Development of a Hybrid MDF/IDF Multidisciplinary Optimization Solution Method with Coupling Suspension

Abstract

Multidisciplinary Design Optimization (MDO) is a discipline, which solves complex engineering systems by decomposing them into a set of subsystems. Couplings connect these subsystems together, illustrating the passage of information from one subsystem to another. These couplings result in the increase in time and cost of the execution of the MDO cycle. Subsystem reordering, coupling suspension and coupling elimination are a few methods used for reducing time and cost of exe cution. Previous research in coupling suspensions shows that due to the reduction in couplings an error is introduced into the solution with a possibility of divergence of the design. Hybrid MDF/IDF is a MDO solution method developed in this work, which reduces the error introduced by coupling suspension in the subsystem outputs and the final value of the objective function. The Hybrid method is a compromise between the MDF and IDF solution methods. The method reduces the error by adding equality constraints for the subsystem outputs affected by the suspension of couplings. These equality constraints restrict the path of the solution and direct it towards the solution attained by unsuspended analysis. Introduction In this new age of computer aided engineering, the design and analysis of engineering systems is carried out using computer simulations even before such systems are realized. Design of complex engineering systems requires the analysis of multiple disciplines that interact with each other. Efforts of analyzing and optimizing complex systems in a computationally effective and efficient manner led to the emergence of Multidisciplinary Design Optimization (MDO). MDO solves complex engineering systems by breaking them into smaller manageable sub-tasks known as subsystems. The information passage between the subsystems is known as the “coupling”. Typically the design of an engineering system is driven by time deadlines. Hence, researchers in the MDO field are identifying ways and means of reducing the computation time and cost of the MDO cycle. Subsystem Reordering and System Reduction are two methods of reducing time and cost of a MDO cycle. System Reduction is carried out by eliminating or suspending couplings. Previous MDO solution methods with coupling suspension resulted in the introduction of error in the solution achieved. The present research focuses on developing a MDO solution method that balances the tradeoff between efficiency and accuracy, to obtain a solution that matches the unsuspended solution even when couplings are suspended. Decomposition of Complex Systems In 1980’s Sobieski introduced an approach of decomposing complex systems into manageable sequence of subsystems. This approach included decomposing systems in hierarchic, non-hierarchic or hybrid-hierarchic group of interconnecting subsystems. The interactions between subsystems were known as couplings and the outputs from the subsystems known as behavior variables. Figure 1 illustrates a Design Structure Matrix (DSM) developed by Steward that represents the ordering and coupling information of a decomposed system. In this work, the couplings above the diagonal are known as feed-forward couplings and those below the diagonal are known as feedback couplings. Figure 1 Design Structure Matrix (DSM) Global Sensitivity Equations In the MDO cycle, linear approximation of the objective function and constraints is carried out. For the linear approximations, the total derivatives of subsystem outputs with respect to the design variables is required. These derivatives are obtained using Sobieski’s Global Sensitivity Equations (GSE). The 1