## 6 Results
### Regression Using Support Vector Regression  
The procedure for model building using support vector regression is more or less identical to the procedure for model building using artificial neural networks in Section 6.1. During training, the data of the training dataset are used in the cross-validation procedure. For this purpose, the data set is divided into five equal parts. Within five runs, four parts are used to train one model at a time and the remaining part is used to determine performance. By using a different part for performance evaluation in each run, an average performance can be determined afterwards. Before training, the mean value of each feature of the training parts is removed and the variance is scaled to 1. In addition, the influence of a principal component transformation, in particular the number of principal components used, is examined. A change in the number of principal components also affects the optimal value of the SVR hyperparameters. Therefore, Bayesian optimization is used to obtain optimized hyperparameters for each number of principal components that is analyzed. Again, the optimization is performed using only the mean performance of the cross-validation with the training data to prevent data leakage. Finally, after the optimal hyperparameters have been found, the complete set of training data is used for fitting the model and the performance on the test data is determined. The RMSEP is used as the performance metric.  
Figure 26 shows the RMSEP values of the cross-validation with training data. Additionally, the error bars represent the standard deviation of the RMSEP within the five parts. The performance using a single principal component is out of scale with a value of 30 A h. This is no surprise, as the constant current is now also part of the feature vector and the principal component transformation has to bring in this information as well. After applying PCA, the mean error decreases with increasing number of principal components. At a number of seven or more principal components, even better performance is achieved than when the principal component transformation is not applied. Here, we see that SVR is relatively immune to overfitting, as regulation is already built into the optimization function and small deviations within the \(e\) band are not penalized.  
Table 4 shows the resulting metrics when using the optimized hyperparameters to fit a model using all training data and predicting the test data depending on the number of principal components used. Again, model accuracy is very poor when only one principal component is used. It is interesting to note that the results of the test data are in most cases even better than the results of the cross-validation with the training data. This may be due to the fact that the number of training data used is now 20% larger without cross-validation. Another aspect is that the results seem to be better when the value of the DC current falls within the range of the training data. Due to the fact that in the previous cross-validation only 1 A and 3 A data were available that mark the current limits, now only 2 A direct current data is tested. In some cases, the reduced information content through the PCA  
Figure 26: RMSEP and standard deviation of crossvalidated training data depending on number of principal components.