## 3 Results and Discussion  
The SHM approach is applied to data of the spoiler demonstrator, introduced as a case example in Section 2.1. The \(3\times 3\) sensor grid (three-element strain gauge rosettes, HBM RY93-6/120) installed on its surface provides \(J=27\) spatially discrete strain values (features) upon application of a specific, static load case. Parallel to the physical model, the corresponding numerical FE model is utilized by the aforementioned framework for the generation of a large amount of synthetic training data. An illustration of this workflow is provided in Figure 7.  
To provide more insight into the proposed SHM approach, the following section visualizes key aspects of the underlying data. Figure 8 compares the range of the synthetic training data, visualized by the grayed out area, with the experimental strain data measured on the spoiler demonstrator. The framework ultimately serves the goal of improving the robustness of a ML-based SHM approach by generating a large and diverse set of synthetic strain data that represents hypothetical, yet physically plausible, load case variations. This process functions as a form of physics-informed training data augmentation, aimed at improving the resilience to operational variability and unseen loading scenarios in the experimental data. The visualized data additionally shows the effect of a damage on the measured strains, as the individual data lines represent strains due to the same load case, but with different structural damages. The highest deviation from the pristine state can be observed at sensor 8, which is closest to the damage. Following the training stage, unseen strain data from the spoiler demonstrator (experimental) is passed to the SHM model to be transformed into the residual space. The resulting residual values are visualized in Figure 9, together with a small number of transformed samples of the (numerical) benchmark set from the training stage. As expected, the residual values of samples with different structural configurations is largest at sensors 7, 8 and 9. Another view on the transformed data is achieved by a dimensionality reduction via Multidimensional Scaling (MDS). MDS maps high dimensional data to a lower-dimensional space while trying to preserve all pairwise distances of the data points [26, 27]. Figure 10 shows the two-dimensional embedding of the transformed experimental data, together with a set of 40 randomly picked benchmark residuals. Figure 8: Experimental sensor grid data of the pristine and damaged structure due to the same load case. The grayed out area visualizes the range of the available synthetic training data. Figure 7: General workflow of the proposed SHM approach. The training routine is preceded by the generation of a large amount of synthetic training data (Path 1). The trained SHM approach then identifies experimental strain data acquired from the idealized spoiler demonstrator (Path 2). In general, four visually distinct groups of points can be identified. The largest one is formed by the benchmark residuals. Closest to this is the group of pristine experimental residuals. The groups of damaged experimental residuals are located at a greater distance. Both are clearly distinguishable from each other, where the group containing residuals of the larger damage (diameter 19 mm) is located furthest away from the benchmark samples. This view on the data indicates a further challenge of the upcoming classification task, namely the generalization of the numerical training data to an extent such that real experimental data can be classified. In an ideal case, the pristine samples, regardless of their source, would not be distinguishable, i.e., as seen in the overlap in Figure 10. Here, without any labels, it is quite difficult to clearly ascertain if the pristine experimental samples are truly pristine or if they represent yet another damage state.