A method for online remaining life prediction of machinery using recursive model updating strategy

Abstract

A method for online remaining life prediction of machinery using a recursive model update strategy first establishes a degradation model and model library for the mechanical equipment, then determines three thresholds and, based on the thresholds, determines the starting degradation time and the starting prediction time. Model parameters are then updated using a maximum likelihood estimation-expectation maximization combined algorithm based on a sequence of observations after the starting degradation time, and the optimal degradation model is automatically selected using the recursive Bayesian Information Criterion (RBIC). Finally, the remaining life prediction result is obtained based on the selected model and its updated parameters. The method is driven by the mechanical equipment's own condition monitoring data and uses the RBIC score to match the monitoring data to the optimal degradation model in real time. This method effectively characterizes the degradation of the mechanical equipment during operation in industrial practice and improves the accuracy of the remaining life prediction of the mechanical equipment.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical equipment remaining life prediction, and in particular relates to a mechanical online remaining life prediction method using a model recursive updating strategy. Background Art

[0002] Mechanical equipment, a vital component of industrial development, is widely used across various industries. However, as its structure becomes increasingly complex, the probability of equipment failure increases significantly. Failure to effectively predict and maintain faults before they occur can often lead to serious consequences. Therefore, it is crucial to accurately predict the remaining useful life of mechanical equipment and proactively maintain equipment with insufficient remaining useful life to ensure its efficient and safe operation.

[0003] Most current data-driven RUL prediction methods (X.Liu, Y.Lei, N.Li, X.Si, X.Li, RUL prediction of machinery using convolutional-vector fusion network through multi-feature dynamic weighting [J]. Mechanical Systems and Signal Processing, 2023, 185: 109788.) rely on high-quality, full-life degradation data to train prediction models. These methods assume two key factors: 1. The availability of a large amount of failure data in advance; 2. The similarity of degradation behavior among different mechanical equipment. However, for actual engineering equipment, only a small amount of degradation data is often available. Even when sufficient failure data is available, the degradation process can vary among the same batch of equipment due to various uncertainties such as manufacturing variations and service environments. This results in limited applicability and flexibility of these data-dependent training methods.

[0004] Although there are some data-driven methods (N.Li, P.Xu, Y.Lei, X.Cai, D.Kong, A self-data-driven method for remaining useful life prediction of wind turbines considering continuously varying speeds[J]. Mechanical Systems and SignalProcessing, 2022, 165: 108315.) that can predict the life of mechanical equipment based on its own degradation data, solving the problem of dependence on training data in the process of predicting the remaining life of mechanical equipment, these methods still have problems such as the need to store and reuse all historical data, large computing resource requirements, and high computational complexity. It is difficult to implement online and real-time remaining life prediction for mechanical equipment in actual industrial sites. Summary of the Invention

[0005] In order to overcome the above shortcomings of the prior art, the purpose of the present invention is to provide an online remaining life prediction method for machinery using a model recursive update strategy, which uses the condition monitoring data of the mechanical equipment itself to predict its remaining life, and can adaptively update the model parameters according to the latest monitoring data and select the optimal degradation model in real time, thereby reducing the calculation time and improving the prediction accuracy of the remaining life of the mechanical equipment.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for predicting the remaining service life of machinery online using a model recursive updating strategy comprises the following steps:

[0008] Step 1: Establish a mechanical equipment degradation model and degradation model library;

[0009] Step 2: Determine three thresholds: warning threshold D1, alarm threshold D2, and failure threshold D3. These three thresholds divide the monitoring value into four different levels.

[0010] 2.1) The warning threshold D1 is the dividing line between Level I and Level II, which represent the healthy stage and the initial degradation stage, respectively. During the early operation of the mechanical equipment, the recorded observations are used as a random sample of the healthy stage. The 3σ interval of these observations is calculated, and the upper or lower boundary of the interval is selected as the warning threshold D1.

[0011] 2.2) Failure threshold D3 is the boundary between Level III and Level IV, which represent the severe degradation stage and the failure stage, respectively. It needs to be pre-specified based on national and industry standards or actual conditions.

[0012] 2.3) Alarm threshold D2 is the boundary between Level II and Level III and is defined as the average of warning threshold D1 and failure threshold D3;

[0013] Step 3: Determine the initial degradation time FDT and the initial prediction time FPT from the online monitoring data of the in-service mechanical equipment. When the observed value reaches the warning threshold D1, this time point is defined as the initial degradation time FDT of the mechanical equipment. When the observed value reaches the alarm threshold D2, this time point is defined as the initial prediction time FPT.

[0014] Step 4: Estimation of mechanical equipment degradation model parameters: Use the maximum likelihood estimation and expectation maximization combination algorithm to estimate the parameters in the degradation model;

[0015] Step 5: Real-time parameter update: When the initial prediction time (FPT) is reached, the remaining life of the mechanical equipment is predicted. The sequential Bayesian algorithm is used to update the parameters based on the latest monitoring data.

[0016] Step 6: Automatic selection of the optimal degradation model: Based on the recursive Bayesian information criterion (RBIC) to evaluate the fitting performance of the established state-space model, the current optimal state-space model is automatically selected.

[0017] Step 7: Calculate the remaining lifespan.

[0018] The first step is specifically: using a random coefficient regression model with adaptive drift to describe the degradation process at time t:

[0019]

[0020] Where y(t) is the observed value of the health status of the mechanical equipment at time t; y0 is the initial value; α is the drift coefficient, and its mean is μ α , the variance is Normal distribution is a trend function used to describe the degradation trend over time, β is a fixed parameter; ω(t) has a mean of 0 and a variance of The noise term follows a normal distribution

[0021] A degradation model library containing four degradation trends including linear function, polynomial function, exponential function and power function is established.

[0022] The degradation models contained in the degradation model library are not fixed. Continuous differentiable functions are constructed according to user requirements and added to a new degradation model library.

[0023] In step 2.1), the upper boundary of the 3σ interval is selected to monitor the increase of the monitored value during the degradation process, while the lower boundary of the 3σ interval is used to observe the decrease of the observed value during the degradation process.

[0024] The specific content of step 4 is as follows: The unknown parameters in the mechanical equipment degradation model are represented in vector form as A series of monitoring data after the initial degradation time FDT is represented as Y FDT:n =(y FDT , y FDT+1 , …, y n )', n < FPT, and the time series corresponding to the monitoring data is represented as (t FDT , t FDT+1 , …, t n ), n < FPT;

[0025] The model parameters are estimated by the maximum likelihood estimation method Unknown parameters The estimated value of is the value that maximizes equation (2):

[0026]

[0027] In the formula, t i represents the moment when the i-th monitoring data is located; y i is the health state observed value of the mechanical equipment at time t i ; y D is the amplitude of the warning threshold D1; ψ is the function for calculating the probability density;

[0028] Based on the mechanical equipment degradation model defined by formula (1), the complete log-likelihood function based on the historical monitoring data Y FDT:n is expressed as:

[0029]

[0030] Among them, N represents the number of all monitoring data from FDT to n; μ α,0 and are the mean and variance of the initial distribution of the drift coefficient α;

[0031] When using the expectation maximization algorithm for iterative estimation of parameters, the model parameter estimation value obtained by the maximum likelihood estimation method is used as the initial value of the expectation maximization algorithm Here is the randomly initialized value. Assuming that the estimation result of the parameter Θ in the j-th iteration has been obtained, then the estimation process of the parameter Θ in the (j + 1)-th iteration is divided into the E-step and the M-step;

[0032] E-step, the expectation E(Θ|Θ) of formula (3) (j) ) is expressed as:

[0033]

[0034] Among them, E(α|Θ (j) ,Y FDT:n ) and E(α 2 |Θ (j) ,Y FDT:n ) is α and α 2 The conditional expectation of

[0035] M steps, maximize the expected value E(Θ|Θ (j) ), Θ (j+1) The estimated result of is solved by formula (5):

[0036]

[0037] Calculation formula (4) about The partial derivative of , and let but The estimated value of is represented by β, and the formula is as follows:

[0038]

[0039] Substituting formula (6) into formula (4), the result of further simplification of the complete log-likelihood function is expressed by formula (7):

[0040]

[0041] Where c is a constant;

[0042] Based on formula (7), the downhill simplex method is used to solve β (j+1) The estimated results are then converted into β (j+1) The estimate of is input into formula (6) to calculate The estimation result of the drift coefficient α is calculated; the expectation maximization algorithm is iterated multiple times until the convergence criterion is met. The defined convergence criterion is expressed as formula (8);

[0043]

[0044] Among them, ζ is a very small fixed value.

[0045] The specific step 5 is: Assume that all the current monitoring data is Y FDT:k =(y FDT ,y FDT+1 ,…y FPT ,…y k )',k>FPT,Y FDT:kThe corresponding time series is (t FDT ,t FDT+1 ,…t FPT ,…t k )', the posterior distribution of the drift coefficient α is expressed as:

[0046]

[0047] Among them, p(y k |α) represents y k Based on the conditional probability distribution of α, p(α|Y FDT:k-1 ) represents t k-1 The posterior distribution at time t, p(y k |Y FDT:k-1 ) is the normalization coefficient; based on the latest monitoring data y k The update formula of the drift coefficient α is expressed as formula (10) and formula (11);

[0048]

[0049] in, and represents the mean and variance of the drift parameter α obtained based on the k-1th monitoring data; and From the parameter estimation result Θ; when receiving the next monitoring data y k+1 Then, the posterior distribution of the drift coefficient α is As a prior distribution and update the parameters.

[0050] The specific step 6 is: the expression of RBIC is as follows:

[0051]

[0052] The calculation formula of BIC is as follows:

[0053] BIC=-2 max(l(Θ|Y FDT:k ))+ln(k)N P (13) Where N P represents the number of unknown parameters in the degradation model; max(l(Θ|Y FDT:k )) represents the likelihood function l(Θ|Y FDT:k ) maximum value; K is Y FDT:k the number of observations;

[0054] Observe formula (12), the RBIC score is based on the latest monitoring data y k The RBIC score is recursively updated with the previous one, and the model with the minimum RBIC score is selected as the optimal degradation model.

[0055] The seventh step is as follows: Substitute the optimal degradation model and the corresponding parameters into formula (4), then at t k The remaining life prediction result at the moment is expressed as:

[0056]

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] Since the present invention adopts a model recursive update strategy, when predicting the remaining life of mechanical equipment, it uses the mechanical equipment's own condition monitoring data and utilizes the recursive Bayesian Information Criterion (RBIC) to adaptively select the optimal degradation model. Therefore, it has the advantages of no need to store and reuse historical data and low computational complexity. The method of the present invention can effectively characterize the degradation of mechanical equipment during operation in industrial practice, enable the monitoring data to match the optimal degradation model in real time, and improve the accuracy of the remaining life prediction of mechanical equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Flowchart of the present invention.

[0060] Figure 2 Example refrigerator degradation curve and three thresholds.

[0061] Figure 3 This is an example of real-time remaining life prediction and model selection results for a Stirling refrigerator. DETAILED DESCRIPTION

[0062] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0063] Reference Figure 1 , a method for predicting the remaining service life of machinery online using a model recursive updating strategy, comprising the following steps:

[0064] Step 1: Establish a mechanical equipment degradation model and degradation model library: Use a random coefficient regression model with adaptive drift to describe the degradation process at time t:

[0065]

[0066] Where y(t) is the observed value of the health status of the mechanical equipment at time t; y0 is the initial value; α is the drift coefficient, and its mean is μ α , the variance is Normal distribution is a trend function used to describe the degradation trend over time, β is a fixed parameter; ω(t) has a mean of 0 and a variance of The noise term follows a normal distribution

[0067] Considering the individual differences in the equipment degradation process, a degradation model library containing four degradation trends of linear function, polynomial function, exponential function and power function is established to more accurately capture the overall degradation trend during the remaining useful life prediction. The degradation models included in the degradation model library are not fixed. A continuously differentiable function is constructed according to the user's requirements and added to the new degradation model library;

[0068] Step 2: Determine three thresholds: warning threshold D1, alarm threshold D2 and failure threshold D3. These three thresholds divide the monitoring values into 4 different levels;

[0069] 2.1) The warning threshold D1 is the boundary between level I and level II, where level I and level II represent the healthy stage and the initial degradation stage respectively; in the early operation stage of the mechanical equipment, the recorded observation values are used as random samples in the healthy stage, and the 3σ interval of these observation values is calculated, and the upper or lower boundary of it is selected as the warning threshold D1. The upper boundary of the 3σ interval is used for the case where the monitoring value increases with the degradation process, while the lower boundary of the 3σ interval is used for the case where the observation value decreases with the degradation process;

[0070] 2.2) The failure threshold D3 is the boundary between level III and level IV, where level III and level IV represent the severe degradation stage and the failure stage respectively, and it needs to be pre-specified according to national and industry standards or actual situations;

[0071] 2.3) The alarm threshold D2 is the boundary between level II and level III, and is defined as the average value of the warning threshold D1 and the failure threshold D3;

[0072] Step 3: Determine the starting degradation time FDT and the starting prediction time FPT in the on-line monitoring data of the in-service mechanical equipment; when the observation value reaches the warning threshold D1, this time point is defined as the starting degradation time FDT of the mechanical equipment; when the observation value reaches the alarm threshold D2, this time point is defined as the starting prediction time FPT;

[0073] Step 4: Parameter estimation of the mechanical equipment degradation model: Use the combined algorithm of maximum likelihood estimation and expectation maximization to estimate the parameters in the degradation model. The unknown parameters in the mechanical equipment degradation model are represented in vector form as A series of monitoring data after the starting degradation time FDT is represented as Y FDT:n =(y FDT , y FDT+1 , …, y n )', n < FPT, and the time series corresponding to the monitoring data is represented as (t FDT , t FDT+1 , …, t n),n <FPT;

[0074] Estimate model parameters by maximum likelihood estimation Unknown parameters Estimated value of is the value that maximizes formula (2):

[0075]

[0076] Where, t i Indicates the time of the i-th monitoring data; y i For mechanical equipment in t i The health status observation value at the moment; y D is the amplitude of the warning threshold D1; ψ is the function for calculating the probability density;

[0077] According to the mechanical equipment degradation model defined by formula (1), based on the historical monitoring data Y FDT:n The complete log-likelihood function is expressed as:

[0078]

[0079] Where N represents the total number of monitoring data from FDT to n; μ α,0 and is the mean and variance of the initial distribution of the drift coefficient α;

[0080] When using the expectation maximization algorithm to iteratively estimate parameters, the model parameter estimates obtained by the maximum likelihood estimation method are used as the initial values ​​of the expectation maximization algorithm. here Assume that the estimated result of the parameter Θ jth iteration is a random initialization value. It has been obtained, then, the estimation process of the j+1th parameter Θ is divided into E steps and M steps;

[0081] E-step, the expectation E(Θ|Θ) of formula (3) (j) ) is expressed as:

[0082]

[0083] Among them, E(α|Θ (j) ,Y FDT:n ) and E(α 2 |Θ (j) ,Y FDT:n ) is α and α 2 The conditional expectation of

[0084] M steps, maximize the expected value E(Θ|Θ (j) ), Θ (j+1) The estimated result of is solved by formula (5):

[0085]

[0086] Calculation formula (4) about The partial derivative of , and let but The estimated value of is represented by β, and the formula is as follows:

[0087]

[0088] Substituting formula (6) into formula (4), the result of further simplification of the complete log-likelihood function is expressed by formula (7):

[0089]

[0090] Where c is a constant;

[0091] Based on formula (7), the downhill simplex method is used to solve β (j+1) The estimated results are then converted into β (j+1) The estimate of is input into formula (6) to calculate The estimation result; Once these two parameters are calculated, the posterior distribution of the drift coefficient α is also calculated; the expectation maximization algorithm is iterated multiple times until the convergence criterion is met. The convergence criterion defined is expressed as formula (8);

[0092]

[0093] Among them, ξ is a very small fixed value.

[0094] Step 5: Real-time parameter update: When the starting prediction time FPT is reached, the remaining life of the mechanical equipment is predicted. In this process, the sequential Bayesian algorithm is used to update the parameters based on the latest monitoring data. Assuming that all the current monitoring data is Y FDT:k =(y FDT ,y FDT+1 ,…y FPT ,…y k )',k>FPT,Y FDT:k The corresponding time series is (t FDT ,t FDT+1 ,…t FPT ,…t k )', the posterior distribution of the drift coefficient α is expressed as:

[0095]

[0096] Among them, p(y k |α) represents y k Based on the conditional probability distribution of α, p(α|Y FDT:k-1) represents t k-1 The posterior distribution at time t, p(y k |Y FDT:k-1 ) is the normalization coefficient; based on the latest monitoring data y k The update formula of the drift coefficient α is expressed as formula (10) and formula (11);

[0097]

[0098] in, and represents the mean and variance of the drift parameter α obtained based on the k-1th monitoring data; and From the parameter estimation result Θ; when receiving the next monitoring data y k+1 Then, the posterior distribution of the drift coefficient α is As a prior distribution and update the parameters.

[0099] Step 6: Automatic selection of the optimal degradation model: As the observation sequence continues to increase, the fitting performance of the established state-space model is evaluated based on the Recursive Bayesian Information Criterion (RBIC), and the current optimal state-space model is automatically selected;

[0100] The expression of RBIC is as follows:

[0101]

[0102] The calculation formula of BIC is as follows:

[0103] BIC=-2 max(l(Θ|Y FDT:k ))+ln(K)N P (13)

[0104] Where N P represents the number of unknown parameters in the degradation model; max(l(Θ|Y FDT:k )) represents the likelihood function l(Θ|Y FDT:k ) maximum value; K is Y FDT:k the number of observations;

[0105] Observe formula (12), the RBIC score is based on the latest monitoring data y k Recursively update the previous RBIC score and select the model with the minimum RBIC score as the optimal degradation model;

[0106] Step 7: Calculate the remaining life: After updating the parameters and selecting the model based on the latest monitoring data, the optimal degradation model and the corresponding parameters are substituted into formula (4). k The remaining life prediction result at the moment is expressed as:

[0107]

[0108] The effectiveness of the method of the present invention is verified by using an embodiment. This embodiment is derived from the full life cycle test platform of the Stirling refrigerator. The health index of the refrigerator is defined as the average value of the input current signal per hour. The refrigerator degradation curve used is as follows: Figure 2 As shown in FIG1 , the FDT and FPT of refrigerator 1 are 275 hours and 595 hours respectively; the FDT and FPT of refrigerator 2 are 98 hours and 364 hours respectively; the failure threshold of the health monitoring indicator is set to 0.85A; the failure time of refrigerator 1 and refrigerator 2 occurs at 893 hours and 416 hours respectively; the health indicators of the two refrigerators obtained from the test platform are input into the method of the present invention, and the corresponding real-time remaining life prediction results and model selection results are shown in FIG1 . Figure 3 As shown in the figure, it can be seen that the prediction results of the remaining service life of the method of the present invention are not much different from the actual remaining service life. The model selection results highlight that RBIC can dynamically select the most appropriate degradation model based on the latest monitoring data, which proves the effectiveness of the method of the present invention in practical applications.

[0109] It should be pointed out that, without departing from the concept of the present invention, adjustments and modifications made to the method of the present invention should also be considered as falling within the scope of protection of the present invention.

Claims

1. A method for predicting the remaining service life of machinery online using a model recursive update strategy, characterized in that: The following steps are involved: Step 1: Establish a mechanical equipment degradation model and degradation model library; The first step is specifically: using a random coefficient regression model with adaptive drift to describe the degradation process at time t: Where y(t) is the observed value of the health status of the mechanical equipment at time t; y0 is the initial value; α is the drift coefficient, and its mean is μ α , the variance is Normal distribution is a trend function used to describe the degradation trend over time, β is a fixed parameter; ω(t) has a mean of 0 and a variance of The noise term follows a normal distribution Establish a degradation model library containing four degradation trends: linear function, polynomial function, exponential function and power function; Step 2: Determine three thresholds: warning threshold D1, alarm threshold D2, and failure threshold D3. These three thresholds divide the monitoring value into four different levels. 2.1) The warning threshold D1 is the dividing line between Level I and Level II, which represent the healthy stage and the initial degradation stage, respectively. During the early operation of the mechanical equipment, the recorded observations are used as a random sample of the healthy stage. The 3σ interval of these observations is calculated, and the upper or lower boundary of the interval is selected as the warning threshold D1. 2.2) Failure threshold D3 is the boundary between Level III and Level IV, which represent the severe degradation stage and the failure stage, respectively. It needs to be pre-specified based on national and industry standards or actual conditions. 2.3) Alarm threshold D2 is the boundary between Level II and Level III and is defined as the average of warning threshold D1 and failure threshold D3; Step 3: Determine the initial degradation time FDT and the initial prediction time FPT from the online monitoring data of the in-service mechanical equipment. When the observed value reaches the warning threshold D1, this time point is defined as the initial degradation time FDT of the mechanical equipment. When the observed value reaches the alarm threshold D2, this time point is defined as the initial prediction time FPT. Step 4: Estimation of mechanical equipment degradation model parameters: Use the maximum likelihood estimation and expectation maximization combination algorithm to estimate the parameters in the degradation model; The specific content of the fourth step is as follows: The unknown parameters in the mechanical equipment degradation model are represented in vector form as A series of monitoring data after the starting degradation time FDT is represented as Y FDT:n =(y FDT , y FDT+1 , …, y n ), n < FPT, and the time series corresponding to the monitoring data is represented as (t FDT , t FDT+1 , …, t n ), n < FPT;; Estimate model parameters by maximum likelihood estimation Unknown parameters Estimated value of is the value that maximizes formula (2): Where, t i Indicates the time of the i-th monitoring data; y i For mechanical equipment in t i The health status observation value at the moment; y D is the amplitude of the warning threshold D1; ψ is the function for calculating the probability density; According to the mechanical equipment degradation model defined by formula (1), based on the historical monitoring data Y FDT:n The complete log-likelihood function is expressed as: Where N represents the total number of monitoring data from FDT to n; μ α,0 and is the mean and variance of the initial distribution of the drift coefficient α; When using the expectation maximization algorithm to iteratively estimate parameters, the model parameter estimates obtained by the maximum likelihood estimation method are used as the initial values ​​of the expectation maximization algorithm. here Assume that the estimated result of the parameter Θ jth iteration is a random initialization value. It has been obtained, then, the estimation process of the j+1th parameter Θ is divided into E steps and M steps; E-step, the expectation E(Θ|Θ) of formula (3) ( j ) ) is expressed as: Among them, E(α|Θ (j) ,Y FDT:n ) and E(α 2 |Θ (j) ,Y FDT:n ) is α and α 2 The conditional expectation of M steps, maximize the expected value E(Θ|Θ (j) ), Θ (j+1) The estimated result of is solved by formula (5): Calculation formula (4) about The partial derivative of , and let but The estimated value of is represented by β, and the formula is as follows: Substituting formula (6) into formula (4), the result of further simplification of the complete log-likelihood function is expressed by formula (7): Where c is a constant; Based on formula (7), the downhill simplex method is used to solve β (j+1) The estimated results are then converted into β (j+1) The estimate of is input into formula (6) to calculate The estimation result of the drift coefficient α is calculated; the expectation maximization algorithm is iterated multiple times until the convergence criterion is met. The defined convergence criterion is expressed as formula (8); Among them, ξ is a very small fixed value; Step 5: Real-time parameter update: When the initial prediction time (FPT) is reached, the remaining life of the mechanical equipment is predicted. The sequential Bayesian algorithm is used to update the parameters based on the latest monitoring data. Step 6: Automatic selection of the optimal degradation model: Based on the recursive Bayesian information criterion (RBIC), the fitting performance of the established state-space model is evaluated and the current optimal state-space model is automatically selected. Step 7: Calculate the remaining lifespan.

2. The prediction method according to claim 1, wherein: The degradation models contained in the degradation model library are not fixed. Continuous differentiable functions are constructed according to user requirements and added to a new degradation model library.

3. The prediction method according to claim 1, wherein: In step 2.1), the upper boundary of the 3σ interval is selected for the case where the monitoring value increases with the degradation process, while the lower boundary of the 3σ interval is selected for the case where the observation value decreases with the degradation process.

4. The prediction method according to claim 1, wherein: The specific step 5 is: Assume that all the current monitoring data is Y FDT:k =(y FDT ,y FDT+1 ,…y FPT ,…y k )',k>FPT,Y FDT:k The corresponding time series is (t FDT ,t FDT+1 ,…t FPT ,…t k )', the posterior distribution of the drift coefficient α is expressed as: Among them, p(y k |α) represents y k Based on the conditional probability distribution of α, p(α|Y FDT:k-1 ) represents t k-1 The posterior distribution at time t, p(y k |Y FDT:k-1 ) is the normalization coefficient; based on the latest monitoring data y k The update formula of the drift coefficient α is expressed as formula (10) and formula (11); in, and represents the mean and variance of the drift parameter α obtained based on the k-1th monitoring data; and From the parameter estimation result Θ; when receiving the next monitoring data y k+1 Then, the posterior distribution of the drift coefficient α is As a prior distribution and update the parameters.

5. The prediction method according to claim 4, characterized in that The specific step 6 is: the expression of RBIC is as follows: The calculation formula of BIC is as follows: BIC=-2 max(l(Θ|Y FDT:k ))+ln(K)N P (13) Where N P represents the number of unknown parameters in the degradation model; max(l(Θ|Y FDT:k )) represents the likelihood function l(Θ|Y FDT:k ) maximum value; K is Y FDT:k the number of observations; Observe formula (12), the RBIC score is based on the latest monitoring data y k The RBIC score is recursively updated with the previous one, and the model with the minimum RBIC score is selected as the optimal degradation model.

6. The prediction method according to claim 5, characterized in that The seventh step is as follows: Substitute the optimal degradation model and the corresponding parameters into formula (4), then at t k The remaining life prediction result at the moment is expressed as:

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