# Explainable Artificial Intelligence for State of Charge Estimation of Lithium-Ion Batteries
## 4 Experiments and Results
### E2: SoC Estimation Using Fusion Hybrid Model  
In the domain of multivariate time series regression, the fusion of static and time series features has emerged as a critical avenue for enhancing predictive models [42]. As mentioned previously in Section 3.2, the signals within an EV battery are features of a time series. More specifically, the signals can be referred to as the dynamic features, whilst the  
Figure 5: GRU SoC prediction: SoC predictions (blue) versus real SoC (orange). (**a**) EI’s result. (**b**) E3’s result, trained only with CURRENT and VOLTAGE. (**c**) E3’s result, trained only with CURRENT and VOLTAGE as well as a reduced window size. Subfigures (**a,b**) show no stark visual difference, whereas (**c**) show a clear visual difference despite being informed by xAI; this suggests that finding the optimal reduced window size is not trivial. static features would be some further information extracted from the signals. An example of a static feature would be the average of a signal. Such features can be obtained during the preprocessing of time series signals [53]. The concept behind the fusion [54] of features is to make maximum use of the information available in sequences. This would require a hybrid model that can combine temporal patterns with sequential dependencies and the contextual information of other external features. In woek of [PERSON], et al. [47], the success from the fusion of static and time features via NN attention mechanisms suggests that the same can be transferred to SoC estimation of EV batteries. The **Fusion Hybrid Model** approach seeks to connect the unchanging characteristics of the data with their temporal evolution, aiming to provide a comprehensive understanding of the underlying relationships with contextual information. In the case of EV battery modeling, dynamic features will be signals such as those in Table 3, and static features will be information extracted from signals, such as the following:  
* Average current in each window (CURRENT_AVG_WINDOW)
* Average voltage in each window (VOLTAGE_AVG_WINDOW)
* Difference in voltage in each window (VOLTAGE_DIFF_WINDOW)
* Average cumulative discharge energy in each window (CUMULATIVE_DE_AVG)
* Average temperature for each window (T_AVG_WINDOW)
* Difference in SoC in each window (SOC_REAL_DIFF)
* Average SoC in each window (SOC_REAL_AVG)
* Difference between the max voltage and min voltage in each window (VOLTAGE_MAXMIN_DIFF)  
The features were fused based on a concatenation-based approach, which was characterized by the straightforward merging of static and dynamic features, forming an extended feature space [48]. By directly combining these attributes, the model gained immediate access to both the stable attributes and the evolving temporal patterns. However, this requires the managing of potentially high-dimensional feature spaces and would also require careful consideration of normalization techniques to maintain balanced contributions from each feature. The following settings were used in the experiment. **Dataset**: The dataset consists of 269 sessions (265 single-labeled and 4 multi-labeled) recorded for the car model e-Golf. Window segments of 20 min were used as input, with a time step interpolation of 1 s and a 20 min stride. **Features**: As this is a hybrid model, there are two sets of features: the dynamic and static features. The dynamic features for SoC include the following:  
* CURRENT
* VOLTAGE_DIFF
* T_CELL_AVG* T_DIFF
* DIFF_CAP
* DELTA_RESISTANCE  
The static features consisted of the aforementioned static features from the list above. The features were picked based on expert opinions regarding SoC and the outcome from Section 4.1. **Preprocessing**: The dataset was subjected to outlier removal and interpolation. Using MinMaxScaler, all data, including the labels, were normalized to the range of 0 to 1. The process was the same as that described in Section 4.1. **Train, validation, test split**: Stratified session splitting was performed with a total of 296 sessions.