Model-Based Systems Engineering (MBSE)

• MBSE is an engineering approach that uses formal models to represent a system's form, function, and concept across its lifecycle.
• It integrates SysML, domain-specific ontologies, and quantitative methods like hetero-functional graph theory for precise simulation and validation.
• MBSE promotes high model fidelity by emphasizing soundness, completeness, lucidity, and laconicity to support cross-disciplinary engineering.

Model-Based Systems Engineering (MBSE) is an engineering methodology that emphasizes systematic model-based representation of complex systems for the duration of their lifecycle—from initial conception through design, development, validation, deployment, and operation. MBSE serves as a foundation for coordinated, cross-disciplinary engineering activities and addresses the challenges of complexity, integration, analysis, and traceability in modern engineering domains. The methodology leverages formal modeling languages (notably SysML), domain-specific ontologies, and increasingly advanced computational techniques—including formal verification, knowledge-graph frameworks, and graph-theoretic and algebraic structures—to enable rigorous specification, analysis, and execution of engineered systems.

1. Core Principles and Ontological Foundations

MBSE distinguishes itself from document-centric approaches by relying on the explicit, formal representation of engineering knowledge as interconnected, consistently managed models. These models encompass system structure (form), behavior (function), requirements, interfaces, and, in advanced frameworks, allocation and concept. The approach is built on fundamental ontological constructs:

• System Form: The static/architectural view of the system, typically captured via block definitions, component hierarchies, and physical or logical architectures.
• System Function: The suite of processes, actions, or behaviors that a system must perform, captured through behaviors (state machines, activity diagrams, etc.).
• System Concept: The allocation or mapping of functions to forms—the rationale and justification for specific engineering decisions.

Leading MBSE frameworks are grounded in precise ontological formalisms such as the Subject-Verb-Object (SVO) construct (subject = resource, verb = process, object = operand), facilitating both natural language compatibility and machine-executable semantics (Farid et al., 29 May 2025, Farid et al., 2021).

2. Modeling Languages, Meta-architectures, and Unified Semantics

SysML (Systems Modeling Language) is the predominant modeling language adopted in MBSE, offering a suite of diagrams and constructs to support structural, behavioral, and requirement capture for engineered systems. Recent research has identified the need for robust meta-architectures—formalisms that ensure the semantic unity of diverse user-model diagrams.

Conventional SysML metamodels often lack a core semantic framework to unify diverse diagram views. To address this, advanced approaches such as Channel-Based Multi-Queue Structure-Behavior Coalescence Process Algebra (C-M-SBC-PA) have been developed (Chao, 2021), providing an integrated semantic domain for structural and behavioral constructs. In this framework, all system interactions are mediated by channels (value-passing), and system behaviors are mapped to a unified transition graph:

$\text{ITG} = (\Psi, S_0, E, A, O, T, \text{ITGR})$

where states ($\Psi$), actors/blocks ($E$), channel names ($A$), parameters ($O$), and blocks ($T$) are related via transitions ($$\text{ITGR}\subseteq\Psi \times E \times A \times O \times T \times \Psi$$).

This unified semantic base supports the consistent projection of internal block, state machine, and activity diagrams, enforcing rigorous model consistency and facilitating automated validation.

3. Quantitative Analysis: Graph-Theoretic and Algebraic Extensions

While standard MBSE approaches provide rich qualitative abstractions, the need for integrated quantitative analysis has led to the development of mathematical formalisms directly tied to MBSE ontologies. Notably, Hetero-functional Graph Theory (HFGT) fuses concepts from network science and MBSE to provide:

• Matrix and Tensor-Based Analytic Tools: Instead of restricting system relationships to two-dimensional adjacency matrices, HFGT employs higher-order tensors to encode the multidimensional relationships between resources, processes, and operands (i.e., system capabilities and their interconnectedness) (Farid et al., 2021).
  • For example, the hetero-functional incidence tensor captures allocations as

  $\mathcal{J}^H(y_1, y_2, v) = 1$

  if the transportation process from buffer $y_1$ to $y_2$ is executed by resource $v$.

• System Concept Tensorization: The system concept is formalized as

$A_s = J_s \circ K_s$

where $J_s$ is the knowledge base matrix/tensor, and $K_s$ represents system constraints, preserving both ontological completeness and analytic tractability.

• Support for Multilayer and Heterogeneous Networks: Tensor structures naturally represent systems with non-correspondent, multi-domain (e.g., energy, material, information) components and enable the generalization of modularity, centrality, and flow optimization concepts to MBSE-modeled systems.

These structures establish a direct and mathematically rigorous pathway from SysML models to network-based simulation, optimization, and analysis, enabling verification of both static architecture and dynamic system properties.

4. Model Fidelity and Meta-architectural Assessment

Effective MBSE requires not only the construction of ontologically rich and analytic-ready models but also the rigorous assessment of model fidelity. Four linguistic properties underpin model assessment:

• Soundness: The extent to which all model elements correspond to valid system abstractions, excluding contradictions or ambiguities.
• Completeness: Degree to which all relevant system aspects and stakeholder requirements are represented in the model.
• Lucidity: Clarity and ease of understanding for intended stakeholders, promoting maintainability and communicability.
• Laconicity: Minimization of redundancy—ensuring that all content is essential and contributes to the model's objectives.

Meta-architecture in MBSE—which spans both domain-specific reference architectures and case-specific instantiations—aims to reconcile the diversity of disciplinary models, facilitate traceable model transformations, and maintain the fidelity properties above.

Unlike other meta-architectures that focus solely on model structure or syntax, approaches inspired by HFGT are rooted in linguistic structures, representing resources as subjects, processes as predicates, and operands (including matter, energy, organisms, information, money) as the objects of predicates. This linguistic mapping supports both human-centric clarity and machine-level semantic rigor (Farid et al., 29 May 2025).

5. Integration with Network Science and Beyond

A key challenge for MBSE has been the integration of quantitative methods from network science with the qualitative, heterogeneous models prevalent in engineering practice. HFGT acts as a conceptual and technical bridge by preserving the non-uniform ontological constructs of MBSE (system form, function, concept) while providing a quantitative analytic toolbox paralleling developments in multilayer and commodity-flow networks.

For systems engineers, this means the MBSE model can be directly leveraged for advanced simulation (e.g., via Petri nets and state transition modeling), optimization (minimum cost/resource/energy flows), and vulnerability or contingency analysis. For network scientists, the methodology provides a systematic way to endow nodes and edges with physical, functional, and process-level semantics, overcoming the abstractions and correspondence limits of classical network models.

6. Formalization within SysML and Interoperability

The practical integration of these meta-architectural and analytic formalisms is facilitated by advanced SysML profiles. These profiles encode subject–predicate–object triplets directly into SysML diagrams, supporting enhanced automation, traceability, and consistency checking. This includes the systematic management of resources (as blocks or components), processes (as activities/functions), and operand exchanges (as flows or state transitions).

The integration of HFGT concepts is enabled via meta-architectures expressed within SysML and complemented by machine-readable metadata and constraints (often OCL-based). SysML tools adopting these formalisms facilitate the direct transfer of models for simulation, verification, and quantitative systems analysis, supporting complex, adaptive, and multi-domain systems-of-systems.

7. Future Directions and Methodological Evolution

The convergence of MBSE, advanced graph theory, and network science underpinned by rigorous ontological/mathematical structures positions MBSE as a key methodology for addressing increasingly complex engineering domains—such as environmental systems, societal infrastructure, and cyber-physical systems. Future directions include:

• Enhanced model management and transformation across heterogeneous domains and scales,
• Automated verification of multidimensional system constraints and emergent behaviors,
• Full integration with semantic web and digital engineering asset marketplaces,
• Interoperability with domain-agnostic and domain-specific modeling languages via common ontological backbones (Jinzhi et al., 2020, Farid et al., 2021, Farid et al., 29 May 2025).

Current challenges include maintaining lucidity and usability in the face of growing model complexity, and managing trade-offs between expressive power, model tractability, and interpretability, especially for cross-disciplinary teams.

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MBSE, as currently formalized and extended through ontologically grounded, mathematically expressive structures such as hetero-functional graph theory, continues to advance the rigorous and scalable development of complex systems, aligning conceptual clarity, analytic power, and practical system realization.