## 4 Analyses
### Q3: What Is the Recommended Aggregation Frequency? To find the optimal trade-off between minimizing the data footprint and preserving enough information to model and assess the turbine behavior, it is necessary to study the relation between information content and aggregation frequency. By knowing the behavior of an information loss over resolution it is possible to determine the critical aggregation time for a given signal, after which a great part of the information is inevitably lost. Thus, these information can be used to chose a suitable data storage solution. Methodology  
To address this relevant question the following methodology was used, that is also summarized in Algorithm 1. ```
Data :\(s(t)\)--Signal values time series Input :\(\Lambda_{\text{max}}\)--Tolerable information loss \(P_{\text{min}}\)--Minimum amount of \(\Lambda_{\text{max}}\) in data \(T_{\text{agg}}\)--List of possible aggregation times Result :\(P[\Delta t]\)--Information loss amount per aggregation time \(\Delta t\) \(\Delta t_{\text{max}}\)--Maximum aggregation time allowed begin for\(\Delta t\) in \(T_{\text{agg}}\)do  Calculate \(\Lambda(t)_{\Delta t}\) from data \(s(t)\); \(n_{\text{all}}\) := count all timestamps \(t\)in\(\Lambda(t)_{\Delta t}\); \(n_{\text{tolerable}}\) := count all timestamps \(t\)in\(\Lambda(t)_{\Delta t}\)where \(\Lambda(t)_{\Delta t}\leq\Lambda_{\text{max}}\); \(P[\Delta t]=n_{\text{tolerable}}/n_{\text{all}}\);  end for \(\Delta t_{\text{max}}=\max\Delta t\)in\(P[\Delta t]\)where \(P[\Delta t]\leq P_{\text{min}}\);  end for
```  
**Algorithm 1**Determination of the maximum aggregation time allowed for a prechosen tolerable information loss of a signal. First, a maximum tolerable error \(\Lambda_{\text{max}}\) and a minimum amount of data points \(P_{\text{min}}\) with an error lower than this error was defined. As we wanted to compare our results to each other, we used IQR normalized signal values. Therefore, \(\Lambda_{\text{max}}\) must be given in a percentage of the IQR. Of course, if only one signal was investigated this tolerable information loss could also be defined in real units. Then, for each signal \(s(t)\) and resolution \(\Delta t\) out of a list of possible aggregation resolutions \(T_{\text{agg}}\), the information loss \(\Lambda(t)_{\Delta t}\) was calculated as defined in Equation (3). This allowed us to determine the percentage \(P[\Delta t]\) of data having an aggregation error lower than the chosen threshold. Thereafter, the maximum aggregation time \(\Delta t_{\text{max}}\) could be derived by finding the highest resolution possible for \(P[\Delta t]\leq P_{\text{min}}\). Of course, the choice of the maximum error threshold had to take into consideration the final use of the data as well as the marginal cost of storing additional information. Results  
For Figure 12 we chose various tolerable error thresholds that define our closed error-bins \([0,\Lambda_{\text{max}}]\), see legend, and analyzed the available signals for a resolution range varying from 0 to 600 seconds. The horizontal axis shows the time resolution in seconds. On the vertical axis the percentage \(P[\Delta t]\) of data having an aggregation error lower than the error threshold is represented. We further chose a reasonable minimal amount of \(P_{\text{min}}=80\%\) for further evaluation of the curves, indicated by a dashed line. As the figures do not share the same scale on the y-axis, it also facilitates a better orientation. Numerical results are available in the Supplementary Materials. The resulting curves show the information loss amount over resolution and lead to the following observations:  
* There existed different behaviors depending on the nature of the signals. Some signals followed an \"elbow curve\" trend, whereas others--these include mainly temperatures--showed a more linear decay or no decay at all in information loss.