A comparative study of data-driven battery capacity estimation based on partial charging curves

With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.

Battery pack capacity estimation for electric vehicles based on enhanced machine learning and field data

Accurate capacity estimation is of great importance for the reliable state monitoring,timely maintenance,and second-life utilization of lithium-ion batteries.Despite numerous works on battery capacity estimation using laboratory datasets,most of them are applied to battery cells and lack satisfactory fidelity when extended to real-world electric vehicle(EV)battery packs.The challenges intensify for large-sized EV battery packs,where unpredictable operating profiles and low-quality data acquisition hinder precise capacity estimation.To fill the gap,this study introduces a novel data-driven battery pack capacity estimation method grounded in field data.The proposed approach begins by determining labeled capacity through an innovative combination of the inverse ampere-hour integral,open circuit voltage-based,and resistance-based correction methods.Then,multiple health features are extracted from incremental capacity curves,voltage curves,equivalent circuit model parameters,and operating temperature to thoroughly characterize battery aging behavior.A feature selection procedure is performed to determine the optimal feature set based on the Pearson correlation coefficient.Moreover,a convolutional neural network and bidirectional gated recurrent unit,enhanced by an attention mechanism,are employed to estimate the battery pack capacity in real-world EV applications.Finally,the proposed method is validated with a field dataset from two EVs,covering approximately 35,000 kilometers.The results demonstrate that the proposed method exhibits better estimation performance with an error of less than 1.1%compared to existing methods.This work shows great potential for accurate large-sized EV battery pack capacity estimation based on field data,which provides significant insights into reliable labeled capacity calculation,effective features extraction,and machine learning-enabled health diagnosis.

A hierarchical enhanced data-driven battery pack capacity estimation framework for real-world operating conditions with fewer labeled data

Battery pack capacity estimation under real-world operating conditions is important for battery performance optimization and health management,contributing to the reliability and longevity of batterypowered systems.However,complex operating conditions,coupling cell-to-cell inconsistency,and limited labeled data pose great challenges to accurate and robust battery pack capacity estimation.To address these issues,this paper proposes a hierarchical data-driven framework aimed at enhancing the training of machine learning models with fewer labeled data.Unlike traditional data-driven methods that lack interpretability,the hierarchical data-driven framework unveils the“mechanism”of the black box inside the data-driven framework by splitting the final estimation target into cell-level and pack-level intermediate targets.A generalized feature matrix is devised without requiring all cell voltages,significantly reducing the computational cost and memory resources.The generated intermediate target labels and the corresponding features are hierarchically employed to enhance the training of two machine learning models,effectively alleviating the difficulty of learning the relationship from all features due to fewer labeled data and addressing the dilemma of requiring extensive labeled data for accurate estimation.Using only 10%of degradation data,the proposed framework outperforms the state-of-the-art battery pack capacity estimation methods,achieving mean absolute percentage errors of 0.608%,0.601%,and 1.128%for three battery packs whose degradation load profiles represent real-world operating conditions.Its high accuracy,adaptability,and robustness indicate the potential in different application scenarios,which is promising for reducing laborious and expensive aging experiments at the pack level and facilitating the development of battery technology.

Investigation into Impedance Measurements for Rapid Capacity Estimation of Lithium-ion Batteries in Electric Vehicles

With the dramatic increase in electric vehicles(EVs)globally,the demand for lithium-ion batteries has grown dramatically,resulting in many batteries being retired in the future.Developing a rapid and robust capacity estimation method is a challenging work to recognize the battery aging level on service and provide regroup strategy of the retied batteries in secondary use.There are still limitations on the current rapid battery capacity estimation methods,such as direct current internal resistance(DCIR)and electrochemical impedance spectroscopy(EIS),in terms of efficiency and robustness.To address the challenges,this paper proposes an improved version of DCIR,named pulse impedance technique(PIT),for rapid battery capacity estimation with more robustness.First,PIT is carried out based on the transient current excitation and dynamic voltage measurement using the high sampling frequency,in which the coherence analysis is used to guide the selection of a reliable frequency band.The battery impedance can be extracted in a wide range of frequency bands compared to the traditional DCIR method,which obtains more information on the battery capacity evaluation.Second,various statistical variables are used to extract aging features,and Pearson correlation analysis is applied to determine the highly correlated features.Then a linear regression model is developed to map the relationship between extracted features and battery capacity.To validate the performance of the proposed method,the experimental system is designed to conduct comparative studies between PIT and EIS based on the two 18650 batteries connected in series.The results reveal that the proposed PIT can provide comparative indicators to EIS,which contributes higher estimation accuracy of the proposed PIT method than EIS technology with lower time and cost.

Fast Remaining Capacity Estimation for Lithium-ion Batteries Based on Short-time Pulse Test and Gaussian Process Regression

It remains challenging to effectively estimate the remaining capacity of the secondary lithium-ion batteries that have been widely adopted for consumer electronics,energy storage,and electric vehicles.Herein,by integrating regular real-time current short pulse tests with data-driven Gaussian process regression algorithm,an efficient battery estimation has been successfully developed and validated for batteries with capacity ranging from 100%of the state of health(SOH)to below 50%,reaching an average accuracy as high as 95%.Interestingly,the proposed pulse test strategy for battery capacity measurement could reduce test time by more than 80%compared with regular long charge/discharge tests.The short-term features of the current pulse test were selected for an optimal training process.Data at different voltage stages and state of charge(SOC)are collected and explored to find the most suitable estimation model.In particular,we explore the validity of five different machine-learning methods for estimating capacity driven by pulse features,whereas Gaussian process regression with Matern kernel performs the best,providing guidance for future exploration.The new strategy of combining short pulse tests with machine-learning algorithms could further open window for efficiently forecasting lithium-ion battery remaining capacity.

Co-Estimation of State of Charge and Capacity for Lithium-Ion Batteries with Multi-Stage Model Fusion Method

Lithium-ion batteries(LIBs)have emerged as the preferred energy storage systems for various types of electric transports,including electric vehicles,electric boats,electric trains,and electric airplanes.The energy management of LIBs in electric transports for all-climate and long-life operation requires the accurate estimation of state of charge(SOC)and capacity in real-time.This study proposes a multistage model fusion algorithm to co-estimate SOC and capacity.Firstly,based on the assumption of a normal distribution,the mean and variance of the residual error from the model at different ageing levels are used to calculate the weight for the establishment of a fusion model with stable parameters.Secondly,a differential error gain with forward-looking ability is introduced into a proportional–integral observer(PIO)to accelerate convergence speed.Thirdly,a fusion algorithm is developed by combining a multistage model and proportional–integral–differential observer(PIDO)to co-estimate SOC and capacity under a complex application environment.Fourthly,the convergence and anti-noise performance of the fusion algorithm are discussed.Finally,the hardware-in-the-loop platform is set up to verify the performance of the fusion algorithm.The validation results of different aged LIBs over a wide range of temperature show that the presented fusion algorithm can realize a high-accuracy estimation of SOC and capacity with the relative errors within 2%and 3.3%,respectively.

Residential PV capacity estimation and power disaggregation using net metering measurements

As the intermittency and uncertainty of photovoltaic(PV)power generation poses considerable challenges to the power system operation,accurate PV generation estimates are critical for the distribution operation,maintenance,and demand response program implementation because of the increasing usage of distributed PVs.Currently,most residential PVs are installed behind the meter,with only the net load available to the utilities.Therefore,a method for disaggregating the residential PV generation from the net load data is needed to enhance the grid-edge observability.In this study,an unsupervised PV capacity estimation method based on net metering data is proposed,for estimating the PV capacity in the customer’s premise based on the distribution characteristics of nocturnal and diurnal net load extremes.Then,the PV generation disaggregation method is presented.Based on the analysis of the correlation between the nocturnal and diurnal actual loads and the correlation between the PV capacity and their actual PV generation,the PV generation of customers is estimated by applying linear fitting of multiple typical solar exemplars and then disaggregating them into hourly-resolution power profiles.Finally,the anomalies of disaggregated PV power are calibrated and corrected using the estimated capacity.Experiment results on a real-world hourly dataset involving 260 customers show that the proposed PV capacity estimation method achieves good accuracy because of the advantages of robustness and low complexity.Compared with the state-of-the-art PV disaggregation algorithm,the proposed method exhibits a reduction of over 15%for the mean absolute percentage error and over 20%for the root mean square error.

Sector Capacity Estimation Based on Differentiated Routes and Busy Levels

Sector capacity estimation plays an important role in applied research of airspace management.Previous researches manifest that sector capacity should be influenced by its standard flow,or routes in that sector.However,if air traffic controller(ATCO)workload busy levels(level of proactivity of an ATCO)are ignored,the estimated sector capacity may not be accurate.There is a need to compare the estimated sector capacity with and without busy levels consideration,both with differentiated routes consideration.This paper proposes a method for sector capacity estimation based on ATCO workload considering differentiated routes and busy levels.Firstly,the main routes in the sector are identified,and for each route,the ATCO workload per flight is determined.Secondly,the workload for each route at three busy levels is determined.Regression analysis is then applied to determine the relationship between workload and the number of flights(with and without considering busy levels)in 15 min and 1h time slices.Sector capacity is then determined on the basis of a specified workload threshold,for the two cases with and without considering busy levels.Comparing the two scenarios and following validation by ATCO survey,it is found that capacity estimation considering busy levels is a more realistic and accurate approach.The validated capacity values for the Zhengzhou approach(ZHCC AP)airspace sector accounting for the busy levels were determined accurately as 10 and 33 flights for the 15 min and 1h slices,respectively.The corresponding results without considering busy levels were 12 and 41 flights for the 15 min and 1h time slices,respectively.

FAST CAPACITY ESTIMATION ALGORITHMS FOR MANETS USING DIRECTIONAL ANTENNAS

In this letter,capacity estimation for Mobile Ad hoc NETworks (MANETs) using direc- tional antennas are studied.Two Matrix-based Fast Calculation Algorithms (MFCAs) are proposed to estimate the network capacity in a network scenario in which there is no channel sharing among multiple sessions and traffic is sensitive to delay with an end-to-end delay constraint.The first algo- rithm MFCA-1 is used to estimate network capacity in a situation where all links have the same delay. It estimates the maximum number of k-hop sessions in a network based on the k-hop adjacency matrix of the network.The second algorithm MFCA-2 is used to estimate network capacity in a situation where different links may have different delays.It calculates the maximum number of sessions in a network with an end-to-end delay constraint based on the adjacency matrix and the link-delay matrix of the network.Numerical and simulation results show that both MFCA-1 and MFCA-2 can calculate network capacity much faster than the well-known Brute-Force Search Algorithm (BFSA) but with the same accuracy.

Aspects of Railway Capacity and Occupation Time Estimation

The priority of the EU transport policy in railway sector is to open up the railway market. The objective is to provide railway undertakings with access to the railway network on equal terms. The main problem is determining the infrastructure capacity. A variety of methodologies are used across Europe for the capacity estimation of railway infrastructure. This diversity has forced railway infrastructure managers to seek a new, common methodology. The UIC methodology is an easy way to calculate the capacity consumption. However, there the possibility to expound this methodology in different ways, which can result in different capacity consumptions. There isan advantage to improve this methodology and to set a clear and unified method of occupation time estimation. The fundamental improvement to UIC methodology is the definition of the occupation time by the trains. This paper gives a description of Slovak and UIC methodologies as a basis for a newly developed approach. The new way of estimation of the capacity consumption （occupation time） is based on a graphic approach. The new methodology concerns the estimation of the infrastructure occupation time and is a conceptual framework developed by the authors for an easier evaluation of occupation time in train traffic diagrams. The new methodology makes the UIC methodology more usable and enables more exact results to be obtained from infrastructure capacity examination.

Approach to estimating non-point pollutant load removal rates based on water environmental capacity: a case study in Shenzhen

An innovative approach based on water environmental capacity for non-point source NPS pollution removal rate estimation was discussed by using both univariate and multivariate data analysis.Taking Shenzhen city as the study case a 67% to 74% NPS pollutant load removal rate can lead to meeting the chemical oxygen demand COD pollution control target for most watersheds.In contrast it is hardly to achieve the ammonia nitrogen NH4-N total phosphorus TP and biological oxygen demand BOD5 pollution control target by simply removing NPS pollutants. This highlights that the pollution control strategies should be taken according to different pollutant species and sources in different watersheds rather than one-size-fits-all .

An analysis of four methodologies for estimating highway capacity from ITS data

With the recent advent of Intelligent Transporta- tion Systems （ITS）, and their associated data collection and archiving capabilities, there is now a rich data source for transportation professionals to develop capacity values for their own jurisdictions. Unfortunately, there is no consensus on the best approach for estimating capacity from ITS data. The motivation of this paper is to compare and contrast four of the most popular capacity estimation techniques in terms of （1） data requirements, （2） modeling effort required, （3） esti- mated parameter values, （4） theoretical background, and （5） statistical differences across time and over geographically dispersed locations. Specifically, the first method is the maximum observed value, the second is a standard funda- mental diagram curve fitting approach using the popular Van Aerde model, the third method uses the breakdown identifi- cation approach, and the fourth method is the survival prob- ability based on product limit method. These four approaches were tested on two test beds： one is located in San Diego, California, U.S., and has data from 112 work days; the other is located in Shanghai, China, and consists of 81 work days. It was found that, irrespective of the estimation methodology and the definition of capacity, the estimated capacity can vary considerably over time. The second finding was that, as ex- pected, the different approaches yielded different capacity results. These estimated capacities varied by as much as 26 % at the San Diego test site and by 34 % at the Shanghai test site. It was also found that each of the methodologies has advantages and disadvantages, and the best method will be the function of the available data, the application, and the goals of the modeler. Consequently, it is critical for users of automatic capacity estimation techniques, which utilize ITS data, to understand the underlying assumptions of each of the different approaches.

A novel combined multi-battery dataset based approach for enhanced prediction accuracy of data driven prognostic models in capacity estimation of lithium ion batteries

To ensure smooth and reliable operations of battery systems,reliable prognosis with accurate prediction of State of Health of lithium ion batteries is of utmost importance.However,battery degradation is a complex challenge involving many electrochemical reactions at anode,separator,cathode and electrolyte/electrode interfaces.Also,there is significant effect of the operating conditions on the battery degradation.Various machine learning tech-niques have been applied to estimate the capacity and State of Health of lithium ion batteries to ensure reliable operation and timely maintenance.In this paper,we study the Gaussian Process Regression(GPR)and Support Vector Machine(SVM)model-based approaches in estimating the capacity and State of Health of batteries.Bat-tery capacity and State of Health estimations are carried out using GPR and SVM models and the predictions comparatively studied for accuracy based on RMSE values.The prediction accuracy is further compared with re-spect to single sensor and multi sensor data.Further,a combined multi battery data set model is used to improve the prediction accuracy.Combining the data of multiple batteries with similar operating conditions for training a model resulted in higher prediction accuracy.

Estimation of highway capacity under environmental constraints vs.conventional traffic flow criteria:A case study of Tehran

In this paper,the concept of environmental capacity is developed to identify a convenient maximum traffic volume which will not reduce the life quality of residents.The presented method investigates the idea of traffic capacity under environmental constraints by calculating the maximum number of vehicles allowed on roads based on acceptable levels of air and noise pollutants.In this study,the permissible noise pollution level and permissible levels of CO and NOxpollution are considered for determining environmental capacity.Results show the significant difference between environmental capacity and functional traffic capacity,introduced by the highway capacity manual(HCM)as a conventional method for estimating functional capacity.Thus,maximum allowed pollution is considered a constraint on a vehicle flow rate,which shows the proper traffic flow for selected streets in Tehran,Iran’s capital.The paper concludes that traffic capacity under noise and air pollution constraints is much less(approximately one-fourth and one-eighth for noise and air pollution respectively)than the current highway capacity estimated using HCM guidelines.Therefore,to save the cities like Tehran from noise and air pollution,traffic flows should be limited to the level of environmental capacity by implementing some travel demand management(TDM)policies like road pricing.

Basics of estimation

This paper outlines a theory of estimation,where optimality is defined for all sizes of data—not only asymptotically.Also one principle is needed to cover estimation of both real-valued parameters and their number.To achieve this we have to abandon the traditional assumption that the observed data have been generated by a“true”distribution,and that the objective of estimation is to recover this from the data.Instead,the objective in this theory is to fit‘models’as distributions to the data in order to find the regular statistical features.The performance of the fitted models is measured by the probability they assign to the data:a large probability means a good fit and a small probability a bad fit.Equivalently,the negative logarithm of the probability should be minimized,which has the interpretation of code length.There are three equivalent characterizations of optimal estimators,the first defined by estimation capacity,the second to satisfy necessary conditions for optimality for all data,and the third by the complete Minimum Description Length(MDL)principle.

Theory of optimal blocking for fractional factorial split-plot designs

The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.

A Multitime-scale Deep Learning Model for Lithium-ion Battery Health Assessment Using Soft Parameter-sharing Mechanism

Efficient assessment of battery degradation is important to effectively utilize and maintain battery management systems.This study introduces an innovative residual convolutional network(RCN)-gated recurrent unit(GRU)model to accurately assess health of lithium-ion batteries on multiple time scales.The model employs a soft parameter-sharing mechanism to identify both short-d dT and long-term degradation patterns.The continuously looped(V),T(V),dQ/dV and dT/dV are extracted to form a four-channel image,dV dV from which the RCN can automatically extract the features and the GRU can capture the temporal features.By designing a soft parameter-sharing mechanism,the model can seamlessly predict the capacity and remaining useful life(RUL)on a dual time scale.The proposed method is validated on a large MIT-Stanford dataset comprising 124 cells,showing a high accuracy in terms of mean absolute errors of 0.00477 for capacity and 83 for RUL.Furthermore,studying the partial voltage fragment reveals the promising performance of the proposed method across various voltage ranges.Specifically,in the partial voltage segment of 2.8-3.2 V,root mean square errors of 0.0107 for capacity and 140 for RUL are achieved.