Browsing by Subject "nonlinear optimization"
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Item An effective dimensional inspection method based on zone fitting(Texas A&M University, 2006-04-12) Pendse, Nachiket VishwasCoordinate measuring machines are widely used to generate data points from an actual surface. The generated measurement data must be analyzed to yield critical geometric deviations of the measured part according to the requirements specified by the designer. However, ANSI standards do not specify the methods that should be used to evaluate the tolerances. The coordinate measuring machines employ different verification algorithms which may yield different results. Functional requirements or assembly conditions on a manufactured part are normally translated into geometric constraints to which the part must conform. Minimum zone evaluation technique is used when the measured data is regarded as an exact copy of the actual surface and the tolerance zone is represented as geometric constraints on the data. In the present study, a new zone-fitting algorithm is proposed. The algorithm evaluates the minimum zone that encompasses the set of measured points from the actual surface. The search for the rigid body transformation that places the set of points in the zone is modeled as a nonlinear optimization problem. The algorithm is employed to find the form tolerance of 2-D (line, circle) as well as 3-D geometries (cylinder). It is also used to propose an inspection methodology for turbine blades. By constraining the transformation parameters, the proposed methodology determines whether the points measured at the 2-D cross-sections fit in the corresponding tolerance zones simultaneously.Item Efficient Nonlinear Optimization with Rigorous Models for Large Scale Industrial Chemical Processes(2011-08-08) Zhu, YuLarge scale nonlinear programming (NLP) has proven to be an effective framework for obtaining profit gains through optimal process design and operations in chemical engineering. While the classical SQP and Interior Point methods have been successfully applied to solve many optimization problems, the focus of both academia and industry on larger and more complicated problems requires further development of numerical algorithms which can provide improved computational efficiency. The primary purpose of this dissertation is to develop effective problem formulations and an advanced numerical algorithms for efficient solution of these challenging problems. As problem sizes increase, there is a need for tailored algorithms that can exploit problem specific structure. Furthermore, computer chip manufacturers are no longer focusing on increased clock-speeds, but rather on hyperthreading and multi-core architectures. Therefore, to see continued performance improvement, we must focus on algorithms that can exploit emerging parallel computing architectures. In this dissertation, we develop an advanced parallel solution strategy for nonlinear programming problems with block-angular structure. The effectiveness of this and modern off-the-shelf tools are demonstrated on a wide range of problem classes. Here, we treat optimal design, optimal operation, dynamic optimization, and parameter estimation. Two case studies (air separation units and heat-integrated columns) are investigated to deal with design under uncertainty with rigorous models. For optimal operation, this dissertation takes cryogenic air separation units as a primary case study and focuses on formulations for handling uncertain product demands, contractual constraints on customer satisfaction levels, and variable power pricing. Multiperiod formulations provide operating plans that consider inventory to meet customer demands and improve profits. In the area of dynamic optimization, optimal reference trajectories are determined for load changes in an air separation process. A multiscenario programming formulation is again used, this time with large-scale discretized dynamic models. Finally, to emphasize a different decomposition approach, we address a problem with significant spatial complexity. Unknown water demands within a large scale city-wide distribution network are estimated. This problem provides a different decomposition mechanism than the multiscenario or multiperiod problems; nevertheless, our parallel approach provides effective speedup.Item Optimal Screening for Preclinical Diseases(2014-05-19) Li, AngCertain diseases comprise an initial asymptomatic period during which they can be identified only by a screening test. In many such cases, early detection translates into benefits of more treatment options and potentially better prognosis. In this dissertation, we consider the optimal policy to screen for a preclinical disease while under limited budget. Our objective is to place any given number of screening epochs over an individual's lifetime, such that the probability of identifying the disease while preclinical is maximized. We make mild assumptions about the sojourn times of the individual in the healthy and preclinical states, and we consider the possibility of fallible screening tests. We show that a unique optimal sequence of screening times exist for our model, and that it can be quickly found by any greedy-search algorithm. We further conduct numerical experimentations by which we identify sensitive model inputs. We lastly apply our model to breast cancer screening using practical information and we investigate additional characteristics of this model.