A method for predicting the residual life of a device based on a wiener process

Abstract

The application relates to a device residual life prediction method based on a Wiener process, which comprises the following steps: constructing a degradation model based on an age and state related Wiener process model; estimating parameters in the degradation model by using maximum likelihood estimation combined with an improved artificial bee colony algorithm; updating random parameters in the degradation model by using a strong tracking filter; and calculating a probability density function of the device residual life by using a degradation process simulation method. Compared with the prior art, the application can be applied to the case that the degradation model contains a time-varying diffusion term and a random failure threshold, has wider applicability, and the prediction result is accurate.

Description

Technical Field

[0001] This invention relates to the prediction of the remaining useful life of equipment, and more particularly to a method for predicting the remaining useful life of equipment based on the Wiener process. Background Technology

[0002] Currently, the following problems exist in research on equipment remaining life prediction based on age- and state-related Wiener process models:

[0003] (1) Remaining lifetime prediction methods generally target degradation models with fixed diffusion term coefficients. During equipment degradation, the development of faults may lead to a decrease in the stability of the entire system, and the uncertainty of the degradation process will also increase. If the time-varying diffusion term coefficient is not considered in the degradation model, it will affect the model's fitting effect and the accuracy of remaining lifetime prediction.

[0004] (2) Random thresholds are not considered. In practical applications, failure thresholds are often unclear, such as due to different user requirements, external environmental influences, and ambiguity regarding the specific threshold that leads to failure. If the remaining lifetime prediction method is only applicable to fixed failure thresholds, it will affect its practicality. Summary of the Invention

[0005] The purpose of this invention is to improve the accuracy of remaining lifetime prediction and the applicability of the prediction method by considering time-varying diffusion term coefficients and random thresholds in the process of equipment remaining lifetime prediction, and to provide an equipment remaining lifetime prediction method based on Wiener process.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for predicting the remaining life of equipment based on the Wiener process includes the following steps:

[0008] S1. Construct a degradation model based on the age- and state-related Wiener process model;

[0009] S2. Estimate the parameters in the degradation model using maximum likelihood estimation combined with the improved artificial bee colony algorithm;

[0010] S3. Update the random parameters in the degradation model using a strong tracking filter;

[0011] S4. Calculate the probability density function of the remaining lifespan of the equipment using a degradation process simulation method.

[0012] Furthermore, in step S1, the specific content of constructing the degradation model includes:

[0013] The degradation model is constructed based on the general expression of the age- and state-related Wiener process model as follows:

[0014]

[0015] In the formula, x(t) represents the state of the device at time t; x k This indicates that the device is at its initial time t. k The state of time; τ is a random parameter used to describe the differences between individuals; θ is a vector composed of other unknown parameters; aΛ(x(τ),τ;θ) is the drift term coefficient function; σ(τ;θ) is the diffusion term coefficient function; B(τ) is the standard Brownian motion.

[0016] Furthermore, in step S2, the specific content of parameter estimation includes:

[0017] The degenerate model (1) is discretized using the Euler discretization method. The state change Δx between two adjacent observation points... n,k-1 It can be represented as:

[0018] Δx n,k-1 =x n,k -x n,k-1 =aΛ(x n,k-1 ,t n,k-1 ;θ)Δt n,k-1 +σ(t n,k-1 ;θ)B(Δt n,k-1 )#(2)

[0019] In the formula, n = 1, 2, ..., N, where N represents the number of degraded samples; k = 1, 2, ..., K n K n Δt represents the number of observation points in the nth degenerate sample; n,k-1 =t n,k -t n,k-1 This represents the time interval between two observation points.

[0020] Let Δx n =[x n,1 -x n,0 ,...x n,Kn -x n,Kn-1 ] T According to the properties of nonlinear Wiener processes, Δx n Follows a multivariate normal distribution N(μ) a T n ,Σ n ), where T n The expression is:

[0021]

[0022]

[0023] In the formula, Tn,k-1 =Λ(x n,k-1 ,t n,k-1 ;θ)Δt n,k-1 ;D n It is a K n ×K n A diagonal matrix whose diagonal elements are

[0024] Then Δx n Log-likelihood function l(μ) a ,σ a ,θ|x) can be expressed as

[0025]

[0026] For equation (5), find the value of μ. a The first-order partial derivative of , and let Get μ a The estimation results are as follows:

[0027]

[0028] Substituting equation (6) into equation (5), the log-likelihood function l(μ) a ,σ a ,θ|x) becomes the following form:

[0029]

[0030] Equation (7) contains the unknown parameter σ. a Parameters like θ are difficult to estimate using partial derivatives. We will use an improved artificial bee colony algorithm for estimation. Let v = [σ...]. a ,θ T ] T The specific steps are as follows:

[0031] Step 1: Determine the initial value range for each parameter and construct a search space. Generate a series of initial solutions within the search space according to the following expression. Where M is the number of initial solutions.

[0032]

[0033] In the formula, d = 1, 2, ..., D, where D is the number of parameters in v; R is a random number that follows a uniform distribution in the interval (0, 1); L d and U d These represent the upper and lower bounds of the initial value range of the d-th parameter, respectively.

[0034] Step 2: Establish the following search mechanism to find new solutions.

[0035]

[0036] In the formula, s represents the random index of the parameter, used to select the parameter to be searched in the i-th iteration; v best Let r1, r2 ∈ {1, 2, ..., M}, and r1, r2 are not equal, nor are they equal to m; φ ~ U(-u, u), where u represents the perturbation amplitude; p is a random number that follows a uniform distribution in the interval (0, 1), and the search strategy is determined based on the value of p; SP represents the selection probability.

[0037] Step 3: Determine which solutions to keep based on the greedy selection method.

[0038]

[0039] Step 4: Select the solution that needs to be updated based on probability, and denote the new solution as... The search mechanism for the new solution is the same as in step 2. The probabilities of different solutions being selected are as follows:

[0040]

[0041] In the formula, F m Solution The fitness value.

[0042] Step 5: Set the iteration limit C max If a certain solution is in C max If no better solution is found in the surrounding area within +1 searches, discard it and generate a new solution again according to the method in step 1.

[0043] The optimal solution in the i-th iteration The parameter estimation results of this iteration Repeat steps 2-5 until... It is less than the preset threshold.

[0044] Furthermore, in step S3, the specific content of the parameter update includes:

[0045] Step 1: Establish the following state-space model based on equation (3):

[0046]

[0047] In the formula, ξ(t) k-1 )=σ(t k-1 )B(Δt k-1 ) follows a normal distribution N(0,σ) 2 (t k-1 )Δt k-1 ).

[0048] Step 2: Select appropriate weakening factor β (β≥1) and forgetting factor ρ (0<ρ≤1). The weakening factor is generally chosen as an empirical value that meets the specified range, and the forgetting factor is generally ρ=0.95. Then calculate the suboptimal fading factor:

[0049]

[0050] in

[0051]

[0052]

[0053]

[0054]

[0055] Step 3: Calculate the Kalman gain:

[0056]

[0057] In the formula,

[0058] Step 4: Update the mean and variance of the random parameters:

[0059]

[0060]

[0061] Whenever a new observation is generated, the random parameters are updated by performing steps 2-4.

[0062] Furthermore, in step S4, the specific details of the remaining lifetime estimation include:

[0063] Remaining lifetime is defined as the time when a device's condition first degrades beyond a failure threshold, also known as the first-hit time. According to the definition of first-hit time, the device... k The remaining lifetime at that time is expressed as:

[0064] l k =inf{l:x(t k +l)≥ω|x k <ω}#(22)

[0065] In the formula, l k Indicates the device at t k The remaining lifetime at time ω, where inf{·} represents the lower bound of a variable and ω represents the failure threshold.

[0066] Assume the failure threshold follows a truncated normal distribution with values ​​greater than 0. The probability density function of remaining lifetime can be expressed as:

[0067]

[0068] in,

[0069]

[0070]

[0071]

[0072] Furthermore, the degradation process is simulated to approximate equation (23). The specific steps are as follows:

[0073] Step 1: Generate a series of uniformly distributed U(μ) a -3σ a ,μ a +3σ a Discrete {a} n} n＝1:SN , where SN represents the number of simulated degradation paths.

[0074] Step 2: Set the boundary of the failure threshold to (μ ω -3σ ω ,μ ω +3σ ω The degradation path is generated step by step according to the following expression until the degradation path exceeds the upper bound of the failure threshold.

[0075] x n (l i +t k )=x n (l i-1 +t k )+a n Λ(x n (l i-1 +t k ),l i-1 +t k )Δl i-1 +R i-1 #(27)

[0076] In the formula, x n (l i +t k )express At time t, the state of the nth degenerate path; Δl i-1 It is the step size; R i-1 ~U(-r i-1 ,ri-1 ),in

[0077] Step 3: Substitute the simulated degradation path from Step 2 into Equation (23) to calculate the probability density of the remaining lifetime for each observation point within the failure threshold boundary. Equation (25) is approximated using the following discrete form.

[0078]

[0079] In the formula, Where P represents the number of different remaining lifetimes corresponding to the observation point.

[0080] Step 4: Integrate the probability density of all observation points:

[0081]

[0082] In the formula, N p Indicates remaining lifespan The number of corresponding observation points.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] 1. This invention can be applied to the prediction of the remaining life of equipment based on complex degradation models, especially degradation models containing time-varying diffusion terms, and is not limited to degradation models with fixed diffusion term coefficients, thus having a wider range of applicability.

[0085] 2. This invention considers the random failure threshold in the prediction of remaining equipment life, which improves the accuracy of remaining life prediction and the practicality of the prediction method.

[0086] 3. This invention facilitates the formulation of subsequent maintenance plans, improves the efficiency of maintenance work, and reduces costs. Attached Figure Description

[0087] Figure 1 This is a schematic diagram of the process of the present invention;

[0088] Figure 2 This is a schematic diagram of fatigue crack propagation data in an embodiment of the present invention;

[0089] Figure 3 This is a schematic diagram illustrating the estimation parameters in an embodiment of the present invention;

[0090] Figure 4 This is a schematic diagram illustrating the parameter update in an embodiment of the present invention;

[0091] Figure 5 This is a schematic diagram illustrating the estimation of remaining lifetime in an embodiment of the present invention;

[0092] Figure 6This is a schematic diagram illustrating the fitting effect of the model established in an embodiment of the present invention;

[0093] Figure 7 This is a schematic diagram illustrating the effect of parameter estimation in an embodiment of the present invention;

[0094] Figure 8 This is a schematic diagram illustrating the estimation of remaining lifetime under a fixed failure threshold according to an embodiment of the present invention. Detailed Implementation

[0095] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0096] This embodiment uses fatigue crack propagation data to verify the effectiveness of the invention. The fatigue crack propagation dataset is as follows: Figure 2 As shown, this includes crack size observation data for 21 alloy specimens. The initial crack length for each specimen was 0.9 inches; specimens were considered to have failed when the crack length exceeded 1.6 inches, and observation was stopped. Initially, crack length was recorded every 0.01 million stress cycles. Ultimately, 12 specimens exceeded the failure threshold; one of these failed specimens was selected as the test specimen for subsequent remaining life prediction experiments.

[0097] like Figure 1 As shown, this embodiment provides a method for predicting remaining lifespan based on an age- and state-related Wiener process model, including the following steps:

[0098] 1. Establish a degradation model

[0099] Based on the characteristics of fatigue crack propagation, an age- and state-dependent Wiener process model is established to describe the fatigue crack propagation process.

[0100]

[0101] Where x(t) represents the state of the device at time t; x k This indicates that the device is at its initial time t. k The state of time; is a random parameter used to describe the differences between individuals; b, c, d, e are fixed parameters; (bx(τ)+cexp(cτ)) is the drift term coefficient function; It is the diffusion term coefficient function, and B(τ) is the standard Brownian motion.

[0102] 2. Parameter estimation

[0103] The degenerate model (1) is discretized using the Euler discretization method. The state change Δx between two adjacent observation points...n,k-1 It can be represented as:

[0104]

[0105] In the formula, n = 1, 2, ..., 21 represents the number of alloy samples; k = 1, 2, ..., K n K n Δt represents the number of observation points in the nth alloy sample; n,k-1 =t n,k -t n,k-1 This represents the time interval between two observation points.

[0106] remember Based on the properties of nonlinear Wiener processes, Δx n Follows a multivariate normal distribution N(μ) a T n ,∑ n ),in

[0107]

[0108]

[0109] In the formula, T n,k-1 =(bx n,k-1 +cexp(ct n,k-1 ))Δt n,k-1 ;D n It is a K n ×K n A diagonal matrix whose diagonal elements are

[0110] Then Δx n Log-likelihood function l(μ) a ,σ a ,θ|x) can be represented as:

[0111]

[0112] For equation (5), find the value of μ. a The first-order partial derivative of , and let Get μ a The estimation results are as follows:

[0113]

[0114] Substituting equation (6) into equation (5), the log-likelihood function l(μ) a ,σ a ,θ|x) becomes the following form:

[0115]

[0116] By maximizing equation (7) using the improved artificial bee colony algorithm, the remaining parameter σ can be obtained. a Estimate the values ​​of b, c, d, and e. Let v = [σ]. a [b,c,d,e] T The specific steps are as follows:

[0117] Step 1: Set the initial value range of each parameter to (0, 10), and generate 100 initial solutions in the initial search space according to the following expression.

[0118]

[0119] In the formula, d = 1, 2, ..., 5; R is a random number that follows a uniform distribution in the interval (0, 1); L d and U d These represent the upper and lower bounds of the initial value range of the d-th parameter, respectively.

[0120] Step 2: Establish the following search mechanism to find new solutions.

[0121]

[0122] In the formula, s represents the random index of the parameter, used to select the parameter to be searched in the i-th iteration; v best Let r1, r2 ∈ {1, 2, ..., 100}, and r1, r2 are not equal, nor are they equal to m; φ ~ U(-0.6, 0.6), where u represents the perturbation amplitude; p is a random number that follows a uniform distribution in the interval (0, 1), and the search strategy is selected based on the value of p, with a selection probability of 0.1.

[0123] Step 3: Determine which solutions to keep based on the greedy selection method.

[0124]

[0125] Step 4: Select the solution that needs to be updated based on probability, and denote the new solution as... The search mechanism for the new solution is the same as in step 2. The probabilities of different solutions being selected are as follows:

[0126]

[0127] In the formula, F m Solution The fitness value is expressed as follows:

[0128]

[0129] Step 6: Set the iteration limit to 300. If a solution does not find a better solution in its vicinity in the 301st search, discard it and generate a new solution again according to the method in Step 1.

[0130] The optimal solution in the i-th iteration The parameter estimation results of this iteration Repeat steps 2-6 until... Less than the preset threshold. For example... Figure 3 The diagram shows the change of the log-likelihood function over 50 iterations. The log-likelihood function begins to converge after the 12th iteration, with a final result of 715.28. The parameter estimation results in this embodiment are as follows:

[0131] 3. Parameter update

[0132] Step 1: Establish the following state-space model based on equation (3):

[0133]

[0134] In the formula, ξ(t) k-1 )~N(0,(dt k-1 +e)Δt k-1 ).

[0135] Step 2: Set the weakening factor β = 4 and the forgetting factor ρ = 0.95. Then calculate the suboptimal fading factor:

[0136]

[0137] in

[0138]

[0139] N(t k )=V0(t k )-β(dt k-1 +e)Δt k-1 #(16)

[0140]

[0141]

[0142]

[0143] Step 3: Calculate the Kalman gain:

[0144]

[0145] In the formula,

[0146] Step 4: Update the mean and variance of the random parameters:

[0147]

[0148]

[0149] Whenever a new observation is generated, the random parameters are updated by executing steps 2-4. Taking the test sample as an example, the parameter update process is as follows: Figure 4 As shown.

[0150] In this invention, the remaining lifespan of the equipment is defined as the time when the equipment's condition first degrades beyond a failure threshold, also known as the first hit time. According to the definition of the first hit time, the equipment... k The remaining lifetime at that time is expressed as

[0151] l k =inf{l:x(t k +l)≥ω|x k <ω}#(23)

[0152] In the formula, l k Indicates the device at t k The remaining lifetime at time ω, where inf{·} represents the lower bound of a variable and ω represents the failure threshold.

[0153] Assume the failure threshold follows a truncated normal distribution with values ​​greater than 0. The probability density function of remaining lifetime can be expressed as:

[0154]

[0155] in,

[0156]

[0157]

[0158]

[0159] Taking the test sample as an example, let μ ω =1.56; The following steps approximate the calculation of equation (24) using a degradation process simulation method.

[0160] Step 1: Generate 1000 uniformly distributed U(μ) values. a -3σ a ,μ a +3σ a Discrete {a} n} n＝1:1000 .

[0161] Step 2: Set the boundary of the failure threshold to (1.462, 1.658), and generate the degradation path step by step according to the following expression until the degradation path exceeds the upper bound of the failure threshold.

[0162] x n (l i +t k )=x n (l i-1 +t k )+a n (bx n (l i-1 +t k )+cexp(c(l i-1 +t k )))Δl i-1 +R i-1 #(28)

[0163] In the formula, x n (l i +t k )express The state of the nth degenerate path at time n; Δl i-1 It is the step size; R i-1 ~U(-r i-1 ,r i-1 ),in

[0164] Step 3: Substitute the simulated degradation path from Step 2 into Equation (24) to calculate the probability density of the remaining lifetime for each observation point within the failure threshold boundary. Equation (26) is approximated using the following discrete form.

[0165]

[0166] In the formula, Where P represents the number of different remaining lifetimes corresponding to the observation point.

[0167] Step 4: Integrate the probability density of all observation points:

[0168]

[0169] In the formula, N p Indicates remaining lifespan The number of corresponding observation points.

[0170] like Figure 5 The figure shows the predicted remaining life of the test specimen. It can be seen that the present invention can accurately predict the remaining life of the test specimen.

[0171] To verify the superiority of this invention in establishing degradation models, a comparison was made between degradation models with fixed diffusion term coefficients and time-varying diffusion term coefficients, assuming the same drift term. For example... Figure 6 As shown, the Akaike Information Criterion value of the degradation model containing the time-varying diffusion term coefficient is smaller in multiple estimations, indicating a better fit. This is because the degradation model with the time-varying diffusion term coefficient can capture the nonlinear degradation characteristics caused by fault development, and thus can more accurately describe the evolution process of the physical system.

[0172] To verify the superiority of this invention in parameter estimation, the traditional maximum likelihood estimation is compared with the proposed improved maximum likelihood estimation. Figure 7 As shown, the improved maximum likelihood estimation yields a larger and more stable log-likelihood function estimate. This is because traditional maximum likelihood estimation methods typically use the "fminsearch" function in MATLAB to optimize the log-likelihood function, which is sensitive to initial values ​​and cannot constrain the range of parameter values. However, this invention utilizes an improved artificial bee colony algorithm to optimize the log-likelihood function, effectively overcoming these shortcomings and thus achieving a more stable and superior estimation result.

[0173] To verify the superiority of this invention in remaining lifetime estimation, the results of prediction methods considering fixed failure thresholds are compared with the prediction method considering random failure thresholds proposed in this invention. Figure 8 The figure shows the remaining lifetime estimation results under a fixed failure threshold. Compared to... Figure 5 The estimation results shown in this invention, while exhibiting less uncertainty under a fixed failure threshold, are of poorer performance and may lead to delays in maintenance. Since random thresholds are more common in practice, the remaining lifetime estimation method proposed in this invention is more practical and effective.

[0174] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for predicting the remaining life of equipment based on the Wiener process, characterized in that, Includes the following steps: S1. Construct a degradation model based on the age- and state-related Wiener process model; S2. Estimate the parameters in the degradation model using maximum likelihood estimation combined with the improved artificial bee colony algorithm; S3. Update the random parameters in the degradation model using a strong tracking filter; S4. Calculate the probability density function of the remaining life of the equipment using a degradation process simulation method; In step S1, the construction of the degradation model specifically includes: A degradation model is constructed based on the general expression of the age- and state-related Wiener process model, which is as follows: In the formula, express The status of the device at all times; Indicates the device at the initial moment The state of time; The parameter is random. A vector consisting of other unknown parameters; The coefficient function of the drift term; This is a function of the diffusion term coefficients; This is standard Brownian motion; In step S4, the device is in The remaining lifetime at that time is expressed as: In the formula, Indicates that the device is in Remaining lifespan at any given moment It represents the lower bound of a variable. Indicates the fault threshold. Indicates the device at the initial moment The state of time; Assume the failure threshold follows a truncated normal distribution with values ​​greater than 0. The probability density function of the remaining lifetime is expressed as: in, The probability density function of the remaining lifetime is calculated using a degradation process simulation method, specifically including the following steps: S401, Generate a series of uniformly distributed... discrete ,in Indicates the number of degradation paths simulated; S402, Set the boundary of the failure threshold as follows The degradation path is generated progressively until it exceeds the upper bound of the failure threshold; the degradation path generation formula is: In the formula, express ( At that moment, the first The state of a degenerate path; It is the step size; ,in ; S403. Substitute the degradation path in step S402 into the probability density function of the remaining lifetime, and calculate the probability density of the remaining lifetime for each observation point within the failure threshold boundary. S404, Integrate the probability density of all observation points: In the formula, Indicates remaining lifespan The number of corresponding observation points.

2. The method for predicting the remaining life of equipment based on the Wiener process according to claim 1, characterized in that, In step S2, estimating the parameters in the degradation model includes the following steps: S201. Discretize the degenerate model using the Euler discretization method; The change in state between two adjacent observation points Represented as: In the formula, ,in Indicates the number of degraded samples; ,in Indicates the first The number of observation points in each degraded sample; This represents the time interval between two observation points; S202, Note ,structure log-likelihood function ; S203. Estimate the log-likelihood function using the improved artificial bee colony algorithm. Unknown parameters in .

3. The method for predicting the remaining life of equipment based on the Wiener process according to claim 2, characterized in that, In step S203, record Estimate the log-likelihood function Unknown parameters in Includes the following steps: Step 1: Determine the initial value range for each parameter and construct a search space based on... The expression generates a series of initial solutions within the search space. ,in It is the number of initial solutions; In the formula, ,in yes The number of parameters; It is a random number that follows a uniform distribution in the interval (0,1); Indicates the first The upper bound of the initial value range of each parameter. Indicates the first The lower bound of the initial value range of each parameter; Step 2: Establish a search mechanism to find new solutions. The expression for the search mechanism is: In the formula, Represents a random index of the parameter, used to select the first... The parameters that need to be searched in the next iteration; Indicates the optimal solution; ,and They are not equal, and at the same time, none of them are equal to each other. ; ,in Indicates the magnitude of the disturbance; It is a random number that follows a uniform distribution in the interval (0,1), according to The value determines the search strategy; Indicates the probability of selection; Step 3: Determine which solutions to keep based on the greedy selection method: Step 4: Select the solution that needs to be updated based on probability, and denote the new solution as... The search mechanism for the new solution is the same as in step 2, and the probability of different solutions being selected is: In the formula, Solution fitness value; Step 5: Set the iteration limit If a certain solution is in If no better solution is found in the surrounding area during the search, then the solution is rejected, and a new solution is generated again according to the method in step 1. The first The optimal solution in the next iteration The parameter estimation results of this iteration Repeat steps 2-5 until... It is less than the preset threshold.

4. The method for predicting the remaining life of equipment based on the Wiener process according to claim 2, characterized in that, Based on the properties of the nonlinear Wiener process, the Follows a multivariate normal distribution ,in The expression is: In the formula, ; for diagonal matrix, The diagonal elements are ; log-likelihood function Represented as: Seeking answers regarding The first-order partial derivative of , and let ,get The estimation results are as follows: 。 5. The method for predicting the remaining life of equipment based on the Wiener process according to claim 4, characterized in that, Combination The estimation results are obtained. log-likelihood function Represented as: 。 6. The method for predicting the remaining life of equipment based on the Wiener process according to claim 4, characterized in that, In step S3, the random parameters in the degenerate model are updated using a strong tracking filter, specifically including the following steps: S301, according to The expression establishes the state-space model as follows: In the formula, Follows a normal distribution ; S302, Set the weakening factor and forgetting factor Calculate the suboptimal attenuation factor: in, The expression is: S303. Calculate the Kalman gain: In the formula, ; S304. Update the mean and variance of the random parameters: Whenever a new observation is generated, the random parameters are updated by executing steps S302 to S304.

7. The method for predicting the remaining life of equipment based on the Wiener process according to claim 1, characterized in that, in, The following discrete form is used for approximate calculation: In the formula, ,in This indicates the number of different remaining lifetimes corresponding to the observation point.

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