## 3 SES/MB Framework
### SES and PES Bases  
The SES is an ontology-based framework for specifying a set of modular, hierarchical system designs by a single formal description [50]. A system design consists of a specific system structure and a set of system parameters. That means that the SES does not define any dynamic behavior on its own. The SES is represented by a tree structure comprising entity nodes, descriptive nodes and attributes [51]. Different system structures can be coded in the SES trees. Modeling and simulation entity nodes are linked to basic models organized in MB. The attributes of an entity node correspond to the parameters of the associated basic model. As shown in Figure 1(a), an SES tree is represented as a labeled tree with attached attributes, which satisfies the following axioms: uniformity, strict hierarchy, alternating  
Figure 2: Transformation Process in SES/MB framework. mode, valid brother, and attached variables [22]. There are three types of node in the tree. The entity node (like ABC in Figure 2a) consists of a composite entity and an atomic entity, which represents a real-world object, denoted by 1. The composite entity connects with other entities (composite or atomic entity); while the atomic entity is located at the end of the tree. The composite entity is attached with variables, which have several aspects and/or specializations. An aspect node (like abc-dec in Figure 2a) is connected by a single vertical line from an entity. This node represents one decomposition of the entity. Each node includes coupling information. In addition, an aspect node is able to be a multiple-decomposition (like cs-mdec in Figure 2a) of another entity, denoted by \(\parallel\). The multiple-decomposition is used to represent the number of children of the entity with coupling information. The coupling information can be specified as properties of descriptive nodes of the type decomposition or multi-decomposition, and consist of pairs of entity names and port names, such as (source entity, source port, sink entity, sink port). The specialization node (like ab-spec in Figure 2a) is connected by a double vertical line to an entity, denoted by \(\parallel\). This node describes the taxonomy of the entity. The node represents the way in which a specialized entity is chosen in the pruning process according to selection rules. In [15], The SES includes three tuples as follows  
\[SES=\langle Item,\ Relation,\ Attribute\rangle \tag{2}\]  
where  
\(Item=E\cup A\cup S\): Set of items:  
* E: set of entities;
* A: set of aspects;
* S: set of specialization;  
\(Relation=Asp\cup Spec\): set of relations among items:  
* \(Asp\subset E\times A\times 2^{E}\): aspect relationships;  
\(Spec\subset E\times S\times 2^{E}\): specialization relationship;  
\(Attributes=Coup\cup Rules\): set of attributes attached to items:  
* \(Coup:\ A\to 2^{(E.IO\times E.IO)}\): couplings attached to aspects;
* \(Rules:\ S\to 2^{R}\): selection rules attached to specializations and multiple-decomposition. In Equation (2), IO represents a set of input and/or output ports of respective entities, R is a set of selection rules in the form of \((cond\to E)\). According to Equation (2), the SES tree of Figure 2a is defined as follows:  
* \(E=\{\)ABC, AB, CS, A, B, C\(\}\);
* \(A=\{\)A-dec, cs-mdec\(\}\);
* \(S=\{\)ab-spec\(\}\);
* \(Asp=\{\)(ABC, abc-dec, \(\{\)AB, CS\(\}\)), (CS, cs-mdec, \(\{\)C\(\}\))\(\}\);
* \(Spec=\{\)(AB, ab-spec, \(\{\)A, B\(\}\))\(\}\);
* \(Coup=\{\)(abc-dec, \(\{\)(AB.out, CS.in), (CS.out, AB.in)\(\}\)), (cs-mdec, \(\{\)(CS.in, C.in), (C.out, CS.out)\(\}\))\(\}\);
* \(Rules=\{\)(ab-spec, \(\{\)A, B\(\}\)), (cs-mdec, \(\{\)selection of kernel-models, number of entities\(\}\))\(\}\).