## 5 Conclusions  
In this work, four different artificial neural network models were tested for their ability to predict stresses related to the excitation frequency for the launch scenario of the Near-Infrared Spectrograph. In addition, they were tested on a theoretical case with differing numbers of sensors. With correctly trained ANNs, the monitoring of real shaker tests and thus the avoidance of overstressing the test specimens are possible. The conducted investigation allowed the comparison of all ANN models with respect to the requirements formulated in Section 2. From Tables 2-4 in Section 4, it can be clearly deduced that the NARX model is the most promising one. Figure 7, Figure 9, and Figure 11 illustrate this conclusion. Thus, a trained NARX model could be used during vibration tests and decrease the time of prediction of the given structural parameters, which is crucial for adapting and notching the input load of the shaker in time. As could also be seen, the recurrent ANN generally performs better than the feedforward ANN, handling the input as concurrent data. The ANN with biLSTM layer is able to make accurate predictions, even though its training is not conducted thoroughly due to the lack of data for a deep ANN. However, if such an ANN is trained with more data and more varied data, it possibly makes the most accurate predictions. In future studies, the potential of this network can be further investigated. For instance, the training data set for this model could be increased by including training data from FEA with several varied Young's moduli or varied damping parameters or by varying other material parameters that have an impact on the natural frequency. While the NARX model performs the best, its performance is highly dependent on the number of available frequency steps. For example, if the frequency range to be predicted (from 5 to 200 Hz) is poorly resolved and only divided into 100 instead of 600 frequency steps, this situation has a negative effect on the quality of the NARX model's predictions. The other networks are not as sensible to the division of the frequency range. In particular, the ranges of eigenmodes should have a higher resolution by having additional frequency steps. Each time step \(t\) of the sequence is treated as a single layer, which can lead to an extremely deep ANN. On the one hand, this results in increasing the computational time, but on the other hand it increases the performance of the network. The performance of the NARX model can thus be maximized by training it with as many frequency steps as possible. However, in practice, this can be a hurdle, as the required higher resolution may not be available during the test. Table 5 outlines the qualitative evaluation for the different models in terms of the requirements introduced in the introduction. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **R** & **RMSE (MPa)** \\ \hline Frequency-dependent ANN & 0.9801 & 0.0862 \\ NARX & 0.9936 & 0.0454 \\ biLSTM & 0.9895 & 0.0656 \\ Pretrained ANN & 0.9724 & 0.1219 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression coefficients and RMSE for the different ANN models on the NIRSpec data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criterion** & \multicolumn{4}{c}{**Method**} \\ \cline{2-5}  & **Frequency-Dependent** & **NARX** & **biLSTM** & **Pretrained ANN** \\ \cline{2-5}  & **ANN** & & & \\ \hline Robustness with regard to frequency shift & \(\sim\) & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ Fast deployment during test & \(\sim\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ Accuracy for stresses & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ Fast training & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ Robustness with regard to lack of sensors & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation of models for various criteria.