Remaining useful life prediction of lithium-ion battery using an improved UPF method based on MCMC

Lithium-ion batteries are widely used as power sources in various portable electronics, hybrid electric vehicles, aeronautic and aerospace engineering, etc. To ensure an uninterruptible power supply, the remaining useful life (RUL) prediction of lithium-ion batteries has attracted extensive attention in recent years. This paper proposed an improved unscented particle filter (IUPF) method for lithium-ion battery RUL prediction based on Markov chain Monte Carlo (MCMC). The method uses the MCMC to solve the problem of sample impoverishment in UPF algorithm. Additionally, the IUPF method is proposed on the basis of UPF, so it can also suppress the particle degradation existing in the standard PF algorithm. In this work, the IUPF method is introduced firstly. Then, the capacity data of lithium-ion batteries are collected and the empirical capacity degradation model is established. The proposed method is used to estimate the RUL of lithium-ion battery. The RUL prediction results demonstrate the effectiveness and advantage.     

Prognostics of Lithium-ion batteries based on state space modeling with heterogeneous noise variances

Prognostics and health management of lithium-ion batteries, especially their remaining useful life (RUL) prediction, has attracted much attention in recent years because accurate battery RUL prediction is beneficial to ensuring high reliability of lithium-ion batteries for providing power sources for many electronic products. In the common state space modeling of battery RUL prediction, noise variances are usually assumed to be fixed. However, noise variances have great influence on state space modeling. If noise variances are too small, it takes long time for initial guess states to approach true states, and thus estimated states and measurements are biased. If noise variances are too large, state space modeling based filtering will suffer divergence. Besides, even though a same type of lithium-ion batteries are investigated, their degradation paths vary quite differently in practice due to unit-to-unit variation, ambient temperature and other working conditions. Consequently, heterogeneity of noise variances should be taken into consideration in state space modeling so as to improve RUL prediction accuracy. More importantly, noise variances should be posteriorly updated by using up-to-date battery capacity degradation measurements. In this paper, an efficient prognostic method for battery RUL prediction is proposed based on state space modeling with heterogeneity of noise variances. 26 lithium-ion batteries degradation data are used to illustrate how the proposed prognostic method works. Some comparisons with other common prognostic methods are conducted to show the superiority of the proposed prognostic method.     

Data-driven hybrid remaining useful life estimation approach for spacecraft lithium-ion battery

Electrical power system (EPS) is one of the most critical sub-systems of the spacecraft. Lithium-ion battery is the vital component is the EPS. Remaining useful life (RUL) prediction is an effective mean to evaluate the battery reliability. Autoregressive model (AR) and particle filter (PF) are two traditional approaches in battery prognosis. However, the parameters in a trained AR model cannot be updated which will cause the under-fitting in the long term prediction and further decrease the RUL prediction accuracy. On the other hand, the measurement function in the PF algorithm cannot be obtained in the long term prediction process. To address these two challenges, a hybrid method of IND-AR model and PF algorithm are proposed in this work. Compared with basic AR model, a nonlinear degradation factor and an iterative parameter updating method are utilized to improve the long term prediction performance. The capacity prediction results are applied as the measurement function for the PF algorithm. The nonlinear degradation factor can make the linear AR model suitable for nonlinear degradation estimation. And once the capacity is predicted, the state-space model in the PF is activated to obtain an optimized result. Optimized capacity prediction result of each cycle is utilized to re-train the regression model and update the parameters. The predictor keeps working iteratively until the capacity hit the failure threshold to calculate the RUL value. The uncertainty involved in the RUL prediction result is presented by PF algorithm as well. Experiments are conducted based on commercial lithium-ion batteries and real-applied satellite lithium-ion batteries. The results have high accuracy in capacity fade prediction and RUL prediction of the proposed method. The real applied lithium-ion battery can meet the requirement of spacecraft. All the experiments results show great potential of the proposed framework.     

Interacting multiple model particle filter for prognostics of lithium-ion batteries

We propose a new data-driven prognostic method based on the interacting multiple model particle filter (IMMPF) for determining the remaining useful life (RUL) of lithium-ion (Li-ion) batteries and the probability distribution function (PDF) of the associated uncertainty. The method applies the IMMPF to different state equations. Modeling the battery capacity degradation is very important for predicting the RUL of Li-ion batteries. In this study, improvements are made on various Li-ion battery capacity models (i.e., polynomial, exponential, and Verhulst models). Further, three different one-step state transition equations are developed, and the IMMPF method is applied to estimate the RUL of Li-ion batteries with the use of the three improved models. The PDF of the predicted RUL is obtained by combining the PDFs obtained with each individual model. We conduct four case studies to validate the proposed method. The results are as follows: (1) the three improved models require fewer parameters than the original models, (2) the proposed prognostic method shows stable and high prediction accuracy, and (3) the proposed method narrows the uncertainty PDF of the predicted RUL of Li-ion batteries.     

Lithium-ion batteries remaining useful life prediction based on a mixture of empirical mode decomposition and ARIMA model

Prediction of lithium-ion batteries remaining useful life (RUL) plays an important role in battery management system (BMS) used in electric vehicles. A novel approach which combines empirical mode decomposition (EMD) and autoregressive integrated moving average (ARIMA) model is proposed for RUL prognostic in this paper. At first, EMD is utilized to decouple global deterioration trend and capacity regeneration from state-of-health (SOH) time series, which are then used in ARIMA model to predict the global deterioration trend and capacity regeneration, respectively. Next, all the separate prediction results are added up to obtain a comprehensive SOH prediction from which the RUL is acquired. The proposed method is validated through lithium-ion batteries aging test data. By comparison with relevance vector machine, monotonic echo sate networks and ARIMA methods, EMD-ARIMA approach gives a more satisfying and accurate prediction result.     

Prognostics of Li(NiMnCo)O2-based lithium-ion batteries using a novel battery degradation model

Some lithium-ion battery materials show two-phase degradation behavior with evident inflection points, such as lithium nickel manganese cobalt oxide (Li(NiMnCo)O₂ or NMC) cells. A model-based Bayesian approach is proposed in this paper to predict remaining useful life (RUL) for these types of batteries. First, a two-term logarithmic model is developed to capture the degradation trends of NMC batteries. By fitting the battery degradation data, it is experimentally demonstrated that the developed model is superior to existing empirical battery degradation models. A particle filtering–based prognostic method is then incorporated into the model to estimate the batteries' possible degradation trajectories. Correspondingly, the RUL values of NMC batteries are expressed in terms of probability density function. The effectiveness of the developed method is verified with our collected experimental data. The results indicate that the proposed prognostic method can achieve higher predictive accuracy than the existing two-term exponential model.     

An improved unscented particle filter approach for lithium-ion battery remaining useful life prediction

Lithium-ion rechargeable batteries are widely used as power sources for mobile phones, laptops and electric cars, and gradually extended to military communication, navigation, aviation, aerospace and other fields. Accurate remaining useful life (RUL) prediction of lithium-ion battery plays an important role in avoiding serious security and economic consequences caused by failure to supply required power levels. Thus, the RUL prediction for lithium-ion battery has become a critical task in engineering practices. With its superiority in handling nonlinear and non-Gaussian system behaviors, the particle filtering (PF) technique is widely used in the remaining life prediction. However, the choice of importance function and the degradation of diversity in sampling particles limit the estimation accuracy. This paper presents an improved PF algorithm, that is, the unscented particle filter (UPF) based on linear optimizing combination resampling (U-LOCR-PF) to improve the prediction accuracy. In one aspect, the unscented Kalman filter (UKF) is used to generate a proposal distribution as an importance function for particle filtering. In the other aspect, the linear optimizing combination resampling (LOCR) algorithm is used to overcome the particle diversity deficiency. It should be noted that the step coefficient K can affect the performance of LOCR algorithm, and the fuzzy inference system is applied to determine the value of step coefficient K. According to the analysis results, it can be seen that the proposed prognostic method shows higher accuracy in the RUL prediction of lithium-ion battery, compared with the existing PF-based and UPF-based prognostic methods.     

Multi-Scale Prediction of RUL and SOH for Lithium-Ion Batteries Based on WNN-UPF Combined Model

The prediction of Remaining useful life (RUL) and the estimation of State of health (SOH) are extremely important issues for operating performance of Lithium-ion (Li-ion) batteries in the Battery management system (BMS). A multi-scale prediction approach of RUL and SOH is presented, which combines Wavelet neural network (WNN) with Unscented particle filter (UPF) model. The capacity degradation data of Li-ion batteries are decomposed into the low-frequency degradation trend and high-frequency fluctuation components by Discrete wavelet transform (DWT). Based on the WNN-UPF model, the long-term RUL of Li-ion batteries is predicted with the low-frequency degradation trend data. The high-frequency fluctuation data and RUL prediction results are integrated effectively to estimate the short-term SOH of Li-ion batteries. The experimental results show that the proposed method achieves high accuracy and strong robustness, even if the prediction starting point is set to the early stage of Li-ion batteries' lifespan.     

Battery remaining useful life prediction at different discharge rates

Lithium-ion batteries are widely used in hybrid electric vehicles, consumer electronics, etc. As of today, given a room temperature, many battery prognostic methods working at a constant discharge rate have been proposed to predict battery remaining useful life (RUL). However, different discharge rates (DDRs) affect both usable battery capacity and battery degradation rate. Consequently, it is necessary to take DDRs into consideration when a battery prognostic method is designed. In this paper, we propose a discharge-rate-dependent battery prognostic method that is able to track usable battery capacity affected by DDRs in the process of battery degradation and to predict RUL at DDRs. An experiment was designed to collect accelerated battery life testing data at DDRs, which are used to investigate how DDRs influence usable battery capacity, to design a discharge-rate-dependent state space model and to validate the effectiveness of the proposed battery prognostic method. Results show that the proposed battery prognostic method can work at DDRs and achieve high RUL prediction accuracies at DDRs.     

多核相关向量机优化模型的锂电池剩余寿命预测方法

基于相关向量机的剩余寿命预测方法,核函数是影响相关向量机模型预测性能的重要因素.目前的相关向量机预测模型以单核为主,且核函数的选择存在较大主观性,导致所构建的预测模型性能有限.本文提出一种融合多个核函数构建相关向量机预测模型的方法,通过果蝇算法优化多个核函数优化组合的线性方程系数,提高了模型的预测性能,并将该方法应用于预测锂离子电池的循环剩余寿命.分别采用美国NASA和马里兰大学的电池退化数据集,对本文的方法进行了实验验证.实验结果表明：多核相关向量机预测方法的平均绝对误差和均方根误差都小于最优的单核相关向量机预测方法.     

A novel prediction method based on the support vector regression for the remaining useful life of lithium-ion batteries

Traditional approaches to lithium-ion battery health management mostly focus on the state of charge (SOC) estimation issues, whereas the state of health (SOH) estimation is also critical to lithium-ion batteries for safe operation. For online battery prognostics, it is critical to make timely and accurate response to SOH. The loss of rated capacity of a battery is usually used to determine the battery SOH, whereas the measurement of the capacity of an operating battery is quite challenging. Normally, the rated capacity fading largely relies on laboratory measurements and offline analysis. In this paper, two real-time measurable health indicators (HI) - one is the time interval of an equal charging voltage difference (TIECVD), and the other is the time interval of an equal discharging voltage difference (TIEDVD) - are extracted. A novel method which combines feature vector selection (FVS) with SVR is utilized to model the relationship between these two HIs and capacity, then the online capacity can be evaluated, more accurate prognostics of SOH and remaining useful life (RUL) can be made. Besides, compared to standard SVR, the proposed method takes FVS to cut down the training data size, which improves the efficiency of model training and prediction. In the end, two datasets demonstrated this approach performs both well in accuracy and efficiency.     

A life-prediction method for lithium-ion batteries based on a fusion model and an attention mechanism

The current life-prediction models for lithium-ion batteries have several problems, such as the construction of complex feature structures, a high number of feature dimensions, and inaccurate prediction results. To overcome these problems, this paper proposes a deep-learning model combining an autoencoder network and a long short-term memory network. First, this model applies the characteristics of the autoencoder to reduce the dimensionality of the high-dimensional features extracted from the battery data set and realize the fusion of complex time-domain features, which overcomes the problems of redundant model information and low computational efficiency. This model then uses a long short-term memory network that is sensitive to time-series data to solve the long-path dependence problem in the prediction of battery life. Lastly, the attention mechanism is used to give greater weight to features that have a greater impact on the target value, which enhances the learning effect of the model on the long input sequence. To verify the efficacy of the proposed model, this paper uses NASA''s lithium-ion battery cycle life data set.     

Fault prognostic of electronics based on optimal multi-order particle filter

The accurate fault prediction is of great importance in electronics high reliability applications for condition based maintenance. Traditional Particle filter (TPF) used for fault prognostic mainly uses the first-order state equation which represents the relationship between the current state and one-step-before state without considering the relation with multi-step-before states. This paper presents an optimal multi-order particle filter method to improve the prediction accuracy. The multiple τth-order state equation is established by training Least Squares Support Vector Regression (LSSVR) via electronics historical failure data, the τ value and LSSVR parameters are optimized through Genetic Algorithm (GA). The optimal τth-order state equation which can really reflect electronics degradation process is used in particle filter to predict the electronics status, remaining useful life (RUL) or other performances. An online update scheme is developed to adapt the optimal τth-order state transformation model to dynamic electronics. The performance of the proposed method is evaluated by using the testing data from CG36A transistor degradation and lithium-ion battery data. Results show that it surpasses classical prediction methods, such as LSSVR, TPF.     

基于VMD和DAIPSO-GPR解决容量再生现象的锂离子电池寿命预测研究

锂离子电池应用时表现出的时变、动态、非线性等特征,以及容量再生现象,导致传统模型对锂离子电池剩余使用寿命(RUL)预测的准确性低,该文将变分模态分解(VMD)和高斯过程回归(GPR)以及动态自适应免疫粒子群(DAIPSO)结合,建立RUL预测模型。首先利用等压降放电时间分析法,提取健康因子,利用VMD对其进行分解处理,挖掘数据内在信息,降低数据复杂度,并针对不同分量,利用不同协方差函数建立GPR预测模型,有效捕获了数据的长期下降趋势和短期再生波动。利用DAIPSO算法优化GPR模型,实现核函数超参数的优化,建立了更准确的退化关系模型,最终实现剩余使用寿命的准确预测,以及不确定性表征。最后利用NASA电池数据进行验证,离线预测结果表明所提方法具有较高预测精度和泛化适应能力。     

A New Dynamic-Copula Based Correlated Degradation Feature for Remaining Useful Life Prediction

Feature extraction plays an important role in Remaining useful life (RUL) prediction. Feature extraction mainly depends on the performance degradation signal in the previous study, in which the dynamic correlations among different signals are ignored, and the RUL accuracy is affected. A new dynamic feature based on the correlations of the performance degradation signal is proposed. First, dynamic correlation coefficients are calculated by copula function as the multivariate correlation performance degradation features. Second, the random effect Wiener process is used for RUL prediction based on the new features, and the maximum likelihood estimation is adopted to calculate the unknown parameters of the Wiener process. Finally, the RUL estimation for solder joints under vibration load is carried out compared with the quantile and quantile-Principal component analysis (PCA) mixed feature extraction method. The research results show that the proposed method improved the prediction accuracy of RUL.     

A new prognostics method for state of health estimation of lithium-ion batteries based on a mixture of Gaussian process models and particle filter

State of health (SOH) estimation for batteries is a key component in the prognostics and health management (PHM) of battery driven systems. Due to the complicated operating conditions, it is necessary to implement the prognostics under uncertain situations. In this paper, a novel integrated approach based on a mixture of Gaussian process (MGP) model and particle filtering (PF) is presented for lithium-ion battery SOH estimation under uncertain conditions. Instead of directly assuming a certain state space model for capacity degradation, in this paper, the distribution of the degradation process is learnt from the inputs based on the available capacity monitoring data. To capture the time-varying degradation behavior, the proposed method fuses the training data from different battery conditions as the multiple inputs for the distribution learning using the MGP model. Then, a recursive updating of the distribution parameters is conducted. By exploiting the distribution information of the degradation model parameters, the PF can be implemented to predict the battery SOH. Experiments and comparison analysis are provided to demonstrate the efficiency of the proposed approach.     

Search for an optimal rapid charging pattern for lithium-ion batteries using ant colony system algorithm

Commercial lithium-ion batteries are playing important roles as supplies for mobile phones, laptop computers, and other electronics. In order to maximize the performance of lithium-ion batteries, an advanced rapid charging pattern is required. In this paper, an Ant-Colony-System (ACS)-based algorithm is presented. The proposed ACS-based algorithm can be integrated into a commercially available battery tester to search for the optimal rapid charging pattern. Experimental results show that the obtained rapid charging pattern is capable of charging the lithium-ion batteries to 70% capacity in 30 min. The obtained pattern also provides 25% more cycle life than the conventional constant current-constant voltage method.     

EMA remaining useful life prediction with weighted bagging GPR algorithm

Electro-mechanical actuators (EMAs) are one type of the key components for the next generation aircraft. In order to ensure its safety and reliability, it is critical to predict the remaining useful life (RUL) of EMAs. The data-driven RUL prediction can be implemented by utilizing Gaussian process regression (GPR) due to its uncertainty representation and nonlinear modeling capability. In order to enhance the stability and achieve high precision of EMA RUL prediction, a weighted bagging GPR (WB_GPR) algorithm is presented in this work, in which ensemble learning is utilized. To be specific, the degradation features for EMA RUL prediction are analyzed and the parameters which can represent the degradation process and health status of EMAs are selected. Then the data-driven framework which estimates the RUL of EMAs is implemented with the proposed WB_GPR algorithm. Finally the RUL prediction performance based on WB_GPR is validated by utilizing the sensor data sets. Furthermore, the RUL prediction comparison with GPR and bagging GPR is also conducted. Experimental results demonstrate that the WB_GPR is superior in the RUL prediction with lower error rate and standard deviation.     

基于ARIMA和PF的锂电池剩余使用寿命预测方法

有效的电池剩余使用寿命(RUL)预测方法能够极大地提高系统的可靠性。提出一种基于自回归集成滑动平均模型(ARIMA)和粒子滤波(PF)融合预测框架,该框架由ARIMA方法和PF方法构成,ARIMA 应用于短期预测,而粒子滤波应用于长期预测。首先在线对锂离子电池进行监测,然后根据短期预测或长期预测要求执行相应的算法,得出横纵坐标分别为周期和容量的 RUL 预测图。实验结果表明,该预测框架能够快速准确地预测锂离子电池 RUL。     

采用门控循环神经网络估计锂离子电池健康状态

锂离子电池健康状态（State of Health，SOH）描述了电池当前老化程度，对于提前对电池的故障及失控做出预警避免电池的不安全行为具有重要意义。其估计难点在于难以确定数量合适、相关性高的估计输入以及设计合适的估计算法。通过对现有电池老化数据集的研究发现，电池充电过程中电压曲线数据相对稳定，且随着电池的老化出现规律性变化。因此，文中直接采用充电过程中电压数据作为估计SOH的输入，并在数据驱动的框架下，提出了一种基于门控循环神经网络（Recurrent Neural Networks with Gated Recurrent Unit, GRU-RNN）的锂电池SOH估计方法。该方法能够挖掘出一维电压数据中的时序特征和SOH之间的映射规律。在两个公开的电池老化数据集上的实验结果表明，提出的方法达到了1.25%的均方绝对误差和低于5.62%的最大误差，在估计精度上达到现有技术发展水平。