Browsing by Subject "Response surface"
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Item Design, synthesis, and engineering of advanced materials for block copolymer lithography(2015-05) Durand, William John; Willson, C. Grant, 1939-; Ellison, Christopher J.; Bonnecaze, Roger T; Truskett, Thomas M; Akinwande, DejiBlock copolymers (BCPs) are an attractive alternative for patterning applications used to produce next-generation microelectronic devices. Advancements require the development of high interaction parameter χ BCPs that enable patterning at the sub-10 nm length scale. Several organosilicon BCPs were designed to both enhance χ and impart an inherent etch selectivity that facilitates pattern transfer processes. Increasing the BCP silicon content both increases χ and bolsters the etch resistance, providing a pathway to designing new high-χ materials. Unfortunately, the BCPs investigated are not amenable to thermal annealing because the organosilicon block preferentially segregates to an air/vacuum interface and drives orientation parallel to the surface. A series of spin-coatable, polarity-switching top coats (as well as other strategies) were developed to provide a “neutral” top interface and promote the perpendicular orientation of BCP domains. In addition, a methodology for evaluating the neutral condition, relying on thickness quantization and the corresponding wetting behavior (i.e. island/hole topography) of lamellae. The top coat strategy was demonstrated for several BCP systems, and perpendicular structures can successfully be etched on commercial tools and be transferred into underlying substrates. The interaction parameter χ was evaluated using two methods to compare the performance of several BCPs: the order-disorder transition (ODT) of symmetric diblock copolymers, and the absolute scattering profile of a disordered BCP melt. Both methods, while severely limited for quantitative comparison, indicate trends towards higher χ with additional appended polar and organosilicon functional groups. Furthermore, the pattern fidelity is shown to be a function of the overall BCP segregation strength. The free energy of confined lamella was modeled algebraically to produce response surface plots capable of identifying process conditions favorable for perpendicular orientation. Thickness independent perpendicular orientation is only favorable using two neutral interfaces. Incommensurate film thicknesses are the most favorable, with commensurability conditions dependent on the wetting behavior at each interface. The modeling was supplemented with an extensive body of thin film experimental work that qualitatively agrees well with the above conclusions.Item Hessian-based response surface approximations for uncertainty quantification in large-scale statistical inverse problems, with applications to groundwater flow(2013-08) Flath, Hannah Pearl; Ghattas, Omar N.Subsurface flow phenomena characterize many important societal issues in energy and the environment. A key feature of these problems is that subsurface properties are uncertain, due to the sparsity of direct observations of the subsurface. The Bayesian formulation of this inverse problem provides a systematic framework for inferring uncertainty in the properties given uncertainties in the data, the forward model, and prior knowledge of the properties. We address the problem: given noisy measurements of the head, the pdf describing the noise, prior information in the form of a pdf of the hydraulic conductivity, and a groundwater flow model relating the head to the hydraulic conductivity, find the posterior probability density function (pdf) of the parameters describing the hydraulic conductivity field. Unfortunately, conventional sampling of this pdf to compute statistical moments is intractable for problems governed by large-scale forward models and high-dimensional parameter spaces. We construct a Gaussian process surrogate of the posterior pdf based on Bayesian interpolation between a set of "training" points. We employ a greedy algorithm to find the training points by solving a sequence of optimization problems where each new training point is placed at the maximizer of the error in the approximation. Scalable Newton optimization methods solve this "optimal" training point problem. We tailor the Gaussian process surrogate to the curvature of the underlying posterior pdf according to the Hessian of the log posterior at a subset of training points, made computationally tractable by a low-rank approximation of the data misfit Hessian. A Gaussian mixture approximation of the posterior is extracted from the Gaussian process surrogate, and used as a proposal in a Markov chain Monte Carlo method for sampling both the surrogate as well as the true posterior. The Gaussian process surrogate is used as a first stage approximation in a two-stage delayed acceptance MCMC method. We provide evidence for the viability of the low-rank approximation of the Hessian through numerical experiments on a large scale atmospheric contaminant transport problem and analysis of an infinite dimensional model problem. We provide similar results for our groundwater problem. We then present results from the proposed MCMC algorithms.Item Optimization using sequential approach for triangular tube structure in crashworthiness(2005-05) Sun, Junning; Ekwaro-Osire, Stephen; Maxwell, Timothy T.; Zhang, Hong-Chao; Hsiang, Simon M.; Ertas, AtilaCrashworthiness technology strives to protect occupants by maintaining the structural integrity and by converting the kinetic energy into other forms; and at the same time, the lower crashing force the occupants are being undertaken, the more safety the occupants would obtain. This is a dissertation research that intends to design a component (front horn) of a vehicle’s bumper through optimizing the shape, dimension and parameters of a triangular tube structure in deterministic and probabilistic method in order to accomplish such purpose. The design has combined two new characteristics into the front horn: triangular tube structure and Reliability-Based Design Optimization (RBDO), using explicit finite element code Ls-Dyna as a simulation tool. The research is based on the fact that a triangular thin tube possesses the lowest crushing mean force, and the front horn is an important tubular structure for reducing injuries of front collision. RSM is used to identify the optimal shape of the triangular tube, applying the lowest Load Difference LD as objective function. The result shows that the equilateral triangular tube possesses the lowest LD value. The dimension optimization is carried out to determine the optimal dimensions of triangular tube under the same impacting condition, taking the load uniformity LU as the objective function and mean crushing force and absorbed energy as constraints based on Least Square method and nonlinear programming. The optimal dimension is 80 (mm) and 3 (mm) for lateral length and thickness respectively. Using the result and the formulation of dimension optimization, the tapered part of front horn is designed and optimized on the bases of RBDO, which assumes design variables with normal distribution. With addition of Monte Carlo method as another simulation tool, performance functions of reliability are generated in the same design domain. The final result is genetic shape and dimensions of a front horn possessing LU = 1.36, Fm = 52.47 (KN) with the reliability 0.94 of less than 55.04 (KN), and E = 9247 (J) with the reliability 1.0 larger than 8000 (J). Meanwhile a novel method of RBDO with a mapping technique for optimization is developed instead of using a safety index or performance objective, through determination of reliability domain.Item Optimization using sequential approach for triangular tube structure in crashworthiness(Texas Tech University, 2005-05) Sun, Junning; Ekwaro-Osire, Stephen; Maxwell, Timothy T.; Zhang, Hong-Chao; Hsiang, Simon M.; Ertas, AtilaCrashworthiness technology strives to protect occupants by maintaining the structural integrity and by converting the kinetic energy into other forms; and at the same time, the lower crashing force the occupants are being undertaken, the more safety the occupants would obtain. This is a dissertation research that intends to design a component (front horn) of a vehicle’s bumper through optimizing the shape, dimension and parameters of a triangular tube structure in deterministic and probabilistic method in order to accomplish such purpose. The design has combined two new characteristics into the front horn: triangular tube structure and Reliability-Based Design Optimization (RBDO), using explicit finite element code Ls-Dyna as a simulation tool. The research is based on the fact that a triangular thin tube possesses the lowest crushing mean force, and the front horn is an important tubular structure for reducing injuries of front collision. RSM is used to identify the optimal shape of the triangular tube, applying the lowest Load Difference LD as objective function. The result shows that the equilateral triangular tube possesses the lowest LD value. The dimension optimization is carried out to determine the optimal dimensions of triangular tube under the same impacting condition, taking the load uniformity LU as the objective function and mean crushing force and absorbed energy as constraints based on Least Square method and nonlinear programming. The optimal dimension is 80 (mm) and 3 (mm) for lateral length and thickness respectively. Using the result and the formulation of dimension optimization, the tapered part of front horn is designed and optimized on the bases of RBDO, which assumes design variables with normal distribution. With addition of Monte Carlo method as another simulation tool, performance functions of reliability are generated in the same design domain. The final result is genetic shape and dimensions of a front horn possessing LU = 1.36, Fm = 52.47 (KN) with the reliability 0.94 of less than 55.04 (KN), and E = 9247 (J) with the reliability 1.0 larger than 8000 (J). Meanwhile a novel method of RBDO with a mapping technique for optimization is developed instead of using a safety index or performance objective, through determination of reliability domain.