## 2 Materials and Methods
### Reference Network and Training  
The ANN used for the evaluation of the acoustic data is built with a four-layer feedforward network which uses tansig activation functions (specified in Equation (1)) for the hidden layers and the softmax function (specified in Equation (2)) for the output layer. In general, such a network is well suited for pattern recognition, where different input vectors are classified into given target categories [18]. We use supervised ANNs in contrast to unsupervised ANNs to ensure the best possible success rate in the classification problem.  
Figure 2: Flow chart for the recording of 30 nozzle shots in one data block.  
The additional experimental effort for labeling the training data in an industrial application will be small compared to the repeated manual effort of monitoring the print head with a test pattern. The Fast Fourier Transformation (FFT) of the recorded signal is utilized as input data. After specifying input and target values, the training function for the ANN was determined. In principle, Matlab provides a large number of different training functions, which can be selected depending on the application and the available computing power. A detailed overview can be found under [19]. The algorithm trainscg was selected, where scg is the abbreviation for Scaled Conjugate Gradient Backpropagation. This algorithm is used by default in Matlab for pattern recognition problems and is also well suited for large networks, according to the work in [20], as it is very efficient. As the number of input and output neurons was already specified by the input and target matrices, only the size and number of hidden layers had to be specified to fully define the network size. All relevant parameters can be found in Table 2.  
The available input data were divided into training data, validation data, and test data. The distribution was random; 70% of the data was used for training, 15% for validation, and the remaining 15% as test data. The training data are used for the actual training. Based on these data, the gradients are calculated and the individual weights are updated at each iteration. In contrast, the validation data are used to prevent overfitting. An overfitted ANN is overtrained on the given training data, reducing the prediction accuracy for further unknown data sets which were not part of the training data set. To prevent this, so-called early stopping is used. If the calculated error between the target and initial values of the network exceeds the error limit for the validation data over several iterations and, at the same time, the error of the training data continues to decrease, this is an indicator of so-called overfitting [20]. By specifying a maximum number of training epochs, an early stop of the training is enforced. Finally, the weights are assigned the values that produced the minimum error in the validation data set, thus preventing overfitting.  
The FFT of the respective signal is used as input values of the ANN. In advance, a short overview of the most important settings and parameters of the used reference networks is given in Table 2. These parameters will be optimized in the next section.  
\[\text{tansig(N)}=\frac{2}{1+\exp(-2N)}-1 \tag{1}\]  
\[\text{softmax(N)}=\frac{\exp(N)}{\sum(\exp(N))} \tag{2}\]