CN117572250A - Method for estimating SOH of battery based on multi-feature fusion and XGBoost - Google Patents
Method for estimating SOH of battery based on multi-feature fusion and XGBoost Download PDFInfo
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- 238000010801 machine learning Methods 0.000 description 1
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Abstract
The invention belongs to the technical field of battery state of health evaluation, and particularly relates to a method for estimating SOH of a battery based on multi-feature fusion and XGBoost, which comprises the following steps: and (3) data acquisition: collecting aging data in the cyclic aging process of the battery; feature extraction: analyzing the aging data, and extracting battery SOH data and health characteristic data closely related to the battery SOH; and (3) data processing: processing the health characteristic data and the battery SOH data, including abnormal value detection, correlation analysis and standardization processing; feature depth fusion: constructing a feature fusion model for feature depth fusion, so as to extract fusion features; establishing an estimation model: and establishing a complex relation model of the fusion characteristic and the SOH based on XGBoost, so as to estimate the SOH of the battery and obtain an estimated SOH value. The invention can accurately estimate the SOH of the battery, is suitable for different types of lithium ion batteries, and has good accuracy and universality.
Description
Technical Field
The invention belongs to the technical field of battery state of health evaluation, and particularly relates to a method for estimating SOH of a battery based on multi-feature fusion and XGBoost.
Background
Lithium ion batteries are widely used in various fields such as portable electronic devices, electric vehicles, and energy storage systems as a secondary battery having high energy density, low self-discharge rate, and environmental friendliness. However, the health state of the lithium ion battery is gradually reduced along with the increase of the service time and the charge and discharge cycle times, and the phenomena of capacity reduction, internal resistance increase, safety reduction and the like occur. Therefore, accurate estimation of the state of Health (SOH) of a lithium ion battery is of great importance for optimizing battery management, extending battery life, improving energy utilization efficiency, and ensuring safety of battery use.
Existing lithium ion battery SOH estimation methods fall into three main categories: direct measurement, modeling, data driving. Compared with the traditional direct measurement method and model method, the data driving method is more universal, and is suitable for estimating the SOH of the battery under different types and different working conditions because the relation between the health characteristics and the SOH of the battery is established through a machine learning algorithm based on historical data so as to estimate the SOH of the battery without a severe measurement environment or intensive research on the aging mechanism of the battery.
However, the existing data driving method has the problem of insufficient treatment of health features, simply extracts or screens features, directly inputs the normalized features into a network model for training, or re-optimizes an estimation result of a network model, and lacks deep analysis of complex relationships between features and between features and SOH, so that the accuracy and universality of an algorithm model are difficult to be obviously improved.
Disclosure of Invention
According to the defects in the prior art, the invention provides a method for estimating the SOH of the battery based on multi-feature fusion and XGBoost, which can accurately estimate the SOH of the battery, is applicable to different types of lithium ion batteries, and has good accuracy and universality.
To achieve the above object, the present invention provides a method for estimating SOH of a battery based on multi-feature fusion and XGBoost, comprising the steps of:
s1, data acquisition: collecting aging data in the cyclic aging process of the battery;
s2, feature extraction: analyzing the aging data, and extracting battery SOH data and health characteristic data closely related to the battery SOH;
s3, data processing: processing the health characteristic data and the battery SOH data, including abnormal value detection, correlation analysis and standardization processing;
s4, feature depth fusion: constructing a feature fusion model for feature depth fusion, so as to extract fusion features;
s5, establishing an estimation model: and establishing a complex relation model of the fusion characteristic and the SOH based on XGBoost, namely an estimation model, so as to estimate the SOH of the battery and obtain an estimated value of the SOH.
In the step S1, the aging data acquisition process is as follows:
s11, collecting time and voltage data of a battery charging stage under different cycles, and constructing a charging voltage curve;
and S12, collecting time and current data of a battery discharge stage under different cycles, and calculating the battery capacity.
Based on the corresponding data, constructing a charging voltage curve and calculating the battery capacity are prior art.
In S2, the extracted health feature data closely related to the SOH of the battery includes:
s21, constructing a charging voltage curve based on aging data of the battery in the charging stage acquired in the S11;
s22, calculating the battery capacity, including the maximum discharge capacity and the initial capacity, based on the aging data of the battery in the discharge stage acquired in the S12;
s23, extracting constant-current charging time based on a charging voltage curve;
s24, extracting constant-voltage charging time based on a charging voltage curve;
s25, extracting a curve peak value of an incremental capacity IC based on a charging voltage curve, wherein a calculation formula of the IC is as follows:
（1）；
wherein Q is battery capacity, V is voltage, I is current, and t is time;
s26, extracting a voltage sample entropy value in a constant current charging stage based on a charging voltage curve;
and S27, extracting SOH data of the battery based on the aging data and the battery capacity of the battery in the discharging stage, wherein the SOH data is defined as follows as a tag value corresponding to the health characteristic data:
（2）；
in the method, in the process of the invention,represents the maximum discharge capacity of the current battery,/-)>Indicating the initial capacity of the battery.
In the step S3, the step of processing the health feature data is as follows:
s31, detecting abnormal values of all extracted health characteristic data by adopting a 3 sigma principle, deleting the abnormal values and other data of the cycle times, wherein the 3 sigma principle is expressed as follows:
（3）；
each health characteristic data is represented by a characteristic x, wherein,representing the i-th cycle acquisition value of the feature x, μ representing the mean value of the feature x, σ representing the standard deviation of the feature x;
s32, primarily analyzing the correlation between the health feature data and the battery SOH data by adopting the Pearson correlation coefficient, and removing the feature that the absolute value of the correlation coefficient is lower than 0.8 to avoid interference to the result, wherein the more the absolute value of the correlation coefficient is more than 1, the higher the correlation is, and the calculation formula of the Pearson correlation coefficient is as follows:
（4）；
where r is the pearson correlation coefficient, n is the sample size,SOH value of the ith cycle, < >>And->Is the average of the selected feature and the battery SOH sample, respectively;
s33, carrying out standardization processing on the health characteristic data and the battery SOH data which are filtered by the S31 and the S32 to form a data set, and dividing a training set, a verification set and a test set, wherein a standardization formula is as follows:
（5）；
in the method, in the process of the invention,for the mean of the selected features, +.>Is the standard deviation of the selected feature.
In the step S4, the step of constructing a feature fusion model for feature depth fusion is as follows:
s41, constructing a feature fusion model for processing sequence data, wherein the feature fusion model comprises an input layer, a convolution layer, a pooling layer, a flat layer, a full connection layer, a Dropout layer and an output layer;
s42, adjusting the data shape of the data in the data set to enable the data shape to meet the input requirement of the feature fusion model;
s43, compiling a feature fusion model, wherein a loss function adopts root mean square error, and an optimizer selects adam;
s44, inputting original health feature data and corresponding battery SOH data in a training set, performing preliminary training on a feature fusion model, excavating complex relations between features and SOH, and continuously adjusting model parameters by using a verification set to achieve an expected effect;
s45, storing the trained feature fusion model;
s46, extracting data information of the full-connection layer from the trained feature fusion model (namely extracting fusion features) to serve as a feature fusion result.
In the step S41, the filters of the convolution layer are 64, the convolution kernel size is 3, and the activation function is a relu function; the size of the pooling layer core is 2; the number of neurons of the full-connection layer is 32, and the activation function is a relu function; the Dropout rate was 0.5.
In the step S5, the steps of establishing an estimation model and obtaining an SOH estimation value are as follows:
s51, in a python environment, an XGBoost regression model is built by importing an XGBoost third party library; wherein, XGBoost uses CART as basic learner, establishes integrated model through iteration promotes tree, and for regression problem, XGBoost uses square loss function as the optimization target of estimation model, XGBoost objective function defines as follows:
（6）；
where j represents the j-th iteration, N is the number of samples,is a square loss function, +.>Is the actual target value of the i-th sample, +.>Representing the estimated value of the model at the j-1 th iteration, T being the number of decision trees,/->Regularized item about tree, +.>Represents the kth tree;
s52, inputting the fusion characteristics and the corresponding SOH values acquired in the S46, and setting super parameters: the maximum iteration number is 100, the learning rate is 0.1, and the maximum depth of the decision tree is 4;
s53, training is carried out, parameters are adjusted until the result reaches the expectation, and a trained estimation model is stored; the model establishes a complex nonlinear relationship between the fusion features and the battery SOH.
S54, outputting an estimated value, and inversely normalizing and inversely converting to obtain a final SOH estimated value.
After the final SOH estimated value is obtained, a test set is used for verification, and an algorithm model consisting of a feature fusion model and an estimation model is evaluated.
The steps of using the test set for verification are:
s61, adjusting the shape of the health feature data of the test set, inputting the shape into the feature fusion model stored in S45, and extracting fusion features of the test set;
s62, inputting the extracted fusion characteristics into an estimation model stored in S53 to obtain an estimation value;
s63, inversely normalizing the inverse conversion estimated value to obtain a final SOH estimated value, and storing the final SOH estimated value;
s64, evaluating the effect of an algorithm model by adopting Root Mean Square Error (RMSE), wherein the calculation formula is as follows:
（7）；
in the method, in the process of the invention,is the final SOH estimate.
The algorithm according to the present invention may be executed by an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the algorithm being implemented by the processor executing software.
The invention has the beneficial effects that:
according to the invention, through extracting a plurality of health features closely related to battery aging, carrying out deep analysis on complex nonlinear relation analysis between features and between features and SOH through a feature fusion model, extracting fusion features containing deep feature information, and then establishing complex relation between fusion features and SOH through XGBoost, the problem of insufficient analysis on complex relation between features and between features and SOH in the past is solved, so that the accuracy and universality of an algorithm model are improved. Through verification, the method can accurately estimate the SOH of the battery, is suitable for different types of lithium ion batteries, and has good accuracy and universality.
Drawings
FIG. 1 is a flow schematic of the present invention;
FIG. 2 is a graph showing the comparison of SOH estimation results based on the test set cell CS35 in the verification process of the present invention;
fig. 3 is a graph showing the comparison of SOH estimation results based on the test battery set M009 during the verification process of the present invention.
Detailed Description
Embodiments of the invention are further described below with reference to the accompanying drawings:
as shown in fig. 1, the method for estimating the SOH of the battery based on multi-feature fusion and XGBoost comprises the following steps:
s1, data acquisition: collecting aging data in the cyclic aging process of the battery;
s2, feature extraction: analyzing the aging data, and extracting battery SOH data and health characteristic data closely related to the battery SOH;
s3, data processing: processing the health characteristic data and the battery SOH data, including abnormal value detection, correlation analysis and standardization processing;
s4, feature depth fusion: constructing a feature fusion model for feature depth fusion, so as to extract fusion features;
s5, establishing an estimation model: and establishing a complex relation model of the fusion characteristic and the SOH based on XGBoost, namely an estimation model, so as to estimate the SOH of the battery and obtain an estimated value of the SOH.
In S1, the process of collecting aging data is as follows:
s11, collecting time and voltage data of a battery charging stage under different cycles, and constructing a charging voltage curve;
and S12, collecting time and current data of a battery discharge stage under different cycles, and calculating the battery capacity.
In S2, the extracted health feature data closely related to the SOH of the battery includes:
s21, constructing a charging voltage curve based on aging data of the battery in the charging stage acquired in the S11;
s22, calculating the battery capacity, including the maximum discharge capacity and the initial capacity, based on the aging data of the battery in the discharge stage acquired in the S12;
s23, extracting constant-current charging time based on a charging voltage curve;
s24, extracting constant-voltage charging time based on a charging voltage curve;
s25, extracting a curve peak value of the increment capacity IC (Incremental Capacity) based on a charging voltage curve, wherein a calculation formula of the IC is as follows:
（1）；
wherein Q is battery capacity, V is voltage, I is current, and t is time;
s26, extracting a voltage sample entropy value in a constant current charging stage based on a charging voltage curve;
and S27, extracting SOH data of the battery based on the aging data and the battery capacity of the battery in the discharging stage, wherein the SOH data is defined as follows as a tag value corresponding to the health characteristic data:
（2）；
in the method, in the process of the invention,indicating the current maximum discharge capacity of the battery，/>Indicating the initial capacity of the battery.
In S3, the step of processing the health characteristic data is as follows:
s31, detecting abnormal values of all extracted health characteristic data by adopting a 3 sigma principle, deleting the abnormal values and other data of the cycle times, wherein the 3 sigma principle is expressed as follows:
（3）；
each health characteristic data is represented by a characteristic x, wherein,representing the i-th cycle acquisition value of the feature x, μ representing the mean value of the feature x, σ representing the standard deviation of the feature x;
s32, primarily analyzing the correlation between the health feature data and the battery SOH data by adopting the Pearson correlation coefficient, and removing the feature that the absolute value of the correlation coefficient is lower than 0.8 to avoid interference to the result, wherein the more the absolute value of the correlation coefficient is more than 1, the higher the correlation is, and the calculation formula of the Pearson correlation coefficient is as follows:
（4）；
where r is the pearson correlation coefficient, n is the sample size,SOH value of the ith cycle, < >>And->Is the average of the selected feature and the battery SOH sample, respectively;
s33, carrying out standardization processing on the health characteristic data and the battery SOH data which are filtered by the S31 and the S32 to form a data set, and dividing a training set, a verification set and a test set, wherein a standardization formula is as follows:
（5）；
in the method, in the process of the invention,for the mean of the selected features, +.>Is the standard deviation of the selected feature.
In S4, the step of constructing a feature fusion model for feature depth fusion is as follows:
s41, constructing a feature fusion model for processing sequence data, wherein the feature fusion model comprises an input layer, a convolution layer, a pooling layer, a flat layer, a full connection layer, a Dropout layer and an output layer; wherein, the filters of the convolution layer is 64, the convolution kernel size is 3, and the activation function is a relu function; the size of the pooling layer core is 2; the number of neurons of the full-connection layer is 32, and the activation function is a relu function; the Dropout rate is 0.5;
s42, adjusting the data shape of the data in the data set to enable the data shape to meet the input requirement of the feature fusion model; in this embodiment, the data shape is: (number of samples, number of features, 1);
s43, compiling a feature fusion model, wherein a loss function adopts root mean square error, and an optimizer selects adam;
s44, inputting original health feature data and corresponding battery SOH data in a training set, performing preliminary training on a feature fusion model, excavating complex relations between features and SOH, and continuously adjusting model parameters by using a verification set to achieve an expected effect;
s45, storing the trained feature fusion model;
s46, extracting data information of the full-connection layer from the trained feature fusion model to serve as a feature fusion result.
S5, establishing an estimation model and obtaining an SOH estimation value, wherein the step of establishing the estimation model comprises the following steps of:
s51, in a python environment, an XGBoost regression model is built by importing an XGBoost third party library; wherein, XGBoost uses CART (Classification and Regression Trees) as basic learner, through iterative lifting tree to build integrated model, for regression problem, XGBoost uses square loss function as the optimization target of estimation model, XGBoost objective function is defined as follows:
（6）；
where j represents the j-th iteration, N is the number of samples,is a square loss function, +.>Is the actual target value of the i-th sample, +.>Representing the estimated value of the model at the j-1 th iteration, T being the number of decision trees,/->Regularized item about tree, +.>Represents the kth tree;
s52, inputting the fusion characteristics and the corresponding SOH values obtained in the S46, and setting super parameters;
s53, training is carried out, parameters are adjusted until the result reaches the expectation, and a trained estimation model is stored;
s54, outputting an estimated value, and inversely normalizing and inversely converting to obtain a final SOH estimated value.
After the final SOH estimated value is obtained, a test set is used for verification, and an algorithm model consisting of a feature fusion model and an estimation model is evaluated.
The step of verifying using the test set is (this verification step is noted as S6):
s61, adjusting the shape of the health feature data of the test set, inputting the shape into the feature fusion model stored in S45, and extracting fusion features of the test set;
s62, inputting the extracted fusion characteristics into an estimation model stored in S53 to obtain an estimation value;
s63, inversely normalizing the inverse conversion estimated value to obtain a final SOH estimated value, and storing the final SOH estimated value;
s64, evaluating the effect of an algorithm model by adopting root mean square error RMSE (Root Mean Square Error), wherein the calculation formula is as follows:
（7）；
in the method, in the process of the invention,is the final SOH estimate.
The verification process is as follows:
the method provided by the invention is used for model training and SOH estimation test by taking part of data in a battery aging public data set of university of maryland and a battery aging experimental data set of university of Shandong as test sets.
The battery aging data of lithium cobaltate batteries with the numbers CS35 and CS38 are selected from the battery aging public data set of the university of Maryland, the rated capacity of the battery is 1.1Ah, the battery is fully charged by adopting a constant current-constant voltage charging protocol, waiting for 60s, and then collecting experimental data by adopting a constant current discharging cyclic aging strategy. After the CS35 and CS38 battery data are subjected to the steps S1-S3, the CS38 is divided into a training set (80%) and a verification set (20%), and training and verification of the feature fusion model and the estimation model are performed through the steps S4 and S5, and the trained model is stored. The CS35 battery total data is subjected to a model test through S6, and the comparison between the battery SOH estimation result obtained by the test and the actual SOH is shown in fig. 2, and the calculated SOH estimation error rmse= 0.0052655.
And selecting aging data of lithium iron phosphate batteries with the numbers of M009 and M010 from the battery experimental data set of Shandong university, wherein the rated capacity of the battery is 1.55Ah, the battery is fully charged by adopting a constant current-constant voltage charging protocol, the interval is 1 hour, and then the experimental data are collected by adopting a constant current discharging cyclic aging strategy. After the M009 and M010 battery data are subjected to the steps S1-S3, the M010 is divided into a training set (80%) and a verification set (20%), training and verification of the feature fusion model and the estimation model are carried out through the steps S4 and S5, and the trained model is stored. The model test is performed on all data of the M009 battery through S6, and the pair of the battery SOH estimation result obtained through the test and the real SOH is as shown in fig. 3, and the calculated SOH estimation error rmse= 0.0036633.
The method provided by the invention is subjected to model training and SOH estimation test through a Maryland university battery aging public data set and a Shandong university battery aging experimental data set, so that the method provided by the invention is verified to be capable of accurately estimating the SOH of the battery, and is suitable for different types of lithium ion batteries, and has good accuracy and universality.
Claims (9)
1. The method for estimating the SOH of the battery based on multi-feature fusion and XGBoost is characterized by comprising the following steps of:
s1, data acquisition: collecting aging data in the cyclic aging process of the battery;
s2, feature extraction: analyzing the aging data, and extracting battery SOH data and health characteristic data closely related to the battery SOH;
s3, data processing: processing the health characteristic data and the battery SOH data, including abnormal value detection, correlation analysis and standardization processing;
s4, feature depth fusion: constructing a feature fusion model for feature depth fusion, so as to extract fusion features;
s5, establishing an estimation model: and establishing a complex relation model of the fusion characteristic and the SOH based on XGBoost, namely an estimation model, so as to estimate the SOH of the battery and obtain an estimated value of the SOH.
2. The method for estimating battery SOH based on multi-feature fusion and XGBoost of claim 1, wherein: in the step S1, the aging data acquisition process is as follows:
s11, collecting time and voltage data of a battery charging stage under different cycles, and constructing a charging voltage curve;
and S12, collecting time and current data of a battery discharge stage under different cycles, and calculating the battery capacity.
3. The method for estimating battery SOH based on multi-feature fusion and XGBoost of claim 2, wherein: in S2, the extracted health feature data closely related to the SOH of the battery includes:
s21, constructing a charging voltage curve based on aging data of the battery in the charging stage acquired in the S11;
s22, calculating the battery capacity, including the maximum discharge capacity and the initial capacity, based on the aging data of the battery in the discharge stage acquired in the S12;
s23, extracting constant-current charging time based on a charging voltage curve;
s24, extracting constant-voltage charging time based on a charging voltage curve;
s25, extracting a curve peak value of an incremental capacity IC based on a charging voltage curve, wherein a calculation formula of the IC is as follows:
（1）；
wherein Q is battery capacity, V is voltage, I is current, and t is time;
s26, extracting a voltage sample entropy value in a constant current charging stage based on a charging voltage curve;
and S27, extracting SOH data of the battery based on the aging data and the battery capacity of the battery in the discharging stage, wherein the SOH data is defined as follows as a tag value corresponding to the health characteristic data:
（2）；
in the method, in the process of the invention,represents the maximum discharge capacity of the current battery,/-)>Indicating the initial capacity of the battery.
4. A method of estimating battery SOH based on multi-feature fusion and XGBoost according to claim 3, characterized by: in the step S3, the step of processing the health feature data is as follows:
s31, detecting abnormal values of all extracted health characteristic data by adopting a 3 sigma principle, deleting the abnormal values and other data of the cycle times, wherein the 3 sigma principle is expressed as follows:
（3）；
each health characteristic data is represented by a characteristic x, wherein,representing the i-th cycle acquisition value of the feature x, μ representing the mean value of the feature x, σ representing the standard deviation of the feature x;
s32, primarily analyzing the correlation between the health feature data and the battery SOH data by adopting the Pearson correlation coefficient, and removing the feature that the absolute value of the correlation coefficient is lower than 0.8 to avoid interference to the result, wherein the more the absolute value of the correlation coefficient is more than 1, the higher the correlation is, and the calculation formula of the Pearson correlation coefficient is as follows:
（4）；
where r is the pearson correlation coefficient, n is the sample size,SOH value of the ith cycle, < >>And->Is the average of the selected feature and the battery SOH sample, respectively;
s33, carrying out standardization processing on the health characteristic data and the battery SOH data which are filtered by the S31 and the S32 to form a data set, and dividing a training set, a verification set and a test set, wherein a standardization formula is as follows:
（5）；
in the method, in the process of the invention,for the mean of the selected features, +.>Is the standard deviation of the selected feature.
5. The method for estimating battery SOH based on multi-feature fusion and XGBoost of claim 4, wherein: in the step S4, the step of constructing a feature fusion model for feature depth fusion is as follows:
s41, constructing a feature fusion model for processing sequence data, wherein the feature fusion model comprises an input layer, a convolution layer, a pooling layer, a flat layer, a full connection layer, a Dropout layer and an output layer;
s42, adjusting the data shape of the data in the data set to enable the data shape to meet the input requirement of the feature fusion model;
s43, compiling a feature fusion model, wherein a loss function adopts root mean square error, and an optimizer selects adam;
s44, inputting original health feature data and corresponding battery SOH data in a training set, performing preliminary training on a feature fusion model, excavating complex relations between features and SOH, and continuously adjusting model parameters by using a verification set to achieve an expected effect;
s45, storing the trained feature fusion model;
s46, extracting data information of the full-connection layer from the trained feature fusion model to serve as a feature fusion result.
6. The method for estimating battery SOH based on multi-feature fusion and XGBoost of claim 5, wherein: in the step S41, the filters of the convolution layer are 64, the convolution kernel size is 3, and the activation function is a relu function; the size of the pooling layer core is 2; the number of neurons of the full-connection layer is 32, and the activation function is a relu function; the Dropout rate was 0.5.
7. The method for estimating battery SOH based on multi-feature fusion and XGBoost of claim 5, wherein: in the step S5, the steps of establishing an estimation model and obtaining an SOH estimation value are as follows:
s51, in a python environment, an XGBoost regression model is built by importing an XGBoost third party library; wherein, XGBoost uses CART as basic learner, establishes integrated model through iteration promotes tree, and for regression problem, XGBoost uses square loss function as the optimization target of estimation model, XGBoost objective function defines as follows:
（6）；
where j represents the j-th iteration, N is the number of samples,is a square loss function, +.>Is the actual target value of the i-th sample, +.>Representing the estimated value of the model at the j-1 th iteration, T being the number of decision trees,/->Regularized item about tree, +.>Represents the kth tree;
s52, inputting the fusion characteristics and the corresponding SOH values obtained in the S46, and setting super parameters;
s53, training is carried out, parameters are adjusted until the result reaches the expectation, and a trained estimation model is stored;
s54, outputting an estimated value, and inversely normalizing and inversely converting to obtain a final SOH estimated value.
8. The method for estimating battery SOH based on multi-feature fusion and XGBoost of claim 7, wherein: after the final SOH estimated value is obtained, a test set is used for verification, and an algorithm model consisting of a feature fusion model and an estimation model is evaluated.
9. The method for estimating battery SOH based on multi-feature fusion and XGBoost of claim 8, wherein: the steps of using the test set for verification are:
s61, adjusting the shape of the health feature data of the test set, inputting the shape into the feature fusion model stored in S45, and extracting fusion features of the test set;
s62, inputting the extracted fusion characteristics into an estimation model stored in S53 to obtain an estimation value;
s63, inversely normalizing the inverse conversion estimated value to obtain a final SOH estimated value, and storing the final SOH estimated value;
s64, evaluating the effect of an algorithm model by adopting Root Mean Square Error (RMSE), wherein the calculation formula is as follows:
（7）；
in the method, in the process of the invention,is the final SOH estimate.
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