Improved LightGBM-Based Framework for Electric Vehicle Lithium-Ion Battery Remaining Useful Life Prediction Using Multi Health Indicators

: To improve the prediction accuracy and prediction speed of battery remaining useful life (RUL), this paper proposes an improved light gradient boosting machine (LightGBM)-based framework. Firstly, the features from the electrochemical impedance spectroscopy (EIS) and incremental capacity-differential voltage (IC-DV) curve are extracted, and the open circuit voltage and temperature are measured; then, those are regarded as multi HIs to improve the prediction accuracy. Secondly, to adaptively adjust to multi HIs and improve prediction speed, the loss function of the LightGBM model is improved by the adaptive loss. The adaptive loss is utilized to adjust the loss function form and limit the saturation value for the ﬁrst-order derivative of the loss function so that the improved LightGBM can achieve an adaptive adjustment to multiple HIs (ohmic resistance, charge transfer resistance, solid electrolyte interface (SEI) ﬁlm resistance, Warburg resistance, loss of conductivity, loss of active material, loss of lithium ion, isobaric voltage drop time, and surface average temperature) and limit the impact of error on the gradient. The model parameters are optimized by the hyperparameter optimization method, which can avoid the lower training efﬁciency caused by manual parameter adjustment and obtain the optimal prediction performance. Finally, the proposed framework is validated by the database from the battery aging and performance testing experimental system. Compared with traditional prediction methods, GBDT (1.893%, 4.324 s), 1D-CNN (1.308%, 47.381 s), SVR (1.510%, 80.333 s), RF (1.476%, 852.075 s), and XGBoost (1.119%, 24.912 s), the RMSE and prediction time of the proposed framework are 1.078% and 15.728 s under the total HIs. The performance of the proposed framework under a different number of HIs is also analyzed. The experimental results show that the proposed framework can achieve the optimal prediction accuracy (98.978%) under the HIs of resistances, loss modes, and isobaric voltage drop time. prediction performance under different number of HIs. The results demonstrate that the proposed framework can realize the accurate and rapid RUL prediction through different HI training, which has proved applicable for different experimental conditions. As the battery RUL prediction is of signiﬁcance in practice, further work will focus on the development and validation of this framework using some features conveniently obtained in real applications under different external factors.


Introduction
The power batteries mainly include the lead-acid battery, the nickel-metal hydride battery, and the lithium-ion battery. Among them, lithium-ion batteries have been widely used in electric vehicles (EV) or hybrid electric vehicles (HEV) and other fields [1,2], with the merits of high energy density, long cycle lifetime, low self-discharge rate, great chargedischarge performance, and a wide operating temperature range [3]. However, with the using the features from partial charging voltage curves to obtain the precise capacity. An XGBoost-based model is established in [23], comparing the battery voltage with the cutoff voltage to achieve the previous overdischarge fault diagnosis. In [24], the LightGBM-based model is proposed to accomplish RUL prediction using the features from the discharge voltage curve, which proves that LightGBM can improve the training speed and reduce the impact of noise on the prediction. However, the single HI has a limited effect on improving prediction accuracy. Hence, the attention of this paper is to utilize multi HIs to improve prediction accuracy.
Meanwhile, multi HIs can improve the prediction accuracy; however, long training time caused by multi HIs may lower training efficiency. For the above problem, although the XGBoost-based model can solve the problems of prediction accuracy and speed, the XGBoost-based model uses the traditional boosting integrated learning method, which needs to traverse the entirety of the training samples many times during prediction and select the best segmentation point, lowering the training efficiency. LightGBM [24] can improve training efficiency. LightGBM reduces the sample and feature dimensions, reduces memory usage, and further improves training efficiency and prediction accuracy through histogram optimization, gradient-based one-side sampling, exclusive feature bundling, and the depth-limited leaf-wise method. Based on the performance merits of LightGBM mentioned in the literature, the LightGBM is used to build an RUL prediction model, which is helpful in improving the efficiency and accuracy of RUL prediction.
The contributions of the proposed method can be summarized as follows: (1) To improve prediction accuracy and avoid low training efficiency caused by HIs. This paper proposes a LightGBM-based RUL prediction framework, which derives the multi HIs extraction and an improved RUL prediction model. (2) The extracted HIs can be mainly divided into indirect HIs (i.e., resistances from EIS and loss modes from IC-DV curves) and direct HIs (i.e., OCV and temperature). To adapt to multi HIs, the loss function of the LightGBM model is improved by the adaptive loss. (3) To obtain the optimal performance, the parameters of the model are optimized by the hyperparameter optimization method. The proposed framework is validated by the database from a battery aging and performance testing experimental system. The performance of the proposed framework under different numbers of HIs is also analyzed.
The rest of this paper is organized as follows: Section 2 introduces the multi health indicators extraction and battery aging and performance testing experimental system. Section 3 establishes the RUL prediction framework based on the improved LightGBM. Section 4 discusses the effectiveness validation and performance evaluation of the proposed RUL prediction framework. Section 5 provides the summary and conclusion.

HIs Extracted from IC-DV Curves
Based on the electrochemical theory in [27,28], the shift in the IC curve towards lower voltage, identified as a loss of conductivity (LC), indicates collector corrosion or electrolyte decomposition inside the battery. The IC peak variation difference, identified as loss of active material (LAM), indicates possible electrode decomposition, electrolyte oxidation, active particle denaturation, lithium dendrite formation, or disordered crystal structure inside the battery. The shift in the DV curve towards lower capacity, identified as loss of lithium ion (LLI), indicates the possibility of electrolyte oxidation and decomposition or lithium dendrite formation inside the battery. The ith cycle degradation mode quantification is as follows.
where LC i , LAM i , and LLI i are quantified degradation modes. V 0 and Q 0 are initial voltage and capacity, respectively.

HIs Extracted from EIS
According to [29], the EIS shown in Figure 1 consists of four main components: (1) the high-frequency region: a semicircle associated with the diffusive migration of lithium ions through the SEI film on the surface of the active material particles. (2) The mid-high frequency region: a semicircle associated with the transport of electrons inside the active material particles. (3) The mid-frequency region: a semicircle associated with the charge transfer process. (4) The low-frequency region: a diagonal line associated with the solid diffusion process of the lithium ions of the active material particles.
where LCi, LAMi, and LLIi are quantified degradation modes. V0 and Q0 are initial voltage and capacity, respectively.

HIs Extracted from EIS
According to [29], the EIS shown in Figure 1 consists of four main components: (1) the high-frequency region: a semicircle associated with the diffusive migration of lithium ions through the SEI film on the surface of the active material particles. (2) The mid-high frequency region: a semicircle associated with the transport of electrons inside the active material particles. (3) The mid-frequency region: a semicircle associated with the charge transfer process. (4) The low-frequency region: a diagonal line associated with the solid diffusion process of the lithium ions of the active material particles.
The EIS can be refined into ohmic resistance (Rohm), SEI film resistance (RSEI), charge transfer resistance (Rct), and Warburg resistance (Rw). The Rohm is linear and independent of the current and battery type. Due to the ionic conductivity of the electrolyte, the Rohm is highly dependent on the temperature and varies greatly in the lifetime of the battery. The RSEI is the characterization of the diffusion migration process of the SEI films on the surface of the lithium ion active material particles. The Rct is primarily a reflection of the charge transfer in the solid electrolyte interface layer or the electrode and the electrode/electrolyte interface layer. The Rw reflects the solid diffusion process of the lithium ions of the active material particles. The CPE reflects the characteristics of the non-ideal capacitor.

Other HIs Extracted from OCV and Temperature
The HI extracted from OCV is the isobaric voltage drop time curve, which is the time of the battery voltage drop from 4.2 V to 3.6 V. The voltage drop is the value after 8 min of static state operation. The HI extracted from temperature is the surface average temperature value of the temperature at every cycle. The detailed HIs are shown in Section 4.
The above-mentioned HIs are based on the characteristics analysis of the battery, which is the input of the prediction model (introduced in Section 3). To achieve the accurate RUL prediction, the multi HIs are selected to train the prediction model. For The EIS can be refined into ohmic resistance (R ohm ), SEI film resistance (R SEI ), charge transfer resistance (R ct ), and Warburg resistance (R w ). The R ohm is linear and independent of the current and battery type. Due to the ionic conductivity of the electrolyte, the R ohm is highly dependent on the temperature and varies greatly in the lifetime of the battery. The R SEI is the characterization of the diffusion migration process of the SEI films on the surface of the lithium ion active material particles. The R ct is primarily a reflection of the charge transfer in the solid electrolyte interface layer or the electrode and the electrode/electrolyte interface layer. The R w reflects the solid diffusion process of the lithium ions of the active material particles. The CPE reflects the characteristics of the non-ideal capacitor.

Other HIs Extracted from OCV and Temperature
The HI extracted from OCV is the isobaric voltage drop time curve, which is the time of the battery voltage drop from 4.2 V to 3.6 V. The voltage drop is the value after 8 min of static state operation. The HI extracted from temperature is the surface average temperature value of the temperature at every cycle. The detailed HIs are shown in Section 4.
The above-mentioned HIs are based on the characteristics analysis of the battery, which is the input of the prediction model (introduced in Section 3). To achieve the accurate RUL prediction, the multi HIs are selected to train the prediction model. For adjustment to the multi HIs, the LightGBM-based prediction model is improved by adaptive loss.

Experimental System
To establish a battery database for features extraction and validation of the proposed framework, the battery aging and testing experiment under vibration stress is carried out, and the IC-DV curves and the EIS are measured; this is based on the battery performance  Table 1.

Experimental System
To establish a battery database for features extraction and validation of the proposed framework, the battery aging and testing experiment under vibration stress is carried out, and the IC-DV curves and the EIS are measured; this is based on the battery performance experimental bench, as shown in Figure 2. The selected battery has a 2.4 Ah nominal capacity with the positive electrode of LNCM and the negative electrode of graphite. Its lower/upper cutoff voltages are 3.0 V/4.2 V, as shown in Table 1.  Here, the battery aging and performance testing experimental profiles are designed, including vibration conditions simulation, the cycling test, the capacity test, voltage measurement, surface temperature measurement, the IC-DV curves test, and the EIS test. The Arbin battery charger operates a charge-discharge profile based on the driving conditions illustrated in Figure 3a. The vibration platform simulates the vibration conditions illustrated in Figure 3b. The electrochemical workstation operates the EIS test. According to [30], the EIS test ranges from 0.01 k to 100 kHz. The computer controls the experimental profile and manages the data.

Computer
In [31], it is demonstrated that the road vibration on EVs can be equated to a sixdegree-of-freedom model, which is widely used to simulate the vibration environment. The international standard ISO8608 illustrates that the power spectral density (PSD) spectrum shown in Table 2 and Figure 3a can reflect road vibration levels [17]. The vibration platform shown in Figure 2 simulates the component force of forward/backward, left/right, up/down, yaw, pitch, and roll as ΔX, ΔY, ΔZ, ω, θ, and ψ. The aging test profile shown in Figure 3b is conducted to simulate the idling, uniform speed, acceleration, and deceleration of real-world driving conditions [28]. Table 2. Vibration target spectrum parameters of lithium-ion battery.

Experimental Profile
Here, the battery aging and performance testing experimental profiles are designed, including vibration conditions simulation, the cycling test, the capacity test, voltage measurement, surface temperature measurement, the IC-DV curves test, and the EIS test. The Arbin battery charger operates a charge-discharge profile based on the driving conditions illustrated in Figure 3a. The vibration platform simulates the vibration conditions illustrated in Figure 3b. The electrochemical workstation operates the EIS test. According to [30], the EIS test ranges from 0.01 k to 100 kHz. The computer controls the experimental profile and manages the data.
In [31], it is demonstrated that the road vibration on EVs can be equated to a sixdegree-of-freedom model, which is widely used to simulate the vibration environment. The international standard ISO8608 illustrates that the power spectral density (PSD) spectrum shown in Table 2 and Figure 3a can reflect road vibration levels [17]. The vibration platform shown in Figure 2 simulates the component force of forward/backward, left/right, up/down, yaw, pitch, and roll as ∆X, ∆Y, ∆Z, ω, θ, and ψ. The aging test profile shown in Figure 3b is conducted to simulate the idling, uniform speed, acceleration, and deceleration of real-world driving conditions [28].

Improved LightGBM
LightGBM is an integrated strong learner HT based on the gradient boosting decision tree (GBDT) as the base learner, which can be expressed as (4). LightGBM has the merits of fast prediction, low memory consumption, and high accuracy [21], which is available for the prediction model.
where Ht represents the t th learner, and Θ represents the set of all learners.
For the training dataset {x1, …, xn}, the performance of the learner Ht(x) is reinforced through multiple rounds of iterations. In the previous round of iteration, the learner Ht−1(x) and loss function L(y, Ht−1(x)) were obtained. This round of iteration is to train the weak learner ht−1(x) to minimize the loss function, which can be expressed as (5).

Improved LightGBM
LightGBM is an integrated strong learner H T based on the gradient boosting decision tree (GBDT) as the base learner, which can be expressed as (4). LightGBM has the merits of fast prediction, low memory consumption, and high accuracy [21], which is available for the prediction model.
where H t represents the t th learner, and Θ represents the set of all learners. For the training dataset {x 1 , . . . , x n }, the performance of the learner H t (x) is reinforced through multiple rounds of iterations. In the previous round of iteration, the learner H t−1 (x) and loss function L(y, H t−1 (x)) were obtained. This round of iteration is to train the weak learner h t−1 (x) to minimize the loss function, which can be expressed as (5).
For fast convergence, the negative gradient of the loss function is used to approximately replace the loss function in the iteration, which can be expressed as (6). In addition, this is also the reason why the first-order derivative of the loss function is required.
where y is the RUL prediction value. The root mean square error is an objective function, and the weak learner h t (x) can be expressed as follows.
h t (x) = arg min Symmetry 2022, 14, 1584 The learner in this round of iteration is obtained.
When dealing with multi HIs, the conventional loss functions of the Cauchy loss, L 1 norm loss, L 2 norm loss, Welsch loss, and Geman-McClure loss [17] make it difficult to achieve adaptive adjustment and alter data characteristics. The loss function of the LightGBM model is improved by adaptive loss, as in (9). The adaptive loss can be expressed as (9), and the first-order derivative of the AR loss can be expressed as (10).
where x is residual. a is the hyperparameter, which is used to adjust the different expressions of the loss function; the coordination parameter c is used to adjust the bending scale of the loss function at x = 0, which determines whether the loss function is suitable for the gradient-based prediction method.

The Proposed RUL Prediction Framework
The proposed framework based on the improved LightGBM with Hyperopt (H-iLightGBM) is to learn multi HIs for battery RUL prediction, which is as shown in Figure 4, with the following steps. Step 3. Improved LightGBM model training and optimization: to adaptively adjust to multi HIs, the loss function of the LightGBM model is improved by the adaptive loss, expressed as (9) and (10). Based on the multithreaded parallel histogram strategy, each one-dimensional feature (the continuous floating-point datum) is transferred into discrete K ranges to obtain K "bins". In addition, a histogram with a width of K is constructed, as shown in c) in Figure 3. The K-fold cross-validation is the validation procedure during the process of the prediction model training and the testing process [32]. To obtain an optimal prediction performance, the hyperparameter optimization is used to obtain the optimal parameters of the LightGBM model, and it sets the performance evaluation function (root mean square error, RMSE) as (11), which is used to describe the fitting degree between the real value and the predicted value. Hence, the RMSE is used to estimate the performance of the proposed RUL prediction model [33].
where ypred,i and ytrue,I are the capacity prediction value and real value at i th cycle, respectively, and n is lifetime cycles.
Step 4. RUL prediction under vibration stress: the battery lifecycle capacity data under driving conditions are divided into the training set and the test set. The training set is used to train the model and obtain relevant parameters, and the test set is used to verify the effectiveness of the model.

IC-DV Curves
The IC curve and the DV curve have symmetrical shapes. The voltage corresponding to the peak value of the IC curve gradually increases, and the capacity corresponding to the valley value of the DV curve gradually decreases. The peak of the IC curve gradually decreases until it disappears at 3.52 V, which is shown in Figure 5. Step 1. Experimental system establishment: battery aging and testing experimental profiles are designed, including vibration conditions simulation, the cycling test, the capacity test, voltage measurement, surface temperature measurement, the IC-DV curves test, and the EIS test.
Step 2. Multi Health Indicators extraction: based on electrochemical theory, the IC-DV curves, and the EIS from the battery aging and testing dataset are utilized to extract the loss modes and calculate the resistances. The isobaric voltage drop time and surface temperature are also regarded as HIs. The feature database is adopted to divide the dataset into the training dataset and the testing dataset for the RUL prediction model.
Step 3. Improved LightGBM model training and optimization: to adaptively adjust to multi HIs, the loss function of the LightGBM model is improved by the adaptive loss, expressed as (9) and (10). Based on the multithreaded parallel histogram strategy, each one-dimensional feature (the continuous floating-point datum) is transferred into discrete K ranges to obtain K "bins". In addition, a histogram with a width of K is constructed, as shown in c) in Figure 3. The K-fold cross-validation is the validation procedure during the process of the prediction model training and the testing process [32]. To obtain an optimal prediction performance, the hyperparameter optimization is used to obtain the optimal parameters of the LightGBM model, and it sets the performance evaluation function (root mean square error, RMSE) as (11), which is used to describe the fitting degree between the real value and the predicted value. Hence, the RMSE is used to estimate the performance of the proposed RUL prediction model [33].
where y pred,i and y true,I are the capacity prediction value and real value at i th cycle, respectively, and n is lifetime cycles.
Step 4. RUL prediction under vibration stress: the battery lifecycle capacity data under driving conditions are divided into the training set and the test set. The training set is used to train the model and obtain relevant parameters, and the test set is used to verify the effectiveness of the model.

IC-DV Curves
The IC curve and the DV curve have symmetrical shapes. The voltage corresponding to the peak value of the IC curve gradually increases, and the capacity corresponding to the valley value of the DV curve gradually decreases. The peak of the IC curve gradually decreases until it disappears at 3.52 V, which is shown in Figure 5.

Capacity Degradation Curve
For the lithium-ion battery (LNCM) selected in this paper, during the charge-discharge process, besides the oxidation-reduction reaction caused by the lithium ion deinterlacing, there are also many side reactions, such as electrolyte decomposition, active substance dissolution, metal lithium deposition, etc. These side reactions lead to the degradation of the battery capacity in addition to the oxidation-reduction reaction caused by the lithium ion deintercalation; there are also many side reactions, such as electrolyte decomposition, active material dissolution, metal lithium deposition, etc. These side reactions lead to battery capacity degradation. When the capacity of the battery is up to 80% of the nominal capacity (end of life, EOL) [2], the test is stopped. The battery capacity degradation curve is shown in Figure 6. Figure 6 shows that the battery capacity in the reference decays to EOL at about 150 cycles, and the battery capacity under vibration stress is about 140 cycles. In the first 50 cycles, there is no obvious difference in capacity decay between these two conditions. At this stage, the main cause of capacity decay may be due to SEI formation. As the number of cycles increases, the chemical reactions inside the battery are intensified, and the degradation modes are complicated by external factors. Hence, there is an increasingly noticeable difference in battery degradation between these two conditions.

Capacity Degradation Curve
For the lithium-ion battery (LNCM) selected in this paper, during the charge-d charge process, besides the oxidation-reduction reaction caused by the lithium ion de terlacing, there are also many side reactions, such as electrolyte decomposition, acti substance dissolution, metal lithium deposition, etc. These side reactions lead to the de radation of the battery capacity in addition to the oxidation-reduction reaction caused the lithium ion deintercalation; there are also many side reactions, such as electrolyte d composition, active material dissolution, metal lithium deposition, etc. These side rea tions lead to battery capacity degradation. When the capacity of the battery is up to 80 of the nominal capacity (end of life, EOL) [2], the test is stopped. The battery capac degradation curve is shown in Figure 6.  Figure 6 shows that the battery capacity in the reference decays to EOL at about 1

Capacity Degradation Curve
For the lithium-ion battery (LNCM) selected in this paper, during the chargecharge process, besides the oxidation-reduction reaction caused by the lithium ion de terlacing, there are also many side reactions, such as electrolyte decomposition, ac substance dissolution, metal lithium deposition, etc. These side reactions lead to the d radation of the battery capacity in addition to the oxidation-reduction reaction caused the lithium ion deintercalation; there are also many side reactions, such as electrolyte composition, active material dissolution, metal lithium deposition, etc. These side re tions lead to battery capacity degradation. When the capacity of the battery is up to 8 of the nominal capacity (end of life, EOL) [2], the test is stopped. The battery capa degradation curve is shown in Figure 6.  Figure 6 shows that the battery capacity in the reference decays to EOL at about cycles, and the battery capacity under vibration stress is about 140 cycles. In the firs cycles, there is no obvious difference in capacity decay between these two conditions  Figure 8 shows the surface average temperature, which is the average value of the temperature at every cycle. It can be seen that the surface temperature increases with the increase in charge-discharge cycles. At the EOL of the battery, the temperature is 5 • C higher than the original temperature. ticeable difference in battery degradation between these two conditions.   Figure 8 shows the surface average temperature, which is the average value of the temperature at every cycle. It can be seen that the surface temperature increases with the increase in charge-discharge cycles. At the EOL of the battery, the temperature is 5 °C higher than the original temperature.

Loss Modes
Extracting the loss modes by (1)-(3), as shown in Figure 9, the LCs in the two conditions are 1.63% and 1.90%, respectively. The LAMs are 22.08% and 36.94%, respectively. The LLIs are 27.87% and 35.12%, respectively. The increase in LAM and LLI is much   Figure 8 shows the surface average temperature, which is the average value of the temperature at every cycle. It can be seen that the surface temperature increases with the increase in charge-discharge cycles. At the EOL of the battery, the temperature is 5 °C higher than the original temperature.

Loss Modes
Extracting the loss modes by (1)-(3), as shown in Figure 9, the LCs in the two conditions are 1.63% and 1.90%, respectively. The LAMs are 22.08% and 36.94%, respectively. The LLIs are 27.87% and 35.12%, respectively. The increase in LAM and LLI is much

Loss Modes
Extracting the loss modes by (1)-(3), as shown in Figure 9, the LCs in the two conditions are 1.63% and 1.90%, respectively. The LAMs are 22.08% and 36.94%, respectively. The LLIs are 27.87% and 35.12%, respectively. The increase in LAM and LLI is much greater than that of the LC. It is considered that LAM and LLI are the two main factors contributing to the RUL degradation [22]. greater than that of the LC. It is considered that LAM and LLI are the two main factors contributing to the RUL degradation [22].

Four Types of Resistances
Based on electrochemical theory, Figure 10 shows the ohmic resistance (Rohm), SEI film resistance (RSEI), charge transfer resistance (Rct), and Warburg resistance (Rw) under the vibration stress and static condition, which is obtained through the second-order equivalent model (in Figure 1). The values of Rohm, Rct, and Rw gradually increase with the

Four Types of Resistances
Based on electrochemical theory, Figure 10 shows the ohmic resistance (R ohm ), SEI film resistance (R SEI ), charge transfer resistance (R ct ), and Warburg resistance (R w ) under the vibration stress and static condition, which is obtained through the second-order equivalent model (in Figure 1). The values of R ohm , R ct , and R w gradually increase with the cycles, and R ct and R w are the most obvious. There is no regular change in R SEI .

Four Types of Resistances
Based on electrochemical theory, Figure 10 shows the ohmic resistance (Rohm), SEI film resistance (RSEI), charge transfer resistance (Rct), and Warburg resistance (Rw) under the vibration stress and static condition, which is obtained through the second-order equivalent model (in Figure 1). The values of Rohm, Rct, and Rw gradually increase with the cycles, and Rct and Rw are the most obvious. There is no regular change in RSEI.  Figure 11 shows the RUL prediction results of the different methods under driving conditions. All the HIs mentioned above are used to validate the prediction performance of the GBDT [15]; the one-dimensional convolutional neural networks (1D-CNN) [18], the SVR [19], the RF [20], the XGBoost [21], and the proposed framework are compared to the RUL prediction under driving conditions. The parameters of those different RUL predic-  Figure 11 shows the RUL prediction results of the different methods under driving conditions. All the HIs mentioned above are used to validate the prediction performance of the GBDT [15]; the one-dimensional convolutional neural networks (1D-CNN) [18], the SVR [19], the RF [20], the XGBoost [21], and the proposed framework are compared to the RUL prediction under driving conditions. The parameters of those different RUL prediction models are shown in Table 2. The prediction results are shown in Figure 11, and the prediction errors are as follows: the proposed framework is 1.078%, XGBoost is 1.119%, RF is 1.476%, SVR is 1.510%, 1D-CNN is 1.308%, and GBDT is 1.893%, indicating that the proposed framework can achieve accurate RUL prediction under driving conditions. The performances of the different RUL prediction methods are provided in Table 3. It can be seen that the proposed framework has obvious merits of prediction speed and accuracy.   Figure 12 shows the RUL prediction performance of the different methods under different numbers of HIs (ohmic resistance, charge transfer resistance, SEI film resistance, Warburg resistance, LC, LAM, LLI, isobaric voltage drop time, and surface average temperature). It can be seen that the prediction accuracy is improved with the increase in the number of HIs. However, when the number of HIs is three, the prediction accuracy of XGBoost and the proposed framework is higher than that of the condition of the four HIs. It is considered that multi HIs may affect the selection of the split point or overfit to some extent. The proposed framework can achieve the best prediction accuracy (98.978%) under the HIs of resistances, loss modes, and isobaric voltage drop time.  According to Table 4, the proposed framework has obvious merits of prediction speed over the other methods. Considering the heavy model training burden led by multi HIs, the different number of HIs are used for analysis to obtain the optimal number of HIs, which can guarantee both prediction accuracy and speed. Figure 12 shows the RUL prediction performance of the different methods under different numbers of HIs (ohmic resistance, charge transfer resistance, SEI film resistance, Warburg resistance, LC, LAM, LLI, isobaric voltage drop time, and surface average temperature). It can be seen that the prediction accuracy is improved with the increase in the number of HIs. However, when the number of HIs is three, the prediction accuracy of XGBoost and the proposed framework is higher than that of the condition of the four HIs.

Validation of the Proposed Framework
It is considered that multi HIs may affect the selection of the split point or overfit to some extent. The proposed framework can achieve the best prediction accuracy (98.978%) under the HIs of resistances, loss modes, and isobaric voltage drop time.   Figure 12 shows the RUL prediction performance of the different methods under different numbers of HIs (ohmic resistance, charge transfer resistance, SEI film resistance, Warburg resistance, LC, LAM, LLI, isobaric voltage drop time, and surface average temperature). It can be seen that the prediction accuracy is improved with the increase in the number of HIs. However, when the number of HIs is three, the prediction accuracy of XGBoost and the proposed framework is higher than that of the condition of the four HIs. It is considered that multi HIs may affect the selection of the split point or overfit to some extent. The proposed framework can achieve the best prediction accuracy (98.978%) under the HIs of resistances, loss modes, and isobaric voltage drop time.

Conclusions
An improved light gradient boosting machine (LightGBM)-based RUL prediction framework is proposed, which derives multi HIs extraction and an improved RUL prediction model to improve prediction accuracy and avoid low training efficiency. A series of comparative experiments and data analyses is conducted, and the conclusion can be summarized as follows: (1) The battery aging and performance testing experimental system is established to extract multi HIs. The extracted HIs are mainly divided into indirect HIs (i.e., resistances from EIS and loss modes from IC-DV curves) and direct HIs (i.e., OCV and temperature). It can be concluded that vibration stress promotes the reactions inside the battery and mainly affects the LLI and LAM. The LC, LAM, and LLI are about 1.90%, 36.94%, and 35.12%, respectively.
(3) The proposed framework can achieve the optimal prediction accuracy (98.978%) under the HI of resistances, loss modes, and isobaric voltage drop times. It can be concluded that the RUL prediction model trained by the appropriate HIs can achieve optimal prediction accuracy.
Considering that different experimental conditions can obtain different HIs, this paper discusses the RUL prediction results under training with different numbers of HIs.
The results demonstrate that the proposed framework can realize the accurate and rapid RUL prediction through different HI training, which has proved applicable for different experimental conditions. As the battery RUL prediction is of significance in practice, further work will focus on the development and validation of this framework using some features conveniently obtained in real applications under different external factors.

Conflicts of Interest:
The authors declare no conflict of interest.