## 3 Method
### Algorithmic Implementation
The total simulation time is chosen so that the slowest wave in the investigated frequency range reaches the outermost sensors. With these settings, a frequency step of \(5\,\mathrm{kHz}\) is achieved, where the first 160 discrete frequencies (up to \(795\,\mathrm{kHz}\)) are investigated. Based on these six simulations, a dictionary is formed. For each of the 101 radial directions and each of the 160 frequencies, a sine is fitted through the 8 radial points, with the phase found through a PSO. In a second step, the obtained amplitudes and phases are linearly interpolated through the circumference. In Figures 9-11, the scattering characteristics and accuracy of the created dictionary are assessed. Firstly, Figure 9 shows the scattering amplitude of the notch for different angles for the frequency of 400 kHz. It is visible that for some angles, the scattering is very low. Figure 10 shows an instance of the FRF for an angle of 126\({}^{\circ}\) between the incident and the scattered wave. The decaying periodic function, described in Equation (14), is clearly visible. The surrogate accurately represents the behavior of the FOM, despite being trained only at 8 points along a line. Only for some points close to the notch, larger deviations can be observed. The error for individual training points can be seen in Figure 11. In comparison with Figure 9, it should be noticed that lines of high errors often correspond to angles of low amplitude and, therefore, a small denominator, when computing relative errors. Figure 8: Meshes of the plates, in the area of the features. (**a**) Mesh of the plate, in the area of the hole. (**b**) Mesh of the plate, in the area of the notch. Figure 7: Plate configuration for training. (**a**) Sketch of the plate, dimensions in [m]. (**b**) Mesh of the plate, with hole as a feature. Points are the sensor locations, and the large point marks the excitation. The size of the sensors is 0, and the feature has a radius of 5 mm. Figure 9: Absolute value of the FRF at 400 kHz at a distance of 0.2 m to the notch for different angles. Incoming wave propagates from 0\({}^{\circ}\). (**a**) Symmetric response. (**b**) Anti-symmetric response. ### Online Phase

In Figure 12, a sketch of the plate configuration mesh used to test the online phase of the proposed approach is illustrated. This setup reflects a square plate with a single actuator, two features, and seven sensors. The origin of the coordinate system is assumed to coincide with the position of the actuator with a distance of 0.05 m to the left, 0.15 m to the right, and 0.1 m to the top and bottom boundary of the plate. The features are located at (0.05 m 1.04 m) and (0.07 m -0.02 m). Around the plate, there are 30 layers of ALID, to prevent boundary reflections. We first examine the scenario where Feature 1 corresponds to a hole (as shown in Figure 8a) and Feature 2 is inactive. This means that a pure reflection without mode conversion is expected. Further, at most sensor locations, two wave packets are expected--the direct and the reflected wave packet--which may or may not overlap. For the sensor at location (0.09 1.09), the wave packet stemming from the feature is expected to result in a direction that is opposing the direct wave, as the sensor lies in the shadow of the feature. The plots for the sensors at locations (0.05 1 -0.04) and (0.09 1.09) are shown in Figures 13 and 14, respectively. Figure 10: Transmissibility function (\(T(400\,\mathrm{kHz})\)) along a line from a notch. The angle between the incident wave and the scattering line is \(126^{\circ}\) and the frequency is \(400\,\mathrm{kHz}\). (**a**) Real, symmetric response. (**b**) Imaginary, symmetric response. (**c**) Real, anti-symmetric response. (**d**) Imaginary, anti-symmetric response. It can be seen in Figure 13, that there is an additional wave packet for both symmetric and anti-symmetric excitation, and that the additional wave packets are captured well by the surrogate, both in amplitude and in phase. For the sensor at location (0.09!