## 3 Results and Discussion
### Influence of Sample Time  
This section focuses on the optimization of the recording time, which may improve the success rate, as well as the technical feasibility. As all nozzles must be tested one after the other for their functionality when checking the complete print head, the sampling time is an important parameter for the technical feasibility. With 768 individual nozzles, it is advantageous to reduce the recording time per nozzle as far as possible. The reduction of the recording time \(t_{recording}\) affects the number of samples \(n_{sample}\) available for the evaluation at a constant sample rate \(f_{s}\), which becomes clear from Equation (3). \[n_{sample}=t_{recording}\cdot f_{s} \tag{3}\]  
Equation (3) shows that there is a linear relationship between sample number and recording time. The number of samples available for the evaluation in turn affects the sampling interval \(\Delta f\) of the discrete Fourier transform, which is used as input for the ANN. The sampling interval can be determined from the sample rate \(f_{sample}\) and the sample number \(n_{Sample}\). With Equation (3), the sampling interval \(\Delta f\) is calculated according to  
\[\Delta f=\frac{f_{s}}{n_{sample}}=\frac{1}{t_{recording}} \tag{4}\]  
Equation (4) shows that the reduction of the recording time causes an increase of the sampling interval. This influence on the success rate will be examined in the following. The reduced recording time is simulated by cutting of the respective signal. Starting from the maximum recording duration, which corresponds to a sample number of 40,000, the sample number is continuously reduced and the success rate is determined. The architecture of the ANN is analogous to the previous experiments. In addition, the amplitude of the input values in the time domain are again normalized. As the evaluation of parameter influences is based on the available test data, these can now no longer be regarded as independent. In order to ensure the general validity of the success rate nevertheless, the principle of data splitting is utilized again. For this purpose, the test data sets used in the cross-validation are divided into two parts by numbering the totality of all test data and combining all even or all odd measurement values into one test data level each. The first part of the data (1 st stage) is used to determine the success rate and, on the basis of this, to evaluate the influence of the parameters. To ensure that the optimization is not specifically tailored to the first part of the test data set, the success rate achieved is then checked with the independent part: the second stage of the data. Figure 7 shows the independent results for the variation of the number of samples. Please note that up to 5000 samples five different networks were utilized, while 20 networks were utilized from 5000-40,000 samples to increase to validity of the results. The mean values are marked by a blue x, additionally the standard deviation is given for each sample size. Particularly striking is the steep drop in the success rate below a sample number of 2500. Below this limit, the reduction of the sample number and the associated increase of the sampling interval seems to make it very difficult for the ANN to recognize the nozzle state. At a sample number of 100, the success rate is only 56%. Figure 7 shows that an increase in the sample number does not necessarily lead to an increase in the success rate. Based on these considerations, the optimization potential can now be evaluated by varying the number of samples. The analysis of Figure 7 shows that the maximum success rate of 74% is achieved with a sample number of 30,000. Compared to the original setting with a sample number of 40,000, this corresponds to an improvement of 3.6%. In order to test the statistical significance of this improvement, a z-test was performed in Matlab which rejected the hypothesis that the results at 30,000 samples and 40,000 samples originate from the same distribution at a 4% significance level.