## 5 Conclusions  
The primary contribution of this work is to provide a framework for the use of previous knowledge for determining the laminar-turbulent transition on rotor blades of wind turbines by means of thermographic flow visualization. The Bayesian inference is verified and validated as a method to use previous knowledge to lower the position uncertainty of the laminar-turbulent transition on rotor blades of wind turbines. As a result, using previous knowledge reduces the uncertainty for determining the laminar-turbulent transition position on rotor blades when the measured thermogram provides an image with a low CNR. However, the width of the distribution of the previous knowledge is crucial. For the studied measurement data, a normally distributed prior needs to have a standard deviation \(\sigma_{\text{prior}}\leq 3\) px in order to improve the measurement on a thermogram with a CNR of 7. As a potential application, the Bayesian-based image processing enables a smoothening of the course of the transition position data along a rotor blade and over time, respectively, where the determination without previous knowledge produces implausible results. The previous knowledge can be obtained from the spatially or temporally neighboring data, but must be taken under the same measurement conditions as the measurement itself. Furthermore, the Markov chain implicitly provides a probability distribution for the measurand and, thus, a measure for the uncertainty of the Bayesian result. Future investigations should focus on how previous knowledge can be extracted from flow simulations or experiments that fulfill the above-mentioned criteria. Comparing the standard deviation of a newly generated prior and the CNR of the measurement to the results from this publication allows for an evaluation whether the quality of the prior lowers the uncertainty of determining the laminar-turbulent transition position. In addition, it is of great interest to research whether the Bayesian inference can be used to observe a moving \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Classical Estimation**} & \multicolumn{2}{c}{**Bayesian Estimation**} \\ \hline  & **Least Squares** & **Principal Component** & **Spatial Previous** & **Temporal Previous** \\  & **Estimation (LSE) [12]** & **Analysis and LSE [19]** & **Knowledge** & **Knowledge** \\ \hline
**Previous knowledge is** & & & & \\
**taken into account** & No & No & Yes & Yes \\ \hline
**Preconditions** & None & Image time series & \
\begin{tabular}{c} 2D measurement \\ (image) under spatially \\ smooth/steady \\ conditions \\ \end{tabular} &
\begin{tabular}{c} Time series \\ measurement, under \\ temporally \\ smooth/steady \\ conditions \\ \end{tabular} \\ \hline
**Obtaining a measure** & & & & & \\
**of the measurement uncertainty** & Explicit & Explicit & Implicit & Implicit \\ \hline
**Measurement uncertainty** & Depends on CNR & \(\sim\)5\% smaller than with & \
\begin{tabular}{c} Smaller than with LSE, \\ but may introduce a \\ systematic error \\ \end{tabular} &
\begin{tabular}{c} Reduces uncertainty on \\ falsely detected \\ transition positions, but \\ introduces an error on \\ correctly detected \\ transition positions \\ \end{tabular} \\ \hline
**Spatio-temporal resolution** & Full resolution &
\begin{tabular}{c} Reduced temporal \\ resolution due to \\ averaging artefacts \\ \end{tabular} & Full resolution & Full resolution \\ \hline \hline \end{tabular}
\end{table} 
Table 1: This table qualitatively compares the Bayesian estimation for the use of previous knowledge with two classical estimation approaches, which are the least squares estimation from [PERSON] et al. and its combination with a principal component analysis method from [PERSON] et al. [19]. It compares the advantages and limits of all methods. transition line resulting from unsteady inflow conditions or to detect further fluid-dynamic phenomena such as stall. Conceptualization: J.D., A.v.F. and A.F. ; methodology: J.D. and A.F. ; software: J.D. ; validation: J.D., C.D. and N.B.