CN112629862A - Rolling bearing weak fault diagnosis method based on bistable stochastic resonance and CEEMDAN-TEO - Google Patents
Rolling bearing weak fault diagnosis method based on bistable stochastic resonance and CEEMDAN-TEO Download PDFInfo
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Abstract
The invention discloses a bistable random resonance and CEEMDAN-TEO rolling bearing weak fault diagnosis method, which comprises the following steps: step 1: noise reduction is carried out and weak signal characteristics are improved through a bistable stochastic resonance method; step 2: decomposing the signal into a finite number of eigenmode functions IMF through a CEEMDAN algorithm; and step 3: and (4) performing teager energy operator reconstruction on each IMF component, and identifying the fault frequency. The invention uses the bistable stochastic resonance method to improve the weak fault signal and reduce the noise, improves the prior EMD, LMD and other algorithm decomposition, and replaces the algorithm decomposition by CEEMDAN with better decomposition effect, thereby better solving the end point effect and the mode aliasing. And drawing a teager energy spectrum on the IMF component obtained by decomposition, further strengthening the impact characteristic, and easily distinguishing weak fault frequency and the existing secondary phase coupling phenomenon.
Description
Technical Field
The invention relates to a weak fault diagnosis method for a rolling bearing, in particular to a weak fault diagnosis method for a rolling bearing based on bistable stochastic resonance and CEEMDAN-TEO, and belongs to the technical field of fault diagnosis.
Background
The rolling bearing is one of important parts in mechanical equipment, and because the failure probability is high, the failure of the rolling bearing easily causes the shutdown of the whole equipment, so that the diagnosis of the early weak failure is particularly important, the hidden danger is found in time and repaired or replaced, the production safety can be effectively ensured, and the maintenance cost can be reduced.
When a rolling bearing has a local fault, a periodic pulse signal is generated in a vibration signal of the rolling bearing, however, in an early stage, the pulse signal is very weak and is easily submerged by strong environmental noise, so that fault characteristics are difficult to extract, and therefore, it is necessary to reduce noise influence and improve the weak fault signal by a method. The local mean decomposition improves the problem of over-enveloping or under-enveloping in the empirical mode decomposition, and is effectively applied to the aspect of fault diagnosis. However, the essence is still based on the recursive decomposition principle, which leads to the accumulation of errors and cannot fundamentally overcome modal aliasing and end point effects.
In summary, the defects of the existing rolling bearing weak signal fault diagnosis are mainly as follows:
1. at present, the traditional method for decomposing and extracting the fault characteristics by the signals has the defects of modal aliasing, end point effect and the like, and the accuracy of the finally obtained analysis result is low.
2. The traditional noise reduction method such as EMD and LMD reduces noise of a severely-polluted weak characteristic signal to a certain extent, but weakens the characteristic signal to cause 'two-side damage'
3. When a rolling bearing is in fault, the characteristic shown by a fault signal is a modulation phenomenon, windowing is involved in most widely used Hibert transformation calculation, which often brings errors to results, and especially, the Hibert transformation analysis edge errors are very large for non-whole period signals.
Disclosure of Invention
The method aims at solving the problems that the traditional decomposition denoising method has modal aliasing and end point effect in the weak signal fault diagnosis of the existing rolling bearing; the noise is reduced, meanwhile, the characteristic signal is damaged, and a rolling bearing weak fault diagnosis method of bistable stochastic resonance and CEEMDAN-TEO is provided.
In order to solve the problems, the invention adopts the technical scheme that:
a bistable stochastic resonance and CEEMDAN-TEO rolling bearing weak fault diagnosis method is characterized by comprising the following steps:
step 1: noise reduction is carried out and weak signal characteristics are improved through a bistable stochastic resonance method;
step 2: decomposing the signal into a finite number of eigenmode functions IMF through a CEEMDAN algorithm;
and step 3: and (4) performing teager energy operator reconstruction on each IMF component, and identifying the fault frequency.
Preferably, in step 1, the bistable stochastic resonance method comprises the following specific steps:
step A1: stochastic resonance systems generally include three factors: the nonlinear system, periodic signal and noise, when the three reach the best matching relation, the stochastic resonance has the most obvious amplification effect on the signal, the commonly used stochastic model is a bistable system, and is described by the nonlinear langevin equation:
in the formula: a. b is a non-zero system parameter, S (t) is a weak periodic signal (the amplitude A is less than 1), and xi (t) is zero mean Gaussian white noise, and the following conditions are met:
E[ξ(t)ξ(t+τ)]=2Dδ(t-τ) (2)
in the formula: d is noise intensity and tau is time variable;
the potential function of the bistable system is:
in the formula: a. b is a non-zero system parameter;
step A2: the bistable potential function has two stable states and one unstable state, when no external input exists, the system is positioned at the lowest point of the potential well, the potential energy is minimum, and the system is most stable; when a weak signal is input into the system, the signal energy cannot overcome the blocking of the potential barrier, and the output state of the system can only move in one potential well; if noise is added into the system, part of noise energy is transferred to the signal to enable the signal to generate interaction to overcome a system potential barrier, and transition is generated between two stable states according to the signal frequency; since the potential difference between the bistable states is much larger than the amplitude of the input signal, it acts to amplify the input signal, i.e. to resonate randomly.
Preferably, in the step 2, the CEEMDAN algorithm includes the following specific steps:
step B1: constructing a signal xi(n)=x(n)+σωi(n),i=(1,…,N),
In the formula: σ is the standard deviation of the noise, ωi(N) is white noise that follows an N (0,1) distribution;
decomposition is performed using EMD, and the first modal component of each signal is obtained and calculated:and the margin r of the first stage1(n)=x(n)-IMF1(n)。
step B2: for the signal r1(n)+σM1[ωi(n)]The EMD decomposition is performed, and the second modal component of CEEEMDAN is calculated by the following formula:
in the formula: m1Namely the 1 st modal component obtained by the EMD method;
step B3: assuming the number of decomposition layers as K, the K-th residual signal for each of the remaining stages is calculated by the following formula (K ═ 1, …, K-1):
rk(n)=rk-1-IMFk(n) (5)
the (k + 1) th modal component is calculated simultaneously, similar to the calculation process in step B2:
step B4: executing the step B3 until the obtained residual signal can not be decomposed any more, wherein the judgment standard is that the residual signal does not meet the EMD decomposition condition or the number of the extreme points is not more than two;
when the algorithm is terminated, the number of all modal components is K, and the final residual signal is:
the original signal sequence x (n) is finally decomposed into:
preferably, in step 3, step 3 further includes the following steps:
step C1: for the continuous signal x (t), the teager energy operator ψ is calculated as follows:
step C2: for a linear undamped free vibration system with mass m and a spring constant k, a second-order motion difference equation is obtained according to Newton's law of motion:
in the formula: x (t) is the position displacement of mass m relative to equilibrium,is the second derivative of x (t);
step C3: the simple harmonic vibration equation can be expressed as:
in the formula: a is the vibration amplitude at time t, ω is the natural frequency,is the initial phase;
the total instantaneous energy E at time t can be expressed as:
in the formula: a is the vibration amplitude at time t, ω is the natural frequency, k is the spring constant;
step C4: the traditional definition of signal energy is the square of the amplitude, which represents only kinetic or potential energy; if periodic vibration impact occurs when the rolling bearing has weak faults, and the strength of the vibration impact is small, the vibration impact of the type is easily submerged by noise; from equation (12), the teager energy operator represents the total energy of the signal, including kinetic energy and potential energy, compared with the conventional signal energy definition; the output of the device is the product of the square of the instantaneous amplitude and the square of the instantaneous vibration frequency, because the amplitude of the transient impact is smaller when the rolling bearing has a weak fault and is easily submerged in background noise, but the frequency of the transient impact is higher, the transient impact component can be increased by a teager energy operator, so that the purpose of enhancing the transient impact characteristic is achieved, and the difficulty of extracting the fault characteristic is reduced;
step C5: analyzing the energy spectrum of the teager, and identifying the fault of the rolling bearing.
The invention has the beneficial effects that: the invention carries out stochastic resonance on the original signal to strengthen the weak fault signal, then improves the former decomposition, and replaces the former decomposition by CEEMDAN with better decomposition effect, thereby better lightening the end effect and the mode aliasing. Finally, the tegaser energy spectrum is used for better reflecting the fault characteristics.
Drawings
FIG. 1 is a flow chart of a weak fault diagnosis method for a rolling bearing according to the present invention;
FIG. 2 is a time domain waveform and a frequency spectrum of an original signal provided by the present invention;
FIG. 3 is a time domain waveform and then a frequency spectrum of a signal subjected to stochastic resonance denoising according to the present invention;
FIG. 4 is a spectrum of the first three IMF components after CEEMDAN provided by the present invention;
FIG. 5 is an envelope spectrum of the first three IMF components after CEEMDAN provided by the present invention;
FIG. 6 is a teager's energy spectrum of the IMF1 components provided by the present invention.
Detailed Description
The invention will be described with reference to fig. 1 to 6, and the specific steps of the rolling bearing weak fault diagnosis method based on bistable stochastic resonance and CEEMDAN-TEO according to the embodiment are as follows:
a method for diagnosing weak faults of a rolling bearing with bistable stochastic resonance and CEEMDAN-TEO is characterized by comprising the following steps as shown in the figure I:
step 1: noise reduction is carried out and weak signal characteristics are improved through a bistable stochastic resonance method;
step 2: decomposing the signal into a finite number of eigenmode functions IMF through a CEEMDAN algorithm;
and step 3: and (4) performing teager energy operator reconstruction on each IMF component, and identifying the fault frequency.
As a possible implementation manner, in step 1, fig. 2 is a time-domain waveform and a frequency spectrum of an original signal, and the specific steps of the bistable stochastic resonance method are as follows:
step A1: stochastic resonance systems generally include three factors: the nonlinear system, the periodic signal and the noise have the most obvious amplification effect on the signal when the nonlinear system, the periodic signal and the noise reach the optimal matching relation. A commonly used stochastic model is a bistable system, described by the nonlinear langevin equation:
in the formula: a. b is a non-zero system parameter, S (t) is a weak periodic signal (amplitude A < <1), and xi (t) is white Gaussian noise with zero mean value, and the following conditions are met:
E[ξ(t)ξ(t+τ)]=2Dδ(t-τ) (2)
in the formula: and D is the noise intensity.
The potential function of the bistable system is:
step A2: the bistable potential function has two stable states and one unstable state, when no external input exists, the system is positioned at the lowest point of the potential well, the potential energy is minimum, and the system is most stable; when a weak signal is input into the system, the signal energy cannot overcome the blocking of the potential barrier, and the output state of the system can only move in one potential well; if noise is added to the system, the noise energy will be partially transferred to the signal causing it to interact against the system barrier, creating a transition between two stable states at the signal frequency. Since the potential difference between the bistable states is much larger than the amplitude of the input signal, it acts to amplify the input signal, i.e. to resonate randomly.
The time domain waveform and spectrum of the signal obtained for this purpose are shown in fig. 3.
As a possible implementation manner, in the step 2, the CEEMDAN algorithm includes the following specific steps:
step B1: constructing a signal xi(n)=x(n)+σ0ωi(n),i=(1,…,N),σ0Is the standard deviation of the noise, omegai(N) is white noise following an N (0,1) distribution. Decomposition is performed using EMD, the first modal component of each signal is obtained, and:and the margin r of the first stage1(n)=x(n)-IMF1(n)。
Step B2: for the signal r1(n)+σ1M1[ωi(n)]The EMD decomposition is performed, and the second modal component of CEEEMDAN is calculated by the following formula:
step B3: assuming that the number of decomposition layers is K, the K-th residual signal of each of the remaining stages is calculated by the following formula (K is 1, …, K-1), and the K + 1-th modal component is calculated at the same time, similar to the calculation process in fig. 2:
rk(n)=rk-1-IMFk(n) (5)
step B4: and executing 3 until the acquired residual signal can not be decomposed any more, wherein the judgment standard is that the residual signal does not meet the EMD decomposition condition or the number of extreme points is not more than two. At the termination of the algorithm, the number of all modal components is K. The final residual signal is:
the original signal sequence x (n) is finally decomposed into:
the first three IMFs containing primary fault information are taken as shown in fig. 4.
As a possible implementation manner, in step 3, step 3 further includes the following steps:
step C1: for the continuous signal x (t), the teager energy operator ψ is calculated as follows:
Step C2: for a linear undamped free vibration system with mass m and a spring constant k, a second-order motion difference equation is obtained according to Newton's law of motion:
in the formula: x (t) is the position displacement of mass m relative to equilibrium,is the second derivative of x (t).
Step C3: the simple harmonic vibration equation can be expressed as:
in the formula: a is the vibration amplitude at time t, ω is the natural frequency,is the initial phase.
The total instantaneous energy at time t can be expressed as:
step C4: the traditional definition of signal energy is the square of the amplitude, which represents only kinetic or potential energy. If periodic vibration shocks occur when the rolling bearing is in a weak failure and the vibration shocks are small in intensity, the vibration shocks of this type are extremely liable to be submerged by noise. From equation (12), the teager's energy operator represents the total energy of the signal, including both kinetic and potential energy, as compared to the conventional definition of signal energy. The output of the transient impact energy operator is the product of the square of the instantaneous amplitude and the square of the instantaneous vibration frequency, because the transient impact amplitude is smaller when the rolling bearing has a weak fault and is easily submerged in background noise, but the transient impact frequency is higher, the transient impact component can be increased by the transient energy operator, so that the purpose of enhancing the transient impact characteristic is achieved, and the difficulty of extracting the fault characteristic is reduced.
Step C5: analyzing the energy spectrum of the teager, and identifying the fault of the rolling bearing.
From fig. 5 and 6, it can be seen that the teager energy spectrum can enhance the impact characteristics, and can identify weak fault frequency and the existing secondary phase coupling phenomenon more easily.
The data used in this example are the rolling bearing test data of the bearing data center of the electrical engineering laboratory at the university of Kaiser Sichu, USA. The bearing model is 6205-2RS SKF type deep groove ball bearing, and the electric spark technology is adopted to process single point failure on the bearing, the pitting diameter is 0.1778mm, so as to simulate early weak failure. Data were collected under experimental conditions with relatively little ambient noise, so white gaussian noise was added to simulate an industrial field environment. The fault data of the inner ring of the rolling bearing at the driving end of the motor are acquired under the working condition that the rotating speed is 1797r/min and no load exists, the sampling frequency is 12kHz, the data length is 12000 data points, the fundamental frequency of the motor is 29.95Hz, and the fault characteristic frequency is 161.1 Hz.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and the preferred embodiments of the present invention are described in the above embodiments and the description, and are not intended to limit the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. A bistable stochastic resonance and CEEMDAN-TEO rolling bearing weak fault diagnosis method is characterized by comprising the following steps:
step 1: noise reduction is carried out and weak signal characteristics are improved through a bistable stochastic resonance method;
step 2: decomposing the signal into a finite number of eigenmode functions IMF through a CEEMDAN algorithm;
and step 3: and (4) performing teager energy operator reconstruction on each IMF component, and identifying the fault frequency.
2. The method for diagnosing weak faults of a rolling bearing with bistable stochastic resonance and CEEMDAN-TEO according to claim 1, wherein in the step 1, the bistable stochastic resonance method comprises the following specific steps:
step A1: stochastic resonance systems generally include three factors: the nonlinear system, periodic signal and noise, when the three reach the best matching relation, the stochastic resonance has the most obvious amplification effect on the signal, the commonly used stochastic model is a bistable system, and is described by the nonlinear langevin equation:
in the formula: a. b is a non-zero system parameter, S (t) is a weak periodic signal (the amplitude A is less than 1), and xi (t) is zero mean Gaussian white noise, and the following conditions are met:
E[ξ(t)ξ(t+τ)]=2Dδ(t-τ) (2)
in the formula: d is noise intensity and tau is time variable;
the potential function of the bistable system is:
in the formula: a. b is a non-zero system parameter;
step A2: the bistable potential function has two stable states and one unstable state, when no external input exists, the system is positioned at the lowest point of the potential well, the potential energy is minimum, and the system is most stable; when a weak signal is input into the system, the signal energy cannot overcome the blocking of the potential barrier, and the output state of the system can only move in one potential well; if noise is added into the system, part of noise energy is transferred to the signal to enable the signal to generate interaction to overcome a system potential barrier, and transition is generated between two stable states according to the signal frequency; since the potential difference between the bistable states is much larger than the amplitude of the input signal, it acts to amplify the input signal, i.e. to resonate randomly.
3. The method for diagnosing weak faults of a rolling bearing with bistable stochastic resonance and CEEMDAN-TEO according to claim 1, wherein in the step 2, the CEEMDAN algorithm comprises the following specific steps:
step B1: constructing a signal xi(n)=x(n)+σωi(n),i=(1,…,N),
In the formula: σ is the standard deviation of the noise, ωi(N) is white noise that follows an N (0,1) distribution;
decomposition is performed using EMD, and the first modal component of each signal is obtained and calculated:and the margin r of the first stage1(n)=x(n)-IMF1(n)。
step B2: for the signal r1(n)+σM1[ωi(n)]The EMD decomposition is performed, and the second modal component of CEEEMDAN is calculated by the following formula:
in the formula: m1Namely the 1 st modal component obtained by the EMD method;
step B3: assuming the number of decomposition layers as K, the K-th residual signal for each of the remaining stages is calculated by the following formula (K ═ 1, …, K-1):
rk(n)=rk-1-IMFk(n) (5)
the (k + 1) th modal component is calculated simultaneously, similar to the calculation process in step B2:
step B4: executing the step B3 until the obtained residual signal can not be decomposed any more, wherein the judgment standard is that the residual signal does not meet the EMD decomposition condition or the number of the extreme points is not more than two;
when the algorithm is terminated, the number of all modal components is K, and the final residual signal is:
the original signal sequence x (n) is finally decomposed into:
4. the method for diagnosing weak fault of rolling bearing with bistable stochastic resonance and CEEMDAN-TEO according to claim 1, wherein in the step 3, the step 3 further comprises the following steps:
step C1: for the continuous signal x (t), the teager energy operator ψ is calculated as follows:
step C2: for a linear undamped free vibration system with mass m and a spring constant k, a second-order motion difference equation is obtained according to Newton's law of motion:
in the formula: x (t) is the mass m relative to the equilibriumIs displaced from the position of the first and second movable parts,is the second derivative of x (t);
step C3: the simple harmonic vibration equation can be expressed as:
in the formula: a is the vibration amplitude at time t, ω is the natural frequency,is the initial phase;
the total instantaneous energy E at time t can be expressed as:
in the formula: a is the vibration amplitude at time t, ω is the natural frequency, k is the spring constant;
step C4: the traditional definition of signal energy is the square of the amplitude, which represents only kinetic or potential energy; if periodic vibration impact occurs when the rolling bearing has weak faults, and the strength of the vibration impact is small, the vibration impact of the type is easily submerged by noise; from equation (12), the teager energy operator represents the total energy of the signal, including kinetic energy and potential energy, compared with the conventional signal energy definition; the output of the device is the product of the square of the instantaneous amplitude and the square of the instantaneous vibration frequency, because the amplitude of the transient impact is smaller when the rolling bearing has a weak fault and is easily submerged in background noise, but the frequency of the transient impact is higher, the transient impact component can be increased by a teager energy operator, so that the purpose of enhancing the transient impact characteristic is achieved, and the difficulty of extracting the fault characteristic is reduced;
step C5: analyzing the energy spectrum of the teager, and identifying the fault of the rolling bearing.
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CN113654750A (en) * | 2021-08-13 | 2021-11-16 | 华北电力大学(保定) | Vibration feature extraction method for circuit breaker operating mechanism |
CN113654750B (en) * | 2021-08-13 | 2022-05-03 | 华北电力大学(保定) | Vibration feature extraction method for circuit breaker operating mechanism |
CN114018581A (en) * | 2021-11-08 | 2022-02-08 | 中国航发哈尔滨轴承有限公司 | CEEMDAN-based rolling bearing vibration signal decomposition method |
CN114018581B (en) * | 2021-11-08 | 2024-04-16 | 中国航发哈尔滨轴承有限公司 | Rolling bearing vibration signal decomposition method based on CEEMDAN |
CN114608827A (en) * | 2022-03-23 | 2022-06-10 | 郑州恩普特科技股份有限公司 | Bearing weak fault diagnosis method |
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