CN111159846A - Rolling bearing residual effective life prediction method based on fractional levy stable motion - Google Patents
Rolling bearing residual effective life prediction method based on fractional levy stable motion Download PDFInfo
- Publication number
- CN111159846A CN111159846A CN201911223070.2A CN201911223070A CN111159846A CN 111159846 A CN111159846 A CN 111159846A CN 201911223070 A CN201911223070 A CN 201911223070A CN 111159846 A CN111159846 A CN 111159846A
- Authority
- CN
- China
- Prior art keywords
- fractional
- levy
- index
- rolling bearing
- stable motion
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 63
- 230000033001 locomotion Effects 0.000 title claims abstract description 47
- 238000005096 rolling process Methods 0.000 title claims abstract description 36
- 238000006731 degradation reaction Methods 0.000 claims abstract description 46
- 230000006870 function Effects 0.000 claims abstract description 28
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 24
- 230000015556 catabolic process Effects 0.000 claims abstract description 21
- 238000009792 diffusion process Methods 0.000 claims abstract description 13
- 238000000342 Monte Carlo simulation Methods 0.000 claims abstract description 4
- 230000014509 gene expression Effects 0.000 claims description 11
- 238000004088 simulation Methods 0.000 claims description 5
- 239000006185 dispersion Substances 0.000 claims description 3
- 239000002699 waste material Substances 0.000 abstract description 2
- 230000008569 process Effects 0.000 description 8
- 230000000694 effects Effects 0.000 description 7
- 238000009826 distribution Methods 0.000 description 5
- 230000005653 Brownian motion process Effects 0.000 description 4
- 238000005537 brownian motion Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 4
- 238000011156 evaluation Methods 0.000 description 4
- 101001095088 Homo sapiens Melanoma antigen preferentially expressed in tumors Proteins 0.000 description 3
- 102100037020 Melanoma antigen preferentially expressed in tumors Human genes 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 3
- 238000002474 experimental method Methods 0.000 description 3
- 230000001133 acceleration Effects 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 239000000126 substance Substances 0.000 description 2
- 238000007476 Maximum Likelihood Methods 0.000 description 1
- 230000002159 abnormal effect Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 230000036541 health Effects 0.000 description 1
- 238000009776 industrial production Methods 0.000 description 1
- 230000007774 longterm Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
Abstract
The invention relates to a method for predicting the residual effective life of a rolling bearing based on fractional levy stable motion, which comprises the following steps: 1) decomposing the original vibration signal of the rolling bearing into K intrinsic mode functions by using a variational mode decomposition method, and selecting an optimal mode according to monotonicity, robustness and tendency indexes; 2) modeling the degradation process of the bearing by utilizing the score Levy-based stable motion to obtain a degradation model; 3) setting a fault threshold, acquiring a Hurst index of the fraction Levy stable motion for the degradation model in the step 2), estimating model parameters, and acquiring an estimated value of a characteristic index, an estimated value of a drift coefficient and an estimated value of a diffusion coefficient; 4) substituting the parameters obtained in the step 3) into the degradation model in the step 2), and predicting the residual effective life of the bearing by using a Monte Carlo method. Compared with the prior art, the method has the advantages of accurate prediction, reduction of resource waste and the like.
Description
Technical Field
The invention relates to the field of prediction of residual service life of a rolling bearing, in particular to a prediction method of residual effective service life of a rolling bearing based on fractional levy stable motion.
Background
Nowadays, various mechanical devices in modern industry have certain service lives, and if the mechanical devices are not processed, the mechanical devices beyond the service lives can be out of order, so that the prediction of the remaining service life of large rotating equipment becomes a problem which is concerned day by day. There are many methods for predicting the remaining useful life of a rotating device, such as the wiener process, the markov process, the gamma process, which are all memoryless. Since the degradation process of the rolling bearing is not only related to the current state but also related to the historical state, i.e. the degradation process is a long-term slowly-changing process with long memory or long correlation, the above process cannot accurately predict the remaining service life of the rotating equipment.
In large rotating equipment, the inner ring vibration signal is collected by an acceleration sensor mounted on the bearing outer ring. The vibration signal has great attenuation and great noise in the transmission process. Therefore, how the accelerometer recognizes the degradation process of the inner ring from weak to complete failure is a key issue in the capture process. The common approach is to use FBM (Fractional-order brownian motion) to identify the degradation process of the inner ring from weak to complete failure, however, this method is less accurate. In addition, the original vibration signal is decomposed by a method such as local average decomposition, empirical mode decomposition, and VMD (variable modal decomposition) to extract a characteristic signal component of the degradation process. However, both the local mean decomposition and empirical mode decomposition methods have problems with modal aliasing and boundary effects. In order to solve the above problems, the VMD method is proposed in the existing research, so that the disadvantages of the VMD method are effectively alleviated, and signal components containing rich characteristic information are extracted from the original vibration signal, so that the variational modal decomposition is widely popularized in the processing of the original vibration signal.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for predicting the residual effective service life of a rolling bearing based on fractional levy stable motion, which can improve the accuracy of the residual service life of the rolling bearing in the degradation process.
The purpose of the invention can be realized by the following technical scheme:
the method for predicting the residual effective life of the rolling bearing based on fractional levy stable motion comprises the following steps:
s1, decomposing the original vibration signals of the rolling bearing into K intrinsic mode functions by using a variational mode decomposition method, and selecting an optimal mode according to monotonicity, robustness and tendency indexes.
The expression of decomposing the original vibration signal into K intrinsic mode functions by using a variational mode decomposition method is as follows:
uk(t)＝Ak(t)cos(φk(t))
in the formula, Ak(t) and ωk＝φk' (t) are respectively K variation modes uk(t) instantaneous amplitude and instantaneous frequency.
Three goodness indexes are introduced to judge and select a proper component, an optimal mode is selected from K modes through the three indexes, the three goodness indexes are a monotonicity index Mon, a robustness index Rob and a trend index Tre respectively, and the optimal mode is selected through comprehensively considering the three indexes, namely:
Com＝a1Mon+a2Rob+a3Tre
in the formula, a1, a2 and a3 are weights of a monotonicity index, a robustness index and a trend index, respectively, and satisfy a1+ a2+ a3 as 1, and Com has a value range of 0 to 1. The expressions of the three goodness indexes are respectively:
and S2, modeling the degradation process of the bearing by utilizing the stable motion based on the fraction Levy to obtain a degradation model.
The expression of the degradation model is:
X(t)＝X(0)+μtb+δLH,α(t)
where μ is the drift coefficient, δ is the diffusion coefficient, b is the power law index, LH,α(t) is a fractional Levy model.
And S3, setting a fault threshold, acquiring the Hurst index and the characteristic index of the fraction Levy stable motion by using an R/S method, estimating the model parameters by using a CF method, and acquiring the estimated value of the characteristic index, the estimated value of the drift coefficient and the estimated value of the diffusion coefficient.
Method for obtaining score Levy stable movement L by utilizing R/S methodH,αThe specific formula for the Hurst index H in (t) is:
wherein X (i, n) is dispersion, R is range, and S is standard deviation, repeating the above formula to obtain n different values Rn/Sn(ii) a For formula Rn/Sn＝bnHLogarithm on both sides to obtain ln (R)n/Sn) When the Hurst parameter H is equal to lnb + Hlnn, straight line fitting is carried out on the formula for obtaining the logarithm, and the slope of the straight line is the value of the Hurst parameter H;
the expression for the estimate of the characteristic index α is:
in the formula
As a function of the characteristics of the fractional Levy steady motion.
The specific contents of the estimation value of the characteristic index, the estimation value of the drift coefficient and the diffusion coefficient obtained by estimating the model parameters by using the CF method are as follows:
judging whether the sample data has long correlation according to the estimated Hurst index H and the characteristic index α, namely judging whether α H & gt 1 is met, if so, the sample data has long correlation, and then respectively performing parameter estimation on a drift coefficient mu and a diffusion coefficient delta to obtain an estimated value:
if not, the sample data does not have long correlation and needs to be resampled.
And S4, substituting the parameters acquired in the step S3 into the degradation model in the step S2, and predicting the residual effective life of the bearing by using a Monte Carlo method. The method specifically comprises the following steps:
41) performing Monte Carlo experimental simulation on the optimal mode selected in the step S1, and obtaining N groups of data by using an iterative equation;
42) introducing time for reaching a threshold value for the first time, setting the threshold value, and when the degradation process exceeds the set threshold value for the first time, the rolling bearing fails, and the specific content of the iterative data in the judgment step 41) is as follows:
Lk＝inf{lk:X(lk+tk)≥w}
wherein w is a set threshold value, tkIs an initial time,/kFor the remaining service life, inf is the infimum limit, i.e. the remaining usage l is obtainedkThe minimum value of the lifetime, i.e. the time to first reach the threshold value w.
Compared with the prior art, the invention has the following advantages:
(1) the invention predicts the residual service life by using the current and historical data of the rolling bearing, and timely adjusts the equipment which is possibly failed according to the prediction result of the residual service life, thereby timely avoiding a series of problems caused by the equipment failure and reducing the loss in industrial production;
(2) the model for the rolling bearing degradation process has linearity, power law and exponential, and the degradation process of the rolling bearing is nonlinear, and the Fractional Levy stable motion is the heavy tail distribution of power exponential decay, so that the invention utilizes the Fractional Levy stable motion to model the degradation process of the bearing, compared with the prior art that the residual service life is predicted by the degradation process based on FBM (Fractional-Order Brown motion), the prediction result of the invention is closer to the actual residual service life, the prediction accuracy is greatly improved, and the predicted residual service life is more accurate, so the resource waste when equipment is replaced is reduced;
(3) the method adopts the VMD to decompose the original vibration signals into K intrinsic mode functions, selects a proper signal component for analysis through monotonicity, robustness and trend indexes, adopts variational mode decomposition to replace empirical mode decomposition, can effectively inhibit the problems of mode aliasing, boundary effect and the like, and further can inhibit noise interference.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a diagram of vibration signals of a rolling bearing;
FIG. 3 is a graph showing the evaluation results of IMF components in the example of the present invention;
FIG. 4 is a 4 th IMF after decomposition of the VMD in an embodiment of the present invention;
FIG. 5 is a graph of a probability density function for remaining life prediction using the method of the present invention in an embodiment of the present invention;
FIG. 6 is a graph of the remaining useful life prediction results obtained by the method of the present invention in an embodiment of the present invention;
FIG. 7 is a probability density function distribution diagram of the remaining service life prediction using the FBM method in the embodiment of the present invention;
fig. 8 is a diagram of a residual service life prediction result obtained by using the FBM method in the embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
As shown in fig. 1, the present invention relates to a method for predicting the remaining useful life of a rolling bearing based on fractional levy stable motion, which comprises the following steps:
firstly, decomposing an original vibration signal into K Intrinsic Mode Functions (IMFs) by a Variational Mode Decomposition (VMD) method, and selecting a proper signal component for analysis through monotonicity, robustness and trend indexes, wherein the Variational Mode decomposition (IMD) method specifically comprises the following steps of:
(1.1) since the vibration signal of the inner ring is indirectly detected by installing an acceleration sensor on the outer ring when the inner ring of the rolling bearing is predicted, noise interference and errors are inevitable to occur. In order to avoid the influence of noise, modal decomposition is adopted to suppress noise interference, such as empirical modal decomposition, variation modal decomposition and the like. Due to the defects of the empirical mode decomposition on mode aliasing and boundary effects, the method proposes that the empirical mode decomposition is replaced by the variational mode decomposition, the problems of mode aliasing, boundary effects and the like are effectively inhibited, and the original vibration signal is decomposed into K modes by the variational mode decomposition:
uk(t)＝Ak(t)cos(φk(t))
wherein A isk(t) and ωk＝φk' (t) are respectively K variation modes uk(t) instantaneous amplitude and instantaneous frequency.
(1.2) the constraint conditions of K variation modes are as follows:
wherein the content of the first and second substances,
is a hilbert transform of the individual modes,
is used for adjusting the modal componentAnd solving the constraint conditions to obtain an modal component optimization solution.
(1.3) selecting a proper IMF is very important for predicting the residual service life of the bearing equipment, so that three goodness indexes are introduced to judge and select a proper component, and an optimal mode is selected from K modes through the three indexes for analysis. The three goodness indexes are respectively:
wherein K is the number of IMF after decomposition, No. ofd/dx > 0 is the number of derivative more than 0, xkIs tkThe degree of degradation at a point in time,
is xkK, Mon is a monotonicity index, Rob is a robustness index, Tre is a trend index, and the value ranges of the three indexes are all 0 to 1. The increasing or decreasing trend of each component in the IMF is further measured by monotonicity indexes, and the monotonicity is determined by the number of positive and negative derivatives of each IMF component characteristic value, so that the bigger the monotonicity index Mon is, the better the prediction effect of the IMF component is; the robustness ensures the stability of trend prediction under the condition of existence of abnormal values, and the uncertainty of bearing degradation trend prediction is reduced along with the increase of the robustness of the IMF component, so that the larger the robustness index Rob is, the better the prediction effect of the IMF component is; the trend refers to the degree of association between the IMF component feature sequence and time, also called correlation, and the larger the trend index Tre, the better the degree of correlation.
And (3) comprehensively considering three indexes to select an optimal mode:
Com＝a1Mon+a2Rob+a3Tre
wherein a1, a2, a3 are weights of monotonicity, robustness and tendency indexes respectively, and satisfy a1+ a2+ a3 as 1, and the value ranges of monotonicity, robustness and tendency indexes are all 1, so the value range of Com is also 0 to 1. The values selected in this example are a 1-0.4, a 2-0.3 and a 3-0.3, respectively.
Obtaining 8 IMFs after the VMD of the steps (1.1) and (1.2), calculating monotonicity, robustness and trend indexes of each decomposed component, selecting proper IMFs by using a comprehensive index Com (comprehensive), and calculating results are shown in the following table:
TABLE 1 characteristic evaluation results of IMF components
As can be seen from table 1, the comprehensive index Com of IMF4 is the largest, so the evaluation index of IMF4 is the best, and has better information characteristics, and the results shown in fig. 3 are obtained by plotting table 1. And the IMF4 component is analyzed to obtain the prediction result of the residual service life of the inner ring of the rolling bearing.
And step two, the degradation process of the rolling bearing is not only related to the current state but also related to the historical state, and the degradation process is a slow process and has long memory and long correlation. The degradation process model is various and generally comprises a linear model, a power law model and an exponential model, and the power law model is selected from the degradation models because the degradation process of the rolling bearing is nonlinear, and the fractional Levy stable motion is the heavy tail distribution of power exponential decay. Modeling the degradation process of the bearing by utilizing the stable motion based on the fraction Levy to obtain a degradation model:
X(t)＝X(0)+μtb+δLH,α(t)
wherein X (0) is the degradation degree at 0 moment, X (t) is the degradation degree at t moment, mu is the drift coefficient, delta is the diffusion coefficient, b is the power law index, LH,α(t) is a fractional Levy model.
And step three, setting a fault threshold, and obtaining the Hurst index H of the fraction Levy stable motion and the parameter estimation of the model by a CF method for the degradation model in the step two by using an R/S method to obtain the estimation value of the characteristic index, the drift coefficient and the estimation values mu and delta of the diffusion coefficient. Specifically, the method comprises the following steps:
(3.1) Stable motion L for fractional LevyH,αParameters H and α in (t) are respectively estimated by a re-standard range method and a characteristic function method, and the specific formula is as follows:
wherein X (i, n) is dispersion, R is range, and S is standard deviation, repeating the above formula to obtain n groups of different values Rn/SnTo formula Rn/Sn＝bnHLogarithm on both sides to obtain ln (R)n/Sn) And (3) fitting a straight line by using a logarithmic formula, wherein the slope of the straight line is the value of the Hurst parameter H.
The expression for the estimated value of the characteristic index is:
wherein E is a mean sign, X (t) is a fractional Levy stable motion degradation process,
as a characteristic function of the fractional Levy stationary motion degradation process,
as a function of characteristics
α is a score Levy a characteristic index of the steady motion,
is an estimate of the characteristic index α.
(3.2) judging whether the sample data has long correlation according to the Hurst index H and the characteristic index α estimated in the step (3.1), judging whether α H & gt 1 is met, if yes, the sample data has long correlation, and then respectively carrying out parameter estimation on the drift coefficient mu and the diffusion coefficient delta to obtain estimated values:
if not, the sample data does not have long correlation and needs to be resampled.
(3.3) for the nonlinear power-law index b, an analytical expression of the nonlinear power-law index b is difficult to obtain, so that in the experiment, an fminsearch function is called in MATLAB, is used for solving a multidimensional unconstrained optimization problem and is usually used for solving a nonlinear problem, the minimum value of a scalar function can be found from the initial moment, and an optimal power-law index b is selected through fminsearch function simulation.
Call b ═ fminsearch (fun, x0) in MATLAB.
Where, fun is the maximum likelihood function of the degradation process, x0 is the initial time of the degradation process, and b is the required power law exponent. By calling the fminsearch function, starting from x0, a local minimum b in the fun function is found, so that an optimal power law exponent b solution is obtained.
In order to prove the effectiveness of the Fractional Levy stable motion model, this example uses FBM (Fractional-Brownian motion) for comparison test, and the parameter calculation steps are similar to the Fractional Levy stable operation, and the results are shown in table 2 below:
TABLE 2 model parameter estimation
| Degradation model | H | α | μ | δ | b |
| fLsm | 0.5191 | 1.9408 | 1.8072 | 0.4431 | 0.3740 |
| fBm | 0.5191 | - | 1.1547 | 0.2850 | 0.1020 |
And step four, substituting the parameters obtained in the step three into the degradation model in the step two, and predicting the residual effective life of the bearing by using a Monte Carlo method. The method comprises the following specific steps:
(4.1) carrying out Monte Carlo experimental simulation on the optimal mode selected in the step one, and obtaining N groups of data by using an iterative equation:
X(tk+(i+1)Δlk)＝X(tk+iΔlk)+ΔX
wherein the content of the first and second substances,
the motion model is stabilized for a fraction Levy.
Since the fractional Levy stationary motion is a non-stationary random process, the generated random sequence is not fixed and the actual remaining lifetime cannot be accurately represented by a small number of remaining lifetime distributions. The probability density function of the remaining life degradation model therefore requires a large amount of data to be generated by monte carlo experimental simulations. The probability density function of the remaining service life represents the most possible value of the remaining service life, namely the maximum value in the probability density function is the most possible value of the remaining service life.
(4.2) for the prediction of the residual life of the rolling bearing, introducing a first arrival time, namely a first arrival time. A threshold value w is set, and the rolling bearing fails when the degradation process exceeds the set threshold value for the first time, wherein the time is the service life of the rolling bearing. Judging the iterative data in the step (4.1) to obtain the remaining service life:
Lk＝inf{lk:X(lk+tk)≥w}
where w is a set threshold value, tkIs an initial time,/kFor the remaining service life, inf is the infimum limit, which can be understood as the determination of the remaining usage lkThe minimum value of the lifetime, i.e. the first time the threshold value w is reached.
(4.3) in the experiment of this embodiment, the fault threshold is set to 100, the probability density function of the remaining service life is calculated by using the plurality of sets of remaining service lives obtained in step (4.2), and as shown by the curve in fig. 5, 12 different sets of initial time t are setkAnd obtaining the probability density function of the predicted 12 different residual service lives. Each stripThe maximum value of the probability density function curve is the most possible value of the remaining service life, the predicted remaining service life is drawn, as shown in fig. 6, the pentagram is the predicted value of the remaining service life, i.e., the maximum value in the probability density function of the remaining service life, and the straight line is the actual remaining service life. Similarly, according to the calculation idea of the fraction Levy stable motion model, the probability density function of the remaining service life of the FBM bearing and the predicted value of the remaining service life are obtained, as shown in fig. 7 and 8, respectively. Comparing the fractional Levy stable motion model with the fractional Brownian motion model, and judging the prediction effects of the two distribution models by adopting the following three indexes:
wherein R isiThe actual value of the remaining service life, i.e. the straight line in figures 6 and 8,
an estimate of the remaining useful life, namely the five-pointed star in figures 6 and 8,
the average value of the actual remaining service life is shown, n is the predicted number of the remaining service life, n in the experiment is 12, HD is a health degree index, RMSE is a root mean square error index, and MAPE is an average absolute percentage error index. As can be seen from the expression values, the prediction of the residual service life is more accurate as the HD is closer to 1, and the prediction of the residual service life is more accurate as the RMSE and MAPE indexes are smaller. The results of the calculations for the three indices for the two models are shown in table 3 below:
TABLE 3 evaluation index of model
| Degradation model | HD | RMSE | MAPE |
| fBm | 0.7588 | 33.9104 | 31.3878 |
| fLsm | 0.8851 | 23.4058 | 22.9369 |
From the results in table 3, the prediction result of the remaining service life of the stable motion bearing based on the fraction Levy is better than the prediction result of the remaining service life of the stable motion bearing based on the fraction brownian motion, and the prediction result of the remaining service life is more accurate, so that the effectiveness of the prediction of the remaining service life of the stable motion bearing based on the fraction Levy is also proved.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and those skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. The method for predicting the residual effective life of the rolling bearing based on fractional levy stable motion is characterized by comprising the following steps of:
1) decomposing the original vibration signal of the rolling bearing into K intrinsic mode functions by using a variational mode decomposition method, and selecting an optimal mode according to monotonicity, robustness and tendency indexes;
2) modeling the degradation process of the bearing by utilizing the score Levy-based stable motion to obtain a degradation model;
3) setting a fault threshold, acquiring a Hurst index of the fraction Levy stable motion for the degradation model in the step 2), estimating model parameters, and acquiring an estimated value of a characteristic index, an estimated value of a drift coefficient and an estimated value of a diffusion coefficient;
4) substituting the parameters obtained in the step 3) into the degradation model in the step 2), and predicting the residual effective life of the bearing by using a Monte Carlo method.
2. The method for predicting the remaining useful life of a rolling bearing based on fractional levy stable motion according to claim 1, wherein in the step 1), the original vibration signal is decomposed into K eigenmode functions by using a variational mode decomposition method, and the expressions are as follows:
uk(t)＝Ak(t)cos(φk(t))
in the formula, Ak(t) and ωk＝φk' (t) are respectively K variation modes uk(t) instantaneous amplitude and instantaneous frequency.
3. The method for predicting the remaining effective life of the rolling bearing based on the fractional levy stable motion according to claim 1, wherein in the step 1), specific contents of an optimal mode are selected as follows:
three goodness indexes are introduced to judge and select a proper component, an optimal mode is selected from K modes through the three indexes, the three goodness indexes are a monotonicity index Mon, a robustness index Rob and a trend index Tre respectively, and the optimal mode is selected through comprehensively considering the three indexes, namely:
Com＝a1Mon+a2Rob+a3Tre
in the formula, a1, a2 and a3 are weights of a monotonicity index, a robustness index and a trend index, respectively, and satisfy a1+ a2+ a3 as 1, and Com has a value range of 0 to 1.
4. The method for predicting the remaining useful life of a rolling bearing based on fractional levy stable motion according to claim 3, wherein the expressions of the three goodness indexes are respectively:
5. the method for predicting the remaining useful life of the rolling bearing based on the fractional levy stable motion according to claim 1, wherein in the step 2), the expression of the degradation model is as follows:
X(t)＝X(0)+μtb+δLH,α(t)
where μ is the drift coefficient, δ is the diffusion coefficient, b is the power law index, LH,α(t) is a fractional Levy model.
6. The method for predicting the remaining useful life of the rolling bearing based on the fractional Levy stable motion according to claim 1, wherein in the step 3), a fault threshold is set, the Hurst index and the characteristic index of the fractional Levy stable motion are obtained by using an R/S method, the model parameters are estimated by using a CF method, and the estimated value of the characteristic index, the estimated value of the drift coefficient and the estimated value of the diffusion coefficient are obtained.
7. The method for predicting the remaining useful life of the rolling bearing based on the fractional Levy stable motion according to claim 6, wherein the specific content of the Hurst index for obtaining the fractional Levy stable motion by using the R/S method is as follows:
method for obtaining score Levy stable movement L by utilizing R/S methodH,αThe Hurst index H in (t) is specifically represented by the formula:
wherein X (i, n) is dispersion, R is range, and S is standard deviation, repeating the above formula to obtain n different values Rn/Sn(ii) a For formula Rn/Sn＝bnHLogarithm on both sides to obtain ln (R)n/Sn) When the Hurst parameter H is equal to lnb + Hlnn, straight line fitting is carried out on the formula for obtaining the logarithm, and the slope of the straight line after fitting is the value of the Hurst parameter H;
the expression for the estimate of the characteristic index α is:
in the formula
As a function of the characteristics of the fractional Levy steady motion.
8. The method for predicting the remaining effective life of the rolling bearing based on the fractional levy stable motion according to claim 7, wherein the specific contents of the estimation value of the characteristic index, the estimation value of the drift coefficient and the diffusion coefficient obtained by estimating the model parameters by using the CF method are as follows:
judging whether the sample data has long correlation according to the estimated Hurst index H and the characteristic index α, namely judging whether α H & gt 1 is met, if so, the sample data has long correlation, and then respectively performing parameter estimation on a drift coefficient mu and a diffusion coefficient delta to obtain an estimated value:
if not, the sample data does not have long correlation and is resampled.
9. The method for predicting the remaining useful life of a rolling bearing based on fractional levy stable motion according to claim 1, wherein the step 4) comprises the following steps:
41) carrying out Monte Carlo experimental simulation on the optimal mode selected in the step 1), and obtaining N groups of data by using an iterative equation;
42) setting a threshold value, and judging the iterative data in the step 41) to obtain the residual service life.
10. The method for predicting the remaining useful life of the rolling bearing based on the fractional levy stable motion according to claim 9, wherein the specific content of the step 42) is as follows:
introducing time for reaching a threshold value for the first time, setting the threshold value, and when the degradation process exceeds the set threshold value for the first time, the rolling bearing fails, and the specific content of the iterative data in the judgment step 41) is as follows:
Lk＝inf{lk:X(lk+tk)≥w}
wherein w is a set threshold value, tkIs an initial time,/kFor the remaining service life, inf is the infimum limit, i.e. the remaining usage l is obtainedkThe minimum value of the lifetime, i.e. the time to first reach the threshold value w.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911223070.2A CN111159846B (en) | 2019-12-03 | 2019-12-03 | Rolling bearing residual effective life prediction method based on fraction levy stable motion |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911223070.2A CN111159846B (en) | 2019-12-03 | 2019-12-03 | Rolling bearing residual effective life prediction method based on fraction levy stable motion |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111159846A true CN111159846A (en) | 2020-05-15 |
| CN111159846B CN111159846B (en) | 2023-10-31 |
Family
ID=70556370
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911223070.2A Active CN111159846B (en) | 2019-12-03 | 2019-12-03 | Rolling bearing residual effective life prediction method based on fraction levy stable motion |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111159846B (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112257904A (en) * | 2020-09-29 | 2021-01-22 | 上海工程技术大学 | Method for predicting remaining effective life of lithium ion battery based on long-correlation fractional order degradation model |
| CN112906157A (en) * | 2021-02-20 | 2021-06-04 | 南京航空航天大学 | Method and device for evaluating health state of main shaft bearing and predicting residual life |
| CN113625164A (en) * | 2021-08-02 | 2021-11-09 | 南京航空航天大学 | Aviation generator fault feature extraction method, system, medium and computing device |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019174142A1 (en) * | 2018-03-14 | 2019-09-19 | 山东科技大学 | Multi-mode degradation process modelling and remaining service life prediction method |
| CN110398368A (en) * | 2019-07-26 | 2019-11-01 | 上海工程技术大学 | The bearing inner race failure method for predicting residual useful life of long correlation model based on FBM |
-
2019
- 2019-12-03 CN CN201911223070.2A patent/CN111159846B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019174142A1 (en) * | 2018-03-14 | 2019-09-19 | 山东科技大学 | Multi-mode degradation process modelling and remaining service life prediction method |
| CN110398368A (en) * | 2019-07-26 | 2019-11-01 | 上海工程技术大学 | The bearing inner race failure method for predicting residual useful life of long correlation model based on FBM |
Non-Patent Citations (1)
| Title |
|---|
| 阙子俊;金晓航;孙毅: "基于UKF的轴承剩余寿命预测方法研究", 仪器仪表学报, vol. 37, no. 9 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112257904A (en) * | 2020-09-29 | 2021-01-22 | 上海工程技术大学 | Method for predicting remaining effective life of lithium ion battery based on long-correlation fractional order degradation model |
| CN112257904B (en) * | 2020-09-29 | 2022-09-30 | 上海工程技术大学 | Method for predicting remaining effective life of lithium ion battery based on long-correlation fractional order degradation model |
| CN112906157A (en) * | 2021-02-20 | 2021-06-04 | 南京航空航天大学 | Method and device for evaluating health state of main shaft bearing and predicting residual life |
| CN113625164A (en) * | 2021-08-02 | 2021-11-09 | 南京航空航天大学 | Aviation generator fault feature extraction method, system, medium and computing device |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111159846B (en) | 2023-10-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Wang et al. | Statistical modeling of bearing degradation signals | |
| CN111159846B (en) | Rolling bearing residual effective life prediction method based on fraction levy stable motion | |
| CN111046564B (en) | Residual life prediction method for two-stage degraded product | |
| CN110232249B (en) | Method for predicting residual life of rolling bearing | |
| Wang et al. | A hybrid prognostics approach for estimating remaining useful life of wind turbine bearings | |
| CN108304348B (en) | Bearing residual life prediction method based on binary wiener process | |
| CN109255395B (en) | Service life prediction method of ball screw pair | |
| CN111414703B (en) | Method and device for predicting residual life of rolling bearing | |
| CN111122423B (en) | Reliability-based storage tank bottom plate corrosion residual life evaluation method and device | |
| CN107403279B (en) | Oil transfer pump working condition self-adaptive state early warning system and method | |
| CN112100574A (en) | Resampling-based AAKR model uncertainty calculation method and system | |
| CN114997607A (en) | Anomaly assessment early warning method and system based on engineering detection data | |
| CN115422687A (en) | Service life prediction method of rolling bearing | |
| CN111783242A (en) | RVM-KF-based rolling bearing residual life prediction method and device | |
| CN115186701A (en) | Bearing life prediction method, device, electronic device and storage medium | |
| CN111523727A (en) | Method for predicting remaining life of battery by considering recovery effect based on uncertain process | |
| CN114861349A (en) | Rolling bearing RUL prediction method based on model migration and wiener process | |
| CN117010442A (en) | Equipment residual life prediction model training method, residual life prediction method and system | |
| CN112068519A (en) | Quality control method and device for product assembly process | |
| CN114912372B (en) | High-precision filling pipeline fault early warning method based on artificial intelligence algorithm | |
| CN116151470A (en) | Product quality prediction method, device, equipment and storage medium | |
| CN108182306B (en) | Method for determining degradation failure threshold of abrasive particle characteristic parameters of vehicle power transmission device | |
| Sun et al. | Remaining Useful Life Prediction of Quay Crane Hoist Gearbox Bearing under Dynamic Operating Conditions Based on ARIMA‐CAPF Framework | |
| Zhao et al. | Fuzzy scalar quantisation based on hidden Markov model and application in fault diagnosis of wind turbine | |
| CN105187143B (en) | A kind of fast spectrum perception method and device based on bi-distribution |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |