## 7 Summary and Conclusions  
One important step in this context is a deeper understanding of statistical distributions of weld geometry parameters and stress concentrations along weld seams. This study presents an approach to statistically characterize different types of butt joint weld seams made by different welding methods. For this purpose, an artificial neural network was created from thousands of finite element simulations to determine SCFs at arc- and laser-welded butt joints with sheet thickness ranging from 1 mm to 100 mm. The following conclusions are drawn from the statistical characterization of weld geometry parameters and stress concentrations along butt joint weld seams using deep neural networks:  
* Establishing a DNN for a recurring task such as the determination of SCFs at weld transition significantly decreases the required time to determine the severity of notches along weld seams by combining the mutual influence of stress-raising effects from local weld geometry factors such as weld toe radii, angles, and undercuts. * The comparison of skewness and kurtosis of the measured samples with theoretical distributions showed that it is difficult to determine suitable distribution functions for the investigated weld geometry parameters and SCFs. This might be related to non-stationary processes that result in variations along weld seams (e.g., due to inhomogeneous temperature fields) but also measurement inaccuracies. Modelling inaccuracies are mitigated by using highly refined FE meshes to calculate the input data for the DNN. * Weld toe radii seem to follow a lognormal distribution. This agrees with a number of recent studies [20, 36, 37], but also rejects mainly older investigations. * The majority of weld toe angle sample distributions are only slightly skewed. This is an indication for a symmetrical distribution like a normal distribution; nevertheless, the partially high kurtosis indicates that the tails of the distributions are wider (more outlier-prone) than typical for a normal distribution. * The distributions of undercuts are the most skewed. The reason is that very small shape parameters \(\alpha\) are required to fit distributions as presented in Figure 9, which increases the skewness and kurtosis; nevertheless, the data is close to a gamma distribution. A gamma distribution might be better suited to describe undercut depths (for which the maximum of data is equal to zero) as a lognormal distribution. * The data for the weld reinforcement heights are clustered around the normal distribution and the region where lognormal, gamma, and inverse gamma distribution are close to each other. * The distributions of weld widths and SCFs show a large scatter. This makes it difficult to relate them to a typical distribution function. The reason for the scatter of the sample parameters of the SCFs might be related to the fact that the SCF calculation is based on the input of a number of geometrical features. Thus, the variability and any possible inaccuracy in the input parameters and numerical modelling is transferred to the SCFs. In addition, the combination of various parameters could be the reason typical two-parameter distribution functions are not suitable to describe a complex parameter such as a SCF. In summary, this study presents promising results, but more data should be assessed to verify the result of this study and in order to establish a basis for automatic inlinequality inspections of welded joints beyond the scope of current manual weld inspections after welding. Conceptualization and methodology, M.B. and J.N. ; investigation, data curation, and validation, M.B., F.R., L.K., J.N. and M.D. ; software, F.R. and M.J.; writing--original draft preparation and visualization, M.B. and J.N. ; writing--review and editing, M.D., F.R., L.K., J.S., M.J., K.R. and S.E. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Data Availability Statement. Data available on request due to restrictions.