## 2 State of the Art on Characterization of Weld Geometries and Stress Concentrations
### Characterization of Stress Concentrations along Weld Seams  
Besides the fast development of weld geometry measurement systems and algorithms to post-process the measured data, the characterization of stress concentrations at welded joints has also seen significant progress, and it was shown that fatigue cracks often initiate at locations with high stress concentrations [14, 16, 18].  
In the past, parametric SCF equations offered a quick estimation tool to determine SCFs for notched structures such as welded joints [19]; however, a number of recent studies have shown that these equations are less accurate than direct finite element (FE) calculations, see [20, 21, 22, 23, 24]. Performing direct FE calculations is, however, quite time consuming, especially for 3D weld geometries. Thus, fitting complex functions to the data provides a fast and reliable way to determine SCFs at welded joints. Various researchers proposed polynomial regression with coupling terms (PRC) and ANN for this task, see [23, 24, 25, 26, 27]. By performing several thousand parametric FE simulations, they showed that SCFs can be determined accurately and fast. In addition, their solutions significantly exceed the parameter range of parametric SCF formulas.  
Data-driven methods (i.e., machine learning) are increasingly used to predict fatigue of components and parts [28]. Machine learning using ANN is the most common approach [29] and is suitable when large, complex data sets are available and there is no accurate physical description of the phenomenon [30, 31, 32].  
In terms of computational efficiency, ANN, once trained, are superior to other computer-based methods such as FE simulations [29]; however, ANN have very limited ability to make predictions outside the training data space [33, 34, 35]. In addition, \"overfitting\" of data can prove problematic, resulting in large deviations when predicting on new data points [33]. A common problem for machine learning algorithm is that the noise or random fluctuations in the training dataset are picked up and memorized as concepts by the model.  
By combining advanced tools to determine weld geometry parameters and tools to determine SCFs, it is possible to quickly calculate the change of SCFs along weld seams and to perform inline quality and fatigue strength assessments. For this purpose, a basis for comparison is required to relate measurements to.  
To this day, there are only a few studies that consider distributions of weld geometries or stress concentration factors [12, 13, 16, 36, 37, 38, 39, 40, 41, 42, 43]; however, there is no thorough investigation of what type of distribution type is suitable for the different geometry parameters and SCFs. Thus, a better understanding of statistical distributions of weld geometry parameters and stress concentrations is needed; nevertheless, first reliable tools to determine stress concentration factors are required. Below, a method to determine stress concentration factors at seam welds of butt joints based on a machine learning approach is presented. This method is then applied to determine statistical distributions of weld geometry parameters and SCFs of weld seams of butt joints made by different welding methods.