# Multidisciplinary Reliability Design Optimization Modeling Based on SysML
## 4 System Optimization Model Extraction Method
### SysML Parametric Diagram Expression Mechanism  
The metamodel of the system optimization problem is inherited from the parameter graph. When extracting the optimization model from the system design model, it is necessary to parse the SysML parameter graph, so it is necessary to analyze the mechanism of the parameter graph expression in SysML, which is related to the completeness and validity of the mathematical properties of the output target model. Table 3 summarizes the model elements of the parameter graph in SysML.  
The principle of equation or inequality constraint extraction from a parameter map is illustrated with the example of a constraint module for a spring component that follows [PERSON]'s law, F = -KX, where F is the elastic force, K is the coefficient of elasticity, and X is the amount of displacement for spring extension or compression. This is only the equation extraction for a single component, and when the component is inside a subsystem associated with other components through an interface, the parameters in this component constraint may be influenced by the value properties of other components, thus increasing the complexity of the equation transformation. Therefore, this paper adopts the following principles to extract the optimization model from the constraint module of SysML: (1) the equation constraints and inequality constraints in the extended constraint module correspond to the equation constraints and inequality constraints in optimization, and the constraint expressions and the values in their attributes and the upper and lower boundaries constitute the complete optimization equation constraints and inequality constraints; (2) to facilitate the understanding and extraction of the optimization model, each extended constraint module includes only one constraint expression and all its related variables and constraint parameters; (3) the constraint attributes expressed by each extended constraint module correspond to a parameter map used for equation extraction; (4) the binding connector is fully utilized to bind the constraint parameters to the value attributes of the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**SysML Parametric Graph** & **Description** \\
**Model Elements** & \\ \hline \multirow{3}{*}{Constraint} & Common mechanism for expressing system constraints, applied to model elements in the form of mathematical expressions, containing equations or inequalities represented in text \\  & Encapsulation of constraint expressions, which can be applied in \\ \multirow{3}{*}{Constraint module} & different contexts to facilitate the reuse of constraint information, usually including constraints and constraint parameters \\  & One of the properties of the system structure module, defined by \\ \multirow{3}{*}{Constraint properties} & the constraints module, used to bind the value attribute \\  & parameters of the structure \\ \multirow{3}{*}{Constraint parameters} & One of the properties of the constraint module, expressing \\  & explicitly the parameters in the constraint expression \\ \multirow{3}{*}{Value properties} & One of the properties of the system structure module, which can \\  & be bound to the constraint parameters in the constraint module \\ \multirow{3}{*}{Binding connector} & Represents the equivalence between the elements at the two ends \\  & of the connector, either as constraint value attributes or as \\ \multicolumn{3}{c}{constraint arguments} \\ \hline \hline \end{tabular}
\end{table}
Table 3: SysML parameter diagram model elements and their meanings.  
Figure 9: XML-based translation mechanism.  
module, so that the equation variables can be named using the value attribute names when the constraint expressions are converted into mathematical equation codes.