Equipment residual life prediction method based on physical-data model

Abstract

The invention relates to an equipment residual life prediction method based on a physical-data model, and the method comprises the steps: building a degradation model based on a physical degradation mechanism and a standard Wiener process model; obtaining fixed parameters in the degradation model by using a maximum likelihood estimation method in combination with a nonlinear regression method; acquiring an equipment state observation value in real time, and updating random parameters in the degradation model by using a weight optimization particle filter algorithm; and utilizing the degradation model, the fixed parameters in the degradation model and the random parameters in the degradation model to obtain a probability density function of the residual life of the equipment under a random failure threshold value, and performing numerical integration on the probability density function of the residual life of the equipment to obtain an expected value of the residual life of the equipment, and outputting the expected value as the residual life of the equipment. Compared with the prior art, high-precision and high-reliability residual life prediction is realized by fusing a physical mechanism and a data driving method.

Description

Technical Field

[0001] The present invention relates to the field of equipment life prediction, and in particular to a method for predicting the remaining life of equipment based on a physical-data model. Background Art

[0002] Currently, in equipment life prediction, the Wiener process model is widely applied. The Wiener process has good mathematical properties in characterizing reversible degradation signals and is widely used in the fields of electronic devices, mechanical structures, and mechatronic systems. Currently, based on factors such as non-linearity, multi-source variability, covariates, and multiplicity, extensive research has been conducted on the existing Wiener process-based models: for non-linear factors, according to the three principles of flexibility in describing degradation, real-time update ability, and time variation of the degradation rate, non-linear drift functions are introduced in the form of power functions and exponential functions; for multi-source variability factors, researchers usually use Wiener processes with diffusion, random coefficients, measurement errors, and multiple models to characterize the degradation process, so as to capture multi-source variability sources, including time variability, unit-to-unit variability, measurement variability, and model variability; for covariate factors, usually referred to as the working environment, i.e., temperature, pressure, humidity, salinity, etc., can be described by introducing a link function in the model parameters; for multiplicity factors, research based on binary and multi-dimensional Wiener process models has been developed, in which non-linearity, multi-dimensional dependence, and multi-source variability are considered.

[0003] The advantages of the current Wiener process-based models in degradation modeling include powerful mathematical properties and wide applications, while the disadvantages include the neglect of the failure mechanism, which will significantly affect the degradation process, resulting in insufficient prediction accuracy. The degradation mechanism has a very crucial impact on the evolution of the health state. Under high cyclic loads, the most typical degradation mechanisms of rotating machinery include creep, fatigue, and wear. Under the action of stress, the fatigue of components will intensify, usually leading to crack propagation.

[0004] Chinese Patent Application CN116595865A discloses a method for predicting the remaining life of equipment based on the Wiener process. Based on the age and state-dependent Wiener process model, a degradation model is constructed; the parameters in the degradation model are estimated by using maximum likelihood estimation combined with an improved artificial bee colony algorithm; the random parameters in the degradation model are updated by using a strong tracking filter; the probability density function of the remaining life of the equipment is calculated through a degradation process simulation method. Compared with the prior art, this invention can be applied to the case where the degradation model contains a time-varying diffusion term and a random failure threshold, and has a wider applicability, but it is still very dependent on data-driven during calculation and does not consider the physical effects in the actual degradation process of the equipment, and data-driven has blindness. Summary of the Invention

[0005] The object of the present invention is to overcome the defects of the above-mentioned existing technologies, and provide a method for predicting the remaining useful life of equipment based on a physics-data model. By integrating physical mechanisms and data-driven methods, high-precision and high-reliability remaining useful life prediction is achieved, providing theoretical support for the health management of mechanical systems.

[0006] The object of the present invention can be achieved by the following technical solutions:

[0007] A method for predicting the remaining useful life of equipment based on a physics-data model, the method comprising:

[0008] Step S1, obtaining real-time device status observation values, and constructing a degradation model based on a physical degradation mechanism and a standard Wiener process model;

[0009] Step S2, using the maximum likelihood estimation method combined with the non-linear regression method to obtain the fixed parameters in the degradation model;

[0010] Step S3, obtaining real-time device status observation values, and updating the random parameters in the degradation model by using a weighted optimized particle filter algorithm;

[0011] Step S4, using the degradation model, the fixed parameters in the degradation model, and the random parameters in the degradation model to obtain the probability density function of the remaining useful life of the device under a random failure threshold, and performing numerical integration on the probability density function of the remaining useful life of the device to obtain the expected value of the remaining useful life of the device, which is output as the remaining useful life of the device.

[0012] Further, the physical degradation mechanism includes crack propagation and random effects. In step S1, the process of constructing the degradation model includes:

[0013] Step S101, transforming the physical degradation mechanism into a stochastic differential equation, the stochastic differential equation including a drift term coefficient function and a diffusion term coefficient function, wherein the drift term coefficient function is constructed based on the Paris formula, and the diffusion term coefficient function is constructed based on the standard Wiener process model;

[0014] Step S102, using the device status observation values, the drift term coefficient function, and the diffusion term coefficient function to construct the degradation model;

[0015] Wherein, the device status observation value is an observable degradation quantity of the device, including crack length, vibration amplitude, temperature change, environmental noise, and measurement error.

[0016] Furthermore, the expression of the drift term coefficient function is:

[0017]

[0018] Among them, α is a random parameter, and μ α is the mean value of α, and σ α is the standard deviation of the parameter α, b is a material-related constant, and x 1 (t) is the drift term coefficient function;

[0019] The expression of the diffusion term coefficient function is:

[0020] x 2 (t) = σB(τ),

[0021] where σ is the diffusion term coefficient, B(τ) is a standard Wiener process, and x 2 (t) is the diffusion term coefficient function;

[0022] The expression of the degradation model is:

[0023] x(t) = x k +x 1 (t)+x 2 (t),

[0024] where x(t) represents the state of the device at time t, and x k represents the state of the device at the initial time t k 0.

[0025] Furthermore, in step S2, the process of obtaining the fixed parameters in the degradation model includes:

[0026] Step S201, discretize the degradation model using the Euler discretization method to obtain an expression for the state change;

[0027] Step S202, according to the properties of the nonlinear Wiener process, make the state change follow a multivariate normal distribution and construct a log-likelihood function for the state change;

[0028] Step S203, use the maximum likelihood estimation method and the nonlinear regression method to obtain the parameters in the log-likelihood function and output them as the fixed parameters in the degradation model.

[0029] Even further, the expression for the state change is:

[0030]

[0031] where Δx n is the state change of the nth sample, and Δx n,k-1 is the state difference between the kth observation and the (k - 1)th observation in the nth degradation sample.

[0032] Further, in step S203, the process of obtaining the parameters in the log-likelihood function includes:

[0033] Obtain a standard Wiener process model and a historical degradation model;

[0034] Process the standard Wiener process model by the maximum likelihood estimation method to obtain an estimated value of the standard Wiener process model, and use the estimated value of the standard Wiener process model as the initial assignment of the first parameter in the log-likelihood function;

[0035] Process the historical degradation model by non-linear regression to obtain an estimated value of the historical degradation model, and use the estimated value of the historical degradation model as the initial assignment of the second parameter in the log-likelihood function;

[0036] Based on the initial assignments of the first parameter and the second parameter in the log-likelihood function, respectively take partial derivatives of the log-likelihood function;

[0037] Substitute the partial derivative calculation results into the log-likelihood function to obtain the sectional log-likelihood function of the first parameter and the second parameter;

[0038] According to the sectional log-likelihood function of the first parameter and the second parameter, use a two-dimensional search function to obtain the parameters in the log-likelihood function.

[0039] Further, the state change amount follows a multivariate normal distribution, and the expression of the normal distribution is: N(μ α T n ,Σ n 0, where,

[0040]

[0041] T n,k-1 =Λ(x n,k-1 ,t n,k-1 ;θ)Δt n,k-1 ,

[0042]

[0043] where, μ α is the mean of α, T n is the time correlation matrix, is the time interval, Σ n is the covariance matrix, σ α is the standard deviation of the parameter α, Ω n is the diffusion term covariance matrix, Q n is the time accumulation matrix, is the variance coefficient of Brownian motion, Δx n,k-1 is the difference between the k-th and the (k - 1)-th observation points in the n-th degradation sample.

[0044] Further, in step S3, the process of updating the random parameters in the degradation model by using the weighted optimized particle filter algorithm includes:

[0045] According to the initial random parameters in the degradation model, particles are randomly selected and uniform weights are assigned to the particles;

[0046] Particle initialization, particle state update, weight update, particle optimization, weight normalization, particle state estimation and weight repair are performed on the particles, and the random parameters in the degradation model are updated by using the processed particles.

[0047] Furthermore, when each new device state observation value is obtained, the process of updating the random parameters in the degradation model by using the weighted optimized particle filter algorithm is repeated, so that the updated degradation model can fully reflect the current degradation characteristics of the device.

[0048] Further, the random failure threshold follows a truncated normal distribution, and the expression of the truncated normal distribution is:

[0049]

[0050] where ω is the random failure threshold, μ ω is the average failure threshold, is the threshold fluctuation variance, and TN represents the truncated normal distribution;

[0051] The probability density function of the remaining life of the device under the random failure threshold is:

[0052]

[0053] where f(l∣x k ) is the probability density function of the remaining life of the device under the random failure threshold, x k is the state of the device at the initial time t k , and l k is the remaining life of the device at the initial time t k .

[0054] Compared with the prior art, the beneficial effects of the present invention include:

[0055] 1. Based on the original Wiener model, the present invention introduces a physical degradation mechanism to construct a degradation model. The physical mechanism and data-driven are complementary, avoiding the "black box" problem of pure data-driven. Compared with the traditional linear and nonlinear Wiener process degradation models, it is more interpretable and can calculate the remaining life of the device more accurately;

[0056] 2. The present invention makes real-time adjustments to random parameters. By optimizing the weights of particle filtering and dynamically updating the distribution of random parameters, it can reflect the individual differences and degradation state changes of devices in real time, well adapt to random factors such as environmental fluctuations and measurement noise, avoid the prediction deviation caused by fixed parameters in traditional models, reduce the prediction error for alloy specimens by 30% compared with traditional methods, be closer to the actual engineering background, and improve the accuracy of remaining life prediction and the practicality of the prediction method;

[0057] 3. The present invention uses the Euler discretization method to discretize the degradation model, transforms complex continuous problems into computable discrete optimization problems. A series of processes for particles are suitable for parallelization, perform more stably in non-linear and high-dimensional parameter scenarios, and have a high degree of automation. With the acceleration of hardware such as GPUs, millisecond-level prediction can be achieved, shortening the time for predicting the remaining life of the device, with a short single prediction time, and enabling real-time monitoring of the device life;

[0058] 4. The present invention distinguishes the degradation characteristics of different devices through dynamic parameters, provides customized life prediction for each device, helps formulate preventive maintenance plans, reduces the risk of sudden failures. If the prediction result shows that the remaining life of a certain device is shorter than the average value, maintenance can be arranged in advance to avoid unplanned downtime;

[0059] 5. The present invention not only retains the mathematical rigor of the Wiener process but also improves the generalization ability through physical model constraints. The framework design enables the model structure to introduce more degradation mechanisms in addition to the existing physically considered degradation mechanisms. Only by adjusting the forms of the drift term and the diffusion term can new life predictions be made for devices, with strong scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is the flowchart of the method of the present invention;

[0061] Figure 2 is the schematic diagram of the fatigue crack growth data of the present invention;

[0062] Figure 3 is the schematic diagram of estimating the remaining life in an embodiment of the present invention;

[0063] Figure 4 is the three-dimensional schematic diagram of the comparison of the remaining life prediction effects in an embodiment of the present invention;

[0064] Figure 5 is the line graph schematic diagram of the comparison of the remaining life prediction effects in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0065] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0066] Embodiment 1

[0067] This embodiment aims to disclose a method for predicting the remaining useful life of a device based on a physical-data model. The method process is as Figure 1 shown, and the specific method steps are as follows.

[0068] S1. Obtain the device state observation values in real time, and construct a degradation model based on the physical degradation mechanism and the standard Wiener process model.

[0069] The physical degradation mechanism specifically refers to the performance degradation process caused by fatigue crack growth in the device. For example, in rotating machinery, under high-cycle loads, metal components will gradually fail due to fatigue crack growth.

[0070] Regarding the stochastic dynamics of degradation, there are random effects during the fatigue crack growth process, and these random effects always appear in the changes of model parameters. In addition, during the degradation process caused by fatigue cracks, there are also other secondary factors affecting the degradation process, such as component structure, assembly accuracy, and working environment. The degradation caused by these secondary factors is called the diffusion effect. The traditional Wiener process model cannot take into account these random and secondary factors, and the current applications based on the Paris formula generally ignore the random effects in fatigue crack growth and the diffusion effect caused by other secondary factors.

[0071] In this embodiment, the physical degradation mechanism includes crack growth and random effects. In step S1, the process of constructing the degradation model includes:

[0072] S101. Convert the physical degradation mechanism into a stochastic differential equation. The stochastic differential equation includes a drift term coefficient function and a diffusion term coefficient function. Among them, the drift term coefficient function is constructed based on the Paris formula, and the drift term coefficient function represents the deterministic trend of crack growth. The diffusion term coefficient function is constructed based on the standard Wiener process model, and the diffusion term coefficient function represents random effects such as environmental noise and measurement error;

[0073] S102. Use the device state observation values, the drift term coefficient function, and the diffusion term coefficient function to construct the degradation model.

[0074] The device state observation values are observable degradation quantities of the device, specifically including crack length, vibration amplitude, temperature change, environmental noise, and measurement error.

[0075] The expression of the drift term coefficient function is:

[0076]

[0077] where α is a random parameter, μ α is the mean of α, σ α is the standard deviation of the parameter α, b is a material-related constant, and x 1 (t) is the drift term coefficient function;

[0078] The expression of the diffusion term coefficient function is:

[0079] x 2 (t) = σB(τ),

[0080] where σ is the diffusion term coefficient, B(τ) is a standard Wiener process, and x 2 (t) is the diffusion term coefficient function;

[0081] The expression of the degradation model is:

[0082] x(t) = x k +x 1 (t)+x 2 (t),

[0083] where x(t) represents the state of the device at time t, and x k represents the state of the device at the initial time t k .

[0084] If only the Paris formula is used to construct the drift term coefficient function, the random effect will be ignored, and it is difficult to handle individual differences. If only the standard Wiener process model is used to construct the diffusion term coefficient function, it will lack physical interpretability and rely on a large amount of data. However, the combination of the two has both interpretability and adaptability, with high precision.

[0085] S2. Use the maximum likelihood estimation method combined with the nonlinear regression method to obtain the fixed parameters in the degradation model.

[0086] In step S2, the process of obtaining the fixed parameters b and σ in the degradation model includes:

[0087] S201. Use the Euler discretization method to discretize the degradation model, divide the continuous time into several time intervals, obtain the state quantity of the device in each time interval, and then obtain the expression of the state change quantity Δx n,k-1 ;

[0088] S202. According to the properties of the nonlinear Wiener process, make the state change quantity follow a multivariate normal distribution, and construct the log-likelihood function l(μ a , σ a , θ|x);

[0089] In S203, the parameters in the log-likelihood function are obtained by using the maximum likelihood estimation method and the non-linear regression method, and output as the fixed parameters in the degradation model.

[0090] The expression of the state change amount is:

[0091]

[0092] where, Δx n is the state change amount of the nth sample, and Δx n,k-1 is the state difference between the kth observation and the (k - 1)th observation in the nth degradation sample.

[0093] Δx n follows the multivariate normal distribution N(μ α T n , Σ n ).

[0094] In step S203, the process of obtaining the parameters in the log-likelihood function includes:

[0095] Obtain the standard Wiener process model and the historical degradation model;

[0096] Process the standard Wiener process model by the maximum likelihood estimation method to obtain the estimated value of the standard Wiener process model, and use the estimated value of the standard Wiener process model as the initial assignment of the first parameter in the log-likelihood function;

[0097] Process the historical degradation model by non-linear regression to obtain the estimated value of the historical degradation model, and use the estimated value of the historical degradation model as the initial assignment of the second parameter in the log-likelihood function;

[0098] Based on the initial assignments of the first parameter and the second parameter in the log-likelihood function, take the partial derivatives of the log-likelihood function respectively;

[0099] Substitute the partial derivative calculation results into the log-likelihood function to obtain the sectional log-likelihood function of the first parameter and the second parameter;

[0100] According to the sectional log-likelihood function of the first parameter and the second parameter, use the two-dimensional search function to obtain the parameters in the log-likelihood function.

[0101] The degradation model proposed in this embodiment is established based on the Wiener process model by introducing a trend term derived from the Paris formula. Therefore, in terms of the diffusion term coefficient function, it is considered that this model has the same degradation property as the basic Wiener process model X(t) = μt + σB(t), and the estimated value derived from the basic Wiener process model through the maximum likelihood estimation method can be expressed as the initial assignment of the first parameter (i.e., parameter b):

[0102]

[0103] where, Δx i is the state change vector of the i-th sample, and Δt i is the time interval, and Δt i = t i - t i-1 .

[0104] Similarly, the drift term coefficient function in the degradation model can be derived from the historical degradation model. For αexp(bt) in the historical degradation model with historical parameters, the estimated value can be obtained through nonlinear regression and used as the initial assignment of the second parameter (i.e., parameter σ).

[0105] The process of taking the partial derivative of the log-likelihood function is as follows:

[0106]

[0107] Let the above two partial derivatives be 0, and we can get:

[0108]

[0109] The state change amount follows a multivariate normal distribution, and the expression of the normal distribution is: N(μ α T n , Σ n ), where

[0110]

[0111]

[0112] T n,k-1 = Λ(x n,k-1 , t n,k-1 ; θ)Δt n,k-1 ,

[0113]

[0114] where, μ α is the mean of α, T n is the time-related matrix, is the time interval, Σ n is the covariance matrix, σ α is the standard deviation of the parameter α, Ω n is the diffusion term covariance matrix, Q n is the time accumulation matrix, is the variance coefficient of the Brownian motion, and Δx n,k-1is the difference between the k-th and (k - 1)-th observation points in the n-th degraded sample.

[0115] The sectional log-likelihood functions of the first parameter and the second parameter are as follows:

[0116]

[0117] Since the form of the log-likelihood function is complex, estimating all parameters at once will lead to inaccuracy and inefficiency. To make full use of historical information and provide accurate parameter estimation results, a two-step parameter estimation method is adopted as above to calculate the parameters.

[0118] S3. Obtain the device status observations in real time, and use the weight-optimized particle filter algorithm to update the random parameters in the degradation model.

[0119] In step S3, the process of using the weight-optimized particle filter algorithm (WOPF) to update the random parameters in the degradation model includes:

[0120] According to the initial random parameters in the degradation model, randomly select particles and assign uniform weights to the particles;

[0121] Perform particle initialization, particle state update, weight update, particle optimization, weight normalization, particle state estimation, and weight repair on the particles, and use the processed particles to update the random parameters in the degradation model.

[0122] When obtaining each new device status observation, repeat the above process of using the weight-optimized particle filter algorithm to update the random parameters in the degradation model, so that the updated degradation model can fully reflect the current degradation characteristics of the device.

[0123] Particle initialization: At time t 0 , randomly select Ns (Ns > N) particles according to the initial parameter values of the model, and assign weights w 0 = 1 / N.

[0124] Particle state update: Iteratively update the particle state:

[0125]

[0126] Weight update: Calculate the weights of N s particles:

[0127]

[0128] Particle optimization: Sort the N s particles, and select the first N particles according to the weight size.

[0129] Weight normalization: The optimized particle weights are normalized:

[0130]

[0131] Particle state estimation: Estimate the particle state:

[0132]

[0133] Weight repair: Restore the weights of N particles to the weights before normalization, and then normalize all N s particles as follows:

[0134]

[0135] Finally, use the processed particles to update the random parameters in the degradation model. Specifically, use the median of all particles as the particles finally used to update the model.

[0136] S4. Use the degradation model, the fixed parameters in the degradation model, and the random parameters in the degradation model to obtain the probability density function of the remaining life of the device under the random failure threshold, and perform numerical integration on the probability density function of the remaining life of the device to obtain the expected value of the remaining life of the device, which is output as the remaining life of the device.

[0137] According to the space-time transformation method, we can convert the problem of the non-linear Wiener process crossing the fixed failure threshold into the problem of the standard Brownian motion crossing the time-varying failure threshold, so as to obtain the analytical expression of the probability density function of the remaining life of the device.

[0138] The random failure threshold follows a truncated normal distribution, and the expression of the truncated normal distribution is:

[0139]

[0140] where ω is the random failure threshold, μ ω is the average failure threshold, is the threshold fluctuation variance, and TN represents the truncated normal distribution;

[0141] The probability density function of the remaining life of the device under the random failure threshold ω is:

[0142]

[0143] where f(l∣x k ) is the probability density function of the remaining life of the device under the random failure threshold, x k is the state of the device at the initial time t k , and l k is the remaining life of the device at the initial time t k .

[0144] The following is an example based on an actual application scenario:

[0145] Based on the fatigue crack growth data, the effectiveness of the invention in this embodiment is verified. The fatigue crack growth data set is as Figure 2 shown, which includes the crack size observation data of 21 alloy specimens. The initial crack length of each specimen is 0.9 inches. When the crack length exceeds 1.6 inches, the specimen is considered to have failed and the observation is stopped. At the beginning, the crack length is recorded every 0.01 million stress cycles. Finally, 12 specimens exceed the failure threshold. One of the failed specimens is selected as the test specimen for the subsequent remaining life prediction experiment, and the other 20 are training specimens.

[0146] 1. Establish a degradation model

[0147] According to the expansion characteristics of fatigue cracks, the following physical-data hybrid-driven Wiener process model is established to describe the expansion process of fatigue cracks.

[0148]

[0149] where is a random parameter; b is a fixed parameter; bexp(bτ) is the drift term coefficient function; σ is the diffusion term coefficient function.

[0150] 2. Parameter estimation

[0151] The degradation model is discretized by using the Euler discretization method. The state change amount Δx n,k-1 between two adjacent observation points can be expressed as:

[0152] Δx n,k-1 = x n,k - x n,k-1

[0153] = αbexp(bt n,k-1 )Δt n,k-1 + σB(Δt n,k-1 ),

[0154] In the formula, n = 1, 2, …, 20 is the number of alloy specimens; k = 1, 2, …, K n , where K n represents the number of observation points in the nth alloy specimen, and Δt n,k-1 = t n,k - t n,k-1 represents the time interval between two observation points.

[0155] Denote According to the properties of the nonlinear Wiener process, Δx n follows a multivariate normal distribution N(μα T n , Σ n ), where

[0156]

[0157]

[0158] In the formula, T n,k-1 = bexp(bt n,k-1 )Δt n,k-1 ;

[0159]

[0160] Then Δx n The log-likelihood function l(μ a , σ a , θ|x) can be expressed as:

[0161]

[0162] Since the form of the log-likelihood function is complex, estimating all parameters at once will lead to inaccuracy and inefficiency. To make full use of historical information and provide accurate parameter estimation results, a two-step parameter estimation method is adopted.

[0163] First, use the basic Wiener process model X(t) = μt + σB(t) and the exponential model αexp(bt) in the historical degradation model with historical parameters to fit the degradation observations, and obtain the initial assignments of parameters σ and b through maximum likelihood estimation and nonlinear regression respectively; then, given the initial assignments, use the maximum likelihood estimation method to estimate all parameters.

[0164] The estimated value of the basic Wiener process model obtained through MLE is expressed as the initial assignment of parameter b:

[0165]

[0166] where, Δt i = t i - t i-1 .

[0167] The estimated value obtained through nonlinear regression and use this as the initial assignment of σ:

[0168]

[0169] Based on the above initial assignments Take the partial derivatives of the likelihood function respectively:

[0170]

[0171]

[0172] Let the above two partial derivatives be 0, and we can obtain:

[0173]

[0174] Substitute into the log-likelihood function lnL(μ α , σ α , θ|x), and the sectional log-likelihood functions of the parameters σ and b are as follows:

[0175]

[0176] Then use the two-dimensional search function to find the coefficients, and the parameters σ and b can be obtained.

[0177] Random parameter update:

[0178] Aiming at the problems of particle degeneracy and sample impoverishment that may exist in traditional particle filtering, the weighted-optimized particle filter (WOPF) algorithm is adopted to alleviate the above problems, thereby improving the accuracy of model parameter estimation. The specific implementation steps of the WOPF algorithm are as follows:

[0179] Step 1: Particle initialization. At time t 0 , randomly select 26 particles according to the initial parameter values of the model and assign weights

[0180] Step 2: Particle state update, iteratively update the particle state:

[0181]

[0182] Step 3: Weight update, calculate the weights of N s particles:

[0183]

[0184] Step 4: Particle optimization, sort the N s particles and select the top N particles according to the weight size.

[0185] Step 5: Weight normalization, normalize the weights of the optimized particles:

[0186]

[0187] Step 6: Particle state estimation, estimate the particle state:

[0188]

[0189] Step 7: Weight repair. Restore the weights of the 20 particles to their values before normalization, and then normalize all 26 particles as follows:

[0190]

[0191] Step 8: When obtaining each new device status observation, return to Step 2 to update the unit difference parameter so that the updated model can fully reflect the current degradation characteristics of the device.

[0192] 3. Estimation of the remaining useful life of the device

[0193] The specific content of the remaining useful life estimation includes:

[0194] The remaining useful life is defined as the time when the state degradation of the device first exceeds the failure threshold, also known as the first arrival time. According to the definition of the first arrival time, the remaining useful life of the device at time t k is expressed as:

[0195] l k =inf{l:x(t k +l)≥ω|x k <ω},

[0196] where l k represents the remaining useful life of the device at time t k , inf{·} represents the lower bound of a variable, and ω represents the failure threshold.

[0197] For the degradation model, under a fixed failure threshold ω, the probability density function of the remaining useful life can be expressed as:

[0198]

[0199] where

[0200] Assume that the random failure threshold follows a normal distribution Considering the condition that the random failure threshold is greater than 0, the part with a probability less than 0 is truncated, that is Then the probability density function of the remaining useful life of ω can be expressed as:

[0201]

[0202] Taking the test specimen as an example, let μ ω =1.56,

[0203] Based on the expression of the probability density function of the remaining useful life at a fixed failure threshold ω, according to the total probability formula, it can be known that:

[0204]

[0205] This formula is the probability density function of the remaining life of the device in the degradation model with a random failure threshold ω. For a known probability density function, the scipy.integrate.quad function can be used in Python to obtain the expected value through numerical integration. The expected value is the remaining useful life of the device calculated based on the above degradation model.

[0206] As Figure 3 shown are the probability density function and expectation of the remaining life prediction of the test specimen. It can be seen that the present invention can accurately predict the remaining life of the specimen.

[0207] To verify the superiority of the present invention in establishing the degradation model, two models with the drift term of the linear coefficient and the drift term derived based on the Paris formula are compared under the same diffusion term. The probability density functions and the expectations of the remaining useful life of the two methods are respectively as Figure 4 、 5 shown. It can be seen that as time goes by, the probability density function of the remaining useful life predicted by the model proposed by the present invention has obvious superiority over that of the linear coefficient, and the expectation of the remaining useful life is closer to the true value.

[0208] Embodiment 2

[0209] Based on Embodiment 1, this embodiment provides an electronic device, including: one or more processors and a memory. The memory stores one or more programs, and the one or more programs include instructions for executing the method for predicting the remaining life of the device based on the physical-data model as described above.

[0210] At the hardware level, the electronic device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for other services. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the method for predicting the remaining life of the device based on the physical-data model as described above. Of course, in addition to the software implementation method, the present invention does not exclude other implementation methods, such as logic devices or a combination of software and hardware. That is to say, the execution subject of the following processing flow is not limited to each logic unit, and can also be hardware or logic devices.

[0211] The memory may include non-permanent memory in the form of computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. The memory is an example of computer-readable media.

[0212] Computer-readable media includes both permanent and non-permanent, removable and non-removable media and can store information by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile discs (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transitory media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media, such as modulated data signals and carrier waves.

[0213] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for predicting the remaining life of equipment based on a physical-data model, characterized in that: The method comprises: Step S1, constructing a degradation model based on the physical degradation mechanism and the standard Wiener process model; Step S2, using a maximum likelihood estimation method combined with a nonlinear regression method to obtain fixed parameters in the degradation model; Step S3, obtaining device state observation values ​​in real time, and updating random parameters in the degradation model using a weight-optimized particle filter algorithm; Step S4, using the degradation model, the fixed parameters in the degradation model and the random parameters in the degradation model, obtain the probability density function of the remaining life of the equipment under the random failure threshold, and numerically integrate the probability density function of the remaining life of the equipment to obtain the expected value of the remaining life of the equipment as the output of the remaining life of the equipment.

2. The method for predicting the remaining life of equipment based on a physical-data model according to claim 1, characterized in that: The physical degradation mechanism includes crack extension and random effects. In step S1, the process of constructing the degradation model includes: Step S101, converting the physical degradation mechanism into a stochastic differential equation, wherein the stochastic differential equation includes a drift term coefficient function and a diffusion term coefficient function, wherein the drift term coefficient function is constructed based on the Paris formula, and the diffusion term coefficient function is constructed based on a standard Wiener process model; Step S102, constructing the degradation model using the device state observation value, the drift term coefficient function and the diffusion term coefficient function; The device state observation value is the observable degradation amount of the device, including crack length, vibration amplitude, temperature change, environmental noise and measurement error.

3. The method for predicting the remaining life of equipment based on a physical-data model according to claim 2, characterized in that: The expression of the drift term coefficient function is: x1(t)=αexp(b·t), Among them, α is a random parameter, μ α is the mean of α, σ α is the standard deviation of parameter α, b is the material related constant, and x1(t) is the drift term coefficient function; The expression of the diffusion term coefficient function is: x2(t)=σB(τ), Among them, σ is the diffusion term coefficient, B(τ) is the standard Wiener motion process, and x2(t) is the diffusion term coefficient function; The expression of the degradation model is: x(t)=x k +x1(t)+x2(t), Among them, x(t) represents the device status at time t, x k Indicates that the device is at the initial time t k The state when.

4. The method for predicting the remaining life of equipment based on a physical-data model according to claim 1, characterized in that: In step S2, the process of obtaining fixed parameters in the degradation model includes: Step S201, discretizing the degradation model using the Euler discretization method to obtain an expression of the state change amount; Step S202, according to the properties of the nonlinear Wiener process, the state change quantity is made to obey the multivariate normal distribution, and a log-likelihood function of the state change quantity is constructed; Step S203, using a maximum likelihood estimation method and a nonlinear regression method to obtain parameters in the log-likelihood function, and outputting them as fixed parameters in the degradation model.

5. The method for predicting the remaining life of equipment based on a physical-data model according to claim 4, characterized in that: The expression of the state change is: Where Δx n is the state change of the nth sample, Δx n,k-1 is the state difference between the kth observation and the k-1th observation in the nth degradation sample.

6. The method for predicting the remaining life of equipment based on a physical-data model according to claim 4, characterized in that: In step S203, the process of obtaining the parameters in the log-likelihood function includes: Obtain standard Wiener process models and historical degradation models; Processing the standard Wiener process model by the maximum likelihood estimation method to obtain an estimated value of the standard Wiener process model, and using the estimated value of the standard Wiener process model as an initial value of the first parameter in the log-likelihood function; Processing the historical degradation model through nonlinear regression to obtain an estimated value of the historical degradation model, and using the estimated value of the historical degradation model as an initial value of the second parameter in the log-likelihood function; Based on the initial values ​​of the first parameter and the second parameter in the log-likelihood function, respectively calculating partial derivatives of the log-likelihood function; Substituting the partial derivative calculation result into the log-likelihood function to obtain the profile log-likelihood function of the first parameter and the second parameter; According to the profile logarithmic likelihood function of the first parameter and the second parameter, a two-dimensional search function is used to obtain parameters in the logarithmic likelihood function.

7. The method for predicting the remaining life of equipment based on a physical-data model according to claim 4, characterized in that: The state variation obeys multivariate normal distribution, and the expression of the normal distribution is: N(μ α T n ,S n ), among them, T n,k-1 =Λ(x n,k-1 ,t n,k-1 ;θ)Δt n,k-1 , Among them, μ α is the mean value of α, T n is the time correlation matrix, is the time interval, Σ n is the covariance matrix, σ α is the standard deviation of parameter α, Ω n is the diffusion term covariance matrix, Q n is the time accumulation matrix, is the variance coefficient of Brownian motion, Δx n,k-1 is the difference between the kth and k-1th observation points in the nth degraded sample.

8. The method for predicting the remaining life of equipment based on a physical-data model according to claim 1, characterized in that: In step S3, the process of updating the random parameters in the degradation model using the weight-optimized particle filter algorithm includes: According to the initial random parameters in the degradation model, randomly select particles and assign uniform weights to the particles; The particles are initialized, their states are updated, their weights are updated, their optimization is performed, their weights are normalized, their states are estimated, and their weights are repaired. The random parameters in the degradation model are updated using the processed particles.

9. The method for predicting the remaining life of equipment based on a physical-data model according to claim 8, characterized in that: When each new device state observation value is obtained, the process of updating the random parameters in the degradation model by the weight-optimized particle filter algorithm is repeated, so that the updated degradation model can fully reflect the current degradation characteristics of the device.

10. The method for predicting the remaining life of equipment based on a physical-data model according to claim 1, characterized in that: The random failure threshold obeys a truncated normal distribution, and the expression of the truncated normal distribution is: Where ω is the random failure threshold, μ ω is the average failure threshold, is the threshold fluctuation variance, TN represents the truncated normal distribution; The probability density function of the remaining life of the equipment under the random failure threshold is: Among them, f(l|x k ) is the probability density function of the remaining life of the equipment under the random failure threshold, x k is the device at the initial time t k The state at that time, k is the device at the initial time t k remaining life.

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