CN112100919A - Rolling bearing residual life prediction method based on RE-CF-EKF algorithm - Google Patents

Rolling bearing residual life prediction method based on RE-CF-EKF algorithm Download PDF

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CN112100919A
CN112100919A CN202010968660.4A CN202010968660A CN112100919A CN 112100919 A CN112100919 A CN 112100919A CN 202010968660 A CN202010968660 A CN 202010968660A CN 112100919 A CN112100919 A CN 112100919A
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prediction
residual life
characteristic curve
ekf algorithm
bearing
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张永
张敬
刘振兴
赵敏
苏茜
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Wuhan University of Science and Engineering WUSE
Wuhan University of Science and Technology WHUST
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
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    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G01M13/045—Acoustic or vibration analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06F2119/04—Ageing analysis or optimisation against ageing

Abstract

The invention provides a rolling bearing residual life prediction method based on an RE-CF-EKF algorithm, which is characterized by comprising the following steps: the method comprises the following steps: screening the obtained bearing vibration data set, selecting a plurality of bearings under the same working condition as an experimental data set, and grouping the experimental data set with the bearings under the same working condition into a training set and a test set; step two: linear filtering is carried out after the time domain characteristics of the original signal are taken, a relative error value RE between filtered data and a filtering error is calculated, and a prediction starting point TSP is determined based on an RE curve; step three: denoising the selected time domain characteristics, and obtaining an accumulated characteristic CF with smoother trend by an accumulated function; step four: and combining the second step and the third step to obtain a characteristic curve section suitable for modeling prediction, establishing a state space model, obtaining model initial parameters from the characteristic curve section of the training set, and then combining an EKF algorithm to predict the residual life of the bearing.

Description

Rolling bearing residual life prediction method based on RE-CF-EKF algorithm
Technical Field
The invention belongs to the technical field of rolling bearings, and relates to a rolling bearing residual life prediction method based on an RE-CF-EKF algorithm.
Background
Today, the pace of economic development is rapid, the development level of science and technology has been taken as an important sign of the comprehensive strength of the country, wherein the development of the manufacturing industry has a great influence on the development of the science and technology of the country. As one of the key components of a rotating machine, a bearing whose smooth and reliable operation is essential to maintain production. Unfortunately, bearing failure is one of the most common failure modes in machine failure. If the health condition of the rolling bearing can be evaluated and estimated in the working process of the rolling bearing, the service life of the bearing can be utilized to the maximum extent before safety is ensured, and the maintenance and guarantee cost is reduced. In recent years, a lot of research has been conducted in the field of Prognostic Health Management (PHM) both domestically and abroad, and the first method is a physical model-based method, which relies on a priori knowledge of the intrinsic system failure mechanism to construct a degradation model, thereby describing the physical properties of the failure. The second method is a data-driven method, which usually does not need to know the physical properties of equipment failure and degradation, and only needs to use a large amount of data to find the degradation rule of the equipment. Chang proposes a mixed method of error correction ideas to predict the residual service life, integrates unscented Kalman filtering algorithm (UKF), complete set empirical mode decomposition (CEEMD) and relevance vector machine (RVR) methods to realize RUL prediction, but does not consider the prediction starting point and more trending characteristics.
Disclosure of Invention
The invention aims to overcome the defects and provides a method for accurately predicting the residual service life of a rolling bearing. The method adopts the RE-CF-EKF algorithm, can realize accurate detection of the degradation starting point, reduces the influence of potential health factors on fault factor prediction, and simultaneously utilizes the accumulation feature (CF) with stronger trend after accumulation function processing, can effectively improve the EKF prediction precision and realize accurate residual life prediction result.
The invention provides a rolling bearing residual life prediction method based on an RE-CF-EKF algorithm, which is characterized by comprising the following steps:
the method comprises the following steps: screening the obtained bearing vibration data set, selecting a plurality of bearings under the same working condition as an experimental data set, and grouping the experimental data set with the bearings under the same working condition into a training set and a test set;
step two: linear filtering is carried out after the time domain characteristics of the original signal are taken, a relative error value RE between filtered data and a filtering error is calculated, and a prediction starting point TSP is determined based on an RE curve;
step three: denoising the selected time domain characteristics, and obtaining an accumulated characteristic CF with smoother trend by an accumulated function;
step four: and combining the second step and the third step to obtain a characteristic curve section suitable for modeling prediction, establishing a state space model, obtaining model initial parameters from the characteristic curve section of the training set, and then combining an EKF algorithm to predict the residual life of the bearing.
Further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
selecting a time domain characteristic representation capable of representing the whole service life trend of the bearing in the second step, and performing linear filtering on the time domain characteristic representation to obtain a filtered characteristic curve and a filtered error curve;
setting the size of a sliding window as m;
calculating the relative error RE (k) of F (k) and E (k) in each window, wherein the specific expression is as follows:
Figure BDA0002683271890000021
the RE curve is obtained and the RE curve,
selecting a threshold boundary line from an RE curve obtained from a current data set;
according to the threshold boundary, a degradation starting point is found and used as a prediction starting point TSP for subsequent prediction.
Generally, the degradation starting point is determined by the obtained RE curve and the selected threshold boundary, and when a certain value of the RE curve is greater than or equal to the threshold boundary, it is determined as the degradation point, for example: the predicted starting point TSP is the intersection of the RE curve and the relative error threshold boundary.
Further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
the sliding window size is X% of the known data length T;
the threshold boundary is the mean of the first A1% -A2% of the data of the relative error of the training set;
wherein X is a natural number;
a1 and A2 are selected from natural numbers, and A1 is less than A2.
The X, A1 and A2 can be adjusted according to the number of samples and actual needs.
Further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
in the third step, an improved algorithm CEEMDAN of empirical mode decomposition is used for reconstructing the variance characteristics and then carrying out noise reduction processing;
processing the variance characteristics after noise reduction according to an accumulation function to obtain an accumulation characteristic CF;
wherein the cumulative function is formulated as follows:
Figure BDA0002683271890000031
further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
the training set is life cycle data;
the test set takes the former part as known data, and the rest part is used for verifying the quality of the prediction result.
Further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
the fourth step comprises the following steps:
the EKF algorithm prediction test set known data state estimation value after last time T
Figure BDA0002683271890000032
Forming new model parameters;
obtaining bearing characteristic data corresponding to T + i (i is 1, 2, …, n) according to the prediction result;
when the characteristic curve of the bearing vibration data reaches a defined threshold value, the remaining service life RUL is the time interval from the time T to the bearing failure threshold point.
Further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
in the fourth step, the characteristic curve segment CF' (k) of the current data set more suitable for modeling prediction is obtained from the prediction starting point obtained in the second step and the accumulated characteristics obtained in the third step,k＝TSP，…，T；
calculating the slope th of the last point of each characteristic curve segment of the training setiTaking the average value as a threshold value in the prediction of the test set:
Figure BDA0002683271890000041
the state space equation established is:
Figure BDA0002683271890000042
wherein x isk＝[ak，bk，ck，dk]；
k represents the number of cycles;
xkrepresenting state model parameters;
Ykan observed value representing a cumulative characteristic curve segment;
wkrepresenting state noise;
vkrepresenting observation noise;
fitting according to the characteristic curve segment of the training set to obtain initial parameters of a prediction model;
and inputting the initial model parameters and the characteristic curve segment of the current data of the test set into an EFK algorithm, and predicting to obtain a state value X (T) at the time T.
Further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
the specific flow of the EKF algorithm is as follows:
s1, considering the following state space equation:
Figure BDA0002683271890000051
Y(k)＝HX(k)+V(k)
s2, prediction part:
s2-1. State prediction:
Figure BDA0002683271890000052
s2-2. Observation prediction:
Y(k|k-1)＝HX(k|k-1)
s2-3. covariance prediction:
Figure BDA0002683271890000053
s3, updating:
s3-1, calculating a kalman gain:
K(k)＝P(k|k-1)HT[HP(k|k-1)HT+R]-1
s3-2, status updating:
X(k)＝X(k|k-1)+K(k)[Y(k)-Y(k|k-1)]
s3-3. covariance update:
P(k)＝[In-K(k)H]P(k|k-1)。
further, the invention provides a rolling bearing residual life prediction method based on the RE-CF-EKF algorithm, which is characterized in that:
the calculation method of the measurement estimation value is as follows:
Figure BDA0002683271890000061
wherein Y (k) represents the input bearing cumulative characteristic curve segment CF' (k), corresponding to Y in the state space equationkObtaining the state value X at the time of T through an EKF algorithmkCalculating to obtain a measurement estimation value after T time according to a prediction model
Figure BDA0002683271890000062
When in use
Figure BDA0002683271890000063
And when the threshold value is reached, stopping prediction, and calculating the predicted residual life value of the current bearing:
R＝k-T
in which, for the characteristic curve segment CF' (k),k＝TSP，…，Titeratively bringing the TSP time to t,TSP＜t≤Tthe characteristic curve segment of the time is used as the input of the EKF, and the residual life is predicted.
The invention has the following functions and effects:
in the invention, a relative error curve is obtained by linearly filtering time domain characteristics and then sliding a window, and a prediction starting point is determined according to curve characteristics; then, obtaining more trend accumulated characteristics by selecting and processing time domain characteristics, and then constructing a state space equation based on the characteristic curve segment after the starting point is predicted; according to the established state space model, a state prediction value of the last point of the known data is obtained by using an extended Kalman filtering method, the subsequent trend of the characteristic curve is predicted according to the state prediction value and the prediction model, the prediction is stopped when the threshold value is reached, the corresponding residual service life is calculated, repeated tests are carried out by changing the size of the known data volume, and the accuracy and the robustness of the method are verified through the experimental results.
In addition, in the following embodiments, the present invention further evaluates two indexes, namely, a mean error and a root mean square error, of a plurality of remaining life values predicted by input samples with different data sizes and a true remaining life value as a test set, and compares the two indexes with other models and methods to verify the effectiveness of the method.
Drawings
Fig. 1 is a graph of a life cycle vibration signal of a Bearing used in the present embodiment, which is taken as an example of a training set Bearing 1-1.
FIG. 2 is a block diagram of the RE-CF-EKF algorithm used in this example.
FIG. 3 is a graph illustrating the effect of the method used in this embodiment on the Bearing1-3 data to determine the predicted starting point according to the relative error curve.
FIG. 4 is a comparison graph of the health index and the general variance characteristics constructed by the method used in the present embodiment on the Bearing1-3 data.
FIG. 5 is a comparison graph of the predicted effect of the method used in the present embodiment and other prediction models on Bearing1-3 data.
FIG. 6 is a table showing the comparison of the predicted effect indexes of the lower bearing data under the working conditions used in the present embodiment
Detailed Description
The technical solution of the present invention will be described in detail with reference to the accompanying drawings 1-6. Simulation was performed on Bearing data for condition one, but only a comparison graph of the simulation effect of Bearing1-3 Bearing data is presented here to verify the effectiveness of the algorithm.
As shown in fig. 1, the simulation experiment is performed based on data of the bearing in PHM2012 under the first working condition, and the validity of the algorithm is verified in a test set by simulation according to the given training set data.
As shown in fig. 2, the invention provides a method for predicting the residual life of a bearing based on an RE-CF-EKF algorithm, which comprises the following steps:
firstly, screening an obtained PHM2012 Bearing data set, selecting 7 bearings under a first working condition as an experimental data set, and defining according to the data set, taking Bearing1-1 and Bearing1-2 as training sets, and taking the remaining Bearing1-3 to Bearing1-7 as test sets. The training set is full life cycle data, the test set takes the former part as known data, and the rest part is used for verifying the quality of the prediction result.
Step two: firstly, time domain characteristics are obtained for an original signal, then simple linear filtering is carried out, finally, a relative error value (RE) between filtered data and filtering errors is calculated, a prediction starting point is determined based on an RE curve, and the specific flow is as follows:
and extracting time domain characteristics of the original vibration signals, wherein variance characteristics which can better show the service life trend of the bearing are selected.
And performing linear filtering on the square difference characteristic to obtain a filtered characteristic curve F (k) and a filtered error curve E (k).
The sliding window size is set to 5% of the known data length T.
The relative error RE (k) for windows F (k) and E (k) is calculated, i.e., the continuous curve in FIG. 3.
Figure BDA0002683271890000081
The mean of the first 10% -20% of the data of the relative error of the current data set is chosen as the threshold boundary, i.e. the dashed line in fig. 3.
The degradation start point is determined from the first 20% data point according to the threshold boundary and used as a prediction start point for a subsequent prediction, i.e., the TSP shown in fig. 3.
Step three: the selected time domain features, namely the continuous curves in fig. 4, are subjected to noise reduction processing, and then an accumulation function is used to obtain an accumulation feature (CF) with a smoother trend, wherein the specific flow is as follows:
and (3) reconstructing the variance characteristics by using an improved algorithm CEEMDAN of empirical mode decomposition and then performing noise reduction.
The variance feature after noise reduction is processed according to an accumulation function to obtain an accumulation feature (CF), i.e. a dotted line in fig. 4, and the accumulation function formula is as follows:
Figure BDA0002683271890000082
step four: and (4) combining the second step and the third step to obtain a characteristic curve more suitable for modeling prediction, and establishing a state space model. Obtaining initial parameters of a model by a characteristic curve of a training set, and predicting the residual life of a bearing by combining an EKF algorithm, wherein the specific process comprises the following steps:
obtaining a characteristic curve segment CF' (k) of the current data set which is more suitable for modeling and prediction by the TSP obtained in the second step and the CF (k) obtained in the third step,k＝TSP，…，T
calculating the slope th of the last point of each characteristic curve segment of the training setiTaking the average value as a threshold value in the prediction of the test set:
Figure BDA0002683271890000091
the state space equation established is:
Figure BDA0002683271890000092
wherein x isk＝[ak，bk，ck，dk]K denotes the number of cycles, xkRepresenting a state model parameter, YkRepresents an observed value of the cumulative characteristic curve segment, and wkAnd vkRepresenting state noise and observation noise, respectively.
And fitting the characteristic curve segments of the training set to obtain initial parameters of the prediction model. Inputting the initial model parameters and the characteristic curve segment of the current data of the test set into an EFK algorithm, and predicting to obtain a state value X (T) at the time T:
(1) consider the following state space equation:
Figure BDA0002683271890000093
Y(k)＝HX(k)+V(k)
(2) and a prediction part:
state prediction:
Figure BDA0002683271890000094
observation and prediction:
Y(k|k-1)＝HX(k|k-1)
and thirdly, covariance prediction:
Figure BDA0002683271890000095
(3) an updating part:
computing a kalman gain:
K(k)＝P(k|k-1)HT[HP(k|k-1)HT+R]-1
state updating:
X(k)＝X(k|k-1)+K(k)[Y(k)-Y(k|k-1)]
updating the covariance:
P(k)＝[In-K(k)H]P(k|k-1)
calculating a measurement estimation value:
Figure BDA0002683271890000101
where Y (k) represents the input bearing cumulative characteristic segment CF' (k), corresponding to Y in the state space equationkObtaining the state value X at the time of T through an EKF algorithmkThen, according to the prediction model, the measurement estimation value after T time is calculated and obtained
Figure BDA0002683271890000102
When in use
Figure BDA0002683271890000103
And when the threshold value is reached, stopping prediction, and calculating the predicted residual life value of the current bearing:
R＝k-T
for the characteristic curve segment CF' (k),k＝TSP，…，Titeratively bringing the TSP time to t,TSP＜t≤Tthe characteristic curve segment CF' (k) of the time is used as an input for the EKF and the remaining life is predicted.
And evaluating two indexes, namely mean error and root mean square error, of a plurality of residual life values predicted by input samples with different data sizes and real residual life values serving as a test set, comparing the indexes with other models and methods, and verifying the effectiveness of the method.
And evaluating two indexes, namely mean error and root mean square error, of a plurality of residual life values predicted by input samples with different data sizes and real residual life values serving as a test set, comparing the indexes with other models and methods, and verifying the effectiveness of the method.
FIG. 5 illustrates Bearing data of Bearing1-3, and compares the bi-exponential model used in the method with the Weibull model and Paris model, and sets a confidence interval of + -20%. As can be seen from the comparison result of the prediction result in FIG. 5 and the index in FIG. 6, the proposed RE-CF-EKF algorithm has better residual life prediction effect and prediction robustness.
Aiming at the problem of residual life prediction of a rolling bearing, the invention provides an RE-CF-EKF algorithm, a simulation experiment is realized based on PHM2012 bearing data, and the effectiveness of the RE-CF-EKF algorithm is proved through the experiment.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (9)

1. A rolling bearing residual life prediction method based on an RE-CF-EKF algorithm is characterized by comprising the following steps:
the method comprises the following steps: screening the obtained bearing vibration data set, selecting a plurality of bearings under the same working condition as an experimental data set, and grouping the experimental data set with the bearings under the same working condition into a training set and a test set;
step two: linear filtering is carried out after the time domain characteristics of the original signal are taken, a relative error value RE between filtered data and a filtering error is calculated, and a prediction starting point TSP is determined based on an RE curve;
step three: denoising the selected time domain characteristics, and obtaining an accumulated characteristic CF with smoother trend by an accumulated function;
step four: and combining the second step and the third step to obtain a characteristic curve section suitable for modeling prediction, establishing a state space model, obtaining model initial parameters from the characteristic curve section of the training set, and then combining an EKF algorithm to predict the residual life of the bearing.
2. The rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 1, characterized in that:
selecting a time domain characteristic representation capable of representing the whole service life trend of the bearing in the second step, and performing linear filtering on the time domain characteristic representation to obtain a filtered characteristic curve and a filtered error curve;
setting the size of a sliding window as m;
calculating the relative error RE (k) of F (k) and E (k) in each window, wherein the specific expression is as follows:
Figure FDA0002683271880000011
the RE curve is obtained and the RE curve,
selecting a threshold boundary line from an RE curve obtained from a current data set;
according to the threshold boundary, a degradation starting point is found and used as a prediction starting point TSP for subsequent prediction.
3. The rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 2, characterized in that:
the sliding window size is X% of the known data length T;
the threshold boundary is the mean of the first A1% -A2% of the data of the relative error of the training set;
wherein X is a natural number;
a1 and A2 are selected from natural numbers, and A1 is less than A2.
4. The rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 1, characterized in that:
in the third step, an improved algorithm CEEMDAN of empirical mode decomposition is used for reconstructing the variance characteristics and then carrying out noise reduction processing;
processing the variance feature V subjected to noise reduction according to an accumulation function to obtain an accumulation feature CF;
wherein the cumulative function is formulated as follows:
Figure FDA0002683271880000021
5. the rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 1, characterized in that:
the training set is life cycle data;
the test set takes the former part as known data, and the rest part is used for verifying the quality of the prediction result.
6. The rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 5, characterized in that:
the fourth step comprises the following steps:
the EKF algorithm predicts the state estimation value after the last time T of the known data of the test set
Figure FDA0002683271880000022
Forming new model parameters;
obtaining bearing characteristic data corresponding to T + i (i is 1, 2, …, n) according to the prediction result;
when the characteristic curve of the bearing vibration data reaches a defined threshold value, the remaining service life RUL is the time interval from the time T to the bearing failure threshold point.
7. The rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 5, characterized in that:
in the fourth step, the characteristic curve segment CF' (k) of the current data set more suitable for modeling prediction is obtained from the prediction starting point obtained in the second step and the accumulated characteristics obtained in the third step,k＝TSP，…，T；
calculating the slope th of the last point of each characteristic curve segment of the training setiTaking the average value as a threshold value in the prediction of the test set:
Figure FDA0002683271880000031
the state space equation established is:
Figure FDA0002683271880000032
wherein x isk＝[ak，bk，ck，dk]；
k represents the number of cycles;
xkrepresenting state model parameters;
Ykan observed value representing a cumulative characteristic curve segment;
wkrepresenting state noise;
vkrepresenting observation noise;
fitting according to the characteristic curve segment of the training set to obtain initial parameters of a prediction model;
and inputting the initial model parameters and the characteristic curve segment of the current data of the test set into an EFK algorithm, and predicting to obtain a state value X (T) at the time T.
8. The rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 7, wherein:
the specific flow of the EKF algorithm is as follows:
s1, considering the following state space equation:
Figure FDA0002683271880000041
Y(k)＝HX(k)+V(k)
s2, prediction part:
s2-1. State prediction:
Figure FDA0002683271880000042
s2-2. Observation prediction:
Y(k|k-1)＝HX(k|k-1)
s2-3. covariance prediction:
Figure FDA0002683271880000043
s3, updating:
s3-1, calculating a kalman gain:
K(k)＝P(k|k-1)HT[HP(k|k-1)HT+R]-1
s3-2, status updating:
X(k)＝X(k|k-1)+K(k)[Y(k)-Y(k|k-1)]
s3-3. covariance update:
P(k)＝[In-K(k)H]P(k|k-1)。
9. the rolling bearing residual life prediction method based on the RE-CF-EKF algorithm as claimed in claim 8, characterized in that:
the calculation method of the measurement estimation value is as follows:
Figure FDA0002683271880000051
wherein Y (k) represents the input bearing cumulative characteristic curve segment CF' (k), corresponding to Y in the state space equationkObtaining the state value X at the time of T through an EKF algorithmkCalculating to obtain a measurement estimation value after T time according to a prediction model
Figure FDA0002683271880000052
When in use
Figure FDA0002683271880000053
And when the threshold value is reached, stopping prediction, and calculating the predicted residual life value of the current bearing:
R＝k-T
in which, for the characteristic curve segment CF' (k),k＝TSP，…，Titeratively bringing the TSP time to t,TSP＜t≤Tthe characteristic curve segment of the time is used as the input of the EKF, and the residual life is predicted.
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