## 3 Results and Discussion  
### Analysis in the Time Domain vs. in the Frequency Domain  
Before creating an ANN for the data evaluation, we attempted to find analytical correlations within the data. In a first step, the acoustic signals of the clogged and correctly operating nozzle are compared in the time domain.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value/Setting** \\ \hline Neurons—input layer & 20,000 \\ Neurons—hidden layer 1 & 100 \\ Neurons—hidden layer 2 & 60 \\ Neurons—output layer & 2 \\ Activation function—hidden layers & tansig \\ Transfer function—output layer & softmax \\ Error measure & mean squared error (mse) \\ Training function & Scaled Conjugate Gradient Backpropagation \\ Early Stopping & 80 epochs \\ \hline \hline \end{tabular}
\end{table}
Table 2: Important parameters of the reference-ANN utilized for the data evaluation.  
Figure 3 shows the mean values of the amplitudes of the recorded signals, which are normalized to the highest amplitude mean value occurring. Thirty data points were grouped in each case. In Figure 3, the state of the nozzle was set to the same value within these 30 data points (functional or clogged). The amplitude average of the functional nozzles tends to be higher than the amplitude average of the clogged nozzles. One possible explanation would be that the sound propagation is damped due to a clogged nozzle, which would be reflected accordingly in a lower amplitude. However, the amplitudes have a high scatter from data block to data block compared to this amplitude difference between clogged and functional nozzles.  
In addition to the observations of the amplitude averages in the time domain, the signals will be analyzed in the frequency domain in the following. For this purpose, a FFT of the signals was performed in Matlab. The resulting frequencies are calculated with the sample rate and the associated number of samples.  
Figure 4 shows that the maximum is at a frequency of 10 kHz, which corresponds to the frequency settings of the piezoelectric actuators. In addition, the first harmonic can be seen at twice the fundamental frequency of the piezoelectric actuators. The hypothesis is that the amplitudes at a frequency of 10 kHz are higher in the frequency range for a functional nozzle than those of a clogged nozzle. While Figure 4 (left) shows the complete signal in the frequency domain, Figure 4 (right) shows a zoom representation of the previous figure, which also allows the analysis of lower amplitude values. Functional nozzles (blue) show a higher amplitude than clogged nozzles (red) not only at a frequency of 10 kHz and 20 kHz, but also in the surrounding frequency ranges. In the low-frequency range from 0 to 7.5 kHz, no difference in amplitude can be found between functional and clogged nozzles. This also seems quite plausible, as in this range it is mainly background noise that is independent of the nozzle condition. Furthermore, no shift in the frequency peaks can be detected. In summary, it can be stated that in both the time and frequency domain, the evaluated amplitudes of a functional nozzle tend to be higher than the amplitudes of a clogged nozzle. However, as the observations are mean amplitudes and there is significant scatter between the data blocks, no clear correlation for the classification of the nozzle condition can be concluded on the basis of these analytic investigations. For this purpose, an ANN will be set up in the next section and used for noise pattern analysis.  
Figure 3: Comparison of the signal amplitudes of the individual data blocks in the time domain.