Matching Items (3)

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Toward an Uncertain Modeling of Hypersonic Aerodynamic Forces

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The focus of this investigation is on the development of a surrogate model of hypersonic aerodynamic forces on structures to reduce the computational effort involved in the determination of the

The focus of this investigation is on the development of a surrogate model of hypersonic aerodynamic forces on structures to reduce the computational effort involved in the determination of the structural response. The application is more precisely focused on uncertain structures. Then, following an uncertainty management strategy, the surrogate may exhibit an error with respect to Computational Fluid Dynamics (CFD) reference data as long as that error does not significantly affect the uncertainty band of the structural response. Moreover, this error will be treated as an epistemic uncertainty introduced in the model thereby generating an uncertain surrogate. Given this second step, the aerodynamic surrogate is limited to those exhibiting simple analytic forms with parameters that can be identified from CFD data.

The first phase of the investigation focuses on the selection of an appropriate form for the surrogate for the 1-dimensional flow over a flat clamped-clamped. Following piston theory, the model search started with purely local models, linear and nonlinear of the local slope. A second set of models was considered that involve also the local displacement, curvature, and integral of displacement and an improvement was observed that can be attributed to a global effect of the pressure distribution. Various ways to involve such a global effect were next investigated eventually leading to a two-level composite model based on the sum of a local component represented as a cubic polynomial of the downwash and a global component represented by an auto-regressive moving average (ARMA) model driven nonlinearly by the local downwash. This composite model is applicable to both steady pressure distributions with the downwash equal to the slope and to unsteady cases with the downwash as partial derivative with time in addition to steady.

The second part of the investigation focused on the introduction of the epistemic uncertainty in the aerodynamic surrogate and it was recognized that it could be achieved by randomizing the coefficients of the local and/or the auto-regressive components of the model. In fact, the combination of the two effects provided an applicable strategy.

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Created

Date Created
  • 2017

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Least-squares fit for points measured along line-profiles formed from line and arc segments

Description

Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. A full life cycle for many mechanical devices depends (i) on a wise assignment

Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. A full life cycle for many mechanical devices depends (i) on a wise assignment of tolerances during design and (ii) on careful quality control of the manufacturing process to ensure adherence to the specified tolerances. This thesis describes a new method for quality control of a manufacturing process by improving the method used to convert measured points on a part to a geometric entity that can be compared directly with tolerance specifications. The focus of this paper is the development of a new computational method for obtaining the least-squares fit of a set of points that have been measured with a coordinate measurement machine along a line-profile. The pseudo-inverse of a rectangular matrix is used to convert the measured points to the least-squares fit of the profile. Numerical examples are included for convex and concave line-profiles, that are formed from line- and circular arc-segments.

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Created

Date Created
  • 2013

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Multi-label dimensionality reduction

Description

Multi-label learning, which deals with data associated with multiple labels simultaneously, is ubiquitous in real-world applications. To overcome the curse of dimensionality in multi-label learning, in this thesis I study

Multi-label learning, which deals with data associated with multiple labels simultaneously, is ubiquitous in real-world applications. To overcome the curse of dimensionality in multi-label learning, in this thesis I study multi-label dimensionality reduction, which extracts a small number of features by removing the irrelevant, redundant, and noisy information while considering the correlation among different labels in multi-label learning. Specifically, I propose Hypergraph Spectral Learning (HSL) to perform dimensionality reduction for multi-label data by exploiting correlations among different labels using a hypergraph. The regularization effect on the classical dimensionality reduction algorithm known as Canonical Correlation Analysis (CCA) is elucidated in this thesis. The relationship between CCA and Orthonormalized Partial Least Squares (OPLS) is also investigated. To perform dimensionality reduction efficiently for large-scale problems, two efficient implementations are proposed for a class of dimensionality reduction algorithms, including canonical correlation analysis, orthonormalized partial least squares, linear discriminant analysis, and hypergraph spectral learning. The first approach is a direct least squares approach which allows the use of different regularization penalties, but is applicable under a certain assumption; the second one is a two-stage approach which can be applied in the regularization setting without any assumption. Furthermore, an online implementation for the same class of dimensionality reduction algorithms is proposed when the data comes sequentially. A Matlab toolbox for multi-label dimensionality reduction has been developed and released. The proposed algorithms have been applied successfully in the Drosophila gene expression pattern image annotation. The experimental results on some benchmark data sets in multi-label learning also demonstrate the effectiveness and efficiency of the proposed algorithms.

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Created

Date Created
  • 2011