The State of Health (SOH) is a critical parameter in a Battery Management System (BMS) that indicates the aging condition of the battery. The SOH is typically defined as the ratio between the current maximum capacity of the battery and its nominal capacity, which is usually measured through a full discharge cycle at a rated C-rate. However, only a partial discharging or charging cycle is available in practice. In this work, a SOH estimation algorithm based on Long Short-Term Memory machine learning model is proposed. The proposed model takes partial data from Incremental Capacity (ICA) curves as Health Indicator (HI) and therefore fewer data are required for SOH estimation. A second order Thevenin model is used to calculate the over potential. Therefore, the HIs can be extracted under the commonly used Multiple-Constant-Current (MCC) charging profile and approximate CC discharging profile with small current variation. Two one-hot codes are included in input to indicate feature position and charging/discharging status. In this way, the model can be adapted to both charge and discharge data and feature from different voltage ranges can be used. Open-source datasets of Lithium Cobalt Oxide (LCO) and Nickel Manganese Cobalt (NMC) batteries are used for training and validation. A high accuracy with Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) less than 1% can be achieved through partial data with SOC change of less than 30%.

The proposed algorithm includes data preprocessing, feature extraction and SOH estimation based on LSTM. For the part of data preprocess, an Equivalent Circuit Model (ECM) combined with Kalman Filter is used to estimate the Open Circuit Voltage (OCV) based on the measured terminal voltage and current. One challenge of using ICA related features for SOH estimation is that there will be peak shifting and peak overlapping when the applied current is not at low C-rate. Therefore, the trained model can only be applied to a specified C-rate. The idea in this work is to perform SOH estimation based on a partial charging and discharging data, where the battery may be under a Multiple Constant Current (MCC) charging profile or under discharging with small current variation. Therefore, the data preprocess is designed to adapt the model to different CC current profiles. The measured terminal voltage is firstly transformed into OCV based on the ECM model. The overpotential caused by ohmic resistance and diffusion inside the battery is calculated by the RC (resistance and capacitance) components in the ECM model. The SOC is calculated through coulomb counting method and the parameters in the ECM model is updated according to the SOC through a look-up-table, including OCV, resistance and capacitance. The OCV, resistance and capacitance are provided by the open-source dataset. The Kalman filter is used to correct the OCV estimation error caused by the deviation of initial SOC. In this way, the estimated OCV can be derived from the measurement of terminal voltage and current. Therefore. the proposed model can be adapted to charging and discharging process with different C-rate.

For the part of feature extraction, the common operation voltage ranging from 2.5V to 4.2V is divided into several voltage segments based on an equal interval of 20mV. The measurement of terminal voltage is firstly transformed into OCV during data preprocess and then split into voltage segments based on an equal interval. The coulomb counting capacity within each voltage segment is calculated and formed into capacity sequence. To reduce the amount of data for SOH estimation, a sub-slice of capacity sequence is used as the HI for SOH estimation and a one-hot code is used to indicate the feature position. For the NMC dataset, 4 peaks can be observed in the entire capacity sequence, and the first, second and third peaks ranging from 3.4V to 4.0V are used because fully charging may not be a common case due to long charging time and fully discharging is neither common due to range anxiety. Therefore, the proposed voltage range can cover the common operation range for both charging and discharging scenarios in daily operation. The second peak is further split into left- and right-half peak. Because the peak width of the second one is larger and half peak is therefore used to reduce the amount of required data. Considering the peak and valley may shift and the features may overlap during the degradation, a sub-slice of capacity sequence with voltage change of 200mV is used to cover the feature shifting and overlapping from the Beginning of Life to the End of Life. Besides, a one-hot code with 4 indicators is used to indicate the feature position. The indicator filled with 1 in one-hot-code indicate the feature is used and the others for unused feature are padded with 0. And the four slots in the position feature one-hot-code stands for the first peak, the left half side of the second peak, the right half side of the second peak and the third peak accordingly. For LCO dataset, there are two peaks observed in the capacity sequence. The testing profile is based on Constant-Current (CC) and no CV phase is included. Therefore, both peaks are used and two of the indicators in one-hot-code are used to show the feature position. The first two slots are used to stand for the two peaks and the rest slots are padded with 0. The selected voltage range for feature extraction is between 3.3V and 4.0V. To adapt the algorithm to both charging and discharging data, another one-hot-code with two slots is used as working mode indicator, the charging slot is filled with 1 and the discharging slot is padded with 0 when the data is from charging process, which is the similar case when the data are from discharging process.

The model takes data slice from capacity sequence, position indicator and mode indicator for SOH estimation. Many other ICA feature-based models take curve features like peak or valley position, peak or valley height as HI and perform regression from input HI to SOH estimation. Different from the methods mentioned above, the proposed model takes data slice from entire capacity sequence and performs SOH estimation based on curve classification by LSTM. For the models based on ICA peak or valley features, partial charging or discharging data related to one entire single peak are required for peak or valley searching. However, only half peak data are required in this work and therefore the amount of input data can be reduced.

The proposed model consists of two Fully Connected layers (FC layers) and one LSTM layer. The capacity sequence data slice, position indicator and mode indicator are concatenated and fed to the first FC layer before LSTM for further feature extraction. The dimension of capacity sequence slice is M*1, where M stands for the length of data slice. The dimension of position indicator and working mode indicator are padded to M*4 and M*2 before concatenating separately, where 4 and 2 is the amount of slot in the one-hot-code. The seven-dimension input with multiple time steps by concatenating capacity sequence, position indicator and working mode indicator is transformed into dimension of M*N by the first FC layer, where N stands for the number of nodes in FC layer which is also a hyper parameter. The first FC layer is then connected to the LSTM layer. The LSTM layer does further feature extraction for each input step by iteration and store the inter-mediate result (hidden state) in the cell state. During each iteration, the LSTM updates the hidden state considering both the current input, the hidden state from previous iteration. Therefore, the output of LSTM layer summarizes the feature information for entire input data slice considering all history steps and gives the output of dimension 1*L, where L is the amount of cell nodes in LSTM. Finally, the output of LSTM is fed to the second FC layer with softmax activation function, which is commonly used for classification. The last FC layer gives the possibility distribution among the SOH categories. The categories used in this work are 100%, 95%, 90%, 85% and 80%. The final SOH estimation is derived based on the weighted average according to the possibility amount each SOH category.

To train the mode, the Kullback Leiber Divergence loss function is used, which is a commonly used loss function for multi-label classification problem with softmax activation function. The SOH estimation after weighted averaging is validated based on RMSE and MAE metrics. The average MAE and RMSE for SOH estimation are less than 0.5% and 1.2 % for the both cases when charging and discharging data are used. When the SOH is above 95%, the SOH estimation based on the feature from the first single peak shows higher MAE and RMSE than the other cases. The voltage range used for feature extraction is from 3.3V to 3.5V for discharging case and the range is from 3.4V to 3.6V for charging case. The MAE is around 0.85% for both charging and discharging cases and the RMSE is from 1.2%. And the MAE and RMSE are between 0.4% and 0.6% when features from the other half peaks are used. For the case when the SOH is between 95% and 85%, the MAE and RMSE are lower than 0.6%.