## 4 Modeling and Simulation Methods and Their Applications
### Descriptive Modeling for Swarm Ontology  
This section serves as the basic theoretical and top-level guidance for our methodology and emphasizes a complete description of system conceptualization and contextualization from the loop of Conceive-Design-Implementation-Operation (CDIO) to make the ontology a fundamental approach to addressing swarm complexity, thereby also reflecting the basic key drivers and processes of MBSE and the innovation of specific engineering applications. Therefore, in the context of complex operations, the architecture framework is placed at the intersection of the above four CDIO domains of a complex system. It is highlighted that the functionality and characteristics of the systems and elements within the overall framework should be considered during the mission concept, which requires establishing a top-level framework for analysis and synthesis, concentrating on the architecture model of the swarm ontology. The goal of the work is to entirely model a problem in business terms without refining the solution or its implementation, which relates to the Computation-Independent Model (CIM) of Model-Driven Architecture (MDA) [25].  
For our study and other AI systems, what \"exists\" is that which can be represented in models. For the research of complex systems such as swarm, the formal representation of autonomous systems based on ontology is currently one of the research hotspots, while modeling and simulation are regarded as the most effective solution. Our aim in the research is to provide a comprehensive modeling and simulation framework for future applications of swarm ontology that enables us to leverage the advances in graphical modeling languages (such as SysML) and the process of MBSE, while further enabling us to perform formal analyses of consistency and correctness with respect to the ontology of the domain of swarm.  
The ontology is traditionally defined in OWL2 with open-source ontology tools, such as Protege [10]. In order to reason about the properties of the concept model and particularly facilitate the simplification of the model-to-model transformation from one domain into another in MBSE, SysML has the same abilities as OWL2 to map the domain concepts into SysML entities or relations without affecting the concepts. In SysML, the Block Definition Diagram (BDD) has enough expressiveness to represent a detailed design. When we suitably restrict SysML's BDD, it can be transformed into OWL2 to achieve the equivalent  
Figure 1: The overall research blueprint of this study.  
effect. A SysML BDD is a kind of first-order equational logic and provides an abstract syntax for the kind of terms in which logical axioms are expressed using equality, instances, and subclass relations between terms. The knowledge presentation of a system of concepts is suitable for representing designs which will have distinct \"has a part of\" properties, with domains and range classes that represent the graph structure of the BDD, and with a cardinality restriction on these properties to depict the number of instances of the class during implementation [27].  
The general principle is to map the swarm ontology into SysML to define the ontological concepts and relationships as SysML constructs that can be applied to appropriate modeling entities: concepts to blocks, and relationships to a semantically compatible SysML relationship. See Figure 2 for an example of an autonomous swarm ontology model for a specific mission. The macro-behavior corresponds to the swarm tasks; that is, the autonomous swarm needs to possess top-level capabilities to achieve its mission. The meso-behavior to corresponds to a teaming strategy, which refers to the collective behavior of an autonomous system to be negotiated in interaction with the outside world. The micro behavior corresponds to atomic actions, which are various operations that autonomous-system individuals should possess.