## 3 Results and Discussion
### Analysis of ANN
#### 3.2.2 Analysis of ANN and Created Correlations  
Below, the correlation of predicted distortion with the input parameters for the enhanced ANNs are examined for a single selected ANN. In analogy to the plot in Figure 9b, the enhanced ANN with the lowest absolute test error was chosen. For this ANN, the standardized residual of the prediction errors over the predicted distortion is shown in Figure 10.  
Even though there are some outliers surpassing an upper and lower limit of three times the standard deviation, this plot visualizes the good fit of this enhanced approach, as over 95% of datapoints are within these boundaries. The standardized residual is even lower for most points, with the average of the absolute standardized residual being 0.485. The five outliers are listed at the bottom of the figure. The low amount of outliers compared to the total amount of 144 datapoints only allows very limited statements about their nature. The only obvious common ground is a current welded layer count of one, which suggests that the ANN is mostly challenged by the prediction of early layers. As noted in Section 3.2, these outliers appear in a broad area where the bulk of the predicted data points are also located. In summary, Figure 10 confirms low prediction errors even for predictions of high and low distortions and an overall ability to predict all trained ranges of parameter values for this preliminary application of an enhanced approach. For further analysis, the complete dataset is predicted with the enhanced ANN from Figures 9b and 10 and compared to the results from the experiments. This makes it possible to analyze the influence of different input parameters on the predicted distortion. Analyzing the correlations for the non-continuous datasets such as wire feed is difficult, as the points are mostly stacked on top of each other and are difficult to interpret. Therefore, Figure 11 shows the plots for the predicted distortion of the next layer over the continuous dataset energy input as well as the enhanced inputs for the geometries and the previously welded current distortion. Figure 10: Standardized residual over predicted distortion for an enhanced ANN with unedited data of output distortion (see Figure 9b). Additional list of parameters for the five outliers (Marked as A–E) given. The plots \(b\) and \(d\) with the weld bead widths as inputs show no correlation. Plot \(a\) with the current upper weld bead height shows two seemingly separate columns. The reason for this is the current upper height being either a result of welding a single layer or two layers, as these are the two possible input bead counts for the enhanced ANN. Plot \(f\) for the predicted next distortion over the current distortion shows a distribution that appears to be a linear correlation. As a result, the created ANN seem to predict higher distortions for already pre-distorted objects, which is the expected behavior and reinforces the good fit of the created ANN. Plots \(c\) for the lower weld bead height and \(e\) for the energy input illustrate the effect of large amounts of thermal energy causing full-penetration welding as well as reduced distortion. In plot \(c\), for current bead heights above 0.7 mm, no predicted distortion above 10 mm was achieved. This is a reasonable correlation trained by the ANN, when considering the increased bending moment required for large material depositions on the underside of the plate. For very high energy inputs above 40 kJ, the predicted distortion also tends to be lower; this models the effects of full-penetration welding, as described in Section 3.1. In the diagrams of Figure 11, the error of the predicted distortion to the actual distortion is shown by the color of the dots. No particular areas that tend to result in large errors were identified. Merely the areas with low current lower weld bead height can be described as the area with all of the larger errors.