## 3 Results and Discussion
### Battery Pack Model Development
#### 3.2.1 Artificial Neural Network  
An artificial neural network (ANN) is a set of interconnected neurons that mimic information processing, similar to humans. It provides a function for creating, training, visualizing and simulating neural networks capable of performing classification, regression, clustering time-series forecasting and dynamic modeling [23; 24]. A neural network consists of a two layer feed-forward network with sigmoid hidden neuron and linear output neurons that can fit multidimensional mapping problems arbitrarily well, given consistent data and enough neurons.  
Several types of neural network and how they are applied to solve the specific problems they are suited for have been demonstrated in literature. Peculiar to research on lithium ion batteries, [PERSON], et al. in [25] applied neural networks in optimization of his design parameters for a proposed battery pack model and [PERSON] et al. applied ANN to an empirical data set to develop a model to predict the State of Charge (SOC) level of lithium ion cells studied in their work [23].  
In this study, an ANN architecture model (Figure 19) is trained offline with the input data set from all experiments conducted in this study. Input data included the charge cycle (represented as 1), discharge cycle (represented as 0), the ambient temperature during the experiment, the current rate and the air flow rate (Table 6) while the maximum temperature of all monitored cells were fed as output data to the neural network.  
In total, a matrix of 4 by 37 and 16 by 37 data size were used as input and output data sets respectively. Seventy percent of input data was allocated for the neural network for model training while 15% each was allocated for the testing and validation phase of the ANN model development.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment** & **Cycle** & **Flow Rate (m/s)** & **Current Rate (C)** & **Ambient Temp \({}^{\circ}\)C** \\ \hline
0.5 DS1.3 & 0 & 1.4 & 0.5 & 17.10 \\ \hline
0.75 DS2.1 & 0 & 2.4 & 0.75 & 18.76 \\ \hline
0.75 CS1.1 & 1 & 1.4 & 0.75 & 19.08 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Artificial Neural Network (ANN) Input Training Data Sample.  
Figure 19: ANN architecture.  
After several iterations of training, a model obtained with an R value (correlation value) of 0.99139 was obtained between the fitted model and the given training data, 0.9812 correlation R value between the fitted model and the given data for testing and an R value of 0.98869 for an overall correlation between the actual outputs and the targets was obtained (see Figure 20). In Figure 21, the error histogram is plotted showing the difference between the target and actual output of the ANN training, which revealed that among the total samples considered, the majority of the error lies in the range 0.1034 to 2.08.  
The training algorithm selected for training the ANN module in this thesis study was the 'Bayesian Regularization' algorithm for its performance with difficult, small and noisy data sets [24]--a critical feature of the data output obtained during the conducted experiments in this study.