Data-Driven Remaining Useful Life Prediction for Lithium-Ion Batteries Using Multi-Charging Proﬁle Framework: A Recurrent Neural Network Approach

: Remaining Useful Life (RUL) prediction for lithium-ion batteries has received increasing attention as it evaluates the reliability of batteries to determine the advent of failure and mitigate battery risks. The accurate prediction of RUL can ensure safe operation and prevent risk failure and unwanted catastrophic occurrence of the battery storage system. However, precise prediction for RUL is challenging due to the battery capacity degradation and performance variation under temperature and aging impacts. Therefore, this paper proposes the Multi-Channel Input (MCI) proﬁle with the Recurrent Neural Network (RNN) algorithm to predict RUL for lithium-ion batteries under the various combinations of datasets. Two methodologies, namely the Single-Channel Input (SCI) proﬁle and the MCI proﬁle, are implemented, and their results are analyzed. The veriﬁcation of the proposed model is carried out by combining various datasets provided by NASA. The experimental results suggest that the MCI proﬁle-based method demonstrates better prediction results than the SCI proﬁle-based method with a signiﬁcant reduction in prediction error with regard to various evaluation metrics. Additionally, the comparative analysis has illustrated that the proposed RNN method signiﬁcantly outperforms the Feed Forward Neural Network (FFNN), Back Propagation Neural Network (BPNN), Function Fitting Neural Network (FNN), and Cascade Forward Neural Network (CFNN) under different battery datasets.


Introduction
Globally, the battery storage system has received significant consideration in addressing carbon emissions and climate change problems [1,2]. Among various energy storage systems, lithium-ion batteries offer high energy density, low voltage drops, high lifespan, and wide operating temperatures. Hence, they have gained wide acceptance in numerous applications including electric vehicles, aerospace, energy management systems, and communication [3,4]. When a battery is utilized for a particular application over a duration of time, its capacity starts declining due to the aging of its chemical substances, which leads to issues relating to performance degradation, cell energy storage, and loss of money [5,6]. Moreover, the life of the lithium-ion battery is influenced by many factors such as temperature, humidity, and quality of usage. The performance of the lithium-ion battery can be measured by evaluating the health prognostics so that acceptable results can be delivered within the design limits and storage lifetime [7]. Hence, it is essential to predict the health and remaining lifetime of the battery to ensure safe and reliable usage. during the charging cycle was chosen as an input parameter, and importance sampling was performed. Even though a simple technique was employed for the RUL prediction, suitable hyper-parameter adjustment can be performed to achieve better prediction results. Nuhic et al. [26] proposed a Support Vector Machine (SVM) to predict the state of health (SOH) and RUL of the battery. Liu et al. [27] proposed a Relevance Vector Machine (RVM) algorithm with an online training method to enhance the accuracy of RUL prediction. Patil et al. [28] proposed an SVM algorithm-based RUL prediction by utilizing battery voltage and temperature as key parameters. However, these models rely on the historical data of the battery degradation curve. Additionally, the accuracy and robustness of the model are affected by the non-availability of a large amount of data and hence the forecasting accuracy of the battery capacity is compromised. Recently, the recurrent neural network (RNN) has received widespread attention due to its improved learning performance, high accuracy, and robustness [29,30]. Shaheer et al. [31] presented the cascaded forward neural network (CFNN) for RUL prediction by employing various battery datasets. Liu et al. [32] introduced a Recurrent Neural Network (RNN) for system dynamic forecasting to predict the RUL of batteries. The above-mentioned techniques work satisfactorily for RUL prediction but require suitable hyper-parameter adjustments and an adequate amount of critical data for training the algorithm efficiently. The applicability of various parameters from the operating profiles of lithium-ion batteries to design an efficient model for RUL prediction was not considered. Therefore, it is necessary to utilize key parameters of the operating profiles and identify the critical samples for training the network towards achieving better prediction results, which are accomplished in the presented work.
In this paper, an enhanced RUL prediction framework is developed for lithium-ion batteries. The contributions of this paper are highlighted below: • An improved data-driven method based on RNN with multi-channel input (MCI) profile is employed to predict the RUL of lithium-ion batteries under various training datasets. • A 31-dimensional input data format is generated using the multi parameters under the charging profile including battery discharge capacity, voltage, current, and temperature. • Systematic sampling is implemented to identify and extract critical samples from charging parameters such as voltage, current, and temperature, where 10 samples are collected from every charging cycle. The execution of systematic sampling assists in reconstructing the predicted curve while training the models.

•
The effectiveness of the proposed intelligent RNN algorithm is executed under various training datasets, and a comparative analysis is carried out with other notable datadriven methods by evaluating various performance metrics.
The rest of the paper is organized into six sections. Section 2 presents the degradation mechanism of the lithium-ion battery. Section 3 delivers the acquisition of lithium-ion battery data from NASA. Section 4 explains the proposed methodology for RUL prediction. Section 5 describes the proposed framework consisting of data pre-processing, model selection, and RUL prediction. The results and discussion are outlined in Section 6. The concluding comments are highlighted in Section 7.

Degradation Mechanism of the Lithium-Ion Battery
The lithium-ion battery comprises four main components, namely a cathode, an anode, a separator, and an electrolyte. During the charging process, the lithium ions transfer from the cathode and are deposited on the anode, resulting in energy storage of the lithium-ion battery. However, when the lithium-ion battery is fully charged, lithium ions start to move towards the cathode, resulting in the release of stored energy. During continuous charging and discharging, battery degradation takes place [33]. One of the limiting factors in battery lifetime is attributed to battery degradation, which needs to be addressed efficiently [34].
A lithium-ion battery is regarded as a dynamic and time-varying electrochemical system that consists of non-linear behaviour and a complex internal degradation mechanism [35]. The deterioration in performance and life of a lithium-ion battery takes place due to the increase in the number of charging and discharging cycles [36]. The degradation takes places due to Sustainability 2021, 13, 13333 4 of 25 various causes consisting of physical mechanisms such as mechanical and thermal stress and a chemical mechanism comprising cell reactions [37]. The illustration of a common degradation mechanism in a lithium-ion battery is shown in Figure 1. Battery degradation takes place due to several degradation mechanisms, which can be classified into two categories, i.e., loss of lithium inventory, which takes place due to the utilization of lithium ions during side reaction, and active material loss, which causes a decline in storage capacity [38]. The active material loss occurs specifically due to solvent co-intercalation, graphite exfoliation, as well as copper current collector corrosion resulting in loss of electrical contact and electrode cracking [39]. Lithium-ion inventory loss takes place due to the formation of solid electrolyte interphase (SEI) film, decomposition of electrolytic material, and the occurrence of lithium plating, respectively. It is considered that the occurrence of the degradation process relates to the material composition of the lithium-ion battery. For instance, the development of SEI film occurs due to the lower operating voltage of the graphite anode compared to the electrochemical window of the electrolyte. However, there is no occurrence of SEI film formation when the graphite anode is replaced with a lithium titanium oxide (LTO) anode [40]. Additionally, the structural disordering is highly significant in lithium magnesium oxide (LMO) in comparison with lithium iron phosphate (LIP) cathode. This is due to the small volume change in the LIP cathode. Apart from material composition, the degradation mechanism in the lithium ion battery is closely linked with the operating condition and battery design.
system that consists of non-linear behaviour and a complex internal degradation mechanism [35]. The deterioration in performance and life of a lithium-ion battery takes place due to the increase in the number of charging and discharging cycles [36]. The degradation takes places due to various causes consisting of physical mechanisms such as mechanical and thermal stress and a chemical mechanism comprising cell reactions [37]. The illustration of a common degradation mechanism in a lithium-ion battery is shown in Figure 1. Battery degradation takes place due to several degradation mechanisms, which can be classified into two categories, i.e., loss of lithium inventory, which takes place due to the utilization of lithium ions during side reaction, and active material loss, which causes a decline in storage capacity [38]. The active material loss occurs specifically due to solvent co-intercalation, graphite exfoliation, as well as copper current collector corrosion resulting in loss of electrical contact and electrode cracking [39]. Lithium-ion inventory loss takes place due to the formation of solid electrolyte interphase (SEI) film, decomposition of electrolytic material, and the occurrence of lithium plating, respectively. It is considered that the occurrence of the degradation process relates to the material composition of the lithium-ion battery. For instance, the development of SEI film occurs due to the lower operating voltage of the graphite anode compared to the electrochemical window of the electrolyte. However, there is no occurrence of SEI film formation when the graphite anode is replaced with a lithium titanium oxide (LTO) anode [40]. Additionally, the structural disordering is highly significant in lithium magnesium oxide (LMO) in comparison with lithium iron phosphate (LIP) cathode. This is due to the small volume change in the LIP cathode. Apart from material composition, the degradation mechanism in the lithium ion battery is closely linked with the operating condition and battery design.  Therefore, the RUL prediction of a lithium-ion battery is challenging due to the complex battery degradation mechanism. Nonetheless, accurate prediction of the battery RUL is essential for the battery management system (BMS) in ensuring consistency and reliability of the BMS operation in terms of timely maintenance to avert any unwanted Therefore, the RUL prediction of a lithium-ion battery is challenging due to the complex battery degradation mechanism. Nonetheless, accurate prediction of the battery RUL is essential for the battery management system (BMS) in ensuring consistency and reliability of the BMS operation in terms of timely maintenance to avert any unwanted circumstances. The degradation of battery performance is associated with various mechanisms, and the obtained degradation profile is non-linear. Therefore, the RUL prediction of the lithium-ion battery can be accomplished by acquiring battery aging data. The battery aging data are achieved by employing an accelerated aging test under pre-defined conditions. Currently, the RUL prediction of the lithium-ion battery is carried out by utilizing public datasets due to the complex and time-consuming parameter extraction mechanism.

Acquisition of Lithium-Ion Battery Data for RUL Prediction
The acquisition of critical health indicators (HI) depicts the battery capability towards delivering effective performance as well as indicates the battery degradation state. The acquisition of critical HI is essential for accurate RUL prediction of the battery. In this work, the NASA battery dataset is analysed to acquire four HI for RUL prediction as discussed.

Battery Dataset
The NASA battery dataset is used to predict RUL for lithium-ion batteries. The effectiveness of the proposed model is evaluated using four battery datasets including B0005, B0006, B0007, and B0018. The battery datasets consist of three operating profiles, namely charging, discharging, and impedance at room temperature [41]. The batteries underwent a charging process through the constant current and constant voltage (CCCV) principle, where charging was performed with a constant current of 1.5 A until the voltage reaches 4.2 V. Subsequently, constant voltage was applied until the current drops at 20 mA. Similarly, the discharging profile takes place at a constant current of 2 A until the cell voltage falls to 2.7, 2.5, 2.2, and 2.5 V for each battery. The impedance profile and discharging profile are also studied in the dataset, but it is not employed in the current method. The degradation curve of capacity for various batteries under continuous charging and discharging is presented in Figure 2.
defined conditions. Currently, the RUL prediction of the lithium-ion battery is carried ou by utilizing public datasets due to the complex and time-consuming parameter extraction mechanism.

Acquisition of Lithium-Ion Battery Data for RUL Prediction
The acquisition of critical health indicators (HI) depicts the battery capability towards delivering effective performance as well as indicates the battery degradation state. The acquisition of critical HI is essential for accurate RUL prediction of the battery. In this work, the NASA battery dataset is analysed to acquire four HI for RUL prediction as discussed.

Battery Dataset
The NASA battery dataset is used to predict RUL for lithium-ion batteries. The effectiveness of the proposed model is evaluated using four battery datasets including B0005, B0006, B0007, and B0018. The battery datasets consist of three operating profiles namely charging, discharging, and impedance at room temperature [41]. The batteries underwent a charging process through the constant current and constant voltage (CCCV) principle, where charging was performed with a constant current of 1.5 A until the voltage reaches 4.2 V. Subsequently, constant voltage was applied until the current drops at 20 mA. Similarly, the discharging profile takes place at a constant current of 2 A until the cel voltage falls to 2.7, 2.5, 2.2, and 2.5 V for each battery. The impedance profile and discharging profile are also studied in the dataset, but it is not employed in the current method. The degradation curve of capacity for various batteries under continuous charging and discharging is presented in Figure 2.

Data Sampling from the Charging Profile
During the charging and discharging process, lithium ions escape and enter the electrode particles continuously. The life of the battery is affected by the irregular scattering of lithium ions. The more the scattering and unevenness of the lithium ion, the more battery particles are affected and hence the life of the battery becomes small. Hence it becomes important to understand the characteristics of the charging as well as discharging profile for various battery parameters. It is studied that current during the

Data Sampling from the Charging Profile
During the charging and discharging process, lithium ions escape and enter the electrode particles continuously. The life of the battery is affected by the irregular scattering of lithium ions. The more the scattering and unevenness of the lithium ion, the more battery particles are affected and hence the life of the battery becomes small. Hence, it becomes important to understand the characteristics of the charging as well as discharging profile for various battery parameters. It is studied that current during the discharging process is highly irregular with time, and thus it is difficult to obtain internal parameters, whereas it is easier to obtain internal parameters in the charging profile as it is based on pre-set protocols. Thereby, the data are extracted from the charging profiles to capture the change of internal battery parameters. With regards to data sampling, 10 samples of voltage, current, and temperature from each charging cycle are extracted at equal intervals systematically to reconstitute charging profile parameters [42]. From Figure 3, it is realized that voltage, current, and temperature vary at different charging cycles. In terms of voltage, the aged battery reaches 4.2 V earlier as compared to the fresh battery. In addition, the value of the current drops early in the aged battery compared to the fresh ones. Similarly, the temperature in aged batteries reaches a higher temperature in comparison with fresh batteries. It is noticed that voltage, current, and temperature parameters depend on the cyclic charging and discharging as well as associated battery capacity. Hence, the charging profile parameters are extracted, sampled, and utilized to develop a 31-dimensional input dataset to execute the training operation of the proposed algorithm to determine the RUL of lithium-ion batteries.
capture the change of internal battery parameters. With regards to data sampling, 10 samples of voltage, current, and temperature from each charging cycle are extracted at equal intervals systematically to reconstitute charging profile parameters [42]. From Figure 3, it is realized that voltage, current, and temperature vary at different charging cycles. In terms of voltage, the aged battery reaches 4.2 V earlier as compared to the fresh battery. In addition, the value of the current drops early in the aged battery compared to the fresh ones. Similarly, the temperature in aged batteries reaches a higher temperature in comparison with fresh batteries. It is noticed that voltage, current, and temperature parameters depend on the cyclic charging and discharging as well as associated battery capacity. Hence, the charging profile parameters are extracted, sampled, and utilized to develop a 31-dimensional input dataset to execute the training operation of the proposed algorithm to determine the RUL of lithium-ion batteries.

Phenomena of Capacity Regeneration
One of the important HI for predicting RUL of battery is its capacity [43]. Capacity regeneration phenomena is detected in the batteries during the rest time between the charging and discharging process. This occurs due to the movement of the lithium ion from the negative electrode to the positive electrode and vice versa. A secondary reaction is observed on the electrode surface, which leads to degradation and hence poor performance of the battery. Meanwhile, a re-balancing phenomenon occurs during the

Phenomena of Capacity Regeneration
One of the important HI for predicting RUL of battery is its capacity [43]. Capacity regeneration phenomena is detected in the batteries during the rest time between the charging and discharging process. This occurs due to the movement of the lithium ion from the negative electrode to the positive electrode and vice versa. A secondary reaction is observed on the electrode surface, which leads to degradation and hence poor performance of the battery. Meanwhile, a re-balancing phenomenon occurs during the rest time between active materials and relaxation of gradients produced due to current flow. The re-balancing phenomenon is known as the capacity regeneration phenomenon. The phenomena affect the degradation curve during rest time between charging and discharging process and performance of RUL of battery. Thus, the capacity regeneration phenomena are adopted as a critical input parameter in determining the RUL of the battery.

Recurrent Neural Network Approach
RNN is employed in addressing time series problems due to its powerful computational capabilities [44]. It is utilized in numerous applications such as image processing, feature extraction, prediction, and forecasting. RNN consists of a dynamic memory that can address complex problems by assigning appropriate values of weights. Although RNNs are identical to FFNN, each layer in RNN consists of a recurrent connection with a tap delay. In addition, there exist some differences in the training process between FFNN and RNN. In RNN, the output is calculated depending upon the feedback process consisting of the output of the hidden layer at the present instant and previous instant. The structure of RNN is shown in Figure 4.
rest time between active materials and relaxation of gradients produced due to current flow. The re-balancing phenomenon is known as the capacity regeneration phenomenon. The phenomena affect the degradation curve during rest time between charging and discharging process and performance of RUL of battery. Thus, the capacity regeneration phenomena are adopted as a critical input parameter in determining the RUL of the battery.

Recurrent Neural Network Approach
RNN is employed in addressing time series problems due to its powerful computational capabilities [44]. It is utilized in numerous applications such as image processing, feature extraction, prediction, and forecasting. RNN consists of a dynamic memory that can address complex problems by assigning appropriate values of weights. Although RNNs are identical to FFNN, each layer in RNN consists of a recurrent connection with a tap delay. In addition, there exist some differences in the training process between FFNN and RNN. In RNN, the output is calculated depending upon the feedback process consisting of the output of the hidden layer at the present instant and previous instant. The structure of RNN is shown in Figure 4. The prediction of RUL is carried out based on the input time series (X1, X2…Xt), hidden series (ht−1, ht, ht+1), and output vector yk. The expression for the procedure is as [45]: where i denotes the weight between the input layer and hidden layer, ℎℎ is the weight between a hidden layer and itself at adjacent time steps, and is the weight between the hidden layer and output layer. Oh and Oo represent the output of the hidden layer and output layer. Θx, y and θy, z denote the hidden layer bias and output layer bias, respectively. The sigmoid activation function of RNN is defined as f (), which is expressed as: The backpropagation through time (BPTT) was implemented to train the RNN algorithm, which consists of two stages, namely forward pass and backward pass. Input and other hyperparameters are utilized in obtaining the output from the forward pass, The prediction of RUL is carried out based on the input time series (X 1 , X 2 , . . . , X t ), hidden series (h t−1 , h t , h t+1 ), and output vector y k . The expression for the procedure is as [45]: where x i denotes the weight between the input layer and hidden layer, w hh is the weight between a hidden layer and itself at adjacent time steps, and x j is the weight between the hidden layer and output layer. O h and O o represent the output of the hidden layer and output layer. Θ x,y and θ y,z denote the hidden layer bias and output layer bias, respectively. The sigmoid activation function of RNN is defined as f (), which is expressed as: The backpropagation through time (BPTT) was implemented to train the RNN algorithm, which consists of two stages, namely forward pass and backward pass. Input and other hyperparameters are utilized in obtaining the output from the forward pass, whereas the error from the output layer is calculated by the backward pass algorithm, which is expressed as: where T o is actual output while O o is predicted output, respectively.
In the proposed framework based on the RNN algorithm, the network consists of an input layer, a single hidden layer, and an output layer. The input layer takes a 31dimensional input vector from the battery dataset to train the network. In addition, Hyper-parameters such as hidden neurons, learning rate, epochs, and number of iterations for training the RNN model are selected by the validation method.

Levenberg-Marquardt Algorithm
The LM algorithm is based on approximation of Newton method and is considered one of the fastest training algorithms [46]. The weight of the RNN-based algorithm is updated by the following mathematical expression.
where J P (W) defines the Jacobian matrix of the error vector e P(W) is calculated in w; and I denotes the identity matrix. The error of the network P is characterized by vector JP(w), which is expressed as: The LM algorithm is executed through the following steps, as shown in Figure 5. The network output, error vector, and Jacobian matrix are calculated. Moreover, ∆w is calculated to recalculate the error with w + ∆w as network weights. For any new process, the new weights are introduced when the error is reduced, and further µ is divided by a factor of β. However, the iteration continues if the error is not decreased.
whereas the error from the output layer is calculated by the backward pass algorithm, which is expressed as: where To is actual output while Oo is predicted output, respectively. In the proposed framework based on the RNN algorithm, the network consists of an input layer, a single hidden layer, and an output layer. The input layer takes a 31dimensional input vector from the battery dataset to train the network. In addition, the hidden layer consists of a single layer of 10 neurons with a sigmoid function as the activation function. The output layer consists of single output in terms of capacity. The weight and bias are optimized by utilizing the Levenberg-Marquardt (LM) algorithm. Hyper-parameters such as hidden neurons, learning rate, epochs, and number of iterations for training the RNN model are selected by the validation method.

4.2.. Levenberg-Marquardt Algorithm
The LM algorithm is based on approximation of Newton method and is considered one of the fastest training algorithms [46]. The weight of the RNN-based algorithm is updated by the following mathematical expression.
where ( ) defines the Jacobian matrix of the error vector ( ) is calculated in ; and denotes the identity matrix. The error of the network P is characterized by vector ( ), which is expressed as: The LM algorithm is executed through the following steps, as shown in Figure 5. The network output, error vector, and Jacobian matrix are calculated. Moreover, ∆ is calculated to recalculate the error with w + ∆w as network weights. For any new process, the new weights are introduced when the error is reduced, and further is divided by a factor of . However, the iteration continues if the error is not decreased.

Systematic Sampling Technique for Feature Extraction
Systematic sampling is also known as probability sampling and consists of selecting the number of samples from an ordered sampling frame with fixed and periodic intervals. The periodic interval is known as a sampling interval and is obtained by dividing population size with sampling size. The technique is utilized due to its prediction simplicity. The sampling method is easy to perform when the data are arranged in an

Systematic Sampling Technique for Feature Extraction
Systematic sampling is also known as probability sampling and consists of selecting the number of samples from an ordered sampling frame with fixed and periodic intervals. The periodic interval is known as a sampling interval and is obtained by dividing population size with sampling size. The technique is utilized due to its prediction simplicity. The sampling method is easy to perform when the data are arranged in an ordered manner, ensuring the coverage of all the data presented. In the proposed method, 10 values from each cycle of the charging profile are extracted for voltage, current, and temperature by the utilization of systematic sampling to frame 31-dimensional input data format for training the model. The method of sampling consists of three steps such as computation of the sampling interval (p), which is equal to the population size divided by preferred sampling size, selection of the sample from the population size in a random manner, and, lastly, selecting all the desired samples. While observing the systematic sampling, the population of voltage, current, and temperature at each charge cycle varies. The sampling size is selected as 10, while the sampling interval varies according to the population size of each parameter in each cycle.
In the conventional method for training the algorithm to predict the RUL of the battery, training depends on a single time series data input such as capacity. However, the single input may not be sufficient and efficient enough in training the algorithm for prediction. In addition, the prediction accuracy is not much affected by the inclusion of various input parameters from the same battery dataset. Hence, a 31-dimensional input vector feature is developed for training RNN consisting of different battery datasets.
In this study, a 31-dimensional input profile consisting of voltage, current, temperature, and discharge capacity from a single battery is selected for the SCI profile to train the model, as shown in Figure 6. In addition, the proposed MCI profile consists of 31-dimensional input profile features comprising of 10 samples of voltage, current, and temperature from each charging cycle and discharge capacity from multi, i.e., four batteries where input parameters are combined to train the model. It is noted that 168 charging cycles from battery datasets B0005, B0006, and B0007 and 132 from B0018 have been utilized for training the proposed model, as shown in Figure 7. ordered manner, ensuring the coverage of all the data presented. In the proposed method, 10 values from each cycle of the charging profile are extracted for voltage, current, and temperature by the utilization of systematic sampling to frame 31-dimensional input data format for training the model. The method of sampling consists of three steps such as computation of the sampling interval (p), which is equal to the population size divided by preferred sampling size, selection of the sample from the population size in a random manner, and, lastly, selecting all the desired samples. While observing the systematic sampling, the population of voltage, current, and temperature at each charge cycle varies. The sampling size is selected as 10, while the sampling interval varies according to the population size of each parameter in each cycle.
In the conventional method for training the algorithm to predict the RUL of the battery, training depends on a single time series data input such as capacity. However, the single input may not be sufficient and efficient enough in training the algorithm for prediction. In addition, the prediction accuracy is not much affected by the inclusion of various input parameters from the same battery dataset. Hence, a 31-dimensional input vector feature is developed for training RNN consisting of different battery datasets.

Methodological Framework and Implementation for RUL Prediction Using Multi-Charging Profile
The overall framework for predicting the RUL of a battery by utilizing the MCI profile is presented in Figure 8. The proposed framework consists of three phases. The

Methodological Framework and Implementation for RUL Prediction Using Multi-Charging Profile
The overall framework for predicting the RUL of a battery by utilizing the MCI profile is presented in Figure 8. The proposed framework consists of three phases. The first phase of the framework consists of feature extraction and data pre-processing, where features of various parameters such as charging voltage, current, temperature, and discharge capacity are extracted with data cleansing and data normalization. In the second phase, the data are split for training and testing. The training of the model is executed with various combinations of 31-dimensional input from batteries. Lastly, the RUL for lithium-ion batteries is predicted, and accuracy is checked using key assessment indicators including MAE, RMSE, MAPE, MSE, and SD.  In the first phase, raw data are extracted from NASA prognostics to construct an input feature profile for training the data-driven models. Multiple inputs from the charging profiles are selected including battery discharge capacity, current, voltage, and temperature. In addition, systematic sampling is implemented to extract 10 samples of each input from every charging cycle. Moreover, the extracted samples are organized in a 31-dimensional format based on multi-charging input variables, which then proceed into different data preprocessing steps consisting of data cleansing and data normalization. In the first phase, raw data are extracted from NASA prognostics to construct an input feature profile for training the data-driven models. Multiple inputs from the charging profiles are selected including battery discharge capacity, current, voltage, and temperature. In addition, systematic sampling is implemented to extract 10 samples of each input from every charging cycle. Moreover, the extracted samples are organized in a 31-dimensional format based on multi-charging input variables, which then proceed into different data preprocessing steps consisting of data cleansing and data normalization. The normalization of extracted data consists of a minimum and maximum value of data, which is expressed as [47] where x denotes the summation of charging cycle x k s . The number of charging cycles is represented by s. The maximum and minimum values of the sample data are characterized by max(x) and min(x), respectively.
In the second stage, the data are split into two parts, i.e., training data and test data. In the proposed methodology for analysis, the data are split into various combinations for training the model to comprehensively analyze the prediction outcome while testing the same battery dataset as shown in Figure 9. where ck is actual capacity, whereasĉk is the predicted capacity and n is the number of cycles.  I1, I2 I10   I1, I2 I10   I1, I2 I10   I1, I2 I10   I1, I2 I10   T1, T2 T10   T1, T2 T10   T1, T2 T10   T1, T2 T10   T1, T2 T10   T1, T2 T10 C C C C C C Tested battery dataset 31 Dimensional Multi-Charging Input data format profile Figure 9. Proposed MCI profile with input data format configuration together with the training data format and testing dataset.
In the third phase of the algorithm, the estimated capacity of the battery under each case is observed, which is further utilized in predicting battery RUL. The RUL prediction is carried out for both SCI and MCI profiles. The expression for the is expressed as: where and are referred to as predicted RUL and actual RUL, respectively.
The negative suggests that predicted RUL is less than actual RUL and vice versa. The predicted RUL is obtained by calculating the number of cycles from the starting point until the threshold limit. The presented work considers Cycle 1 as the starting point in each case for RUL prediction. The accuracy of the trained model is calculated by assessing various performance metrics. In addition, the validation of the proposed model is executed with various data-driven methods such as BPNN, FNN, FFNN, and CFNN, respectively. In the third phase of the algorithm, the estimated capacity of the battery under each case is observed, which is further utilized in predicting battery RUL. The RUL prediction is carried out for both SCI and MCI profiles. The expression for the RUL error is expressed as: where RUL predicted and RUL actual are referred to as predicted RUL and actual RUL, respectively. The negative RUL error suggests that predicted RUL is less than actual RUL and vice versa. The predicted RUL is obtained by calculating the number of cycles from the starting point until the threshold limit. The presented work considers Cycle 1 as the starting point in each case for RUL prediction. The accuracy of the trained model is calculated by assessing various performance metrics. In addition, the validation of the proposed model is executed with various data-driven methods such as BPNN, FNN, FFNN, and CFNN, respectively.

Results and Discussion
The dataset from NASA is utilized to evaluate the effectiveness and robustness of the proposed RNN model for RUL prediction of lithium-ion batteries under various training datasets. Four data-driven models are employed for the comparative analysis, which are BPNN, FNN, FFN, and CFNN, respectively. The proposed MCI-based RNN methodology is compared to the SCI methodology, and accordingly, the results are discussed. The accuracy of the RUL prediction under different training datasets is evaluated based on several performance matrices such as RMSE, MSE, MAE, MAPE, and SD. For the SCI profile-based model, the algorithm is tested with the 70:30 ratio of the dataset, where 70% is assigned for training while 30% is assigned for testing. In addition, the MCI-profile-based RNN model is trained by utilizing various combinations of training datasets, as discussed earlier. The threshold value for each battery has been marked individually during the development of the prediction curve, including 1.41 Ah for B0005, 1.39 Ah for B0006, 1.51 Ah for B0007, and 1.41 Ah for B0018, respectively. In terms of the number of cycles, the threshold cycle for B0005 is 126, 110 for B0006, 122 for B0007, and 92 for B0018. The capacity regeneration for B0006 and B0018 battery datasets is also analysed.

Analysis for SCI Profile
For predicting the RUL based on the SCI profile, a 31-dimensional input vector is taken as an input to the model consisting of a single battery dataset. It is validated that the RNN model worked better than other data-driven models for various batteries under test. The RUL prediction of RNN model is more accurate and precise in comparison to BPNN, FNN, FFNN, and CFNN  The RUL error for each case of the battery dataset is very small due to the implementation of a systematic sampling approach, which leads to reconstitution of the predicted curve in an efficient manner. Although the training of each model is performed with 70:30 data, it is concluded that the capability of BPNN, FNN, FFNN, and CFNN is not comprehensive with regard to regeneration phenomena compared to RNN due to an insufficient feedback connection structure, resulting in its low 'memory' ability. The RNN model delivers better results compared to other data-driven techniques in terms of RUL prediction for various batteries. The capacity curve for RUL prediction of different batteries is presented in Figure 10.

Analysis for MCI Profile
In terms of prediction of the RUL of the battery under MCI profile, a 31-dimensional input vector is created with multiple battery datasets. The proposed model is trained with the combination of various datasets under individual battery cells. For each battery, the training of each model is performed with three datasets, combinations of two datasets and a single battery dataset. From the proposed algorithm, the RNN approach outperforms other data-driven methods such as BPNN, FNN, FFNN, and CFNN in terms of accuracy and error under each case of training datasets. The MCI profile results are divided into three categories, namely training with three datasets, training with two datasets, and training with single datasets, respectively. It is seen that the reduction in the training datasets affects the performance of the algorithm as well as the prediction accuracy.

Analysis for MCI Profile
In terms of prediction of the RUL of the battery under MCI profile, a 31-dimensional input vector is created with multiple battery datasets. The proposed model is trained with the combination of various datasets under individual battery cells. For each battery, the training of each model is performed with three datasets, combinations of two datasets and a single battery dataset. From the proposed algorithm, the RNN approach outperforms other data-driven methods such as BPNN, FNN, FFNN, and CFNN in terms of accuracy and error under each case of training datasets. The MCI profile results are divided into three categories, namely training with three datasets, training with two datasets, and training with single datasets, respectively. It is seen that the reduction in the training datasets affects the performance of the algorithm as well as the prediction accuracy.

Training with Three Datasets
The training of the MCI profile-based algorithm with three datasets is examined to calculate the prediction accuracy of the various models. The RNN model outperforms other data-driven methods for each case of RUL prediction. Due to the phenomena of capacity regeneration in B0006 and B0018, the performance metrics are notably higher in comparison to B0005 and B0007, as presented in Table 2 battery datasets under several models of operation is displayed in Figure 11. RNN model achieves the highest accuracy among other data-driven methods. With regards to RUL error, each data-driven model performs satisfactorily and delivered accurate results, but the RNN techniques outperforms other models to achieve higher accuracy. calculate the prediction accuracy of the various models. The RNN model outperforms other data-driven methods for each case of RUL prediction. Due to the phenomena of capacity regeneration in B0006 and B0018, the performance metrics are notably higher in comparison to B0005 and B0007, as presented in  Figure 11. RNN model achieves the highest accuracy among other data-driven methods. With regards to RUL error, each data-driven model performs satisfactorily and delivered accurate results, but the RNN techniques outperforms other models to achieve higher accuracy. (c) (d) Figure 11. SCI profile-based RUL prediction curve for different batteries: (a) B0005, (b) B0006, (c) B0007, and (d) B0018.

Training with Two Datasets
When the proposed RNN method is trained with two battery datasets, the RNN approach performs better than the SCI profile in terms of accuracy and convergence of predicted curve with the original capacity degradation curve. Each battery under test is trained with three dataset combinations and, accordingly, the RUL prediction curve is

Training with Two Datasets
When the proposed RNN method is trained with two battery datasets, the RNN approach performs better than the SCI profile in terms of accuracy and convergence of predicted curve with the original capacity degradation curve. Each battery under test is trained with three dataset combinations and, accordingly, the RUL prediction curve is obtained and presented in Table 3. It is realized that the RNN approach is highly convergent compared to BPNN, FNN, FFNN, and CFNN methods, respectively. The RUL prediction of all batteries while training the model under several combinations is presented in Figure 12. A significant reduction in the performance error is noted with the RNN approach for all the trained battery datasets. When B0005 is selected as the test battery while the RNN model is trained with B0006 and B0007, RMSE is calculated to be 0.0132 compared to 0.3041 for BPNN, 0.1422 for FNN, 0.0656 for FFNN, and 0.0398 for CFNN respectively. Significant phenomena of capacity regeneration in B0006 and B0018 result in performance metrics that are higher than B0005 and B0007, respectively. For instance, the RMSE reported in B0005 is 0.0520 when the proposed RNN model is trained with B0006, B0018. When the RNN model is trained with other two combinations of dataset i.e., B0006, B0007 and B0007, B0018 under the same condition, the calculated RMSE values are 0.0132 and 0.0204, respectively, describing the impact of capacity regeneration phenomena in the above results. Simultaneously, the assessment for RUL error during each testing battery was carried out. The BPNN model performed the least among other data-driven models. Due to the phenomena of capacity regeneration, the RUL error was higher when the model was trained with B0006 and B0018, respectively. For instance, in B0007, the RUL error for BPNN is 8 when trained with B0006, B0018, while it is 2 when trained with B0005, B0007 and B0005, B0018, respectively.

Training with One Dataset
Lastly, each battery is tested under a single dataset, and the prediction results are obtained and presented in Table 4 and Figure 13. It is noticed that RNN performs better with other respective models such as BPNN, FNN, FFNN, and CFNN in terms of prediction accuracy, but the training efficiency of each model is lower due to the smaller quantity of training data, thus making it difficult in capturing the capacity degradation

Training with One Dataset
Lastly, each battery is tested under a single dataset, and the prediction results are obtained and presented in Table 4 and Figure 13. It is noticed that RNN performs better with other respective models such as BPNN, FNN, FFNN, and CFNN in terms of prediction accuracy, but the training efficiency of each model is lower due to the smaller quantity of training data, thus making it difficult in capturing the capacity degradation curve in an enhanced manner. Furthermore, due to the introduction of systematic sampling in the proposed methodology, it is predicted that a significant sample for reconstitution will concentrate around a certain value, and thus lower prediction accuracy is attained. The prediction error of the RNN model is the lowest compared to BPNN, FNN, FFNN, and CFNN, respectively. In the case of B0005, when the RNN is trained under various battery datasets such as B0006, B0007, and B0018, RMSE, MAE, MAPE, MSE, and SD are estimated to be the lowest among other trained data-driven models. Additionally, due to the significant occurrence of capacity regeneration phenomena in B0006 and B0018, the performance metrics are higher than B0005 and B0007, respectively. For instance, the RMSE observed for B0007 while training with B0006 and B0018 was 0.7132 and 1.7598, which is comparatively higher when trained with B0005, i.e., 0.3995. The RUL error for various batteries has been evaluated to demonstrate the effectiveness of the proposed RNN model. It is noticed that capacity regeneration phenomena demonstrate a substantial role in the RUL prediction. The training of each data-driven model delivers higher RUL error when trained with B0006, B0018 as seen in the cases of B0005 and B0007, respectively.

Conclusions
In this paper, a comprehensive analysis of the MCI-profile-based RNN approach for RUL prediction under various datasets is performed. To achieve the target, NASA prognostics battery datasets are utilized for acquiring input parameters consisting of discharge capacity, current, voltage. and temperature. The input dataset framework including a 31-dimensional vector is created by extracting 10 samples of each input parameter at equal intervals of every charging cycle. In addition, the MCI-profile-based method is compared to the SCI profile under various battery datasets. Several performance metrics are assessed under different training conditions. It is examined that the RNN-based MCI profile technique predicts more accurate results than the SCI profile under the application of diverse datasets to train the model. For datasets under B0005, the RMSE for RNN model under the SCI profile is 0.1708, whereas RMSE was 0.0030 under the MCI profile while training with three datasets (B0006, B0007, and B0018). Further, the RMSE was 0.0132 when trained with B0006, B0007 datasets, 0.0204 when trained with the B0007, B0018 dataset, and 0.0364 when trained with the B0006, B0018 datasets, respectively. This suggests the effectiveness of MCI over the SCI profile by utilizing different input parameters. In terms of RUL error, each data-driven model performs satisfactorily due to the application of systematic sampling, which assists in developing the predicted capacity curve in similar manner compared to the actual curve. The BPNN performs the least, while the performance of RNN model was the most accurate among other data-driven techniques. However, when the proposed RNN models are trained with a single battery dataset under the MCI profile, the performance metrics are comparatively higher. Overall, it is concluded that performance metrics dropped when the trained data are more diverse under the MCI profile.
For future work, other internal battery parameters such as impedance and aging can be taken into consideration. Additionally, the validation of the proposed algorithm could be extended by considering discharging profile parameters. In addition, some heuristic optimization techniques can be proposed to find the best hyperparameters for training the model with a smaller amount of data. Institutional Review Board Statement: Not applicable.