AdaBoost.Rt-LSTM Based Joint SOC and SOH Estimation Method for Retired Batteries

: Achieving accurate retired battery state of health (SOH) and state of charge (SOC) estimation is a safe prerequisite for securing the battery secondary utilization and thus effectively improving the energy utilization efﬁciency. The data-driven approach is efﬁcient and accurate, and does not rely on accurate battery models, which is a hot direction in battery state estimation research. However, the huge number of retired batteries and obvious consistency differences bring bottleneck problems such as long learning time and low model updating efﬁciency to the traditional data-driven algorithm. In view of this, this paper proposes an integrated learning algorithm based on AdaBoost. Rt-LSTM to realize the joint estimation of SOC and SOH of retired lithium batteries, which relies on the LSTM neural network model and completes the correlation adaption in the spatio-temporal dimension of the whole life cycle sample data. The LSTM model is used as the base learner to construct the AdaBoost. Rt-LSTM strong learning model. The LSTM weak predictor is combined with weights to form a strong predictor, which greatly solves the problem of low accuracy of state estimation due to the large number and variability of retired batteries. Simulation and experimental comparison show that the integrated algorithm proposed in this paper is suitable for improving the SOC and SOH prediction accuracy and the generalization performance of the model.


Introduction
Due to the widespread popularity of electric vehicles in recent years, the amount of retired power batteries will also increase rapidly [1]. Among the retired power batteries, many still have high residual capacity (70% to 80% of the rated capacity of the battery), and these batteries can potentially be used in scenarios such as energy storage in power grids and backup in communication base stations to realize the secondary utilization of power batteries [2,3]. However, since the state of power batteries is usually unknown when they are retired, it is necessary to accurately estimate the State of Health (SOH) of the batteries before the batteries are used in the secondary process, so that the batteries with a greater degree of aging can be eliminated in time and the batteries with different aging states can enter the step-up environment in the corresponding stage. At the same time, the accurate estimation of State of Charge (SOC) in the process of step-up utilization can improve the utilization efficiency of retired batteries.
The existing SOC estimation methods mainly include time integration method [4], open circuit voltage method [5], adaptive filtering method [6] and neural network method [7]. Among them, the time-integral method discretely sums the current flowing through the battery, and obtains the SOC value through simple division [8]. The open-circuit voltage method is to measure the open-circuit voltage of the battery and obtain the charge state according to the correspondence between the open-circuit voltage and the charge state [9]. introducing a threshold constant, which transforms the regression problem into a simple binary classification problem, and combined with a specific weak learning machine, it can effectively achieve the prediction of time series, which greatly enhances the practicality of the AdaBoost algorithm and improves the learning efficiency of the algorithm as well as the model accuracy of the estimation [23]. The above literature shows that data-driven algorithmic models have considerabl potential and application prospects in joint battery estimation, but the large number o retired battery samples makes the previous data-driven algorithms face problems such a long learning time and low model update efficiency.AdaBoost, as one of the most typica Boosting algorithms, breaks the distribution law of the original samples by resampling AdaBoost, as a typical Boosting algorithm, breaks the distribution of the original sample by resampling, so that the learning machine focuses more on the hard-to-learn samples thus making Boosting an integrated algorithm with real practical value. The AdaBoos RT algorithm, as one of the AdaBoost algorithm family, improves the AdaBoost algorithm by introducing a threshold constant, which transforms the regression problem into a sim ple binary classification problem, and combined with a specific weak learning machine, i can effectively achieve the prediction of time series, which greatly enhances the practical ity of the AdaBoost algorithm and improves the learning efficiency of the algorithm a well as the model accuracy of the estimation [23].
In summary, the data-driven battery estimation algorithm is simple and reliable and does not depend on the establishment of an accurate battery model, but most of the exist ing data-driven algorithms rely on the life cycle experimental data of a few batteries in th laboratory to estimate the SOH of the remaining battery cells, while in practice, the retired batteries are widely sourced and large in number, and the SOH estimation model estab lished based on the laboratory environment has high accuracy but poor generalizatio The SOH estimation model based on the laboratory environment has high accuracy bu poor generalization capability. Therefore, in this paper, an improved AdaBoost.Rt-LSTM battery SOC and SOH joint estimation method is proposed in a data-driven framework The same batch of retired lithium battery packs are selected, and after screening and per formance testing, 75 lithium iron phosphate batteries with good appearance and can b reused are finally obtained, five health characteristics of retired lithium batteries are ex tracted, and the correlation between health characteristics and capacity is analyzed usin Pearson correlation coefficient, and the AdaBoost.Rt-LSTM model is used to jointly realiz In summary, the data-driven battery estimation algorithm is simple and reliable and does not depend on the establishment of an accurate battery model, but most of the existing data-driven algorithms rely on the life cycle experimental data of a few batteries in the laboratory to estimate the SOH of the remaining battery cells, while in practice, the retired batteries are widely sourced and large in number, and the SOH estimation model established based on the laboratory environment has high accuracy but poor generalization The SOH estimation model based on the laboratory environment has high accuracy but poor generalization capability. Therefore, in this paper, an improved AdaBoost.Rt-LSTM battery SOC and SOH joint estimation method is proposed in a data-driven framework. The same batch of retired lithium battery packs are selected, and after screening and performance testing, 75 lithium iron phosphate batteries with good appearance and can be reused are finally obtained, five health characteristics of retired lithium batteries are extracted, and the correlation between health characteristics and capacity is analyzed using Pearson correlation coefficient, and the AdaBoost.Rt-LSTM model is used to jointly realize the retired lithium battery charge state and health state estimation. The long and short-term memory neural network used in this method not only has the advantages of recurrent neural network, but also can solve the problems of gradient disappearance and gradient explosion. The AdaBoost.Rt integration algorithm, which combines the LSTM weak predictors with weights to form a strong predictor, greatly solves the problem of low accuracy of state estimation due to the large number of retired batteries and large variability. Simulation and experimental comparison show that the proposed AdaBoost.Rt-LSTM algorithm can jointly estimate the SOC and SOH of Li-ion batteries, ensuring the prediction accuracy and generalization performance of the model. Long Short Term Memory (LSTM) is a temporal recurrent neural network that effectively solves the gradient disappearance and gradient explosion problems of recurrent neural networks (RNNs) when processing long time series data by invoking a "gating" device. Figure 2 shows the principle structure of LSTM algorithm.
Simulation and experimental comparison show that the proposed AdaBoost.Rt-LSTM algorithm can jointly estimate the SOC and SOH of Li-ion batteries, ensuring the prediction accuracy and generalization performance of the model.

LSTM (Long Short Term Memory) Algorithm Principle
Long Short Term Memory (LSTM) is a temporal recurrent neural network that effectively solves the gradient disappearance and gradient explosion problems of recurrent neural networks (RNNs) when processing long time series data by invoking a "gating" device. Figure 2 shows the principle structure of LSTM algorithm. The order of information transmission in LSTM is that it first passes through the input gate to decide the input of information, then the forgetting gate selects whether to forget the information of the neuron, and finally it passes through the output gate to determine whether to output the information at this moment.
(1) Input Gate Input gate for updating cell status. When the switch is turned on, the information is input through the sigmoid activation function and multiplied (×) with the information through the double tangent activation function (tanh) to input a new t C into the "memory". The input gate calculation formula is shown in Equations (1) and (2).
where t i is the input gate at the moment t , σ is the sigmoid activation function, t C is the cell state, − t 1 h is the information of the hidden layer at the previous moment − t 1 , and t X is the input information at the moment t .
(2) Forgetting Gate At each moment, the value in the "memory" undergoes a process of forgetting or not which is controlled by the forgetting gate. By reading the information from the hidden layer − t 1 h and the input t x of the previous moment, the information forgotten at that moment is determined and a value between 0-1 is output to the neuron, which indicates the degree of forgetting of the information. The forgetting gate calculation formula is shown in Equation (3).
where: t f is the forgetting gate at the moment t .
(3) Output Gate The order of information transmission in LSTM is that it first passes through the input gate to decide the input of information, then the forgetting gate selects whether to forget the information of the neuron, and finally it passes through the output gate to determine whether to output the information at this moment.
(1) Input Gate Input gate for updating cell status. When the switch is turned on, the information is input through the sigmoid activation function and multiplied (×) with the information through the double tangent activation function (tanh) to input a new C t into the "memory". The input gate calculation formula is shown in Equations (1) and (2).
where i t is the input gate at the moment t, σ is the sigmoid activation function, C t is the cell state, h t−1 is the information of the hidden layer at the previous moment t − 1, and X t is the input information at the moment t.
(2) Forgetting Gate At each moment, the value in the "memory" undergoes a process of forgetting or not, which is controlled by the forgetting gate. By reading the information from the hidden layer h t−1 and the input x t of the previous moment, the information forgotten at that moment is determined and a value between 0-1 is output to the neuron, which indicates the degree of forgetting of the information. The forgetting gate calculation formula is shown in Equation (3).
where: f t is the forgetting gate at the moment t.
(3) Output Gate The output gate determines whether there is information from the "memory" output at each moment. The input information of the gate is passed through the sigmoid activation function and multiplied (×) with the "memory" updated by the tanh activation function to obtain the output value, as shown in Equations (4) and (5).
where: o t is the output gate at the time of t.
Batteries 2023, 9, 425 5 of 16 In summary, the sigmoid layer determines the output cell state, and the tanh function processes the cell state, compresses it between [−1, 1] and multiplies it with the output of the sigmoid gate to finally output the desired fraction.

AdaBoost.Rt Integration Algorithm Principle
In the training process of machine learning algorithm models, usually we can only get multiple models with different preferences, and integration learning is the combination of these weak learners to seek a better and more stable strong learning model. The Adaboost integration algorithm is an adaptive and iterative algorithm based on the idea of boost. The main idea of the algorithm is to continuously recombine and adjust the training samples according to the prediction effect of the base learner, so that the samples with poor prediction effect of the previous base learner receive more attention in the following, and then retrain the next base learner according to the recombined samples. The iteration is not stopped until the pre-specified maximum number of iterations or error rate is reached or below. The specific implementation is shown in Figure 3.
where: t o is the output gate at the time of t .
In summary, the sigmoid layer determines the output cell state, and the tanh function processes the cell state, compresses it between [−1,1] and multiplies it with the output o the sigmoid gate to finally output the desired fraction.

AdaBoost.Rt Integration Algorithm Principle
In the training process of machine learning algorithm models, usually we can only get multiple models with different preferences, and integration learning is the combina tion of these weak learners to seek a better and more stable strong learning model. The Adaboost integration algorithm is an adaptive and iterative algorithm based on the idea of boost. The main idea of the algorithm is to continuously recombine and adjust the train ing samples according to the prediction effect of the base learner, so that the samples with poor prediction effect of the previous base learner receive more attention in the following and then retrain the next base learner according to the recombined samples. The iteration is not stopped until the pre-specified maximum number of iterations or error rate is reached or below. The specific implementation is shown in Figure 3.  3. According to the weight distribution t D , the original sample set is sampled and the weak learning machine is invoked for training to build the regression mode ( ) t f x y → . Accordingly, the relative error of each sample is calculated. The computational procedure of the AdaBoost.Rt algorithm is as follows:

1.
Given a training set m of S samples, determine the number of iterations T and the threshold ϕ. 2.
Initialize the sample weights D t (i) = 1/m, where i is the number of training sets and t is the number of current iterations; error rate ε t = 0.

3.
According to the weight distribution D t , the original sample set is sampled and the weak learning machine is invoked for training to build the regression model f t (x) → y . Accordingly, the relative error of each sample is calculated.

5.
Update the sample weights as follows.
where: Z t is a normalization factor to ensure that the updated D t+1 is a distribution. 6.
Determine whether the stopping condition is satisfied: if t < T, make t = t + 1, and go to step 3, otherwise output the final strong learner.

Joint Estimation Model Construction Based on LSTM Algorithm
In order to improve the accuracy of the SOC and SOH estimation results of Li-ion batteries, this paper adopts an integrated learning model with LSTM as the weak predictor to jointly estimate the SOC and SOH of Li-ion batteries. The specific joint estimation process is shown below.

1.
Initialize the LSTM model with the relevant parameters k (Hidden state dimensions), L 1 (L 1 regularization), L 2 (L 2 regularization) and I r (Learning rate).

2.
Set the maximum number of iterations T max and the prediction error accuracy ε t . 3.
The voltage U t , current I t and capacity C t at the moment t are input to the LSTM model and the charge state SOC t at the moment t is estimated as the output.
4. 5 health features and SOC t are input to the LSTM model to estimate the health state SOH t at the moment t, and finally the joint estimation result Y t of SOC and SOH at the moment t is obtained.

5.
Determine whether the termination iteration condition is reached. If the number of iterations reaches the preset value T max , stop the iteration and finally output the SOC and SOH estimation results of the lithium battery.

Adaboost.Rt Reinforcement Learning Modeling Approach
In this paper, Adaboost.Rt-LSTM model is used to estimate the SOC and SOH of lithium batteries. Firstly, the experimental data of decommissioned batteries are preprocessed, and unqualified battery data are proposed. Then, the preprocessed battery data set is input into the model, and the weak learner is trained according to the initial weight, and the learning error rate of the learner is calculated. At the same time, the weights of all training samples are updated and iterated until all weak learners are obtained. Finally, all the weak learners are combined into one strong learner to achieve SOC estimation of lithium batteries. The SOC estimation results and five health characteristics at the same time are used as input parameters to jointly estimate the SOH of lithium batteries, and finally achieve the joint estimation of lithium battery SOC and SOH. The specific estimation process is as follows.

1.
Initialize the relevant parameters of K LSTM model.

2.
Adaboost.Rt-LSTM model training. Input sample training set X 1 t and X 2 t . Initialize the initial weights of the sample training set, train the weak predictor LSTM1 and calculate the relative error, update the weights of the training samples according to the error results, and iterate continuously until the weights D of the K weak predictor LSTM are determined. combine with the independent evaluation dataset P, aggregate the K LSTM models by AdaBoost.Rt, and finally constitute the AdaBoost.Rt-LSTM model.

3.
Input the voltage U t , current I t and capacity C t at the current moment into the model and estimate the state of charge at that moment as the output. 4.
5 health characteristics and SOC t are jointly used as input parameters of health state to estimate the health state of current moment SOH t . 5.
The final results of SOC and SOH prediction for Li-ion batteries are obtained. Figure 4 shows the overall structure of the proposed Adaboost.Rt-LSTM lithium battery state estimation method in this paper.
3. Input the voltage t U , current t I and capacity t C at the current moment into the model and estimate the state of charge at that moment as the output. 4. 5 health characteristics and t SOC are jointly used as input parameters of health state to estimate the health state of current moment t SOH .
5. The final results of SOC and SOH prediction for Li-ion batteries are obtained. Figure 4 shows the overall structure of the proposed Adaboost.Rt-LSTM lithium battery state estimation method in this paper.   In this paper, the same batch of retired lithium battery packs were selected, and after disassembly, grinding, appearance screening and performance testing, 100 lithium iron phosphate batteries with good appearance and able to be reused were finally obtained, and their model number was LR18650EH. The samples of retired lithium batteries used in the experiments are shown in Figure 5. The specific parameters and specifications of the lithium batteries are shown in Table 1.

Simulation Test and Result Analysis
Batteries 2023, 9, x FOR PEER REVIEW 8

Experimental Protocol Design
In this paper, the same batch of retired lithium battery packs were selected, and disassembly, grinding, appearance screening and performance testing, 100 lithium phosphate batteries with good appearance and able to be reused were finally obtai and their model number was LR18650EH. The samples of retired lithium batteries in the experiments are shown in Figure 5. The specific parameters and specification the lithium batteries are shown in Table 1.    The experimental data in this paper come from: Arbin BT-ML-30 V/10 A power tester produced by Arbin USA and ZM-7520 battery performance tester produced by Harbin Zimu. Figure 6 shows the experimental test platform of retired lithium battery.  Operating temperature range −20~60 °C The experimental data in this paper come from: Arbin BT-ML-30 V/10 A power teste produced by Arbin USA and ZM-7520 battery performance tester produced by Harbin Zimu. Figure 6 shows the experimental test platform of retired lithium battery. In this paper, the capacity and ohmic internal resistance of retired lithium batteries are tested by Hybrid Pulse Power Charasteristic (HPPC) condition test with Arbin BT-ML-30 V/10 A power tester. This method requires simple experimental equipment, simple operation, short experiment time and accurate measurement results. The internal resistance of the battery under different SOC can be obtained by establishing the relationship between the response voltage and current during discharge, resting and charging. The specific experimental steps are shown in Table 2. According to the actual test data of 100 batteries retired from the same batch obtained from the experiment for capacity and internal resistance testing, the capacity and internal resistance distribution of single cells are shown in Figure 7. The batteries numbered 4, 11, 41, and 75 have been severely damaged and cannot be charged; the batteries numbered 1 , 8, 10, 13, 26, 36, 40, 42, 43, 56, 78, 89, 91, 93, 95, and 99 have lower capacities and differ significantly from other retired batteries; the batteries numbered 2, 5, 29, 32, and 67 have ohmic internal resistance significantly higher than the average. Therefore, these batteries will not be used as the research object of this paper.

3
Resting 60 min 4 1 C constant current discharge 10% decrease in SOC 5 Resting 60 min 6 Cycle (step 1-5) Voltage up to 2.5 V According to the actual test data of 100 batteries retired from the same batch obtained from the experiment for capacity and internal resistance testing, the capacity and internal resistance distribution of single cells are shown in Figure 7. The batteries numbered 4, 11, 41, and 75 have been severely damaged and cannot be charged; the batteries numbered 1,8,10,13,26,36,40,42,43,56,78,89,91,93,95, and 99 have lower capacities and differ significantly from other retired batteries; the batteries numbered 2, 5, 29, 32, and 67 have ohmic internal resistance significantly higher than the average. Therefore, these batteries will not be used as the research object of this paper. After eliminating the unqualified batteries, the remaining 75 batteries were subjected to cyclic aging experiments. The aging test of retired lithium batteries is conducted by ZM-7520 battery performance tester with two 16-channel channels, and the experimental steps are shown in Table 3.  After eliminating the unqualified batteries, the remaining 75 batteries were subjected to cyclic aging experiments. The aging test of retired lithium batteries is conducted by ZM-7520 battery performance tester with two 16-channel channels, and the experimental steps are shown in Table 3.

Eigenvalue Extraction
In this paper, the health characteristics of retired lithium batteries are selected based on the important parameters affecting the health status of lithium batteries obtained from the analysis of the basic structure and characteristics of lithium batteries in the previous paper, and the mapping relationship between the health status of retired lithium batteries and experimental data is established on this basis. The charge/discharge aging experiment of Li-ion battery can obtain the relevant parameters of its whole life cycle, such as voltage, current, internal resistance and cycle capacity at each moment. These parameters can directly predict the SOH of Li-ion battery, but the large amount of data increases its computational effort and cannot be estimated online. In addition, the capacity increment curve as the health characteristic of Li-ion battery is more effective in predicting its SOH, but the original IC curve data of Li-ion battery needs to be filtered before estimation. In summary, in this paper, five health features (HF), denoted as HF 1~H F 5 , are selected based on the charge/discharge voltage curves of retired lithium batteries to improve the computational rate of the SOH prediction process of retired lithium batteries with more efficient and concise features. Figure 8 shows the voltage curves of Li-ion battery under different SOH with constant current discharge and pause. As can be seen from the figure, there is a large gap between the discharge voltage curves of Li-ion battery under different SOH. Therefore, in this paper, five health characteristics are selected to estimate the retired Li-ion battery SOH: equal time charging voltage (HF1:charge_v), constant current charging time percentage (HF2:cc/(cc+cv)), mean value of capacity increment curve (HF3:mean_IC), maximum value of capacity increment curve (HF 4 :IC_max), and variance of capacity increment curve (HF 5  current, internal resistance and cycle capacity at each moment. These parameters can directly predict the SOH of Li-ion battery, but the large amount of data increases its computational effort and cannot be estimated online. In addition, the capacity increment curve as the health characteristic of Li-ion battery is more effective in predicting its SOH, but the original IC curve data of Li-ion battery needs to be filtered before estimation. In summary, in this paper, five health features (HF), denoted as HF1~HF5, are selected based on the charge/discharge voltage curves of retired lithium batteries to improve the computational rate of the SOH prediction process of retired lithium batteries with more efficient and concise features. Figure 8 shows the voltage curves of Li-ion battery under different SOH with constant current discharge and pause. As can be seen from the figure, there is a large gap between the discharge voltage curves of Li-ion battery under different SOH. Therefore, in this paper, five health characteristics are selected to estimate the retired Li-ion battery SOH: equal time charging voltage (HF1:charge_v), constant current charging time percentage (HF2:cc/(cc+cv)), mean value of capacity increment curve (HF3:mean_IC), maximum value of capacity increment curve (HF4:IC_max), and variance of capacity increment curve (HF5:area_IC). SOH values of Li-ion batteries, randomly selected sample batteries are No. 9,No. 15,No. 23,No. 35,No. 49,No. 66,No. 72,No. 85 and No. 97,and No. 9 battery is used as the validation set to test the accuracy of the AdaBoost.Rt-LSTM model. In order to verify that the five selected health characteristics can effectively reflect the health status of retired lithium batteries, the Pearson Correlation Coefficient is used to reflect the correlation degree between health characteristics and SOH.  In order to verify that the five selected health characteristics can effectively reflect the health status of retired lithium batteries, the Pearson Correlation Coefficient is used to reflect the correlation degree between health characteristics and SOH.
The Pearson correlation coefficient method can respond to the degree of linear correlation between two variables. For the two data sets X = {X 1 , X 2 , · · · , X n } and Y = {Y 1 , Y 2 , · · · , Y n }, the correlation coefficient is calculated as shown below.
where: σ X and σ Y are the standard deviations of X and Y respectively, which are calculated as shown in Equation (15).
The closer the absolute value of ρ is to 1, the stronger the correlation between its health characteristics and lithium SOH; conversely, the closer the absolute value of ρ is to 0, the less correlated they are.
From the results in Table 4, it can be seen that the absolute values of Pearson correlation coefficients between the five health features and SOH of the retired lithium battery of sample No. 9 are all greater than 0.9. This result indicates that there is a strong linear and monotonic correlation between the five selected health features and SOH of the lithium battery. Therefore, in this paper, the above five health features are selected as the input of Adaboost.Rt-LSTM model to improve its training efficiency and prediction accuracy. Finally, the minimum-maximum (min-max) normalization method is used to normalize the data to speed up the solution and improve the prediction accuracy, and the results fall in interval [0, 1], as shown in Equation (16).

Experimental Results and Comparative Analysis
For the experimentally obtained dataset, half of the entire lithium battery dataset is used as the training set and the remaining half is used as the test set to verify the accuracy of the model. Following the experimental steps described in Section 3.2, the experimental data from the retired Li-ion battery No. 9 described above is fed into the single LSTM model and the Ada-boost.Rt-LSTM model so as to perform the estimation of SOC and SOH.
It can be seen from Figure 9 that the SOC estimates of the AdaBoost.Rt-LSTM model are closer to the reference value than the estimates of the single LSTM model. The absolute error values of the two models for the lithium battery SOC estimation are shown in (a) of Figure 10. It can be seen that the AdaBoost.Rt-LSTM algorithm model has less error in the prediction of Li-ion battery SOC compared to the single LSTM estimation algorithm. In order to more accurately describe the dispersion of the Li-ion battery SOC error, the RMSE values predicted by the two models under different SOCs were compared, and the comparison results are shown in Figure 10b. It can be seen from the figure that the RMSE values of the AdaBoost.Rt-LSTM model are smaller than those of the single LSTM model regardless of the SOC state of the battery, which reflects the generalizability of the proposed algorithm to a certain extent. A comparison of the SOC estimation error results of retired lithium batteries with different algorithms is shown in Table 5. From the specific values in Table 5, it can be seen that the MAE values of the SOC estimation results of the single LSTM model and the Adaboost.Rt-LSTM model are 3.02% and 1.58%, respectively. Their RMSE values are 3.78% and 2.05%, respectively. And compared with the rest of the battery SOC estimation methods such as RNN(Recurrent Neural Network) [24], XGBoost(Extreme Gradient Boosting) [24], SMO(Sliding Mode Observer) [25]. Adaboost.Rt-LSTM model estimation is improved. In summary, the results show that the estimation results of the lithium battery SOC prediction model based on AdaBoost.Rt-LSTM are closer to the real value and have a strong feasibility compared to the single LSTM prediction model.  Table 5. From the specific values in Table 5, it can be seen that the MAE values of the SOC estimation results of the single LSTM model and the Adaboost.Rt-LSTM model are 3.02% and 1.58%, respectively. Their RMSE values are 3.78% and 2.05%, respectively. And compared with the rest of the battery SOC estimation methods such as RNN(Recurrent Neural Network) [24], XGBoost(Extreme Gradient Boosting) [24], SMO(Sliding Mode Observer) [25]. Adaboost.Rt-LSTM model estimation is improved. In summary, the results show that the estimation results of the lithium battery SOC prediction model based on AdaBoost.Rt-LSTM are closer to the real value and have a strong feasibility compared to the single LSTM prediction model.   [24] 0.0302 0.0378 XGBoost [24] 0.0235 0.0304 SMO [25] 0.01536 0.02663 AdaBoost.Rt-LSTM 0.0154 0.0215   [24] 0.0302 0.0378 XGBoost [24] 0.0235 0.0304 SMO [25] 0.01536 0.02663 AdaBoost.Rt-LSTM 0.0154 0.0215 For the SOH prediction results, it can be seen from Figure 11 that the SOH prediction results of the Adaboost.Rt-LSTM model are closer to the real values compared to the single LSTM model. A comparison of the SOH estimation error results for decommissioned lithium batteries with different algorithms is shown in Table 6. From the specific values in Table 6, it can be seen that the MAE values of the SOH estimation results of the single LSTM model and the Adaboost.Rt-LSTM model are 3.17% and 1.47%, respectively. Their RMSE values are 3.52% and 2.09% respectively. We also compare the results of SMO (Sliding Mode Observer) [25], FNN(Feedforward Neural Network) [26], CNN(Convolutional Neural Network) [26]. The algorithms described in this paper have improved in prediction accuracy. The above results show that the Adaboost.Rt integrated model based on LSTM optimization has higher prediction accuracy and is more feasible. For the SOH prediction results, it can be seen from Figure 11 that the SOH prediction results of the Adaboost.Rt-LSTM model are closer to the real values compared to the single LSTM model. A comparison of the SOH estimation error results for decommissioned lithium batteries with different algorithms is shown in Table 6. From the specific values in Table 6, it can be seen that the MAE values of the SOH estimation results of the single LSTM model and the Adaboost.Rt-LSTM model are 3.17% and 1.47%, respectively. Their RMSE values are 3.52% and 2.09% respectively. We also compare the results of SMO (Sliding Mode Observer) [25], FNN(Feedforward Neural Network) [26], CNN(Convolutional Neural Network) [26]. The algorithms described in this paper have improved in prediction accuracy. The above results show that the Adaboost.Rt integrated model based on LSTM optimization has higher prediction accuracy and is more feasible.   The following AdaBoost.Rt-LSTM model algorithm is used to estimate the health status of the above randomly selected remaining eight retired lithium batteries. Due to the differences caused by the changes in the aging process of the eight batteries due to prolonged charging and discharging, their SOH change patterns also differ slightly as shown in Figure 12 for the simulation results.  [25] 0.0267 0.0523 FNN [26] 0.0253 0.0316 CNN [26] 0.239 0.0332 AdaBoost.Rt-LSTM 0.0148 0.0202 Figure 11. Comparison of SOH estimation results of different algorithms.  [25] 0.0267 0.0523 FNN [26] 0.0253 0.0316 CNN [26] 0.239 0.0332 AdaBoost.Rt-LSTM 0.0148 0.0202 The following AdaBoost.Rt-LSTM model algorithm is used to estimate the health status of the above randomly selected remaining eight retired lithium batteries. Due to the differences caused by the changes in the aging process of the eight batteries due to prolonged charging and discharging, their SOH change patterns also differ slightly as shown in Figure 12 for the simulation results.   As can be seen from Figure 12, the prediction results of the health status of all eight sample retired lithium batteries are good, which verifies the feasibility and accuracy of the Adaboost.Rt-LSTM model proposed in this paper, and the values of its MAE and RMSE are shown in Table 7. Among all the prediction results, the prediction effect of battery No. 72 is relatively good, with the MAE and RMSE values of 1.17% and 2.06%, respectively. the prediction effect of battery No. 23 is relatively poor, with the MAE and As can be seen from Figure 12, the prediction results of the health status of all eight sample retired lithium batteries are good, which verifies the feasibility and accuracy of the Adaboost.Rt-LSTM model proposed in this paper, and the values of its MAE and RMSE are shown in Table 7. Among all the prediction results, the prediction effect of battery No. 72 is relatively good, with the MAE and RMSE values of 1.17% and 2.06%, respectively. the prediction effect of battery No. 23 is relatively poor, with the MAE and RMSE values of 1.64% and 2.44%, respectively, but it also meets the accuracy requirement of binning. Therefore, the SOH results of 75 retired lithium batteries estimated by the AdaBoost.Rt -LSTM model in this paper all achieve more satisfactory results. The comparison of the SOH estimation error results of the sample retired lithium batteries is shown in Figure 13. of the SOH estimation error results of the sample retired lithium batteries is shown in Figure 13.

Conclusions
Accurate estimation of lithium battery status can effectively reduce the risk and loss caused by failure when decommissioned batteries are reused. Therefore, based on the improved Adaboost.Rt-LSTM state prediction model, the SOC and SOH of decommissioned batteries are jointly estimated in this paper, which provides strong data support for the subsequent reuse of decommissioned batteries. Aiming at the problems of narrow application range, weak genetic ability and low accuracy of traditional neural network battery estimation method, this paper adopts LSTM recurrent neural network model algorithm and calls "gating" device to effectively solve the problem of gradient disappearance and gradient explosion caused by recurrent neural network when processing long time series data. Rt integrated learning algorithm was used to combine several LSTM weak learners

Conclusions
Accurate estimation of lithium battery status can effectively reduce the risk and loss caused by failure when decommissioned batteries are reused. Therefore, based on the improved Adaboost.Rt-LSTM state prediction model, the SOC and SOH of decommissioned batteries are jointly estimated in this paper, which provides strong data support for the subsequent reuse of decommissioned batteries. Aiming at the problems of narrow application range, weak genetic ability and low accuracy of traditional neural network battery estimation method, this paper adopts LSTM recurrent neural network model algorithm and calls "gating" device to effectively solve the problem of gradient disappearance and gradient explosion caused by recurrent neural network when processing long time series data. Rt integrated learning algorithm was used to combine several LSTM weak learners into strong learners according to their weights, and the prediction model established significantly improved the estimation accuracy of SOC and SOH of decommissioned batteries. According to the analysis of simulation and experimental results, the average absolute error of SOC and SOH prediction results of Adaboost.Rt-LSTM is 1.54% and 1.48%, and the root-mean-square error is 2.15% and 2.02%, respectively. This shows that the Adaboost.Rt-LSTM algorithm model still has high estimation accuracy and good convergence when there is a large amount of decommissioned battery data, which verifies the feasibility of the Adaboost.Rt-LSTM model in the state estimation of decommissioned lithium batteries.