# Multidisciplinary Reliability Design Optimization Modeling Based on SysML
## 5 Evaluation and Discussion
### MDO Modeling Application for In-Vehicle Environmental Control Integration System  
This section demonstrates the effectiveness of the approach proposed in this paper by using an example of multidisciplinary optimization modeling of an integrated system for in-vehicle environmental control of a vehicle. The integrated in-vehicle environmental control system is an important component of a vehicle. Its main components include the air conditioning subsystem and the integrated air supply subsystem, among others. The air conditioning subsystem primarily handles temperature and humidity control, and its structural composition is shown in Figure 13.  
The integrated air supply subsystem provides functions including cabin air supply, internal and external air circulation conversion, overpressure control, dust filtration, flexible air delivery, and biological deactivation. Its structural composition is depicted in Figure 14.  
Figure 12: SysML optimization metamodel extension. With the overall quality of the two analyzed systems as the goal, a Multidisciplinary Design Optimization model formulation for the integrated in-vehicle environmental control system was constructed as follows. (1) Air conditioning subsystem. Design variables include expansion valve parameters (\(x_{PR}\)), condenser heat exchange (\(x_{HE}\)), condensing fan air volume (\(x_{Airv}\)), evaporator volume (\(x_{V}\)), compressor cooling capacity (\(x_{cc}\)), and the objective function. \(M_{1}=m_{1}+m_{2}+m_{3}+m_{4}+m_{5}\) in the equation \(M_{1}\) denotes the overall mass of the air conditioning subsystem, and \(m_{1},\ m_{2},\ m_{3},\ m_{4},\) and \(m_{5}\) denote the masses of the expansion valve, condenser, condenser fan, evaporator, and compressor, respectively. The empirical formula for the mass of each component and the design variables can be summarized as follows:  
\[ \begin{array}{c}m_{1}=\alpha\cdot x^{2}_{PR}\\ m_{2}=k\cdot\frac{\sqrt{x_{HE}}}{2}\\ m_{3}=243.1\cdot x_{Airv}\cdot\eta\\ m_{4}=\rho\frac{x_{V}}{\xi}\\ m_{5}=\epsilon\cdot x_{cc}\end{array}  \tag{4}\]  
where \(\alpha,k,\eta,\rho,\) and \(\varepsilon\) are the design parameters, taking the values 5.5, 1.4, 62, 3.8, and 7. Taking the compressor displacement, \(g_{1}\), to be greater than 260 cm\({}^{2}\)/r and the air supply volume of the air conditioning, \(g_{2}\), to be greater than 450 cm\({}^{3}\)/min as the constraints, the  
Figure 14: Structural composition of integrated air supply subsystem. Figure 13: Structural composition of air conditioning subsystem. disciplinary optimization expression of the air conditioning subsystem can be expressed as follows:  
\[Find:x_{PR},x_{HE},x_{Air},x_{V},x_{cc} \tag{5}\] \[min\ M_{1}=m_{1}+m_{2}+m_{3}+m_{4}+m_{5}\] \[\text{s.t.}\ \ g_{1}>260,\ g_{2}>450\]  
(2) Integrated air supply subsystem  
The design variables of the integrated air supply subsystem include ventilation fan air pressure (\(x_{WP}\)), the air volume of the internal circulator (\(x_{Vicm}\)), integrated duct diameter (\(x_{d}\)), and dust collector volume (\(x_{Vdc}\)); the objective function selects the mass of the integrated air supply subsystem, whose empirical expression can be expressed as \(M_{2}=0.45 exp(x_{wp}-12)+x_{wp}x_{Vicm}^{2}+1.67x_{d}^{2}+14.94x_{vdc}\); the constrained air supply volume, \(g_{3}\), is greater than 121 cm\({}^{3}\)/min, and the pressure relief velocity, \(g_{4}\), is greater than 15 pa/min. The optimization model of the integrated air supply subsystem can be expressed as follows:  
\[Find:x_{WP},x_{Vicm},x_{d},x_{Vdc}\] \[min\ M_{2}=0.45 exp\ (x_{wp}-12)+x_{wp}x_{Vicm}^{2}+1.67x_{d}^{2}+ 14.94x_{vdc} \tag{6}\] \[\text{s.t.}\ \ g_{3}>121,g_{4}>15\]  
A Multidisciplinary Design Optimization model for the integrated in-vehicle environmental control system was constructed based on the above information and the completed system design model.