Capacity Degradation Model Research Articles

Remaining Service Life Prediction of Lithium-Ion Batteries Based on Randomly Perturbed Traceless Particle Filtering

To address the limitations in the prediction accuracy of the remaining useful life (RUL) of lithium-ion batteries, stemming from model accuracy, particle degradation, and insufficient diversity in the particle filter (PF) algorithm, this paper proposes a battery RUL prediction method utilizing a randomly perturbed unscented particle filter (RP-UPF) algorithm, based on the constructed battery capacity degradation model. The method utilizes evaluation metrics adjusted R-squared (Radj2) and the Akaike Information Criterion (AIC) to select the battery capacity decline model C5 with a higher goodness of fit. The initial values for constructing the C5 model are obtained using the relevance vector machine (RVM) and nonlinear least squares methods. Based on the constructed battery capacity decline model C5, the RP-UPF algorithm is employed to estimate the posterior parameters and iteratively approach the true battery capacity decline curve, thereby predicting the battery’s RUL. The research results indicate that, using battery B0005 as an example and starting the prediction from the 50th cycle, the RUL prediction results obtained with the RP-UPF algorithm demonstrate reductions in absolute error, relative error, and probability density function (PDF) width of 2%, 2.71%, and 10%, respectively, compared to the PF algorithm. Similar conclusions were drawn for batteries B0006 and B0018. Under the constructed battery capacity degradation model C5, the RP-UPF algorithm shows higher prediction accuracy for battery RUL and a narrower PDF range compared to the PF algorithm. This approach effectively addresses the issue of particle weight degradation in the PF algorithm, providing a more valuable reference for battery RUL prediction.

A hybrid battery degradation model combining arrhenius equation and neural network for capacity prediction under time-varying operating conditions

Capacity degradation modeling and remaining useful life (RUL) prediction play a pivotal role in enhancing the safety of battery energy storage systems. Lithium-ion batteries utilized in the systems are subjected to intricate and variable operating conditions, including temperature, charging/discharging rates and depth, which result in time-varying degradation rates. However, most existing models for battery capacity prediction have the limitation of ignoring the quantitative effects of time-varying operating conditions on degradation. Therefore, a hybrid battery capacity degradation model combining Arrhenius equation and lightweight Transformer is constructed. The effects of operating conditions on capacity degradation rates are introduced by an improved Arrhenius degradation equation. The coordinate ascent method embedded with Newton descent is used for estimating the model parameters. Then, the unknown mapping relationships between the degradation statistical features extracted from monitoring data and the degradation factors are captured by the light-weight Transformer. Finally, a novel framework consisting of future capacity and RUL predicting is constructed based on sequential importance resampling (SIR). For the purpose of verification, the cyclic charge-discharge experiments of eight battery cells under two distinct operating profiles are designed and conducted. Compared with other models, the proposed model achieves the best prognostics performance on the tested cells.

Capacity fading knee-point recognition method and life prediction for lithium-ion batteries using segmented capacity degradation model

Aiming at the problem that the cycle life of the battery is hard to be accurately estimated, a segmented capacity degradation model is established based on the trend of capacity degradation rate. By applying a genetic algorithm (GA) to optimize the model parameters, GA-Weibull and GA-SVR (support vector regression) degradation models and their corresponding segmented models are established, and the battery life is calculated. Furthermore, a method taking the RMSE as the target is put forward to calculate the knee-point of capacity degradation. Finally, the life is predicted by segmented models. The results show that compared with unsegmented models, describing the process of capacity degradation by segmented models reduces the error notably, makes the determination coefficient closer to 1, and improves the model accuracy effectively. Later, the proposed method makes the fitting error of the segmented model smaller than that of Bacon-Watts method, thus obtaining a more accurate knee-point. In addition, it is found that there exists linear relationship between the estimated knee-point and the battery life. Finally, the prediction results based on segmented model show that the prediction accuracy of segmented GA-SVR model is higher, and the MAPE is only 4.32%. The relevant results can provide some guidance for the reliability evaluation and product quality management of lithium-ion batteries, which is conducive to establishing more accurate models for battery life prediction.

Empirical Capacity Degradation Model for a Lithium-Ion Battery Based on Various C-Rate Charging Conditions

Lithium-ion batteries are widely used in many applications due to their high energy density, high efficiency, and excellent cycle ability. Once an unknown Li-ion battery is reusable, it is important to measure its lifetime and state of health. The most favorable measurement method is the cycle test, which is accurate but time- and capacity-consuming. In this study, instead of a cycle test, we present an empirical model based on the C-rate test to understand the state of health of the battery in a short time. As a result, we show that the partially accelerated charge/discharge condition of the Li-ion battery is highly effective for the degradation of battery capacity, even when half of the charge/discharge conditions are the same. This observation provides a measurable method for predicting battery reuse and future capacity degradation.

Multi-time scale scheduling for virtual power plants: Integrating the flexibility of power generation and multi-user loads while considering the capacity degradation of energy storage systems

With the high proportion of renewable energy connected to the grid, the problem of insufficient flexibility in the power system has emerged. Renewable energy and controllable distributed resources can be aggregated and managed through virtual power plants, reducing the need for flexibility to a certain extent. Although building new energy storage systems can compensate for the lack of flexibility, it requires high initial investment costs. To address this, this paper proposes a lease mechanism for coal-fired units based on the combination of carbon credits and prices, providing the right to use coal-fired units for virtual power plants. Subsequently, different demand response strategies are utilized to control the controllable loads of various users, thereby providing certain controllable resources for the virtual power plant. Additionally, to ensure the optimal decision-making of the virtual power plant operator, a cost model accurately describing the capacity degradation state of the energy storage system is adopted. Moreover, a multi-time scale scheduling strategy of virtual power plant is implemented to fully utilize controllable resources of different time scales, effectively dealing with the power imbalance caused by multiple uncertainties. The results show that utilizing the leasing mechanism of coal-fired units and employing demand response strategies from different users can provide flexibility to the virtual power plant. The accuracy of the capacity degradation model used by the operator significantly impacts the optimality of the scheduling plan.

A data and physical model joint driven method for lithium-ion battery remaining useful life prediction under complex dynamic conditions

Accurate remaining useful life (RUL) prediction of batteries plays an important role in battery management. The existing methods mainly rely on the battery test data under ideal operating conditions to show good performance. However, the actual operating conditions of batteries are usually complex, which bring great challenges to the RUL prediction. To improve the accuracy and the generalization ability of RUL prediction method, a fusion method of electrochemical–thermal model (ECT) and unscented kalman filter (UKF) is proposed for lithium-ion battery. Firstly, an ECT–based capacity degradation model is established by coupling pseudo two dimensions (P2D) electrochemistry model, 3D thermal model and solid electrolyte interface (SEI) formation model. Secondly, the UKF method is used to update iteratively the parameters of model to improve its accuracy. Finally, several sets of operating data of lithium-ion battery under different conditions are used for RUL prediction, followed by the comparative analysis of different models and algorithms. As a result, the proposed fusion method not only exhibits better accuracy in RUL prediction under ideal conditions, but also shows excellent accuracy and generalization for other dynamic stochastic operating conditions.

Remaining useful life prediction for lithium-ion batteries based on sliding window technique and Box-Cox transformation

Accurate remaining useful life (RUL) prediction technique matters in lithium-ion battery use, optimization, and replacement. This article presents an RUL prediction method combining the sliding window (SW) technique and Box-Cox transformation (BCT). This method achieves online RUL prediction with acceptable accuracy, is independent of offline training data, and only brings a low computational burden. The SW technique is employed for gathering a certain amount of capacity data, which is subsequently transformed using BCT-related techniques to construct a capacity degradation model. The identified model is then extrapolated to predict battery RUL, and the prediction uncertainties are calculated through Monte Carlo (MC) simulation. A simple implementation shows that this hybrid method outperforms the history-based polynomial and BCT methods in battery RUL prediction. Given the segmented capacity degradation trend, a constraint can be imposed on the model parameter for optimization purposes. Experimental results demonstrate that the optimized method obtains lower root-mean-square errors (RMSEs) of RUL predictions during the last 20 % of the battery lifetime than the original one, and the precise RULs are predicted with standard deviations mainly within [1, 10] cycles.

Data-Driven Semi-Empirical Model Approximation Method for Capacity Degradation of Retired Lithium-Ion Battery Considering SOC Range

The rapid development of the electric vehicle industry produces large amounts of retired power lithium-ion batteries, thus resulting in the echelon utilization technology of such retired batteries becoming a research hotspot in the field of renewable energy. The relationship between the cycle times and capacity decline of retired batteries performs as a fundamental guideline to determine the echelon utilization. The cycle conditions can influence the characteristics of the degradation of battery capacity; especially neglection of the SOC ranges of batteries leads to a large error in estimating the capacity degradation. Practically, the limited cycle test data of the SOC ranges of the retired battery cannot support a model to comprehensively describe the characteristics of the capacity decline. In this background, based on the limited cycle test data of SOC ranges, this paper studies and establishes a capacity degradation model of retired batteries that considers the factors affecting the battery cycle more comprehensively. In detail, based on the data-driven method and combined with the empirical model of retired battery capacity degradation, three semi-empirical modeling methods of retired battery capacity degradation based on limited test data of SOC ranges are proposed. The feasibility and accuracy of these methods are verified through the experimental data of retired battery cycling, and the conclusions are drawn to illustrate their respective scenarios of applicability.

A Physics-Constrained Bayesian neural network for battery remaining useful life prediction

In order to predict the remaining useful life (RUL) of lithium-ion batteries, a capacity degradation model may be developed using either simplified physical laws or machine learning-based methods. It is observed that even though degradation models based on simplified physical laws are easy to implement, they may result in large error in the application of failure prognostics. While data-driven prognostics models can provide more accurate degradation forecasting, they may require a large volume of training data and may invoke predictions inconsistent with physical laws. It is also very challenging for existing methods to predict the RUL at the early stages of battery life. In this paper, we propose a Bayesian physics-constrained neural network for battery RUL prediction by overcoming limitations of the current methods. In the proposed method, a neural differential operator is learned from the first 100 cycles of data. The neural differential operator is modeled with a Bayesian neural network architecture that separates the fixed history dependence from the time dependence to isolate epistemic uncertainty quantification. Using the battery dataset presented in the paper by Severson et al. as an example, we compare our proposed method with a simplified physics-based degradation forecasting model and two data-driven prognostics models. The results show that the proposed physics-constrained neural network can provide more accurate RUL estimation than the other methods with the same group of training data. Most importantly, the proposed method allows for RUL prediction at earlier stages of the battery life cycle.

Research Progress of Battery Life Prediction Methods Based on Physical Model

Remaining useful life prediction is of great significance for battery safety and maintenance. The remaining useful life prediction method, based on a physical model, has wide applicability and high prediction accuracy, which is the research hotspot of the next generation battery life prediction method. In this study, the prediction methods of battery life were compared and analyzed, and the prediction methods based on the physical model were summarized. The prediction methods were classified according to their different characteristics including the electrochemical model, equivalent circuit model, and empirical model. By analyzing the emphasis of electrochemical process simplification, different electrochemical models were classified including the P2D model, SP model, and electrochemical fusion model. The equivalent circuit model was divided into the Rint model, Thevenin model, PNGV model, and RC model for the change of electronic components in the model. According to the different mathematical expressions of constructing the empirical model, it can be divided into the exponential model, polynomial model, exponential and polynomial mixed model, and capacity degradation model. Through the collocation of different filtering methods, the different efficiency of the models is described in detail. The research progress of various prediction methods as well as the changes and characteristics of traditional models were compared and analyzed, and the future development of battery life prediction methods was prospected.

Lithium-ion battery remaining useful life prediction using a two-phase degradation model with a dynamic change point

An accurate remaining useful life (RUL) prediction plays a crucial role in the prognostics and health management of lithium-ion (Li-ion) batteries. Current studies on the RUL prediction of Li-ion batteries commonly use single-phase degradation models, which result in inaccurate RUL predictions due to their insufficient capabilities in capturing various degradation patterns. The existing two-phase degradation models can divide battery degradation into two phases using a change point, a slowly decreasing phase, and a rapidly decreasing phase. The change point in the current two-phase degradation models is usually modeled in two ways. First, the change point is treated as a random variable and that however greatly increases the computational complexity. Second, a fixed change point is assigned for all battery cells for model simplification, which may not be realistic in practice. For example, battery cells' degradation data collected from our laboratory tests show a two-phase degradation pattern with different change points. By considering such differences in change points, this study first utilizes binary segmentation to identify the change point of a battery cell and then proposes a two-phase capacity degradation model with a dynamic change point. Further, variations have been observed in the degradation behaviors of tested battery cells. Therefore, by using the proposed two-phase degradation model, we develop a particle filtering-based framework considering uncertainties to predict the RULs of battery cells. Finally, the proposed framework shows superior prediction performance compared with the existing degradation models by providing the RUL prediction with an average absolute estimation error percentage of 27 % for laboratory data and an average absolute estimation error percentage of 24 % for NASA battery data.

An Improved Weighting Coefficient Optimization-Particle Filtering Algorithm Based on Gaussian Degradation Model for Remaining Useful Life Prediction of Lithium-ion Batteries

Establishing a capacity degradation model accurately and predicting the remaining useful life of lithium-ion batteries scientifically are of great significance for ensuring safety and reliability throughout the batteries’ whole life cycle. Aiming at the problems of “particle degradation” and “sample poverty” in traditional particle filtering, an improved weighting coefficient optimization - particle filtering algorithm based on a new Gaussian degradation model for the remaining useful life prediction is proposed in this research. The main idea of the algorithm is to weight the selected particles, sort them according to the particle weights, and then select the particles with relatively large weights to estimate the filtering density, thereby improving the filtering accuracy and enhancing the tracking ability. The experimental verification results under the National Aeronautics and Space Administration data show that the improved weighting coefficient optimization - particle filtering algorithm based on the Gaussian degradation model has significantly improved accuracy in predicting the remaining useful life of lithium-ion batteries. The RMSE of the B05 battery can be controlled within 1.40% and 1.17% at the prediction starting point of 40 cycles and 70 cycles respectively, and the RMSE of the B06 battery can be controlled within 2.45% and 1.93% at the prediction starting point of 40 cycles and 70 cycles respectively. It can be seen that the algorithm proposed in this study has strong traceability and convergence ability, which is important for the development of high-reliability battery management systems.

A Digital Twin-Driven Life Prediction Method of Lithium-Ion Batteries Based on Adaptive Model Evolution.

Accurate life prediction and reliability evaluation of lithium-ion batteries are of great significance for predictive maintenance. In the whole life cycle of a battery, the accurate description of the dynamic and stochastic characteristics of life has always been a key problem. In this paper, the concept of the digital twin is introduced, and a digital twin for reliability based on remaining useful cycle life prediction is proposed for lithium-ion batteries. The capacity degradation model, stochastic degradation model, life prediction, and reliability evaluation model are established to describe the randomness of battery degradation and the dispersion of the life of multiple cells. Based on the Bayesian algorithm, an adaptive evolution method for the model of the digital twin is proposed to improve prediction accuracy, followed by experimental verification. Finally, the life prediction, reliability evaluation, and predictive maintenance of the battery based on the digital twin are implemented. The results show the digital twin for reliability has good accuracy in the whole life cycle. The error can be controlled at about 5% with the adaptive evolution algorithm. For battery L1 and L6 in this case, predictive maintenance costs are expected to decrease by 62.0% and 52.5%, respectively.

Seismic performance evaluation of base-isolated nuclear power plant reactor building considering aging effect of isolation device

ABSTRACT The base isolation (BI) device is widely used for reducing seismic energy transmitted to the upper part of the structures. The rubber property of lead rubber bearing (LRB) BI devices degrades with time and environmental conditions, affecting the controlling performance of BI devices. This study investigates the degradation of capacity of base-isolated nuclear power plant (BI-NPP) considering the aging of rubber material used in the LRB BI device. An NPP reactor building with BI devices is numerically modeled. To capture the nonlinear behavior of the BI device, a bilinear hysteretic model is considered. Assuming different ages, the nonlinear incremental dynamic analysis is conducted using a set of 25 earthquakes and the seismic outcomes are evaluated through fragility analysis. The seismic capacity is extracted from the fragility parameters in terms of High Confidence of Low Probability of Failure (HCLPF) capacity. The outcome shows that the capacity degraded remarkably up to 21% for 100 years of service life. Finally, the seismic capacity degradation model is proposed through the investigation, which will be helpful to evaluate the capacity of the BI-NPP structure for any instant of time.

Analysis of the lithium-ion battery capacity degradation behavior with a comprehensive mathematical model

The influence of transition metal deposition on the capacity of lithium-ion batteries (LIBs) can not be ignored. The current model lacks a comprehensive analysis of the coupling phenomenon. Based on the classic P2D model, we propose a comprehensive capacity degradation model of LIBs, with a complete description of the side effects of transition metal dissolution in the positive electrode, solid electrolyte interphase (SEI) formation, and metal deposition in the negative electrode. Simulations are implemented and compared for the evolution of the battery capacity as cycling progressed in different cases of only SEI layer growth, SEI growth couples with Li plating, SEI growth couples with Mn dissolution and deposition, and all the three factors fully couples. The capacity degradation behavior is revealed from the perspective of lithium-ion inventory, diffusion coefficient, and porosity. The results show that the plating of Li leads to a significant decrease of the lithium-ion concentration, which is the prime for the attenuation of capacity. The growth of SEI alone has little effect on the capacity, which maintains 95.9% even after 2500 cycles. Although the dissolved content of Mn is just ppm scale, it can accelerate the growth of SEI layer and thus obviously affect the battery capacity. • Presenting a comprehensive lithium-ion battery model. • A lithium-ion battery model to predict capacity degradation. • Revealing the coupling relationship of side reactions. • Clarifying the influence level of each side reaction on capacity degradation. • The model fully reflects the behavior of Mn-ions.

Remaining useful life prediction for lithium-ion battery based on the particle filter considering temperature effect

Temperature would affect the degradation process of lithium-ion battery. Therefore, considering the influence of temperature, this paper proposes method to predict the Remaining useful life (RUL) of the lithium-ion battery based on Arrhenius and double exponential model. And update the parameter by particle filter. Firstly, we establish a capacity degradation model with considering the influence of temperature, which is based on Arrhenius model and double exponential model. And then, in order to obtain the initial value of the parameters, we process the fitted the lithium-ion battery degradation data. Next, we use the particle filter (PF) algorithm to update the model parameters to realize the capacity estimation and the RUL prediction. Finally, according the experiment, we prove that the accuracy of the method proposed in this paper is better than that the method without considering the influence of temperature change. The result shows that the lithium-ion battery capacity degradation model established in this paper has great potential in the RUL prediction of the lithium-ion battery.

Charging Strategy Optimization at Low Temperatures for Li-Ion Batteries Based on Multi-Factor Coupling Aging Model

Lithium-ion batteries (LIBs) charging at low temperatures will easily accelerate the aging of LIBs and reduce the useful life. This paper applies advanced multi-factors coupling aging model and bi-objective particle swarm optimization (PSO) algorithm to derive suitable charging patterns for LIBs at low temperatures. Based on the results of orthogonal experiments, which consider the effects of charging rate, charging temperature and charging cut-off voltage on battery aging, the low-temperature capacity degradation model was established. Furthermore, two important yet competing charging objectives, including battery health and charging time, are taken into account simultaneously. These two conflicting charging objectives are traded off by solving a bi-objective optimization problem based on battery electrothermal and aging behavior. Combined with PSO algorithm, the optimal low-temperature charging strategy is obtained. As a result, the three-stage constant current and constant voltage (CC-CV) charging strategy is optimized to balance various combinations of charging objectives. Different tradeoffs are compared and analyzed based on the Pareto frontiers. The verification results show that the optimized three-stage CC-CV charging strategy can effectively offer feasible health-conscious charging with desirable tradeoffs among charging speed and battery health under low-temperature charging conditions.

A novel approach for health management online-monitoring of lithium-ion batteries based on model-data fusion

In order to ensure the safe and stable operation of electric vehicles and energy storage systems, online monitoring of the state of health and the remaining useful life of lithium-ion batteries is the key to the health management of lithium-ion batteries. A novel approach for health management online monitoring of lithium-ion batteries based on mechanism modeling and data-driven fusion is proposed in this paper. An improved semi-empirical capacity degradation model of the lithium-ion batteries fully considering internal resistance and temperature is established. After the data sets of the lithium-ion batteries are de-noised by the wavelet packet, the parameters of the model are identified according to the genetic algorithm and a particle filter framework is designed to online update the parameters of the model. Through the fusion of the two, the remaining useful life and state of health of the lithium-ion batteries can be predicted accurately. The proposed method is verified by the battery cycle test data from the Advanced Life Cycle Engineering Center of University of Maryland and the NASA Ames Prognostics Center of Excellence, the mean absolute error and root mean square error of the remaining useful life for the lithium-ion batteries are respectively less than 20 and 25 cycles at constant temperature condition, and respectively less than 3.30 and 3.60 cycles at non-constant temperature condition. Compared with the existing methods, the proposed method has higher prediction accuracy and better fitting performance, which can provide a certain theoretical basis for the safe operation of lithium-ion batteries.

State-of-Charge Estimation of Lithium-ion Battery Based on Capacity Degradation Model Considering the Dynamic Currents and Temperatures

State-of-Charge Estimation of Lithium-ion Battery Based on Capacity Degradation Model Considering the Dynamic Currents and Temperatures

Adaptive State-of-Charge Estimation for Lithium-Ion Batteries by Considering Capacity Degradation

The accurate estimation of a lithium-ion battery’s state of charge (SOC) plays an important role in the operational safety and driving mileage improvement of electrical vehicles (EVs). The Adaptive Extended Kalman filter (AEKF) estimator is commonly used to estimate SOC; however, this method relies on the precise estimation of the battery’s model parameters and capacity. Furthermore, the actual capacity and battery parameters change in real time with the aging of the batteries. Therefore, to eliminate the influence of above-mentioned factors on SOC estimation, the main contributions of this paper are as follows: (1) the equivalent circuit model (ECM) is presented, and the parameter identification of ECM is performed by using the forgetting-factor recursive-least-squares (FFRLS) method; (2) the sensitivity of battery SOC estimation to capacity degradation is analyzed to prove the importance of considering capacity degradation in SOC estimation; and (3) the capacity degradation model is proposed to perform the battery capacity prediction online. Furthermore, an online adaptive SOC estimator based on capacity degradation is proposed to improve the robustness of the AEKF algorithm. Experimental results show that the maximum error of SOC estimation is less than 1.3%.