CN114218979A - Method for constructing weighted joint lifting envelope spectrum based on local features of spectral coherence - Google Patents

Method for constructing weighted joint lifting envelope spectrum based on local features of spectral coherence Download PDF

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CN114218979A
CN114218979A CN202111363661.7A CN202111363661A CN114218979A CN 114218979 A CN114218979 A CN 114218979A CN 202111363661 A CN202111363661 A CN 202111363661A CN 114218979 A CN114218979 A CN 114218979A
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程尧
张凡
陈丙炎
张卫华
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Abstract

The invention discloses a method for constructing a weighted joint lifting envelope spectrum based on local features of spectral coherence, which specifically comprises the following steps: calculating the spectral coherence of the actually measured signal; identifying a bearing candidate fault frequency based on the spectral coherent local features; dividing spectrum coherent spectrum frequency bands by using 1/3-binary tree, and quantizing fault information of each spectrum frequency narrow band by using the identified candidate fault frequency; and constructing a weighted combined lifting envelope spectrum WCIES, selecting a narrow-band lifting envelope spectrum IES with diagnosis information in each decomposition layer, constructing a combined lifting envelope spectrum CIES, and then carrying out weighted average on the CIES to obtain the WCIES. The method has the advantages that the bearing fault information distributed in different narrow bands can be fully integrated, and the method does not depend on the nominal fault period information; the method can effectively extract the local defect fault characteristic information of the rotary machine, and can be used for early fault diagnosis of the rotary machine.

Description

Method for constructing weighted joint lifting envelope spectrum based on local features of spectral coherence
Technical Field
The invention belongs to the field of health monitoring of rotating machinery structures, and particularly relates to a method for building weighted combined lifting envelope spectrum based on local features of spectrum coherence.
Background
Rolling bearings are one of the key precision mechanical parts of rotary machines, which are susceptible to axial loads, radial loads, impact loads and various external excitations under severe working conditions, with the risk of inducing structural fatigue damage internally. Failure to implement an appropriate maintenance strategy in a timely manner can easily cause failure of the mechanical system, potentially resulting in significant economic loss. Therefore, early failure detection of rolling bearings is essential to ensure safety and reliability of the railway vehicle.
The local damage region periodically passes through the bearing carrying area to excite a series of transient impacts, which are expressed as second-order cyclostationary characteristics in the vibration signal. The spectrum coherent energy can map the vibration signal to a two-dimensional frequency-frequency domain consisting of a frequency spectrum frequency and a cycle frequency, and is a typical method for revealing the second-order cyclostationary feature of the vibration signal of the rotating machine. The method for identifying the bearing fault is an effective method for identifying the bearing fault based on the full-spectrum frequency band information, but is easily polluted by broadband noise, in this case, the narrow-band frequency spectrum narrow band containing fault information is identified, and then the method for constructing the spectrum analysis tool is the key for diagnosing the weak fault of the bearing. Wang et al screens a spectrum band with a fixed bandwidth based on a maximized L2/L1 norm, generates a lifting envelope spectrum for normal coherent mode integration in a narrow-band spectrum band, and realizes fault identification of a rolling bearing (WANG Dong, ZHAO Xuejun, KOU Lin-Lin, et al. evaluation and fast identification for generating enhanced/square enhanced spectrum from spectral coherence for detecting fault diagnosis [ J ]. Mechanical Systems and Signal Processing,2019,122: 754-. Mauricio et al propose IESFOgram, divide the frequency Spectrum band into different narrow bands by using 1/3-binary tree filter, select information narrow band based on Fault Characteristic Frequency (FCF) to generate IES, and realize fault identification of rolling bearing under different conditions (Mauricio A, Smith W A, Randall R B, et al.
The methods provide ideas for identifying the narrow frequency band of the information spectrum of the SCoh, but when the fault information is distributed in a plurality of narrow bands, the fault information is easy to miss. Therefore, Mauricio et al constructs a weight function about spectrum frequency based on FCF on The basis of IESFOgram, and performs weighted integration on SCoh modulus along spectrum frequency axis to obtain Combined IES (Mauricio A, Griylias K. cyclic-based Multi band Envelope spectrum Extraction for bearing diagnostics: The Combined Improved Envelope Spectra, mechanical Systems and Signal Processing,2021,149: 107150.). However, small fluctuations in shaft speed near the nominal speed may adversely affect these FCF-based methods, even resulting in poor fault detection capabilities. Therefore, when the rotating speed information is unknown or inaccurate, how to utilize the characteristics of SCoh, and how to construct a spectrum analysis tool independent of sparse indexes and FCF to realize the weak fault detection of the bearing is very critical.
Disclosure of Invention
The invention provides a method for building weighted combined lifting envelope spectrum based on local features of spectrum coherence, aiming at solving the problem that weak fault features of a train axle box bearing are difficult to extract in a wide frequency band and based on the second-order cyclostationarity of fault signals.
The invention discloses a method for constructing a weighted joint lifting envelope spectrum based on local characteristics of spectral coherence, which comprises the following steps:
step 1: the spectral coherence of the measured signal is calculated.
Actually measured rotary mechanical vibration signal x (t)n),tn＝n/FsN-0, 1, …, the spectral correlation SC of N-1 being defined as:
Figure BDA0003359790320000021
in the formula: k ═ 2N +1) FsN is the signal length, FsIs the sampling frequency of the signal; alpha is the cycle frequency; f is frequencyA spectral frequency; r (t)n,τm) Is x (t)n) Instantaneous autocorrelation function of, tn＝n/FsFor the sampling instant, τmIs a delay factor. Spectral coherence is a normalized version of spectral correlation defined as follows:
Figure BDA0003359790320000022
estimating the spectral coherence of the signal by selecting a proper numerical calculation method to obtain gamma (alpha)n,fm)，αnIs a discrete cycle frequency; f. ofmAre discrete spectral frequencies.
Step 2: candidate failure frequencies are identified based on the spectral coherent local features.
Firstly, noise reduction processing is carried out on spectral coherence based on median filtering:
Figure BDA0003359790320000023
in the formula: mean () stands for median filtering; operator [ ·]+Setting all numbers less than zero to zero; delta (n) ═ alphan－kΔα,αn+kΔα]Is at alphanThe central neighborhood is delta alpha, the resolution of the cycle frequency is delta alpha, and the value of the parameter k is 5-50.
Then, for an arbitrary fixed spectral frequency fmDefining:
Figure BDA0003359790320000024
in the formula: the parameter L determines the cyclic frequency slice
Figure BDA0003359790320000025
Sparsity of local maxima of the modes of (a); for any cycle frequency of alphanDefining a spectral frequency slice gamma (alpha)nThe number of local maxima on η (n) then:
Figure BDA0003359790320000026
in the formula: m is the number of discrete spectral frequencies; g is the number of discrete cycle frequencies; alpha is alphanThe value of η (n) tends to be larger for frequencies associated with bearing failure; for this purpose, η (n) is sorted by size to obtain
Figure BDA0003359790320000031
If it is not
Figure BDA0003359790320000032
Then there is kiAnd ki+1So that omega (k)i)>Ω(ki+1) Is formed in which
Figure BDA0003359790320000033
And
Figure BDA0003359790320000034
the function Ω (-) is defined as follows:
Figure BDA0003359790320000035
before selection, of maximum D
Figure BDA0003359790320000036
Cycle frequency used
Figure BDA0003359790320000037
D is a candidate failure frequency, and there are:
Figure BDA0003359790320000038
and reasonably setting the parameter D to ensure that the candidate fault frequency mainly contains frequency components related to the bearing fault.
And step 3: and (4) based on 1/3-spectrum coherent spectrum band division of a binary tree, and quantizing the fault information of each spectrum frequency narrow band by using the identified candidate fault frequency.
Dividing the frequency spectrum by using an 1/3-binary tree filter bank to obtain frequency spectrum frequency narrow bands with different center frequencies and bandwidths; the kth, k of the l, l-0, 1,1.6,2,2.6,3, … layer is 1, …,2lA narrow band Bl,k＝[Fs·(k-1)/2l +1,Fs·k/2l+1]Center frequency fc ═ Fs·(2k-1)/2l+1Bandwidth Bw ═ Fs/2l+1(ii) a Based on narrow band Bl,kCalculating narrow-band lifting envelope spectrum IESl,k(α)：
Figure BDA0003359790320000039
Next, define IESl,k(α) energy at CFFs vs. entire IESl,kEnergy ratio ER of (. alpha.)l,kAs diagnostic indicators:
Figure BDA00033597903200000310
ERl,kquantizes the frequency spectrum narrow band Bl,kIncluded second order cyclostationary feature information related to the fault; ERl,kLarger, indicating a narrow band Bl,kThe more fault information that is contained.
And 4, step 4: constructing a weighted combined lifting envelope spectrum WCIES, firstly selecting a narrow-band lifting envelope spectrum IES with diagnosis information in each decomposition layer to construct a combined lifting envelope spectrum CIES, and then carrying out weighted average on the CIES to obtain the WCIES, wherein the WCIES is specifically as follows:
(1) computing all IES's on layer ll,k(α),k＝1,…,2lMaximum value ER of the diagnostic index of (1)l,max：
ERl,max＝max{ERl,k,k＝1,...,2l} (10)
Let SKl＝Rs·ERl,max(0<Rs<1) Set as a threshold value as identifying value in layer lThe basis of IES.
(2) The identified valuable IES are averaged over each number of decomposition layers to yield a CIES:
Figure BDA00033597903200000311
in the formula: h (l) is the number of IES selected at layer l; exemplary function I { ERl,k≥SKlValue 0 or 1 only, and only in ERl,k≥SKlAnd when true, takes a value of 1.
(3) Finally, the CIES of each decomposition layerl(α) performing a weighted summation to obtain WCIES:
Figure BDA0003359790320000041
in the formula: nlevel is the maximum number of decomposition layers; w (l) is a weight function of the l-th layer, from CIESl(alpha) a diagnostic index ERlDetermining:
Figure BDA0003359790320000042
preferably, the algorithm for estimating the spectral coherence of the signal in step 1 is the Fast SC algorithm.
Preferably, the value of the parameter k in the step 2 is not more than N/10.
Preferably, the value of the parameter L in the step 2 is 3-10.
Preferably, when the parameter D in step 3 is too small, a sufficient frequency related to the fault cannot be identified; when D is too large, too many failure-independent frequencies are introduced in the CFFs; therefore, by setting the parameter D reasonably to ensure that the CFFs mainly contain frequency components related to bearing faults, considering that the fault signature frequency and the number of harmonics thereof are roughly proportional to the maximum cycle frequency, the parameter D is set as follows:
D＝p·αmax (14)
in the formula:αmaxthe maximum cycle frequency; p is a ratio parameter and is in the range of [0.01,0.1 ]]An internal value.
Preferably, the value of the parameter Rs in the step 4 is 0.5.
The beneficial technical effects of the invention are as follows:
the method has the advantages that the bearing fault information distributed in different narrow bands can be fully integrated, and the method does not depend on the nominal fault period information. The method can effectively extract the local defect fault characteristic information of the rotary machine, and can be used for early fault diagnosis of the rotary machine.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a spectral coherence diagram of the measured signal in the present invention.
Fig. 3 is a schematic diagram of candidate fault signature frequencies in the present invention.
Fig. 4 shows the joint lifting envelope spectrum CIES of the various decomposition layers in the present invention.
Fig. 5 is a weighted joint lifting envelope spectrum WCIES in the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description.
The method for building weighted combined lifting envelope spectrum based on local features of spectrum coherence is shown in fig. 1, and based on spectrum coherence/spectrum coherence of an actually measured signal, discrete spectrum frequency containing fault feature information is screened by using local peak value distribution information of a cyclic frequency spectrum slice, and then an enhanced envelope spectrum is built through an integral operator to identify rotary machine faults. The method specifically comprises the following steps:
step 1: and collecting vibration acceleration signals of the rotating machine by using sensing equipment, and calculating the spectrum coherence of the actually measured signals.
Actually measured rotary mechanical vibration signal x (t)n),tn＝n/FsN-0, 1, …, the spectral correlation SC of N-1 being defined as:
Figure BDA0003359790320000051
in the formula: k ═ 2N +1) FsN is the signal length, FsIs the sampling frequency of the signal; alpha is the cycle frequency; f is the frequency spectrum; r (t)n,τm) Is x (t)n) Instantaneous autocorrelation function of, tn＝n/FsFor the sampling instant, τmIs a delay factor. Spectral coherence is a normalized version of spectral correlation defined as follows:
Figure BDA0003359790320000052
estimating the spectral coherence of the signal by selecting a suitable numerical calculation method (such as a fast spectral correlation algorithm, but not limited to the fast spectral correlation algorithm) to obtain gamma (alpha)n,fm)，αnIs a discrete cycle frequency; f. ofmAre discrete spectral frequencies. The spectral coherence map of the measured signal is shown in figure 2.
Step 2: candidate failure frequencies are identified based on the spectral coherent local features.
Firstly, noise reduction processing is carried out on spectral coherence based on median filtering:
Figure BDA0003359790320000053
in the formula: mean () stands for median filtering; operator [ ·]+Setting all numbers less than zero to zero; delta (n) ═ alphan－kΔα,αn+kΔα]Is at alphanThe central neighborhood is delta alpha, the resolution of the cycle frequency is delta alpha, and the value of the parameter k is 5-50.
Then, for an arbitrary fixed spectral frequency fmDefining:
Figure BDA0003359790320000054
in the formula: the parameter L determines the cyclic frequency slice
Figure BDA0003359790320000055
Sparsity of local maxima of the modes of (a); for any cycle frequency of alphanDefining a spectral frequency slice gamma (alpha)nThe number of local maxima on η (n) then:
Figure BDA0003359790320000056
in the formula: m is the number of discrete spectral frequencies; g is the number of discrete cycle frequencies; alpha is alphanThe value of η (n) tends to be larger for frequencies associated with bearing failure; for this purpose, η (n) is sorted by size to obtain
Figure BDA0003359790320000057
If it is not
Figure BDA0003359790320000058
Then there is kiAnd ki+1So that omega (k)i)>Ω(ki+1) Is formed in which
Figure BDA0003359790320000059
And
Figure BDA00033597903200000510
the function Ω (-) is defined as follows:
Figure BDA0003359790320000061
before selection, of maximum D
Figure BDA0003359790320000062
Cycle frequency used
Figure BDA0003359790320000063
D is a candidate failure frequency, and there are:
Figure BDA0003359790320000064
and reasonably setting the parameter D to ensure that the candidate fault frequency mainly contains frequency components related to the bearing fault.
The identified candidate fault signature frequencies are shown in fig. 3.
And step 3: and (4) based on 1/3-spectrum coherent spectrum band division of a binary tree, and quantizing the fault information of each spectrum frequency narrow band by using the identified candidate fault frequency.
Dividing the frequency spectrum by using an 1/3-binary tree filter bank to obtain frequency spectrum frequency narrow bands with different center frequencies and bandwidths; the kth, k of the l, l-0, 1,1.6,2,2.6,3, … layer is 1, …,2lA narrow band Bl,k＝[Fs·(k-1)/2l +1,Fs·k/2l+1]Center frequency fc ═ Fs·(2k-1)/2l+1Bandwidth Bw ═ Fs/2l+1(ii) a Based on narrow band Bl,kCalculating narrow-band lifting envelope spectrum IESl,k(α)：
Figure BDA0003359790320000065
Next, define IESl,k(α) energy at CFFs vs. entire IESl,kEnergy ratio ER of (. alpha.)l,kAs diagnostic indicators:
Figure BDA0003359790320000066
ERl,kquantizes the frequency spectrum narrow band Bl,kIncluded second order cyclostationary feature information related to the fault; ERl,kLarger, indicating a narrow band Bl,kThe more fault information that is contained.
And 4, step 4: constructing a weighted combined lifting envelope spectrum WCIES, firstly selecting a narrow-band lifting envelope spectrum IES with diagnosis information in each decomposition layer to construct a combined lifting envelope spectrum CIES, and then carrying out weighted average on the CIES to obtain the WCIES, wherein the WCIES is specifically as follows:
(1) Computing all IES's on layer ll,k(α),k＝1,…,2lMaximum value ER of the diagnostic index of (1)l,max：
ERl,max＝max{ERl,k,k＝1,...,2l} (10)
Let SKl＝Rs·ERl,max(0<Rs<1) Set as a threshold as a basis for identifying valuable IES in level i.
(2) The identified valuable IES are averaged over each number of decomposition layers to yield CIES (as shown in fig. 4):
Figure BDA0003359790320000067
in the formula: h (l) is the number of IES selected at layer l; exemplary function I { ERl,k≥SKlValue 0 or 1 only, and only in ERl,k≥SKlAnd when true, takes a value of 1.
(3) Finally, the CIES of each decomposition layerl(α) weighted sum to get WCIES (as shown in fig. 5):
Figure BDA0003359790320000068
in the formula: nlevel is the maximum number of decomposition layers; w (l) is a weight function of the l-th layer, from CIESl(alpha) a diagnostic index ERlDetermining:
Figure BDA0003359790320000071
finally, a rotating machine fault is identified.

Claims (6)

1. A method for constructing a weighted joint lifting envelope spectrum based on local features of spectral coherence is characterized by comprising the following steps:
step 1: calculating the spectral coherence of the actually measured signal;
actually measured rotating machinery vibration signal x (tn),tn＝n/FsN-0, 1, …, the spectral correlation SC of N-1 being defined as:
Figure FDA0003359790310000011
in the formula: k ═ 2N +1) FsN is the signal length, FsIs the sampling frequency of the signal; alpha is the cycle frequency; f is the frequency spectrum; r (t)n,τm) Is x (t)n) Instantaneous autocorrelation function of, tn＝n/FsFor the sampling instant, τmIs a delay factor; spectral coherence is a normalized version of spectral correlation defined as follows:
Figure FDA0003359790310000012
estimating the spectral coherence of the signal by selecting a proper numerical calculation method to obtain gamma (alpha)n,fm)，αnIs a discrete cycle frequency; f. ofmIs a discrete spectral frequency;
step 2: identifying candidate fault frequencies based on the spectral coherent local features;
firstly, noise reduction processing is carried out on spectral coherence based on median filtering:
Figure FDA0003359790310000013
in the formula: mean () stands for median filtering; operator [ ·]+Setting all numbers less than zero to zero; delta (n) ═ alphan－kΔα,αn+kΔα]Is at alphanThe neighborhood is the center, delta alpha is the resolution of the cycle frequency, and the value of the parameter k is 5-50;
then, for an arbitrary fixed spectral frequency fmDefining:
Figure FDA0003359790310000014
in the formula: the parameter L determines the cyclic frequency slice
Figure FDA0003359790310000015
Sparsity of local maxima of the modes of (a); for any cycle frequency of alphanDefining a spectral frequency slice gamma (alpha)nThe number of local maxima on η (n) then:
Figure FDA0003359790310000016
in the formula: m is the number of discrete spectral frequencies; g is the number of discrete cycle frequencies; alpha is alphanThe value of η (n) tends to be larger for frequencies associated with bearing failure; for this purpose, η (n) is sorted by size to obtain
Figure FDA0003359790310000017
If it is not
Figure FDA0003359790310000018
Then there is kiAnd ki+1So that omega (k)i)>Ω(ki+1) Is formed in which
Figure FDA0003359790310000019
And
Figure FDA00033597903100000110
the function Ω (-) is defined as follows:
Figure FDA0003359790310000021
before selection, of maximum D
Figure FDA0003359790310000022
Cycle frequency used
Figure FDA0003359790310000023
D is a candidate failure frequency, and there are:
Figure FDA0003359790310000024
by reasonably setting the parameter D, the candidate fault frequency is ensured to mainly contain frequency components related to bearing faults;
and step 3: based on 1/3-spectrum coherent spectrum band division of the binary tree, and quantizing fault information of each spectrum frequency narrow band by using the identified candidate fault frequency;
dividing the frequency spectrum by using an 1/3-binary tree filter bank to obtain frequency spectrum frequency narrow bands with different center frequencies and bandwidths; the kth, k of the l, l-0, 1,1.6,2,2.6,3, … layer is 1, …,2lA narrow band Bl,k＝[Fs·(k-1)/2l+1,Fs·k/2l+1]Center frequency fc ═ Fs·(2k-1)/2l+1Bandwidth Bw ═ Fs/2l+1(ii) a Based on narrow band Bl,kCalculating narrow-band lifting envelope spectrum IESl,k(α)：
Figure FDA0003359790310000025
Next, define IESl,k(α) energy at CFFs vs. entire IESl,kEnergy ratio ER of (. alpha.)l,kAs diagnostic indicators:
Figure FDA0003359790310000026
ERl,kquantizes the frequency spectrum narrow band Bl,kIncluded second order cyclostationary feature information related to the fault; ERl,kLarger, indicating a narrow band Bl,kThe more fault information that is contained;
and 4, step 4: constructing a weighted combined lifting envelope spectrum WCIES, firstly selecting a narrow-band lifting envelope spectrum IES with diagnosis information in each decomposition layer to construct a combined lifting envelope spectrum CIES, and then carrying out weighted average on the CIES to obtain the WCIES, wherein the WCIES is specifically as follows:
(1) computing all IES's on layer ll,k(α),k＝1,…,2lMaximum value ER of the diagnostic index of (1)l,max：
ERl,max＝max{ERl,k,k＝1,...,2l} (10)
Let SKl＝Rs·ERl,max(0<Rs<1) Set as a threshold as a basis for identifying valuable IES in level i;
(2) the identified valuable IES are averaged over each number of decomposition layers to yield a CIES:
Figure FDA0003359790310000027
in the formula: h (l) is the number of IES selected at layer l; exemplary function I { ERl,k≥SKlValue 0 or 1 only, and only in ERl,k≥SKlIf the result is true, the value is 1;
(3) finally, the CIES of each decomposition layerl(α) performing a weighted summation to obtain WCIES:
Figure FDA0003359790310000028
in the formula: nlevel is the maximum number of decomposition layers; w (l) is a weight function of the l-th layer, from CIESl(alpha) a diagnostic index ERlDetermining:
Figure FDA0003359790310000031
2. the method for constructing a weighted joint lifting envelope spectrum based on the local features of spectral coherence according to claim 1, wherein the algorithm for estimating the spectral coherence of the signal in step 1 is Fast SC algorithm.
3. The method for constructing the weighted joint lifting envelope spectrum based on the local features of the spectral coherence according to claim 1, wherein the value of the parameter k in the step 2 is not more than N/10.
4. The method for constructing the weighted joint lifting envelope spectrum based on the local features of the spectral coherence according to claim 1, wherein a value of a parameter L in the step 2 is 3-10.
5. The method for constructing a weighted joint lifting envelope spectrum based on the local features of spectral coherence as claimed in claim 1, wherein if the parameter D in step 3 is too small, it will result in that a sufficient number of frequencies related to faults cannot be identified; when D is too large, too many failure-independent frequencies are introduced in the CFFs; therefore, by setting the parameter D reasonably to ensure that the CFFs mainly contain frequency components related to bearing faults, considering that the fault signature frequency and the number of harmonics thereof are roughly proportional to the maximum cycle frequency, the parameter D is set as follows:
D＝p·αmax (14)
in the formula: alpha is alphamaxThe maximum cycle frequency; p is a ratio parameter and is in the range of [0.01,0.1 ]]An internal value.
6. The method for constructing the weighted joint lifting envelope spectrum based on the local features of the spectral coherence according to claim 1, wherein a value of the parameter Rs in the step 4 is 0.5.
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