Cumulative global metamodels with uncertainty — a tool for aerospace integration

Abstract

The integration of multidisciplinary data is key to supporting decisions during the development of aerospace products.Multidimensional metamodels can now be automatically constructed using limited experimental or numerical data, including data from heterogeneous sources. Recent progress in multidimensional response surface technology, for example, provides the ability to interpolate between sparse data points in a multidimensional parameter space. These analytical representations act as surrogates that are based on and complement higher fidelity models and/or experiments. These high-level representations or metamodels can include technical data from multiple fidelity levels and multiple disciplines, but also nontechnical data such as costs and schedules. Most importantly, these representations can be constructed on-the-fly and are cumulatively enriched as more data become available. The purpose of the present paper is to highlight applications of these Cumulative Global Metamodels (CGM), their ease of construction, and the role they can play in aerospace integration. This paper focuses on two types of applications, namely, design optimization and mutual data set enrichment via data fusion. I.Nomenclature II. BackgroundL s OBAL metamodels and response surface technology are increasing used in a variety of fields, including tructural reliability, instrument calibration, and aerodynamic and trajectory optimization, to name a few. 1-11Because of their analytical nature, these models can be used for automated searches and are naturally well-suited to the acceleration of optimization tasks and rapid strategy evaluation. A central issue to constructing appropriate response surface models is the so-called curse of dimensionality, in which the number of data points required to characterize/support the surface increases exponentially with the number of independent variables. This difficulty is well-known and, in effect, precludes the use of conventional schemes, such as polynomial and piecewise-polynomial (finite-element) approximations. Neural networks, support vector machines, and multidimensional splines all have proven capable of multidimensional data generalization and (partially) circumventing this difficulty. The particular approach used in this paper is based on self-training radial basis function networks which form the basis of the NEAR-RS (response surface) technology.

Assessment of CFD-based Response Surface Model for Ares I Supersonic Ascent Aerodynamics

“…The intent of this paper is not to delve into the mathematics of radial basis function response surface methods (which are available elsewhere [14][15][16] ); instead, this paper focuses on the application of RBF algorithms to a practical problem. However, a short discussion of RBF methodology is presented here for clarity.…”

“…However, a short discussion of RBF methodology is presented here for clarity. In general terms, radial basis function networks are analogous to solving a system of equations where each input data point has an "island of [16][17][18][19] used to develop the CFD-based A106 AFMA DB) constructs a global response surface across multiple dimensions based on a sparse set of input data.…”

Conceptual design of UAV using Kriging based multi-objective genetic algorithm

“…Meta-models are models that seek to provide a simple mathematical representation of a complex physical system. Reisenthel et al (11) describe the key role played by meta-models in surrogate based optimisation. They show how the global metamodels can be used for data fusion.…”

Surrogate based design optimisation of composite aerofoil cross-section for helicopter vibration reduction

“…One way to reduce the sensitivity of optimisation results is to use surrogates such as response surface methods which tend to avoid local minimum by smoothing out the objective function and constraints (11) . The surrogates are mathematical approximations for the objective functions and constraints used during the optimisation process (12,13) .…”