Rolling bearing residual life prediction method based on Brownian motion and degradation related diffusion coefficient

Abstract

The invention discloses a rolling bearing residual life prediction method based on Brownian motion and degradation related diffusion coefficients, and belongs to the field of residual life prediction. Comprising the following steps: constructing a performance degradation model based on Brownian motion and degradation related diffusion coefficients in combination with a power exponential function; obtaining a performance degradation index representing the performance degradation trend of the rolling bearing, and taking the performance degradation index as an input sequence of the prediction model; estimating related unknown parameters of the model based on a least square method principle; obtaining a performance degradation increment process distribution form about the residual life; adopting a Monte Carlo simulation technology to quantitatively describe the probability distribution form of the residual life prediction result; and the expected value of the life distribution is used as a prediction result, and life prediction and uncertainty quantification of the rolling bearing are realized. According to the method, the real-time life prediction of the bearing can be realized without depending on the pre-training of a bearing full-life-cycle data model; and meanwhile, the uncertainty of the life prediction result can be quantified.

Description

Technical Field

[0001] The present invention belongs to the technical field of remaining life prediction, and relates to the problem of predicting the remaining service life of rolling bearings. Specifically, it is a method for predicting the remaining life of rolling bearings based on Brownian motion and degradation-related diffusion coefficients. Background Art

[0002] Rolling bearings are one of the indispensable important components in rotating machinery. Their accidental failure may cause equipment shutdown, resulting in huge economic losses and even threatening the safety of personnel. In industrial production practice, if the life prediction result is inaccurate, it may cause problems of over-maintenance or under-maintenance, thus affecting the normal operation of the equipment. Therefore, in-depth research on the prediction method of the remaining life of rolling bearings and formulating a reasonable maintenance strategy based on this are of great significance for improving production efficiency and ensuring the stability and reliability of equipment.

[0003] Currently, the research on the prediction of the remaining life of rolling bearings mainly focuses on two major directions: physical model-based methods and data-driven methods. Among them, physical model-based methods rely on an accurate understanding of the equipment operation principle and damage evolution mechanism. However, due to the complexity of actual engineering systems, the modeling process of such methods usually has a high degree of difficulty. And data-driven methods, including deep learning models and statistical models, have gradually received extensive attention in applications. Although deep learning models have advantages in processing large-scale data, their high requirements for data quality and quantity and poor model interpretability still pose certain limitations in the field of life prediction, especially in terms of quantifying the uncertainty of prediction results. In contrast, statistical models have significant advantages in describing the randomness and uncertainty of prediction results. Given the complexity and harshness of the operating environment of rolling bearings in industrial scenarios, their performance degradation process usually exhibits significant random characteristics and non-linear behavior. Therefore, studying statistical modeling methods that can effectively quantify uncertainty has important academic value and practical significance for improving the accuracy and reliability of the remaining life prediction of rolling bearings. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention provides a method for predicting the remaining life of rolling bearings based on Brownian motion and degradation-related diffusion coefficients. The remaining life of the rolling bearing can be dynamically predicted based on real-time observation data without relying on a historical training data set similar to the degradation trend of the bearing, and can quantify the uncertainty in the life prediction result, effectively improving the accuracy and reliability of the remaining life prediction of the rolling bearing.

[0005] The technical solution of the present invention is as follows:

[0006] A method for predicting the remaining useful life of a rolling bearing based on Brownian motion and degradation-related diffusion coefficient, comprising the following steps:

[0007] Step 1: Construct a performance degradation model based on Brownian motion and degradation-related diffusion coefficient by combining power-exponential function;

[0008] By collecting the vibration signal data of the rolling bearing, calculate the RMS value, i.e., the effective value, for each sample, and use the RMS value as the performance degradation index reflecting the operating state of the rolling bearing, denoted as Y; the calculation formula of Y is:

[0009]

[0010] where, X i represents the i-th data point of the vibration signal data sequence, and I represents the length of the vibration signal sample data sequence X;

[0011] Based on the calculated performance degradation index of the rolling bearing, construct the performance degradation model of the rolling bearing based on Brownian motion and degradation-related diffusion coefficient as follows:

[0012] Y(t) = Y(0) + At B + η(Y′(t))·B(t)

[0013] where, t is the operating time of the rolling bearing, and t > 0. Y(t) is the performance degradation index value at the t-th moment, and Y(0) is the initial value of performance degradation; the power-exponential function At B is used to describe the change of the average cumulative effect in the degradation process of the rolling bearing, reflecting the non-linear drift characteristic of the degradation amount Y(t); the unknown parameters A and B respectively represent the coefficients and exponents corresponding to At B ; B(t) is the standard Brownian motion, which follows a normal distribution with a mean of 0 and a variance of t; η(Y′(t)) represents the degradation-related diffusion coefficient corresponding to the performance degradation model;

[0014] where, the unknown parameters A and B in the power-exponential function are estimated by minimizing the error function:

[0015]

[0016] Based on the principle of non-linear least squares method, by calculating the partial derivatives of the error function ε with respect to the parameters A and B respectively, and setting the partial derivatives to zero, the estimated values of the parameters A and B can be obtained by solving the following equations:

[0017]

[0018] In the formula, N represents the length of the performance degradation index;

[0019] Among them, the calculation of the degradation-related diffusion coefficient η(Y′(t)) satisfies the following system of equations:

[0020]

[0021] In the formula, Y′(t) is the first derivative of the performance degradation level Y(t) with respect to time t; Δt is the performance degradation time increment;

[0022] Step 2: Calculate the process of the performance degradation increment of the rolling bearing;

[0023] ΔY t = Y(t + Δt) - Y(t)

[0024] = A·(t + Δt) B - At B +(η(Y′(t + Δt)) - η(Y′(t)))·B(Δt)

[0025] In the formula, ΔY t is the degradation increment corresponding to the rolling bearing at time t;

[0026] Step 3: Calculate the distribution form of the rolling bearing degradation increment process;

[0027] According to the linear transformation property of the normal distribution, calculate that the rolling bearing degradation increment process ΔY t satisfies the following distribution form:

[0028] ΔY t ~N(A·B·t B-1 ·Δt, (η(Y′(t + Δt)) - η(Y′(t))) 2 ·Δt)

[0029] Step 4: Estimate the remaining service life of the rolling bearing;

[0030] The defined expression of the remaining service life corresponding to the rolling bearing at the current moment is:

[0031] R = inf{r: Y(t + r) ≥ ω | Y(t) ≤ ω}

[0032] Among them, ω is the failure threshold of the rolling bearing, r represents the remaining life corresponding to the current moment t, R is the set of remaining lives, and inf{·} represents the infimum; according to the definition of the remaining service life, the solution of the remaining life result of the rolling bearing at the current moment is realized.

[0033] Furthermore, the remaining life r corresponding to the current moment satisfies the following inequality:

[0034] Y(t)+(η(Y′(t + r)) - η(Y′(t)))·B(r) - ω ≥ At B-A·(t + r) B

[0035] Among them, according to the properties of the normal distribution, {Y(t) + (η(Y′(t + r)) - η(Y′(t)))·B(r) - ω} satisfies the following distribution:

[0036] {Y(t) + (η(Y′(t + r)) - η(Y′(t)))·B(r) - ω} ~ N(Y(t) - ω, (η(Y′(t + r)) - η(Y′(t))) 2 ·r). Then generate data that follows the distribution form of N(Y(t) - ω, (η(Y′(t + r)) - η(Y′(t))) 2 ·r). Through the random sampling method based on the Monte Carlo simulation technique, evaluate the uncertainty of the result of predicting the remaining life of the rolling bearing, and obtain the remaining life distribution result R of the rolling bearing. Use the expectation of the life distribution R as the reference value of the prediction result to achieve the prediction of the remaining life of the rolling bearing and the uncertainty evaluation of the prediction result.

[0037] The beneficial effects of the present invention are as follows:

[0038] The present invention proposes a method for predicting the remaining life of a rolling bearing based on Brownian motion and degradation-related diffusion coefficients. The remaining life of the rolling bearing can be dynamically predicted based on real-time observation data, without relying on historical training data sets similar to the degradation trend of the bearing, and can quantify the uncertainty in the life prediction results, effectively improving the accuracy and reliability of predicting the remaining life of the rolling bearing. Description of the Drawings

[0039] Figure 1 is the flow chart of the method for predicting the remaining life of a rolling bearing based on Brownian motion and degradation-related diffusion coefficients provided by the present invention;

[0040] Figure 2 is the performance degradation index of the rolling bearing in the embodiment of the present invention;

[0041] Figure 3 is the prediction result of the remaining life of the rolling bearing in the embodiment of the present invention. Detailed Embodiments

[0042] The following details the specific embodiments of the present invention in combination with the technical solutions and the drawings.

[0043] In this embodiment, a method for predicting the remaining life of a rolling bearing based on Brownian motion and degradation-related diffusion coefficients, Figure 1 indicating the flow chart of the method for predicting the remaining life of the rolling bearing, includes the following steps:

[0044] Step 1: The data in this embodiment is sourced from the XJTU-SY rolling bearing full-life cycle open dataset; in the data preprocessing stage, the axial vibration signal within 160 minutes of the equipment operation is intercepted as the original signal X, and a bearing remaining useful life prediction model based on vibration characteristics is constructed.

[0045] Step 2: Combine the power exponential function to construct a performance degradation model based on Brownian motion and degradation-related diffusion coefficient.

[0046] Calculate the root mean square (RMS) value of the intercepted original vibration signal X, and use it as the performance degradation index Y reflecting the operating state of the rolling bearing. Its calculation formula is:

[0047]

[0048] where, X i represents the i-th data point in the vibration signal X sequence, and I represents the length of the vibration signal sample data X;

[0049] Characterize the rolling bearing performance degradation index Y as Figure 2 shown, and use it as the input sequence {Y(t): t = 1, 2,...} of the prediction model; combine the power exponential function to construct a performance degradation model based on Brownian motion and degradation-related diffusion coefficient, specifically as follows:

[0050] Y(t) = Y(0) + At B + η(Y′(t))·B(t) (2)

[0051] where, t is the operating time variable of the rolling bearing, and in this example t ∈ (0, 160min]. Y(t) is the performance degradation index value at the t-th moment, Y(0) is the initial value of performance degradation, and Y(0) is generally set to 0; the power exponential function At B is used to describe the change of the average cumulative effect during the bearing degradation process, reflecting the non-linear drift characteristic of the degradation amount Y(t); the unknown parameters A and B respectively represent the coefficients and exponents corresponding to At B ; B(t) is the standard Brownian motion, which follows a normal distribution with a mean of 0 and a variance of t; η(Y′(t)) represents the degradation-related diffusion coefficient corresponding to the performance degradation model;

[0052] where, the unknown parameters A and B in the power exponential function are estimated by minimizing the error function:

[0053]

[0054] Based on the principle of non-linear least squares method, by calculating the partial derivatives of the error function ε with respect to the parameters A and B respectively, and setting the partial derivatives to zero, the estimated values of the parameters A and B can be obtained by solving the following equations:

[0055]

[0056] In the formula, N represents the length of the performance degradation index;

[0057] Among them, the calculation of the degradation-related diffusion coefficient η(Y′(t)) satisfies the following system of equations:

[0058]

[0059] In the formula, Y′(t) is the first derivative of the performance degradation level Y(t) with respect to time t; Δt is the performance degradation time increment;

[0060] Step 3: Calculate the degradation increment process of the rolling bearing performance Y;

[0061]

[0062] In the formula, ΔY t is the degradation increment corresponding to the rolling bearing at time t;

[0063] Step 4: Calculate the distribution form of the rolling bearing degradation increment process;

[0064] According to the linear transformation property of the normal distribution, calculate the rolling bearing degradation increment process ΔY t satisfies the following distribution form:

[0065] ΔY t ~N(A·B·t B-1 ·Δt,(η(Y′(t + Δt)) - η(Y′(t))) 2 ·Δt)(7)

[0066] Step 5: Estimate the remaining service life of the rolling bearing;

[0067] The defined expression of the remaining service life corresponding to the rolling bearing at the current moment is:

[0068] R = inf{r: Y(t + r) ≥ ω|Y(t) ≤ ω}, (8)

[0069] Among them, ω is the rolling bearing failure threshold, r represents the remaining life corresponding to the current moment t, R is the set of remaining lives, inf{·}

[0070] represents the infimum;

[0071] Furthermore, the remaining life r corresponding to the current moment satisfies the following inequality:

[0072] Y(t)+(η(Y′(t + r)) - η(Y′(t)))·B(r) - ω ≥ At B -A·(t + r)B (9)

[0073] Among them, according to the properties of the normal distribution, {Y(t)+(η(Y′(t+r)) - η(Y′(t)))·B(r)-ω} satisfies the following distribution:

[0074] {Y(t)+(η(Y′(t+r)) - η(Y′(t)))·B(r)-ω}~N(Y(t)-ω,(η(Y′(t+r)) - η(Y′(t))) 2 ·r)(10)

[0075] Then generate data that follows the distribution form of N(Y(t)-ω,(η(Y′(t+r)) - η(Y′(t))) 2 ·r). Through the random sampling method based on the Monte Carlo simulation technique, the uncertainty of the result of predicting the remaining life of the rolling bearing is evaluated, and the remaining life distribution result R of the rolling bearing is obtained. Taking the expectation of the life distribution R as the reference value of the prediction result, the prediction of the remaining life of the rolling bearing and the uncertainty evaluation of the prediction result are realized; the prediction result of the remaining life of the rolling bearing is as Figure 3 shown, where the X-axis represents the running time, the Y-axis represents the remaining life values corresponding to different running times, and the Z-axis represents the probability density curve corresponding to the predicted remaining life values. The black circles represent the actual remaining life, and the asterisks * represent the remaining service life values obtained by the proposed method. The curve represents the probability density curve corresponding to the predicted remaining life values. Therefore, it can be seen that the predicted life by the method proposed in the present invention has a very high probability density with the actual remaining life and has good prediction performance.

Claims

1. A method for predicting the remaining life of a rolling bearing based on Brownian motion and degradation-related diffusion coefficient, characterized in that: The following steps are involved: Step 1: Construct a performance degradation model based on Brownian motion and degradation-related diffusion coefficient in combination with the power exponential function; By collecting the vibration signal data of the rolling bearing, the RMS value, i.e. the effective value, is calculated for each sample, and the RMS value is used as a performance degradation index reflecting the running state of the rolling bearing, denoted as Y; the calculation formula of Y is: Among them, X i represents the i-th data point of the vibration signal data sequence, and I represents the length of the vibration signal sample data sequence y; Based on the calculated performance degradation index of rolling bearings, a rolling bearing performance degradation model based on Brownian motion and degradation-related diffusion coefficient is constructed as follows: Y(t)=Y(0)+At B +η(Y′(t))·B(t) Where t is the running time of the rolling bearing, and t>0; Y(t) is the performance degradation index value at the tth moment, and Y(0) is the initial value of performance degradation; the power exponential function At B It is used to describe the change of the average cumulative effect during the rolling bearing degradation process, reflecting the nonlinear drift characteristics of the degradation amount Y(t); the unknown parameters A and B represent At B The corresponding coefficients and exponents; B(t) is the standard Brownian motion, which obeys the normal distribution with mean 0 and variance t; η(Y′(t)) represents the degradation-related diffusion coefficient corresponding to the performance degradation model; The unknown parameters A and B in the power exponential function are estimated by minimizing the error function: Based on the principle of nonlinear least squares method, the partial derivatives of the error function ε with respect to parameters A and B are calculated respectively, and the partial derivatives are set to zero. The estimated values ​​of parameters A and B are obtained by solving the following set of equations: Where N represents the length of the performance degradation index; Among them, the calculation of the degradation-related diffusion coefficient η(Y′(t)) satisfies the following equations: Where Y′(t) is the first-order derivative of the performance degradation level Y(t) with respect to time t; Δt is the performance degradation time increment; Step 2: Calculate the incremental process of rolling bearing performance degradation; ΔY t =Y(t+Δt)-Y(t)=A·(t+Δt) B -At B +(η(Y′(t+Δt))-η(Y′(t)))·B(Δt) In the formula, ΔY t is the degradation increment of the rolling bearing corresponding to time t; Step 3: Calculate the incremental process distribution form of rolling bearing degradation; According to the linear transformation properties of normal distribution, the incremental process ΔY of rolling bearing degradation is calculated t Satisfies the following distribution form: Y t ~N(A·B·t B-1 ·Δt,(η(Y′(t+Δt))-η(Y′(t))) 2 ·Δt) Step 4: Estimation of the remaining service life of rolling bearings; The remaining service life of the rolling bearing at the current moment is defined as: R=inf{r:Y(t+r)≥ω|Y(t)≤ω} Where ω is the failure threshold of the rolling bearing, r represents the remaining life corresponding to the current time t, R is the remaining life set, and inf{·} represents the infimum. Based on the definition of the remaining service life, the remaining life result of the rolling bearing at the current time can be solved.

2. The method for predicting the remaining life of a rolling bearing based on Brownian motion and degradation-related diffusion coefficient according to claim 1 is characterized in that: The remaining life r corresponding to the current moment satisfies the following inequality: Y(t)+(η(Y′(t+r))-η(Y′(t)))·B(r)-ω≥At B -A·(t+r) B According to the normal distribution property, {Y(t)+(η(Y′(t+r))-η(Y′(t)))·B(r)-ω} satisfies the following distribution: {Y(t)+(η(Y′(t+r))-η(Y′(t)))·B(r)-ω}~N(Y(t)-ω,(η(Y′(t+r))-η(Y′(t))) 2 ·r) Then the generated distribution is in the form of N(Y(t)-ω,(η(Y′(t+r))-η(Y′(t))) 2 ·r), and through the random sampling method based on Monte Carlo simulation technology, the uncertainty of the results of the remaining life prediction of the rolling bearing is evaluated to obtain the remaining life distribution result R of the rolling bearing; the expectation of the life distribution R is used as the reference value of the prediction result to realize the prediction of the remaining life of the rolling bearing and the uncertainty evaluation of the prediction result.

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