## 1 Introduction
As the names imply, randomization refers to the practice of randomly ordering the planned experiments while replication refers to the practice of repeating the planned experiments [16; 41]. Randomization provides a line of defense against systemic bias due to unplanned changes in nonexperimental factors, while replication allows for an assessment of the generalization of the conclusions made as it shows how consistent the findings are over multiple identically designed experiments [41; 42]. Figure 1: Illustration of an example of: (**a**) design space for a 3-factor experiment (**b**) the same design space discretized into five factor levels per factor. This investigation aims to design experiments covering the realistic regions of the design space of the factors that a Vestas V52 WT can be expected to experience during operation. In this investigation, the experiments are designed in preparation for a measurement campaign to be performed on a purposely instrumented V52 drivetrain using a WT system test rig, as illustrated in Figure 2, where the factors can be controllably applied to the drivetrain. As previously introduced, the purpose of the campaign is to collect real world data for the development of a virtual 6-DOF gearbox (GB) input loads sensing solution. The responses, or dependent variables, in the planned experiments are the signals from a sensor set up primarily applied to the GB housing and consisting of stationary, non-rotating sensors for a more feasible estimation of the 6-DOF GB input loads during WT operation. As demonstrated by Figure 1, the design space and the resulting experiments highly depend on the chosen ranges for the respective factors. Additionally, the fact that the number of factors in this investigation is seven means that the number of needed experiments to perform a full factorial DOE would exponentially grow. In a full factorial DOE without replication, the number of experiments would be the selected number of factor levels the power of seven, which could result in an unfeasibly high number of experiments. Figure 1 also demonstrates a different issue that requires limiting the combinations of factor levels to realistic load combinations. A challenge remains to avoid a premature end to the planned experiments by applying loading combinations in regions of the design space that are unrealistic and therefore unsustainable for the experimental unit. For example, an experiment with all loads set to their respective maximum values would subject the WT drivetrain to an unrealistic and unsustainable load situation, which it was not designed to handle and therefore can cause a costly failure during testing. Hence, a need exists to identify realistic ranges and combinations of loads that a WT drivetrain can be expected to experience in its lifetime and to design time-efficient experiments that cover these load combinations during targeted tests. The methodology presented in this investigation tackles this challenge by aiming to identify and target realistic regions of the design space on the basis of purposely developed computer simulations. In this investigation, this need is addressed by analyzing simulated time-series data generated from targeted aeroelastic multibody simulations (MBS) of a WT undergoing wind conditions that cover design load cases (DLC) based on the IEC 61400-1 standard [43]. The standard provides guidelines to certify each installed wind turbine according to its predicted response to a variety of operational conditions, which are categorized into DLCs [44]. The simulated time-series data is analyzed to identify the ranges and combinations of the factors that are expected to take place during the lifetime of the WT under investigation. In this work, the Vestas V52 is the WT under investigation due to the availability of a V52 drivetrain for subsequent testing. In a previous investigation,  
Figure 2: Illustration of the 4 Megawatt WT system test rig during WT drivetrain testing at the Center for Wind Power Drives in Aachen, Germany.