## 4 Analyses
### Q1: How Much Information Is Lost with Reduced Temporal Resolution?
#### 4.1.1 Comparison of Descriptive Statistics  
The effect of different levels of aggregation of data is studied by comparing the values of a set of descriptive statistics. The objective is to identify global changes in the signals that are reflected in their range, central behavior and overall shape of distribution. Methodology  
In order to evaluate the effects of temporal aggregation, the first approach constituted the calculation of key descriptive statistics, which captured the central behavior, shape and dispersion of the data. To examine the effect of temporal aggregation, these statistics were computed for the non-aggregated, i.e., raw data (1 second of temporal resolution) and for temporally aggregated data with reduced time resolutions, namely 10 s, 60 s, 300 s, and 600 s. For each signal listed in Table 1 the following statistics were computed for all resolutions mentioned above: sample mean, median, maximum, minimum, standard deviation, first quartile, third quartile, skewness, and kurtosis. For the calculation specification of these quantifiers we refer to Ref. [39]. In contrast to the subsequent analyses, the calculations of this part were carried out on the entire dataset. To keep extreme outliers out of the scope for less distorted results, during this analysis the data for wind speed and generator speed were filtered for only positive values and temperatures for values <200 \({}^{\circ}\)C.  
Results  
Selected results are shown in Figure 2 for one turbine. The full list of computed statistics based on different temporal resolutions for the entire set of signals is provided in the \begin{table}
\begin{tabular}{c c|c c|c c} \hline
**t (1 s)** & **Wind Speed (m/s)** & **t (5 s)** & **Wind Speed (m/s)** & **t (10 s)** & **Wind Speed (m/s)** \\ \hline
09:00:00 & 6.26 & 09:00:00 & 6.25 & 09:00:00 & 6.42 \\
09:00:01 & 6.11 & & & & \\
09:00:02 & 6.17 & & & & \\
09:00:03 & 6.39 & & & & \\
09:00:04 & 6.32 & & & & \\
09:00:05 & 6.37 & 09:00:05 & 6.71 & & \\
09:00:06 & 6.66 & & & & \\
09:00:07 & 6.72 & & & & \\
09:00:08 & 6.72 & & & & \\
09:00:09 & 7.07 & & & & \\
09:00:10 & 7.29 & 09:00:10 &... & 09:00:10 &... \\ \hline \end{tabular}
\end{table} 
Table 2: Illustration of the temporal aggregation scheme: The original data, i.e., t (1 s), is averaged over the lower temporal range and given a new timestamp at the beginning of this interval, see t (5 s) and t (10s). Supplementary Materials. Here, we present an appropriate graphical representation using a box-and-whisker-plot [40], which includes the mean (denoted by the green triangles), the median (denoted by a horizontal yellow bar in the box), the first quartile (denoted by the bottom edge of the box), the third quartile (denoted by the top edge of the box), the minimum (denoted by the bottom edge of the whisker) and the maximum (denoted by the top edge of the whisker). Moreover, the green bars in the plot represent the mean value \(\pm\) the standard deviation. These are shown for four exemplary signals, namely wind speed, active power generation, generator speed, one temperature of the gearbox shaft bearings, and the voltage of phase A. Note that in this version of box-and-whisker-plots the whiskers represent the minimum and maximum of the underlying data and therefore include outliers. To display the results of skewness and kurtosis we chose a simple scatter plot that is displayed in the second row of Figure 2 for the same signals mentioned above accordingly. As both measures are normalized to the standard deviation they are both plotted against the same dimensionless ordinate. From the representative statistics of the graphical presentation in Figure 2 and the additional data in the Supplementary Materials the following results can be obtained:  
* Temporal aggregation had a pronounced effect on the maxima: with lower temporal resolution the maxima decreased. Especially for the wind speed we saw a distinct decreasing trend of the maxima (for this presented turbine and investigated time period a reduction of 10 m/s).