In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs...

https://epubs.siam.org/doi/pdf/10.1137/16M1082469

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

https://www.colonius.caltech.edu/pdfs/ColoniusLele2004.pdf

Computational aeroacoustics: progress on nonlinear problems of sound generation

Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function

The efficiency of building a surrogate model for the output of a computer code can be dramatically improved via variable-fidelity surrogate modeling techniques. In this article, a hierarchical kriging model is proposed and used for variable-fidelity surrogate modeling problems. Here, hierarchical kriging refers to a surrogate model of a highfidelity function that uses a kriging model of a sampled lower-fidelity function as a model trend. As a consequence, the variation in the lower-fidelity data is mapped to the high-fidelity data, and a more accurate surrogate model for the high-fidelity function is obtained. A self-contained derivation of the hierarchical kriging model is presented. The proposed method is demonstrated with an analytical example and used for modeling the aerodynamic data of an RAE 2822 airfoil and an industrial transport aircraft configuration. The numerical examples show that it is efficient, accurate, and robust. It is also observed that hierarchical kriging provides a more reasonable mean-squared-error estimation than traditional cokriging. It can be applied to the efficient aerodynamic analysis and shape optimization of aircraft or any other research areas where computer codes of varying fidelity are in use.

Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling

We consider multiphysics applications from algorithmic and architectural perspectives, where âalgorithmicâ includes both mathematical analysis and computational complexity, and âarchitecturalâ includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

https://journals.sagepub.com/doi/pdf/10.1177/1094342012468181

Multiphysics simulations: Challenges and opportunities

The practical use of high-fidelity multidisciplinary optimization techniques in low-boom supersonic business-jet designs has been limited because of the high computational cost associated with computational fluid dynamics-based evaluations of both the performance and the loudness of the ground boom of the aircraft. This is particularly true of designs that involve the sonic boom loudness as either a cost function or a constraint because gradient-free optimization techniques may become necessary, leading to even larger numbers of function evaluations. If, in addition, the objective of the design method is to account for the performance of the aircraft throughout its full-flight mission while including important multidisciplinary tradeoffs between the relevant disciplines the situation only complicates. To overcome these limitations, we propose a hierarchical multifidelity design approach where high-fidelity models are only used where and when they are needed to correct the shortcomings of the low-fidelity models. Our design approach consists of two basic components: a multidisciplinary aircraft synthesis tool (PASS) that uses highly tuned low-fidelity models of all of the relevant disciplines and computes the complete mission profile of the aircraft, and a hierarchical, multifidelity environment for the creation of response surfaces for aerodynamic performance and sonic boom loudness (BOOM-UA) that attempts to achieve the accuracy of an Euler-based design strategy. This procedure is used to create three design alternatives for a Mach 1.6, 6-8 passenger supersonic business-jet configuration with a range of 4500 n mile and with a takeoff field length that is shorter than 6000 ft. Optimized results are obtained with much lower computational cost than the direct, high-fidelity design alternative. The validation of these design results using the high-fidelity model shows very good agreement for the aircraft performance and highlights the need for improved response surface fitting techniques for the boom loudness approximations.

Multifidelity design optimization of low-boom supersonic jets

The conceptual/preliminary design of supersonic jet configurations requires multidisciplinary analyses tools, which are able to provide a level of flexibility that permits the exploration of large areas of the design space. High-fidelity analysis for each discipline is desired for credible results; however, the corresponding computational cost can be prohibitively expensive, often limiting the ability to make drastic modifications to the aircraft configuration in question. Our work has progressed in this area, and we have introduced a truly hybrid, multifidelity approach in multidisciplinary analyses and demonstrated, in previous work, its application to the design optimization of a low-boom supersonic business jet. In this paper, we extend our multifidelity approach to the design procedure and present a two-level design of a supersonic business-jet configuration, in which we combine a conceptual low-fidelity optimization tool with a hierarchy of flow solvers of increasing fidelity and advanced adjoint-based sequential quadratic programming optimization approaches. In this work, we focus on the aerodynamic performance aspects alone: no attempt is made to reduce the acoustic signature. The results show that this particular combination of modeling and design techniques is quite effective for our design problem and the ones in general and that high-fidelity aerodynamic shape optimization techniques for complex configurations (such as the adjoint method) can be effectively used within the context of a truly multidisciplinary design environment. Detailed configuration results of our optimizations are also presented.

Two-Level Multifidelity Design Optimization Studies for Supersonic Jets

A time-spectral and adjoint-based optimization procedure that is particularly efficient for the analysis and shape design of helicopter rotors is developed. The time-spectral method is a fast and accurate algorithm to simulate periodic, unsteady flows by transforming them to a steady-state analysis using a Fourier spectral derivative temporal operator. An accompanying steady-state adjoint formulation for periodic unsteady problems is then possible and enables an unsteady flow design optimization procedure. The time-spectral CFD analysis is validated against conventional time-accurate CFD and flight test data for a UH-60A Black Hawk helicopter rotor in high speed forward flight. A multidisciplinary structural dynamics and comprehensive analysis coupling is employed for validation study to include blade structural dynamics and to enforce vehicle trim. Application of the adjointbased design method is carried out to optimize blade shape for a UH-60A. An uncoupled aerodynamics only calculation is performed for design application, holding the blade deformations and trim angles fixed to the previously calculated values. Minimization of power is pursued with non-linear constraints on thrust and drag force, resulting in a simplified form of the trim condition. The blade twist distribution, airfoil section shapes, and outboard planform shape comprise over 100 design variables. Starting from the initial configuration, the optimizer found a new design that shows good performance improvement, amounting to a 2% decrease in torque and 7% increase in thrust compared to the baseline UH-60A. The results demonstrate the potential of the time-spectral and adjoint-based design method for helicopter rotors.

Helicopter Rotor Design Using a Time-Spectral and Adjoint-Based Method

A time-spectral and adjoint-based optimization method was developed and applied to helicopter rotor design for unsteady level flight. The time-spectral method is a fast and accurate computational fluid dynamics algorithm for computing unsteady flows. It transforms the flow-governing equations into a periodic steady state by using a Fourier spectral derivative operator. An accompanying steady-state adjoint formulation was implemented in the time-spectral form of the governing equations to enable design optimization for unsteady flows. The time-spectral analysis was validated against conventional time-accurate computational fluid dynamics computation and flight test data of a UH-60A helicopter rotor during high-speed forward flight. A multidisciplinary analysis of blade structural dynamics was carried out through a comprehensive analysis coupling procedure that accounted for aeroelasticity and enforced vehicle trim. The adjoint-based design method was applied to optimize the blade shape of the UH-60A rotor....

http://adl.stanford.edu/papers/aiaa-2008-5810-664.pdf

The practical use of high-fidelity multidisciplinary optimization techniques in low-boom supersonic business jet designs has been limited because of the high computational cost associated with CFD-based evaluations of both the performance and the loudness of the ground boom of the aircraft. This is particularly true of designs that involve the sonic boom loudness as either a cost function or a constraint because gradient-free optimization techniques may become necessary, leading to even larger numbers of function evaluations. If, in addition, the objective of the design method is to account for the performance of the aircraft throughout its mission (T/O and landing, climb, acceleration , etc.) while including important multidisciplinary trade-offs between the relevant disciplines (performance, boom, structures, stability and control, propulsion, etc.) the situation only worsens. In order to overcome these limitations, we propose a hierarchical multi-fidelity design approach where high-fidelity models are only used where and when they are needed to correct the shortcomings of the low-fidelity models. Our design approach consists of two basic components: a multidisciplinary aircraft synthesis tool (PASS) that uses highly-tuned low-fidelity models of all of the relevant disciplines and computes the complete mission profile of the aircraft, and a hierarchical, multi-fidelity environment for the creation of response surfaces for aerodynamic performance and sonic boom loudness (BOOM-UA) that attempts to achieve the accuracy of an Euler-based design strategy. This procedure is used to create three design alternatives for a Mach 1.6, 6-8 passenger supersonic business jet configuration with a range of 4,500 nmi and with a T/O field length that is shorter than 6,000 ft. Optimized results are obtained with much lower computational cost than the direct, high-fidelity design alternative. The validation of these design results using the high-fidelity model show very good agreement for the aircraft performance and highlights the need for improved response surface fitting techniques for the boom loudness approximations.

Seongim Choi

Papers

Multifidelity design optimization of low-boom supersonic jets

Two-Level Multifidelity Design Optimization Studies for Supersonic Jets

Helicopter Rotor Design Using a Time-Spectral and Adjoint-Based Method

Helicopter Rotor Design Using a Time-Spectral and Adjoint-Based Method

Multi-fidelity Design Optimization of Low-boom Supersonic Business Jets