Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries

Persistent Link:
http://hdl.handle.net/10150/201491
Title:
Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries
Author:
Basudhar, Anirban
Issue Date:
2011
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This dissertation presents a sampling-based method that can be used for uncertainty quantification and deterministic or probabilistic optimization. The objective is to simultaneously address several difficulties faced by classical techniques based on response values and their gradients. In particular, this research addresses issues with discontinuous and binary (pass or fail) responses, and multiple failure modes. All methods in this research are developed with the aim of addressing problems that have limited data due to high cost of computation or experiment, e.g. vehicle crashworthiness, fluid-structure interaction etc.The core idea of this research is to construct an explicit boundary separating allowable and unallowable behaviors, based on classification information of responses instead of their actual values. As a result, the proposed method is naturally suited to handle discontinuities and binary states. A machine learning technique referred to as support vector machines (SVMs) is used to construct the explicit boundaries. SVM boundaries can be highly nonlinear, which allows one to use a single SVM for representing multiple failure modes.One of the major concerns in the design and uncertainty quantification communities is to reduce computational costs. To address this issue, several adaptive sampling methods have been developed as part of this dissertation. Specific sampling methods have been developed for reliability assessment, deterministic optimization, and reliability-based design optimization. Adaptive sampling allows the construction of accurate SVMs with limited samples. However, like any approximation method, construction of SVM is subject to errors. A new method to quantify the prediction error of SVMs, based on probabilistic support vector machines (PSVMs) is also developed. It is used to provide a relatively conservative probability of failure to mitigate some of the adverse effects of an inaccurate SVM. In the context of reliability assessment, the proposed method is presented for uncertainties represented by random variables as well as spatially varying random fields.In order to validate the developed methods, analytical problems with known solutions are used. In addition, the approach is applied to some application problems, such as structural impact and tolerance optimization, to demonstrate its strengths in the context of discontinuous responses and multiple failure modes.
Type:
text; Electronic Dissertation
Keywords:
explicit decision boundaries; multiple failure modes; reliability based design optimization; support vector machines; Mechanical Engineering; adaptive sampling; discontinuous and binary responses
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mechanical Engineering
Degree Grantor:
University of Arizona
Advisor:
Missoum, Samy

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleComputational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundariesen_US
dc.creatorBasudhar, Anirbanen_US
dc.contributor.authorBasudhar, Anirbanen_US
dc.date.issued2011-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis dissertation presents a sampling-based method that can be used for uncertainty quantification and deterministic or probabilistic optimization. The objective is to simultaneously address several difficulties faced by classical techniques based on response values and their gradients. In particular, this research addresses issues with discontinuous and binary (pass or fail) responses, and multiple failure modes. All methods in this research are developed with the aim of addressing problems that have limited data due to high cost of computation or experiment, e.g. vehicle crashworthiness, fluid-structure interaction etc.The core idea of this research is to construct an explicit boundary separating allowable and unallowable behaviors, based on classification information of responses instead of their actual values. As a result, the proposed method is naturally suited to handle discontinuities and binary states. A machine learning technique referred to as support vector machines (SVMs) is used to construct the explicit boundaries. SVM boundaries can be highly nonlinear, which allows one to use a single SVM for representing multiple failure modes.One of the major concerns in the design and uncertainty quantification communities is to reduce computational costs. To address this issue, several adaptive sampling methods have been developed as part of this dissertation. Specific sampling methods have been developed for reliability assessment, deterministic optimization, and reliability-based design optimization. Adaptive sampling allows the construction of accurate SVMs with limited samples. However, like any approximation method, construction of SVM is subject to errors. A new method to quantify the prediction error of SVMs, based on probabilistic support vector machines (PSVMs) is also developed. It is used to provide a relatively conservative probability of failure to mitigate some of the adverse effects of an inaccurate SVM. In the context of reliability assessment, the proposed method is presented for uncertainties represented by random variables as well as spatially varying random fields.In order to validate the developed methods, analytical problems with known solutions are used. In addition, the approach is applied to some application problems, such as structural impact and tolerance optimization, to demonstrate its strengths in the context of discontinuous responses and multiple failure modes.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectexplicit decision boundariesen_US
dc.subjectmultiple failure modesen_US
dc.subjectreliability based design optimizationen_US
dc.subjectsupport vector machinesen_US
dc.subjectMechanical Engineeringen_US
dc.subjectadaptive samplingen_US
dc.subjectdiscontinuous and binary responsesen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMechanical Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorMissoum, Samyen_US
dc.contributor.committeememberMissoum, Samyen_US
dc.contributor.committeememberNikravesh, Parvisen_US
dc.contributor.committeememberHaldar, Achintyaen_US
dc.contributor.committeememberBayraksan, Guzinen_US
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