CN111159846B - Rolling bearing residual effective life prediction method based on fraction levy stable motion - Google Patents
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Abstract
The invention relates to a rolling bearing residual effective life prediction method based on fractional levy stable motion, which comprises the following steps: 1) Decomposing an original vibration signal of the rolling bearing into K eigenmode functions by utilizing a variational mode decomposition method, and selecting an optimal mode through monotonicity, robustness and trend indexes; 2) Modeling a degradation process of the bearing by utilizing a stabilized motion based on the fraction Levy to obtain a degradation model; 3) Setting a fault threshold, and for the degradation model in the step 2), acquiring a Hurst index of the fractional Levy stable motion, estimating model parameters, and acquiring an estimated value of a characteristic index, a drift coefficient and an estimated value of a diffusion coefficient; 4) Substituting the parameters obtained in the step 3) into the degradation model of 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, resource waste reduction 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 method for predicting the residual service life of the rolling bearing based on fractional levy stable motion.
Background
Nowadays, various mechanical devices in modern industry have a certain service life, and if the mechanical devices are not processed, mechanical devices exceeding the service life may malfunction, so the prediction of the remaining service life of large rotating devices is a growing concern. There are many methods to predict the remaining useful life of rotating equipment, such as wiener processes, markov processes, gamma processes, which are all memoryless. Since the degradation process of the rolling bearing is not only related to the current state but also to the history state, i.e. the degradation process is a long-term slowly varying process with long memory or long correlation, the above process does not accurately predict the remaining service life of the rotating equipment.
In large rotary devices, the inner ring vibration signal is collected by an acceleration sensor mounted on the outer ring of the bearing. The vibration signal has great attenuation and 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 usual approach is to use FBM (Fractional-order Brownian motion) to identify the degradation process of the inner ring from weak to complete failure, however the accuracy of this approach is poor. Further, the original vibration signal is decomposed by a method such as a local average decomposition, an empirical mode decomposition, a VMD (Variational mode decomposition, a variational mode decomposition method) to extract a characteristic signal component of the degradation process. However, both the local average decomposition and the empirical mode decomposition methods have problems such as mode aliasing and boundary effects. Aiming at the problems, the prior research proposes a VMD method, so that the defects of the method are effectively alleviated, and signal components containing rich characteristic information are extracted from an original vibration signal, so that the variation 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 rolling bearing residual effective life prediction method based on the fractional levy stable motion, which improves the accuracy of the residual service life of the rolling bearing in the degradation process.
The aim of the invention can be achieved by the following technical scheme:
the method for predicting the residual effective life of the rolling bearing based on the fractional levy stable motion comprises the following steps:
s1, decomposing an original vibration signal of the rolling bearing into K eigenmode functions by using a variational mode decomposition method, and selecting an optimal mode through monotonicity, robustness and trend indexes.
The expression for decomposing the original vibration signal into K eigenmode functions by using the variational mode decomposition method is as follows:
u k (t)＝A k (t)cos(φ k (t))
wherein A is k (t) and ω k ＝φ k 't' are K variation modes u k The instantaneous amplitude and instantaneous frequency of (t).
Three goodness indexes are introduced to judge and select a proper component, an optimal mode is selected from K modes through the three indexes, wherein 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
wherein a1, a2 and a3 are weights of a monotonicity index, a robustness index and a trend index respectively, and satisfy a1+a2+a3=1, and the value range of com is 0 to 1. The expressions of the three goodness indexes are respectively:
s2, modeling a degradation process of the bearing by utilizing the stabilized motion based on the fraction Levy, and obtaining a degradation model.
The expression of the degradation model is:
X(t)＝X(0)+μt b +δL H,α (t)
wherein μ is a drift coefficient, δ is a diffusion coefficient, b is a power law exponent, L H,α And (t) is a fractional Levy model.
S3, setting a fault threshold, acquiring Hurst indexes and characteristic indexes of the fraction Levy stable motion by using an R/S method, estimating model parameters by using a CF method, and acquiring estimated values of the characteristic indexes, drift coefficients and diffusion coefficients.
Obtaining a fraction Levy stabilized motion L using an R/S method H,α The specific formula of Hurst index H in (t) is:
wherein X (i, n) isThe dispersion, R is the extreme difference, S is the standard deviation, and n groups of different values R are obtained by repeating the above formula n /S n The method comprises the steps of carrying out a first treatment on the surface of the For formula R n /S n ＝bn H The logarithm of each side is calculated to obtain ln (R n /S n ) = lnb +hlnn, then fitting a straight line to the logarithmic equation, where the slope of the straight line is the value of Hurst parameter H;
the expression of the estimated value of the characteristic index α is:
in the middle ofIs a characteristic function of the fractional Levy steady motion.
Estimating model parameters by using a CF method, and obtaining the estimated value of the characteristic index, the drift coefficient and the estimated value of the diffusion coefficient, wherein the specific contents are as follows:
judging whether the sample data has long correlation according to the estimated Hurst index H and the characteristic index alpha, namely judging whether the sample data meets alpha H & gt 1, if so, the sample data has long correlation, and then carrying out parameter estimation on the drift coefficient mu and the diffusion coefficient delta respectively to obtain an estimated value:
if not, the sample data does not have long correlation and needs to be resampled.
S4, substituting the parameters acquired in the step S3 into the degradation model of 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 the time of reaching the threshold for the first time, setting the threshold, and judging the specific content of the iterative data in the step 41) as follows when the degradation process exceeds the set threshold for the first time:
L k ＝inf{l k :X(l k +t k )≥w}
wherein w is a set threshold value, t k For the initial moment, l k For the remaining service life, inf is the infinitesimal, i.e. the remaining service l is found k The minimum of lifetime, i.e. the time when the threshold w is reached for the first time.
Compared with the prior art, the invention has the following advantages:
(1) The invention predicts the residual service life by utilizing the current and historical data of the rolling bearing, and timely adjusts equipment which is possibly failed according to the prediction result of the residual service life, thereby timely avoiding a series of problems caused by equipment failure and reducing the loss in industrial production;
(2) The model for the degradation process of the rolling bearing has linearity, power law and exponential property, and because the degradation process of the rolling bearing is nonlinear, the fraction Levy stable motion is the heavy tail distribution of power exponential decay, the invention models the degradation process of the bearing by using the degradation process based on the fraction Levy stable motion, compared with the prior art for predicting the residual service life based on the degradation process of FBM (Fractional Brownian-order Brownian motion), the prediction result of the invention is more similar 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) According to the invention, the VMD is adopted to decompose an original vibration signal into K eigenmode functions, a proper signal component is selected for analysis through monotonicity, robustness and trend indexes, and the variational mode decomposition is adopted to replace empirical mode decomposition, so that the problems of mode aliasing, boundary effect and the like can be effectively suppressed, and further noise interference can be suppressed.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a graph of rolling bearing vibration signals;
FIG. 3 is a graph showing the evaluation result of IMF components in the embodiment of the present invention;
FIG. 4 is a view of the 4 th IMF after VMD decomposition in an embodiment of the present invention;
FIG. 5 is a graph of probability density function of residual life prediction using the method of the present invention in an embodiment of the present invention;
FIG. 6 is a graph of the predicted remaining life using the method of the present invention in an embodiment of the present invention;
FIG. 7 is a graph showing probability density function of residual life prediction using the FBM method according to the embodiment of the invention;
fig. 8 is a graph showing a residual life prediction result using the FBM method in the embodiment of the present invention.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
As shown in fig. 1, the invention relates to a rolling bearing residual effective life prediction method based on fractional levy stable motion, which comprises the following steps:
firstly, decomposing an original vibration signal into K eigenmode functions (Intrinsic Mode Function, IMF) by using a variation mode decomposition (Variational mode decomposition, VMD) method, and selecting a proper signal component for analysis through monotonicity, robustness and trend indexes, wherein the method specifically comprises the following steps:
(1.1) since the vibration signal of the inner ring is indirectly detected by mounting the acceleration sensor on the outer ring when predicting the inner ring of the rolling bearing, noise interference and errors are inevitably generated. In order to avoid the influence of noise, modal decomposition is employed to suppress noise interference, such as empirical modal decomposition, variational modal decomposition, and the like. Because of the defect of the empirical mode decomposition on the mode aliasing and the boundary effect, the problems of the empirical mode decomposition, such as the modal aliasing and the boundary effect, are effectively restrained by replacing the empirical mode decomposition with the variational mode decomposition, and the original vibration signal is decomposed into K modes by using the variational mode decomposition:
u k (t)＝A k (t)cos(φ k (t))
wherein A is k (t) and ω k ＝φ k 't' are K variation modes u k The instantaneous amplitude and instantaneous frequency of (t).
(1.2) constraint conditions of K variation modes are:
wherein, the liquid crystal display device comprises a liquid crystal display device,hilbert transform for individual modes, < >>The method is used for adjusting the center frequency of the whole modal component, and solving the constraint condition to obtain a modal component optimization solution.
(1.3) selecting a suitable IMF is important for predicting the residual service life of the bearing equipment, so that three goodness indexes are introduced to judge selecting a suitable component, and an optimal mode among K modes is selected for analysis through the three indexes. The three goodness indexes are respectively:
wherein K is the number of IMFs after decomposition, no. ofd/dx > 0 is the number of derivatives greater than 0, x k At t k The degree of degradation of the time of day,is x k K=1, 2, K, mon are monotonicity indices, rob is a robustness index, tre is a trend index, and the three indices all range from 0 to 1. The increasing or decreasing trend of each component in the IMF is also measured by a monotonicity index, the monotonicity is determined by the number of positive and negative derivatives of the characteristic value of each IMF component, and therefore the larger the monotonicity index Mon is, the better the predicting effect of the IMF component is; the robustness ensures the stability of trend prediction under the condition 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 greater the robustness index Rob is, the better the prediction effect of the IMF component is; the trend refers to the degree of correlation between the IMF component feature sequence and time, which is also called correlation, and the greater the trend index Tre, the better the degree of correlation.
The optimal mode is selected by comprehensively considering three indexes:
Com＝a1Mon+a2Rob+a3Tre
wherein a1, a2 and a3 are weights of monotonicity, robustness and trend indexes respectively, and a1+a2+a3=1 is satisfied, and the value ranges of monotonicity, robustness and trend indexes are all 1, so that the value range of Com is 0 to 1. The values selected in this example are a1=0.4, a2=0.3, a3=0.3, respectively.
8 IMFs are obtained after VMD in the steps (1.1) and (1.2), monotonicity, robustness and trend indexes of each component after decomposition are calculated, a proper IMF is selected by using a comprehensive index Com (Comprehensive), and the calculation results are shown in the following table:
TABLE 1 characterization evaluation results of IMF components
As can be seen from Table 1, the comprehensive index Com of IMF4 is the largest, so that the evaluation index of IMF4 is optimal, and the results shown in FIG. 3 are obtained by plotting Table 1 with good information characteristics. And the IMF4 component is analyzed to obtain a prediction result of the residual service life of the inner ring of the rolling bearing.
The second step, the degradation process of the rolling bearing, which is a slow process with long memory, also called long correlation, is not only related to the current state but also to the historical state. There are many models of the degradation process, including typically linear, power law and exponential models, and since the degradation process of rolling bearings is nonlinear, the fractional Levy steady motion is a heavy tail distribution of power exponential decay, and the power law model is selected from the degradation models. Modeling a degradation process of the bearing by using a stabilized motion based on a fraction Levy to obtain a degradation model:
X(t)＝X(0)+μt b +δL H,α (t)
wherein X (0) is the degradation degree at time 0, X (t) is the degradation degree at time t, mu is the drift coefficient, delta is the diffusion coefficient, b is the power law exponent, L H,α And (t) is a fractional Levy model.
Setting a fault threshold, and obtaining the Hurst index H of the fraction Levy stable motion and the parameter estimation of the model by the CF method for the degradation model in the second step by using the R/S method to obtain the estimated value of the characteristic index, the estimated values mu and delta of the drift coefficient and the diffusion coefficient. Specifically:
(3.1) stabilizing motion L for fractional Levy H,α The parameters H and alpha in (t) are estimated by a re-standard polar difference method and a characteristic function method respectively, and the specific formulas are as follows:
wherein X (i, n) is dispersion, R is extremely poor, S is standard deviation, and n groups of different values R are obtained by repeating the above formula n /S n For formula R n /S n ＝bn H The logarithm of each side is calculated to obtain ln (R n /S n ) = lnb +hlnn, and then fitting a straight line to the logarithmic equation, where the slope of the straight line is the value of Hurst parameter H.
The expression of the estimated value of the characteristic index is:
wherein E is a mean sign, X (t) is a fractional Levy stable motion degradation process,stabilizing the characteristic function of the motion degradation process for the score Levy, < >>Is a characteristic function->Alpha is the characteristic index of the stabilized motion of the score Levy, +.>Is an estimate of the characteristic index α.
(3.2) judging whether the sample data has long correlation or not according to the Hurst index H and the characteristic index α estimated in the step (3.1), and judging whether αh > 1 is satisfied or not. If the sample data meets the requirement, the sample data has long correlation, and then parameter estimation is carried out on the drift coefficient mu and the diffusion coefficient delta respectively to obtain an estimated value:
if not, the sample data does not have long correlation and needs to be resampled.
(3.3) for the nonlinear power law index b, it is difficult to obtain its analytical expression, so this experiment is to call fminearch function in MATLAB, which is used to solve multidimensional unconstrained optimization problem, and is usually used to solve nonlinear problem, and the minimum value of scalar function can be found from the initial moment, so that an optimal power law index b is simulated and selected by fminearch function.
B=fminearch (fun, x 0) is called 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 desired power law exponent. And (3) by calling the fminearch function and starting from x0, finding the local minimum value b in the fun function, thereby obtaining the optimal solution of the power law index b.
From the third step, the estimated values of H, α, μ, δ, and b are obtained, and in order to prove the effectiveness of the Fractional Levy steady motion model, in this embodiment, FBM (Fractional-order Brownian motion, fractional brownian motion) is used for comparison test, and the parameter calculation step is similar to the Fractional Levy steady operation, and the result is shown in the following table 2:
table 2 model parameter estimates
| 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 of 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) performing 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(t k +(i+1)Δl k )＝X(t k +iΔl k )+ΔX
wherein, the liquid crystal display device comprises a liquid crystal display device,the motion model is stabilized for a score Levy.
Since the fractional Levy steady motion is a non-stationary random process, the random sequence generated is not fixed and the actual remaining useful life cannot be accurately represented by a small number of remaining useful life distributions. The probability density function of the remaining life degradation model therefore requires the generation of a large amount of data through monte carlo experimental simulation. The probability density function of the remaining service life represents the most likely value of the remaining service life, namely, the maximum value in the probability density function is the most likely value of the remaining service life.
(4.2) for the prediction of the remaining life of the rolling bearing, a first arrival time, i.e. a first arrival time, is introduced. The threshold w is set and the rolling bearing will fail when the degradation process exceeds the set threshold for the first time, the time at which this is the life of the rolling bearing. Judging iterative data in the step (4.1) to obtain the residual service life:
L k ＝inf{l k :X(l k +t k )≥w}
where w is a set threshold, t k For the initial moment, l k For the remaining service life, inf is the infinitesimal and can be understood as finding the remaining usage l k The minimum value of lifetime, i.e. when the threshold value w is reached for the first time.
(4.3) setting the failure threshold to 100 in the experiment of this embodiment, calculating the probability density function of the remaining service life using the multiple sets of remaining service lives obtained in the step (4.2), as shown in the graph of FIG. 5, setting 12 different initial times t k A predicted probability density function of 12 different remaining useful lives is obtained. The maximum value of each probability density function curve is the most probable value of the residual service life, the predicted residual service life is drawn, as shown in fig. 6, the five-pointed star is the predicted value of the residual service life, that is, the maximum value in the probability density function of the residual service life, and the straight line is the actual residual service life. Similarly, according to the calculation thought of the score Levy stable motion model, the probability density of the residual service life of the FBM bearing is obtainedThe function and the predicted value of the remaining useful life are shown in fig. 7 and 8, respectively. Comparing the score Levy stable motion model with the score Brownian motion model, and judging the predicted effect of the two distribution models by adopting the following three indexes:
wherein R is i For the actual value of the remaining useful life, i.e. the straight line in figures 6 and 8,for the estimation of the remaining useful life, i.e. five-pointed star in fig. 6 and 8, +.>For the average value of the actual remaining service life, n is the number of the predictions of the remaining service life, n is 12 in this experiment, hd is a health index, RMSE is a root mean square error index, and MAPE is an average absolute percentage error index. From the expression values, the closer the HD is to 1, the more accurate the prediction of the residual service life is, and the smaller the RMSE and MAPE indexes are, the more accurate the prediction of the residual service life is. The results of the three indices calculation for the two models are shown in table 3 below:
TABLE 3 model evaluation index
| 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 result of predicting the remaining service life of the stabilized motion bearing based on the score Levy is better than the result of predicting the remaining service life of the stabilized motion bearing based on the score brownian motion, and the result of predicting the remaining service life is more accurate, thereby proving the validity of the prediction of the remaining service life of the stabilized motion bearing based on the score Levy.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions may be made without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the protection scope of the invention is subject to the protection scope of the claims.
Claims (7)
1. A method for predicting the remaining useful life of a rolling bearing based on fractional levy steady motion, characterized in that it comprises the steps of:
1) Decomposing an original vibration signal of the rolling bearing into K eigenmode functions by utilizing a variational mode decomposition method, and selecting an optimal mode through monotonicity, robustness and trend indexes;
2) Modeling a degradation process of the bearing by utilizing a stabilized motion based on the fraction Levy to obtain a degradation model;
3) Setting a fault threshold, and for the degradation model in the step 2), acquiring a Hurst index of the fractional Levy stable motion, estimating model parameters, and acquiring an estimated value of a characteristic index, a drift coefficient and an estimated value of a diffusion coefficient;
4) Substituting the parameters obtained in the step 3) into the degradation model of the step 2), and predicting the residual effective life of the bearing by using a Monte Carlo method;
in the step 1), the original vibration signal is decomposed into K eigenvalue functions by using a variational modal decomposition method, wherein the expression is as follows:
u k (t)＝A k (t)cos(φ k (t))
wherein A is k (t) and ω k ＝φ k (t) K variation modes u k The instantaneous amplitude and instantaneous frequency of (t);
in the step 1), the specific content of the selected optimal mode is 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, wherein 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
wherein a1, a2 and a3 are weights of a monotonicity index, a robustness index and a trend index respectively, and satisfy a1+a2+a3=1, and the value range of com is 0 to 1;
in step 2), the expression of the degradation model is:
X(t)＝X(0)+μt b +δL H,α (t)
wherein μ is a drift coefficient, δ is a diffusion coefficient, b is a power law exponent, L H,α And (t) is a fractional Levy model.
2. The method for predicting the remaining useful life of a rolling bearing based on the fractional levy steady motion according to claim 1, wherein the expressions of the three goodness indexes are respectively:
3. the method for predicting the residual effective 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, a Hurst index and a characteristic index of the fractional Levy stable motion are obtained by using an R/S method, model parameters are estimated by using a CF method, and an estimated value of the characteristic index, an estimated value of a drift coefficient and an estimated value of a diffusion coefficient are obtained.
4. The method for predicting the residual effective life of the rolling bearing based on the fractional Levy stable motion according to claim 3, wherein the specific content of the Hurst index for obtaining the fractional Levy stable motion by using the R/S method is as follows:
obtaining a fraction Levy stabilized motion L using an R/S method H,α The Hurst index H in (t) has the specific formula:
wherein X (i, n) is the dispersion, R is the polar difference, S is the standard deviation, and n groups of different values R are obtained by repeating the above formula n /S n The method comprises the steps of carrying out a first treatment on the surface of the For formula R n /S n ＝bn H The logarithm of each side is calculated to obtain ln (R n /S n ) = lnb +H lnn, then performing linear fitting on the logarithmic equation, wherein the slope of the fitted linear is the value of the Hurst parameter H;
the expression of the estimated value of the characteristic index α is:
in the middle ofIs a characteristic function of the fractional Levy steady motion.
5. The method for predicting the residual effective life of the rolling bearing based on the fractional levy stable motion according to claim 4, wherein the specific contents of estimating values of the characteristic indexes, drift coefficients and diffusion coefficients by estimating model parameters by using a CF method are as follows:
judging whether the sample data has long correlation according to the estimated Hurst index H and the characteristic index alpha, namely judging whether the sample data meets alpha H & gt 1, if so, the sample data has long correlation, and then carrying out parameter estimation on the drift coefficient mu and the diffusion coefficient delta respectively to obtain an estimated value:
if not, the sample data does not have long correlation and is resampled.
6. The method for predicting the remaining useful life of a rolling bearing based on a fractional levy steady motion according to claim 1, characterized in that step 4) comprises in particular the following steps:
41 Performing 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 A threshold is set, and the iterative data in the step 41) is judged to obtain the residual service life.
7. The method for predicting the remaining useful life of a rolling bearing based on fractional levy steady motion of claim 6, wherein the specific contents of step 42) are:
introducing time for reaching the threshold for the first time, setting the threshold, and judging that the rolling bearing fails when the degradation process exceeds the set threshold for the first time, wherein the specific content of the iterative data in the step 41) is as follows:
L k ＝inf{l k :X(l k +t k )≥w}
wherein w is a set threshold value, t k For the initial moment, l k For the remaining service life, inf is the infinitesimal, i.e. the remaining service l is found k The minimum of lifetime, i.e. the time when the threshold w is reached for the first time.
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| 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 |
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 |
|---|
| 基于UKF的轴承剩余寿命预测方法研究;阙子俊;金晓航;孙毅;仪器仪表学报;第37卷(第9期);全文 * |
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