A method for predicting the remaining useful life of an electronic system

Abstract

The invention discloses a method for predicting the remaining useful life of an electronic system, which relates to the field of electronic system reliability and remaining useful life prediction. In order to enhance the effect of the filtering model and minimize the additional computational burden as much as possible, the invention adopts a probability density function with multiple parameters as the state space equation in the particle filter, and optimizes the function with the measured data. The optimization of the state space equation is beneficial to the faster convergence of the filter, and thus more accurate prediction of the system state.

Description

Technical Field

[0001] The present invention relates to the field of reliability and remaining useful life prediction of electronic systems. Background Art

[0002] With the increasingly wide application of electronic systems in various military and civilian equipment, such as aerospace applications, electric vehicles, etc., their reliability has attracted more and more attention. The electronic systems of equipment generally include control systems, communication systems, storage systems, energy storage systems, etc. In order to ensure the safety and reliability of each system, it is very important to manage the health state of the electronic system. Especially in application scenarios where intrusive testing and offline testing are not easy to perform, predicting and warning based on the state monitoring data of the current working conditions of the system that can be obtained is still one of the challenges faced by electronic systems.

[0003] Generally, the remaining useful life (RUL) can indicate the degradation (aging) state of an electronic system and is an important indicator for reliability judgment or warning. However, modern electronic systems often have time-varying, dynamic, and non-linear characteristics. The change in reliability is not only related to the materials and working mechanisms of the circuit system but also related to uncertain environmental and load conditions. Therefore, how to accurately predict the RUL of an electronic system has become a particularly challenging task and research hotspot.

[0004] Currently, the methods for predicting the life of electronic systems include the following three categories: model-based, data-driven, and hybrid methods.

[0005] The model-based analysis method is generally based on the physical mechanism of the electronic system. It often establishes a mathematical model based on historical data, constructs a suitable filtering algorithm, and uses the selected model and filter to predict the RUL. This is essentially a model parameter estimation process [3] , which adopts mechanical models, equivalent circuit models, empirical models, and fusion models based on the first three models. Kalman Filters (KFs), Particle Filters (PFs), and their optimizations are commonly used filters in model-based methods. To improve the filters, some studies have tried to improve the KFs for non-linear models, such as the unscented KF; some work has tried to enhance the PFs, for example, using the artificial fish swarm algorithm and combining SVR with PFs. However, many attempts to improve the PFs have focused on the resampling process to avoid sample degradation and sample impoverishment. However, initialization is also important for PFs. Inappropriate initialization may slow down the prediction speed or reduce the accuracy, and even cause divergence. Obviously, expert experience is crucial for establishing an accurate model. Since the degradation of electronic systems is a dynamic non-linear process, researchers usually have to make a trade-off between prediction accuracy and model complexity.

[0006] On the other hand, data-driven methods usually utilize the acquired data and use statistical theories or machine learning algorithms to build prediction models. This method has received increasing attention due to the fact that it does not require exploring specific physical mechanisms, the progress of machine learning algorithms in recent years, and the enhancement of the computing power of computing devices. Commonly used data-driven prediction methods can be divided into three categories: artificial intelligence methods, statistical analysis methods, and signal processing methods. Artificial intelligence methods usually adopt the Naive Bayes model, Support Vector Regression (SVR), Relevance Vector Machine, Gaussian Process Regression, artificial neural network, and neuro-fuzzy model. Statistical methods usually use Autoregressive Integrated Moving Average, Grey Model, Wiener process, and entropy analysis. Discrete wavelet transform and others in signal processing methods can also be applied to RUL prediction. Compared with model-based methods, data-driven methods are more flexible. However, it should be noted that training a data-driven predictor requires a large amount of training data, and some algorithms are sensitive to data quality. At the same time, since a large amount of data is required for training, and the degradation data of electronic devices needs to accelerate the aging of electronic devices to obtain, the cost of obtaining a large amount of degradation data is very high, and it is impossible to conduct a large number of repeated aging experiments on electronic devices used in some scenarios, such as aerospace working equipment. Therefore, the practicality of data-driven methods is greatly limited.

[0007] Recently, hybrid methods have attempted to combine the advantages of model-based and data-driven methods. For example, model-based methods have less data requirements and stronger robustness, while data-driven methods have higher flexibility. For example, Xue Z, Zhang Y, Cheng C, et al. Remaining Useful Life Prediction of Lithium-ion Batteries with Adaptive Unscented Kalman Filter and Optimized Support Vector Regression[J]. Neurocomputing, 2019, 376. Therefore, more and more researchers are focusing on the research of hybrid methods. Hybrid methods usually integrate different methods to improve filters, generate more future observation data for long-term prediction, and process raw data. However, hybrid methods are often relatively complex, with a large amount of computation and high algorithm complexity. Summary of the Invention

[0008] In order to enhance the effect of the model method and minimize the additional computational burden, the present invention adopts a prediction method that combines data-driven and physical model methods. The probability density function with multiple parameters is used in the particle filter (PF) as the state space equation, and the function is optimized using the measured data. The optimization of the state space equation is conducive to faster convergence of the filter, thereby more accurately predicting the system state.

[0009] The present invention combines the data-driven method with the model-driven method. Existing studies have shown that the exponential model is used to describe the reliability degradation of electronic systems. However, because the ordinary exponential function does not include parameters that can be driven by historical data (measured data), it is difficult to obtain more sufficient prior information through historical data, and then it is difficult to adjust the prediction model according to different systems. The present invention will use the generalized exponential distribution as the state space equation of the particle filter. The parameters in the generalized exponential function can be adjusted by historical data, and the prior information is transmitted to the filter through the change of the parameters. At the same time, since the degradation of electronic equipment is a typical time-varying, dynamic, and nonlinear problem, PF is very suitable for dealing with nonlinear problems of non-Gaussian noise. Using PF to predict the RUL of electronic equipment is equivalent to tracking a dynamic target. Therefore, this patent uses a generalized exponential distribution with prior information as the state space equation of PF to predict RUL.

[0010] The technical solution of the present invention is a method for predicting the remaining life of an electronic system, the method comprising:

[0011] Step 1: Obtain historical data of the electronic system;

[0012] Step 2: Establish the generalized exponential function and its parameter estimation;

[0013] For a random variable X, if its distribution is as in Formula 1, then X is said to have a generalized exponential distribution, expressed as X~GE(α,λ,μ):

[0014] F(x;α,λ,μ)=(1-e -(x-μ) / λ ) α (1)

[0015] The corresponding probability density function is:

[0016]

[0017] Where x is a sample, α is a shape parameter, λ is a scale parameter, and μ is a location parameter; x>μ, α>0, λ>0;

[0018] Let X~GE, {x1,x2,...,x i ,...,x n} is a sample of X;

[0019] First, according to Equation 2, the log-likelihood function L is established as Equation 3:

[0020]

[0021] where β = 1 / λ, take the partial derivative of L:

[0022]

[0023]

[0024]

[0025] Solve the system of equations Equation 5, and the estimated results of α and β are:

[0026]

[0027] Step 3: Establish the particle filter model

[0028] Adopt the following state-space model to simulate the degradation process of the electronic system:

[0029]

[0030] where, x k is the actual capacity of the electronic system at the k-th cycle, y k is the predicted capacity of the electronic system at the k-th cycle, w k-1 is the environmental interference, v k is the measurement noise;

[0031] Q(x k ) represents the state of the electronic system. The parameters of the current generalized exponential function are determined from historical data using maximum likelihood estimation, and the particle filter is applied to update the parameters and predict the remaining life of the electronic system.

[0032] The main contributions of the present invention are as follows:

[0033] ① The acquisition of the required prior data is simple, the amount of data required is small, and the computational complexity of parameter estimation is low. Historical test data is an important source of prior information. This method only requires common state monitoring data, such as the number of battery cycles and the corresponding battery capacity, and obtains the information hidden in the prior data through parameter estimation methods. Compared with machine learning methods, it will not increase too much computational burden and does not require a large amount of data, especially suitable for scenarios without a large amount of historical data.

[0034] ② The use of the generalized exponential can effectively transmit prior information into the filtering model. In this method, the generalized exponential function is used as the state space equation of the particle filtering model. This exponential distribution contains three parameters. Based on historical data, these three parameters are estimated through the described parameter estimation method, which can transmit more prior information into the filtering model.

[0035] The results show that by using the particle filter based on the generalized exponential function, this method can effectively improve the prediction accuracy without the need for a large amount of training data. Description of the Drawings

[0036] Figure 1 is the battery capacity curve;

[0037] Figure 2 is the estimated curve of the battery RUL: where (a) is the estimated curve of the RUL of battery 005 using the particle filter with the traditional exponential distribution, (b) is the estimated curve of the RUL of battery 005 using the GE particle filter, (c) is the estimated curve of the RUL of battery 006 using the GE particle filter, and (d) is the estimated curve of the RUL of battery 018 using the GE particle filter. Detailed Implementation Manner

[0038] Currently, lithium batteries have been widely used in portable electronic devices and are increasingly used in electric vehicles and aerospace equipment. At the same time, lithium batteries are complex electrochemical systems with very typical time-varying, dynamic, and nonlinear characteristics, and their lifespan is not only related to their own materials and principles but also closely related to the usage environment and load. Without loss of generality, taking the estimation of the RUL of lithium batteries as an example, the detailed implementation manner of the proposed model is described.

[0039] The estimation process is a process of continuously approaching the actual value, and filtering is a method of approaching the true value. As a filter, the particle filter (PF) has the following characteristics: (1) Compared with the Kalman filter (KFs), the PF does not need to know the type of noise, that is, the PF can be used for tasks with non-Gaussian noise; (2) The PF can handle linear and nonlinear problems; (3) Theoretically, compared with the extended KF and the unscented KF, the PF has higher accuracy. Therefore, the PF is adopted as the estimation model of this method.

[0040] Next, consider the influence of prior information on the model. Obviously, by obtaining more prior information, a more appropriate prior probability density function (PDF) can be obtained, which means having a better starting point and being closer to the actual situation. Therefore, using a more accurate prior PDF usually means better estimation results or a faster estimation speed.

[0041] The RUL of a lithium battery is defined as the remaining number of charge and discharge cycles before the failure threshold, and its trend can be described by an exponential model. However, to obtain more accurate tracking results, more prior information needs to be introduced. Therefore, a parametric exponential function is considered, and the prior information is passed into the estimation model through the parameters. Existing research has shown that the Generalized Exponential (GE) function has strong fitting ability. Compared with the traditional exponential function, it has more parameters. By using historical data to estimate the parameters of GE, GE can mine and carry more prior information.

[0042] The main implementation steps of the proposed method include: (1) estimating the parameters of GE using historical data, so as to obtain hidden information from historical data, which is the prior information for RUL estimation; (2) bringing the prior information into the prediction by using the GE function as the PF observation equation with estimated parameters; (3) using PF to estimate the number of failure cycles (life) of the lithium battery, and the RUL is the difference between the estimated number of failure cycles and the current number of cycles.

[0043] 1) GE Function and Its Parameter Estimation

[0044] For a random variable X, if its distribution is (1), then X is said to have a generalized exponential distribution, denoted as X ∼ GE(α, λ, μ):

[0045] F(x; α, λ, μ) = (1 - e -(x-μ) / λ ) α (1)

[0046] The corresponding Probability Density Function (PDF) is:

[0047]

[0048] where α is the shape parameter, λ is the scale parameter, μ is the location parameter; x > μ, α > 0, λ > 0

[0049] This method uses Maximum Likelihood Estimation (MLE) to estimate the parameters of GE. Assume X ∼ GE, {x1, x2, …, x i , …, x n} is the sample of X.

[0050] First, according to (2), the log-likelihood function L is established as (3):

[0051]

[0052] where β is 1 / λ. Take the partial derivative of L:

[0053]

[0054]

[0055]

[0056] Since μ is a location parameter and in the RUL estimation, the cycle always ranges from 0 to a finite integer, without loss of generality, μ can be assumed to be 0.

[0057] Solving the system of equations (6), the estimation results of α and β can be obtained as:

[0058]

[0059] 2) Particle filter model establishment

[0060] The system degradation process can be simulated by the following state-space model:

[0061]

[0062] where, x k is the actual capacity at the k-th cycle, y k is the predicted capacity at the k-th cycle, w k-1 is the environmental interference, and v k is the measurement noise.

[0063] Therefore, in this method, GE is used to describe the state in Q(x k ), the parameters of GE are determined from historical data using MLE, and PF is applied to update the parameters and predict the RUL.

[0064] 3) Experimental verification

[0065] RUL estimation experiments were conducted. The experimental data were from the NASA Prognostics Center of Excellence (PCoE) dataset repository, and the data of three batteries (005, 006, 018) were used. These batteries are of the same type with a rated capacity of 2 Ah. When the battery capacity drops to 70% (from about 2 Ah to 1.4 Ah), it is regarded as a failure. The measured capacity curves of the three batteries are as Figure 1 shown. From Figure 1 it can be known the battery capacity corresponding to each cycle of the battery, and it can be seen that as the number of cycles increases, the battery capacity gradually decreases. From Figure 1It can be seen that Battery 005 fails at the 124th cycle, and the capacity drops to 1.4012 Ah at this time; Battery 006 fails at the 108th cycle, and the capacity drops to 1.4049 Ah at this time; Battery 018 fails at the 96th cycle, and the corresponding battery capacity is 1.4085 Ah.

[0066] As described in the model description, this method uses the GE as Q(x k ) to describe the state of the battery in the model; at the same time, for comparison, the traditional exponential distribution function is also used as Q(x k ) in the experiment and the prediction effects are compared. Among them, Figure 2 (a) The thin solid line is the measured data of the battery, and the dotted line is the mean value of the output of the particle filter obtained by using the exponential function as the observation function. This method uses this as the prediction data; Figure 2 (b)-(d) The thin solid line is the measured data of the battery, and the thick dotted line is the mean value of the output of the particle filter obtained by using the GE as the observation function (prediction data).

[0067] To verify the effectiveness of the model, the error of the RUL estimation is defined as:

[0068] e RUL = RUL est - RUL true .

[0069] Where RUL est is the estimated number of failure cycles, and RUL true is the actual number of failure cycles.

[0070] From Figure 2 (b), it can be seen that for Battery 005, the estimated failure point is the 123rd cycle; from Figure 1 it can be obtained that the actual failure period is 124. Therefore, the error of the life estimation is:

[0071] e RUL = RUL est - RUL true = 123 - 124 = -1

[0072] According to the experimental results, when using the exponential function as the observation function for estimation, the number of failure cycles is 134 and the error is 10 cycles. In contrast, when using the GE, the error is reduced by 9 cycles.

[0073] Similarly, the predicted failure points, errors, and effect evaluations obtained by using the exponential function and the GE as the observation functions for other batteries can be calculated, as shown in Table 1.

[0074] Table 1 RUL prediction results of lithium batteries using different historical data

[0075]

[0076]

[0077] In Figure 2 (b)-(d), 100, 80, and 60 historical data are used respectively to estimate the failure cycle numbers of the corresponding batteries (Battery 005, Battery 006, and Battery 018), accounting for 59.5%, 47.6%, and 45.5% of the total test data of the battery respectively, and accounting for 80.64%, 74.07%, and 62.50% of the actual life (the cycle number at actual failure) respectively. As can be seen from Table 1, the corresponding prediction errors are -1 cycle, 5 cycles, and -3 cycles respectively (the relative error with respect to the actual life is -0.8%, 4.6%, and -3.1%). It can be seen that even with less data, a good estimation effect can be obtained.

[0078] In addition, from Figure 2 it is not difficult to find that the proposed model can not only predict the remaining life, but also predict the battery capacity corresponding to failure. For example, from Figure 2 (b), it can be seen that the proposed model predicts failure at the 123rd cycle, and the battery capacity corresponding to this cycle is 1.3998 Ah.

[0079] Embodiment 2

[0080] The present invention can also be used for calculating the remaining life of a chip. The chip error frequency is a characteristic of the life. When the number of errors in 5 hours is 1 time, the chip is considered to fail. The main implementation steps include: (1) estimating the parameters of GE using the historical data of the same type of chip, obtaining the hidden information from the historical data, and obtaining the prior information for RUL estimation; (2) substituting the prior information into the prediction by using the GE function as the PF observation equation with the estimated parameters; (3) using PF to estimate the failure cycle number (life) of the chip, and RUL is the difference between the estimated failure cycle number and the current cycle number.

[0081] Adopting the same method, the life of a computer motherboard can also be calculated, taking the data exchange success rate between motherboards as the life characteristic.

Claims

1. A method for predicting the remaining useful life of an electronic system, the method comprising: Step 1: Obtain the historical data of the electronic system; Step 2: Establish the generalized exponential function GE and its parameter estimation; For a random variable X, if its distribution is Formula 1, then X is said to have a generalized exponential distribution, denoted as X ∼ GE(α, λ, μ): F(x;α,λ,μ)=(1 - e -(x-μ) / λ ) α (1) The corresponding probability density function is: where x is the sample, α is the shape parameter, λ is the scale parameter, μ is the location parameter; x > μ, α > 0, λ > 0; Let \(X\sim GE\), \(\{x_1,x_2,\cdots,x i ,\cdots,x n \}\) be a sample of \(X\); First, according to Formula 2, establish the log-likelihood function L as Formula 3: where β = 1 / λ, take the partial derivative of L: Solve the system of equations Formula 5 to obtain the estimation results of α and β as: Step 3: Establish a particle filter model; Use the following state space model to simulate the degradation process of the electronic system: where x k is the actual capacity of the k-th cycle of the electronic system, y k is the predicted capacity of the k-th cycle of the electronic system, w k-1 is the environmental interference, v k is the measurement noise; Q(x k ) represents the state of the electronic system. The parameters of the current Generalized Exponential (GE) function are determined from historical data using maximum likelihood estimation, and a particle filter is applied to update the parameters and predict the remaining life of the electronic system.

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