corresponding spectral peak for the present invention when P is 1.3; FIG. 5 is a graph of the amplitude of the corresponding spectral peak for the present invention when P is 1.5;

FIG. 6 is a flow chart of a fault signature identification method of the present invention;

FIG. 7 is a flow chart of the optimal filtering band selection method of the present invention;

FIG. 8 is a graph of a bearing fault simulation signal of the present invention;

FIGS. 9 to 14 are graphs showing the results of analysis of the original signal by FK, Protrugram and modified methods according to the present invention;

fig. 15 is a time domain waveform diagram of the signal y (t) generated when k is 5 according to the present invention;

FIGS. 16 through 21 are graphs showing the results of analysis of FK, Protrugram and modified methods of the present invention under impulse noise;

FIG. 22 is a time domain waveform of the composite fault vibration signal of the present invention;

fig. 23 to 27 are graphs showing the filtering frequency band selection and processing results of the composite fault vibration signal according to the present invention using FK, protraugram and modified algorithm, respectively;

FIG. 28 is a diagram of the processing result of the present invention using FK, Protrugram and modified methods to select the filtering frequency band for the composite fault vibration signal;

FIG. 29 is a table of analysis of the effect of filtering band selection for the three methods of the present invention.

Detailed Description

An optimal filtering frequency band selection method based on envelope spectrum fault feature identification comprises the following steps:

the method comprises the following steps: setting a bandwidth Bw and a Step length Step; wherein Bw is set as 3 to 5 times of fault characteristic frequency, Step needs to be larger than the frequency resolution of the signal and smaller than the set bandwidth Bw;

step two: dividing the frequency band of an original signal according to set Bw and Step to obtain N sub-frequency bands, and filtering the signal on the N sub-frequency bands to obtain N sub-signals;

when dividing, referring to a Protrugram method, dividing the frequency band of an original signal by a fixed bandwidth Bw and an iteration Step length, so that the center frequency cf of each sub-frequency band_iComprises the following steps:

wherein i is 1, 2, …, N, and N is not more than (f)_s-2Bw)/(2Step) maximum integer. Using the above band division method, the original signal is divided into N sub-bands, corresponding to NSub-signals, as shown in fig. 1.

Step three: calculating the envelope spectrum of each sub-signal, analyzing each envelope spectrum by using a fault feature identification method, calculating a fault feature evaluation index Val of each envelope spectrum, and selecting the frequency band of the sub-signal corresponding to the envelope spectrum with the maximum Val value as an optimal filtering frequency band.

The optimal filter band can be understood as: after the original signal is filtered on the frequency band, the most obvious bearing fault characteristics can be observed in the envelope spectrum of the filtered signal, namely the envelope spectrum has the characteristics of clear fault frequency spectral line and obvious attenuation of frequency doubling components. Considering that the fault characteristic frequency is known information when fault diagnosis is performed on the bearing, the envelope spectrums of N sub-signals obtained after the original signal is subjected to frequency band division are respectively calculated, and the envelope spectrum which reflects the fault characteristic of the bearing is most obvious is found out, so that the frequency band of the sub-signal corresponding to the envelope spectrum is the optimal filtering frequency band. The intelligent fault feature identification method considering artificial neural network and the like needs fault training samples, has low identification accuracy and the like, and is difficult to popularize in engineering application.

The invention provides an envelope spectrum fault feature identification method, which is different from an artificial neural network method, and is characterized in that a computer is used for simulating human eyes to observe an envelope spectrum, the bearing fault feature frequency and the projection degree of spectral lines at a first frequency multiplication and a second frequency multiplication are judged, and the more the spectral line at the fault feature frequency is projected, the clearer the bearing fault feature reflected by the envelope spectrum is, so that the envelope spectrum capable of observing the most obvious bearing fault feature is searched.

Firstly, defining an index Val for evaluating the significance degree of fault characteristics in an envelope spectrum;

Val＝P₁+P₂+P₃；

wherein P is₁、P₂、P₃Respectively representing the ratio of the amplitude at the first frequency multiplication, the second frequency multiplication and the third frequency multiplication of the bearing fault characteristic frequency to the second maximum value of the amplitude in a certain range of frequency bands nearby, i.e. P_i＝A_i1/A_i2，A_i1Characteristic frequency for faultOr amplitude at multiple frequency thereof, A_i2The value is the second largest value of the amplitude in a certain range of frequency bands near the fault characteristic frequency or the frequency multiplication of the fault characteristic frequency, wherein i is 1, 2 and 3.

In the process of A_i1And A_i2In the search of (3), in order to prevent the influence of a peak in the envelope spectrum, which is not related to the bearing failure characteristics, the search is not performed in the global range, but the search range is concentrated on the target frequency f_tarWithin a certain range nearby, the target frequency is the characteristic frequency f of the bearing fault_fault1 to 3 frequency doubling; defining W as the search bandwidth, setting the search bandwidth range to

The larger the search bandwidth is obtained, the more obvious the fault characteristics in the envelope spectrum are, and the text is obtained

The search bandwidth is 50 Hz. Two points of attention are needed for the upper and lower bounds of the search band range:

(1) when f is_tarSmaller, lower bound f of the search band may occur_tar-w/2 < 0, therefore, the size relationship between the lower search boundary and 0 needs to be determined during each search, and the lower search boundary is Max (0, f)_tar-w/2)；

(2) The search band cannot contain a multiple of the frequency of the fault signature, which may result in a second largest value A_i2Selecting amplitude at the fault frequency doubling position; therefore, the upper bound of the search range is taken asα is the error rate.

After the search frequency band is determined, the spectral line with the maximum amplitude in the frequency band range is searched, and the amplitude corresponding to the spectral line is A_i1Assume that this line corresponds to a frequency ofWhen in useSatisfy the requirement ofWhen it is, the searched amplitude A is considered_i1The amplitude at the fault characteristic frequency is represented, wherein alpha is an allowable error rate, the setting of the error rate needs to be determined by referring to the size error value, the signal frequency resolution, and historical operating conditions such as the running time and the operating environment of the bearing, and the like given in a bearing parameter manual, and alpha in the embodiment is 0.05.

When in useSatisfy the formulaThen, search A is continued_i2The value of (c). Otherwise, the clear target frequency component spectral line can not be observed in the envelope spectrum, and the P is recorded_iAnd stop the search at 0. Since the fault impact signal under actual conditions is not a strictly periodic signal and is influenced by the frequency resolution, A_i1The spectral lines do not consist of a single point. As shown in FIG. 2, for the three points marked in the box, they are also located at A_i1On the spectral line, searching for the second largest value A_i2They need to be avoided when necessary, otherwise the determination of the fault signature is affected. According to experimental verification, search A_i2While can be ignored2 points on the left and right sides.

When searching to A_i1And A_i2After the value of (A), P can be calculated_iThe value of (c).

Respectively using the first frequency doubling, the second frequency doubling and the third frequency doubling of the fault characteristic frequency as target frequencies, and respectively obtaining P according to the method₁、P₂、P₃. In addition, as shown in fig. 3, even if the amplitude at the fault signature frequency is a local maximum, this envelope spectrum does not reflect the fault signature. Therefore, a threshold C is defined, only if P_iIs greater than a critical value, thenP_i+1Otherwise P will be_iAnd P_i+1Are all recorded as zero (i + j is less than or equal to 3). The setting of the critical value determines the protrusion degree of the spectral line at the fault characteristic frequency, and the size of the critical value is in positive correlation with the protrusion degree of the spectral line. As shown in fig. 4 and 5, the corresponding peaks when P is 1.3 and P is 1.5, it can be seen that the peaks are already quite obvious when P is 1.5, so the present invention sets the critical value C to 1.5, and specifies that when the P value is greater than the critical value C, the P value is the original value, and when the P value is less than the critical value C, it is considered that no bearing fault feature is extracted from the envelope spectrum, and P is recorded as zero, so that the calculation resources can be saved, and the calculation efficiency can be improved.

Therefore, after two spectral lines with the maximum amplitude and the second largest amplitude are searched, whether the fault characteristics are extracted from the envelope spectrum or not is judged to simultaneously satisfy the following two principles:

(1) the difference between the frequency of the spectral line where the maximum value is located and the theoretical fault characteristic frequency meets the set error rate.

(2) The ratio P of the maximum value to the second maximum value is greater than or equal to a set critical value C.

The fault characteristic identification method provided by the invention not only considers the definition degree of the spectral line at the fault characteristic frequency, but also considers the spectral lines corresponding to the second frequency multiplication and the third frequency multiplication. Because for the most clear envelope spectrum reflecting the bearing fault characteristics, not only can obvious protrusions be seen at the fault characteristic frequency, but also obvious protrusions can be seen at the second frequency and the third frequency of the fault characteristic frequency. Thus, P is obtained by calculation₁Then, the frequency doubling and frequency tripling of the fault characteristic frequency are taken as target frequencies, and P is obtained by calculation respectively₂And P₃. Although there are cases where the amplitude of the higher harmonics of the fault vibration signal may have been attenuated to less than or equal to the background noise, so that P₂Or P₃Is smaller or even smaller than a set critical value, however, the purpose of this step is to select an envelope spectrum, P, from the envelope spectra from which the fault features have been extracted, in which the fault features are more pronounced₂And P₃For assisting selection, not by P₂And P₃To determine whether bearing fault signatures are extracted in the envelope spectrum. In summary,the flow chart of the fault feature identification method provided by the invention is shown in fig. 6.

The fault feature identification method comprises the following steps:

the method comprises the following steps: calculating a fault characteristic evaluation rate;

step two: initializing n to 1, Val to 0, and setting a search broadband and an error rate;

step three: the target frequency is equal to the fault characteristic frequency multiplied by n;

step four: searching a maximum value;

step five: judging whether the corresponding frequency is within an allowable error range; if yes, entering a sixth step; if not, directly outputting Val;

step six: searching the second largest value;

step seven: calculating the ratio Pn of the maximum value to the second maximum value;

step eight: judging whether P is larger than or equal to a critical value C, if so, entering a ninth step, and if not, directly outputting Val;

step nine: val is Val + Pn;

step ten: if n is 3, entering the step eleven; if not, returning to the step three after n is n + 1;

step eleven: and outputting the Val.

Further, the target frequency in the third step is 1-3 frequency multiplication of the bearing fault characteristic frequency.

The frequency band division method can be divided into N sub-frequency bands, the envelope spectrum of the signal on each sub-frequency band is calculated, each envelope spectrum is analyzed by using a fault characteristic identification method, the envelope spectrum which displays the clearest fault characteristic of the bearing is found, and the frequency band of the sub-signal corresponding to the envelope spectrum is the optimal filtering frequency band. The pulse noise does not have the cycle stability, so that a spectrum peak is basically not generated in an envelope spectrum, the characteristic frequency of the cycle stability noise irrelevant to the bearing fault characteristic is different from the bearing fault characteristic frequency, and the position of the spectrum peak generated in the envelope spectrum is different from the position of the spectrum peak reflecting the bearing fault characteristic, so that the interference of the pulse noise in a signal and the cycle stability noise irrelevant to the bearing fault characteristic can be eliminated to the maximum extent by identifying the fault characteristic of the envelope spectrum.

Simulation verification

In order to verify the effectiveness of the optimal filtering frequency band selection method provided by the invention, a bearing fault simulation signal is established, and pulse noise with different degrees and circular stationary noise irrelevant to the bearing fault characteristics are added into the simulation signal. The comparison with two classical frequency band selection methods FK and Protrugram shows that the method provided by the invention has the advantages of filtering frequency band selection under different degrees and different types of noise interference.

Setting a simulation model and parameters;

establishing a bearing fault signal:

X(t)＝e^-βTsin(2πf_nt)+n(t)

wherein:

T＝mod(t，1/f_fault)

in the formula: β is 800, exponential frequency: f. of_fault125Hz, bearing fault characteristic frequency f_n4000Hz, the system resonance frequency caused by bearing fault impact; n (t) is added white noise, and the signal-to-noise ratio of the signal is-8 dB. Sampling frequency f of signal_s25KHz, the sampling time is 1 second.

The simulation signal does not contain shaft frequency interference, gear meshing frequency interference or other low-frequency interference vibration which may exist in the actual signal, because the low-frequency interference can be effectively removed after the noise reduction method provided by the third chapter, and the selection of the demodulation frequency band is not influenced. This section mainly considers the influence of dither noise, which cannot be removed by the noise reduction method proposed in chapter iii, on the selection of the optimal demodulation frequency band. And generating a bearing fault simulation signal according to the parameters, wherein a time domain oscillogram of the bearing fault simulation signal is shown in FIG. 8.

Original signal simulation results and analysis

The original signal was first analyzed using FK, protugram and modified methods, the results of which are shown in fig. 9 to 14. Wherein the filter bandwidth of the proturbram and the improved method is set to 450Hz, which is about 3.5 times the fault signature frequency.

As can be seen from fig. 9 to 14, FK gives a demodulation band having a center frequency of 3906.25Hz and a bandwidth of 520.8Hz (noted as [3906 Hz; 520.8Hz ], which are hereinafter recorded in this form). The demodulation frequency bands given by the Protrugram and the improved method are [4025 Hz; 450Hz and [4000 Hz; 450Hz ]. It can be seen that when the vibration signal of the bearing fault does not contain impulse noise or cyclostationary noise, the filter frequency bands given by the three methods all contain the preset system resonance frequency of 4000Hz, and obvious characteristic frequency of the bearing fault and frequency multiplication components thereof can be observed from the envelope spectrum of the sub-signals on the given filter frequency bands, so that the bearing fault is successfully treated

Failure is diagnosed

The simulation result under the pulse noise and the analysis of the welding seam on the track can cause the pulse noise [32] in the vibration signal of the bearing of the train running part, and the frequency band selection method needs to have good resistance to the pulse noise so as to ensure that the accurate filtering frequency band can be selected in the actual engineering. In the section, random impulse noise with different degrees is added into an original signal, and the resistance of three frequency band selection methods to the impulse noise is compared. Now, the signal obtained by adding impulse noise to the bearing fault simulation signal x (t) is set to y (t).

y(t)＝x(t)+∑_iA_KX_i(t)

Wherein, X_i(t) is a random pulse, and the high-frequency damping vibration is set to have an exponential frequency of 800 and a natural frequency of 10000 Hz. A. the_KTo randomize the amplitude of the pulses, a uniform distribution of 1 to k is obeyed, and different degrees of impulse noise can be simulated by setting different values of k.

Fig. 15 shows a time domain waveform diagram of the generated signal y (t) when k is 5. The FK, protugram and the improved method are used to select the filtering band of the signal mixed with the impulse noise, and the processing results are shown in fig. 16 to fig. 21. Wherein the demodulation bandwidth of the proturbram and the improved method is set to 450Hz, which is about 3.5 times the fault signature frequency.

As can be seen from fig. 16 to 21, FK gives a filter band of [9895.8 Hz; 1041.7Hz ], has deviated significantly from the set resonance frequency of 4000Hz, and no significant bearing fault characteristic frequency component is observed from the envelope spectrum of the sub-signal in the FK given frequency band, failing to complete the fault diagnosis of the bearing. From simulation results, FK is very susceptible to interference from impulsive noise in the signal. The demodulation frequency bands given by the Protrugram and the improved method are [4025 Hz; 450Hz and [4000 Hz; 450Hz ], and obvious bearing fault characteristic frequency and frequency multiplication components thereof can be observed from the envelope spectrum of the sub-signals on the corresponding frequency band, and the bearing fault is successfully diagnosed.

Simulation results and analysis under cyclostationary noise

Rolling bearings in a train running section are not independent but integrated in systems such as a gear box, an axle box, and a motor, and other components in these systems also generate vibrations. In the early stages of bearing failure, the energy of some cyclostationary vibrations unrelated to bearing failure may exceed the energy of bearing failure vibrations [28], which may affect the filtering band selection method, making it impossible to accurately select the frequency band in which the bearing failure vibration signal is located.

The gear box is an important component of a transmission system of a train running gear, mainly comprises gears, bearings and shafts, and can generate impact vibration with high energy and cause resonance of the gears or the gear box system when the gears in the gear box break teeth. The section simulates the condition that the gear tooth breakage fault and the bearing early fault occur in the gear box at the same time through the simulation signal to check whether the optimal filtering frequency band selection method provided by the section can select the frequency band of the bearing fault vibration signal under the interference of the gear fault vibration signal, and the frequency band selection method is compared with two classical frequency band selection methods. Setting a gear broken tooth vibration signal x added into a bearing fault vibration signal x (t)_cThe composite fault vibration signal after (t) is z (t), namely:

Z(t)＝x(t)+n×x_c(t)

wherein the gear tooth breaking vibration signal x_cThe form of (t) is exactly the same as x (t), assuming that the rotation frequency of the shaft of the gear with broken teeth is 1800r/min, the system resonance frequency caused by the gear fault impact is 8000Hz, and no additional Gaussian noise is introduced by the gear fault. Therefore, let T be mod (m)t,1/30)、f_n8000Hz and n (t) 0. The impact vibration amplitude caused by the broken gear fault of the gear can be simulated by setting the value of n.

Considering that gear tooth breakage is a serious fault, the amplitude of the impact generated by the gear tooth breakage is far greater than that generated by the early fault of the bearing, so that the time domain waveform diagram of the composite fault vibration signal z (t) is shown in fig. 22, and the tooth breakage fault vibration signal is dominant in the diagram.

The FK, protugram and the improved method are used to select the filtering frequency band for the composite fault vibration signal, and the processing results are shown in fig. 23 to fig. 28. Wherein the demodulation bandwidth of the proturbram and the improved method is set to 450Hz, which is about 3.5 times the fault signature frequency.

As can be seen from fig. 23 to 28, FK gives a filter band of [11458.3 Hz; 2083.3Hz ], protugram gives a filter band of [8225 Hz; 450Hz ], both methods give a frequency band that has deviated significantly from the set resonance frequency of 4000Hz due to bearing fault vibration. And only the characteristic frequency of the broken gear fault of the gear and frequency multiplication components of the broken gear fault can be seen from the envelope spectrums of the sub signals on the filtering frequency band given by the two methods. This indicates that FK and protugram are susceptible to cyclostationary vibration in the signal that is not related to bearing failure characteristics and does not give the desired filtering band. The filtering frequency band given by the improved method is [3900 Hz; 450Hz ], and obvious bearing fault characteristic frequency and frequency multiplication components thereof can be seen in the envelope spectrum of the sub-signals on a given frequency band, so that the bearing fault is successfully diagnosed. Therefore, when a system where the bearing is located has a combined fault, the FK or Protrugram is used for selecting a filtering frequency band to only detect the broken gear fault of the gear, and the improved method provided by the invention can detect the early fault of the bearing under the strong fault interference of the broken gear of the gear. In addition, the fault characteristic frequency in the frequency band selection method provided by the invention is set as the gear fault characteristic frequency, so that the frequency band where the resonance signal is located caused by the gear fault impact vibration can be searched, and the method has strong engineering application value.

Through the simulation analysis, the improved method has strong resistance to both impulsive noise interference and cyclostationary noise interference existing in the signal compared with FK and Protrugram. The effect of selecting the filtering frequency band when impulse noise interference and cyclostationary noise interference exist in the signal by the three methods is summarized as shown in fig. 29.

The invention aims at key steps in a resonance demodulation method: the selection of the filter band was studied. The principle and the existing defects of FK and Protregmam of two classical frequency band selection methods are firstly analyzed. During the selection of the frequency band, the method is susceptible to interference from impulse noise and cyclostationary noise in the signal. In order to solve the problem, a new evaluation index for the envelope spectrum of the filtered signal is provided, and only the pattern characteristics near the fault characteristic frequency are considered. An improved band selection method is proposed with reference to the narrow bandwidth filtering principle. The simulation signal verifies that the improved method can accurately indicate the optimal demodulation center frequency after different impulse noise and cyclostationary noise are added into the signal. Compared with FK and Protrugram methods, the method has stronger anti-interference capability.

The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.