Abstract
System of Systems (SoS) is designed to deliver value to participant stakeholders in a dynamic and uncertain environment where new systems are added and current systems are removed continuously and on their own volition. This requires effective evolution management at the SoS architectural level with adequate support of process, methods, and tools. This paper follows the principle of Model-Based Systems Engineering (MBSE) and develops a holistic framework integrating MBSE conceptual representations and approximate dynamic programming (ADP) to support the SoS evolution. The conceptual models provide a common architectural representation to improve communication between various decision makers while the dynamic optimization method suggests evolution planning decisions from the analytical perspective. The Department of Defense Architecture Framework (DoDAF) models using Systems Modeling Language (SysML) are used as MBSE artifacts to connect with ADP modeling elements through DoDAF metamodels to increase information traceability and reduce unnecessary information loss. Using a surface warfare SoS as an example, this paper demonstrates and explains the procedures of developing DoDAF models, mapping DoDAF models to ADP elements, formulating ADP formulation, and generating evolutionary decisions. The effectiveness of using ADP in supporting evolution to achieve a near-optimal solution that can maximize the SoS capability over time is illustrated by comparing ADP solution to other alternative solutions. The entire framework also sheds light on bridging the DoDAF-based conceptual models and other mathematical optimization methods.
Highlights
System-of-Systems (SoS) problems have received increased attention in the aerospace industry in recent years with the advancement of communication and information technologies
According to the Department of Defense Architecture Framework (DoDAF) models enabled mathematical formulation and the adopted approximate dynamic programming (ADP) algorithm provided in the previous section, this paper uses “intlinprog” function in Matlab to solve the integer programming problem at each time step for every iteration. e function “intlinprog” might be inefficient for large size problems, in which case we can switch to more efficient commercial computation tools such as CPLEX and Gurobi optimizers. is result section primarily aims to demonstrate the effectiveness of the ADP method in supporting SoS evolution while the usefulness of integrating Model-Based Systems Engineering (MBSE) and ADP will be discussed in the last subsection
Since the deterministic experiment is a special case of the stochastic experiment, we only plot the convergence analysis figure of the stochastic experiment where the capability improvement d tfcapj,i,t of each type of system follows a normal distribution. e initial budget is set as 1000 million dollars and increases at a constant rate of 5% during every decision stage
Summary
System-of-Systems (SoS) problems have received increased attention in the aerospace industry in recent years with the advancement of communication and information technologies. The DoDAF-based conceptual models help to identify the key elements determining the consistent performance delivery during SoS evolution; on the other hand, the ADP method provides sequential decision support from the analytical perspective based on the key information extracted from the DoDAF models. This paper aims to contribute to the SoS research by developing a comprehensive framework that links the architectural models and dynamic optimization method based on the steps in the “wave model” to generate effective decision support for SoS evolution. This paper (1) develops the ADP formulation and solution approach for the evolutionary multistage decision-making process of an SoS problem, (2) links the DoDAF models and ADP formulation through the DoDAF metamodel (DM2) that can enhance the traceability between different phases of analysis, and (3) sheds light on how to build the connections between DoDAF conceptual models and other mathematical optimization methods.
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