## 3 Analysis of Datasets: Dimensional Analysis and Experimental Tests
### Experimental Data  
The availability of experimental data on scouring process at subsea pipelines is very limited. In this study, as can be generally observed in a number of recent articles on the topic under consideration, the experimental datasets extracted from [PERSON] et al. [9] were collected to develop the selected AI approaches. The just-mentioned authors performed three-dimensional scour experiments in a wave flume 50 m long, 4 m wide, and 2.5 m deep. A sandpit 4 m long, 4 m wide, and 0.25 m deep was used as test section. The transitions from the original flume bed to the test section and from the test section back to the original flume bed were achieved through two 1:20 concrete slopes. The upstream end of the sandpit was 21.5 m from the flow inlet, and the downstream end was 14.5 m from the flow outlet. A pipeline with a smooth surface, 50 mm diameter, and 8 mm wall thickness was tested. The experiments were performed for four various flow attack angles (\(\alpha\)) \(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), and \(45^{\circ}\). Furthermore, \(d_{50}\), \(\phi\), and \(\rho_{s}/\rho\) were 0.37 mm, \(32^{\circ}\), and 2.7, respectively. Even though \(d_{50}\) was very small, the viscosity effect could not be significant at the interface flow-sediment bed. Particles of bed sediment were in motion during the experiments (live-bed conditions), and the corresponding Shields' parameter due to wave condition was typically either 0.18 or 0.30 ([PERSON] et al. [9]). A total of 125 tests were conducted, which included 60 wave-only tests and 65 tests under combined wave and current conditions. In the case of wave-only conditions, scour propagation was not observed in the 16 tests. The results of the other three tests were obtained in the state of onset of scour in multiple locations. In addition to this, in three tests, the scour propagation process was only observed on the upstream span shoulder, and these observations cannot be used to feed AI models because the scour propagation should be observed in three dimensions: Longitudinal direction of pipeline, and the left and right sides of pipeline ([PERSON] et al. [9]). In this way, there are 22 experiments where pieces of information are not applied for modeling the scour propagation in the wave-only conditions. Table 1 shows the ranges of experimental datasets. From 38 experiments, 75% (29 datasets) and 25% (9 datasets) were randomly selected to perform training (or calibration) and testing (or validation) tests for AI models, respectively. The three mentioned scour rates are output variables, while the other non-dimensional parameters are inputs feeding the selected AI models. Histograms for all the non-dimensional (independent) variables are depicted in Figure 4a-d. These histograms show the frequency distributions for the parameters governing the scouring processes, providing brief and effective details on the data properties. Incidentally, this analysis might turn out to be useful in further laboratory investigations. Figure 4a shows that the frequency of the flow attack angle, \(\alpha\), exhibits a rather fragmented pattern with a significant percentage of the cumulative relative frequency