A GENERIC RELIABILITY ANALYSIS AND DESIGN FRAMEWORK WITH RANDOM PARAMETER, FIELD, AND PROCESS VARIABLES

This dissertation aims at developing a generic reliability analysis and design framework that enables reliability prediction and design improvement with random parameter, field, and process variables. The capability of this framework is further improved by predicting and managing reliability even with a dearth of data that can be used to characterize random variables. To accomplish the research goal, three research thrusts are set forth. First, advanced techniques are developed to characterize the random field or process. The fundamental idea of these techniques is to model the random field or process with a set of important field signatures and random variables. These techniques enable the use of random parameter, field, and process variables for reliability analysis and design even with a dearth of data. Second, a generic reliability analysis framework is proposed to accurately assess system reliability in the presence of random parameter, field, and process variables. An advanced probability analysis technique, the Eigenvector Dimension Reduction (EDR) method, is developed by integrating the Dimension Reduction (DR) method with three proposed improvements: 1) an eigenvector sampling approach to obtain statistically independent samples over a random space; 2) a Stepwise Moving Least Square (SMLS) method to accurately approximate system responses over a random space; and 3) a Probability Density Function (PDF) generation method to accurately approximate the PDF of system responses for reliability analysis. Third, a generic Reliability-Based Design Optimization (RBDO) framework is developed to solve engineering design problems with random parameter, field, and process variables. This design framework incorporates the EDR method into RBDO. To illustrate the effectiveness of the developed framework, many numerical and engineering examples are employed to conduct the reliability analysis and RBDO with random parameter, field, and process variables. This dissertation demonstrates that the developed framework is very accurate and efficient for the reliability analysis and RBDO of engineering products and processes

A wide field X-ray telescope for astronomical survey purposes: from theory to practice

X-ray mirrors are usually built in the Wolter I (paraboloid-hyperboloid) configuration. This design exhibits no spherical aberration on-axis but suffers from field curvature, coma and astigmatism, therefore the angular resolution degrades rapidly with increasing off-axis angles. Different mirror designs exist in which the primary and secondary mirror profiles are expanded as a power series in order to increase the angular resolution at large off-axis positions, at the expanses of the on-axis performances. Here we present the design and global trade off study of an X-ray mirror systems based on polynomial optics in view of the Wide Field X-ray Telescope (WFXT) mission. WFXT aims at performing an extended cosmological survey in the soft X-ray band with unprecedented flux sensitivity. To achieve these goals the angular resolution required for the mission is very demanding ~5 arcsec mean resolution across a 1-deg field of view. In addition an effective area of 5-9000 cm^2 at 1 keV is needed.Comment: Accepted for publication in the MNRAS (11pages, 3 table, 13 figures

Optimal design of mesostructured materials under uncertainty

The main objective of the topology optimization is to fulfill the objective function with the minimum amount of material. This reduces the overall cost of the structure and at the same time reduces the assembly, manufacturing and maintenance costs because of the reduced number of parts in the final structure. The concept of reliability analysis can be incorporated into the deterministic topology optimization method; this incorporated scheme is referred to as Reliability-based Topology Optimization (RBTO). In RBTO, the statistical nature of constraints and design problems are defined in the objective function and probabilistic constraint. The probabilistic constraint can specify the required reliability level of the system. In practical applications, however, finding global optimum in the presence of uncertainty is a difficult and computationally intensive task, since for every possible design a full stochastic analysis has to be performed for estimating various statistical parameters. Efficient methodologies are therefore required for the solution of the stochastic part and the optimization part of the design process. This research will explore a reliability-based synthesis method which estimates all the statistical parameters and finds the optimum while being less computationally intensive. The efficiency of the proposed method is achieved with the combination of topology optimization and stochastic approximation which utilizes a sampling technique such as Latin Hypercube Sampling (LHS) and surrogate modeling techniques such as Local Regression and Classification using Artificial Neural Networks (ANN). Local regression is comparatively less computationally intensive and produces good results in case of low probability of failures whereas Classification is particularly useful in cases where the reliability of failure has to be estimated with disjoint failure domains. Because classification using ANN is comparatively more computationally demanding than Local regression, classification is only used when local regression fails to give the desired level of goodness of fit. Nevertheless, classification is an indispensible tool in estimating the probability of failure when the failure domain is discontinuous. Representative examples will be demonstrated where the method is used to design customized meso-scale truss structures and a macro-scale hydrogen storage tank. The final deliverable from this research will be a less computationally intensive and robust RBTO procedure that can be used for design of truss structures with variable design parameters and force and boundary conditions.M.S.Committee Chair: Choi, Seung-Kyum; Committee Member: Muhanna, Rafi; Committee Member: Rosen, Davi

Black box simulation optimization:Generalized response surface methodology

The thesis consists of three papers in the area of Response Surface Methodology (RSM). The first paper deals with optimization problems with a single random objective. The contributions of that paper are a scale independent search direction and possible solutions for the step size. The second paper considers optimization problems with a single random objective and multiple random constraints, as well as deterministic box constraints. That paper extends RSM to cope with constraints, using ideas from interior point methods. Furthermore, it provides a heuristic to reach quickly a neighborhood of the optimum. The third paper copes with optimization problems with a single random objective and multiple random constraints. The contribution of that paper is an asymptotic stopping rule that tests the first-order necessary optimality conditions at a feasible point.

A simulation data-driven design approach for rapid product optimization

Traditional design optimization is an iterative process of design, simulation, and redesign, which requires extensive calculations and analysis. The designer needs to adjust and evaluate the design parameters manually and continually based on the simulation results until a satisfactory design is obtained. However, the expensive computational costs and large resource consumption of complex products hinder the wide application of simulation in industry. It is not an easy task to search the optimal design solution intelligently and efficiently. Therefore, a simulation data-driven design approach which combines dynamic simulation data mining and design optimization is proposed to achieve this purpose in this study. The dynamic simulation data mining algorithm—on-line sequential extreme learning machine with adaptive weights (WadaptiveOS-ELM)—is adopted to train the dynamic prediction model to effectively evaluate the merits of new design solutions in the optimization process. Meanwhile, the prediction model is updated incrementally by combining new “good” data set to reduce the modeling cost and improve the prediction accuracy. Furthermore, the improved heuristic optimization algorithm—adaptive and weighted center particle swarm optimization (AWCPSO)—is introduced to guide the design change direction intelligently to improve the search efficiency. In this way, the optimal design solution can be searched automatically with less actual simulation iterations and higher optimization efficiency, and thus supporting the rapid product optimization effectively. The experimental results demonstrate the feasibility and effectiveness of the proposed approach

The Fifth NASA/DOD Controls-Structures Interaction Technology Conference, part 2

This publication is a compilation of the papers presented at the Fifth NASA/DoD Controls-Structures Interaction (CSI) Technology Conference held in Lake Tahoe, Nevada, March 3-5, 1992. The conference, which was jointly sponsored by the NASA Office of Aeronautics and Space Technology and the Department of Defense, was organized by the NASA Langley Research Center. The purpose of this conference was to report to industry, academia, and government agencies on the current status of controls-structures interaction technology. The agenda covered ground testing, integrated design, analysis, flight experiments and concepts

Black Box Simulation Optimization: Generalized Response Surface Methodology.

The thesis consists of three papers in the area of Response Surface Methodology (RSM). The first paper deals with optimization problems with a single random objective. The contributions of that paper are a scale independent search direction and possible solutions for the step size. The second paper considers optimization problems with a single random objective and multiple random constraints, as well as deterministic box constraints. That paper extends RSM to cope with constraints, using ideas from interior point methods. Furthermore, it provides a heuristic to reach quickly a neighborhood of the optimum. The third paper copes with optimization problems with a single random objective and multiple random constraints. The contribution of that paper is an asymptotic stopping rule that tests the first-order necessary optimality conditions at a feasible point.

Non-convex Optimization for Machine Learning

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-convex function. This is especially true of algorithms that operate in high-dimensional spaces or that train non-linear models such as tensor models and deep networks. The freedom to express the learning problem as a non-convex optimization problem gives immense modeling power to the algorithm designer, but often such problems are NP-hard to solve. A popular workaround to this has been to relax non-convex problems to convex ones and use traditional methods to solve the (convex) relaxed optimization problems. However this approach may be lossy and nevertheless presents significant challenges for large scale optimization. On the other hand, direct approaches to non-convex optimization have met with resounding success in several domains and remain the methods of choice for the practitioner, as they frequently outperform relaxation-based techniques - popular heuristics include projected gradient descent and alternating minimization. However, these are often poorly understood in terms of their convergence and other properties. This monograph presents a selection of recent advances that bridge a long-standing gap in our understanding of these heuristics. The monograph will lead the reader through several widely used non-convex optimization techniques, as well as applications thereof. The goal of this monograph is to both, introduce the rich literature in this area, as well as equip the reader with the tools and techniques needed to analyze these simple procedures for non-convex problems.Comment: The official publication is available from now publishers via http://dx.doi.org/10.1561/220000005