## 3 Implementation of the Model-Based Algorithm and the Experimental Setup
### Simulation Setup  
In order to verify the wedge detection algorithm and characterize it with respect to the measurement uncertainties, simulated thermograms are needed, where all measurands of the thermogram are a priori known exactly. The simulated thermogram consists of a matrix with a height \(h_{\text{therm}}\) and a width \(w_{\text{therm}}\). The trailing edge is placed at \(y_{\text{TE}}=0.10\cdot h_{\text{therm}}\), the natural transition at \(y_{\text{NT}}=0.45\cdot h_{\text{therm}}\) and the leading edge at \(y_{\text{LE}}=0.90\cdot h_{\text{therm}}\). The blade edges and natural transition lines are aligned horizontally. The pixel intensities of the turbulent region \(I_{\text{turb}}\) and the laminar region \(I_{\text{lam}}\) are quantities that need to be modelled to values in real thermograms. The pixel intensity of the background is set to 0.1, as a low value results in a strong gradient to the blade edge. However, the pixel intensity of the background does not influence the wedge detection algorithm and the exact value is therefore inconsequential. Moreover, the intensity gradient near the leading edge is simulated. Near the natural transition line, the laminar value is prevalent. Towards the leading edge, the pixel intensities start to linearly decrease at some \(y\)-position \(y_{\text{LE}}-h_{\text{grad}}\), see Figure 1 (right). Then, at a \(y\)-position \(y_{\text{LE}}-h_{\text{grad},0}\) near the leading edge, the decreasing intensity reaches the turbulent intensity value \(I_{\text{turb}}\). After this \(y\)-position up to the leading edge, the pixel intensities are set to \(I_{\text{turb}}\). The parameters \(h_{\text{grad}}\) and \(h_{\text{grad},0}\) are modelled according to real thermograms. Note that both parameters are subsequently presented normalized by \(h_{\text{max}}\) to make them transferable to thermograms of any size. In addition, the amount of Gaussian blur in the thermogram can be set, with a standard deviation \(\sigma_{\text{blur}}\) of the Gaussian kernel of 1.0 pixel. The blur value was estimated manually to match the blur in real thermograms. Furthermore, the noise in real thermograms is simulated by creating a matrix of noise values with the same size as the thermogram, for which each pixel value is drawn from a normal distribution \(\mathcal{N}(\mu_{\text{noise}},\sigma_{\text{noise}}^{2})\) with mean \(\mu_{\text{noise}}=0\) and variance \(\sigma_{\text{noise}}^{2}\) in arbitrary pixel intensity units. By changing the variance \(\sigma_{\text{noise}}^{2}\), the amount of noise in the image can be varied. The matrix is then added to the thermogram to obtain a noisy thermogram. To emulate a turbulence wedge realistically, the parameters additionally required from real thermograms are the typical range of the height \(h_{i}\) and the width \(w_{i}\) of the turbulence wedge. Instead of the absolute height value (in pixels), the relative height \(h_{i}/h_{\text{max}}\) is considered here, which makes the value applicable to thermograms of any size. To emulate the  
Figure 6: Phase space of correlations for a wedge at position \(x_{i}\), over the template height \(h_{k}^{\prime}\) and width \(w_{k}^{\prime}\). The height \(h_{0,i}\) and the width \(w_{0,i}\) are the initial values for the determination of the wedge’s size. The phase space point \((h_{0,i},w_{0,i})\) is marked with a black dot. The point \((h_{k}^{\prime},w_{k}^{\prime})\) with the highest correlation value is marked with a red x.  
average width of the turbulence wedges, the height-to-width ratio \(h_{i}/w_{i}\) is further considered. The angle \(\alpha_{i}\) of each wedges is set, by default, so that the tip position is centered below the middle of the wedge for all turbulence wedges.