# Towards Hierarchical Workflows in SysML to Support Virtual Validation of Technical Systems
## 5 Case Study  
Taking the virtual validation scenario described in Section 3 as an example, the proposed workflows can be used to validate parts of the system functions of the WT system at different hierarchy levels by performing specific virtual tests. When the virtual validation begins, the workflows validate each function in turn from the top functional level to the detailed functional level, until the end of the functional hierarchy. The top-level virtual validation workflow of the WT is created in the SysML package \"Convert Wind Energy to Electricity\" at the function layer. The virtual validation workflow performs an activity called \"Check if the corresponding solution fulfills the function\" to check that the function can be fulfilled by the selected solution \"Wind Turbine A\". The designer parameterizes the solution \"Wind Turbine A\" in the SysML instances. This function can be decomposed into two sub-functions in this case study, which are \"Convert wind energy into mechanical  
Figure 11: Determination of the fidelity of the domain model manually based on decision nodes. energy\" and \"Convert mechanical energy into wind energy\". These two functions also have their own virtual validation workflows. The two workflows can be added to the top-level virtual validation workflow by dragging and dropping from the model tree. By analogy, for each new function created by the engineers, the corresponding virtual validation workflows in different functional hierarchy levels need to be created. Among them, \"Support rotation with low friction\" is a sub-function of the WT system that this case study focuses on. \"Bearing A\" is a sub-solution in \"Wind Turbine A\" designed to satisfy this sub-function. Designers design multiple virtual testing workflows for each solution to provide evidence that the solution can fulfill the corresponding function. For example, as mentioned in Section 3, the AEP calculation is an important virtual test that is used to calculate the performance of the entire system. Therefore, in this case, the AEP calculation is used as a representative criterion to verify that \"Wind Turbine A\" satisfies the function \"Convert wind energy to electricity\". AEP calculation is the predicted annual energy production of a WT calculated based on a given rated average wind speed. In this work, a co-simulation model is used to calculate the AEP. The co-simulation model combines the mechanical and control model, as well as directly providing the engineer with the simulation results of the transient power output of the generator. These simulation results are post-processed to obtain the AEP results. The co-simulation model involving a mechanical model and a control model for wind turbine systems is conducted to optimize speed control using pitch angles as the control output. The mechanical model considers inputs such as wind loads and outputs, including drivetrain torque, rotor speed, structural loads, and blade pitch angles. On the other hand, the control model processes inputs such as current generator speed and current pitch angle as references to determine the appropriate pitch angle settings. For the components in a system, failure analysis can be an important virtual test to test the reliability of the component. The result of the failure analysis (i.e., the Lifetime) can therefore be used as a criterion to verify that \"Bearing A\" satisfies the function \"Support rotation with low friction\". In order to avoid fatigue failure of bearings, engineers often use statistical methods to analyze and calculate bearing lifetime. The basic fatigue rating life is calculated using the number of rotations in which 90% of all bearings in a specific group achieve or exceed without failure (probability of failure: 10%). A standardized formula, also known as the catalog method (ISO 281), is the common means of calculating a bearing's basic rating life. ISO 281 is applicable to the bearing under continuous rotation subjected to axial and radial loads [24].