Lithium-ion Battery Capacity Estimation Research Articles

Capacity estimation of lithium-ion batteries based on optimized charging voltage section and virtual sample generation

Accurate capacity estimation of a lithium-ion battery is crucial to predict its state of health and remaining useful life, determining the reliability and safety of the battery system directly. However, existing data-driven methods usually are based on full battery charging or discharging curves, which are hard to meet in practice because of range anxieties and arbitrary charging behaviors of users. Meanwhile, the lack of sufficient datasets for model training limits the performance of a data-driven model. In this paper, a capacity estimation method for lithium-ion batteries based on an optimized charging voltage section and virtual sample generation is proposed. In the method, characteristics of full and sectional capacity degradation are analyzed to evaluate the feasibility of capacity estimation using a section of charging voltage curve. The extraction of health indicator and optimization of battery voltage range are introduced. A multi-distribution global trend diffusion algorithm is used to generate virtual samples. Based on a long short-term memory neural network, battery capacity estimation model is constructed. Experimental verifications on NASA, CALCE, and Oxford battery datasets are carried out. Results show that the proposed method not only reduces the length of required voltage section for capacity estimation, but also improves the estimation accuracy in comparison to utilization of the full charging curve. Under the operating conditions of NASA B6, CALCE CS36 and Oxford C3, the root mean square error (RMSE) of battery capacity estimation is lower than 1.48%.

A Review of Lithium-Ion Battery Capacity Estimation Methods for Onboard Battery Management Systems: Recent Progress and Perspectives

With the widespread use of Lithium-ion (Li-ion) batteries in Electric Vehicles (EVs), Hybrid EVs and Renewable Energy Systems (RESs), much attention has been given to Battery Management System (BMSs). By monitoring the terminal voltage, current and temperature, BMS can evaluate the status of the Li-ion batteries and manage the operation of cells in a battery pack, which is fundamental for the high efficiency operation of EVs and smart grids. Battery capacity estimation is one of the key functions in the BMS, and battery capacity indicates the maximum storage capability of a battery which is essential for the battery State-of-Charge (SOC) estimation and lifespan management. This paper mainly focusses on a review of capacity estimation methods for BMS in EVs and RES and provides practical and feasible advice for capacity estimation with onboard BMSs. In this work, the mechanisms of Li-ion batteries capacity degradation are analyzed first, and then the recent processes for capacity estimation in BMSs are reviewed, including the direct measurement method, analysis-based method, SOC-based method and data-driven method. After a comprehensive review and comparison, the future prospective of onboard capacity estimation is also discussed. This paper aims to help design and choose a suitable capacity estimation method for BMS application, which can benefit the lifespan management of Li-ion batteries in EVs and RESs.

Feature disentanglement and tendency retainment with domain adaptation for Lithium-ion battery capacity estimation

Online capacity estimation of lithium-ion batteries plays an important role in battery management systems. Accurate estimation of the current capacity of the battery is helpful for predictive maintenance. Data-driven capacity estimation methods have become increasingly popular in recent years. However, most data-driven approaches assume that the battery degradation data used to train and test obeys the same distribution. In practical applications, there is often a discrepancy in the distributions of the training set and the test set due to differences in the internal chemistry of batteries and various operating conditions. The existing methods for domain adaptive capacity estimation force the global features of the source and target domains to be aligned, but do not take into account the domain-specific information. Thus, models may not extract domain-invariant representation. To address this problem, We propose a feature Disentanglement and tendency Retainment network (DR-Net) for domain adaptive capacity estimation. Specifically, our DR-Net can disentangle the extracted features from raw data into domain-invariant shared features and domain-specific private features while retaining degradation trend information. Experimental results show that the proposed method achieves more competitive results in both estimation accuracy and robustness than other state-of-the-art methods. Our code is available at: https://github.com/wang-fujin/battery_capacity_estimation.

An efficient and robust method for lithium-ion battery capacity estimation using constant-voltage charging time

The state-of-health (SoH) estimation based on the constant-voltage (CV) charging data has been an interesting research topic in recent years. However, most of the existing estimation methods based on CV charging data are sensitive to the cut-off condition and/or require a relatively high storage resource as well as computing power, preventing the feasibility in real world applications. To extend the scope of the estimation method based on CV charging data, this paper proposes a quick and robust battery capacity estimation method using a two-layer CV charging time (TCV)-based model. First, the evolution of TCV-based SoH model with respect to different cut-off currents is investigated, and the detailed mathematical expressions of the model coefficients are derived based on the decoupled dynamic characteristics of the CV charging current. Second, considering the actual sampling periods (Tss) utilized in the online application, a Ts-adaptive moving average filter is proposed to filter the high-frequency measurement noise. Third, experimental results demonstrate that the proposed method can determine SoH with a root-mean-square error of less than 2.05% for two types of tested batteries under different charging protocols. In addition, the comparison study further highlights the superiority of the proposed method in terms of robustness, accuracy, computational cost, and storage consumption.

Remaining capacity estimation for lithium-ion batteries via co-operation of multi-machine learning algorithms

Accurate capacity estimation of lithium-ion batteries is of great significance to guarantee their reliability and safety operation. In this paper, a fused capacity estimation method is devised via the co-operation of multi-machine learning algorithms. First, the peak value of incremental capacity curve is extracted as the health feature, and the support vector machine is engaged in data processing and mitigation of the noise-induced unfavorable interference. Then, the preliminary remaining capacity values are estimated based on the incorporation of support vector machine, long short-term memory network and Gaussian process regression with the support of the abstracted health feature. Finally, the random forest algorithm is employed to supply more accurate capacity estimation to fuse the preliminary remaining capacity values. The experimental validations showcase that the advanced algorithm enables to fuse the advantages of individual learners and improve the estimation accuracy. The results indicate that the proposed method can estimate the remaining capacity with the root mean square error of less than 2.4%. In addition, the robustness to noise corruption and the generality to different battery cells are also verified.

Study on the Capacity Degradation Mechanism and Capacity Predication of Lithium-Ion Battery Under Different Vibration Conditions in Six Degrees-of-Freedom

Abstract In order to study the degradation mechanism of lithium-ion batteries subjected to vibration aging in actual use and also to achieve capacity estimation and prediction, the following work has been done: First, the road spectra of two commonly seen domestic roads in China are collected in the field and modeled on a six degrees-of-freedom motion platform as the vibration working conditions of the batteries. Second, aging cycle experiments were conducted on batteries with different placement directions (X-axis direction, Y-axis direction, and Z-axis direction) under two vibration conditions, and the effects of experimental conditions on the decline results were analyzed; third, quantification of battery decline patterns to analyze the main causes of battery capacity decline; and then, through further analysis of the two vibration conditions on the lithium battery by in-situ and ex-situ methods as its internal mechanisms. Finally, the quantified results were input into the generative adversarial networks and long-term and short-term memory network prediction model to predict the capacity, and the errors of 20 predictions are as follows: the average values are 2.8561% for Group X, 2.7997% for Group Y, 3.0182% for Group Z, and 2.9478% for Group N, which meet the requirements of battery management system estimation. This paper provides a basis for the study of aging mechanism and capacity estimation of lithium-ion batteries under vibration aging conditions, which helps manufacturers to package batteries more rationally to extend battery life and develop battery management system (BMS)-related strategies.

An ensemble learning prognostic method for capacity estimation of lithium-ion batteries based on the V-IOWGA operator

Capacity estimation is crucial for assessing the health statuses of lithium-ion batteries to develop better battery usage and maintenance strategies. However, it is difficult to satisfy multiple application situations in which each individual prognostic method has its own particular preconditions and application limitations. Thus, in this paper, an ensemble prognostic framework is proposed to integrate several individual prognostic methods to achieve better capacity estimation accuracy. In the proposed framework, a measurement- and calculation-based combined feature extraction method is first applied to the battery charging phase to better capture the extracted features that are related to the health statuses of lithium-ion batteries. Then, a novel validation dataset-based induced ordered weighted geometric averaging (V-IOWGA) operator is proposed to realize the time-varying weight allocation of each individual prognostic method to solve issue by which the performances of different prognostic algorithms vary in different phases. The advantages of the proposed ensemble model are verified on lithium-ion battery datasets from NASA PCoE and the University of Maryland CALCE Laboratory, and its prediction accuracy is better than that of other individual prognostic models. In addition, comparison experiments involving three types of ensemble models validate the superiority of the proposed model.

Extreme learning machine model for state-of-charge estimation of lithium-ion battery using salp swarm algorithm

Accurate capacity estimation of lithium-ion batteries can effectively avoid over charge/discharge and improve life span. This paper proposes a state-of-charge (SOC) estimation model based on an improved extreme learning machine (ELM). ELM is a single hidden layer network with fast learning speed and good generalization performance, suitable for SOC estimation. For the ELM performance is highly dependent on network weights and hidden layer biases, a salp swarm algorithm (SSA) is applied to search for these parameters. Chaotic mapping is introduced in SSA to make the initialized individuals uniformly distributed. And a sine cosine algorithm (SCA) is embedded in swarm position formulation to promote communication. The model robustness and computational cost are verified by energy storage devices. The mean absolute error is 0.538, and the mean absolute percentage error is 0.887%. The results verified that the proposed model has better performance than other popular models, and shows good traceability and generality.

Capacity Estimation of Lithium-Ion Batteries for Various Aging States Through Knowledge Transfer

In this study, we propose a new capacity estimation scheme for various aging states of lithium-ion batteries based on an inverted bottleneck network (IBN) that learns electrochemical knowledge. Most existing capacity estimation schemes that employ simple models have limitations in accuracy because they cannot reflect the complex aging states inside the batteries. An electrochemical model is sufficiently sophisticated to estimate the capacity of lithium-ion batteries accurately; however, it is computationally expensive. Therefore, we transfer the knowledge of an electrochemical model that deals with the physicochemical behavior of the batteries to a small-sized IBN. Then, the proposed neural network that learns both the synthetic and experimental data can estimate the capacity of different aging states accurately with a lower computational time. Furthermore, the specific structure of the IBN allows the neural network to extract visible information, called an attention map, which represents the decision basis of the neural network when estimating capacity. We propose an estimation score for determining the reliability of the capacity estimation result by analyzing the attention map and input voltage data. We measured capacity data from 12 real 37-Ah standard batteries with different aging states to validate the efficacy of the proposed approach. The resulting estimation errors were about 0.445 Ah, which corresponds to only 1.202% errors based on the 37-Ah capacity.

Capacity estimation of lithium-ion batteries using convolutional neural network and impedance spectra

Capacity estimation of lithium-ion batteries using convolutional neural network and impedance spectra

End-to-end capacity estimation of Lithium-ion batteries with an enhanced long short-term memory network considering domain adaptation

Real-time capacity estimation of lithium-ion batteries is crucial but challenging in battery management systems (BMSs). Due to the complexity of battery degradation mechanism, data-driven methods are prevalent recently. Despite achieved promising results, most of developed approaches still assume that the degradation trajectories of batteries are same between the training and testing domains. However, the inconsistency of batteries and the randomness during degradation process lead to the distribution discrepancy, which further affects the estimation precision of trained model. To overcome this challenge, a novel deep learning framework assisted with domain adaptation is proposed in this paper. First, a deep long short-term memory (LSTM) network is designed to capture the nonlinear mapping from monitored data, specially, terminal voltage and current, to battery capacity. Then, a domain adaptation layer is integrated to the LSTM with the purpose of degradation feature alignment between the source and target batteries. The proposed method is capable of establishing the general capacity estimation model for the discrepant batteries by only using a few cycling data of target batteries. Extensive experiments on two battery datasets from NASA Ames Prognostics Data Repository demonstrate that the proposed method outperforms the state-of-the-art data-driven methods in terms of estimation precision and robustness. • A battery capacity estimation framework integrating domain adaptation is presented. • The LSTM is enhanced by MMD minimization for battery capacity estimation. • Battery capacity is accurately and quickly predicted with fewer training data. • The proposed method is superior to other popular data-driven methods.

A deep belief network approach to remaining capacity estimation for lithium-ion batteries based on charging process features

Accurate remaining capacity estimation for lithium batteries can help people understand the working state of a battery, which ensures the reliability and safety of electric equipment. Since the remaining capacities of lithium-ion batteries are related to internal physicochemical reactions, such as loss of lithium inventory and loss of active material, their remaining capacities are usually difficult to directly estimate. Advancements in deep learning have prompted the development of new data-driven approaches to solve this problem that can capture potential degradation correlation information from high-dimensional data via hidden layers of the deep learning model. This paper presents a novel deep learning method for lithium-ion battery capacity estimation based on charging process features with the following process. First, multiple health indicators are analysed and extracted according to different working conditions of batteries. Next, a grey relation analysis is combined with a cross-validation test, which is employed to eliminate information redundancy and improve prediction accuracy. Moreover, the optimized health indicators are further extracted through the restricted Boltzmann machine component of the deep belief network model, and a fully connected layer is adopted for estimation of lithium-ion battery capacity. A total of 23 battery datasets, including six working condition types, are employed for verification experiments. The maximum root mean square error of a single battery prediction is 3%, and that of multiple battery prediction is still within 6%, which confirms the effectiveness and accuracy of the proposed method.

Attention-based CNN-BiLSTM for SOH and RUL estimation of lithium-ion batteries

The state of health (SOH) and remaining useful life (RUL) of lithium-ion batteries describe the current aging degree of the batteries from different perspectives, and accurate and efficient battery health estimation is essential for their safe use. To improve the effectiveness and accuracy of the batteries’ health assessment models, this paper proposes a new method for SOH and RUL estimation of lithium-ion batteries. Convolutional neural networks (CNNs), bi-directional long short-term memory (BiLSTM), and attention mechanism (AM) to build a hybrid network model for capacity estimation of lithium-ion batteries, and further calculate the SOH and RUL estimation results. By using Center for Advanced Life Cycle Engineering (CALCE) lithium-ion battery capacity degradation data, we extracted the battery health indicator (HI) and verified the reasonableness of HI selection by using Gray Relational Analysis (GRA) and compared it with other network models to calculate the prediction accuracy by various evaluation indexes. The experimental results show that the method has higher estimation accuracy while avoiding the construction of complex battery mechanism degradation models and is highly generalized.

Lithium-ion battery capacity estimation based on battery surface temperature change under constant-current charge scenario

Accurate estimation of battery actual capacity in real time is crucial for a reliable battery management system and the safety of electrical vehicles. In this paper, the battery capacity is estimated based on the battery surface temperature change under constant-current charge scenario. Firstly, the evolution of the smoothed differential thermal voltammetry (DTV) curves throughout the aging process is analyzed. Then, the change of the battery surface temperature, which is equivalent to the area under the DTV curve, over a specific voltage range is introduced as a direct feature of interest to reflect the battery actual capacity. In addition, the temperature variation transformation is utilized to reduce the influence of the initial battery inconsistency. Lastly, two battery degradation datasets are utilized to validate the proposed method. The maximum root mean-square errors of the estimation results by the reference correlation are less than 20 mAh and 60 mAh for the two employed batteries (respective nominal capacities are 740 mAh and 4800 mAh). Specifically, the mean estimation errors for the respective two batteries are reduced by approximately 24.74% and 39.60% after the temperature variation transformation. The proposed method is further compared with the existing DTV analysis method and demonstrates the superior performance.

Lithium-ion battery capacity estimation based on open circuit voltage identification using the iteratively reweighted least squares at different aging levels

In traditional incremental SOC (stage of charge)-capacity method, errors of the selected SOC points inevitably lead to inaccurate capacity estimation. In this paper, a capacity estimation method based on OCV (open circuit voltage) identification and IRLS (iteratively reweighted least squares) algorithm method is proposed. Firstly, the accuracy and complexity of three parameter identification schemes of first-order RC model at different aging levels are studied with the forgetting factor recursive least squares algorithm. Through the online identified OCV by the optimal scheme, the full interval SOC estimation can be obtained indirectly. Finally, the capacity is estimated using the full interval SOC estimation with IRLS algorithm, which avoids the randomness of the SOC point selection, and solves the problem of possible outliers in the SOC estimation or the unknown variance of the random error of the SOC gain. Through the designed aging experiment, the capacity estimation accuracy is verified under different life conditions. The results show that the estimation accuracy of this method is high and the error does not exceed 2.5%.

Capacity estimation of lithium-ion batteries based on Gaussian process regression and feature selection

Capacity estimation of lithium-ion batteries based on Gaussian process regression and feature selection

A method for capacity estimation of lithium-ion batteries based on adaptive time-shifting broad learning system

Accurate capacity estimation of lithium-ion batteries can improve the safety and reliability of equipment. Deep learning provides a new approach for capacity estimation. However, it is still difficult to adapt to the changes in different stages of capacity degradation due to many and complex parameters in deep structure network and the time-invariant model parameters. Considering that Broad Learning System is a neural network independent of deep structure, which has a simple single hidden layer structure and fewer parameters, this paper proposes an Adaptive Time-shifting Broad Learning System (ATBLS) capacity estimation model. For input layer, the input data of each time step is combined with the output of previous time step to get a new input, so as to provide local information to hidden unit of the network and provide guidance for local parameters. For hidden layer, the hidden unit of each time step is weighted-fused with the hidden unit of previous time step to update the parameters, so as to reflect the long-term dynamics of sequence. The experiment are conducted on three different data sets. And the effectiveness of ATBLS is verified by comparing with other methods.

Lithium-ion battery capacity estimation — A pruned convolutional neural network approach assisted with transfer learning

Online battery capacity estimation is a critical task for battery management system to maintain the battery performance and cycling life in electric vehicles and grid energy storage applications. Convolutional Neural Networks, which have shown great potentials in battery capacity estimation, have thousands of parameters to be optimized and demand a substantial number of battery aging data for training. However, these parameters require massive memory storage while collecting a large volume of aging data is time-consuming and costly in real-world applications. To tackle these challenges, this paper proposes a novel framework incorporating the concepts of transfer learning and network pruning to build compact Convolutional Neural Network models on a relatively small dataset with improved estimation performance. First, through the transfer learning technique, the Convolutional Neural Network model pre-trained on a large battery dataset is transferred to a small dataset of the targeted battery to improve the estimation accuracy. Then a contribution-based neuron selection method is proposed to prune the transferred model using a fast recursive algorithm, which reduces the size and computational complexity of the model while maintaining its performance. The proposed model is capable of achieving fast online capacity estimation at any time, and its effectiveness is verified on a target dataset collected from four Lithium iron phosphate battery cells, and the performance is compared with other Convolutional Neural Network models. The test results confirm that the proposed model outperforms other models in terms of accuracy and computational efficiency, achieving up to 68.34% model size reduction and 80.97% computation savings.

Data-Driven State of Health Prognostic Model Using a Global Vehicle Data-Set

Data-driven prediction for battery state estimation provides a simple alternative to standard electrical and/or electrochemical models. Recent efforts have used cycling data from laboratory measurements to predict the state of health (SOH) of a cell over its lifetime [1-5]. Laboratory measurements attempt to capture the expected conditions during aging, however, due to the complex situations experienced by electric vehicles during aging, it is not possible to represent each aging path in a laboratory experiment. Additionally, due to resource and time limitations, measurements extending beyond one year are rare. In this work, a global data-set of over 15,000 readings from 300 vehicles driven under real-world conditions is used to provide context on vehicle aging and as a training set for a data-driven SOH prediction model. This data differs significantly from traditional laboratory data in that it does not contain the time-series sampling of, for example, current and voltage over time, as used in most models- rather averaged data over several days, and sometimes months. At relatively frequent intervals during the life of the vehicle, variables such as state of charge, temperature, kilometers driven and others, are compiled as an average over the measurement interval, resulting in one value per measurement period. These averaged readings offer a snapshot into the conditions the vehicle experienced during the measurement period, but do not offer the same detail as what would be recorded in laboratory settings. From this data, a novel data-driven SOH prediction model is developed. The SOH prediction is compared against the onboard SOH estimation performed in the vehicle, which itself has been validated by the vehicle manufacturers. With a large number of samples, a data-driven approach to predicting the capacity of a vehicle is applied. Using Keras, a neural network API written for Python, a two-layer neural network was cross-validated with 50 % training data and 50 % testing data, achieving a high prediction accuracy using six input parameters. This method has the advantage over traditional SOH prediction models, such as semi-empirical and equivalent circuit models, in that it is able to predict the SOH of vehicles in dynamic aging conditions over many years and does not require time-series values of voltage and current as inputs, or cell parameterization, which are often inaccurate and incur high costs to measure. Barré, F. Saurd, M. Gérard, M. Montaru, D. Riu, Statistical Analysis for understanding and prediction battery degradations in real-life electric vehicle use. Journal of Power Sources 245 (2014) 846-856.Zou, X. Hu, H. Ma, S. Li, Combined State of Charge and State of Health estimation over lithium-ion battery cell cycle lifespan for electrical vehicles. Journal of Power Sources 273 (2015) 793-803You, S. Park, D. Oh, Real-time state-of-health estimation for electric vehicle batteries: A data-driven approach. Applied Energy 176 (2016) 92-103.Li, C. Zou, M. Berecibar, E. Nanini-Maury, J. C.-W. Chan, P. van den Bossche, J. Van Mierlo, N. Omar, Random forest regression for online capacity estimation of lithium-ion batteries. Applied Energy 232 (2018) 197-210.Richardson, M. A. Osborne, D. A. Howey, Gaussian process regression for forecasting battery state of health. Journal of Power Sources 357 (2017) 208-219. Figure 1

Online capacity estimation of lithium-ion batteries with deep long short-term memory networks

There is an increasing demand for modern diagnostic systems for batteries under real-world operation, specifically for the estimation of their state of health, for example, via their remaining capacity. The online estimation of the capacity of a cell is challenging due to the dynamic nature of cell aging and the limited variety of inputs available from a cell under operation. The scope of this work is the development of a data-driven capacity estimation model for cells under real-world working conditions with recurrent neural networks having long short-term memory capability. Voltage-time sensor data from the partial constant current phase charging curve is used as input, reflecting input availability in the real world. The network achieves a best-case mean absolute percentage error of 0.76% and is extremely robust while handling input noise. It also has the ability to handle variations in the length of the input time series and can generate a viable estimation even with an incomplete collection of input due to sensor errors. The model validation with several scenarios is done in a local embedded device, highlighting the use case of such models in future battery management systems.