# Multidisciplinary Reliability Design Optimization Modeling Based on SysML
## 1 Introduction  
With the continuous advancement of technology and growing economic demands, the complexity of engineering systems is on the rise. Designing and developing complex engineering systems involve multiple disciplines, each having varying degrees of coupling. Multidisciplinary Design Optimization (MDO) aims to fully account for the interactions and coupling effects between disciplines, employing suitable optimization methods, strategies, and distributed computing technologies to organize and manage the entire design process. By balancing the various disciplines during the design phase and deeply analyzing the coupling relationships and synergistic effects, MDO achieves the system's optimal overall solution, enhancing system performance, reducing design costs, and shortening development cycles. This approach is effective for solving complex engineering system optimization problems [1]. Conversely, document-based systems engineering can no longer meet current R&D needs when dealing with the complexities of interdisciplinary coupling. Thus, adopting Model-Based Systems Engineering (MBSE) has become an inevitable trend. MBSE involves a model-centric approach adopted by different disciplines (including mechanical, electrical, and software fields) to integrate various models into the systemsengineering process, enabling model-driven product system development and full lifecycle integration. This model-centric approach is poised to replace traditional document-centric methods [2]. MBSE supports systems engineering activities across the lifecycle through formalized modeling, characterized by managing system complexity, ensuring information consistency, and maintaining global traceability. Presently, the aerospace, automotive, and shipbuilding industries are actively exploring and applying MBSE technology in product development [3; 4; 5]. The MBSE approach enables designers to focus on developing system functional and behavioral models while automatically extracting multidisciplinary optimization models from the established system models [6]. This improves optimization verification efficiency and reduces the programming burden on designers. MBSE supports the integration of various models, allowing detailed design processes across different fields to be linked with the abstract system level. Therefore, in the system design process for complex products, optimization information is incorporated into the design information to build formal optimization models, achieving automatic system optimization [7]. Additionally, MDO can be employed at all stages of product design. Establishing MDO models based on MBSE facilitates the extraction of optimization models and allows for the reuse of established MDO models in iterative design processes. System models can define disciplinary interfaces, data flows, strategy process information, and abstract design parameter information. Therefore, this paper analyzes the definitions and mathematical models of MDO and reliability analysis [8]. It implements the representation of optimization models based on the SysML language through the SysML extension mechanism, including the construction of optimization variables, optimization constraints, optimization goal metamodels, and the formal expression of MDO problems [9]. Additionally, the paper analyzes the representation mechanism of SysML parametric diagrams and uses model transformation to convert the SysML optimization models generated in the first stage into XML description models readable by optimization solvers. Furthermore, the multidisciplinary optimization modeling of an in-vehicle environmental control integration system demonstrates the effectiveness of the proposed method. The rest of the paper is organized as follows: Section 2 presents the related research on Reliability-Based Multidisciplinary Design Optimization (RBMDO) and the integration of system design and optimization. Section 3 discusses the SysML-based RBMDO modeling method. Section 4 describes the XML-based approach to optimization model extraction.