Simulations are often computationally expensive and the need for multiple realizations, as in uncertainty quantification or optimization, makes surrogate models an attractive option. For expensive high-fidelity models (HFMs), however, even performing the number of simulations needed for fitting a surrogate may be too expensive. Inexpensive but less accurate low-fidelity models (LFMs) are often also available. Multi-fidelity models (MFMs) combine HFMs and LFMs in order to achieve accuracy at a reasonable cost. With the increasing popularity of MFMs in mind, the aim of this paper is to summarize the state-of-the-art of MFM trends. For this purpose, publications in this field are classified based on application, surrogate selection if any, the difference between fidelities, the method used to combine these fidelities, the field of application and the year published. 
Available methods of combining fidelities are also reviewed, focusing our attention especially on multi-fidelity surrogate models in which fidelities are combined inside a surrogate model. Computation time savings are usually the reason for using MFMs, hence it is important to properly report the achieved savings. Unfortunately, we find that many papers do not present sufficient information to determine these savings. Therefore, the paper also includes guidelines for authors to present their MFM savings in a way that is useful to future MFM users. Based on papers that provided enough information, we find that time savings are highly problem dependent and that MFM methods we surveyed provided time savings up to 90%. 
Keywords: Multi-fidelity, Variable-complexity, Variable-fidelity, Surrogate models, Optimization, Uncertainty quantification, Review, Survey

Review of multi-fidelity models

Multifidelity surrogates are essential in cases where it is not affordable to have more than a few high-fidelity samples, but it is affordable to have as many low-fidelity samples as needed. In the...

Issues in Deciding Whether to Use Multifidelity Surrogates

A summary is provided for the Second AIAA Sonic Boom Workshop held on January 8–9, 2017, in conjunction with AIAA SciTech 2017. The workshop used four models of increasing complexity: an axisymmetr...

/pdf/nearfield-summary-and-statistical-analysis-of-the-second-vjzvj1a9lu.pdf

Nearfield Summary and Statistical Analysis of the Second AIAA Sonic Boom Prediction Workshop

Review and prospect of supersonic business jet design

A summary is provided for the propagation portion of the second AIAA Sonic Boom Prediction Workshop, held 8 January 2017 in conjunction with the AIAA SciTech 2017 Conference. Near-field pressure wa...

/pdf/summary-of-propagation-cases-of-the-second-aiaa-sonic-boom-2kq1n5r1dh.pdf

Summary of Propagation Cases of the Second AIAA Sonic Boom Prediction Workshop

This paper documents the development of a conceptual level integrated process for design and analysis of efficient and environmentally acceptable supersonic aircraft. To overcome the technical challenges to achieve this goal, a conceptual design capability which provides users with the ability to examine the integrated solution between all disciplines and facilitates the application of multidiscipline design, analysis, and optimization on a scale greater than previously achieved, is needed. The described capability is both an interactive design environment as well as a high powered optimization system with a unique blend of low, mixed and high-fidelity engineering tools combined together in the software integration framework, ModelCenter. The various modules are described and capabilities of the system are demonstrated. The current limitations and proposed future enhancements are also discussed.

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Integration of Multifidelity Multidisciplinary Computer Codes for Design and Analysis of Supersonic Aircraft

The detailed outer mold line shaping of a Mach 1.6, demonstrator-sized low-boom concept is presented. Cruise trim is incorporated a priori as part of the shaping objective, using an equivalent-area-based approach. Design work is performed using a gradient-driven optimization framework that incorporates a three-dimensional, nonlinear flow solver, a parametric geometry modeler, and sensitivities derived using the adjoint method. The shaping effort is focused on reducing the under-track sonic boom level using an inverse design approach, while simultaneously satisfying the trim requirement. Conceptual-level geometric constraints are incorporated in the optimization process, including the internal layout of fuel tanks, landing gear, engine, and crew station. Details of the model parameterization and design process are documented for both flow-through and powered states, and the performance of these optimized vehicles presented in terms of inviscid L/D, trim state, pressures in the near-field and at the ground, and predicted sonic boom loudness.

https://ntrs.nasa.gov/api/citations/20160006034/downloads/20160006034.pdf

Under-Track CFD-Based Shape Optimization for a Low-Boom Demonstrator Concept

A new low-boom target generation approach is presented which allows the introduction of a trim requirement during the early conceptual design of supersonic aircraft. The formulation provides an approximation of the center of pressure for a presumed aircraft configuration with a reversed equivalent area matching a low-boom equivalent area target. The center of pressure is approximated from a surrogate lift distribution that is based on the lift component of the classical equivalent area. The assumptions of the formulation are verified to be sufficiently accurate for a supersonic aircraft of high fineness ratio through three case studies. The first two quantify and verify the accuracy and the sensitivity of the surrogate center of pressure corresponding to shape deformation of lifting components. The third verification case shows the capability of the approach to achieve a trim state while maintaining the low-boom characteristics of a previously untrimmed configuration. Finally, the new low-boom target generation approach is demonstrated through the early conceptual design of a demonstrator concept that is low-boom feasible, trimmed, and stable in cruise.

/pdf/conceptual-design-of-low-boom-aircraft-with-flight-trim-b0mh3strct.pdf

James W. Fenbert

Papers

Integration of Multifidelity Multidisciplinary Computer Codes for Design and Analysis of Supersonic Aircraft

Under-Track CFD-Based Shape Optimization for a Low-Boom Demonstrator Concept

Conceptual Design of Low-Boom Aircraft with Flight Trim Requirement