Bearing fault size estimation method based on waveform time interval
By performing time spectrum analysis and random model establishment of bearing vibration signals, the mean of impact duration is calculated, and the bearing fault size is estimated using linear regression fitting method, which solves the problem of difficulty in accurately estimating bearing fault size in the prior art, and achieves high-accurate fault size estimation.
Patent Information
- Application Number
- CN202510327870.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-19
- Publication Date
- 2025-06-24
AI Technical Summary
The prior art is difficult to effectively estimate the fault size of bearings, and there is a lack of accurate estimation methods.
By performing time spectrum analysis on the vibration signal of the bearing, a random model is established and the model parameters are estimated, and the Poisson distribution of time is determined, so as to calculate the mean of the impact duration, and finally the fault size of the bearing is estimated by linear regression fitting method.
Accurate estimation of bearing fault size is achieved, the estimation results are close to the true fault size, and are all within a 90% confidence interval, effectively making up for the defect that the fault size cannot be accurately estimated in the prior art.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of bearing condition monitoring, and particularly relates to a method for estimating bearing fault size based on waveform time interval. Background Art
[0002] As a key component of rotating machinery, rolling bearings are widely used in various industries such as aerospace, transportation, and wind power generation. Since its main functions are to reduce the friction between the rotating shaft and the supporting structure, ensure the smoothness and accuracy of the transmission system, and bear axial and radial loads. Therefore, rolling bearings are in a long-term operating state or even in a harsh operating environment of high speed and heavy load in these industries, making rolling bearings extremely prone to failure. If early faults of bearings can be detected and diagnosed, malignant accidents can be avoided and economic losses can be reduced.
[0003] The assessment of the severity of bearing faults plays a key role in its degradation process. Accurately predicting the deterioration size of bearings can not only assist in formulating maintenance decisions, but also determine the equipment shutdown time in advance and reserve sufficient preparation time for maintenance planning. At present, the estimation of bearing fault size is very challenging, and there is a lack of effective estimation methods in both academia and industry. The technical problem to be solved by the present invention is: to overcome the deficiencies of the existing bearing fault size estimation methods, calculate the duration of the impact using random model parameters, and thus effectively estimate the bearing fault size. Summary of the Invention
[0004] The present invention provides a method for estimating bearing fault size based on waveform time interval, which calculates the duration of the impact using random model parameters, and thus effectively estimates the bearing fault size.
[0005] According to one aspect of the present disclosure, there is provided a method for estimating bearing fault size based on waveform time interval, the method comprising: Performing a time-frequency spectrum on the disturbed non-stationary signal; Establishing a random model based on the time-frequency spectrum of the signal, estimating the model parameters, and determining the Poisson distribution of time in the model; Calculating the mean value of the impact duration based on the Poisson distribution; Estimating the bearing fault size by means of linear regression fitting according to the mean value.
[0006] In a possible implementation manner, performing a time-frequency spectrum on the disturbed non-stationary signal includes: Collecting the vibration signal of the target bearing y t , t = 1, 2, 3,..., T, where T is the number of time points of a single signal sample, and the sampling frequency is ; Select the window function ω(t) and use equation (1) to calculate the vibration signal Perform short-time Fourier transform STFT: (1) where Y(n,f) is the complex amplitude at time n and frequency f, n = 1, 2, 3, ..., , f = 1, 2, 3, ..., ; The STFT coefficient Yn=[Y(n,1),…,Y(n,N_f)] converges to a complex-valued Gaussian distribution. After decentralization, it is further simplified to a circularly symmetric Gaussian distribution, as shown in formula (2): (2) in, represents the covariance matrix of the distribution, represents the conjugate transpose; where the centering is Yn minus its mean.
[0007] In a possible implementation, a random model is established based on the time-frequency spectrum of the signal, and model parameters are estimated to determine the Poisson distribution of time in the model; including: 2-1: Take the sequence Yn as the observation sequence of the random module. The hidden state sequence variable Zn in the model has two states i∈{1,2} in the bearing vibration signal, where the noise state i =1, indicating that only noise exists; transient impact state i =2, indicating that there is an impact phenomenon, and the duration of each state The description is as follows: The Poisson distribution of is as follows: (3) Among them, the Poisson parameter Indicates status i The number of lower averaging windows, p is a positive integer; 2-2: Based on the concept of 2-1, introduce a dynamic variable , indicating that at time n Current state i The number of windows that have been experienced, if the state i The start and end of n 1 and n 2, then ,in ,and is a random variable d i A sample of 2-3: Transition probability matrix in random model is a dependency A 2×2 dynamic matrix with diagonal elements represents the transition probability of the same state. Since the duration follows a Poisson distribution, Will follow Reduce, The Poisson cumulative distribution function is expressed as formula (4): (4) in, Indicates that the parameter is The cumulative distribution function of the Poisson distribution, numerator Represents a time series in time n Keep in state i At least The probability of , then the dynamic transition probability matrix As shown in formula (5): (5) 2-4: Calculate different times n The forward probability and the backward probability , the formula is as follows: (6) (7) in, Indicates at time n Current state i The update formula is as follows: (8) 2-5: Use the forward and backward probability formula to calculate from the state i Transition to state j In a given observation sequence The probability of , formula (9) is as follows: (9) 2-6: In the Poisson distribution, the parameter The maximum likelihood estimate of is the sample mean, and the parameter The estimation method is as follows: (10) Among them, the weight Indicates from the state i Transition to state j The probability of Indicates that it is calculated only at the state transition time The weighted average of .
[0008] In a possible implementation, the mean of the impact duration is calculated based on the Poisson distribution, including: Using the Poisson distribution parameters Calculate the mean impact duration, where Indicates the average number of windows covering the impact state; represents the average number of windows between shocks, then the corresponding mean shock duration The calculation formula is: (11) in, The time consists of two parts. One part is the attenuation resonance time after the bearing rolling element leaves the fault area. The other part of the time is the time it takes for the rolling element to pass through the fault area. .
[0009] In a possible implementation, estimating the bearing fault size by a linear regression fitting method according to the mean value includes: 4-1: For a faulty bearing with a fixed outer ring, fault size l and impact duration The relationship is as follows: (12) in, They represent the outer ring fault size, inner ring fault size and rolling element fault size respectively; D and d represent the outer diameter and inner diameter of the bearing respectively. Indicates the failure frequency of the bearing cage; Formula (12) is transformed into the general form as formula (13): (13) in, yes function, that is, the bearing speed Function of 4-2: For a faulty bearing, collect data at different speeds J groups of vibration signals, j=1,2,...J, calculate the impact duration under different speed signals respectively , resonance decay time Estimated duration of impact and The intercept of the linear regression; 4-3: Through formula (12), using the bearing's collective parameters D and d and the calculated , calculate the size l of the bearing fault.
[0010] Compared with the prior art, the present invention has the following beneficial effects: The classic bimodal estimation theory estimates the fault size using the time interval between two pulses. The present invention uses random model parameters to calculate the average duration of the signal impact, and then cleverly fits the bearing fault size using the least squares method.
[0011] Through the verification of case effects, the estimated bearing fault sizes are close to the actual fault sizes and are all within the 90% confidence interval. This invention makes up for the defect that the fault size cannot be accurately estimated in existing research. This invention can provide good guidance for bearing fault diagnosis and intelligent operation and maintenance. BRIEF DESCRIPTION OF THE DRAWINGS
[0012] Figure 1 Schematic diagram of the explicit duration hidden Markov model (EDHMM).
[0013] Figure 2 Schematic diagram of bearing vibration signal.
[0014] Figure 3 Schematic diagram of fault size estimation by linear regression.
[0015] Figure 4 Verify the bearing fault size calculation effect diagram. DETAILED DESCRIPTION
[0016] Various exemplary embodiments, features and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.
[0017] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.
[0018] In addition, in order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the main purpose of the present disclosure.
[0019] Figure 1 Schematic diagram of the explicit duration hidden Markov model (EDHMM).
[0020] Figure 2 Schematic diagram of bearing vibration signal.
[0021] Figure 3 Schematic diagram of fault size estimation by linear regression.
[0022] Figure 4 Validation of bearing fault size calculation results. The upper and lower limits of each estimated point represent the 90% confidence interval.
[0023] The present invention estimates the bearing fault size by using the signal impact time interval. Figure 1 The schematic diagram of the explicit duration hidden Markov model EDHMM is shown. The hidden state duration function p(d i ), where state i contains di observation samples, and each observation follows a circularly symmetric complex-valued Gaussian distribution. Figure 2 Shows the composition of impact time when a bearing fails, including the time to pass the failure and resonance decay time , where point A indicates that the rolling element enters the fault area, and point B indicates that the rolling element leaves the fault area. The fault passing time is . Figure 3 The calculation method for estimating bearing size is illustrated. Figure 4 The validation results are on the Case Western Reserve University bearing dataset.
[0024] This example uses the bearing data set of Case Western Reserve University, and selects 12 groups of inner ring fault bearings as the verification case set. The fault size, load, and speed data are shown in the following table. The 12 groups are divided into 3 different fault sizes, and each fault size contains 4 types of speed information. The sampling frequency of the data is 48Hz.
[0025] Table 1 shows the working condition information of 12 groups of inner ring fault bearings ; The selected bearing data is subjected to a time-frequency spectrum. This embodiment uses the short-time Fourier transform (STFT) for illustration, and other time-frequency transforms are also applicable. The calculation is shown in formula (1). The window width N of the STFT in the method is w The window shift R needs to be specifically selected according to the speed sampling frequency of the vibration signal. In this embodiment, Nw=128, R=8. After short-time Fourier transform, the coefficients Yn,n=1,2,3,…,N n , used in subsequent random models.
[0026] Through the forward and backward iterative algorithm, the state transition probability in the model is obtained , the specific formula is shown in formula (9), and the Poisson parameter of the signal in different states and , the specific formula is shown in formula (10).
[0027] By using the Poisson parameter under shock state Calculate the average duration of the 12 groups of signals in Table 1 under the impact state , the specific formula is shown in formula (11).
[0028] Using the method of linear regression, linear fitting is performed on four groups of data with different motor speeds, as shown in Figure 3 the schematic illustration. A fitting curve can be obtained, and the intercept is obtained.
[0029] Using formula (12), the bearing sizes of 12 groups of signals are calculated, as shown in Figure 4 the illustration, where the abscissa is the true fault size and the ordinate is the estimated bearing size. Figure 4 The 90% confidence interval is also given.
[0030] Through the verification of the case effect, the estimated bearing fault sizes are all close to the true fault sizes and are all within the 90% confidence interval. The present invention well makes up for the defect that the fault size cannot be accurately estimated in the existing research. The present invention can provide very good guiding significance for bearing fault diagnosis and intelligent operation and maintenance.
[0031] According to one aspect of the present disclosure, there is provided a method for estimating a bearing fault size based on a waveform time interval, the method comprising: Performing a time-frequency spectrum on the disturbed non-steady signal; Establishing a stochastic model based on the time-frequency spectrum of the signal, estimating model parameters, and determining the Poisson distribution of time in the model; Calculating the mean value of the impact duration based on the Poisson distribution; Estimating the bearing fault size by a linear regression fitting method according to the mean value.
[0032] In a possible implementation manner, performing a time-frequency spectrum on the disturbed non-steady signal includes: Collecting the vibration signal of the target bearing y t , t = 1, 2, 3,..., T, where T is the number of time points of a single signal sample, and the sampling frequency is ; Selecting a window function ω(t), and performing a short-time Fourier transform STFT on the vibration signal through formula (1): (1) where Y(n, f) is the complex amplitude at time n and frequency f, n = 1, 2, 3,..., , f = 1, 2, 3,..., ; The STFT coefficients Yn = [Y(n,1), …, Y(n,N_f)] converge to a Gaussian distribution of complex values in distribution, and after de-centering processing, it is further simplified to a circularly symmetric Gaussian distribution, as shown in formula (2): (2) wherein, represents the covariance matrix of the distribution, represents the conjugate transpose; wherein, the de-centering process is that Yn subtracts its mean value.
[0033] In a possible implementation, a random model is established based on the time-frequency spectrum of the signal, and the model parameters are estimated to determine the Poisson distribution of time in the model; it includes: 2-1: The sequence Yn is used as the observation sequence of the random model. There are two states i∈{1,2} for the hidden state sequence variable Zn in the bearing vibration signal. Among them, the noise state i =1 indicates that only noise exists; the transient impact state i =2 indicates that an impact phenomenon appears. The duration of each state is described by a Poisson distribution with parameter , as shown in Equation (3), (3) wherein, the Poisson parameter represents the number of average windows in state i , and p is a positive integer; 2-2: Based on the concept of 2-1, a dynamic variable is introduced, which represents the number of windows that have elapsed at the current state n at time i . If the start and end of state i occur at times n 1 and n 2 respectively, then , where , and is a sample of the random variable d i d i ; 2-3: The transition probability matrix in the random model is a 2×2 dynamic matrix that depends on . Among them, the diagonal element represents the transition probability of the same state. Since the duration follows a Poisson distribution, will decrease as decreases, and is expressed by the Poisson cumulative distribution function as Equation (4): (4) wherein, represents the cumulative distribution function of the Poisson distribution with parameter . The numerator represents that the time series remains in the state n at time iAt least The probability of , then the dynamic transition probability matrix As shown in formula (5): (5) 2-4: Calculate different times n The forward probability and the backward probability , the formula is as follows: (6) (7) in, Indicates at time n Current state i The update formula is as follows: (8) 2-5: Use the forward and backward probability formula to calculate from the state i Transition to state j In a given observation sequence The probability of , formula (9) is as follows: (9) 2-6: In the Poisson distribution, the parameter The maximum likelihood estimate of is the sample mean, and the parameter The estimation method is as follows: (10) Among them, the weight Indicates from the state i Transition to state j The probability of Indicates that it is calculated only at the state transition time The weighted average of .
[0034] In a possible implementation, the mean of the impact duration is calculated based on the Poisson distribution, including: Using the Poisson distribution parameters Calculate the mean impact duration, where Indicates the average number of windows covering the impact state; represents the average number of windows between shocks, then the corresponding mean shock duration The calculation formula is: (11) in, The time consists of two parts. One part is the attenuation resonance time after the bearing rolling element leaves the fault area. , and the other part of the time is the time when the rolling element passes through the fault area .
[0035] In a possible implementation, estimating the bearing fault size according to the mean value by the linear regression fitting method includes: 4-1: For a fault bearing with a fixed outer ring, the fault size l and the impact duration are related as follows: (12) Where respectively represent the outer ring fault size, the inner ring fault size and the rolling element fault size; D and d respectively represent the outer diameter and the inner diameter of the bearing, represents the fault frequency of the bearing cage; Equation (12) is transformed into the general form as Equation (13): (13) Where is a function of, that is, a function of the bearing rotation frequency ; 4-2: For a fault bearing, collect J groups of vibration signals at different rotational speeds j = 1, 2,... J, and calculate the impact duration under the signals at different rotational speeds respectively, and the resonance decay time is estimated as the intercept of the linear regression of the impact duration and ; 4-3: Through Equation (12), using the set parameters D and d of the bearing and the calculated , calculate the size l of the bearing fault.
[0036] The above has described the embodiments of the present disclosure. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art in the technical field without departing from the scope and spirit of the described embodiments. The selection of the terms used herein is intended to best explain the principles of the embodiments, the practical application or the improvement of the technology in the market, or to enable other ordinary skill in the art in the technical field to understand the embodiments disclosed herein.
Claims
1. A method for estimating bearing fault size based on waveform time interval, characterized in that: The method comprises: Make time-frequency spectrum of disturbed non-steady-state signal; A random model is established based on the time-frequency spectrum of the signal, and the model parameters are estimated to determine the Poisson distribution of time in the model; The mean of the shock duration was calculated based on the Poisson distribution; The bearing fault size is estimated based on the mean value by a linear regression fitting method.
2. A method for estimating bearing fault size based on waveform time interval according to claim 1, characterized in that: The time spectrum of the disturbed non-stationary signal includes: Collect vibration signals of target bearings y t， t =1, 2, 3,...,T, where T is the number of time points of a single signal sample and the sampling frequency is ; Select the window function ω(t) and use equation (1) to calculate the vibration signal Perform short-time Fourier transform STFT: (1) where Y(n,f) is the complex amplitude at time n and frequency f, n = 1, 2, 3, ..., , f = 1, 2, 3, ..., ; The STFT coefficient Yn=[Y(n,1),…,Y(n,N_f)] converges to a complex-valued Gaussian distribution. After decentralization, it is further simplified to a circularly symmetric Gaussian distribution, as shown in formula (2): （2） in, represents the covariance matrix of the distribution, represents the conjugate transpose; where the centering is Yn minus its mean.
3. A method for estimating bearing fault size based on waveform time interval according to claim 2, characterized in that: A random model is established based on the time-frequency spectrum of the signal, and the model parameters are estimated to determine the Poisson distribution of time in the model; including: 2-1: Take the sequence Yn as the observation sequence of the random module. The hidden state sequence variable Zn in the model has two states i∈{1,2} in the bearing vibration signal, where the noise state i =1, indicating that only noise exists; transient impact state i =2, indicating that there is an impact phenomenon, and the duration of each state The description is as follows: The Poisson distribution of is as follows: (3) Among them, the Poisson parameter Indicates status i The number of lower averaging windows; 2-2: Based on the concept of 2-1, introduce a dynamic variable , indicating that at time n Current state i The number of windows that have been experienced, if the state i The start and end of n 1 and n 2, then ,in ,and is a random variable d i A sample of 2-3: Transition probability matrix in random model is a dependency A 2×2 dynamic matrix with diagonal elements represents the transition probability of the same state. Since the duration follows a Poisson distribution, Will follow Reduce, The Poisson cumulative distribution function is expressed as formula (4): （4） in, Indicates that the parameter is The cumulative distribution function of the Poisson distribution, numerator Represents a time series in time n Keep in state i At least The probability of , then the dynamic transition probability matrix As shown in formula (5) (5) 2-4: Calculate different times n The forward probability and the backward probability , the formula is as follows: (6) (7) in, Indicates at time n Current state i The update formula is as follows: （8） 2-5: Use the forward and backward probability formula to calculate the state i Transition to state j In a given observation sequence The probability of , formula (9) is as follows: （9） 2-6: In the Poisson distribution, the parameter The maximum likelihood estimate of is the sample mean, and the parameter The estimation method is as follows: (10) Among them, the weight Indicates from the state i Transition to state j The probability of Indicates that it is calculated only at the state transition time The weighted average of .
4. A method for estimating bearing fault size based on waveform time interval according to claim 3, characterized in that: The mean of the impact duration is calculated based on the Poisson distribution, including: Using the Poisson distribution parameters Calculate the mean impact duration, where Indicates the average number of windows covering the impact state; represents the average number of windows between shocks, then the corresponding mean shock duration The calculation formula is: (11) in, The time consists of two parts. One part is the attenuation resonance time after the bearing rolling element leaves the fault area. The other part of the time is the time it takes for the rolling element to pass through the fault area. .
5. A method for estimating bearing fault size based on waveform time interval according to claim 4, characterized in that: The bearing fault size is estimated according to the mean value by a linear regression fitting method, including: 4-1: For a faulty bearing with a fixed outer ring, fault size l and impact duration The relationship is as follows: （12） in, They represent the outer ring fault size, inner ring fault size and rolling element fault size respectively; D and d represent the outer diameter and inner diameter of the bearing respectively. Indicates the failure frequency of the bearing cage; Formula (12) is transformed into the general form as formula (13): (13) in, yes function, that is, the bearing speed Function of 4-2: For a faulty bearing, collect data at different speeds J groups of vibration signals, j=1,2,...J, calculate the impact duration under different speed signals respectively , resonance decay time Estimated duration of impact and The intercept of the linear regression; 4-3: Through formula (12), using the bearing's collective parameters D and d and the calculated , calculate the size l of the bearing fault.