CN111351645A - Weak fault signal diagnosis method for grain mechanical equipment - Google Patents
Weak fault signal diagnosis method for grain mechanical equipment Download PDFInfo
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Abstract
The invention discloses a weak fault signal diagnosis method for grain mechanical equipment, and discloses a time delay dissipative bistable stochastic resonance weak feature extraction method. The method enables the effective potential function of the system to dynamically change along with the change of the time delay feedback parameter, enriches the motion trail of the Brown particles, improves the weak fault characteristic enhanced extraction capability of the classical dissipative bistable system, and then utilizes the time delay control dissipative bistable stochastic resonance method to enhance and extract the fault characteristics of different degrees of the grain mechanical equipment, thereby realizing the effective fault diagnosis and qualitative analysis of the grain mechanical equipment. The method dynamically adjusts the system potential function, thereby obtaining a larger output signal-to-noise ratio and a higher characteristic frequency spectrum peak.
Description
Technical Field
The invention belongs to the field of equipment fault signal diagnosis, and particularly relates to a weak fault signal diagnosis method for grain mechanical equipment.
Background
The grain machinery equipment is increasingly complex and the working environment is severe and variable, which can cause the grain machinery equipment to be out of order and even catastrophic accidents, for example, on a grain harvester running at high speed, the fault point of any slight bearing can bring about very serious accident consequence. Thus, engineers often deal with the problem of detecting signals on the order of nanovolts, where weak signals not only mean that the signal amplitude is small, but more generally that the useful input signal is disturbed or swamped by strong background noise, resulting in a low input signal-to-noise ratio for the system. The monitored fault characteristic signals are very weak due to the interference of factors such as internal and external environments and the like on grain mechanical equipment, and are difficult to directly extract and diagnose.
Most of the traditional signal processing theories are noise filtering, ubiquitous noise in the signal processing process can cause extremely bad influence on the extraction and detection of weak signals, and how to eliminate noise interference is a research hotspot of weak signal detection all the time. However, most studies attempt to analyze the weak signal and noise statistics based on information theory, electronics and physics methods, and construct filters to extract the weak signal. But the filtering method based on the noise cancellation concept has the following difficulties when the signal and the noise frequency band are aliased: firstly, weak signals with low signal-to-noise ratio are difficult to detect; secondly, detection necessarily causes signal damage or information loss.
The stochastic resonance overcomes the defects of the traditional noise filtering method by the unique noise useful characteristics, changes the inherent concept of people from noise damage system performance into noise enhancement signal transmission, and is very suitable for weak signal detection under strong background noise. Therefore, weak signal detection studies based on stochastic resonance mechanisms have important practical implications. In short, stochastic resonance is a nonlinear phenomenon in which the synergy among a nonlinear system, noise and weak features leads to the enhancement of the weak features.
Weak signal detection and enhancement based on a bistable stochastic resonance mechanism are widely applied to grain mechanical fault diagnosis, but the optimal signal enhancement performance is not desirable by adjusting noise, when the noise is in a non-enhanced area, the output signal is only worse by additional noise, so that the weak fault feature enhancement extraction capability of the traditional bistable stochastic resonance system is limited, and the severity of the fault is difficult to analyze qualitatively.
Disclosure of Invention
The invention aims to provide a method for diagnosing weak fault signals of grain mechanical equipment.
The technical solution for realizing the purpose of the invention is as follows: a method for diagnosing weak fault signals of grain mechanical equipment comprises the following steps:
the time delay dissipative bistable stochastic resonance system is obtained by introducing a time delay feedback term into a traditional dissipative bistable stochastic resonance system, and the system is described by a langevin equation as follows:
wherein β and τ are delay feedback parameters, Acos (Ω t) is a weak periodic signal, a is a signal amplitude, Ω is a signal frequency, and ∈ (t) is additive white gaussian noise, and [ ∈ (t) > ] is 0, [ ∈ (t) > ] is 2D δ (t'), the symbol < > is a statistical average, D is a noise intensity, and the dissipative bistable state potential function is:
wherein a, b and c are system parameters, and a > 0, b > 0, c > 0.
the effective potential function U of the time delay dissipative bistable stochastic resonance systemeff(x) Comprises the following steps:
the steady-state concept density of the system is as follows:
the output signal-to-noise ratio is as follows:
in the formula, W0=2W±|s(t)=0,W±For time-delay dissipation of the transition rate between the two stable states of a bistable stochastic resonance system,
in the formula, x±For two steady-state point positions, xunIs the position of an unsteady point, Ueff(x) Representing the effective potential function Ueff(x) The second derivative of (a).
And 3, determining a time delay feedback parameter according to the time delay control stochastic resonance method in the step 2 aiming at the grain mechanical bearing vibration input signals with different fault degrees, and extracting fault characteristics of the output result of the time delay dissipation stochastic resonance system under the parameter to determine the fault severity.
The fault feature extraction is specifically to perform frequency spectrum analysis on the output of the time delay dissipation bi-stable stochastic resonance system under a proper time delay feedback parameter (β, tau), extract fault feature frequency in the grain mechanical vibration signal, and judge the severity of the fault according to the size of a spectrum peak at the fault feature frequency.
Compared with the prior art, the invention has the following remarkable advantages: 1) the invention improves the potential function of the traditional dissipative bistable stochastic resonance system by using the time delay feedback control effect to obtain a dynamic stochastic resonance system of the bistable potential well, enriches the motion tracks of Brown particles, improves the weak fault characteristic enhanced extraction capability of the classical dissipative bistable system, and then applies the time delay control dissipative bistable stochastic resonance method to the detection of fault characteristics of grain mechanical equipment in different degrees to further realize effective fault diagnosis and qualitative analysis of the grain mechanical equipment. 2) The method dynamically adjusts the system potential function, and can obtain a larger output signal-to-noise ratio and a higher characteristic frequency spectrum peak.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
Fig. 1 is a graph of an effective potential function of a time delay dissipative bistable stochastic resonance system, wherein (a) is a graph of a change result of the effective potential function along with the time delay, and (b) is a graph of a change result of the effective potential function along with the feedback strength.
Fig. 2 is a graph of the change of the steady state density function of the system under different delay feedback parameters, wherein (a) is a graph of the change with different delay sizes, and (b) is a graph of the change with different feedback strengths.
Fig. 3 is a graph of the variation of the output signal-to-noise ratio of the system with the noise intensity at different delay feedback parameters, where (a) is a variation graph with different delay sizes, and (b) is a variation graph with different feedback intensities.
Fig. 4 is a waveform diagram of an original grain machinery bearing vibration fault signal, wherein a diagram (a) is a time domain waveform diagram, a diagram (b) is a frequency spectrum waveform diagram, and a diagram (c) is an envelope spectrum waveform diagram.
Fig. 5 is a time domain waveform and a frequency spectrum of an original grain mechanical bearing vibration fault signal enhanced by a time delay dissipation bistable stochastic resonance method, wherein a graph (a) is a time domain waveform graph, and a graph (b) is a frequency spectrum graph.
Detailed Description
The invention discloses a time delay dissipation bistable state stochastic resonance weak feature extraction method, which adjusts the height and width of a bistable state potential well and the steepness degree of a potential well wall by introducing a time delay feedback term, and finally achieves the weak signal enhancement effect. The method enables the effective potential function of the system to dynamically change along with the change of the time delay feedback parameters, enriches the motion trail of Brown particles, improves the weak fault characteristic enhanced extraction capability of a classical dissipative bistable system, and then utilizes a time delay control dissipative bistable stochastic resonance method to enhance and extract the fault characteristics of different degrees of grain mechanical equipment, thereby realizing effective fault diagnosis and qualitative analysis of the grain mechanical equipment. The method dynamically adjusts the system potential function, thereby obtaining a larger output signal-to-noise ratio and a higher characteristic frequency spectrum peak.
The invention relates to a weak fault signal diagnosis method for grain mechanical equipment, which specifically comprises the following steps:
Wherein β and τ are delay feedback parameters, Acos (Ω t) is a weak periodic signal, a is a signal amplitude, Ω is a signal frequency, and ∈ (t) is additive white gaussian noise, and [ [ epsilon ] (t) > ] is 0, [ [ epsilon ] (t ') > ] is 2D δ (t'), the symbol < > is a statistical average, D is a noise intensity, and a dissipative bi-stable posture function is
Wherein a, b and c are system parameters, and a > 0, b > 0, c > 0;
the time delay dissipative bistable stochastic resonance system is described by the langevin equation:
wherein the system effective potential function (without taking into account the periodic signal) is
Fig. 1 shows the result of the change of the effective potential function of the time-delay dissipative bistable stochastic resonance system along with the time delay and the feedback strength, the time-delay feedback item can control the potential well form of the potential function of the traditional dissipative bistable stochastic resonance system, the motion path of particles in the potential well is expanded, the problem of poor system output performance caused by the steep potential well wall of the traditional dissipative bistable stochastic resonance system is effectively solved, and the weak signal diagnosis effect of the dissipative bistable stochastic resonance system is enhanced;
according to the adiabatic approximation theory, the steady state conceptual density function of the system is
FIG. 2 is a graph of the steady state density function of the time delay dissipative bistable state random resonance system under different time delay feedback parameters, wherein the time delay feedback item can change the system steady state density function curve, and the time delay size and the feedback strength have different influences on the particle moving path;
according to the theory of two states, the transition speed of the particle between the two stable states can be calculated to be
In the formula, x±For two steady-state point positions, xunIs the position of an unsteady point, Ueff(x) Representing the effective potential function Ueff(x) The second derivative of (a);
and solving the output signal-to-noise ratio of the time delay dissipative bistable stochastic resonance system by using an adiabatic approximation theory, wherein the evaluation index of the time delay dissipative bistable stochastic resonance system is described by the output signal-to-noise ratio as follows:
in the formula W0=2W±|s(t)=0,W±For the transition rate between two stable states of the time delay dissipative bistable stochastic resonance system, fig. 3 shows the output snr of the time delay dissipative bistable stochastic resonance system (with parameters a, b, and c being 0.5) as a function of the noise intensity when the time delay feedback parameters (a) are different, and (b) when the feedback intensity is different. Wherein, the non-monotonous characteristic of the signal-to-noise ratio along with the noise intensity is found in the two sub-graphs, and the peak value of the signal-to-noise ratio is reduced faster in the process of increasing the feedback intensity than in the process of increasing the time delay, which shows that the time delay is largeThe small selection is crucial;
and 3, determining a time delay feedback parameter according to the time delay control stochastic resonance method in the step 2 aiming at the grain mechanical bearing vibration input signals with different fault degrees, and extracting fault characteristics of the output result of the time delay dissipation stochastic resonance system under the parameter to determine the fault severity.
Substituting properly selected time delay feedback parameters (β, tau) into the time delay dissipative bistable state stochastic resonance system in the step 2, solving the output quantity of the time delay dissipative bistable state stochastic resonance system by adopting a four-order Runge Kutta numerical method, obtaining an enhanced signal of a vibration signal of the grain mechanical bearing through inverse frequency shift and scale change, and finally carrying out spectrum analysis on the enhanced signal to extract the fault characteristics of the grain mechanical bearing.
In order to meet the small-parameter signal input condition under the adiabatic approximation theory of the stochastic resonance system, firstly, the collected vibration signal s of the grain mechanical bearing is preprocessed0(t) calculating the characteristic frequency f of the fault according to the bearing vibration parameter theorydSecondly, according to the calculated fault characteristic frequency value fdTo set the passband cut-off frequency f of the high pass filterhWherein f is to be ensuredh<fdThen, high-pass filtering processing is carried out on the collected bearing vibration signals to eliminate low-frequency noise interference, and frequency shift conversion is carried out on the filtered signals to obtain new frequency fd-f0Therein is shown as fd>f0,f0Representing the amount of frequency shift, here taking f0=fhFinally, selecting a proper variable-scale compression ratio R to convert the input signal of the grain mechanical bearing into a small-parameter frequency input signal conforming to the adiabatic approximation theory:
according to the time delay dissipative bistable stochastic resonance weak feature extraction method, the height and width of a bistable potential well and the steepness of the wall of the potential well are adjusted by introducing a time delay feedback item, so that an effective potential function of the system dynamically changes along with the change of time delay feedback parameters, the motion tracks of Brown particles are enriched, the weak fault feature enhancement extraction capability of a classical dissipative bistable system is improved, then the time delay control dissipative bistable stochastic resonance method is utilized to enhance and extract the fault features of different degrees of grain mechanical equipment, and further the effective fault diagnosis and qualitative analysis of the grain mechanical equipment are realized. The method has the advantage of dynamically adjusting the potential function of the system, thereby obtaining larger output signal-to-noise ratio and higher characteristic frequency spectrum peak. The time delay dissipation bistable stochastic resonance weak feature extraction method is applied to feature enhancement extraction of weak mechanical vibration fault signals of grain mechanical equipment, and weak signal enhancement and fault qualitative analysis are achieved.
The present invention will be described in further detail with reference to examples.
Examples
In order to verify the effectiveness of the weak feature extraction method of the time delay dissipation bistable stochastic resonance system, the method takes the weak useful signal enhancement extraction in the bearing vibration signal of the grain machinery equipment as an example, the outer ring crack of the Rexnord ZA-2115 type rolling bearing is selected for fault diagnosis, the bearing vibration signal is set to be collected once every 10 minutes, the sampling frequency is 20000Hz, the sampling time is 1s, and the relevant structural parameters of the tested bearing are shown in the table 1.
Table 1: testing structural parameters of bearing
Diameter of roller | Pitch diameter of bearing | Number of rolling elements | Contact angle |
71.501mm | 8.407mm | 16 | 15.17 |
Fig. 4 is a waveform diagram of vibration fault signals (a) time domain, (b) frequency spectrum and (c) envelope spectrum of a bearing of an original grain machinery. Wherein, no obvious impact component appears on the time domain waveform, the amplitude of the outer ring fault frequency 236Hz is dominant in the whole envelope spectrum, which indicates that the bearing outer ring is damaged early, and the amplitude of the outer ring fault characteristic frequency is about 0.01; meanwhile, in the whole envelope spectrum, the amplitude of interference frequencies such as noise is large. Therefore, the bearing fault can not be judged by directly carrying out frequency spectrum analysis on the vibration signal of the original grain mechanical bearing.
Therefore, a weak feature extraction method of the time delay dissipative bistable stochastic resonance system is used for diagnosing the fault of the grain mechanical bearing, and the enhanced output time domain waveform and frequency spectrum of the time delay dissipative bistable stochastic resonance system are finally obtained through parameter setting and are shown in fig. 5. According to the frequency spectrum waveform output by the time delay dissipation bistable state stochastic resonance system, the amplitude of the bearing outer ring fault characteristic frequency is amplified by the time delay feedback control stochastic resonance method through collecting noise energy in the bearing vibration signal, the amplitude is about 0.1 and is amplified by about 10 times compared with the amplitude of an original signal envelope spectrum; in addition, the time-delay feedback control stochastic resonance method can accurately optimize weak fault characteristic information in the grain mechanical bearing vibration signal by adjusting the time delay and the feedback strength, so that the weak characteristic extraction method of the time-delay dispersion bistable stochastic resonance system can accurately detect the grain mechanical bearing fault characteristic.
In conclusion, a time delay feedback control item is introduced into the classical dissipative bistable stochastic resonance system to adjust the height and width of the bistable potential well and the steepness of the wall of the potential well, so that the effective potential function of the system dynamically changes along with the change of time delay feedback parameters, the motion trajectory of Brown particles is enriched, the weak fault feature enhancement extraction capability of the classical dissipative bistable system is improved, then the time delay control dissipative bistable stochastic resonance method is used for carrying out enhancement extraction on the fault features of different degrees of mechanical equipment, and the effective fault diagnosis and the qualitative analysis of the mechanical equipment are realized. The method has the advantages that the system potential function is dynamically adjusted, a larger output signal-to-noise ratio and a higher characteristic frequency spectrum peak are obtained, and the method has important significance for extracting weak useful signals in mechanical vibration signals.
While the invention has been described in further detail with reference to specific preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (6)
1. A weak fault signal diagnosis method for grain mechanical equipment is characterized by comprising the following steps:
step 1, introducing a time delay feedback term into a classical dissipative bistable model, and constructing a time delay dissipative bistable stochastic resonance system excited by periodic signals and additive Gaussian noise;
step 2, converting a dominant non-Markov process corresponding to the time delay dissipative bistable state stochastic resonance system constructed in the step 1 into a Markov process, determining an effective potential function of the time delay dissipative bistable state stochastic resonance system, and simultaneously determining the steady-state concept density and the output signal-to-noise ratio of the system;
and 3, aiming at grain mechanical bearing vibration input signals with different fault degrees, determining a time delay feedback parameter according to the time delay control stochastic resonance system effective potential function in the step 2, and extracting fault characteristics of the output result of the time delay dissipation stochastic resonance system under the parameter to determine the fault severity.
2. The weak fault signal diagnosis method for grain machinery equipment according to claim 1, wherein the time delay dissipative bistable stochastic resonance system in step 1 is obtained by introducing a time delay feedback term into a traditional dissipative bistable stochastic resonance system, which is described by langevin equation as:
wherein β and τ are delay feedback parameters, a cos (Ω t) is a weak periodic signal, a is a signal amplitude, Ω is a signal frequency, ε (t) is additive white gaussian noise, and the dissipative bi-stable situation function is:
wherein a, b and c are system parameters, and a > 0, b > 0, c > 0.
4. the method for diagnosing weak fault signals of grain machinery equipment according to claim 2, wherein the system steady-state concept density in step 2 is as follows:
in the formula, D represents the noise intensity.
5. The method for diagnosing the weak fault signal of the grain mechanical equipment according to claim 2, wherein the output signal-to-noise ratio in the step 2 is as follows:
in the formula, W0=2W±|s(t)=0,W±For time-delay dissipation of the transition rate between the two stable states of a bistable stochastic resonance system,
in the formula, x±For two steady-state point positions, xunIs the position of an unsteady point, Ueff(x) Representing the effective potential function Ueff(x) The second derivative of (a).
6. The method for diagnosing the weak fault signal of the grain machinery equipment according to claim 1, wherein the step 3 of extracting the fault feature specifically comprises the steps of performing spectrum analysis on the output of the time delay dissipative bistable stochastic resonance system under a proper time delay feedback parameter (β, τ), extracting the fault feature frequency in the grain machinery vibration signal, and judging the severity of the fault according to the size of a spectrum peak at the fault feature frequency.
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