Model-Based Systems Engineering (MBSE) for Complex Systems

To address three major industry pain points—the lack of quantified profit-sharing standards in the two-stage pricing under the separation model of military research and production, the absence of stable Nash equilibrium in single-layer synchronous optimization, and insufficient incentives for full-cycle process optimization in design units—this paper constructs a two-level Stackelberg leader–follower game model with the general contracting unit as the leader and design and general contracting units as followers. This aligns with current prototype incentives and phased pricing policies for production rewards and penalties. At the theoretical level, it improves the complete proof system for the two-stage concave profit two-level Stackelberg Nash equilibrium, distinguishes the mathematical differences in equilibrium existence between sequential decision-making and synchronous optimization, and extracts general rules for phased differentiated profit sharing: high-innovation segments should be allocated more profit weight; simply maximizing total alliance profit may cause imbalanced interests, while introducing a minimum net profit-weighted objective can achieve Pareto improvements without profit loss. This conclusion can be applied to multi-stage general contracting scenarios across industries, such as EPC and military–civil collaborative innovation, enriching the basic theory of profit sharing and hierarchical games. Theoretically, the existence of the lower-level Nash equilibrium is proven using Brouwer’s fixed-point theorem, and combining it with the strictly monotonically decreasing feature of the best response function, uniqueness of the equilibrium is derived. Multiple sets of differentiated initial values are simulated to rule out multi-equilibrium bifurcation risk. The model incorporates the military’s reward and penalty policies as rigid exogenous constraints, sets dual individual rationality constraints of ‘cooperative profit greater than baseline profit with no allocation, and both parties’ net profit non-negative,’ and introduces differentiated cost-reduction efficiency and quadratic increasing effort costs to characterize the heterogeneous input of the two types of development entities. For models with piecewise nonlinearity and multi-constraint nonconvex structures, this paper modifies the standard PSO into a Bi-PSO solving framework through hierarchical temporal adaptation. It does not innovate the underlying particle update mechanism and is only used to match the sequential decision order of the leader–follower game. By comparing five algorithms—IPM, GA, SA, DE, and adaptive PSO—through 20 repeated simulations: gradient-based interior point methods easily get stuck in locally invalid solutions that violate cooperation thresholds; differential evolution has the best numerical global search performance, but all general evolutionary algorithms optimize allocation and effort variables simultaneously, disrupting the Stackelberg hierarchical timing. Only Bi-PSO maintains consistent game logic. Using a pricing case for a certain type of equipment and jointly calibrating all parameters with policy documents, three simulation scenarios were set up: no allocation, equal 50/50 split, and single-layer profit maximization. Under the no-allocation mode, R&D investment from the design unit drops to zero and alliance benefits plummet; a blanket equal split ignores differences in technical contributions across two stages, leading to clear efficiency losses; single-layer optimization only pursues total profit maximization, causing a severe imbalance in profit distribution. The two-layer basic framework can achieve the upper limit of alliance benefits, and by adding a weighted optimization goal that considers both total profit and cooperation fairness, it can achieve equal net profits for both parties without reducing overall profit. Through single-parameter sweeps and two-factor heatmap simulations, the study further revealed the coupled effects of main party efficiency and mass production rewards and penalties on equilibrium input and optimal sharing ranges. A robust check was performed by replacing the logarithmic concave output function, producing a standardized allocation range resilient to parameter perturbations: optimal split for the prototype stage is 0.4–0.6 for the design unit, and for mass production stage 0.7–0.9. The findings suggest that high-contribution stages in multi-phase collaboration contracts should receive more benefits, and a weighted fairness objective can achieve Pareto improvements. These conclusions can extend to multi-stage collaboration scenarios such as EPC and military–civilian cooperation. Theoretically, this research further completes the equilibrium proof system for two-party concave payoff two-layer games, providing a new reference for the theory of phased differentiated benefit-sharing contracts in the military sector. Methodologically, it proposes a two-layer intelligent solving tool adapted to leader–follower sequential decisions, effectively mitigating issues where single-layer model equilibria fail or analytical algorithms struggle with multi-constraint nonconvex games. The results can provide quantitative support for the military, general contracting unit, and design unit in drafting equipment incentive pricing contracts and managing full-cycle cost collaboration. Full article

Automotive systems are experiencing a rapid increase in complexity driven by the transition towards software-defined vehicles, autonomous functionalities and increasingly interconnected E/E architectures. This transformation intensifies variability across hardware and software domains and challenges established engineering approaches. Traditional modular product development (MPD) provides structural mechanisms to manage hardware complexity, while systems and software product line engineering (SPLE) offers methods for managing software variability. However, these paradigms are typically applied in isolation and lack an integrated methodology capable of addressing cross-domain variability and architectural synchronization in automotive systems. This paper investigates how SPLE and MPD can be systematically integrated to manage variability and architectural complexity in automotive systems. Following a design-oriented research approach, industry requirements are derived from an automotive case study at an OEM. Existing SPLE and modularization approaches are analyzed against these requirements, revealing gaps in cross-domain traceability, synchronization mechanisms, and lifecycle coordination. Based on this analysis, we propose an integrated methodology that combines variability modeling principles from SPLE with architectural modularization concepts. The approach enables management of module structures, supporting system-level consistency in automotive environments. The main contribution is a model-based-integration framework that bridges variability management and modular architecture design to address increasing system complexity in the automotive industry. Full article

This article evaluates two model-based systems engineering (MBSE) toolchains that support aircraft certification under EASA CS-23 Amendment 6. Airworthiness requirements and associated acceptable means of compliance are digitalized as Systems Modeling Language (SysML) models that preserve document structure and encode parameters and expressions needed for substantiation. The maneuvering and gust flight envelope required by CS-23 Subpart C is used as a representative case to compare workflow integration, robustness, and artifact generation. One implementation combines Eclipse Papyrus with MATLAB to export and parse the SysML model and to execute automated calculations and reporting. The second uses CATIA Magic Systems of Systems Architect (MSoSA) to export stereotype fields to JSON and to run C++ routines orchestrated by activity diagrams. Both toolchains generate certification-relevant outputs, including design airspeeds, limit load factors, and flight envelope plots, while improving traceability relative to document-centric practice. The comparison indicates that the Papyrus/MATLAB approach supports rapid prototyping but is more sensitive to regulatory text changes, whereas the MSoSA-based approach reduces dependence on text–pattern parsing and provides more integrated execution. These results suggest that MBSE can improve the efficiency of preparing certification evidence, with adoption trade-offs driven by licensing cost, integration effort, and organizational maturity. Full article

This paper proposes a formal method and associated techniques for completing the ISO/IEC/IEEE Standard 15288 technical process 6.4.2—Stakeholder Needs and Requirements definition within the 15288-SysML Grid framework. The paper is a companion work to Engineering Systems with Standards and Digital Models: Development of a 15288-SysML Grid, which describes an engineering design method that supports the tenets of the Industry 4.0 paradigm. The formal method presented here is grounded using established constructs from systems science; specifically, the systems principles of hierarchy, emergence, requisite parsimony, minimum critical specification, and requisite saliency. The application of accepted principles ensures that stakeholders are able to objectively specify measurable criteria that can satisfy stakeholder needs and capabilities. The method uses: (1) international standards for systems (e.g., ISO/IEC/IEEE 15288); (2) adopts the four fundamental aspects of system design supported by model-based systems engineering (MBSE); (3) invokes the international standard for the systems modeling language (SysML); and (4) adopts a hierarchical requirements tree that specifies Mission, Goals, Objectives, and Sub-objectives (MGOS) to provide the stakeholder-analysis process a means for articulating system-level engineering requirements. Utilization of the MGOS framework is intended to have a positive impact on the system design process by ensuring reproducibility, replicability, transparency, and generalization. Full article

The development of modern production systems involves numerous interdependent disciplines, heterogeneous data sources, and frequent design iterations, making the conceptual design phase particularly complex and error-prone. Model-Based Systems Engineering (MBSE) provides a promising approach to manage this complexity by enabling consistent and structured system representations. While domain-specific modeling languages (DSMLs) can tailor MBSE methods to specific domains, existing approaches often lack standardized semantics, user guidance, and tool support to ensure consistent model creation and verification. This paper introduces a DSML framework tailored for the conceptual design of production systems, integrating both methodological guidance and standard-based domain knowledge. The approach builds upon the Software Platform Embedded Systems (SPES) framework and extends Systems Modeling Language (SysML) through the Unified Modeling Language (UML) profile mechanism, providing clear modeling constructs, viewpoint-specific diagram types, and automated consistency checks. To enhance comprehensibility and domain alignment, the framework incorporates supplementary DSMLs that capture structures and semantics from established industrial standards. The proposed method is evaluated using an aircraft production case study, demonstrating improved applicability of MBSE for the conceptual design of complex production systems. Full article