State of Health Prediction of Electric Vehicles’ Retired Batteries Based on First-Life Historical Degradation Data Using Predictive Time-Series Algorithms

Abstract

The exponential growth of electric and hybrid vehicles, now numbering close to 6 million on the roads, has highlighted the urgent need to address the environmental impact of their lithium-ion batteries as they approach their end-of-life stages. Repurposing these batteries as second-life batteries (SLBs) for less demanding non-automotive applications is a promising avenue for extending their usefulness and reducing environmental harm. However, the shorter lifespan of SLBs brings them perilously close to their ageing knee, a critical point where further use risks thermal runaway and safety hazards. To mitigate these risks, effective battery management systems must accurately predict the state of health of these batteries. In response to this challenge, this study employs time-series artificial intelligence (AI) models to forecast battery degradation parameters using historical data from their first life cycle. Through rigorous analysis of a lithium-ion NMC cylindrical cell, the study tracks the trends in capacity and internal resistance fade across both the initial and second life stages. Leveraging the insights gained from first-life data, predictive models such as the Holt–Winters method and the nonlinear autoregressive (NAR) neural network are trained to anticipate capacity and internal resistance values during the second life period. These models demonstrate high levels of accuracy, with a maximum error rate of only 2%. Notably, the NAR neural network-based algorithm stands out for its exceptional ability to predict local noise within internal resistance values. These findings hold significant implications for the development of specifically designed battery management systems tailored for second-life batteries.

1. Introduction

In recent years, there has been an increase in global concerns about decarbonising energy systems [1]. A promising form of technology for the building sector is distributed energy generation systems such as PV panels [2]. However, despite technological advancements, there are still technical challenges associated with their adoption, such as a mismatch between supply and demand timing [3]. One solution to this challenge is installing energy storage systems (ESSs) [4], which can be integrated with renewable energy systems equipped with PV panels for peak shaving and power shifting [5].

Energy storage systems, while beneficial for energy management solutions, can have significant environmental impacts [6]. The extraction of raw materials, including cobalt, nickel, and lithium, and the energy-intensive processes used to manufacture lithium-ion batteries, are the main contributors to these impacts [7]. To reduce the impact, retired batteries from EVs can be used in less demanding applications, such as buildings, thereby prolonging their service life [8]. SLBs retired from EVs typically have a state of health (SoH) of around 80–85% of their nominal capacity [9,10]. Their significant remaining capacity provides an opportunity to repurpose retired batteries in other applications, as shown below [6,11,12,13,14]:

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They can be used for storing wind and solar power for various household applications, whether on a small or large scale, and can operate in off-grid or grid-connected modes.

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Peak shaving is another application where energy storage systems can help reduce the power demand of industries.

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Energy storage systems can also provide charging for EVs, which helps reduce the overall power demand.

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By reducing the need for large cables, energy storage systems can help to improve the capability and stability of a grid.

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An energy storage system can also function as a battery farm, enabling electricity trading with electricity companies.

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SLB-based energy storage systems can provide financial benefits to end-users, making renewable energy more affordable and desirable.

In order to repurpose SLBs for use in non-automotive applications, a proper visual inspection and technical verification of these batteries is necessary to ensure their reusability [15]. Battery ageing, or degradation, caused by repeated charging and discharging cycles, is an important phenomenon that affects the capacity fade and resistance growth of a battery [16]. Various factors, such as temperature variation, charging and discharging current/voltage, state of charge (SoC), and different charging/discharging techniques, affect the ageing condition [16]. The ability of a battery to store or deliver energy diminishes over time with ageing, making it crucial to accurately estimate (predict) its SoH or capacity by identifying/controlling the factors responsible for its ageing [17]. Such effective predictions can facilitate safe operation, reduce maintenance costs, extend the battery’s life cycle, and identify replacement requirements where necessary [15]. Internal resistance and capacity are the most important factors used to estimate the SoH of a battery [18].

One of the main barriers to using SLBs in stationary energy storage systems is the safety concerns regarding the unknown ageing knee point when a battery is aged during secondary applications [19,20]. Therefore, it is crucial to employ an efficient BMS which can estimate the battery SOH and avoid safety issues when it is used in secondary applications.

Experimental methods for estimating the SoH of a battery involve direct measurement techniques and do not require extensive computation or data learning [21]. However, these methods work under laboratory conditions in offline mode and have comparatively lower accuracy and higher cost than other methods [15]. Indirect methods, such as incremental capacity analysis (ICA) and differential voltage analysis (DVA), extract features from differentiated curves and correlate with battery capacity fade [22,23]. These methods are sensitive to measurement noise and operating temperature, and require low current rates, limiting their applications [24]. Model-based methods use equivalent circuit models (ECM) or electrochemical models (EM) combined with advanced filter techniques like the Kalman filter (KF) or particle filter (PF) to calculate the battery degradation parameters for estimating the SoH [25]. Although these models can accurately reflect the dynamic characteristics of a battery, the complex internal principles and working environment make it challenging to establish a suitable battery model. On the other hand, data-driven methods can predict the state of health or capacity more effectively by collecting ageing data, without requiring explicit models or knowledge of the battery’s working principles [15].

Bhatt et al. [15] proposed the use of machine learning methods to predict the state of health of second-life battery cells. The study utilised charging and discharging curves, as well as first- and second-life degradation experimental data, to train three machine learning models, namely MLP, LSTM, and CNN. The models were trained with various cases, both with and without K-fold cross-validation. The results showed that the K-fold cross-validation trained models had the lowest error, while the LSTM model trained with the battery discharging profile achieved the highest accuracy in predicting the battery’s SoH. Meanwhile, Sarmah et al. [17] conducted a review of the literature and compared the accuracy of various non-destructive methods for SoH estimation of lithium battery cells.

Table 1. The SoH predication methods error comparison [17].

Method	Monitored SoH (from Experiments) [%]	Predicted SoH [%]	Error [%]
Coulomb counting	63.85	69.78	<10
EIS	85	86.27	<2.1
Neural network	82	82.3	<0.5
Support vector machine	60.35	59.19	<2
Kalman filter	84.36	86.57	<5
Sliding mode observer	90.13	90.261	<2.5
Fuzzy logic	88	91.625	1.4–9.2

presents a summary of the comparison of the existing techniques used for SoH prediction [18] and the accuracy of the SoH prediction algorithms available in the literature.

The accuracy of the time-series algorithms, including the NAR neural network and the Holt–Winters method, in SoH prediction have not been reported in the literature. One of the main advantages of the time-series algorithms is that the SoH will be estimated based on historical data. The only input for SoH estimation is the ageing history, the information of which can be saved in the BMS or vehicle ECU to be used for SoH prediction in the battery’s second-life application. This results in significant savings in the time and costs of battery degradation testing as well as optimising the performance of the second life-based battery management system. The results of this paper can provide a basis for using the data from battery passports, which will be installed in EVs to estimate their second-life operating parameters based on their ageing historical data [26,27].

This study, for the first time, evaluated the accuracy of time-series algorithms for SoH prediction of second-life batteries. The degradation analysis of a lithium-ion battery cell is conducted in the lab and the ageing data are generated by applying an accelerated ageing profile. The experimental data generated are then fed into two time-series algorithms to assess their accuracy in predicting capacity and voltage fade as well as resistance increments.

2. Methodology

2.1. Experimental Analysis

Experimental tests are performed in this study to measure the impact of cycle degradation on a battery’s electrochemical parameters. The focus of this testing is on analysing the degradation of the battery cell. To evaluate the cell’s degradation behaviour, cycle ageing tests are designed, while the impacts of calendar ageing are not considered due to the lengthy time required for such tests.

A 3 Ah NMC cylindrical battery cell is tested in a thermal chamber. Cyclic electrical loads are applied to simulate the ageing profile.

Table 2. Second-life battery testing equipment.

Equipment	Model	Calibration Date
Thermal chamber	Binder KB115	30 March 2021
Cell cycler	ARBIN LBT-21084-HC	23 September 2021

provides a list of the equipment necessary for the testing process. The specification of the cell is also presented in

Table 3. The fresh battery cell specifications (from manufacturer).

Chemistry	NMC
Nominal voltage [V]	3.6
$\mathrm{Initial} \mathrm{AC} \mathrm{impedance} [\mathrm{m}\mathsf{\Omega }$]	8–18
Nominal capacity [Ah]	3
Energy density [Wh/kg]	232
Power density [W/kg]	4056

.

In addition, the experimental setup used for testing the cylindrical cells is shown in Figure 1 and Figure 2.

This study aims to evaluate the effects of cycle ageing on the voltage, capacity, and resistance fade of a lithium-ion cell. To achieve this, degradation tests were conducted, and the results were fed into a mathematical model for predicting the cell’s SoH. The proposed cell was subjected to repetitive charging and discharging of current to induce degradation, using an accelerated ageing profile developed by the HVES lab at Oxford Brookes University for battery testing [28]. During the ageing test, the cell was allowed to rest for 3 min after every 11 cycles Every 10 cycles a reference performance was completed, including an internal resistance test and a static capacity at standard charge and C/2 discharge test [28]. The proposed cell had already been aged in the lab to 85% SoH, indicating that its second life had already begun. Subsequently, it was subjected to the degradation test, resulting in an 80% SoH. It should be noted that the cell was stored in the lab for 5 months before its second life began. The current profile applied to the battery cell in the proposed accelerated ageing test is shown in Figure 3.

2.2. Modelling

In this study, the fading parameters of the tested battery in different cycles are predicted using time-series prediction algorithms. The internal resistance and capacity fade of the battery cell is measured during the experiments and fed into the proposed time-series models for training purposes. The study utilises two time-series prediction algorithms, the nonlinear autoregressive (NAR) neural network [29] and the Holt–Winters time-series forecasting algorithm [30], to forecast the SoH of SLBs using first-life historical degradation data. These time-series algorithms are preferred for predicting battery state of health due to their ability to capture temporal patterns and trends in battery performance data, handle seasonality and trends commonly found in battery degradation, forecast future health states based on historical data, provide data-driven insights into degradation factors, model complex relationships between various factors affecting battery health, adapt to changing conditions and update predictions in real-time, and utilise a wide range of techniques including autoregressive models, moving averages, and advanced machine learning methods like ARIMA and LSTM [31]. These algorithms enable accurate predictions and optimisation of battery management strategies.

2.2.1. NAR

Time-series data typically exhibit variations, seasonality, and trends, making a linear model not only cumbersome but also challenging to fit within a dataset. Consequently, nonlinear analysis becomes necessary, and one such approach is the nonlinear autoregressive (NAR) neural network. The topology employed for the NAR model is illustrated in Figure 4 [32]. The NAR model incorporates multiple feedback delays along with a configurable number of hidden layers and neurons, which can be determined through a trial-and-error process to achieve the optimal network topology, typically by minimising the mean absolute percentage error (MAPE) or the root mean square error (RMSE) [11]. In this particular study, the NAR model utilised the number of hidden neurons, and delays within a single hidden layer are provided in the results and discussion section. In addition, the algorithm used in this study for forecasting the battery ageing parameters based on their first-life historical data obtained in the lab is also presented in Figure 5.

2.2.2. Holt–Winters

The Holt–Winters method, introduced by Holt and Winters, is among the various exponential smoothing techniques capable of directly analysing seasonal time series [33]. It relies on three smoothing equations; one for the level component (permanent), one for trend, and one for seasonality (seasonal factor), which can be either additive or multiplicative [33]. The choice between additive or multiplicative seasonality depends on whether the seasonal variation’s magnitude increases with the series’ mean level, with multiplicative seasonality being more common and suitable for our data in this paper. Seasonal changes in the regular trend may indicate factors such as calendar ageing or other conditions affecting cycle ageing fading parameters predictions. The equations below are employed to define the three components (level, trend, and seasonal) [33]:

$$L_t=\alpha \frac{Y_t}{S_{t-s}}+\left(1-\alpha \right)(L_{t-1}+m_{t-1})$$

(1)

$$m_t=\beta (L_t-L_{t-1})+\left(1-\beta \right)m_{t-1}$$

(2)

$$S_t(t)=\gamma \frac{Y_t}{L_t}+\left(1-\gamma \right)S_{t-s}(t)$$

(3)

$$F_{t+\tau }=(L_t+m_t.q)S_{t-s+\tau }$$

(4)

where $L$ is the level estimate (influenced by the amount of $\alpha$), $Y$ are the actual data, $S$ is the seasonality estimate, $m$ is the trend estimate, $F$ is the value forecast for the coming period and s is the seasonal period. The trend component estimation is performed using Equation (5) [33]:

$$m_0=\frac{x_d-x_1}{\left(d-1\right)s}$$

(5)

where “d” represents the number of seasons utilised for establishing the initial values, and $x_r$ denotes the average of the observations during the rth season, with r ranging from 1 to d. The other equations used in this algorithm are listed as below in the order of their use, which is also demonstrated in Figure 6 [33].

$$s_0=x_1$$

(6)

$$h_t=\frac{Y_t}{X_i-[\frac{s+1}{2}-j]m_0}$$

(7)

$$S_t=\frac{1}{d}{\sum }_{k=0}^{d-1}{h}_{t+ks}$$

(8)

$$S_t(0)=S_t\frac{s}{\sum _{t=1}^s{S}_t}$$

(9)

$$F_1=(m_0+L_0)S_1$$

(10)

$$MAPE=\frac{\sum _1^n\left|\frac{Y_t-F_t}{Y_t}\right|}{n} \ast 100\%$$

(11)

The battery ageing data fades, such as capacity, will be fed into the models, and their accuracy in forecasting these ageing parameters will be assessed by comparing them to the experimental data as demonstrated in Figure 5.

3. Results and Discussion

The experimental tests for this study were conducted in the HVES lab. The capacity and internal resistance values for the first life (FL) and the beginning of the cell’s second life (SL) are shown in Figure 7a,b, respectively. The FL data are fed into the forecasting time-series algorithms as the input data for training the model. After observing the values predicted by the proposed time-series algorithm, the SL ageing data are used to find the optimum fitting parameters for each algorithm, as well as testing the accuracy of the predictions.

3.1. NAR Algorithm Prediction

The tested cell’s FL ageing data were entered into the NAR algorithm as the input for training the neural network model. The optimum values of the layer size and time delay parameters, which provide the minimum R-square, were found by trial and error. As presented in

Table 4. The NAR algorithm specifications and results.

Parameter	Training Algorithm	Levenberg–Marquardt
Capacity fade	Layer size	8
	Time delay	5
	Training Mean Squared Error	4.75 × 10−6
	Training R-square	0.99
	Observations	41
	Test Mean Squared Error	2.17 × 10−5
	Test R-square	0.99
Internal resistance increment	Layer size	19
	Time delay	4
	Training Mean Squared Error	1.18 × 10−7
	Training R-square	0.9864
	Observations	401
	Test Mean Squared Error	1.64 × 10−7
	Test R-square	0.9863

, the optimum layer size equals 8 and 19, and the optimum values for time delay equal 5 and 4, for capacity and internal resistance predictions, respectively. The prediction accuracy measurement showed that the NAR algorithm is able to predict the battery’s SL capacity fade and internal resistance using FL historical data for training of the proposed neural network model. The R-square for the predicted values equals 99% and 98.63% for capacity and IR predictions, respectively.

Figure 8a and Figure 9a show the errors of the trained NAR model in each step of the prediction for capacity and internal resistance. The maximum error is below 0.01 Ah for capacity fade prediction as shown in Figure 8a. In addition, for the predicted values in the battery’s SL period (time > 21), the errors increased up to their maximum value; however, the error scale shows the high reliability of the algorithm in making predictions. Figure 9a demonstrates the experimental (target) and predicted (output) values of the NAR model. The maximum error is below 0.0015 Ohm, which shows the reliability of the predicted values.

In the context of using a nonlinear autoregressive (NAR) time-series model for prediction, the graph displaying the mean squared error (MSE) across different epochs provides insights into the model’s performance during training. Each epoch represents a complete pass through the entire dataset during the training process. Figure 8b and Figure 9b demonstrate the variations in the mean squared error over successive epochs. The best epoch refers to the point where the MSE reaches its lowest value during the validation stage of training. The temporal dynamics captured by the NAR time-series model can be assessed by referring to Figure 8c and Figure 9c which show the relationship between the observed data and the predictions made by the NAR time-series model at various time shifts.

The results demonstrate that the employment of the time-series NAR algorithm for predicting the battery capacity fade and internal resistance increment during its SL period leads to achieving reliable predictions that can be used by the BMS to forecast the battery’s SoH based on its historical data.

3.2. Holt–Winters Algorithm Prediction

The following section analyses the results of the Holt–Winters forecasting algorithm to evaluate its accuracy in predicting the battery’s fading parameters due to degradation. The Holt-Winters forecasting algorithm requires a lower load of computational processing and hence offers low-cost low-energy control solutions.

In order to forecast the battery’s degradation parameters, the FL historical data (presented in Figure 7a,b) are used as the input for the algorithms. The output of the Holt–Winters algorithm is the forecasted data and the predicted values with upper and lower confidence bounds.

It was noticed in this study that the Holt–Winters algorithm was not able to forecast data with high noise during the fitting process. Therefore, the average values of the battery’s internal resistance during the degradation process were used, as shown in Figure 10. The three main parameters of this algorithm (Alpha, Beta and Gamma) were found to achieve the maximum R-square for the predicted values, as shown in

Table 5. The forecasting statistics for each predicted parameter using the Holt–Winters algorithm.

	Capacity	Internal Resistance
Alpha	0.9	0.9
Beta	0.9	0.9
Gamma	0	0.1
Forecast start	200	200
R-square	98.2%	99.22%
Confidence interval	11%	12%
Seasonality	1	6

. As is presented in Table 5, it is possible to predict the capacity, starting from 200 cycles (the end of the battery’s FL), with an accuracy of 98.2% (R-square) using the Holt–Winters Algorithm.

The results of the forecasting are shown in Figure 11a,b. For capacity fade, the forecast data with upper confidence bound show the best fit. The average values of the internal resistance increment in various charging and discharging cycles are extracted from Figure 10 and imported to the forecasting algorithm. As demonstrated in Figure 11b, the forecast IR data using lower confidence bounds show the best fit among those in which the prediction started from cycle no. 200 (the end of the battery’s FL). The calculated values of R-square for all of the figures is higher than 98%, proving that employment of such algorithms for SoH estimation in SLBs is reliable and cost-effective, and also results in significant reduction in the time required for the degradation analysis of the batteries in the lab.

3.3. Comparison of the Two Algorithms

One of the main aims of this study was to compare the accuracy of the presented time-series algorithms in SoH prediction of the SLBs using their FL historical data. Accordingly, the predicted values using each algorithm are compared with the experimental data from the laboratory, as shown in Figure 12a,b. As demonstrated in these figures, both algorithms are able to predict battery capacity fade with high accuracy. For IR increment prediction, as the Holt–Winters algorithm is not able to predict the data with high noise, the local fluctuations of the IR in the SL period are not predicted using this algorithm. However, the average value for the experimental data has the same trend as the average values predicted by this algorithm. On the other hand, the NAR algorithm is able to predict local fluctuations of the IR in different ageing cycles with high accuracy, as can be seen in Figure 12. Furthermore, Figure 13a,b also demonstrate that the maximum prediction error for capacity fade and IR prediction belongs to the Holt–Winters algorithm, with higher error peaks than the NAR model.

Table 6. Comparison of the SoH predication errors using other deep learning methods and the ones presented in this study.

Method	Max Error [%]
CNN + GRU + Attention mechanism [34]	<1.3
CNN + LSTM + DNN [35]	<2.5–3.1
RNN [36]	<1
NAR time-series method	<3.2
Holt-Winters time-series method	<4

presents the comparison of the SOH prediction errors using the deep learning algorithms in the literature and the ones introduced in this research. As can be seen in this table, most of the studies used integrated AI techniques to obtain lower rates of errors in SOH predictions. However, it can be also inferred from this table that using simpler deep learning techniques for SOH predictions would result in obtaining acceptable errors in SOH predictions. A comprehensive comparison of the pros and cons of the introduced deep learning-based techniques, compared with other AI-based algorithms, is planned for the future studies.

4. Conclusions

The main challenges in employment of second-life batteries for stationary energy storage systems are the safety concerns raised by unknown ageing history and uncertain point of ageing knee. In this study, time-series algorithms are used to predict the SoH of SLBs using their FL historical ageing data. To train the models, a lithium-ion NMC cylindrical battery cell is degraded in the lab to obtain its capacity fade and internal resistance fade during its first- and second-life periods. The accelerated ageing profile is applied to test the cycle ageing of the batteries and the degradation parameter changes are logged and measured during the experimental tests. The battery’s FL capacity fade and IR increment data are used to train the predictive time-series Holt–Winters and NAR models by finding their optimum functional values for the best fit. After training the models using battery FL ageing data, the capacity and IR values are predicted from 85% SoH to nearly 78% SoH (the SL period) and the results compared with the experimental data. The results of the comparison revealed that both time-series algorithms are able to predict battery ageing parameters during its SL using the FL historical data, with a maximum error of 2%. However, more accurate predictions were observed for the NAR neural network-based algorithm in forecasting the local noise in IR, which is not predictable by the Holt–Winters method.

The findings of this study can inform the design and development of intelligent battery management systems for SLBs. Such intelligent management systems can open up multiple energy saving and operational health and safety opportunities, including significantly reduced time and costs of experimental testing in laboratories, battery SoH monitoring for knee point predictions, and load management optimisation for maximised economic return based on controlling the SLBs’ functional parameters and extending their lifespan.

As the future of this research, the proposed SOH estimation and prediction models will be integrated with equivalent circuit models for the proposed battery to study and predict the impacts of different parameters on the life span of the battery when dynamic load is applied for the second-life application. The results of the current study can form a basis for designing an efficient BMS for the second-life batteries which can address the safety concerns associated with this technology. Regarding the limitations of this study, it should be noted that the degradation analysis was performed in 30 °C environmental temperature. The accuracy of the introduced algorithms should also be evaluated in other environmental temperatures, which will be also considered in future studies.