A method and system for predicting the remaining life of two-stage degraded equipment

Abstract

The present invention relates to a method and system for predicting the remaining life of a two-stage degradation device. The method comprises obtaining degradation trajectory data of the device to be predicted; establishing a two-stage degradation model according to the degradation trajectory data of the device to be predicted; identifying parameters of the two-stage degradation model using the maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted; and predicting the remaining life of the device to be predicted according to the two-stage degradation model after identifying the parameters. The present invention can improve the accuracy of the remaining life prediction.

Description

Technical Field

[0001] The invention relates to the field of reliability engineering analysis, and in particular to a method and system for predicting the remaining life of two-stage degraded equipment. Background Art

[0002] With the continuous improvement of scientific level, many devices are becoming more and more complex while their functions are constantly improving. Accurately predicting the operating time and service life of such equipment can reduce economic losses and reduce the risk of accidents. In recent years, the remaining life prediction method of equipment based on degradation data has received widespread attention and great development from all walks of life. The core problem of this method is to collect data with degradation trends in the equipment through sensors, and use various data analysis techniques to predict the remaining life of the equipment, which can effectively avoid problems such as the difficulty in constructing complex system mechanism models.

[0003] In engineering practice, equipment is often affected by factors such as sudden changes in internal degradation mechanisms, changes in the external environment, and switching of working states, which causes the degradation characteristics of the equipment to change before and after the mutation point, showing two-stage or even multi-stage characteristics. For such equipment, if the traditional single-stage degradation modeling idea is still used to estimate the remaining life, it will inevitably lead to deviations in the prediction results. Accurately predicting the failure time of equipment life is a prerequisite for determining the optimal maintenance time of the equipment, reducing maintenance costs, and reducing the risk of equipment failure.

[0004] So far, many scholars have conducted research on this type of problem. For example, Zhang Jianxun et al. considered the multi-stage degradation problem of the linear Wiener process and solved the precise analytical expression of the remaining life under the first arrival time. However, in actual systems, the degradation trajectory will be affected by various operating factors, causing the increment of the degradation trajectory to change, which has nonlinear characteristics. Therefore, the research on the remaining life prediction of nonlinear multi-stage degradation equipment has potential engineering value.

[0005] Based on the above content, in view of the nonlinear multi-stage characteristics of equipment performance degradation trajectory, it is urgent to propose a nonlinear multi-stage random degradation model to improve the accuracy of remaining life prediction. Summary of the invention

[0006] The purpose of the present invention is to provide a method and system for predicting the remaining life of two-stage degraded equipment, which can improve the accuracy of remaining life prediction.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for predicting the remaining life of two-stage degraded equipment, comprising:

[0009] Obtaining degradation trajectory data of the equipment to be predicted;

[0010] Establishing a two-stage degradation model according to the degradation trajectory data of the equipment to be predicted;

[0011] Identifying parameters of the two-stage degradation model using a maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted;

[0012] The remaining life of the equipment to be predicted is predicted based on the two-stage degradation model after the parameters are identified.

[0013] Optionally, establishing a two-stage degradation model according to the degradation trajectory data of the device to be predicted specifically includes:

[0014] Using the formula Determine the two-stage degradation model;

[0015] Using the formula and Determine the conditions satisfied by the two-stage degradation model;

[0016] Among them, X(t) is the degradation amount at time t, and are the drift term and diffusion term of the first stage, μ 1 and σ 1 are the drift term coefficient and diffusion term coefficient of the first stage respectively, and are the drift term and diffusion term of the second stage, μ 2 and σ 2 are the drift term coefficient and diffusion term coefficient of the second stage respectively. {B(t), t≥0} is the standard Brownian motion, which is used to characterize the uncertainty of random process changing with time. τ is the time when the change point occurs. 0 and x τ are the degradation amounts at the initial moment and the change point moment, respectively. q 1 and q 2 is a fixed constant.

[0017] Optionally, the establishing of a two-stage degradation model according to the degradation trajectory data of the device to be predicted further includes:

[0018] Using the formula Determine the power function form of the two-stage degradation model;

[0019] Using the formula Determine the exponential function form of the two-stage degradation model;

[0020] Among them, when the power function form is In exponential function form, b 1 and b 2 are the parameters of the two-stage degradation model.

[0021] Optionally, the identifying of parameters of the two-stage degradation model using a maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted specifically includes:

[0022] Using the formula Determine the maximum likelihood function of the two-stage degradation model of the i-th device;

[0023] Using the formula and Determine the maximum likelihood estimation result of the mean of the first stage degradation increment and the maximum likelihood estimation result of the mean of the second stage degradation increment;

[0024] Using the formula Determine the profile likelihood function;

[0025] A multi-dimensional search method is used to maximize the profile likelihood function and determine the parameter values ​​of the two-stage degradation model;

[0026] in, is the measurement time of N devices and the i-th device, (·)′ is the transpose of the vector, and the corresponding degradation amount is m i is the number of measurements of the i-th device, and the parameter of the two-stage degradation model is θ = (θ 1 ,θ 2 ,...,θ N )',in μ 1,i ,μ 2,i are the drift coefficient of the first stage of the ith device and the drift coefficient of the second stage of the ith device, respectively. For the first stage, make Degraded increment relative to the initial moment and∑ 1,i are the mean and variance of the degradation increment in the first stage respectively. For the second stage, let make Then the degradation increment relative to the change point is and∑ 2,i are the mean and variance of the degradation increment in the second stage, respectively.

[0027] Optionally, the predicting of the remaining life of the device to be predicted based on the two-stage degradation model after identifying the parameters specifically includes:

[0028] Using the formula Determine the lifetime distribution of a two-stage degradation model;

[0029] in, g τ (x τ ) is the state transition probability under the absorption threshold ω in the first stage, q 1 is a fixed constant,

[0030] Optionally, the predicting of the remaining life of the device to be predicted based on the two-stage degradation model after identifying the parameters specifically includes:

[0031] The life value of the equipment to be predicted is determined by numerical simulation method.

[0032] Optionally, the numerical simulation method includes: trapezoidal approximation method, parabola approximation method or Romberg integration.

[0033] A remaining life prediction system for two-stage degradation equipment, comprising:

[0034] A degradation trajectory data acquisition module, used to acquire degradation trajectory data of the device to be predicted;

[0035] A two-stage degradation model establishment model is used to establish a two-stage degradation model according to the degradation trajectory data of the device to be predicted;

[0036] A parameter identification module of a two-stage degradation model, used to identify the parameters of the two-stage degradation model using a maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted;

[0037] The remaining life prediction module is used to predict the remaining life of the equipment to be predicted based on the two-stage degradation model after identifying the parameters.

[0038] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0039] The present invention provides a method and system for predicting the remaining life of two-stage degraded equipment, which provides a method for predicting the remaining life of equipment with multiple degradation stages, that is, a nonlinear multi-stage random degradation model is proposed to scientifically predict the remaining life of complex equipment. It can effectively improve the accuracy of the remaining life prediction of the equipment, provide a theoretical basis and technical support for subsequent spare parts ordering, health management and other logistics support, and has potential engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0041] Figure 1 A schematic flow chart of a method for predicting the remaining life of a two-stage degraded device provided by the present invention;

[0042] Figure 2 is the degradation data of high voltage pulse capacitor;

[0043] Figure 3 Based on the high voltage pulse capacitance data, model M 1 and M 2 Comparison chart of lifespan probability distribution with the linear model;

[0044] Figure 4 Based on the high voltage pulse capacitance data, model M 1 The remaining life prediction results;

[0045] Figure 5 Based on the high voltage pulse capacitance data, model M 2 The remaining life prediction results;

[0046] Figure 6 The remaining life prediction results of the linear model based on the high-voltage pulse capacitor data;

[0047] Figure 7 It is a comparison chart of the remaining life of nonlinear and linear models;

[0048] Figure 8 This is a comparison chart of the root mean square error (MSE) of the nonlinear and linear models;

[0049] Fig. 9 This is a schematic diagram of the structure of a remaining life prediction system for two-stage degradation equipment provided by the present invention. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] The purpose of the present invention is to provide a method and system for predicting the remaining life of two-stage degraded equipment, which can improve the accuracy of remaining life prediction.

[0052] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] Figure 1 The following is a flow chart of a method for predicting the remaining life of a two-stage degraded device provided by the present invention. Figure 1 As shown, the present invention provides a method for predicting the remaining life of a two-stage degraded device, comprising:

[0054] S101, obtaining degradation trajectory data of a device to be predicted;

[0055] S102, establishing a two-stage degradation model according to the degradation trajectory data of the device to be predicted;

[0056] The two-stage degradation process {X(t), t≥0} based on the nonlinear Wiener process is:

[0057] Using the formula Determine the two-stage degradation model;

[0058] Using the formula and Determine the conditions satisfied by the two-stage degradation model;

[0059] Among them, X(t) is the degradation amount at time t, and are the drift term and diffusion term of the first stage, μ 1 and σ 1 are the drift term coefficient and diffusion term coefficient of the first stage respectively, and are the drift term and diffusion term of the second stage, μ 2 and σ 2 are the drift term coefficient and diffusion term coefficient of the second stage respectively. {B(t), t≥0} is the standard Brownian motion, which is used to characterize the uncertainty of random process changing with time. τ is the time when the change point occurs. 0 and x τ are the degradation amounts at the initial moment and the change point moment, respectively. q 1 and q 2 is a fixed constant.

[0060] S102 and later also include:

[0061] Using the formula Determine the power function form of the two-stage degradation model, denoted as model M 1 ;

[0062] Using the formula Determine the exponential function form of the two-stage degradation model, denoted as model M 2 ;

[0063] Among them, when the power function form is In exponential function form, b 1 and b 2 are the parameters of the two-stage degradation model.

[0064] S103, identifying parameters of the two-stage degradation model by using a maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted;

[0065] S103 specifically includes:

[0066] Using the formula Determine the degradation amount of the i-th device at the j-th time;

[0067] Using the formula ∑ 1,i =σ 1 2 Z′ 1,i Z 1,i Q 1,i OK X 1,i The mean and variance of in,

[0068] Using the formula OK X 2,i The mean and variance of in,

[0069]

[0070] Using the formula Determine the maximum likelihood function of the two-stage degradation model of the i-th device;

[0071] use and Determine μ 1,i and μ 2,i The first partial derivative of

[0072] Let the above two equations be equal to 0, then use the formula and Determine the maximum likelihood estimation result of the mean of the first stage degradation increment and the maximum likelihood estimation result of the mean of the second stage degradation increment;

[0073]

[0074] Using the formula Determine the profile likelihood function;

[0075] A multi-dimensional search method is used to maximize the profile likelihood function and determine the parameter values ​​of the two-stage degradation model;

[0076] in, is the measurement time of N devices and the i-th device, (·)′ is the transpose of the vector, and the corresponding degradation amount is m i is the number of measurements of the i-th device, and the parameter of the two-stage degradation model is θ = (θ 1 ,θ 2 ,...,θ N )',in μ 1,i ,μ 2,i are the drift coefficient of the first stage of the ith device and the drift coefficient of the second stage of the ith device, respectively. Δt is the sampling interval. For the first stage, let make Degraded increment relative to the initial moment and∑ 1,i are the mean and variance of the degradation increment in the first stage respectively. For the second stage, let make Then the degradation increment relative to the change point is and∑ 2,i are the mean and variance of the degradation increment in the second stage, respectively.

[0077] As a specific embodiment, the "fminsearch" function in MATLAB software is used to maximize the profile likelihood function;

[0078] When μ of each device is estimated 1,i and μ 2,i When μ 1 and μ 2 As a specific embodiment, the mean and variance of are implemented by the "mle" function in MATLAB software. The parameter estimation of the initial value variance and mean can also be obtained by using a statistical method based on the initial state of each degradation trajectory.

[0079] S104, predicting the remaining life of the equipment to be predicted according to the two-stage degradation model after identifying the parameters.

[0080] S104 specifically includes:

[0081] The life of the equipment is defined as the first time that the equipment degradation process {X(t), t≥0} reaches the preset failure threshold (absorption threshold) ω, then the equipment is considered to be unable to continue to work normally, that is, it is failed. That is:

[0082] Use the formula T: = inf{t:X(t)≥ω|X(0)<ω} to determine the life of the equipment T;

[0083] Using the formula L κ :=inf{l κ :X(t κ +l κ )≥ω|X(t κ )<ω} determines at the current time t κ When the remaining life of the equipment is L κ ;

[0084] Using the formula Determine the probability distribution of equipment life when a single-stage situation occurs; where,

[0085] The degradation amount is not allowed to exceed the threshold ω, and the state transition probability in the first stage needs to be under the condition of the absorption threshold.

[0086] Using the formula Determine the state transition probability of the first stage; where,

[0087] According to the total probability formula, the life distribution in the second stage requires the degradation amount x at the change point τ integral.

[0088] Using the formula Determine the lifetime distribution of a two-stage degradation model;

[0089] Current time t κ <τ, using the formula Predicting the remaining life of the equipment to be predicted;

[0090] Current time t κ ≥τ, using the formula Predicting the remaining life of the equipment to be predicted;

[0091] in, g τ (x τ) is the state transition probability under the absorption threshold ω in the first stage, q 1 is a fixed constant,

[0092] S104 specifically includes:

[0093] The life value of the equipment to be predicted is determined by numerical simulation method.

[0094] The numerical simulation method includes but is not limited to trapezoidal approximation method, parabolic approximation method or Romberg integration.

[0095] According to the relationship between life and remaining life, the expression of two-stage nonlinear remaining life can be obtained as follows:

[0096] Case 1: Current time t κ <τ

[0097]

[0098] in,

[0099]

[0100]

[0101]

[0102] Case 2: Current time t κ ≥τ

[0103]

[0104] in,

[0105] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention is further described in detail below in combination with the degradation data of high-voltage pulse capacitors. High-voltage pulse capacitors have the characteristics of storing and releasing electrical energy in a short time, and are widely used in the fields of pulsed lasers, radars, nuclear fusion research, particle accelerators, etc. The performance of high-voltage pulse capacitors has a great influence on the stable operation of these special electronic systems. Therefore, accurate prediction of high-voltage pulse capacitors is particularly important to ensure the operational reliability of such special equipment. Its degradation trajectory is as follows Figure 2 As shown in Figure 1, the data records the degradation data of 5 high-voltage pulse capacitors in storage state, with a sampling interval of 1 month and a total of 14 samples. In this experiment, the failure threshold ω=5 is determined. Figure 2It can be seen that its degradation trajectory obviously has the characteristics of two-stage nonlinearity.

[0106] Subsequently, according to the two-stage degradation model, the maximum likelihood method is used to estimate the parameters of the model using the high-voltage pulse capacitor degradation data. It should be noted that since the initial values ​​of the capacitor degradation data are all 0, the initial value x 0 The mean and variance of are both 0, and the maximum likelihood estimation results of the remaining parameters are shown in Table 1:

[0107] Table 1

[0108]

[0109] Correspondingly, according to the estimated parameter values, capacitor C5 is selected as the remaining life prediction sample, and the model M can be obtained. 1 、M 2 And the life probability density distribution diagram of the linear model at the initial moment, such as Figure 3 As shown, from Figure 3 It can be seen that the model M 1 、M 2 The prediction accuracy of the linear model is higher than that of the high-voltage pulse data, which is due to the obvious nonlinear characteristics of the high-voltage pulse data. In addition, the life distribution curve of the linear model is flatter and has greater uncertainty.

[0110] Similarly, using the degradation data of capacitor C5 in model M 1 、M 2 The remaining life prediction results are verified under the linear model. Figure 4 , Figure 5 , Figure 6 Model M is shown respectively 1 、M 2 As well as the probability distribution function, mean value and true remaining life of the linear model. Figure 4 , Figure 5 , Figure 6 It can be seen that the estimated value of the remaining life of the model proposed in the present invention is closer to the true value.

[0111] In addition, in order to further compare the difference between the proposed model and the linear model, the model M 1 、M 2 And the mean square error of the linear model, the expression of the mean square error is as follows:

[0112]

[0113] in, It represents the true lifespan. Generally speaking, the closer the estimated lifespan is to the true lifespan, the smaller the mean square error will be, indicating that the prediction result is more accurate. Figure 7 , Figure 8 Model M 1 、M 2 The remaining life comparison chart and mean square error comparison chart of the linear model. From the results, it can be seen that the model proposed in the present invention has higher prediction accuracy. At the same time, the experimental results prove the necessity of using nonlinear multi-stage modeling of random degradation process when the degradation trajectory has nonlinear characteristics, which shows that the present invention has potential engineering value.

[0114] Fig. 9 The schematic diagram of the remaining life prediction system of a two-stage degradation equipment provided by the present invention is as follows: Fig. 9 As shown, the present invention provides a remaining life prediction system for two-stage degradation equipment, comprising:

[0115] The degradation trajectory data acquisition module 901 is used to acquire the degradation trajectory data of the device to be predicted;

[0116] A two-stage degradation model establishment model 902 is used to establish a two-stage degradation model according to the degradation trajectory data of the device to be predicted;

[0117] A two-stage degradation model parameter identification module 903 is used to identify the parameters of the two-stage degradation model using a maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted;

[0118] The remaining life prediction module 904 is used to predict the remaining life of the equipment to be predicted according to the two-stage degradation model after identifying the parameters.

[0119] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0120] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for predicting the remaining life of a two-stage degraded device, characterized in that: include: Obtaining degradation trajectory data of the equipment to be predicted; Establishing a two-stage degradation model according to the degradation trajectory data of the equipment to be predicted; Identifying parameters of the two-stage degradation model using a maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted; Predicting the remaining life of the equipment to be predicted according to the two-stage degradation model after identifying the parameters; The step of establishing a two-stage degradation model according to the degradation trajectory data of the device to be predicted specifically includes: Using the formula Determine the two-stage degradation model; Using the formula and Determine the conditions satisfied by the two-stage degradation model; Among them, X(t) is the degradation amount at time t, and are the drift term and diffusion term of the first stage, μ1 and σ1 are the drift term coefficient and diffusion term coefficient of the first stage, and are the drift term and diffusion term of the second stage, μ2 and σ2 are the drift term coefficient and diffusion term coefficient of the second stage, {B(t), t≥0} is the standard Brownian motion, which is used to characterize the uncertainty of random process changing with time, τ is the time when the change point occurs, x0 and x τ are the degradation amounts at the initial moment and the change point moment, respectively. q1 and q2 are fixed constants.

2. The method for predicting the remaining life of a two-stage degraded device according to claim 1, characterized in that: The step of establishing a two-stage degradation model according to the degradation trajectory data of the device to be predicted further includes: Using the formula Determine the power function form of the two-stage degradation model; Using the formula Determine the exponential function form of the two-stage degradation model; Among them, when the power function form is In exponential function form, b1 and b2 are parameters of the two-stage degradation model.

3. The method for predicting the remaining life of a two-stage degraded device according to claim 2, characterized in that: The identifying of the parameters of the two-stage degradation model using the maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted specifically includes: Using the formula Determine the maximum likelihood function of the two-stage degradation model of the i-th device; Using the formula and Determine the maximum likelihood estimation result of the mean of the first stage degradation increment and the maximum likelihood estimation result of the mean of the second stage degradation increment; Using the formula Determine the profile likelihood function; A multi-dimensional search method is used to maximize the profile likelihood function and determine the parameter values ​​of the two-stage degradation model; in, is the measurement time of N devices and the i-th device, (·)′ is the transpose of the vector, and the corresponding degradation amount is m i is the number of measurements of the i-th device, and the parameters of the two-stage degradation model are θ = (θ1, θ2, ..., θ N )',in μ 1,i ,μ 2,i are the drift coefficient of the first stage of the ith device and the drift coefficient of the second stage of the ith device, respectively. For the first stage, make Degraded increment relative to the initial moment and∑ 1,i are the mean and variance of the degradation increment in the first stage respectively. For the second stage, let make Then the degradation increment relative to the change point is and∑ 2,i are the mean and variance of the degradation increment in the second stage, respectively.

4. The method for predicting the remaining life of a two-stage degraded device according to claim 3, characterized in that: The predicting of the remaining life of the equipment to be predicted based on the two-stage degradation model after identifying the parameters specifically includes: Using the formula Determine the lifetime distribution of a two-stage degradation model; Current time t κ <τ, using the formula Predicting the remaining life of the equipment to be predicted; Current time t κ ≥τ, using the formula Predicting the remaining life of the equipment to be predicted; in, g τ (x τ ) is the state transition probability under the absorption threshold ω in the first stage, q1 is a fixed constant, and the absorption threshold ω is the failure threshold, when the device cannot continue to work normally, 5. The method for predicting the remaining life of a two-stage degraded device according to claim 4, characterized in that: The predicting of the remaining life of the equipment to be predicted based on the two-stage degradation model after identifying the parameters specifically includes: The life value of the equipment to be predicted is determined by numerical simulation method.

6. The method for predicting the remaining life of a two-stage degraded device according to claim 5, characterized in that: The numerical simulation method includes: trapezoidal approximation method, parabola approximation method or Romberg integration.

7. A system for predicting the remaining life of a two-stage degraded device, used to implement a method for predicting the remaining life of a two-stage degraded device according to any one of claims 1 to 6, characterized in that: The remaining life prediction system of the two-stage degradation equipment includes: A degradation trajectory data acquisition module, used to acquire degradation trajectory data of the device to be predicted; A two-stage degradation model establishment model is used to establish a two-stage degradation model according to the degradation trajectory data of the device to be predicted; A parameter identification module of a two-stage degradation model, used to identify the parameters of the two-stage degradation model using a maximum likelihood method according to the two-stage degradation model and the degradation trajectory data of the device to be predicted; The remaining life prediction module is used to predict the remaining life of the equipment to be predicted based on the two-stage degradation model after identifying the parameters.

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