## 4 Optimizing the Air Supply Parameters of a Dual-Aisle Single-Row Cabin  
### Case Descriptions  
As represented in Figure 10, the cabin (X: 0.82 m; Y: 2.5 m; Z: 5.6 m) had four air inlets, the wall temperatures on both sides were set to 21 \({}^{\circ}\)C [4], the front and rear cross sections were set to interface, and the other surfaces were set to adiabatic. Referring to the setting of [PERSON] (2016) [57], the human body surface temperature in this case was divided into three levels (head: 28.65 \({}^{\circ}\)C, body: 32.1 \({}^{\circ}\)C, and legs: 33.07 \({}^{\circ}\)C). The objective of the optimization was to create a comfortable thermal environment for the upper body areas of all occupants. Based on the analysis of the airflow organization (mainstream converged in the middle) in single-aisle cabin optimization results [47], the two-aisle cabin was likely to face the problem that directly using a total volume satisfying \(\mid\)_PMV_ 1 (Predicted Mean Vote [58]) \(<\) 0.5 as a single objective might neglect thermal comfort in some areas (discarding middle or side occupants). Therefore, it was divided into two controlled areas in this paper (the volumes of controlled areas 1 and 2 are 1.47 and 0.73 m\({}^{3}\), respectively). In addition, for this symmetrical structure, it is common practice to use a symmetrical air supply or to use a half cabin for the simulation [2; 4], which is commonly used in the cabin air supply and optimization processes. This also reduces the number of parameters to make optimization less difficult, so the same symmetric air supply approach was used in this paper. In accordance with the optimization objective, the response values of the samples \(y_{n}\) used to build the OK models were defined with Equation (11):  
\[\begin{array}{rl}OK_{volume1}(D):&y_{n}^{\prime}=average(\underset{V=\text{ Controlled Area 1}}{\iint}IF(\mid\textit{PMV}\mid<0.5)dV)\\ &y_{n}=-\frac{y_{n}^{\prime}}{\max(y_{n}^{\prime})}\\ OK_{volume2}(D):&y_{n}^{\prime}=average(\underset{V=\text{Controlled Area 2}}{\iint}IF(\mid\textit{PMV}\mid<0.5)dV)\\ &y_{n}=-\frac{y_{n}^{\prime}}{\max(y_{n}^{\prime})}\end{array} \tag{11}\]  
where \(V\) refers to the integrated region (the controlled areas), _PMV_ refers to the _PMV_ value of _dV_, the averaging function is used for averaging, and the _IF_ function returns 1 when its internal expression is satisfied; otherwise, it returns 0.  
Figure 10: Three-dimensional model of the dual-aisle single-row cabin.  
The objective function is defined as Equation (12) (MSP side):  
\[\begin{array}{l}F_{1}=\hat{y}|OK_{volume1}(D)\\ F_{2}=\hat{y}|OK_{volume2}(D)\end{array} \tag{12}\]  
Maximizing the total volume is also a primary interest in this paper, so when using the \(F^{\prime}\) to judge stops, the weights are taken as 0.67 for \(F_{1}\) and 0.33 for \(F_{2}\) (volume 1:volume 2 \(\approx\) 0.67:0.33). Because of more parameters, the initial sample size is changed to 60. Otherwise, the optimization tends to fall into a local optimum, which is similar to meta-heuristic optimization approaches. The number of meshes in the simulation is 422, 718.  
According to the viewpoint of Figure 10, with X as the axis of rotation and the direction of the air supply outlet normal vector as the starting direction, the counterclockwise rotation is positive and the range of the air supply outlet angle (\(\theta\)) is all limited to \(-80^{\circ}<\theta<80^{\circ}\). During normal operation of the aircraft's air conditioning system, it should be ensured that the amount of air supplied to each occupant is greater than 0.25 kg/min [59], so the upper and lower limits of air velocity (\(V\)) are 0.1 m/s and 1.5 m/s. The upper and lower limits of temperature (\(t\)) are 8 \({}^{\circ}\)C and 20 \({}^{\circ}\)C. Therefore, the number of air supply parameters to be optimized is 5 (\(t\), \(V_{1}\), \(V_{2}\), \(\theta_{1}\), and \(\theta_{2}\)); subscripts 1 and 2 refer to the numbers of the air inlets in Figure 10. The parameters' range and their accuracy are listed in Table 4: