Document Type

Dissertation

Date of Degree

Spring 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mechanical Engineering

First Advisor

Sharif Rahman

Abstract

The primary objective of this study is to develop new computational methods for robust design optimization (RDO) and reliability-based design optimization (RBDO) of high-dimensional, complex engineering systems. Four major research directions, all anchored in polynomial dimensional decomposition (PDD), have been defined to meet the objective. They involve: (1) development of new sensitivity analysis methods for RDO and RBDO; (2) development of novel optimization methods for solving RDO problems; (3) development of novel optimization methods for solving RBDO problems; and (4) development of a novel scheme and formulation to solve stochastic design optimization problems with both distributional and structural design parameters.

The major achievements are as follows. Firstly, three new computational methods were developed for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random inputs. The first method represents a novel integration of PDD of a multivariate stochastic response function and score functions, leading to analytical expressions of design sensitivities of the first two moments. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the PDD approximation and score functions. For all three methods developed, both the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Secondly, four new methods were developed for RDO of complex engineering systems. The methods involve PDD of a high-dimensional stochastic response for statistical moment analysis, a novel integration of PDD and score functions for calculating the second-moment sensitivities with respect to the design variables, and standard gradient-based optimization algorithms. The methods, depending on how statistical moment and sensitivity analyses are dovetailed with an optimization algorithm, encompass direct, single-step, sequential, and multi-point single-step design processes. Thirdly, two new methods were developed for RBDO of complex engineering systems. The methods involve an adaptive-sparse polynomial dimensional decomposition (AS-PDD) of a high-dimensional stochastic response for reliability analysis, a novel integration of AS-PDD and score functions for calculating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point, single-step design process. The two methods, depending on how the failure probability and its design sensitivities are evaluated, exploit two distinct combinations built on AS-PDD: the AS-PDD-SPA method, entailing SPA and score functions; and the AS-PDD-MCS method, utilizing the embedded MCS of the AS-PDD approximation and score functions. In addition, a new method, named as the augmented PDD method, was developed for RDO and RBDO subject to mixed design variables, comprising both distributional and structural design variables. The method comprises a new augmented PDD of a high-dimensional stochastic response for statistical moment and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms, leading to a multi-point, single-step design process.

The innovative formulations of statistical moment and reliability analysis, design sensitivity analysis, and optimization algorithms have achieved not only highly accurate but also computationally efficient design solutions. Therefore, these new methods are capable of performing industrial-scale design optimization with numerous design variables.

Public Abstract

A great many complex systems and engineering structures are innately plagued by extant uncertainties found in manufacturing processes and operating environments. Under this Ph.D. study, design optimization of complex systems in the presence of uncertainty was conducted; in other words, developing methods to achieve the best possible design solution in which the nature of the system behavior is uncertain. The research involved new fundamental developments and integration of novel computational methods to study two principal classes of design optimization: (1) robust design optimization, which improves product quality by reducing the sensitivity of an optimal design; and (2) reliability-based design optimization, which concentrates on attaining an optimal design by ensuring sufficiently low risk of failure. Depending on the objective set forth by a designer, uncertainty is effectively mitigated by these design optimization methods. The innovative formulations of statistical moment and reliability analyses, design sensitivity analysis, and optimization algorithms - the necessary ingredients of the computer models developed - have achieved not only highly accurate, but also computationally efficient design solutions. Therefore, these new models are capable of performing industrial-scale design optimization with numerous design variables. Potential engineering applications comprise ground vehicle design for improved durability and crashworthiness, fatigue- and fracture-resistant design for civil and aerospace applications, and reliable design of microelectronic packaging under harsh environments, to name a few.

Keywords

publicabstract, Design Under Uncertainties, mixed design variables, Polynomial dimensional decomposition, Orthogonal polynomials, Reliability-based Design Optimization, Robust Design Optimization, Score Function, Saddlepoint approximation

Pages

xviii, 287 pages

Bibliography

Includes bibliographical references (pages 279-287).

Comments

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Copyright

Copyright 2015 Xuchun Ren

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