# A Novel Aerodynamic Modeling Method Based on Data for Tiltrotor evtol
## 3 Data-Driven Modeling Methods
### Sample Data Requirements and Generation  
The aerodynamic characteristics and rotor layout of the XV15 tiltrotor aircraft are similar to some tiltrotor evtol, resulting in largely consistent aerodynamic characteristics. This article conducts data-driven aerodynamic modeling on the tilting rotor evtol, based on wind tunnel test data of the transition maneuver of XV15. Due to space limitations, this article focuses on data-driven model construction for longitudinal aerodynamics, the generation of sample data, model training, and validation.  
According to reference [20; 23], for the longitudinal transition maneuver of the XV15 tiltrotor aircraft, aerodynamic forces and moments (\(C_{L}\)\(C_{D}\)\(C_{M}\)) are defined as functions of a set of flight state values (\(M_{N}\)\(\alpha_{F}\)\(\beta_{M}\)\(F_{X}\)\(\delta_{e}\)). Among them, \(M_{N}\) is the Mach number, \(\alpha_{F}\) is the angle of attack of the fuselage, \(\beta_{M}\) is the tilt angle of the nacelle, \(F_{X}\) is the flap/aileron angle mode selection, and \(\delta_{e}\) is the elevator deflection angle. During the transition phase, the value ranges of variables mentioned above for XV15 are as Table 1.  
By considering the range constraints of explanatory variables during the transition phase of the tiltrotor evtol and the inclined transition corridor determined in reference [20; 23], a multidimensional sample space can be established. This sample space allows for a one-to-one correspondence between the aerodynamic coefficients and the explanatory variables. Additionally, there are constraints between variables, in addition to the range constraints of the variables themselves. Figure 5 shows the transition corridor resulting from the constraint between the tilt angle \(\beta_{M}\) and the horizontal velocity \(V_{X}\). When the nacelle inclination angle is \(0^{\circ}\), XV15 is in helicopter mode, and when the nacelle inclination angle is \(90^{\circ}\), it is in aircraft mode. The dataset needed for the neural network is constructed by selecting points from a vector space consisting of flight envelopes and constraints in multiple dimensions. It is important to note that the aerodynamic coefficient profile has both linear and nonlinear regions that correspond to a single explanatory variable. The nonlinear region has a higher density of points compared with the sparser points in the linear region. The constructed sample dataset comprises 2000 sample points, with each point represented in the form of \(C_{L},C_{D},C_{M}=f(M_{N}\)\(\alpha_{F}\)\(\beta_{M}\)\(F_{X}\)\(\delta_{e})\).  
\begin{table}
\begin{tabular}{c c c} \hline
**Input Variables** & **Minimum** & **Maximum** \\ \hline \(M_{N}\) & \(0\) m/s & \(120\) m/s \\ \(\delta_{e}\) & \(-20^{\circ}\) & \(20^{\circ}\) \\ \(F_{X}\) & \(F_{1}\) (\(0^{\circ}\)/\(0^{\circ}\)) & \(F_{2}\) (\(40^{\circ}\)/\(25^{\circ}\)) \\ \(\beta_{M}\) & \(0^{\circ}\) & \(90^{\circ}\) \\ \(\alpha_{F}\) & \(-15^{\circ}\) & \(15^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 1: Range of explanatory variables for the transition phase of XV15 tiltrotor aircraft.