We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focused on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design- oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors'' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

/pdf/multidisciplinary-aerospace-design-optimization-survey-of-3xuwvr970l.pdf

Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments

The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focussed on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design-oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

/pdf/multidisciplinary-aerospace-design-optimization-survey-of-ghzjxaiur6.pdf

Multidisciplinary aerospace design optimization: Survey of recent developments

Recent developments are reviewed in two major areas of structural sensitivity analysis: sensitivity of static and transient response; and sensitivity of vibration and buckling eigenproblems. Recent developments from the standpoint of computational cost, accuracy, and ease of implementation are presented. In the area of static response, current interest is focused on sensitivity to shape variation and sensitivity of nonlinear response. Two general approaches are used for computing sensitivities: differentiation of the continuum equations followed by discretization, and the reverse approach of discretization followed by differentiation. It is shown that the choice of methods has important accuracy and implementation implications. In the area of eigenproblem sensitivity, there is a great deal of interest and significant progress in sensitivity of problems with repeated eigenvalues. In addition to reviewing recent contributions in this area, the paper raises the issue of differentiability and continuity associated with the occurrence of repeated eigenvalues.

/pdf/recent-developments-in-structural-sensitivity-analysis-23fy9nqyl5.pdf

Recent developments in structural sensitivity analysis

Structural optimization with frequency constraints - A review

Structural optimization of a hingeless rotor is investigated to reduce oscillatory hub loads while maintaining aeroelastic stability in forward flight. Design variables include spanwise distribution of nonstructural mass, chordwise location of blade center of gravity and blade bending stiffnesses (flap, lag and torsion). A comprehensive aeroelastic analysis of rotors, based on a finite element method in space and time, is linked with optimization algorithms to perform optimization of rotor blades. Sensitivity derivatives of blade response, hub loads, and eigenvalues with respect to the design variables are derived using a direct analytical approach, and constitute an integral part of the basic blade response and stability analyses. This approach reduces the computation time substantially; an 80 percent reduction of CPU time to achieve an optimum solution, as compared to the widely adopted finite difference approach. Through stiffness and nonstructural mass distributions, a 60-90 percent reduction in all six 4/rev hub loads is achieved for a four-bladed soft-inplane rotor.

Aeroelastic optimization of a helicopter rotor

Capability Enhancements in Version 3 of the Helios High-Fidelity Rotorcraft Simulation Code

The hover performance data of full-scale and model-scale coaxial rotors have been compared with CAMRAD II predictions having a free vortex wake analysis. Performance correlations of a coaxial rotor were made with a variation of key parameters including the rotor spacing and height. To understand aerodynamic behavior of the U.S. Army Aeroflightdynamics Directorate(AFDD)coaxialrotoroperatingoverarangeofReynoldsnumbersfrom36,000to180,000,theReynoldsnumber scaling effect was explored using an airfoil design code, MSES. It was found that the coaxial rotor spacing effect on hover performance was minimal for the rotor spacing larger than 20% of the rotor diameter. The measured performance data showed that more thrust was lost from the lower rotor of a coaxial than the upper rotor due to a larger rotor-to-rotor wake interference effect, and the lower rotor kept only an 81% of the single rotor OGE (out-of-ground effect) thrust whereas the upper rotor maintained a 90%. The lower rotor IGE (in-ground effect) thrust increased quickly by 26% as the rotor approached to the ground from the position of an 80% of the rotor diameter to 10%, and the corresponding IGE power increased by 17%. These thrust and power characteristics were well predicted. Overall, the performance prediction for the coaxial rotor was satisfactory when compared with the measured data.

Hover Performance Correlation for Full-Scale and Model-Scale Coaxial Rotors

Aeroelastic Optimization of a Helicopter Rotor

Significant advancements in computational fluid dynamics (CFD) and their coupling with computational structural dynamics (CSD, or comprehensive codes) for rotorcraft applications have been achieved recently. Despite this, CSD codes with their engineering level of modeling the rotor blade dynamics, the unsteady sectional aerodynamics and the vortical wake are still the workhorse for the majority of applications. This is especially true when a large number of parameter variations is to be performed and their impact on performance, structural loads, vibration and noise is to be judged in an approximate yet reliable and as accurate as possible manner. In this article, the capabilities of such codes are evaluated using the HART II International Workshop database, focusing on a typical descent operating condition which includes strong blade–vortex interactions. A companion article addresses the CFD/CSD coupled approach. Three cases are of interest: the baseline case and two cases with 3/rev higher harmonic blade root pitch control (HHC) with different control phases employed. One setting is for minimum blade–vortex interaction noise radiation and the other one for minimum vibration generation. The challenge is to correctly predict the wake physics—especially for the cases with HHC—and all the dynamics, aerodynamics, modifications of the wake structure and the aero-acoustics coming with it. It is observed that the comprehensive codes used today have a surprisingly good predictive capability when they appropriately account for all of the physics involved. The minimum requirements to obtain these results are outlined.

Joon W. Lim

Papers

Aeroelastic optimization of a helicopter rotor

Capability Enhancements in Version 3 of the Helios High-Fidelity Rotorcraft Simulation Code

Hover Performance Correlation for Full-Scale and Model-Scale Coaxial Rotors

Aeroelastic Optimization of a Helicopter Rotor

The HART II international workshop: an assessment of the state-of-the-art in comprehensive code prediction