Integrated formulation-solution-design scheme for nonlinear multidisciplinary systems using the MIXEDMODELS platform

Abstract

Most state-of-the-art systems are multidisciplinary in nature and encompass a wide range of components from domains such as electronics, mechanics, hydraulics, etc. Design considerations and design parameters of the system can come from any or a combination of these domains. The traditional optimization approach for multidisciplinary systems utilizes sequential optimization, wherein each subsystem is optimized in isolation in a predetermined order, assuming that the designs of the other subsystems remain fixed. This often leads to system designs that are suboptimal. In recent years emphasis has been placed on development of an integrated scheme for analysis and design of multidisciplinary systems. An important aspect is the software architecture required to support such a scheme. This dissertation presents MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) - a unified analysis and design tool for multidisciplinary systems that is based on a procedural, symbolic-numeric architecture. This architecture offers great modeling flexibility at the component level, allowing any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of nonlinear differential-algebraic equations (DAEs). These equations are differentiated with respect to design variables to obtain an additional set of DAEs that describe the sensitivity coefficients of the system state variables. This combined set of DAEs is solved numerically to obtain the solution for the state variables and the state sensitivity coefficients of the system. Finally, knowing the system performance functions, their design sensitivity coefficients can be calculated by using the values of the state variables and state sensitivity coefficients obtained from the DAEs. For ease in error control and software implementation, sensitivity analysis formulation described in this work uses direct differentiation approach as opposed to the adjoint variable approach. The MIXEDMODELS capabilities are demonstrated through several numerical examples and the results indicate that the MIXEDMODELS formulation and architecture is effective in terms of accuracy, modeling convenience, computational efficiency, and the ability to simulate the behavior of a general class of multidisciplinary systems.