A remaining useful life prediction method for a fused multi-source information implicit Wiener degradation process

Abstract

The present invention discloses a remaining useful life prediction method for a hidden Wiener degradation process integrating multi-source information, comprising the steps of: A. establishing a hidden linear Wiener process degradation model; B. estimating offline parameters: (1) for the case where the prior degradation information is imperfect, integrating the failure life data to estimate the prior drift parameter of the model; (2) for the case where the prior degradation information is scarce, integrating the failure life data and the historical degradation data to estimate the prior drift parameter of the model; C. online updating the parameters; D. predicting the remaining useful life. The present invention can not only overcome the problems of imperfect or scarce prior degradation information, predict and analyze the individual life and overall reliability life characteristic quantities of the equipment, but also serve as an effective analysis tool for predicting the remaining useful life of the equipment, providing a strong theoretical basis and technical support for the condition-based maintenance and support of the equipment, thereby saving the expenditure and avoiding unnecessary economic losses, and having good engineering application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability engineering, and particularly relates to a method for predicting the remaining useful life of an implicit Wiener degradation process by fusing multi-source information. Background Art

[0002] In practical applications, situations often occur where the prior degradation information is imperfect, scarce, or even non-existent. When encountering such prior degradation information, it may lead to inaccurate estimation of prior parameters or inability to estimate prior parameters, thereby reducing the accuracy of remaining useful life prediction or even resulting in failure. Summary of the Invention

[0003] The purpose of the present invention is to overcome the influence of imperfect prior degradation information and scarce degradation information on the prediction of the remaining useful life, and improve the accuracy of the remaining useful life prediction. A method for predicting the remaining useful life of an implicit Wiener degradation process by fusing multi-source information is provided.

[0004] The present invention is implemented by adopting the following technical solutions:

[0005] A method for predicting the remaining useful life of an implicit Wiener degradation process by fusing multi-source information includes the following steps:

[0006] A. Establish an implicit linear Wiener process degradation model;

[0007] B. Estimate the offline parameters;

[0008] Based on the established degradation model, the unknown parameters of the model are estimated respectively for the degradation data in two situations: (1) For the situation of imperfect prior degradation information, the fixed parameters of the model are estimated using the on-site degradation data of the device to be evaluated, and then the prior drift parameter of the model is estimated by fusing the failure life data; (2) For the situation of scarce prior degradation information, the fixed parameters of the model are estimated using the historical degradation data, and then the prior drift parameter of the model is estimated by fusing the failure life data and the historical degradation data;

[0009] C. Update the parameters online;

[0010] Based on the on-site degradation data of the device to be evaluated and the Kalman method, the drift coefficient in the offline parameters is updated online;

[0011] D. Predict the remaining useful life;

[0012] Substitute the updated parameters into the remaining useful life probability density function to predict the remaining useful life.

[0013] A further improvement of the present invention lies in that in step A, establishing an implicit linear Wiener process degradation model specifically includes:

[0014] Key steps of the remaining useful life prediction method under the Bayesian framework: accurately estimate the fixed parameters representing the common characteristics of the model and the random parameters representing the individual differences of the samples in the degradation model;

[0015] First, model the implicit linear Wiener degradation process. When the potential performance degradation value of the device under test exceeds the set failure threshold w, the device is considered to have failed.

[0016] The Wiener process is a class of diffusion processes driven by Brownian motion with a drift coefficient, and its expression is as follows

[0017] X(t) = x0 + λt + σ B B(t) (1)

[0018] In the formula, x0 represents the initial degradation state of the device; λ is the drift coefficient characterizing the device degradation rate; σ B is the diffusion coefficient, and B(t) is the standard Brownian motion, representing the uncertainty of the degradation process; without loss of generality, let x0 = 0; λ follows a normal distribution to describe the individual differences between devices;

[0019] Consider the influence of measurement error in the degradation model, and its degradation process model is expressed as follows

[0020] Y(t) = X(t) + ε (2)

[0021] where, represents the measurement error, ε is independently and identically distributed at different times, and ε, λ, and σ B are independent of each other; for the basic implicit linear Wiener process degradation model, the prior parameters of the model to be estimated are

[0022] The remaining useful life refers to the time length from the current moment to the failure moment of the device; it is defined that the device is considered to have failed when the degradation amount reaches w, and the observed data of the device under test at time t k is Y 1:k = {y1, y2,... y k}, and the true degradation state is X 1:k = {x1, x2,... x k}; according to the concept of the first passage time, obtain the true degradation amount X k of the device at time t 1:k , then the remaining useful life of the device is expressed as:

[0023] L k = inf{l k : X(l k + t k ) ≥ w|X 1:k} (3)

[0024] Among them, L k represents the remaining life of the device to be evaluated at time t k .

[0025] A further improvement of the present invention lies in that, in step B, the prior parameters of the offline estimation model are estimated as follows:

[0026] Fusing multi-source information means fusing failure life data and historical degradation data to estimate the prior drift parameter of the model; including prior parameter estimation methods in two cases, namely the remaining life prediction method by fusing failure life data and the remaining life prediction method by fusing multi-source information, where the method used when the prior degradation information is imperfect is called the remaining life prediction method by fusing failure life data.

[0027] A further improvement of the present invention lies in the remaining life prediction method by fusing failure life data, which is as follows:

[0028] The remaining life prediction method by fusing failure life data divides the prior parameter estimation into two steps. Define y 0:m ={y0, y1,..., y m} as the on-site degradation data, and T 1:n′ ={T1, T2,..., T n′} as the failure life data of n' devices or the failure time when the failure threshold w is first reached. According to the basic implicit linear Wiener process model of Equation (2), the unknown parameters of the model to be estimated are

[0029] First step: Use the on-site degradation data to estimate the fixed parameters of the model

[0030] For the degradation process modeling of a single device, regard λ as a fixed coefficient. Based on the degradation model of Equation (2), let Δy j =y j -y j-1 , Δt j =t j -t j-1 , 1≤j≤m, Δy=(Δy1, Δy2,..., Δy m )′, Δt=(Δt1, Δt2,..., Δt m )′, then there is where Ω = diag(Δt1, Δt2,..., Δt m );

[0031]

[0032] Let D = Ω + φF, where Then the log-likelihood function of a single device is expressed as:

[0033]

[0034] Take the first-order partial derivatives of Equation (4) with respect to λ and respectively, and we get:

[0035]

[0036]

[0037] Let Equation (5) and Equation (6) be equal to 0, and the constrained estimates of λ and are as follows:

[0038]

[0039]

[0040] Substitute Equation (8) into Equation (4), and then we get the expression of the marginal likelihood function of φ, as follows:

[0041]

[0042] Maximize Equation (9) through the "FMINSEARCH" function in MATLAB to obtain the estimated value of φ, and substitute it into Equation (7) and Equation (8) to get λ and Furthermore, we get the estimated value;

[0043] Step 2: Use the expectation-maximization algorithm to convert the failure life data into the prior distributions of u λ and ;

[0044] Since the life distribution function of the implicit linear Wiener degradation process is not affected by measurement errors, given the fixed parameters estimated in the first step and the failure life data T 1:n′ ={T1, T2,..., T n′}, then according to Bayes' theorem, the posterior drift coefficient λ under the condition of the failure time T v of a single device follows a normal distribution, and the log-likelihood function of the further failure time T 1:n′ is expressed as

[0045]

[0046] Let be the parameter estimation result obtained by the expectation-maximization algorithm in the i-th iteration. Then the result of the (i + 1)-th iteration is derived from the following E-step and M-step;

[0047] E-step: Calculate the expectation of Equation (10)

[0048]

[0049] where \(u\) λ,v and is the posterior distribution of \(\lambda\) under the conditions of \(T\) 1:n′ and ;

[0050] M step: Maximize equation (11)

[0051] Take the first-order partial derivatives of equation (11) with respect to \(u\) λ and respectively, and set them to 0 to obtain the estimation formulas for \(u\) λ and at the \((i + 1)\)-th iteration:

[0052]

[0053] By iterating the above E step and M step until \(\|\Theta\) (k+1) -\(\Theta\) (k) \| is small enough.

[0054] A further improvement of the present invention lies in integrating a multi-source information remaining life prediction method, specifically as follows:

[0055] The multi-source information remaining life prediction method is divided into two steps. Suppose there are \(n\) similar devices, and each device detects the degradation state at the same time instants \(t_1,t_2,\cdots,t\) m Based on the degradation model of equation (2), let \(y\) i,j represent the degradation state measured by the \(i\)-th device at \(t\) j . \(\Delta y\) i,j = \(y\) i \((t\) j ) - \(y\) i \((t\) j-1 ), \(\Delta t\) j = \(t\) j - \(t\) j-1 , \(\Delta y\) i = (\(\Delta y\) i,1 , \(\Delta y\) i,2 ,\cdots,\(\Delta y\) i,m )', \(\Delta t = (\Delta t_1,\Delta t_2,\cdots,\Delta t\) m )' and \(Y = (\Delta y'_1,\Delta y'_2,\cdots,\Delta y' n )', where \(1\leq i\leq n\), \(1\leq j\leq m\), \(\lambda\) i represents the degradation rate of the \(i\)-th device, then \(\Delta y\) i follows a multivariate normal distribution with mean \(u\) λ \(\Delta t\) and variance ; Suppose there are \(n'\) groups of failure life data \(T\) 1:n′ = \{T_1,T_2,\cdots,T n′}, the failure life data of the v-th unit is T v , 1 ≤ v ≤ n′, let D = Ω + φF, where The failure threshold of the device is w;

[0056] Step 1: Estimate the fixed parameters of the model using historical degradation data

[0057] The unknown parameters of the hidden linear Wiener process degradation model The unbiased parameter estimation expression is:

[0058]

[0059]

[0060]

[0061] In the formula,

[0062] Maximize formula (16) through the MATLAB function "FMINSEARCH" to obtain the estimated value of parameter φ, and substitute it into formulas (13)-(15) to get μ λ , and values, and further obtain the parameters

[0063]

[0064] Step 2: Estimate the model drift coefficient by fusing historical degradation data and failure life data using the expectation-maximization algorithm

[0065] Regarding The complete log-likelihood function is expressed as:

[0066]

[0067] E-step: Calculate the expectation of formula (17);

[0068]

[0069] In the formula,

[0070]

[0071]

[0072] M-step: Maximize formula (18);

[0073] Take the first-order partial derivatives of formula (18) with respect to u λ and :

[0074]

[0075]

[0076] Next, set equations (21) and (22) to 0, and obtain and the result of the (k + 1)-th iteration of

[0077]

[0078] Similarly, by iterating the above E-step and M-step until ||Θ (k+1) - Θ (k) || is small enough, the prior drift parameter μ λ ,

[0079] A further improvement of the present invention lies in that in step C, the parameters are updated online, specifically as follows:

[0080] In the Wiener process model parameters, the randomness of the drift coefficient describes the individual differences between similar devices. To adapt to the individual degradation characteristics of the device under test, the on-site degradation data is used to update the drift coefficient online; the Kalman method is used to update the drift coefficient online, and the current degradation state of the device is estimated in real time.

[0081] A further improvement of the present invention lies in that for the implicit linear Wiener degradation process shown in equation (2), when the degradation value Y k of the device under test is detected at time t 1:k , the state space equation at time t k is expressed as:

[0082]

[0083] where v k = σ B B(t k ) - σ B B(t k-1 ), λ k is the drift coefficient, x k represents the true degradation state at time t k , ε k represents the measurement error at time t k , and are independently and identically distributed;

[0084] Due to the influence of the measurement error, both the true degradation state x k and the drift coefficient λ k are hidden states, and further, the state space equation (24) is expressed as:

[0085]

[0086] Let Then the online update result of the drift coefficient of the hidden linear Wiener process model and the estimated current degradation state are expressed as:

[0087]

[0088] Wherein,

[0089]

[0090] A further improvement of the present invention lies in that in step D, predicting the remaining life is specifically as follows:

[0091] Let l k represent the remaining service life of the device at time t k Based on the hidden linear Wiener process degradation model of Equation (2), when the true degradation amount x k of the device is known, the remaining life probability density function is expressed as:

[0092]

[0093] Use the expression of the remaining life probability density function considering state estimation;

[0094]

[0095] Wherein,

[0096] The present invention has at least the following beneficial technical effects:

[0097] A method for predicting the remaining life of a hidden Wiener degradation process integrating multi-source information provided by the present invention gives a method for predicting the remaining life of high-reliability devices in the case of imperfect prior degradation information and scarce prior degradation information, and can predict and analyze the individual life and overall reliability life characteristic quantities of the devices, providing a strong theoretical basis and technical support for the state-based maintenance guarantee of the devices, thereby saving funds and avoiding unnecessary economic losses, and having good engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 It is a schematic diagram of the experimental degradation data of lithium batteries.

[0099] Figure 2 It is a schematic diagram of the experimental degradation data of lasers.

[0100] Figure 3Schematic diagram of the estimated remaining life distribution.

[0101] Figure 4 Schematic diagram of the mean square error of the estimated remaining life.

[0102] Figure 5 Schematic diagram of the estimated remaining life distribution.

[0103] Figure 6 Schematic diagram of the mean square error of the estimated remaining life.

[0104] Figure 7 Flowchart of a method for predicting the remaining life of a hidden Wiener degradation process that fuses multi-source information according to the present invention. Detailed implementation mode

[0105] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be completely conveyed to those skilled in the art. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0106] The effectiveness of the present invention is verified based on the lithium battery experimental degradation data publicly disclosed by NASA and the laser degradation data published by Meeker. Among them, the lithium battery data consists of the capacity degradation data of four lithium batteries of the same type operating in three working modes of charging, discharging, and impedance measurement repeatedly at room temperature. In the experiment, according to the technical specifications of the lithium battery, the failure threshold was selected as w = 1.4 Ah. Recorded according to the number of cycles, the monitoring interval is one cycle. The measurement data corresponding to the entire life cycle of the lithium battery degradation monitoring is as Figure 1 shown. Without loss of generality, the battery numbered B0018 was used as the experimental battery, and the life data of the batteries numbered B0005, B0006, and B0007 were used as prior information to estimate the prior parameters, so as to verify the accuracy of the remaining life prediction by the method proposed in the article when the prior degradation information is imperfect. There are 15 units of degradation data, and the detection time of each unit is the same, including 16 detection points, the detection time interval is 250 hours, and the degradation path is as Figure 2 shown. Without loss of generality, taking Figure 2 the solid line in as the measured unit, the dotted line as the historical degradation data, and the failure times of the 3 sets of dash-dotted lines as the failure life data, so as to verify the accuracy of the remaining life prediction by the method proposed in the article when the prior degradation information is scarce.

[0107] As Figure 7As shown, a remaining useful life prediction method for a fused multi-source information implicit Wiener degradation process provided by the present invention includes the following steps:

[0108] A. Establish an implicit linear Wiener process degradation model

[0109] The key steps of the remaining useful life prediction method under the Bayesian framework: accurately estimate the fixed parameters representing the common characteristics of the degradation model and the random parameters representing the individual differences of samples. In practical applications, situations where the prior degradation information is imperfect, scarce, or even completely absent often occur. Therefore, a remaining useful life prediction method that fuses multi-source information is proposed. Among them, the failure life data can be obtained from the maintenance records of similar equipment, while the historical degradation data and on-site degradation data can be directly obtained using monitoring equipment. First, the implicit linear Wiener degradation process is modeled below. When the potential performance degradation value of the device under test exceeds the set failure threshold w, the device is considered to have failed.

[0110] The Wiener process is a type of diffusion process driven by Brownian motion with a drift coefficient. Compared with several commonly used random process degradation models, the mathematical expression of this model is simple, and it is applicable to both monotonic and non-monotonic degradation systems, and is widely used in general degradation modeling. The expression is as follows

[0111] X(t) = x0 + λt + σ B B(t) (1)

[0112] In the formula, x0 represents the initial degradation state of the device; λ is the drift coefficient characterizing the device degradation rate; σ B is the diffusion coefficient, and B(t) is the standard Brownian motion, representing the uncertainty of the degradation process; without loss of generality, it is usually assumed that x0 = 0; λ follows a normal distribution to describe the individual differences between devices.

[0113] In engineering applications, due to factors such as measuring instruments, operator skills, and the environment, the observed degradation data often has measurement errors and cannot directly reflect the true degradation state. If the influence of measurement errors is not considered, it may reduce the prediction accuracy of the remaining useful life and even obtain incorrect estimation results. Therefore, considering the influence of measurement errors in the degradation model, the degradation process of the device can be expressed as follows

[0114] Y(t) = X(t) + ε (2)

[0115] Among them, represents the measurement error, and ε is independently and identically distributed at different times, and ε, λ, and σ B are mutually independent; for the basic linear implicit Wiener process degradation model, the prior parameters of the model to be estimated are

[0116] The remaining useful life refers to the time length from the current moment to the failure moment of the device. Define the device failure threshold as w, and the observed data of the device under test at time t k is Y 1:k ={y1, y2, …, y k}, and the true degradation state is X 1:k ={x1, x2, …, x k}. According to the concept of first passage time, once the true degradation amount X k of the device at time t 1:k is obtained, the remaining useful life of the device is expressed as

[0117] L k = inf{l k : X(l k + t k ) ≥ w | X 1:k} (3)

[0118] where L k represents the remaining useful life of the device under evaluation at time t k .

[0119] B. Prior parameter estimation of the offline estimation model

[0120] Fusing multi-source information means fusing failure life data and historical degradation data to estimate the prior drift parameter of the model. However, when the prior degradation information is imperfect, if the traditional maximum likelihood method is used to estimate the fixed parameters of the model, it may lead to the estimation results of the parameters deviating far from the true values, resulting in low accuracy of the remaining useful life prediction results. For this special case, when using the remaining useful life prediction method based on fusing multi-source information, the historical degradation data used will be converted into failure life time data for remaining useful life prediction. The prior parameter estimation methods in two cases are given below, and the method used when the prior degradation information is imperfect is called the remaining useful life prediction method based on fusing failure life data (the remaining useful life prediction method based on fusing failure life data is a special case of the remaining useful life prediction method based on fusing multi-source information).

[0121] 1) Remaining useful life prediction method based on fusing failure life data

[0122] The remaining useful life prediction method based on fusing failure life data divides the prior parameter estimation into two steps. Define y 0:m ={y0, y1, …, y m} as the on-site degradation data, and T 1:n′ ={T1, T2, …, T n′} is the failure life data of n' devices or the failure time when the failure threshold w is first reached. According to the basic implicit linear Wiener process model in Equation (2), the unknown parameters of the model to be estimated are

[0123] Step 1: Estimate the fixed parameters of the model using on-site degradation data

[0124] For the degradation process modeling of a single device, since there are no differences between individuals, when establishing the implicit linear Wiener process degradation model, the influence of random effects is not considered, and λ is regarded as a fixed coefficient. Based on the degradation model in Equation (2), let Δy j = y j - y j-1 , Δt j = t j - t j-1 , 1 ≤ j ≤ m, Δy = (Δy1, Δy2,..., Δy m )′, Δt = (Δt1, Δt2,..., Δt m )′. Then we have where Ω = diag(Δt1, Δt2,..., Δt m ),

[0125]

[0126] Let D = Ω + φF, where Then the log-likelihood function of a single device can be expressed as

[0127]

[0128] Taking the first-order partial derivatives of Equation (4) with respect to λ and respectively, we can obtain

[0129]

[0130]

[0131] Letting Equations (5) and (6) be 0, we can obtain the constrained estimates of λ and as follows

[0132]

[0133]

[0134] Substituting Equation (8) into Equation (4), we can obtain the expression of the marginal likelihood function of φ, as follows

[0135]

[0136] The estimated value of φ can be obtained by maximizing Equation (9) using the "FMINSEARCH" function in MATLAB. Substituting it into Equations (7) and (8) gives λ and further gives the estimated value.

[0137] Step 2: Use the expectation-maximization algorithm to transform the failure life data into the prior distribution of u λ and of.

[0138] Since the life distribution function of the implicit linear Wiener degradation process is not affected by measurement errors, given the fixed parameters estimated in the first step and the failure life data T 1:n′ ={T1, T2,..., T n′}, then according to Bayes' principle, the posterior drift coefficient λ under the condition of the failure time T v of a single device follows a normal distribution, and the log-likelihood function of the further failure time T 1:n′ can be expressed as

[0139]

[0140] Let be the parameter estimation result obtained by the expectation-maximization algorithm in the i-th iteration. Then the result of the (i + 1)-th iteration can be derived from the following E-step and M-step

[0141] E-step: Calculate the expectation of Equation (10)

[0142]

[0143] where u λ,v and is the posterior distribution of λ under the conditions of T 1:n′ and of.

[0144] M-step: Maximize Equation (11)

[0145] Take the first-order partial derivatives of Equation (11) with respect to u λ and respectively, and set them to 0, the estimation formulas of u λ and for the (i + 1)-th iteration can be obtained

[0146]

[0147] By iterating the above E-step and M-step until ||Θ (k+1) - Θ (k) || is small enough.

[0148] 2) Residual life prediction method for fusing multi-source information

[0149] The method for predicting remaining useful life by fusing multi-source information is divided into two steps. Suppose there are n similar devices, and each device has the same time points t1, t2, …, t m Detect the degradation state. Based on the degradation model in Equation (2), let y i,j represent the degradation state measured by the i-th device at time t j . Δy i,j = y i (t j ) - y i (t j-1 ), Δt j = t j - t j-1 . Δy i = (Δy i,1 , Δy i,2 , …, Δy i,m )′, Δt = (Δt1, Δt2, …, Δt m )′, and Y = (Δy′1, Δy′2, …, Δy′ n )′, where 1 ≤ i ≤ n, 1 ≤ j ≤ m, and λ i represents the degradation rate of the i-th device. Then Δy i follows a multivariate normal distribution with a mean of u λ Δt and a variance of . In addition, assume that there are n′ groups of failure life data T 1:n′ = {T1, T2, …, T n′}, and the failure life data of the v-th unit is T v , 1 ≤ v ≤ n′. Let D = Ω + φF, where the failure threshold of the device is w.

[0150] Step 1: Estimate the fixed parameters of the model using historical degradation data

[0151] The unbiased parameter estimation expression for the unknown parameters of the implicit linear Wiener process degradation model is

[0152]

[0153]

[0154]

[0155] In the formula,

[0156] By maximizing Equation (16) through the MATLAB function "FMINSEARCH", the estimated value of the parameter φ can be obtained. Substituting it into Equations (13)-(15), μ can be obtainedλ , and values, and further the parameters

[0157]

[0158] Step 2: Fuse historical degradation data and failure life data and estimate the model drift coefficient using the Expectation - Maximization algorithm

[0159] Regarding the complete log - likelihood function can be expressed as

[0160]

[0161] E - step: Calculate the expectation of Equation (17)

[0162]

[0163] where

[0164]

[0165]

[0166] M - step: Maximize Equation (18)

[0167] Take the first - order partial derivatives of Equation (18) with respect to u λ and

[0168]

[0169]

[0170] Next, let Equation (21) and Equation (22) be 0, and the results of the (k + 1) - th iteration of and can be obtained

[0171]

[0172] Similarly, by iterating the above E - step and M - step until ||Θ (k+1) - Θ (k) || is small enough, the prior drift parameter μ λ ,

[0173] C. Online update parameters

[0174] ​In the parameters of the Wiener process model, the randomness of the drift coefficient describes the individual differences between similar devices. To adapt to the individual degradation characteristics of the device under test, on-line updating of the drift coefficient is required using on-site degradation data. Since there are measurement errors in the detected degradation data, the true degradation state cannot be reflected. Therefore, the Kalman method can be used to update the drift coefficient on-line and estimate the current degradation state of the device in real time.

[0175] For the implicit linear Wiener degradation process shown in Equation (2), when the degradation value Y of the device under test is detected at time t k the state space equation at time t 1:k can be expressed as k

[0176]

[0177] where v k = σ B B(t k ) - σ B B(t k-1 ), λ k is the drift coefficient, x k represents the true degradation state at time t k , ε k represents the measurement error at time t k , and {v k} k≥1 and {ε k} k≥1 are independently and identically distributed.

[0178] Due to the influence of measurement errors, both the true degradation state x k and the drift coefficient λ k are hidden states. Then, the state space equation (24) can be further expressed as

[0179]

[0180] Let Then, the on-line update result of the drift coefficient and the estimated current degradation state of the implicit linear Wiener process model can be expressed as

[0181]

[0182] where

[0183]

[0184] D. Predicting the remaining life

[0185] Let l k represent the device at time t k ​The remaining useful life at a certain moment. Based on the implicit linear Wiener process degradation model of Equation (2), when the true degradation amount x of the device is known k the remaining life probability density function can be expressed as

[0186]

[0187] However, due to the influence of measurement errors, the true degradation amount x k is an implicit state and cannot be directly used for remaining life prediction. Therefore, the expression of the remaining life probability density function considering state estimation is used

[0188]

[0189] where

[0190]

[0191]

[0192] To verify the superiority of the fusion failure life data prediction method, the B0018 battery is used as the object to be evaluated, and the degradation data of other batteries are used to calculate the prior information of the remaining life prediction. Normalization is carried out when calculating the parameter estimation results, that is, by subtracting the degradation data from the initial value. Furthermore, the failure times of the B0005, B0006, and B0007 batteries are 85.55, 69.5, and 110.3 cycles respectively, and this failure time is used as the prior failure life data of the fusion failure life data prediction method. From Figure 1 it can be seen that the capacity degradation curves of the B0005 and B0007 batteries have non-linear characteristics, while the capacity degradation curves of the B0006 and B0018 batteries have linear characteristics, and this situation is regarded as imperfect prior degradation information. Figure 3 Shows partial remaining life distributions of the fusion failure life data prediction method and the traditional maximum likelihood prediction method. It can be seen that the remaining life distributions calculated by both methods can cover the actual remaining life. However, the remaining life distribution of the fusion failure life data prediction method is more concentrated near the actual remaining life, and the remaining life distribution is narrower, indicating that the fusion failure life data prediction method has higher remaining life prediction accuracy.

[0193] The prediction accuracy of the traditional maximum likelihood prediction method decreases mainly because the imperfect prior degradation information causes the offline parameter estimation to deviate far from the true value. Since there is a period of non-linear degradation characteristics in the capacity degradation curves of the B0005 and B0007 batteries, the linear degradation model cannot effectively track the non-linear degradation part, so the non-linear part is represented by the parameters and Submergence causes its estimated result to be on the high side, further increasing the uncertainty of the remaining life estimation result. According to engineering practice, the cost of maintenance after equipment failure is greater than the cost of preventive maintenance. Therefore, the superiority of the proposed method for predicting remaining life by fusing failure life data is verified.

[0194] To further distinguish the remaining life prediction effects of the two algorithms, the mean square error of the remaining life prediction of the two methods is calculated as Figure 4 shown below.

[0195] It can be seen that the mean square error of the method for predicting remaining life by fusing failure life data is significantly smaller than that of the traditional maximum likelihood prediction method, indicating that the method for predicting remaining life by fusing failure life data can overcome the influence of imperfect prior degradation information, making the prediction result more consistent with the degradation characteristics of the device to be evaluated, and thus having a higher accuracy in predicting the remaining life.

[0196] To verify that the method for predicting remaining life by fusing multi-source information can improve the accuracy of remaining life prediction in the case of scarce prior degradation information, based on the laser degradation data, the methods for predicting remaining life by using failure life data, traditional maximum likelihood prediction method and method for predicting remaining life by fusing multi-source information are respectively used. Figure 5 The remaining life distributions of the unit under test at some moments are shown, Figure 5 in which, although the remaining life distribution graph of the method for predicting remaining life by fusing failure life data is higher than that of the method for predicting remaining life by fusing multi-source information and the traditional maximum likelihood prediction method, that is, the uncertainty of the remaining life prediction result is the smallest, the distribution graph of the method for predicting remaining life by fusing failure life data deviates far from the true remaining life value, and even the remaining life prediction fails at some moments. However, the graphs of the method for predicting remaining life by fusing multi-source information and the traditional maximum likelihood prediction method can cover the true degradation value, and the former distribution graph is higher than the latter, indicating that the former prediction effect is better than the latter. This is because the uncertainty of on-site degradation data is small and the number of detections is small. For the method for predicting remaining life by fusing failure life data, it will lead to a large deviation in the estimation result, further affecting the online update of its drift coefficient in the Bayesian framework, resulting in the failure of remaining life prediction. This shows that for equipment with less on-site degradation data, the method for predicting remaining life by fusing failure life data may not be able to accurately predict the remaining life. Figure 6The mean square error of the remaining life at different times for three methods is shown. In the figure, the mean square error of the method of fusing multi-source information for prediction is overall less than that of the traditional maximum likelihood prediction method. Although the mean square error of the method of fusing failure life data for prediction is less than the previous two methods, there are phenomena of failed remaining life prediction at many times. Therefore, the remaining life prediction result of the method of fusing failure life data for prediction is not stable and the result credibility is poor. So the method of fusing multi-source information for prediction has a better prediction effect. Generally speaking, in the case of scarce prior degradation information, reasonably fusing as much prior degradation information as possible can improve the accuracy of model parameter estimation and thus improve the accuracy of remaining life prediction.

[0197] In summary, the method for predicting the remaining life of the implicit Wiener degradation process by fusing multi-source information proposed by the present invention can improve the accuracy of remaining life estimation, and can effectively overcome the influence of imperfect prior degradation information and scarce prior degradation information, thereby verifying the effectiveness of the present invention.

[0198] Although the present invention has been described in detail with general descriptions and specific embodiments above, based on the present invention, some modifications or improvements can be made, which are obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of protection required by the present invention.

Claims

1. A remaining useful life prediction method for a hidden Wiener degradation process that fuses multi-source information, characterized in that It includes the following steps: A. Establish an implicit linear Wiener process degradation model; B. Estimate the offline parameters; Based on the established degradation model, estimate the unknown parameters of the model for the degradation data in two cases respectively: (1) For the case where the prior degradation information is imperfect, use the on-site degradation data of the device to be evaluated to estimate the fixed parameters of the model, and then fuse the failure life data to estimate the prior drift parameter of the model; (2) For the case where the prior degradation information is scarce, use the historical degradation data to estimate the fixed parameters of the model, and then fuse the failure life data and the historical degradation data to estimate the prior drift parameter of the model; C. Update the parameters online; Based on the on-site degradation data of the device to be evaluated and the Kalman method, online update the drift coefficient in the offline parameters; D. Predict the remaining life; Substitute the updated parameters into the remaining life probability density function to predict the remaining life.

2. The remaining useful life prediction method for the implicit Wiener degradation process integrating multi-source information according to claim 1, wherein, In step A, to establish an implicit linear Wiener process degradation model, it specifically includes: The key steps of the remaining life prediction method under the Bayesian framework: accurately estimate the fixed parameters representing the common characteristics of the model and the random parameters representing the individual differences of the samples in the degradation model; First, model the implicit linear Wiener degradation process. When the potential performance degradation value of the device under test exceeds the set failure threshold w, the device is considered to have failed; The Wiener process is a class of diffusion processes driven by Brownian motion with a drift coefficient, and the expression is as follows X(t) = x0 + λt + σ B B(t) (1) where \(x_0\) represents the initial degradation state of the device; \(\lambda\) is the drift coefficient characterizing the degradation rate of the device; \(\sigma\) B is the diffusion coefficient, and \(B(t)\) is a standard Brownian motion, representing the uncertainty of the degradation process; without loss of generality, let \(x_0 = 0\); \(\lambda\) follows a normal distribution to describe the individual differences between devices; In the degradation model, consider the influence of measurement error, and its degradation process model is expressed as follows Y(t) = X(t) + ε (2) Among them, denotes the measurement error, where ε at different times is independently and identically distributed, and ε, λ, and σ B are mutually independent; for the basic hidden linear Wiener process degradation model, the prior parameters of the model to be estimated are Remaining life refers to the time from the current moment to the moment of failure of the device. The device is considered to have failed when the degradation reaches w. k The observed data of the device under test at the moment is Y 1:k ={y1,y2,…y k }, the actual degradation state is X 1:k ={x1,x2,…x k }; According to the concept of first arrival time, obtain the device at t k The actual degradation amount X at the moment 1:k , then the remaining life of the equipment is expressed as: L k = inf{l k : X(l k + t k ) ≥ w | X 1:k} (3) Among them, L k represents the remaining life of the device to be evaluated at time t k .

3. A remaining useful life prediction method for an implicit Wiener degradation process that fuses multi-source information according to claim 2, characterized in that, In step B, estimate the prior parameters of the model offline, specifically as follows: Fusing multi-source information refers to fusing the failure life data and the historical degradation data to estimate the prior drift parameter of the model; it includes the prior parameter estimation methods in two cases, namely the remaining life prediction method by fusing the failure life data and the remaining life prediction method by fusing multi-source information. Among them, the method used when the prior degradation information is imperfect is called the remaining life prediction method by fusing the failure life data.

4. A remaining useful life prediction method for an implicit Wiener degradation process integrating multi-source information according to claim 3, characterized in that, The remaining life prediction method by fusing the failure life data is specifically as follows: The remaining useful life prediction method that fuses failure life data divides the prior parameter estimation into two steps and defines y 0:m ={y0, y1, …, y m} as the on-site degradation data, and T 1:n′ ={T1, T2, …, T n′} as the failure life data of n′ devices or the failure time when the failure threshold w is first reached. According to the basic implicit linear Wiener process model in Equation (2), the unknown parameters of the model to be estimated are The first step: Use the on-site degradation data to estimate the fixed parameters of the model For the degradation process modeling of a single device, considering λ as a fixed coefficient, based on the degradation model in Equation (2), let Δy j = y j - y j-1 , Δt j = t j - t j-1 , 1 ≤ j ≤ m, Δy = (Δy1, Δy2, …, Δy m )′, Δt = (Δt1, Δt2, …, Δt m )′, then we have where Ω = diag(Δt1, Δt2, …, Δt m ); Let \(D=\Omega+\varphi F\), where The log-likelihood function of a single device is expressed as: Taking the first-order partial derivatives of Equation (4) with respect to λ and respectively gives: Setting equations (5) and (6) to zero gives the constrained estimates of λ and as follows: Substitute Equation (8) into Equation (4), then the expression of the marginal likelihood function of φ is obtained as follows: The estimated value of φ is obtained by maximizing Equation (9) through the "FMINSEARCH" function of MATLAB, and substituting it into Equations (7) and (8) to obtain λ and further obtain estimated value; Step 2: Use the expectation maximization algorithm to convert the failure life data into the prior distributions of u λ and ​ Since the life distribution function of the implicit linear Wiener degradation process is not affected by measurement errors, given the fixed parameters estimated in the first step and the failure life data T 1:n′ ={T1, T2, …, T n′}, then according to the Bayesian principle, the posterior drift coefficient λ under the condition of the failure time T of a single device v follows a normal distribution, and the log-likelihood function of the further failure time T 1:n′ is expressed as Let be the parameter estimation result obtained by the expectation-maximization algorithm in the \(i\)-th iteration. Then the result of the \((i + 1)\)-th iteration is derived from the following E-step and M-step; E step: Calculate the expectation of Equation (10) where u λ,v and are the posterior distributions of λ under the conditions of T 1:n′ and ; M step: Maximize Equation (11) Take the first-order partial derivatives of Equation (11) with respect to u λ and respectively, and set them to 0 to obtain the estimation formulas for u λ and at the (i + 1)-th iteration: By iterating the above E-step and M-step until ||Θ (k+1) - Θ (k) || is small enough.

5. A remaining useful life prediction method for a fused multi-source information implicit Wiener degradation process according to claim 4, characterized in that The remaining life prediction method by fusing multi-source information is specifically as follows: The method for predicting remaining useful life by fusing multi-source information is divided into two steps. Suppose there are n similar devices, and each device is at the same time points t1, t2, …, t m Detect the degradation state. Based on the degradation model in Equation (2), let y i,j represent the degradation state measured by the i-th device at t j time, Δy i,j = y i (t j ) - y i (t j-1 ), Δt j …t j - t j-1 , Δy i = (Δy i,1 , Δy i,2 , …, Δy i,m ), Δt = (Δt1, Δt2, …, Δt m ), and Y = (Δy′1, Δy′2, …, Δy′ n ), where 1 ≤ i ≤ n, 1 ≤ j ≤ m, λ i represents the degradation rate of the i-th device. Then, Δy i follows a multivariate normal distribution with a mean of u λ Δt and a variance of ; Suppose there are n′ groups of failure life data T 1:n′ = {T1, T2, …, T n′}, and the failure life data of the v-th unit is T v , 1 ≤ v ≤ n′. Let D = Ω + φF, where the failure threshold of the device is w; The first step: Use the historical degradation data to estimate the fixed parameters of the model Unknown parameters of the implicit linear Wiener process degradation model The unbiased parameter estimation expression is as follows: In the formula, Maximize Equation (16) through the MATLAB function "FMINSEARCH" to obtain the estimated value of parameter φ, substitute it into Equations (13)-(15) to get the values of μ λ , and , and further obtain the values of parameter The second step: Fuse the historical degradation data and the failure life data and use the expectation-maximization algorithm to estimate the drift coefficient of the model Regarding The complete log-likelihood function is expressed as: E step: Calculate the expectation of Equation (17); In the formula, M step: Maximize Equation (18); Take the first-order partial derivatives of Equation (18) with respect to u λ and : Next, set Equation (21) and Equation (22) to 0, and obtain and the result of the (k + 1)-th iteration: Similarly, by iterating the above E-step and M-step until ||Θ (k+1) -Θ (k) || is small enough, the prior drift parameter is obtained 6. A remaining useful life prediction method for an implicit Wiener degradation process integrating multi-source information according to claim 5, characterized in that In step C, update the parameters online, specifically as follows: Among the parameters of the Wiener process model, the randomness of the drift coefficient describes the individual differences between similar devices. In order to adapt to the individual degradation characteristics of the device under test, use the on-site degradation data to update the drift coefficient online; use the Kalman method to update the drift coefficient online and estimate the current degradation state of the device in real time.

7. A remaining useful life prediction method for a fused multi-source information implicit Wiener degradation process according to claim 6, characterized in that, For the implicit linear Wiener degradation process shown in Equation (2), when the degradation value Y of the device under test at time t k is detected, 1:k the state-space equation at time t k is expressed as: where v k = σ B B(t k ) - σ B B(t k-1 ), λ k is the drift coefficient, x k represents the true degradation state at time t k , ε k represents the measurement error at time t k , and {v k} k≥1 and {ε k} k≥1 are independent and identically distributed; Due to the influence of measurement errors, the true degradation state x k and the drift coefficient λ k are both hidden states. Then, the state space equation (24) is further expressed as: Let Then the online update result of the drift coefficient of the hidden linear Wiener process model and the estimated current degradation state are expressed as: Among them, 8. A remaining useful life prediction method for an implicit Wiener degradation process integrating multi-source information according to claim 7, characterized in that In step D, predict the remaining life, specifically as follows: Let \(l\) k denote the remaining useful life of the device at time \(t\) k . Based on the implicit linear Wiener process degradation model of Equation (2), when the true degradation amount \(x\) of the device is known k , the probability density function of the remaining life is expressed as: Use the expression of the remaining life probability density function considering state estimation; Among them,

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