Online Remaining Useful Life Prediction for Lithium-Ion Batteries Using Partial Discharge Data Features

: Online accurate estimation of remaining useful life (RUL) of lithium-ion batteries is a necessary feature of any smart battery management system (BMS). In this paper, a novel partial discharge data (PDD)-based support vector machine (SVM) model is proposed for RUL prediction. The proposed algorithm extracts the critical features from the voltage and temperature of PDD to train the SVM models. The classiﬁcation and regression attributes of SVM are utilized to classify and predict accurate RUL. The di ﬀ erent ranges of PDD were analyzed to ﬁnd the optimal range for training the SVM model. The SVM model trained with optimal PDD features classiﬁes the RUL into six di ﬀ erent classes for gross estimation, and the support vector regression is used to estimate the accurate value of the last class. The classiﬁcation and predictive performance of SVM model trained using the full discharge data and PDD are compared for publicly available data. Results show that the SVM classiﬁcation and regression model trained with PDD features can accurately predict the RUL with low storage pressure on BMS. The PDD-based SVM model can be utilized for online RUL estimation in electric vehicles.


Introduction
With the ongoing increase in oil prices and environmental pollution, different types of electric vehicles (EVs) are becoming a secondary source of transportation [1].The EVs are expected to penetrate the present transportation market, and around 100 million EVs are expected to be on-road by the end of 2050 [2].The energy storage system (ESS) and motors are the main parts of EVs.Due to their high energy density, long lifetime, low weight, and low self-discharge rate, lithium-ion batteries are currently considered as an optimal choice for the ESS of EVs and smart grids [3][4][5].A smart battery management system (BMS) is necessary to ensure a safe and reliable function under rough conditions [6,7].The accurate online estimation of the state of health (SOH), remaining useful life (RUL), and state of charge (SOC) of the battery are essential parts of a smart BMS.The SOH specifies the time to replace battery packs [8], RUL shows the remaining number of cycles within satisfactory performance [9], and SOC indicates the remaining available charge of the battery [10,11].There are several of techniques reported in the literature to estimate the SOC of the battery [12,13].The accurate SOH estimation of battery is important to avoid over-charge/over-discharge condition.
Energies 2019, 12, 4366 3 of 14 only applied to train the last class (i.e., sixth class).The classification before the regression step eliminates the need to perform regression across the complete battery life cycle data, which results in less computational complexity.The different lithium-ion battery was tested to validate the classification and prediction accuracy of the proposed algorithm.

Remaining Useful Life (RUL)
In this work, the RUL of a lithium-ion battery expressed in terms of its capacity, it can be written as: where C battery , C nominal , and C EOL denotes the present capacity, nominal capacity, and end-of-life capacity of the lithium-ion battery, respectively.The online measurement of the capacity of lithium-ion batteries is not a simple task because it cannot be measured directly using any sensor [33].The most accurate and commonly used method is the offline discharge test.In this method, the battery is discharged at some certain constant conditions such as temperature and discharge current.This method cannot be employed for online prediction, and it is also very time-consuming.For the online measurement of RUL, the online extraction of features from battery data is very pivotal.The selected features should show good variation against battery capacity for accurate RUL prediction.In this work, publicly available battery cycling data is utilized (provided by the Prognostics Center of Excellence at the NASA Ames Research Center, Washington, DC, USA) [35].The cyclic battery data contains battery voltage, battery current, load voltage, load current, time, battery capacity, and battery temperature values.The specifications and operating conditions of the battery data used in this work are listed in Table 1.The parameters of the battery vary with the increase of the cycle number.Figure 1a,b show some of the battery discharging parameters profile of B0005 lithium-ion battery.
Energies 2019, 12, x FOR PEER REVIEW 3 of 14 only applied to train the last class (i.e., sixth class).The classification before the regression step eliminates the need to perform regression across the complete battery life cycle data, which results in less computational complexity.The different lithium-ion battery was tested to validate the classification and prediction accuracy of the proposed algorithm.

Remaining Useful Life (RUL)
In this work, the RUL of a lithium-ion battery expressed in terms of its capacity, it can be written as: where ‫ܥ‬ ௧௧௬ , ‫ܥ‬ , and ‫ܥ‬ ாை denotes the present capacity, nominal capacity, and end-of-life capacity of the lithium-ion battery, respectively.The online measurement of the capacity of lithiumion batteries is not a simple task because it cannot be measured directly using any sensor [33].The most accurate and commonly used method is the offline discharge test.In this method, the battery is discharged at some certain constant conditions such as temperature and discharge current.This method cannot be employed for online prediction, and it is also very time-consuming.For the online measurement of RUL, the online extraction of features from battery data is very pivotal.The selected features should show good variation against battery capacity for accurate RUL prediction.In this work, publicly available battery cycling data is utilized (provided by the Prognostics Center of Excellence at the NASA Ames Research Center, Washington, DC, USA) [35].The cyclic battery data contains battery voltage, battery current, load voltage, load current, time, battery capacity, and battery temperature values.The specifications and operating conditions of the battery data used in this work are listed in Table 1.
Table 1.Specifications and operating conditions of batteries [35].The parameters of the battery vary with the increase of the cycle number.Figure 1a,b show some of the battery discharging parameters profile of B0005 lithium-ion battery.
(a)  Figure 1a,b show the profiles of the discharging voltage and temperature of the lithium-ion battery.It is evident from Figure 1 that the battery degradation has a direct relation with these battery parameters.The battery temperature increased rapidly as the cycle number increases.This employs that the relation between RUL and variation of these discharging parameters can be established for prediction of RUL, which is also discussed in [34].
In this work, the novel RUL prediction approach has been proposed based upon PDV and its corresponding PDT data.The partial data region of the discharging voltage curve selected in a way that every discharge cycle number should reflect in that region.Figure 2a The selection of a voltage region is a very important part, because if the regions do not reflect every cycle data in it, then it will be difficult to estimate the correct value of RUL.The range of the region should be chosen optimally so that the data storage size should be reduced without affecting its prediction accuracy.
(a) Figure 1a,b show the profiles of the discharging voltage and temperature of the lithium-ion battery.It is evident from Figure 1 that the battery degradation has a direct relation with these battery parameters.The battery temperature increased rapidly as the cycle number increases.This employs that the relation between RUL and variation of these discharging parameters can be established for prediction of RUL, which is also discussed in [34].
In this work, the novel RUL prediction approach has been proposed based upon PDV and its corresponding PDT data.The partial data region of the discharging voltage curve selected in a way that every discharge cycle number should reflect in that region.Figure 2a The selection of a voltage region is a very important part, because if the regions do not reflect every cycle data in it, then it will be difficult to estimate the correct value of RUL.The range of the region should be chosen optimally so that the data storage size should be reduced without affecting its prediction accuracy.Figure 1a,b show the profiles of the discharging voltage and temperature of the lithium-ion battery.It is evident from Figure 1 that the battery degradation has a direct relation with these battery parameters.The battery temperature increased rapidly as the cycle number increases.This employs that the relation between RUL and variation of these discharging parameters can be established for prediction of RUL, which is also discussed in [34].
In this work, the novel RUL prediction approach has been proposed based upon PDV and its corresponding PDT data.The partial data region of the discharging voltage curve selected in a way that every discharge cycle number should reflect in that region.The selection of a voltage region is a very important part, because if the regions do not reflect every cycle data in it, then it will be difficult to estimate the correct value of RUL.The range of the region should be chosen optimally so that the data storage size should be reduced without affecting its prediction accuracy.

Support Vector Machine
This section briefly explains the fundamental idea of SVM to solve classification and regression problems [36,37].In classification mode, the SVM supervised classifier that can describe several classes (two or more) by calculating the maximum class separation (the so-called maximum margin hyperplane).In this algorithm, the highly nonlinear input data mapped into a high dimensional feature space.It tries to increase the distance between the hyperplanes and the nearest training data point, also known as support vectors (SVs).For simplification purposes, the algorithm is presented here is for a case of a binary classification problem.The splitting hyperplane for data set ܵ ൌ ൫ , ; ݆ ൌ 1, 2, 3, … , ݉൯ is given by the following equation, where ∈ ܴ is the input and ∈ ሺെ1, 1ሻ are class labels: where ߮ሺሻ: ܴ → ܴ , which maps the input vector to high dimensional feature space, ் is the weight of ߮ሺሻ, and ܾ is the deviation.To find the optimum solution for this problem, the distance between training data points and hyperplane can increase by minimizing the following cost function: where ܿ and ߦ are the user-defined positive regularization value and measure of misclassification training error, respectively.Equation ( 3) is the trade-off between maximum boundary margin and the misclassification error.The Lagrange multiplier method can be utilized to solve this optimization problem:

Support Vector Machine
This section briefly explains the fundamental idea of SVM to solve classification and regression problems [36,37].In classification mode, the SVM supervised classifier that can describe several classes (two or more) by calculating the maximum class separation (the so-called maximum margin hyperplane).In this algorithm, the highly nonlinear input data mapped into a high dimensional feature space.It tries to increase the distance between the hyperplanes and the nearest training data point, also known as support vectors (SVs).For simplification purposes, the algorithm is presented here is for a case of a binary classification problem.The splitting hyperplane for data set S = x j , y j ; j = 1, 2, 3, . . ., m is given by the following equation, where x j ∈ R m is the input and y j ∈ (−1, +1) are class labels: where ϕ(•) : R m → R m h , which maps the input vector to high dimensional feature space, r T is the weight of ϕ(x), and b is the deviation.To find the optimum solution for this problem, the distance between training data points and hyperplane can increase by minimizing the following cost function: subject to: where c and ξ j are the user-defined positive regularization value and measure of misclassification training error, respectively.Equation ( 3) is the trade-off between maximum boundary margin and the misclassification error.The Lagrange multiplier method can be utilized to solve this optimization problem: Energies 2019, 12, 4366 6 of 14 where α and θ are the Lagrange multiplier, the values of α and θ are not equal to zero for small subset of input vectors, these small subsets are also known as SVs.
The SVR algorithm can be utilized for a regression problem, where the main goal is to find an optimal function: The main work of SVR is to obtain a function that has the maximum deviation between the function y(x) and training set with less than the defined value ε.The resultant cost function can be written as: subject to: Again, the Lagrange multiplier method can be introduced to resolve this optimization problem: The solution of the above problem can be written in the following form: where K x, x j is the kernel function.Some commonly used kernel functions are linear, polynomial, radial basis function (RBF), and multi-layer perceptron (MLP) [36,37].In [38], SVM presented in more detail.

Extraction of Features from Battery Discharge Data
Generally, the modeling of SVM consists of following five-step; first is the extraction of critical features, the second one is the processing of data, third is the selection of optimum values of SVM parameters, fourth is the training of the model (Training), and last is the data estimation (Testing).The detail of the lithium-ion battery used in this work is listed in Table 1.
The feature selection is the most important part of the accurate estimation of any data using SVM.The selected features of discharge data should reflect variations for different cycles of the lithium-ion battery.Wang et al. [39] presented the cycle life model of the lithium-ion battery, which can be written as: where R, T, B, E a , Ah, z, and Q loss denotes the gas constant, absolute battery temperature, pre-exponential factor, activation energy, different C rates during discharging, power-law factor, and capacity loss.So, the different features can be extracted from the discharging data to correlate with the capacity degradation.
In this study, the extracted features are energy of the discharge voltage and its corresponding temperature signals (E s ), capacity (Ah), logarithmic band power of voltage and temperature signals (LP s ), and means of voltage and temperature signals (µ s ).The values of these features can be extracted by using given equations [33,34,40]: LP s = log P f , ( 14) where x(t), I, P f , and x(i) represents the signal at time t, discharge current value, power of the signal, and data values, respectively.The energy of voltage and temperature signals are denoted by (E sv ) and (E st ).LP sv and LP st denoted the logarithmic band power of voltage and temperature signal.The means of voltage and temperature denoted by µ sv and µ st , respectively.These features of full discharge data and PDD are shown in Figure 3.

Classification and Regression Model for RUL Prediction
This section explains the design of the classification and regression model for RUL prediction.The machine learning toolbox of MATLAB TM (2019a, MathWorks, Natick, MA, USA) was used for training and testing of the models.For the classification model, the total number of discharge cycles of each cell are counted until it reaches its end of life.The total number of cycles were divided into 6 classes (Class 1-6).Like, battery 0005 and 0006 have a total of 168 discharge cycles, as listed in Table 1.Each class of these two batteries contains 28 discharge cycles.Battery 0036 has 32 discharge cycles in the first five classes and 37 cycles in the last class.Similarly, battery 0056 has 17 cycles in each class.The SVM based classifier model was built by using RBF as a kernel.The grid search algorithm can be used for optimal kernel parameters [33].The regression model used for accurate prediction of RUL.The only features of discharging data which belongs to Class 6 were used to train the regression model by using regression the learner app of MATLAB TM .The RBF kernel function showed the best accuracy to train the regression model.The general flow chart of training and testing of regression and classification models is shown in Figure 4.

Classification and Regression Model for RUL Prediction
This section explains the design of the classification and regression model for RUL prediction.The machine learning toolbox of MATLAB TM (2019a, MathWorks, Natick, MA, USA) was used for training and testing of the models.For the classification model, the total number of discharge cycles of each cell are counted until it reaches its end of life.The total number of cycles were divided into 6 classes (Class 1-6).Like, battery 0005 and 0006 have a total of 168 discharge cycles, as listed in Table 1.Each class of these two batteries contains 28 discharge cycles.Battery 0036 has 32 discharge cycles in the first five classes and 37 cycles in the last class.Similarly, battery 0056 has 17 cycles in each class.The SVM based classifier model was built by using RBF as a kernel.The grid search algorithm can be used for optimal kernel parameters [33].The regression model used for accurate prediction of RUL.The only features of discharging data which belongs to Class 6 were used to train the regression model by using regression the learner app of MATLAB TM .The RBF kernel function showed the best accuracy to train the regression model.The general flow chart of training and testing of regression and classification models is shown in Figure 4.

Results and Analysis
In this section, the performance accuracy of classification and regression models is investigated.The discharging data of battery B0005 was thoroughly analyzed to find the optimum PDD.The 70% (118 cycles of B0005) of the discharge data features were used to train the classification and regression models and the remaining 30% (50 cycles of B0005) were utilized for testing purposes.To check the effectiveness of the proposed methodology the results of both models (full discharge data model and PDD data model) have been compared.In the end, three more battery cells namely B0006, B0036, and B0056 were utilized to validate the proposed technique.

Remaining Useful Life Prediction Using Full Discharge Data
The discharging data of B0005 was used to train the classification and regression models as discussed in Section 3.3.The 70% features of full discharge data were used to train the model, the noted training accuracy of classification model was 94.60%.

Results and Analysis
In this section, the performance accuracy of classification and regression models is investigated.The discharging data of battery B0005 was thoroughly analyzed to find the optimum PDD.The 70% (118 cycles of B0005) of the discharge data features were used to train the classification and regression models and the remaining 30% (50 cycles of B0005) were utilized for testing purposes.To check the effectiveness of the proposed methodology the results of both models (full discharge data model and PDD data model) have been compared.In the end, three more battery cells namely B0006, B0036, and B0056 were utilized to validate the proposed technique.

Remaining Useful Life Prediction Using Full Discharge Data
The discharging data of B0005 was used to train the classification and regression models as discussed in Section 3.3.The 70% features of full discharge data were used to train the model, the noted training accuracy of classification model was 94.60%.
The model was tested by using remaining features of full discharge data.The classification results of RUL classifier are listed in Table 2, where the diagonal values are correctly classified classes.The results reveal that the full discharge data trained model classifies the testing data with 94.11% accuracy.All the test samples which belong to Class 6 are correctly classified.The other 70% samples of Class 6 (18) were utilized to training the regression model for accurate RUL prediction.The results of RUL prediction presented in Figure 5.The model was tested by using remaining features of full discharge data.The classification results of RUL classifier are listed in Table 2, where the diagonal values are correctly classified classes.The results reveal that the full discharge data trained model classifies the testing data with 94.11% accuracy.All the test samples which belong to Class 6 are correctly classified.The other 70% samples of Class 6 (18) were utilized to training the regression model for accurate RUL prediction.The results of RUL prediction presented in Figure 5.The results reveal that the RUL prediction RMSE of the test data is 0.1929%.

Remaining Useful Life Prediction Using Partial Discharge Data
The classification and regression model were trained by using different range of PDD.The training accuracy and error results of both the models are listed in Table 3.The results reveal that the RUL prediction RMSE of the test data is 0.1929%.

Remaining Useful Life Prediction Using Partial Discharge Data
The classification and regression model were trained by using different range of PDD.The training accuracy and error results of both the models are listed in Table 3.The PDD models were also tested for B0006, B0036, and B0056 batteries.The results of classification accuracy and RUL prediction error are summed up in Table 5.

Discussion
The accurate estimation of RUL is an essential component of a smart BMS.In [34], the authors classified the RUL estimation into four different classes.They trained a regression model to estimate The PDD models were also tested for B0006, B0036, and B0056 batteries.The results of classification accuracy and RUL prediction error are summed up in Table 5.

Discussion
The accurate estimation of RUL is an essential component of a smart BMS.In [34], the authors classified the RUL estimation into four different classes.They trained a regression model to estimate the exact value of RUL for the final class.The regression model was trained by using the full discharge data features of only the last class.They used full discharge data features (energy and fluctuation index) of the voltage signal to train the classification and regression models.The shortcoming of this technique is that in real-time applications, the features of full discharge data are not likely to correlate with the testing feature in each cycle because the battery is not fully discharged every time.In addition to this, large storage capacity required to train the SVM models.
In this work, the PDD features (energy of voltage signal and logarithmic band power of temperature signal) were used to train the SVM models.The classifier distributes the RUL in different six classes, and the regression model was utilized to predict the exact value of RUL for the sixth class.Different discharging data ranges were used to train the classifier and regression model (refer to Table 3).After carefully analyzing the training results, we conclude that the best accuracy lies between the range of 3.75-3.5V, and the SOC level of the batteries is around 70-50% for this range.In the best of the authors' knowledge, the battery does not get recharged beyond 70-50% of SOC in most cases.So, it means in every cycle the features of this range can easily be extracted for accurate RUL prediction, and it also requires less storage capacity for training.
To validate our claim, full discharge data and PDD trained models were compared.Full discharge data of battery B0005 correctly classified 48 samples out of 51 (see Table 2), and the RUL prediction RMSE was only 0.1929% (Figure 5).On the other hand, PDD (3.75-3.5 V) trained model correctly classified the 46 samples out of 50 (see Table 4).The regression prediction model almost has a similar RMSE of 0.2159% (see Figure 6) and take almost 12-24 min for the extraction of these features.Full discharge data and PDD used 63,641 and 23,483 samples to train the model and utilized 0.68 ms and 0.31 ms computation time, respectively (for battery B0005).It means the PDD model almost requires 3 times lesser storage space than the full discharge data model with almost the same accuracy.Three more batteries were tested to check the effectiveness of the proposed algorithm.The results validated that the proposed methodology classify and predict the RUL with high accuracy (see Table 5).In the future, the authors will investigate the accuracy of the proposed approach under dynamic conditions such as different operating temperatures, C-rates, and charging modes.Being a data-driven approach, the accuracy of the approach should be checked by training the model using data of one battery and test it by using the data of other battery.

Conclusions
In this work, a novel SVM-based RUL predictive algorithm is presented.The proposed algorithm trains the SVM models using the features (energy of voltage signal and logarithmic band power of temperature signal) of PDD.Firstly, the multiclass algorithm classifies the samples into six classes, and if the classified class is near to the EOL, then the regression model predicts the actual value of RUL.After extensive training of SVM, the optimal PDD range of 3.75-3.5V was found.The PDD based SVM classifies and predicts the RUL with high accuracy.The prediction results of four different batteries validated the effectiveness of the proposed SVM models.The proposed PDD based SVM is adaptable for on-board RUL prediction in electric vehicles.
Figure1a,b show the profiles of the discharging voltage and temperature of the lithium-ion battery.It is evident from Figure1that the battery degradation has a direct relation with these battery parameters.The battery temperature increased rapidly as the cycle number increases.This employs that the relation between RUL and variation of these discharging parameters can be established for prediction of RUL, which is also discussed in[34].In this work, the novel RUL prediction approach has been proposed based upon PDV and its corresponding PDT data.The partial data region of the discharging voltage curve selected in a way that every discharge cycle number should reflect in that region.Figure2a,b show the discharging voltage data of two different regions (3.75-3.5)and (3.1-2.85).The selection of a voltage region is a very important part, because if the regions do not reflect every cycle data in it, then it will be difficult to estimate the correct value of RUL.The range of the region should be chosen optimally so that the data storage size should be reduced without affecting its prediction accuracy.
Figure1a,b show the profiles of the discharging voltage and temperature of the lithium-ion battery.It is evident from Figure1that the battery degradation has a direct relation with these battery parameters.The battery temperature increased rapidly as the cycle number increases.This employs that the relation between RUL and variation of these discharging parameters can be established for prediction of RUL, which is also discussed in[34].In this work, the novel RUL prediction approach has been proposed based upon PDV and its corresponding PDT data.The partial data region of the discharging voltage curve selected in a way that every discharge cycle number should reflect in that region.Figure2a,b show the discharging voltage data of two different regions (3.75-3.5)and (3.1-2.85).The selection of a voltage region is a very important part, because if the regions do not reflect every cycle data in it, then it will be difficult to estimate the correct value of RUL.The range of the region should be chosen optimally so that the data storage size should be reduced without affecting its prediction accuracy.
Figure1a,b show the profiles of the discharging voltage and temperature of the lithium-ion battery.It is evident from Figure1that the battery degradation has a direct relation with these battery parameters.The battery temperature increased rapidly as the cycle number increases.This employs that the relation between RUL and variation of these discharging parameters can be established for prediction of RUL, which is also discussed in[34].In this work, the novel RUL prediction approach has been proposed based upon PDV and its corresponding PDT data.The partial data region of the discharging voltage curve selected in a way that every discharge cycle number should reflect in that region.Figure2a,b show the discharging voltage data of two different regions (3.75-3.5)and (3.1-2.85).The selection of a voltage region is a very important part, because if the regions do not reflect every cycle data in it, then it will be difficult to estimate the correct value of RUL.The range of the region should be chosen optimally so that the data storage size should be reduced without affecting its prediction accuracy.

Figure
Figure 3a,b show the energies of voltage and temperature signals.It is evident from these figures that the energy of the signals decreases with the increase of cycle number.The energies of PDV and PDT for two different regions (3.75-3.5 and 3.1-2.85)were also calculated to check their respective relation with capacity degradation.The energies of PDD almost have similar relation as of full discharge data.‫ܲܮ‬ ௦௩ and ‫ܲܮ‬ ௦௧ of the full discharge data and PDD are shown in Figure 3c,d.The responses of ߤ ௦௩ , ߤ ௦௧ , and ‫ܣ‬ℎ are shown in Figure 3e,f, and g, respectively.It is clear that ‫ܲܮ‬ ௦ and ߤ ௦ almost shown the same behavior.Similarly, ‫ܧ‬ ௦௩ , ‫ܧ‬ ௦௧ , and ‫ܣ‬ℎ also shown the same response with battery degradation.After carefully analyzing the features, ‫ܧ‬ ௦௩ and ‫ܲܮ‬ ௦௧ features were selected to train the SVM model for this work.

Figure 3 .
Figure 3. Extracted features of lithium-ion battery (B0005) discharge data: (a) E sv of full discharge data and PDD; (b) E st of full discharge data and PDD; (c) LP sv of full discharge data and PDD; (d) LP st of full discharge data and PDD; (e) µ sv of full discharge data and PDD; (f) µ st of full discharge data and PDD; (g) Ah of full discharge data and PDD.

Figure
Figure 3a,b show the energies of voltage and temperature signals.It is evident from these figures that the energy of the signals decreases with the increase of cycle number.The energies of PDV and PDT for two different regions (3.75-3.5 and 3.1-2.85)were also calculated to check their respective relation with capacity degradation.The energies of PDD almost have similar relation as of full discharge data.LP sv and LP st of the full discharge data and PDD are shown in Figure 3c,d.The responses of µ sv , µ st , and Ah are shown in Figure 3e-g, respectively.It is clear that LP s and µ s almost shown the same behavior.Similarly, E sv , E st , and Ah also shown the same response with battery degradation.After carefully analyzing the features, E sv and LP st features were selected to train the SVM model for this work.

Figure 4 .
Figure 4. General flow chart of training and testing of classification and regression models for RUL prediction.

Figure 4 .
Figure 4. General flow chart of training and testing of classification and regression models for RUL prediction.

Figure 5 .
Figure 5. Prediction of RUL using features of full discharge data.

Figure 5 .
Figure 5. Prediction of RUL using features of full discharge data.

Table 2 .
Test results of RUL classification model using full discharge data features.

Table 2 .
Test results of RUL classification model using full discharge data features.

Table 3 .
Performance of classification and regression models under different PDD range.It is evident from Table 3 that the ranges of PDD have an impact on the accuracy of both training models.The range 4.2-3.9V shows only 71.40% accuracy for classification with 0.19607 RMSE in regression model training.The PDD region between 4.0-3.5 V has 91.10% training accuracy for classification model, its corresponding RMSE, MAE, and MSE for regression model training are

Table 3 .
Performance of classification and regression models under different PDD range.

Table 5 .
Classification and estimation results of different batteries using features of PDD.

Table 5 .
Classification and estimation results of different batteries using features of PDD.