## 3 Method
### Algorithmic Implementation
0.09), which is placed in the shadow of the hole, it can be seen that the response without a hole would have a higher amplitude than for the case with a hole--an effect which is well captured by the surrogate. Figure 11: Error for 400 kHz response for the notch in Figure 8b for symmetric excitation. The error for the real parts of each point is calculated as \(|Re(FRF_{FOM})-Re(FRF_{ROM})|/|FR_{FOM}|\), where the subscript FOM refers to the FRF evaluated with the high-fidelity model, and the subscript ROM refers to the FRF evaluated with the surrogate. Incoming wave propagates from the right. (**a**) Error for the real part of the symmetric response. (**b**) Error for the imaginary part of the symmetric response. (**c**) Error for the real part of the anti-symmetric response. (**d**) Error for the imaginary part of the anti-symmetric response. Figure 12: Plate configuration for testing. (**a**) Sketch of the plate, dimensions in [m]. (**b**) Mesh of the plate, with hole as a Feature 1 and notch as Feature 2. Points are the sensor locations, and the large point marks the excitation. the surrogate. However, in the case of anti-symmetric excitation (Figure 14b), traces of a periodic signal are discernible in the response of the surrogate. These are artifacts, which likely result from a poorly fitted frequency for a certain angle. This seems tolerable, as the overall response is fitted well. Next, in Figures 15 and 16, the response is displayed for the case where Feature 1 is a notch rather than a hole. Figure 15a allows for clearly distinguishing three arriving wave packets, compared to the two which were visible in the case of the hole (Figure 13a). Therefore, the additional, third wave packet stems from mode conversion from the incident symmetric wave packet into an anti-symmetric wave packet. Further, it can be seen that the amplitude of the reflected symmetric wave packet is smaller in this case, since the notch only reduces the cross section, while the hole goes through the whole cross section. On the other hand, the reduction in the cross section results in a minor drop in the amplitude of the direct wave for the case of the sensor being in the shadow of the feature (Figure 15) compared to the case with the hole. All these effects are captured well by the surrogate. For the sensor located in location (0.09 0.09), the wave packets originating from the notch are hardly distinguishable from the direct wave (Figure 16a). However, the surrogate

Figure 14: Response at the sensor location (0.09 0.09) for the case where Feature 1 is a hole and Feature 2 is inactive. (**a**) Symmetric excitation (error = 0.0185). (**b**) Anti-symmetric excitation (error = 0.2391). Figure 8.0 Response at the sensor location (0.05 \(-\)0.04) for the case where Feature 1 is a hole and Feature 2 is inactive. (**a**) Symmetric excitation (error = 0.0086). (**b**) Anti-symmetric excitation (error = 0.0310). still matches the behavior predicted by the FOM well. Although the effect of the notch is clearly visible for the case of symmetric excitation, there is hardly any effect for the case of the anti-symmetric excitation. This is expected due to the high difference in the amplitude for symmetric and anti-symmetric modes for the out-of-plane displacement (here approximately two orders of magnitude). For the plots in Figure 17, both features are modeled as holes. Focusing on the case of anti-symmetric excitation in Figure 17b, four wave packets are now visible. The first wave packet stems from the direct wave, while the second and third wave packets correspond to the reflections from the two holes. The fourth wave packet stems from a wave path, which includes reflections at both holes (i.e., Actuator-Feature 1-Feature 2-Sensor or Actuator-Feature 2-Feature 1-Sensor), while the wave packet from the other path that includes both wave packets is not clearly visible. This may be attributed to an overlap with one of the other wave packets or to the amplitude for this path dropping significantly, to the point that it is not visibly discernible.