Multidisciplinary Optimization Branch

For the purpose of this talk, fidelity means the accuracy of a model in representing the physical reality. There are two types of fidelity for systems simulation: (i) accuracy of computed systems performance metrics and (ii) resolution of systems description. For example, analysts can use measured data or a simulation model to estimate the lift and drag coefficients of an aerial vehicle. Of course, measured data has a higher fidelity than any simulation data but appropriate data may not be available. In the absence of measured data, a computational fluid dynamics (CFD) solver can estimate the performance metrics (lift and drag) of the vehicle by using a low-fidelity panel code or a high-fidelity Navier-Stokes code. Moreover, for the same CFD code, the fidelity of generated simulation results depends on the grid resolution; and finer grid resolution usually provides increased accuracy of the estimated lift and drag coefficients. Regardless of the CFD fidelity, the structural finite element model (FEM) can be described by using a few parameters that specify a generic shape and simple load bearing structure, or by using hundreds or thousands parameters that capture many critical features of the vehicle structure. These two types of fidelity for systems simulation are usually related to each other, and high-fidelity analysis is employed only when low-fidelity analysis cannot provide credible assessment of the response of the underlying design concept.

Use of high-fidelity analysis tools creates many problems for systems analysts. For example, an analysis code may take hours or even days to generate one response, high-fidelity analysis codes may be difficult to interface with existing conceptual design codes, the needed CFD and FEM models may not exist, and the existing models may not be parameterized appropriately. These problems in obtaining high-fidelity simulation results could deter analysts from meaningful exploration of the design space and disrupt the interactive design process whereby each analysis result provides insight needed to improve the baseline design. Some of these problems may be solved by replacing high-fidelity analysis codes by approximation models, which is the motivation for a comprehensive survey of existing methods for approximation of system responses in conceptual design.

All of the requirements related to the use of approximation methods in conceptual design can be categorized into the following two use cases: (i) to predict a performance metric that can only be estimated by using historical data or expensive computer simulations, and (ii) to improve the accuracy of an existing low-fidelity analysis tool by using a few high-fidelity data points. The second use case arises from the need for tuning an existing low-fidelity model to reflect more accurate systems behaviors.

Due to the need for solving two use cases in conceptual design mentioned above, it is necessary to look beyond least-squares polynomial approximation or Kriging interpolation, and identify useful approximation methods that are promising for conceptual design applications. The main goal of the talk is to give an overview of advanced approximation methods for multivariate approximation problems that cannot be solved by using quadratic polynomial approximation or Kriging interpolation. We will highlight the pros and cons of advanced approximation methods, and identify some challenging problems in approximation method development from conceptual design perspective.