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Keywords = capacity fade remaining useful life

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18 pages, 1112 KiB  
Article
Domain Generalization Using Maximum Mean Discrepancy Loss for Remaining Useful Life Prediction of Lithium-Ion Batteries
by Wenbin Li, Yue Yang and Stefan Pischinger
Batteries 2025, 11(5), 194; https://doi.org/10.3390/batteries11050194 - 14 May 2025
Viewed by 630
Abstract
The capacity of Lithium-ion batteries degrades over the time, making accurate prediction of their Remaining Useful Life (RUL) crucial for maintenance and product lifespan design. However, diverse aging mechanisms, changing working conditions and cell-to-cell variation lead to the inhomogeneous cell lifespan and complicated [...] Read more.
The capacity of Lithium-ion batteries degrades over the time, making accurate prediction of their Remaining Useful Life (RUL) crucial for maintenance and product lifespan design. However, diverse aging mechanisms, changing working conditions and cell-to-cell variation lead to the inhomogeneous cell lifespan and complicated life prediction. In this work, a data-driven algorithm based on stacked Long Short Term Memory (LSTM) encoder–decoders is proposed for RUL prediction. The encoder and upstream decoder form an autoencoder framework for feature extraction. The encoder and the downstream decoder form the encoder–decoder framework for RUL prediction. To enhance generalization during training, the Maximum Mean Discrepancy (MMD) loss is included in the autoencoder framework. The similarity of aging patterns is analyzed during splitting source and target datasets through k-means and Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The Euclidean metric with accumulated Equivalent Cycle Number (ECN) sequence during aging shows better performance for similarity-based data splitting than the Dynamic Time Wrapping (DTW) distance metric based on capacity fading trajectory. The experimental results indicate that the proposed algorithm can provide accurate RUL prediction using 5% fading data and shows good generalization with Coefficient of Determination (R2) score of 0.98. Full article
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16 pages, 5222 KiB  
Article
Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Hybrid Ensembles Allied with Data-Driven Approach
by Shuai Zhao, Daming Sun, Yan Liu and Yuqi Liang
Energies 2025, 18(5), 1114; https://doi.org/10.3390/en18051114 - 25 Feb 2025
Viewed by 864
Abstract
Capacity fade in lithium-ion batteries (LIBs) poses challenges for various industries. Predicting and preventing this fade is crucial, and hybrid methods for estimating remaining useful life (RUL) have become prevalent and achieved significant advancements. In this paper, we introduce a hybrid voting ensemble [...] Read more.
Capacity fade in lithium-ion batteries (LIBs) poses challenges for various industries. Predicting and preventing this fade is crucial, and hybrid methods for estimating remaining useful life (RUL) have become prevalent and achieved significant advancements. In this paper, we introduce a hybrid voting ensemble that combines Gradient Boosting, Random Forest, and K-Nearest Neighbors to forecast the fading capacity trend and knee point. We conducted extensive experiments using the CALCE CS2 datasets. The results indicate that our proposed approach outperforms single deep learning methods for RUL prediction and accurately identifies the knee point. Beyond prediction, this innovative method can potentially be integrated into real-world applications for broader use. Full article
(This article belongs to the Section D: Energy Storage and Application)
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40 pages, 10284 KiB  
Review
A Review of the Technical Challenges and Solutions in Maximising the Potential Use of Second Life Batteries from Electric Vehicles
by Farhad Salek, Shahaboddin Resalati, Meisam Babaie, Paul Henshall, Denise Morrey and Lei Yao
Batteries 2024, 10(3), 79; https://doi.org/10.3390/batteries10030079 - 27 Feb 2024
Cited by 14 | Viewed by 6188
Abstract
The increasing number of electric vehicles (EVs) on the roads has led to a rise in the number of batteries reaching the end of their first life. Such batteries, however, still have a capacity of 75–80% remaining, creating an opportunity for a second [...] Read more.
The increasing number of electric vehicles (EVs) on the roads has led to a rise in the number of batteries reaching the end of their first life. Such batteries, however, still have a capacity of 75–80% remaining, creating an opportunity for a second life in less power-intensive applications. Utilising these second-life batteries (SLBs) requires specific preparation, including grading the batteries based on their State of Health (SoH); repackaging, considering the end-use requirements; and the development of an accurate battery-management system (BMS) based on validated theoretical models. In this paper, we conduct a technical review of mathematical modelling and experimental analyses of SLBs to address existing challenges in BMS development. Our review reveals that most of the recent research focuses on environmental and economic aspects rather than technical challenges. The review suggests the use of equivalent-circuit models with 2RCs and 3RCs, which exhibit good accuracy for estimating the performance of lithium-ion batteries during their second life. Furthermore, electrochemical impedance spectroscopy (EIS) tests provide valuable information about the SLBs’ degradation history and conditions. For addressing calendar-ageing mechanisms, electrochemical models are suggested over empirical models due to their effectiveness and efficiency. Additionally, generating cycle-ageing test profiles based on real application scenarios using synthetic load data is recommended for reliable predictions. Artificial intelligence algorithms show promise in predicting SLB cycle-ageing fading parameters, offering significant time-saving benefits for lab testing. Our study emphasises the importance of focusing on technical challenges to facilitate the effective utilisation of SLBs in stationary applications, such as building energy-storage systems and EV charging stations. Full article
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19 pages, 11357 KiB  
Article
Battery Remaining Useful Life Prediction Using Machine Learning Models: A Comparative Study
by Vahid Safavi, Arash Mohammadi Vaniar, Najmeh Bazmohammadi, Juan C. Vasquez and Josep M. Guerrero
Information 2024, 15(3), 124; https://doi.org/10.3390/info15030124 - 22 Feb 2024
Cited by 16 | Viewed by 7092
Abstract
Predicting the remaining useful life (RUL) of lithium-ion (Li-ion) batteries is crucial to preventing system failures and enhancing operational performance. Knowing the RUL of a battery enables one to perform preventative maintenance or replace the battery before its useful life expires, which is [...] Read more.
Predicting the remaining useful life (RUL) of lithium-ion (Li-ion) batteries is crucial to preventing system failures and enhancing operational performance. Knowing the RUL of a battery enables one to perform preventative maintenance or replace the battery before its useful life expires, which is vital in safety-critical applications. The prediction of the RUL of Li-ion batteries plays a critical role in their optimal utilization throughout their lifetime and supporting sustainable practices. This paper conducts a comparative analysis to assess the effectiveness of multiple machine learning (ML) models in predicting the capacity fade and RUL of Li-ion batteries. Three case studies are analyzed to assess the performances of the state-of-the-art ML models, considering two distinct datasets. These case studies are conducted under various operating conditions such as temperature, C-rate, state of charge (SOC), and depth of discharge (DOD) of the batteries in Cases 1 and 2, and a different set of features and charging policies for the second dataset in Case 3. Meanwhile, diverse extracted features from the initial cycles of the second dataset are considered in Case 3 to predict the RUL of Li-ion batteries in all cycles. In addition, a multi-feature multi-target (MFMT) feature mapping is introduced to investigate the performance of the developed ML models in predicting the battery capacity fade and RUL in the entire life cycle. Multiple ML models that are developed for the comparison analysis in the proposed methodology include Random Forest (RF), extreme gradient boosting (XGBoost), light gradient-boosting machine (LightGBM), multi-layer perceptron (MLP), long short-term memory (LSTM), and attention-LSTM. Furthermore, hyperparameter tuning is applied to improve the performance of the XGBoost and LightGBM models. The results demonstrate that the extreme gradient boosting with hyperparameter tuning (XGBoost-HT) model outperforms the other ML models in terms of the root-mean-squared error (RMSE) and mean absolute percentage error (MAPE) of the battery capacity fade and RUL for all cycles. The obtained RMSE and MAPE values for XGBoost-HT in terms of cycle life are 69 cycles and 6.5%, respectively, for the third case. In addition, the XGBoost-HT model handles the MFMT feature mapping within an acceptable range of RMSE and MAPE, compared to the rest of the developed ML models and similar benchmarks. Full article
(This article belongs to the Section Information Applications)
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16 pages, 3657 KiB  
Article
Real-Time Lithium Battery Aging Prediction Based on Capacity Estimation and Deep Learning Methods
by Joaquín de la Vega, Jordi-Roger Riba and Juan Antonio Ortega-Redondo
Batteries 2024, 10(1), 10; https://doi.org/10.3390/batteries10010010 - 27 Dec 2023
Cited by 6 | Viewed by 4073
Abstract
Lithium-ion batteries are key elements in the development of electrical energy storage solutions. However, due to cycling, environmental, and operating conditions, battery capacity tends to degrade over time. Capacity fade is a common indicator of battery state of health (SOH) because it is [...] Read more.
Lithium-ion batteries are key elements in the development of electrical energy storage solutions. However, due to cycling, environmental, and operating conditions, battery capacity tends to degrade over time. Capacity fade is a common indicator of battery state of health (SOH) because it is an indication of how the capacity has been degraded. However, battery capacity cannot be measured directly, and thus, there is an urgent need to develop methods for estimating battery capacity in real time. By analyzing the historical data of a battery in detail, it is possible to predict the future state of a battery and forecast its remaining useful life. This study developed a real-time, simple, and fast method to estimate the cycle capacity of a battery during the charge cycle using only data from a short period of each charge cycle. This proposal is attractive because it does not require data from the entire charge period since batteries are rarely charged from zero to full. The proposed method allows for simultaneous and accurate real-time prediction of the health and remaining useful life of the battery over its lifetime. The accuracy of the proposed method was tested using experimental data from several lithium-ion batteries with different cathode chemistries under various test conditions. Full article
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17 pages, 4676 KiB  
Article
Second-Life Battery Capacity Estimation and Method Comparison
by Jingxi Yang, Matthew Beatty, Dani Strickland, Mina Abedi-Varnosfaderani and Joe Warren
Energies 2023, 16(7), 3244; https://doi.org/10.3390/en16073244 - 4 Apr 2023
Cited by 10 | Viewed by 3113
Abstract
There is increased talk about using second-life batteries in applications. In first-life applications, the batteries start from new, and a range of life cycle estimation techniques are applied. However, it is not clear how second-life batteries should be monitored compared to first life [...] Read more.
There is increased talk about using second-life batteries in applications. In first-life applications, the batteries start from new, and a range of life cycle estimation techniques are applied. However, it is not clear how second-life batteries should be monitored compared to first life batteries. This paper investigated different algorithms from first-life applications for estimating and forecasting battery cell state of health in conjunction with capacity calculations using second life cells under long term durability testing. The paper looks at how close these models predict capacity fade based on a set of second-life batteries that have been undertaking sweat testing over six different applications. The paper concludes that there are two methods that could be suitable candidates for predicting lifespan. One of these needed to be modified from the original. Full article
(This article belongs to the Topic Battery Design and Management)
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19 pages, 7144 KiB  
Article
Li-Ion Battery Anode State of Charge Estimation and Degradation Monitoring Using Battery Casing via Unknown Input Observer
by Ashikur Rahman, Xianke Lin and Chongming Wang
Energies 2022, 15(15), 5662; https://doi.org/10.3390/en15155662 - 4 Aug 2022
Cited by 10 | Viewed by 4203
Abstract
The anode state of charge (SOC) and degradation information pertaining to lithium-ion batteries (LIBs) is crucial for understanding battery degradation over time. This information about each cell in a battery pack can help prolong the battery pack’s life cycle. Because of the limited [...] Read more.
The anode state of charge (SOC) and degradation information pertaining to lithium-ion batteries (LIBs) is crucial for understanding battery degradation over time. This information about each cell in a battery pack can help prolong the battery pack’s life cycle. Because of the limited observability, estimating the anode state and capacity fade is difficult. This task is even more challenging for the cells in a battery pack, as the current through the individual cell is not constant when cells are connected in parallel. Considering these challenges, this paper presents a novel method to set up three-electrode cells by using the battery’s casing as a reference electrode for building a three-electrode battery pack. This work is a continuation of the authors’ previous research. An unknown input observer (UIO) is employed to estimate the anode SOC of an individual battery in the battery pack. To ensure the stability of a defined Lyapunov function, the UIO parameter matrices are expressed as a linear matrix inequality (LMI). The anode SOC of a lithium nickel manganese cobalt oxide (NMC) battery is estimated by using the standard graphite potential (SGP) and state of lithiation (SOL) characteristic curve. The anode capacity is then calculated by using the total charge transferred in a charging cycle and the estimated SOC of the anode. The degradation of the battery is then evaluated by comparing the capacity fading of the anode to the total charge carried to the cell. The proposed method can estimate the anode SOC and capacity fade of an individual battery in a battery pack, which can monitor the degradation of the individual batteries and the battery pack in real time. By using the proposed method, we can identify the over-degraded batteries in the pack for remaining useful life analysis on the battery. Full article
(This article belongs to the Special Issue Advances in Electrochemical Energy Storage and Conversion)
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18 pages, 3590 KiB  
Article
A Regression-Based Technique for Capacity Estimation of Lithium-Ion Batteries
by Seyed Saeed Madani, Raziye Soghrati and Carlos Ziebert
Batteries 2022, 8(4), 31; https://doi.org/10.3390/batteries8040031 - 31 Mar 2022
Cited by 9 | Viewed by 4068
Abstract
Electric vehicles (EVs) and hybrid vehicles (HEVs) are being increasingly utilized for various reasons. The main reasons for their implementation are that they consume less or do not consume fossil fuel (no carbon dioxide pollution) and do not cause sound pollution. However, this [...] Read more.
Electric vehicles (EVs) and hybrid vehicles (HEVs) are being increasingly utilized for various reasons. The main reasons for their implementation are that they consume less or do not consume fossil fuel (no carbon dioxide pollution) and do not cause sound pollution. However, this technology has some challenges, including complex and troublesome accurate state of health estimation, which is affected by different factors. According to the increase in electric and hybrid vehicles’ application, it is crucial to have a more accurate and reliable estimation of state of charge (SOC) and state of health (SOH) in different environmental conditions. This allows improving battery management system operation for optimal utilization of a battery pack in various operating conditions. This article proposes an approach to estimate battery capacity based on two parameters. First, a practical and straightforward method is introduced to assess the battery’s internal resistance, which is directly related to the battery’s remaining useful life. Second, the different least square algorithm is explored. Finally, a promising, practical, simple, accurate, and reliable technique is proposed to estimate battery capacity appropriately. The root mean square percentage error and the mean absolute percentage error of the proposed methods were calculated and were less than 0.02%. It was concluded the geometry method has all the advantages of a recursive manner, including a fading memory, a close form of a solution, and being applicable in embedded systems. Full article
(This article belongs to the Section Battery Performance, Ageing, Reliability and Safety)
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14 pages, 27508 KiB  
Article
Real-Time Prediction of Capacity Fade and Remaining Useful Life of Lithium-Ion Batteries Based on Charge/Discharge Characteristics
by Chul-Jun Lee, Bo-Kyong Kim, Mi-Kyeong Kwon, Kanghyun Nam and Seok-Won Kang
Electronics 2021, 10(7), 846; https://doi.org/10.3390/electronics10070846 - 1 Apr 2021
Cited by 22 | Viewed by 5162
Abstract
We propose a robust and reliable method based on deep neural networks to estimate the remaining useful life of lithium-ion batteries in electric vehicles. In general, the degradation of a battery can be predicted by monitoring its internal resistance. However, prediction under battery [...] Read more.
We propose a robust and reliable method based on deep neural networks to estimate the remaining useful life of lithium-ion batteries in electric vehicles. In general, the degradation of a battery can be predicted by monitoring its internal resistance. However, prediction under battery operation cannot be achieved using conventional methods such as electrochemical impedance spectroscopy. The battery state can be predicted based on the change in the capacity according to the state of health. For the proposed method, a statistical analysis of capacity fade considering the impedance increase according to the degree of deterioration is conducted by applying a deep neural network to diverse data from charge/discharge characteristics. Then, probabilistic predictions based on the capacity fade trends are obtained to improve the prediction accuracy of the remaining useful life using another deep neural network. Full article
(This article belongs to the Special Issue Advances in Control for Electric Vehicle)
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14 pages, 3095 KiB  
Article
Bilevel vs. Passive Equalizers for Second Life EV Batteries
by Ngalula Sandrine Mubenga, Boluwatito Salami and Thomas Stuart
Electricity 2021, 2(1), 63-76; https://doi.org/10.3390/electricity2010004 - 7 Feb 2021
Cited by 10 | Viewed by 4889
Abstract
Once lithium-ion batteries degrade to below about 80% of their original capacity, they are no longer considered satisfactory for electric vehicles (EVs), but they are still adequate for second-life energy storage applications. However, once this level is reached, capacity fade increases at a [...] Read more.
Once lithium-ion batteries degrade to below about 80% of their original capacity, they are no longer considered satisfactory for electric vehicles (EVs), but they are still adequate for second-life energy storage applications. However, once this level is reached, capacity fade increases at a much faster rate, and the spread between the cell capacities becomes much wider. If the passive equalizer (PEQ) from the EV is still used, battery capacity remains equal to that of the worst cell in the stack, just like it was in the EV. Unfortunately, the worst cell eventually becomes much weaker than the cell average, and the other cells are not fully utilized. If operated while the battery is in use, an active equalizer (AEQ) can increase the battery capacity to a much higher value close to the cell average, but AEQs are much more expensive and are not considered cost effective. However, it can be shown that the bilevel equalizer (BEQ), a PEQ/AEQ hybrid, also can provide a capacity very close to the cell average and at a much lower cost than an AEQ. Full article
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16 pages, 4748 KiB  
Article
Accurate Real Time On-Line Estimation of State-of-Health and Remaining Useful Life of Li ion Batteries
by Cher Ming Tan, Preetpal Singh and Che Chen
Appl. Sci. 2020, 10(21), 7836; https://doi.org/10.3390/app10217836 - 5 Nov 2020
Cited by 23 | Viewed by 3785
Abstract
Inaccurate state-of-health (SoH) estimation of battery can lead to over-discharge as the actual depth of discharge will be deeper, or a more-than-necessary number of charges as the calculated SoC will be underestimated, depending on whether the inaccuracy in the maximum stored charge is [...] Read more.
Inaccurate state-of-health (SoH) estimation of battery can lead to over-discharge as the actual depth of discharge will be deeper, or a more-than-necessary number of charges as the calculated SoC will be underestimated, depending on whether the inaccuracy in the maximum stored charge is over or under estimated. Both can lead to increased degradation of a battery. Inaccurate SoH can also lead to the continuous use of battery below 80% actual SoH that could lead to catastrophic failures. Therefore, an accurate and rapid on-line SoH estimation method for lithium ion batteries, under different operating conditions such as varying ambient temperatures and discharge rates, is important. This work develops a method for this purpose, and the method combines the electrochemistry-based electrical model and semi-empirical capacity fading model on a discharge curve of a lithium-ion battery for the estimation of its maximum stored charge capacity, and thus its state of health. The method developed produces a close form that relates SoH with the number of charge-discharge cycles as well as operating temperatures and currents, and its inverse application allows us to estimate the remaining useful life of lithium ion batteries (LiB) for a given SoH threshold level. The estimation time is less than 5 s as the combined model is a closed-form model, and hence it is suitable for real time and on-line applications. Full article
(This article belongs to the Special Issue Reliability Analysis of Electrotechnical Devices)
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15 pages, 10705 KiB  
Article
Electrical Response of Mechanically Damaged Lithium-Ion Batteries
by Damoon Soudbakhsh, Mehdi Gilaki, William Lynch, Peilin Zhang, Taeyoung Choi and Elham Sahraei
Energies 2020, 13(17), 4284; https://doi.org/10.3390/en13174284 - 19 Aug 2020
Cited by 21 | Viewed by 8521
Abstract
Lithium-ion batteries have found various modern applications due to their high energy density, long cycle life, and low self-discharge. However, increased use of these batteries has been accompanied by an increase in safety concerns, such as spontaneous fires or explosions due to impact [...] Read more.
Lithium-ion batteries have found various modern applications due to their high energy density, long cycle life, and low self-discharge. However, increased use of these batteries has been accompanied by an increase in safety concerns, such as spontaneous fires or explosions due to impact or indentation. Mechanical damage to a battery cell is often enough reason to discard it. However, if an Electric Vehicle is involved in a crash, there is no means to visually inspect all the cells inside a pack, sometimes consisting of thousands of cells. Furthermore, there is no documented report on how mechanical damage may change the electrical response of a cell, which in turn can be used to detect damaged cells by the battery management system (BMS). In this research, we investigated the effects of mechanical deformation on electrical responses of Lithium-ion cells to understand what parameters in electrical response can be used to detect damage where cells cannot be visually inspected. We used charge-discharge cycling data, capacity fade measurement, and Electrochemical Impedance Spectroscopy (EIS) in combination with advanced modeling techniques. Our results indicate that many cell parameters may remain unchanged under moderate indentation, which makes detection of a damaged cell a challenging task for the battery pack and BMS designers. Full article
(This article belongs to the Special Issue Crash Safety of Lithium-Ion Batteries)
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19 pages, 4743 KiB  
Article
Battery Management Systems—Challenges and Some Solutions
by Balakumar Balasingam, Mostafa Ahmed and Krishna Pattipati
Energies 2020, 13(11), 2825; https://doi.org/10.3390/en13112825 - 2 Jun 2020
Cited by 108 | Viewed by 16417
Abstract
Electric vehicles are set to be the dominant form of transportation in the near future and Lithium-based rechargeable battery packs have been widely adopted in them. Battery packs need to be constantly monitored and managed in order to maintain the safety, efficiency and [...] Read more.
Electric vehicles are set to be the dominant form of transportation in the near future and Lithium-based rechargeable battery packs have been widely adopted in them. Battery packs need to be constantly monitored and managed in order to maintain the safety, efficiency and reliability of the overall electric vehicle system. A battery management system consists of a battery fuel gauge, optimal charging algorithm, and cell/thermal balancing circuitry. It uses three non-invasive measurements from the battery, voltage, current and temperature, in order to estimate crucial states and parameters of the battery system, such as battery impedance, battery capacity, state of charge, state of health, power fade, and remaining useful life. These estimates are important for the proper functioning of optimal charging algorithms, charge and thermal balancing strategies, and battery safety mechanisms. Approach to robust battery management consists of accurate characterization, robust estimation of battery states and parameters, and optimal battery control strategies. This paper describes some recent approaches developed by the authors towards developing a robust battery management system. Full article
(This article belongs to the Special Issue Electric Systems for Transportation)
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13 pages, 23465 KiB  
Article
A Unique Failure Mechanism in the Nexus 6P Lithium-Ion Battery
by Saurabh Saxena, Yinjiao Xing and Michael Pecht
Energies 2018, 11(4), 841; https://doi.org/10.3390/en11040841 - 4 Apr 2018
Cited by 8 | Viewed by 7640
Abstract
Nexus 6P smartphones have been beset by battery drain issues, which have been causing premature shutdown of the phone even when the charge indicator displays a significant remaining runtime. To investigate the premature battery drain issue, two Nexus 6P smartphones (one new and [...] Read more.
Nexus 6P smartphones have been beset by battery drain issues, which have been causing premature shutdown of the phone even when the charge indicator displays a significant remaining runtime. To investigate the premature battery drain issue, two Nexus 6P smartphones (one new and one used) were disassembled and their batteries were evaluated using computerized tomography (CT) scan analysis, electrical performance (capacity, resistance, and impedance) tests, and cycle life capacity fade tests. The “used” smartphone battery delivered only 20% of the rated capacity when tested in a first capacity cycle and then 15% of the rated capacity in a second cycle. The new smartphone battery exceeded the rated capacity when first taken out of the box, but exhibited an accelerated capacity fade under C/2 rate cycling and decreased to 10% of its initial capacity in just 50 cycles. The CT scan results revealed the presence of contaminant materials inside the used battery, raising questions about the quality of the manufacturing process. Full article
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15 pages, 2703 KiB  
Article
Novel Approach for Lithium-Ion Battery On-Line Remaining Useful Life Prediction Based on Permutation Entropy
by Luping Chen, Liangjun Xu and Yilin Zhou
Energies 2018, 11(4), 820; https://doi.org/10.3390/en11040820 - 2 Apr 2018
Cited by 54 | Viewed by 4838
Abstract
The degradation of lithium-ion battery often leads to electrical system failure. Battery remaining useful life (RUL) prediction can effectively prevent this failure. Battery capacity is usually utilized as health indicator (HI) for RUL prediction. However, battery capacity is often estimated on-line and it [...] Read more.
The degradation of lithium-ion battery often leads to electrical system failure. Battery remaining useful life (RUL) prediction can effectively prevent this failure. Battery capacity is usually utilized as health indicator (HI) for RUL prediction. However, battery capacity is often estimated on-line and it is difficult to be obtained by monitoring on-line parameters. Therefore, there is a great need to find a simple and on-line prediction method to solve this issue. In this paper, as a novel HI, permutation entropy (PE) is extracted from the discharge voltage curve for analyzing battery degradation. Then the similarity between PE and battery capacity are judged by Pearson and Spearman correlation analyses. Experiment results illustrate the effectiveness and excellent similar performance of the novel HI for battery fading indication. Furthermore, we propose a hybrid approach combining Variational mode decomposition (VMD) denoising technique, autoregressive integrated moving average (ARIMA), and GM(1,1) models for RUL prediction. Experiment results illustrate the accuracy of the proposed approach for lithium-ion battery on-line RUL prediction. Full article
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