CN112683535B - Bearing life prediction method based on multi-stage wiener process - Google Patents
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Abstract
The invention discloses a bearing life prediction method based on a multi-stage wiener process, which comprises the steps of firstly, collecting vibration signals when a bearing runs and extracting degradation characteristic indexes; then dividing the degradation process into a normal stage, a slow degradation stage and an accelerated degradation stage based on a wiener process according to the state change of the bearing in the service period, and establishing a multi-stage random degradation model according to the normal stage, the slow degradation stage and the accelerated degradation stage; meanwhile, estimating and updating the degradation state and the model parameters by using Kalman filtering and an expectation maximization algorithm; and finally, constructing a sliding window identification method to judge the degradation stages of the bearing, deducing a residual life expression corresponding to each stage and predicting the residual life. The method can effectively judge the degradation stage of the bearing, further predict the residual life under the corresponding stage, and has a good application effect.
Description
Technical Field
The invention belongs to the field of residual life prediction, and relates to a bearing life prediction method based on a multi-stage wiener process.
Background
The bearing is one of the key parts for normal operation of mechanical equipment, and is widely applied to various large and small-sized equipment. Due to the influence of internal and external environments, the bearing can fail along with the increase of service time, and the degradation or failure of the bearing can directly influence the performance and reliability of equipment. The residual life is estimated by accurately predicting the performance change of the bearing, so that a reasonable maintenance strategy is established and production is organized in a targeted manner, the loss caused by the failure of the bearing can be greatly reduced, and the operation reliability of mechanical equipment is improved.
In patent specification CN111414703A, a method for predicting the remaining life of a rolling bearing is disclosed, in which historical data of the same kind of bearing is input into an accelerated degradation prediction model, a first probability belonging to a stationary degradation stage and a second probability belonging to an accelerated degradation stage at each moment are calculated, the accelerated degradation stage is determined, the stationary degradation life prediction model and the accelerated degradation life prediction model are established, the stage of the bearing is judged and predicted by real-time vibration data, and life prediction is performed according to the model of the stage. In patent specification CN105653851A, a method for predicting the remaining life of a rolling bearing based on a staged physical model and particle filtering is disclosed, in which an alarm threshold, a staged point threshold and a stop threshold are set as a prediction initial point, a stage boundary point and a prediction cut-off point, then different degradation stage models are established, a least square method is applied to update model parameters, and a particle filtering algorithm is used to predict the remaining life.
In the two methods for establishing the staged model to predict the residual life of the bearing, the change point of the degradation stage of each bearing is different due to the difference between the bearings and the service condition, and dividing the degradation stage of the bearing through related experience or historical data can cause the use of a wrong life prediction model when predicting the residual life, thereby affecting the residual life prediction precision of the bearing. In addition, in the two remaining life prediction methods, since the interval estimation of the remaining life is wider than the point estimation in practical application, the probability density function of the remaining life needs to be derived, and the regression or physical model obtains an approximate solution of the probability density function of the remaining life instead of an analytic solution by introducing normal distribution, so that the accuracy of the remaining life prediction is low. Meanwhile, due to the fact that the degradation forms of the bearing are various and the failure mechanism is complex, the failure reasons of the bearing may include a plurality of reasons, and the prediction accuracy of the regression or physical model depends on the consistency of the regression trend or the failure mechanism and the actual degradation, so that the prediction accuracy of the residual life of the bearing is affected.
Disclosure of Invention
In order to solve the problem of low prediction precision of a staged life prediction model, the invention aims to provide a bearing life prediction method based on a multi-stage wiener process.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the bearing life prediction method based on the multi-stage wiener process comprises the following steps:
the first step is as follows: acquiring a vibration signal of the bearing in real time by using a sensor, and extracting characteristic indexes from the vibration signal to represent the degradation state of the bearing;
the second step is that: based on the state change of the bearing during service, the degradation process is divided into three stages, namely a normal stage, a slow degradation stage and an accelerated degradation stage. Wherein, a normal stage of the bearing is described by using a standard wiener process, a slow degradation stage of the bearing is described by using a linear wiener process, and an accelerated degradation stage of the bearing is described by using a nonlinear wiener process. Based on the degradation stages, the individual difference, the time variation and the measurement uncertainty are fully considered, and a multi-stage random degradation model for representing the bearing degradation is established.
The third step: based on the multi-stage random degradation model, estimating the degradation state of the bearing by using a state estimation method according to real-time collected data, and updating model parameters by using a parameter estimation method;
the fourth step: judging the degradation stage of the bearing by using a sliding window identification method according to the change of real-time acquired data, and predicting the service life according to a degradation model corresponding to the stage;
the fifth step: and deducing probability density functions of the residual life at different degradation stages based on the definition of the bearing life and the first arrival time, and further predicting the residual life of the bearing at each moment.
Preferably, the multi-stage random degradation model constructed in the second step of the bearing life prediction method based on the multi-stage wiener process is as follows:
1) normal phase model:
in the above formula, x is an actual degradation index; sigma is a diffusion coefficient and represents the time-varying property of the bearing degradation; τ is the sampling interval, τk＝tk-tk-1(ii) a B (tau) is Brownian motion, B (t) to N (0, sigma)2τ); y is a measured degradation indicator; pi is the measurement variance, characterizes the uncertainty of the measurement,
2) slow degradation model:
in the formula, eta is a drift coefficient and represents the difference between individuals; v is the variance of the shift coefficient, v-N (0, epsilon)2)。
3) An accelerated degradation model:
in the above formula, Λ (t; xi) is a nonlinear function of time t, and xi is a nonlinear coefficient.
Preferably, in the fourth step of the bearing life prediction method based on the multi-stage wiener process, the sliding window identification method comprises the following steps:
1) establishing a sliding window to calculate relative error: calculating the relative error between the degradation index measured in the window and the degradation index of the filtering according to the real-time collected data; if the relative error exceeds a set threshold, the degradation stage of the bearing is changed. The relative error calculation formula is as follows:
wherein, HImeaIs a measured degradation indicator; HI (high-intensity)filIs a degradation indicator of filtering; n is the length of the data intercepted forward;
2) and (3) detecting the variation distribution: calculating the variable quantity of the degradation index in the sliding window, and judging whether the variable quantity accords with normal distribution by using a Lilliefors test method; if the variation accords with the normal distribution, the bearing is in a normal stage or a slow degradation stage; if the normal distribution is not met, indicating that the accelerated degradation stage is in;
3) calculating a correlation coefficient: calculating a Pearson correlation coefficient between the degradation index and the acquisition time in the sliding window; if the correlation coefficient exceeds a set threshold value, the bearing is in a slow degradation stage; otherwise, the bearing is in the normal phase.
Preferably, in the fifth step of the bearing life prediction method based on the multi-stage wiener process, the predicted residual life calculation formula of the bearing at each moment is as follows:
wherein f (t | θ) is tkAnd (4) bearing residual life probability density function deduced at the moment. According to the first arrival time concept and the definition of the bearing life in the wiener process, the probability density function of the residual life in the slow degradation stage is as follows:
where ω is the failure threshold. The remaining lifetime probability density function of the accelerated degradation phase is:
preferably, in the first step of the bearing life prediction method based on the multi-stage wiener process, a time domain index is extracted from the vibration signal to represent the degradation state of the bearing; and in the third step, the degradation state of the bearing is estimated by using Kalman filtering, and the parameters of the degradation model are updated by using an expectation-maximization algorithm.
The invention has the beneficial effects that:
the method establishes a bearing multi-stage random degradation model based on a multi-stage wiener process, and comprises a normal stage of a standard wiener process, a slow degradation stage of a linear wiener process and an accelerated degradation stage of a nonlinear wiener process; updating the degradation state and model parameters according to the real-time acquisition signals by using Kalman filtering and an expectation-maximization algorithm; and judging the degradation stage of the bearing by using a sliding window identification method, deducing a probability density function of the residual life and predicting the residual life, so that the degradation stage of the bearing is identified, and the residual life at different stages is predicted. According to the method, the property that the first arrival time of the wiener process meets the inverse Gaussian distribution is utilized, the probability density function of the residual life is deduced, the analytical solution of the life prediction model is obtained, and compared with the approximate solutions of other prediction models, the accuracy of residual life prediction is improved. Meanwhile, the invention utilizes the wiener process to represent the continuous process with random characteristics, and compared with other multi-stage life prediction models, the uncertainty of the degradation process is more effectively described. According to the method, the data characteristics of different degradation stages are extracted according to the change of the vibration signal in the degradation process of the bearing, and the stage where the bearing is located is identified according to the data characteristics.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 shows vibration signals of the whole life cycle of the rolling bearing tested by the embodiment.
FIG. 3 shows the effective value extracted by the rolling bearing test of the embodiment; (a) the effective value of the full life cycle (b) the effective value of the degradation process.
Fig. 4 is a graph showing the result of identifying the sliding window of the rolling bearing tested in the example. (a) Recognition of full life cycle (b) recognition of degradation process.
FIG. 5 is a graph of a probability density function of the residual life of a rolling bearing tested according to the embodiment; (a) the slow degradation stage (b) accelerates the degradation stage.
FIG. 6 is a diagram showing the predicted residual life of the rolling bearing in the example.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
In the embodiment, the invention is verified by using the experimental data of the accelerated life of the rolling bearing on the XJTU-SY test platform, the test bearing is an LDK UER204 rolling bearing, the set rotating speed is 2400r/min, and the radial force is 10 kN. And an acceleration sensor is used for collecting vibration signals of the rolling bearing, the sampling frequency is 25.6kHz, the sampling period is 1min, and the sampling time length is 1.28 s. The bearing life prediction method based on the multi-stage wiener process is shown in FIG. 1 and comprises the following steps:
1. the method comprises the steps of utilizing a sensor to collect vibration signals of a rolling bearing in real time, extracting time domain indexes from the vibration signals to represent the degradation state of the bearing, wherein the time domain indexes can select indexes which can represent the degradation of the bearing such as effective values, square root amplitude values, absolute average values, peak-to-peak values, combinations of the effective values and the peak-to-peak values, the effective values are used in the embodiment, and the calculation formula is as follows:
in the above formula, T is sampling duration; and z is the acquired vibration signal.
2. In the present embodiment, the effective value of the rolling bearing is shown in fig. 3(a), and it can be seen that the rolling bearing has three states of health, degradation, and failure in the whole life cycle. The effective value of the degradation stage changes as shown in fig. 3(b), and the degradation process has various trend characteristics from the beginning of degradation to the complete failure. The bearing is divided into three degradation stages, namely a normal stage, a slow degradation stage and an accelerated degradation stage. Wherein the normal phase of the bearing is described using the standard wiener process:
x(t)＝x0+σB(t) (9)
above formula, x0Is a degradation index of the bearing in normal operation; sigma is a diffusion coefficient and represents the time-varying property of the bearing degradation; b (t) is Brownian motion, B (t) N (0, sigma)2t)。
The slow degradation phase of the bearing is described using the linear wiener process:
x(t)＝x0+ηt+σB(t) (10)
in the above formula, η is a drift coefficient, and represents the difference between individuals.
The accelerated degradation phase of the bearing is described using a non-linear wiener process:
in the above formula, Λ (t; xi) is a nonlinear function of time t, and xi is a nonlinear coefficient.
Based on the three degradation stages, the following multi-stage random degradation model is constructed by fully considering individual difference, time variation and measurement uncertainty:
1) normal phase model:
in the above formula, y is an effective value; pi is the measurement variance, characterizes the uncertainty of the measurement,
the measurement variance can be calculated from the vibration signal of the rolling bearing during normal operation.
2) Slow degradation model:
v is the variance of the drift coefficient, v-N (0, epsilon)2)；τk＝tk-tk-1Is the sampling interval.
3) An accelerated degradation model:
3. in this embodiment, the drift coefficient η and the degraded state x are combined into an extended state. And estimating an expansion state by using a Kalman filtering algorithm based on degradation models of different degradation stages. As other embodiments, other state estimation methods may also be used to estimate the extended state, which is not limited in the present invention.
4. And updating unknown parameters in the stochastic degradation model by using an expectation-maximization algorithm according to the change of the real-time collected data. In this embodiment, the model parameters include diffusion coefficient σ and measurement variance
The variance epsilon of change of the drift coefficient and a nonlinear coefficient xi,
when the degradation stage is changed, the initial value of the parameter is the estimated value of the parameter of the last degradation stage, and the model parameter is continuously updated according to the newly acquired data. As another embodiment, other parameter estimation methods may also be used to update the parameters in the model, which is not limited in the present invention.
5. Judging the degradation stage of the bearing by using a sliding window identification method, and predicting the service life according to a degradation model corresponding to the stage, wherein the sliding window identification method comprises the following steps:
1) establishing a sliding window to calculate relative error: and calculating the relative error between the measured degradation index and the filtered degradation index in the sliding window according to the real-time collected data. Errors may occur in the filtering results due to the fact that the degradation model does not match the actual one. Thus, when the relative error exceeds a set threshold, it indicates that the degradation stage of the bearing has changed. The relative error calculation formula is as follows:
wherein, HImeaIs a measured degradation indicator; HI (high-intensity)filIs a degradation indicator of filtering; n is the length of the data intercepted forward.
2) And (3) detecting the variation distribution: and calculating the variation of the degradation index in the sliding window, wherein the calculation formula is as follows:
ΔHI＝HIfil(i)-HIfil(i-1) (16)
and judging whether the variable quantity accords with normal distribution or not by using a Lilliefors test method. If the variation accords with the normal distribution, the bearing is in a normal stage or a slow degradation stage; if the normal distribution is not met, the accelerated degradation stage is indicated. As another embodiment, the distribution of the variation may be determined by a normal distribution test method, which is not limited in the present invention.
3) Calculating a correlation coefficient: and calculating a Pearson correlation coefficient between the degradation index and the acquisition time in the sliding window. The correlation coefficient rho ranges from-1 to +1, the greater the absolute value of rho, the more linear the window is. The correlation coefficient exceeds a set threshold value, which indicates that the bearing is in a slow degradation stage; otherwise, the bearing is in the normal phase.
In this embodiment, the degradation stages of the test bearing are divided by using a sliding window identification method, as shown in fig. 4, "degradation stage 0" represents a normal stage, "degradation stage 1" represents a slow degradation stage, "and" degradation stage 2 "represents an accelerated degradation stage.
6. Defining the life of the bearing as the time t at which the characteristic indicator first reaches or exceeds the failure thresholdlifeThen, the calculation formula of the bearing is as follows:
tlife＝inf{tlife:x(tk)≥ω|x(0)＜ω} (17)
above formula, x (t)k) Is a bearing degradation index; ω is the bearing failure threshold. In this embodiment, the failure threshold of the bearing is determined using a relative method, i.e., when the effective value of the bearing exceeds 10 × AhThe bearing is considered to have failed completely, where AhThe method is the maximum characteristic index of the bearing in a healthy state.
For bearings in different degradation stages, the degradation characteristics are different, and the calculation formula for reaching the failure threshold value for the first time is also different. For the normal phase, the bearing is not degraded and therefore there is no remaining life. For the degradation stage, the first arrival time of the wiener process crossing a certain threshold satisfies the inverse Gaussian distribution, and the slow degradation stage tkThe remaining lifetime probability density function at a time is:
accelerated degradation phase tkThe remaining lifetime probability density function at a time is:
the degradation state estimated at each moment, the model parameters and the failure threshold are substituted into the above formula to obtain the remaining life probability density functions of the slow degradation stage and the accelerated degradation stage, as shown in fig. 5.
Calculating the mathematical expectation of the probability density function at each time, wherein the calculation formula is as follows:
in the above formula, f (t | theta) is tkBearing residual life derived from time to timeProbability of hit density function. The predicted remaining life of the test rolling bearing is shown in fig. 6.
Although the present invention has been disclosed above by way of example, it does not limit the scope of application and protection of the present invention, and the present invention can be used not only for predicting the residual life of a rolling bearing, but also for other mechanical products having a plurality of monotonic degradation processes. When the method is applied, a proper degradation model is established according to the degradation track characteristics of the predicted object, so that the method can be applied to different types of residual life prediction. In addition, any modification and alteration by those skilled in the art without departing from the spirit and scope of the present invention shall fall within the protection scope of the present invention.
Claims (4)
1. The bearing life prediction method based on the multi-stage wiener process is characterized by comprising the following steps of:
the first step is as follows: acquiring a vibration signal of the bearing in real time by using a sensor, and extracting characteristic indexes from the vibration signal to represent the degradation state of the bearing;
the second step is that: dividing a degradation process into a normal stage, a slow degradation stage and an accelerated degradation stage based on the state change of the bearing in a service period; the method comprises the following steps of describing a normal stage of a bearing by using a standard wiener process, describing a slow degradation stage of the bearing by using a linear wiener process, and describing an accelerated degradation stage of the bearing by using a nonlinear wiener process; the method comprises the following specific steps:
wherein x is0Is in an initial degradation state; eta is a drift coefficient; σ b (t) is brownian motion of diffusion coefficient σ; Λ (t; ξ) is a nonlinear function of time t, ξ is a nonlinear coefficient;
based on the degradation stages, fully considering individual difference, time variation and measurement uncertainty, and establishing a multi-stage random degradation model for representing bearing degradation;
1) normal phase model:
in the above formula, x is an actual degradation index; sigma is a diffusion coefficient and represents the time-varying property of the bearing degradation; τ is the sampling interval, τk＝tk-tk-1(ii) a B (tau) is Brownian motion, B (t) to N (0, sigma)2τ); y is a measured degradation indicator; pi is the measurement variance, characterizes the uncertainty of the measurement,
represents the measurement variance;
2) slow degradation model:
in the formula, eta is a drift coefficient and represents the difference between individuals; v is the variance of the shift coefficient, v-N (0, epsilon)2) (ii) a E represents the variance of the change of the drift coefficient;
3) an accelerated degradation model:
in the formula, Λ (t; xi) is a nonlinear function of time t, and xi is a nonlinear coefficient;
the third step: based on the multi-stage random degradation model, estimating the degradation state of the bearing by using a state estimation method according to real-time collected data, and updating model parameters by using a parameter estimation method;
the fourth step: judging the degradation stage of the bearing by using a sliding window identification method according to the change of real-time acquired data, and predicting the service life according to a degradation model corresponding to the stage;
in the fourth step, the sliding window identification method includes the steps of:
1) establishing a sliding window to calculate relative error: calculating the relative error between the degradation index measured in the window and the degradation index of the filtering according to the real-time collected data; if the relative error exceeds a set threshold, indicating that the degradation stage of the bearing is changed; the relative error calculation formula is as follows:
wherein, HImeaIs a measured degradation indicator; HI (high-intensity)filIs a degradation indicator of filtering; n is the length of the data intercepted forward;
2) and (3) detecting the variation distribution: calculating the variable quantity of the degradation index in the sliding window, and judging whether the variable quantity accords with normal distribution by using a Lilliefors test method; if the variation accords with the normal distribution, the bearing is in a normal stage or a slow degradation stage; if the normal distribution is not met, indicating that the accelerated degradation stage is in;
3) calculating a correlation coefficient: calculating a Pearson correlation coefficient between the degradation index and the acquisition time in the sliding window; if the correlation coefficient exceeds a set threshold value, the bearing is in a slow degradation stage; otherwise, the bearing is in a normal stage;
the fifth step: and deducing probability density functions of the residual life at different degradation stages based on the definition of the bearing life and the first arrival time, and further predicting the residual life of the bearing at each moment.
2. The multi-stage wiener process-based bearing life prediction method according to claim 1, wherein in the fifth step, the predicted remaining life calculation formula of the bearing at each time is as follows:
wherein f (t | θ) is tkA residual life probability density function deduced at a moment; according to the first arrival time concept and the definition of the bearing life in the wiener process, the probability density function of the residual life in the slow degradation stage is as follows:
wherein ω is a failure threshold; the remaining lifetime probability density function of the accelerated degradation phase is:
3. the method according to claim 1, wherein in the first step, a time domain index is extracted from the vibration signal to characterize the degradation state of the bearing.
4. The multi-stage wiener process-based bearing life prediction method of claim 1, wherein in the third step, the degradation state of the bearing is estimated by acquiring data in real time and using kalman filtering, and parameters of a degradation model are updated by using an expectation-maximization algorithm.
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