## 2 Methods
### Data Analysis
#### 2.3.2 Discretization of Design Space and Factor Levels Definition  
As discussed in Section 1, the discretization of the design space using factor levels is a common practice in the field of DOE to reach a feasible number of factor combinations while covering the design space. The number of factor levels is also a parameter that investigators can select to better fit the requirements of the investigation at hand. In this investigation, five levels per factor were chosen for several reasons. The ranges of several factors, such as My, Mz, and Fy, reached comparably high magnitudes in both negative and positive values. Due to the presence of asymmetries in the design of a typical WT drivetrain, including that of the Vestas V52, the testing of several points was favorable to not only cover the zero level and the extremities of the range, but also to test at moderate positive and negative values of such factors. Similarly, it was decided to opt for five factor levels for all factors in order to gain an understanding of the drivetrain responses to several moderate load levels in addition to the extreme levels. Figure 4 illustrates the five factor levels of Mz as an example. As discussed earlier, the test boundaries define the extent of each factor in the design space, which is also illustrated in Figure 4. The resulting range of testing for each factor is then evenly split into the desired number of levels, in this case five levels. Factor values that exceed or go below the testing boundaries are assigned to the highest or lowest factor levels, respectively. In other words, the highest and lowest factor levels are bound only one-sidedly by the boundary with the respective adjacent inner level. The factor values within each simulated data point are assigned to a respective factor level via a binning process based on the defined level boundaries. Each value in the available data is binned to the respective factor level containing said value. The following pseudocode, outlined in Algorithm 1, clarifies the algorithm for defining level boundaries for each factor as well as the application of the aforementioned binning process to all simulated data points:  
```
min_test = INPUT(\"Define minimum testing boundary\") max_test = INPUT(\"Define maximum testing boundary\") no_lvl = INPUT(\"Define required number of levels\") lvl_width = (max_test - min_test) / no_lvl  FOR each simulated data point DO IF factor < min_test + lvl_width THEN factor = 1 ELSE IF min_test + lvl_width <= factor < min_test + 2* lvl_width THEN factor = 2 ELSE IF min_test + 2* lvl_width <= factor < min_test + 3* lvl_width THEN factor = 3 ELSE IF min_test + (no_lvl - 1)* lvl_width <= factor THEN factor = no_lvl  END IF END FOR
```  
**Algorithm 1** Algorithm for binning a given factor into desired number of factor levels in available data set according to desired testing boundaries. In the case of high separation between the testing boundaries and the minimum and maximum simulated values of a given factor, it may be favorable to increase the ranges of  
Figure 4: Illustration of an example factor range with factor levels and testing boundaries. the inner levels. This is due to the fact that by increasing the aforementioned separation, the number of data points assigned to the outer levels will likely also increase potentially resulting in an imbalance between factor levels where some factors are overly represented. This may or may not be favorable depending on the investigation. In this investigation, it was desired to limit such an imbalance. Therefore, a variation of the binning algorithm, presented in Algorithm 1, is proposed for this case in Algorithm 2.