Analytical Benchmark Problems for Multifidelity Optimization Methods

The paper presents a collection of analytical benchmark problems specifically selected to provide a set of stress tests for the assessment of multifidelity optimization methods. In addition, the paper discusses a comprehensive ensemble of metrics and criteria recommended for the rigorous and meaningful assessment of the performance of multifidelity strategies and algorithms

Slice Stretching at the Event Horizon when Geodesically Slicing the Schwarzschild Spacetime with Excision

Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.Comment: 5 pages, 2 figures, published version including minor amendments suggested by the refere

An Adjoint-based Derivative Evaluation Method for Time-dependent Aeroelastic Optimization of Flexible Aircraft

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106483/1/AIAA2013-1530.pd

2022: Markus Peer Rumpfkeil, Milestone Book Selection

Promotion to the rank of Professor, Department of Mechanical and Aerospace Engineeringhttps://ecommons.udayton.edu/svc_milestone/1096/thumbnail.jp

Airfoil Optimization for Unsteady Flows with Application to High-lift Noise Reduction

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.Ph

Multi-Fidelity Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Analytical Benchmark Problems

In this article, multi-fidelity kriging and sparse polynomial chaos expansion (SPCE) surrogate models are constructed. In addition, a novel combination of the two surrogate approaches into a multi-fidelity SPCE-Kriging model will be presented. Accurate surrogate models, once obtained, can be employed for evaluating a large number of designs for uncertainty quantification, optimization, or design space exploration. Analytical benchmark problems are used to show that accurate multi-fidelity surrogate models can be obtained at lower computational cost than high-fidelity models. The benchmarks include non-polynomial and polynomial functions of various input dimensions, lower dimensional heterogeneous non-polynomial functions, as well as a coupled spring-mass-system. Overall, multi-fidelity models are more accurate than high-fidelity ones for the same cost, especially when only a few high-fidelity training points are employed. Full-order PCEs tend to be a factor of two or so worse than SPCES in terms of overall accuracy. The combination of the two approaches into the SPCE-Kriging model leads to a more accurate and flexible method overall

Unified Framework for Training Point Selection and Error Estimation for Surrogate Models

A unified framework for surrogate model training point selection and error estimation is proposed. Building auxiliary local surrogate models over subdomains of the global surrogate model forms the basis of the proposed framework. A discrepancy function, defined as the absolute difference between response predictions from local and global surrogate models for randomly chosen test candidates, drives the framework, thereby not requiring any additional exact function evaluations. The benefits of this new approach are demonstrated with analytical test functions and the construction of a two-dimensional aerodynamic database. The results show that the proposed training point selection approach improves the convergence monotonicity and produces more accurate surrogate models compared to random and quasi-random training point selection strategies. The introduced root-mean-square discrepancy and maximum absolute discrepancy exhibit close agreement with the actual root-mean-square error and maximum absolute error, respectively, and are therefore proposed as a measure for the approximation accuracy of surrogate models in applications of practical interest. Multivariate interpolation and regression is employed to build local surrogates, whereas kriging and polynomial chaos expansions serve as global surrogate models in demonstrating the applicability of the proposed framework