CN110940524B - Bearing fault diagnosis method based on sparse theory - Google Patents

Abstract

The invention discloses a bearing fault diagnosis method based on a sparse theory, which comprises the following steps: decomposing the collected original vibration signal X (t) of the bearing into N eigenmode functions by empirical mode decomposition, and calculating each eigenmode function c_iEnergy content ratio of (t) gamma_iSorting according to the sequence from large to small, and selecting an eigenmode function corresponding to the maximum energy ratio as an analysis signal x (t); extracting the natural frequency f of the ith order in the bearing by using the analysis signal x (t)_niExcited free decay response x_i(t) from the free decay response x by an optimization algorithm_iExtracting modal parameters in (t); combining the extracted modal parameter sets to form parameter sets by using an impulse response function of a mass-spring second-order damping system as an atomic model, inputting the parameter sets into the atomic model, and constructing a sparse dictionary; and solving a reconstruction signal by using a matching tracking algorithm and combining the constructed sparse dictionary, carrying out envelope demodulation analysis on the reconstruction signal to form an envelope spectrum, and realizing fault diagnosis when fault characteristic frequency of the bearing exists in the envelope spectrum.

Description

Bearing fault diagnosis method based on sparse theory

Technical Field

The disclosure belongs to the field of fault diagnosis, and particularly relates to a bearing fault diagnosis method based on a sparse theory.

Background

The rolling bearing plays an important role as a key part in a rotary machine, and the fault of the rolling bearing directly influences the stable operation of equipment and sometimes even causes the damage and the halt of the equipment. Due to the particularity of the working environment, if many mechanical devices operate under complex working conditions such as variable load, high temperature and the like for a long time, when a bearing part breaks down, the vibration signal of the mechanical devices often shows nonlinear and non-stable characteristics and is extremely easily interfered by environmental noise, the signal-to-noise ratio of the vibration signal is reduced, and the difficulty in extracting fault characteristics is increased.

The key of the fault diagnosis of the rolling bearing is to extract hidden fault characteristics from vibration signals containing harmonic and noise interference. The traditional Fourier transform equal frequency spectrum analysis method can effectively extract fault features from stationary signals, but is not suitable for processing non-stationary signals, and sometimes even obtains wrong analysis results. Compared with the traditional spectrum analysis, the short-time Fourier transform, wavelet transform, Wigner-Ville distribution and other time frequency analysis method can simultaneously extract the local information of the fault signal in the time domain and the frequency domain, is more suitable for the analysis of the non-stationary signal, and is widely applied to the field of fault diagnosis.

Sparse representation has received much attention as one of the research hotspots in recent years in the field of fault diagnosis due to superior performance in signal processing. The core idea is that atoms which are optimally matched with signals are selected from an ultra-complete sparse dictionary to obtain sparse expression of the signals, so that hidden fault features in the fault signals can be extracted more easily. Two key problems of sparse representation are the design of a sparse dictionary and the solution of sparse coefficients, the solution efficiency can be reduced although a certain redundancy can be ensured by the overlarge sparse dictionary, and the matching precision can be reduced by improving the solution efficiency by the undersize sparse dictionary.

In the conventional fault diagnosis based on sparse representation, research on a method for constructing a sparse dictionary by identifying modal parameters of a system is not found. According to the invention, by extracting and designing the sparse dictionary for the system modal parameters, the dictionary atoms are more similar to the original signal structure, the signal reconstruction precision is improved, meanwhile, the dictionary dimensionality can be greatly reduced, and the matching efficiency is improved. Therefore, the research of constructing the sparse dictionary in a mode of identifying modal parameters of the system for fault diagnosis has great practical application potential.

Disclosure of Invention

In view of the above problems, an object of the present disclosure is to provide a bearing fault diagnosis method based on a sparse theory, which effectively designs sparse dictionary atoms more similar to an original signal structure through modal parameters of a recognition system, improves precision of signal reconstruction, and can greatly reduce dimensionality of the sparse dictionary and improve matching efficiency.

The purpose is achieved through the following technical scheme:

a bearing fault diagnosis method based on a sparse theory comprises the following steps:

s100: decomposing the collected original vibration signal X (t) of the bearing into N eigenmode functions by empirical mode decomposition, and calculating each eigenmode function c_iEnergy content ratio of (t) gamma_iSorting according to the sequence from large to small, and selecting an eigenmode function corresponding to the maximum energy ratio as an analysis signal x (t);

s200: extracting the natural frequency f of the ith order in the bearing by using the analysis signal x (t)_niExcited free decay response x_i(t) from the free decay response x by an optimization algorithm_iExtracting modal parameters in (t);

s300: combining the extracted modal parameter sets to form parameter sets by using an impulse response function of a mass-spring second-order damping system as an atomic model, inputting the parameter sets into the atomic model, and constructing a sparse dictionary;

s400: and solving a reconstruction signal by using a matching tracking algorithm and combining the constructed sparse dictionary, carrying out envelope demodulation analysis on the reconstruction signal to form an envelope spectrum, and realizing fault diagnosis when fault characteristic frequency of the bearing exists in the envelope spectrum.

Preferably, in step S100, the energy ratio of each eigenmode function is:

wherein,

c_iw(t) represents the magnitude of the vibration amplitude of the eigenmode function, W represents the length of the signal, and N represents the number of eigenmode functions.

Preferably, in step S200, the free decay response x_iThe expression of (t) is:

wherein,

t represents a time series, A_iRepresenting the amplitude, f_diRepresents the ith order damped natural frequency, ζ_iRepresenting relative damping ratio, theta_iIndicating the phase.

Preferably, the damping natural frequency and the relative damping ratio constitute the modal parameter.

Preferably, the expression of the damping natural frequency is:

wherein, T_isDenotes the time of occurrence of the s-th peak, T_diRepresenting the period of the damping decay and n representing the selected period.

Preferably, the relative damping ratio is calculated by least squares fitting, and specifically includes the steps of:

s201: for free decay response x_i(t) performing Hilbert transform and constructing an analytic signal

Wherein, U_i(t) represents the amplitude of the analytic signal, θ_i(t) represents phase, j represents imaginary unit;

s202: according to the free decay response x_i(t) and analysis signal Z_i(t) calculating the amplitude U_i(t), the amplitude U_iThe expression of (t) is:

taking logarithm to both sides of the above formula to obtain the logarithm of ln U_iLinear equation of (t) -t:

ln U_i(t)＝-2πf_niζ_it+ln A_i

s203: and fitting the linear equation into a straight line through least square fitting, and calculating the relative damping ratio.

Preferably, in step S300, the atomic model has an expression:

wherein t represents a time series, t₀Indicating the moment of occurrence of the pulse, f_dAnd ζ represent the damped natural frequency and relative damping ratio of the atom, respectively.

Preferably, in step S300, the parameter set formed by combining modality parameters is:

F_d＝[f_lc：Δf_d：f_uc]

κ_ζ＝[ζ_lc：Δζ：ζ_uc]

at the same time, a set of pulse occurrence times T is set₀＝[0：Δt：T_c]

Wherein, [ f ]_lc，f_uc]Representing a parameter set F_dUpper and lower limits of [ ζ ]_lc，ζ_uc]Representing a parameter set k_ζUpper and lower limits of, Δ f_dRepresenting a parameter set F_dΔ ζ represents the parameter set κ_ζΔ T denotes the set T₀Step length of (1), T_cRepresenting the length of time of the signal.

Preferably, said parameter set F_dAnd kappa_ζThe upper and lower limits are set according to the background noise, when the noise is large, the modal parameter identification precision is low, and the parameter set F_dAnd kappa_ζThe upper and lower limits of (2) should be large.

Preferably, in step S400, the fault characteristic frequency includes the following:

outer ring fault frequency: f. of_o＝r/60×1/2×n(1-d/D×cosα)

Inner ring failure frequency: f. of_i＝r/60×1/2×n(1+d/D×cosα)

Frequency of rolling element failure: f. of_r＝r/60×1/2×D/d×[1-(d/D)²×cos²(α)]

Cage failure frequency: f. of_c＝r/60×1/2×(1+d/D×cosα)

Wherein r represents the rotation speed in rpm, n represents the number of balls, D represents the diameter of the rolling element, D represents the pitch diameter of the bearing, and α represents the contact angle of the rolling element.

Compared with the prior art, the beneficial effect that this disclosure brought does: the method can effectively design sparse dictionary atoms with a structure more similar to that of an original signal to improve the signal reconstruction precision, and can greatly reduce the dimensionality of the sparse dictionary to improve the matching efficiency.

Drawings

FIG. 1 is a flowchart of a bearing fault diagnosis method based on a sparse theory according to an embodiment of the present disclosure;

FIG. 2 is a schematic diagram of a free decay response extraction result of a bearing fault diagnosis method based on a sparse theory according to an embodiment of the present disclosure;

fig. 3 is a least squares fitting schematic diagram of a bearing fault diagnosis method based on a sparse theory according to an embodiment of the present disclosure.

Detailed Description

In the following description, numerous details are set forth to provide a more thorough explanation of embodiments of the present disclosure. It will be apparent, however, to one skilled in the art that embodiments of the invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form, rather than in detail, in order to avoid obscuring embodiments of the present disclosure. Furthermore, features of different embodiments described below may be combined with each other, unless specifically stated otherwise.

The terms "including" and "having," and any variations thereof, as used in this disclosure, are intended to cover and not be exhaustive. For example, a process, method, system, or article or apparatus that comprises a list of steps or elements is not limited to only those steps or elements but may alternatively include other steps or elements not expressly listed or inherent to such process, method, system, article, or apparatus.

Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the disclosure, and the embodiment described is a portion of but not all embodiments of the disclosure. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It will be appreciated by those skilled in the art that the embodiments described herein may be combined with other embodiments.

The technical solutions of the present disclosure are described in detail below with reference to the accompanying drawings and examples.

In one embodiment, as shown in fig. 1, the present disclosure provides a bearing fault diagnosis method based on a sparse theory, including the following steps:

s100: through empirical mode decompositionDecomposing the collected original vibration signal X (t) of the bearing into N eigenmode functions, and calculating each eigenmode function c_iEnergy content ratio of (t) gamma_iSorting according to the sequence from large to small, and selecting an eigenmode function corresponding to the maximum energy ratio as an analysis signal x (t);

in the step, firstly, a simulation experiment needs to be carried out on the fault bearing, and simulation parameters are as follows: the sampling frequency is 12kHz, the sampling time is 0.5s, the fault frequency is 60Hz, and the signal-to-noise ratio is-5 dB. The method comprises the steps of collecting original vibration signals through a sensor, and eliminating low-frequency harmonics and high-frequency interference caused by system nonlinearity by carrying out empirical mode decomposition filtering processing on the original vibration signals to obtain analysis signals.

S200: extracting the natural frequency f of the ith order in the bearing by using the analysis signal x (t)_niExcited free decay response x_i(t) from the free decay response x by an optimization algorithm_iExtracting modal parameters in (t);

s300: combining the extracted modal parameter sets to form parameter sets by using an impulse response function of a mass-spring second-order damping system as an atomic model, inputting the parameter sets into the atomic model, and constructing a sparse dictionary;

in the step, assuming that the bearing structure is a single-degree-of-freedom linear vibration system, when the bearing is defective, a vibration response model of the bearing structure can be approximately described as a unit impulse response function of a mass-spring second-order damping system, and the impulse response function is taken as an atomic model.

S400: and solving a reconstruction signal by using a matching tracking algorithm and combining the constructed sparse dictionary, carrying out envelope demodulation analysis on the reconstruction signal to form an envelope spectrum, and realizing fault diagnosis when fault characteristic frequency of the bearing exists in the envelope spectrum.

In the step, the matching pursuit algorithm is a greedy sparse representation algorithm, the signal can be decomposed into a group of linear combinations of basis functions, and the basic idea of the algorithm is to match the signal with a sparse dictionary and select the best matching atom from the sparse dictionary to construct sparse approximation of the signal, so that hidden fault feature information in the signal is extracted. Reconstructing a signal by using a matching pursuit algorithm, wherein the matching precision is directly influenced by the design of sparse dictionary atoms, and the more similar the structure of the dictionary atoms is to the original signal, the higher the matching precision is; meanwhile, the matching efficiency is influenced by the dimension of the sparse dictionary, and the smaller the dimension of the dictionary is, the higher the matching efficiency is. Therefore, the sparse dictionary designed by the method can effectively improve the accuracy and the matching efficiency of signal reconstruction.

In another embodiment, in step S100, the energy ratio of each eigenmode function is:

wherein,

c_iw(t) represents the magnitude of the vibration amplitude of the eigenmode function, W represents the length of the signal, and N represents the number of eigenmode functions.

In another embodiment, as shown in FIG. 2, the free decay response x described in step S200_iThe expression of (t) is:

wherein,

t represents a time series, A_iRepresenting the amplitude, f_diRepresents the ith order damped natural frequency, ζ_iRepresenting relative damping ratio, theta_iIndicating the phase.

In another embodiment, the modal parameters include a damping natural frequency and a relative damping ratio.

In another embodiment, the damping natural frequency is expressed by:

wherein, T_isIndicates the time of occurrence of the S-th peak, T_diRepresenting the period of the damping decay and n representing the selected period.

In this embodiment, the damping natural frequency can be generally determined by the damping decay period T_di(time interval between any two adjacent peaks) and in order to reduce calculation errors caused by cycle number selection, the embodiment solves the damping natural frequency by selecting the first n damping attenuation cycles.

In another embodiment, for the identification of the relative damping ratio, since it is sensitive to the magnitude of the signal amplitude, and a formula solution tends to introduce a large error, the calculation is performed by using a least square fitting method in this embodiment, which specifically includes the following steps:

s201: for free decay response x_i(t) performing Hilbert transform and constructing an analytic signal

Wherein, U_i(t) represents the amplitude of the analytic signal, θ_i(t) represents phase, j represents imaginary unit;

s202: according to the free decay response x_i(t) and analysis signal Z_i(t) calculating the amplitude U_i(t), the amplitude U_iThe expression of (t) is:

taking logarithm to both sides of the above formula to obtain the logarithm of ln U_iLinear equation of (t) -t:

ln U_i(t)＝-2πf_niζ_it+ln A_i

s203: and fitting the linear equation into a straight line through least square fitting, and calculating the relative damping ratio.

In this step, as shown in FIG. 3, the black dot-and-dash line indicates ln U_i(t) -t, it can be seen that the ln U is caused by errors in calculation, measurement, and the like_i(t) -t are not ideal straight lines, and the solid line indicates ln U_i(t) -t least squares fit.

In another embodiment, in step S300, the atomic model has the following expression:

wherein t represents a time series, t₀Indicating the moment of occurrence of the pulse, f_dAnd ζ represent the damped natural frequency and relative damping ratio of the atom, respectively.

In another embodiment, in step S300, the parameter set formed by the combination of modality parameter sets is:

F_d＝[f_lc：Δf_d：f_uc]

κ_ζ＝[ζ_lc：Δζ：ζ_uc]

at the same time, a set of pulse occurrence times T is set₀＝[0：Δt：T_c]

Wherein, [ f ]_lc，f_uc]Representing a parameter set F_dUpper and lower limits of [ ζ ]_lc，ζ_uc]Representing a parameter set k_ζUpper and lower limits of, Δ f_dRepresenting a parameter set F_dΔ ζ represents the parameter set κ_ζΔ T denotes the set T₀Step length of (1), T_cRepresenting the length of time of the signal.

In this embodiment, for the selection of the step length, Δ f is set to better reduce the dimensionality of the sparse dictionary_d＝0.01f_d，Δζ＝0.002，Δt＝1/f_sWherein f is_sRepresenting the sampling frequency of the original signal.

In another embodiment, said parameter set F_dAnd kappa_ζThe upper and lower limits are set according to the background noise, when the noise is large, the modal parameter identification precision is low, and the parameter set F_dAnd kappa_ζThe upper and lower limits of (2) should be large.

In another embodiment, in step S400, the fault characteristic frequency includes the following:

outer ring fault frequency: f. of_o＝r/60×1/2×n(1-d/D×cosα)

Inner ring failure frequency: f. of_i＝r/60×1/2×n(1+d/D×cosα)

Frequency of rolling element failure: f. of_r＝r/60×1/2×D/d×[1-(d/D)²×cos²(α)]

Cage failure frequency: f. of_c＝r/60×1/2×(1+d/D×cosα)

Wherein r represents the rotation speed in rpm, n represents the number of balls, D represents the diameter of the rolling element, D represents the pitch diameter of the bearing, and α represents the contact angle of the rolling element.

The methods proposed by the present disclosure are exemplarily described below.

1. The method comprises the steps of collecting original vibration signals of a fault bearing, obtaining the energy occupation ratio of each eigenmode function through empirical mode decomposition (see table 1), and selecting modal parameters of a component 2 frequency band signal extraction system.

TABLE 1

Eigenmode function	Component	1	Component 2	Component 3	Component 4	Component 5
							Energy ratio	0.4714	0.2862	0.1008	0.0584	0.0333

2. Using step S200, the damping natural frequency f can be obtained_d11785Hz, relative damping ratio ζ₁＝0.0547。

3. With step S300, parameter set F is obtained_d1＝[0.9f_d1：0.01f_d1：1.1f_d1]，κ_ζ1＝[0.8ζ_o：0.002：1.2ζ_o]Simultaneously setting a set of pulse occurrence times T₀＝[0：1/12000：0.5]And constructing a sparse dictionary.

4. And (3) solving a reconstruction signal by using a matching tracking algorithm in combination with the sparse dictionary constructed in the step (S300), carrying out envelope demodulation analysis on the reconstruction signal to form an envelope spectrum, and finding that a peak value with a fault characteristic frequency of 60Hz exists.

In conclusion, the sparse dictionary designed by the method can effectively realize the diagnosis of the bearing fault.

While the embodiments of the disclosure have been described above in connection with the drawings, the disclosure is not limited to the specific embodiments and applications described above, which are intended to be illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto and changes may be made without departing from the scope of the disclosure as set forth in the claims that follow.

Claims (8)

1. A bearing fault diagnosis method based on a sparse theory comprises the following steps:

s100: decomposing the collected original vibration signal X (t) of the bearing into N eigenmode functions by empirical mode decomposition, and calculating each eigenmode function c_iEnergy content ratio of (t) gamma_iSorting according to the sequence from large to small, and selecting an eigenmode function corresponding to the maximum energy ratio as an analysis signal x (t);

s200: extracting the natural frequency f of the ith order in the bearing by using the analysis signal x (t)_niExcited free decay response x_i(t) from the free decay response x by an optimization algorithm_i(t) extracting modal parameters, wherein the free decay response x_iThe expression of (t) is:

wherein,

t represents a time series, A_iRepresenting the amplitude, f_diRepresents the ith order damped natural frequency, ζ_iRepresenting relative damping ratio, theta_iRepresents the phase;

and, the relative damping ratio is calculated by least squares fitting, specifically comprising the steps of:

s201: for free decay response x_i(t) performing Hilbert transform and constructing an analytic signal

Wherein, U_i(t) represents the amplitude of the analytic signal, θ_i(t) represents phase, j represents imaginary unit;

s202: according to the free decay response x_i(t) and analysis signal Z_i(t) calculating the amplitude U_i(t), the amplitude U_iThe expression of (t) is:

taking the logarithm of both sides of the above formula at the same time to obtain lnU_iLinear equation of (t) -t:

lnU_i(t)＝-2πf_niζ_it+lnA_i

s203: fitting the linear equation into a straight line through least square fitting, and calculating a relative damping ratio;

s300: combining the extracted modal parameter sets to form parameter sets by using an impulse response function of a mass-spring second-order damping system as an atomic model, inputting the parameter sets into the atomic model, and constructing a sparse dictionary;

s400: and solving a reconstruction signal by using a matching tracking algorithm and combining the constructed sparse dictionary, carrying out envelope demodulation analysis on the reconstruction signal to form an envelope spectrum, and realizing fault diagnosis when fault characteristic frequency of the bearing exists in the envelope spectrum.

2. The method according to claim 1, wherein in step S100, the energy ratio of each eigenmode function is:

wherein,

c_iw(t) represents the magnitude of the vibration amplitude of the eigenmode function, W represents the length of the signal, and N represents the magnitude of the vibrationThe number of eigenmode functions.

3. The method according to claim 1, wherein the damping natural frequency and relative damping ratio constitute the modal parameters.

4. A method according to claim 1 or 3, wherein the damping natural frequency is expressed by:

wherein, T_isIndicates the time of occurrence of the S-th peak, T_diRepresenting the period of the damping decay and n representing the selected period.

5. The method according to claim 1, wherein in step S300, the atomic model has the expression:

wherein t represents a time series, t₀Indicating the moment of occurrence of the pulse, f_dAnd ζ represent the damped natural frequency and relative damping ratio of the atom, respectively.

6. The method according to claim 1, wherein in step S300, the parameter set formed by the combination of the modal parameter sets is:

F_d＝[f_lc：Δ_fd：f_uc]

κ_ζ＝[ζ_lc：Δζ：ζ_uc]

at the same time, a set of pulse occurrence times T is set₀＝[0：Δt：T_c]

Wherein, [ f ]_lc，f_uc]Representing a parameter set F_dUpper and lower limits of [ ζ ]_lc，ζ_uc]Representing a parameter set k_ζUpper and lower limits of, Δ f_dRepresenting a parameter set F_dΔ ζ represents the parameter set κ_ζΔ T denotes the set T₀Step length of (1), T_cRepresenting the length of time of the signal.

7. Method according to claim 6, characterized in that said parameter set F_dAnd kappa_ζThe upper and lower limits are set according to the background noise, when the noise is large, the modal parameter identification precision is low, and the parameter set F_dAnd kappa_ζThe upper and lower limits of (2) should be large.

8. The method according to claim 1, wherein in step S400, the fault signature frequency comprises the following:

outer ring fault frequency: f. of_o＝r/60×1/2×n(1-d/D×cosα)

Inner ring failure frequency: f. of_i＝r/60×1/2×n(1+d/D×cosα)

Frequency of rolling element failure: f. of_r＝r/60×1/2×D/d×[1-(d/D)²×cos²(α)]Cage failure frequency: f. of_c＝r/60×1/2×(1+d/D×cosα)

Wherein r represents the rotation speed in rpm, n represents the number of balls, D represents the diameter of the rolling element, D represents the pitch diameter of the bearing, and α represents the contact angle of the rolling element.

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