## 4 Neural Network Model and Training
### Fleet Model Structure  
The structure of the fleet model is motivated by the following requirements (summarized in Figure 4) and their respective implications:  
1. Capacity tests cannot be carried out during the conventional operation of a vehicle fleet. The training of the fleet model is thus restricted to the signals measured by the battery monitoring system. We therefore fit the model to the measured voltage and use capacity estimations (for instance from dedicated charging with small currents) only for validation purposes.
2. In contrast to existing approaches, we want to create a model that includes multiple devices. Moreover, information transfer between the fleet vehicles should be enabled.
3. It should be possible to incorporate existing domain knowledge (for instance open circuit voltage (OCV) curves) and recognized constraints (only increasing resistances/decreasing capacities) into the model.
4. The model should be extendible, such that we can couple it with an aging model that not only describes the battery aging of the fleet vehicles but also determines aging stress factors and predicts the aging until EOL.
5. We want to perform virtual experiments to analyze the battery's SOH according to different usage scenarios. The SOH is typically defined as the relative capacity of the battery; in some cases, resistance is also considered. The impact of both parameters on aging strongly depends on the conducted operation. So, in real applications a scenario-based SOH definition might be more relevant, e.g., for the feasibility of a specific usage. This approach leads to a natural weighting of these aging parameters. This can be beneficial for route planning etc.
6. The model should be scalable, i.e., it should also work with larger fleets.  
These requirements are satisfied by the proposed model structure illustrated in Figure 5.  
Figure 4: Requirements of the model invoked by automated field data analysis.  
The model consists of three main parts:  
* core battery model: The structure of this core battery model is shown in Figure 6. It consists of a part which describes the OCV as a function of the SOC and a part modeling the overpotential. Using temperature, current and SOC information as well as the actual SOH (given by the scaling factors \(f_{\rm C}\) and \(f_{\rm R}\)), the battery voltage is predicted. Dynamic effects are taken into account by using multiple low-pass time filters of the current signal. Thus, previous current values are considered. This is inspired by ECMs where this is done using RC-elements. Recurrent neural networks are an alternative implementation, especially with Long Short-Term Memory. Although they are widely employed, our approach reduces the parametrization effort and is more robust as is shown in [26].
* All vehicles of the fleet share this core battery model. Since the neural network is fed with all vehicles, it simulates the average battery behavior. This permits information transfer between different devices, e.g., if some vehicles are only operated at small SOC (or current or temperature) ranges, training the model with the remaining devices enables the extrapolation to a wider SOC (or current or temperature) range.
* aging parameter database: This model part contains the aging information of each vehicle in the fleet and outputs the SOH based on the device's _id_, the lifetime as well as the total charge throughput. To calculate the SOH, vehicle-specific calendric and cyclic aging rates are stored. An advantage is the easy detection of peculiarly aged batteries by investigating the SOH scaling factors (see Section 4.3).
* soc0 model: Since the SOC given by the BMS is no direct measurement and error-prone, we do not use this signal. Instead, we calculate our own SOC signal. After coulomb counting, we recalibrate the signal with adjusting factors to compensate for measurement errors and data gaps.  
The inputs and outputs of the submodels are described in Table 2.  
Figure 5: Structure of the fleet model.  
Figure 6: Structure of the core battery neural network.