## 4 Proof of Concept Implementation
### Comparison Mechanism
Thus, the complexity faced during the verification and validation process can be consequential. The studied system is a geared EMA onboard a small aircraft. The system's mission is to actuate the aileron of the aircraft. The geared EMA consists of an electric motor, a gearbox, a nut screw mechanism, and an electronic control. The gearbox is used as an intermediate reducer. The nut screw mechanism transfers the mechanic power to the control surface. The Electronic Control Unit (ECU) is the device that controls the system. The schematic architecture of the geared EMA is presented in Figure 4, adopted from Reference [39]. ### Design Models of the EMA

In our scenario, we consider three models of the EMA system created during the engineering design process: a SysML model that defines the physical architecture design of a system, a Modelica model that performs dynamic analysis to predict the performance of the system, and an Altarica model which is dedicated to probabilistic risk and safety analysis. In the following, these models are described in more details. Figure 4: The schematic structure of a geared Electro-Mechanical Actuator (EMA) ([PERSON] (2018)). #### 5.1.1 System Engineering Perspective (SysML)

The Systems Modeling Language (SysML) [27] is a general purpose graphical modeling language for systems engineering. SysML assists the specification, analysis, design, verification, and validation of complex systems. It is used to capture requirements and to specify the structure and the behavior of a complex system to support engineering analysis. The IBD diagram illustrates the internal structure decomposition of the EMA. It defines the interconnections between its components as represented in Figure 5.

The main function of the EMA system is to regulate the incidence angle of the aileron. This function is achieved by the ball screw and nut assembly \"bsNA\". It provides the necessary mechanical translation power to modify the aileron angle in a given range [\(\theta_{min},\theta_{max}\)]. The aileron angle is controlled by a Micro-Controller Unit \"MCU\". The MCU provides the DC motor with the regulated electric power that will be transferred into a mechanical rotational power via a gearbox. Then, the bsNA transforms the adapted mechanical rotational power to a mechanical action that will actuate the aileron. #### 5.1.2 System Behavior Analysis (Modelica)

Modelica [28] is an object-oriented and equation-based modeling language. Its main objective is to model the dynamic behavior of large, complex, and heterogeneous physical systems. These systems consist of mechanical, electrical, thermal, and hydraulic, among other components. To predict the dynamic behavior of the EMA system on Modelica, we designed a closed-loop system as represented in Figure 6.

The DC motor receives a regulated signal voltage from the PID (Proportional-Integral-Derivative) controller that employs feedback from the angle sensor. Then, the ideal gear adapts the mechanical rotational power that will be transformed into mechanical transitional power via a set of components (i.e., ideal Gear R2T, prismatic, bodybox2, and bodybox3). The universal joint represents the connection between the wing and the EMA system. The spherical joint represents the joint between the aileron and the EMA system. Moreover, we add an aerodynamic torque to simulate the friction that induces the nonlinearity of the system. Figure 5: IBD model of the EMA system. #### 5.1.3. Dysfunctional Behavior Analysis (Altarica)

Altarica [40] is a high-level modeling language dedicated to safety and performance analysis. Altarica is an event-centric language and is combined of two parts:

* A mathematical framework, based on Guarded Transition Systems (GTS) [41]
* Sets of constructing mechanisms stemmed from object-oriented programming, based on the System Structure Modeling Language (S2 ML) [29]

Once the EMA system is specified in the Altarica language, it can be compiled into a lower-level formalism such as fault trees and stochastic Petri nets, among other safety assessments.