## 4 Results
### Application Scenarios and Suitable Priors
Exemplary, the transition position has been determined 150 times within an hour to determine mean value and standard deviation of the normally distributed  
Figure 9: The course of laminar–turbulent transition line over the axial rotor blade position, while the transition positions are determined with (orange) and without (blue) previous knowledge, respectively. The mean and the \(\pm\sigma_{\text{prior}}\) interval of the prior is additionally shown in green. The previous knowledge of the transition line is obtained with a polynomial regression with the order of 2 (**a**) and 3 (**c**). The case of a lower signal-to-noise ratio is studied in (**b**,**d**), where noise has been added to the original measurement data. prior for the subsequent position measurements. This means a constant transition position over time is assumed here as an example, and the prior information comes solely from the past. The prior is applied for the evaluation of the measurements of the following hour. It is important that the previous knowledge and the measurement are taken under the same conditions. In the measurement it was made sure that between the generation of previous knowledge and the measurement the wind turbine did not yaw or pitch and the wind speed constantly was between 3 m/s and 8 m/s. Figure 10 shows the relative measured transition position (0--leading edge; 1--trailing edge) for 150 randomly chosen moments within 60 min with and without the use of the previous knowledge. For 90% of the measurements, the standard deviation \(\sigma_{\tilde{A}}\) (shown by the error bars) is smaller without the use of previous knowledge and the determined transition positions seem plausible. Thus, the use of previous knowledge does not lower the uncertainty of these measurements. However, for measurements with an extraordinary random error (marked with blue arrows) the use of previous knowledge gained from former experiments strongly lowers the uncertainty \(\sigma_{\tilde{A}}\) of the measurement. In addition, measurements occur (within the red dotted ellipsis), where the determined transition position is significantly apart from the mean position. As the true value is not known, it cannot be concluded if this is due to an actual change in the transition or due to an error in the measurement. Assuming the measurements in the red dotted circle to be falsely detected transition positions, then the use of previous knowledge also lowers the systematic error for the measurement. As a result, previous knowledge gained through former experiments can be incorporated with the Bayesian inference to reduce the measurement uncertainty of erroneous detections of the flow transition position. Thereby, the Bayesian result incorporates an implicit uncertainty evaluation in the Markov chain. As a summary, Table 1 compares the advantageous and disadvantageous features of determining the laminar-turbulent transition on rotor blades of wind turbines with Bayesian and classical, non-Bayesian estimation methods. It is important to note that the possibilities of Bayesian estimation may be expanded by finding alternative sources of previous knowledge in the future. Figure 10: Laminar–turbulent transition position with standard deviation for 50 measurements with and without the use of previous knowledge.