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

/pdf/a-methodology-for-technology-identification-evaluation-and-3chmftfc0g.pdf

A methodology for technology identification, evaluation, and selection in conceptual and preliminary aircraft design

Review and prospect of supersonic business jet design

Presented at the 3rd World Aviation Congress and Exposition, Anaheim, CA, September 28-30, 1998.

Technology Impact Forecasting for a High Speed Civil Transport

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.

/pdf/integration-of-multifidelity-multidisciplinary-computer-39iu3bq45p.pdf

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

The computer codes, AER02S and WINGDES, are now widely used for the analysis and design of airplane lifting surfaces under conditions that tend to induce flow separation. These codes have undergone continued development to provide additional capabilities since the introduction of the original versions over a decade ago. This code development has been reported in a variety of publications (NASA technical papers, NASA contractor reports, and society journals). Some modifications have not been publicized at all. Users of these codes have suggested the desirability of combining in a single document the descriptions of the code development, an outline of the features of each code, and suggestions for effective code usage. This report is intended to supply that need.

/pdf/guide-to-aero2s-and-wingdes-computer-codes-for-prediction-1lpbhvlah7.pdf

Guide to AERO2S and WINGDES Computer Codes for Prediction and Minimization of Drag Due to Lift

Within the Supersonics (SUP) Project of the Fundamental Aeronautics Program (FAP), an initial multidisciplinary design & analysis framework has been developed. A set of low- and intermediate-fidelity discipline design and analysis codes were integrated within a multidisciplinary design and analysis framework and demonstrated on two challenging test cases. The first test case demonstrates an initial capability to design for low boom and performance. The second test case demonstrates rapid assessment of a well-characterized design. The current system has been shown to greatly increase the design and analysis speed and capability, and many future areas for development were identified. This work has established a state-of-the-art capability for immediate use by supersonic concept designers and systems analysts at NASA, while also providing a strong base to build upon for future releases as more multifidelity capabilities are developed and integrated.

https://ntrs.nasa.gov/api/citations/20100024174/downloads/20100024174.pdf

Initial Multidisciplinary Design and Analysis Framework

A performance assessment of eight low-boom high speed civil transport (HSCT) configurations and a reference HSCT configuration has been performed. Although each of the configurations was designed with different engine concepts, for consistency, a year 2005 technology, 0.4 bypass ratio mixed-flow turbofan (MFTF) engine was used for all of the performance assessments. Therefore, all original configuration nacelles were replaced by a year 2005 MFRF nacelle design which corresponds to the engine deck utilized. The engine thrust level was optimized to minimize vehicle takeoff gross weight. To preserve the configuration's sonic-boom shaping, wing area was not optimized or altered from its original design value. Performance sizings were completed when possible for takeoff balanced field lengths of 11,000 ft and 12,000 ft, not considering FAR Part 36 Stage III noise compliance. Additionally, an arbitrary sizing with thrust-to-weight ratio equal to 0.25 was performed, enabling performance levels to be compared independent of takeoff characteristics. The low-boom configurations analyzed included designs from the Boeing Commercial Airplane Group, Douglas Aircraft Company, Ames Research Center, and Langley Research Center. This paper discusses the technology level assumptions, mission profile, analysis methodologies, and the results of the assessment. The results include maximum lift-to-drag ratios, total fuel consumption, number of passengers, optimum engine sizing plots, takeoff performance, mission block time, and takeoff gross weight for all configurations. Results from the low-boom configurations are also compared with a non-low-boom reference configuration. Configuration dependent advantages or deficiencies are discussed as warranted.

A Performance Assessment of Eight Low-Boom High-Speed Civil Transport Concepts

Results of a first-order assessment of the mission performance benefits associated with the technology improvements and goals of the Phase II High-Speed Research (HSR) Program are presented. A breakdown of the four major disciplines resulted in the following estimated TOGW savings from the 1990 vehicle: propulsion at 14.3 percent, structures at 11.7 percent, flight-deck systems at 4.0 percent, and aerodynamics at 15.0 percent. Based on 100 percent success of the HSR Phase II proposed technology advancements, the overall combined impact is estimated to result in a 45 percent reduction in TOGW from a 1990 entry-into-service (EIS) date, which could result in a viable 2005 EIS vehicle with an acceptable TOGW that meets Stage III community noise restrictions. Through supersonic laminar flow control and the possible reduction in reserve fuel requirements resulting from synthetic vision capability, the potential exists for an additional 9.6 percent reduction in TOGW.

Lori P. Ozoroski

Papers

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

Guide to AERO2S and WINGDES Computer Codes for Prediction and Minimization of Drag Due to Lift

Initial Multidisciplinary Design and Analysis Framework

A Performance Assessment of Eight Low-Boom High-Speed Civil Transport Concepts

Benefits associated with advanced technologies applied to a high-speed civil transport concept