EXTENDING AND IMPROVING DESIGNS FOR LARGE-SCALE COMPUTER EXPERIMENTS

This research develops methods that increase the inventory of space-filling designs (SFDs) for large-scale computer-based experiments. We present a technique enabling researchers to add sequential blocks of design points effectively and efficiently to existing SFDs. We accomplish this through a quadratically constrained mixed-integer program that augments cataloged or computationally expensive designs by optimally permuting and stacking columns of an initial base design to minimize the maximum absolute pairwise correlation among columns in the new extended design. We extend many classes of SFDs to dimensions that are currently not easily obtainable. Adding new design points provides more degrees of freedom for building metamodels and assessing fit. The resulting extended designs have better correlation and space-filling properties than the original base designs and compare well with other types of SFDs created from scratch in the extended design space. In addition, through massive computer-based experimentation, we compare popular software packages for generating SFDs and provide insight into the methods and relationships among design measures of correlation and space-fillingness. These results provide experimenters with a broad understanding of SFD software packages, algorithms, and optimality criteria. Further, we provide a probability-distribution model for the maximum absolute pairwise correlation among columns in the widely used maximin Latin hypercube designs.Lieutenant Colonel, United States Marine CorpsApproved for public release. Distribution is unlimited

Inclusion of Geometrically Nonlinear Aeroelastic Effects into Gradient-Based Aircraft Optimization

While aircraft have largely featured flexible wings for decades, more recently, aircraft structures have rapidly become more flexible. The pursuit of longer ranges and higher efficiency through higher aspect ratio wings, as well as the introduction of modern, light-weight materials has yielded moderately and very flexible aircraft configurations. Past accidents, such as the loss of the Helios High Altitude Long Endurance (HALE) aircraft have highlighted the limitations of linear analysis methods and demonstrated the peril of neglecting nonlinear effects when designing such aircraft. In particular, accounting for geometrical nonlinearities in flutter analyses become necessary in aircraft optimization, including transport aircraft, or future aircraft may require costly modifications late in the design process to fulfill certification requirements. As a result, there is a need to account for geometrical nonlinearities earlier in the design process and integrate these analyses directly into the multi-disciplinary design optimization (MDO) problems. This thesis investigates geometrically nonlinear flutter problems and how these should be integrated into aircraft MDO problems. First, flutter problems with and without geometrical nonlinearities are discussed and a unifying interpretation is presented. Furthermore, methods for interpreting nonlinear flutter problems are proposed and differences between linear and nonlinear flutter problem interpretation are discussed. Next, a flutter constraint formulation which accounts for geometrically nonlinear effects using beam-based analyses is presented. The resulting constraint uses a Kreisselmeiser-Steinhauser aggregation function to yield a scalar constraint from flight envelope flutter damping values. While the constraint enforces feasibility over the entire flight envelope, how the flight envelope is sampled largely determines the flutter constraint’s accuracy. To this end, a constrained Maximin approach, which is applicable for non-hypercube spaces, is used to sample the flight envelope and obtain a low-discrepancy sample set. The flutter constraint is then implemented using a beam-based geometrically nonlinear aeroelastic simulation code, UM/NAST. As gradient-based optimization methods are used in MDO due to the large number of design variables in aircraft design problems, the flutter constraint requires the recovery of flutter damping sensitivities. These are obtained by applying algorithmic differentiation (AD) to the UM/NAST code base. This enables the recovery of gradients for any solution type (static, modal, dynamic, and flutter/stability) with respect to any local design variable available within UM/NAST. The performance of the gradient prediction is studied and a hybrid primal-AD scheme is developed to obtain the coupled nonlinear aeroelastic sensitivities. After verifying the accuracy and performance of the gradient evaluation, the flutter constraint was implemented in a sample optimization problem. Finally, a roadmap for including the beam-based flutter constraint within an aircraft design problem is presented using analyses of varying fidelity. To this end, analyses of appropriate fidelity are used depending on the output of interest. While a shell-based FEM model can recover stress distributions, and is therefore well-suited for strength constraints, they are ill-suited for geometrically nonlinear flutter constraints due to their computational cost. Analyses are presented for a high aspect ratio transport aircraft configuration to illustrate the proposed approach and highlight the necessity for the inclusion of a geometrically nonlinear flutter constraint.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163259/1/clupp_1.pd

Circuit Design

Circuit Design = Science + Art! Designers need a skilled "gut feeling" about circuits and related analytical techniques, plus creativity, to solve all problems and to adhere to the specifications, the written and the unwritten ones. You must anticipate a large number of influences, like temperature effects, supply voltages changes, offset voltages, layout parasitics, and numerous kinds of technology variations to end up with a circuit that works. This is challenging for analog, custom-digital, mixed-signal or RF circuits, and often researching new design methods in relevant journals, conference proceedings and design tools unfortunately gives the impression that just a "wild bunch" of "advanced techniques" exist. On the other hand, state-of-the-art tools nowadays indeed offer a good cockpit to steer the design flow, which include clever statistical methods and optimization techniques.Actually, this almost presents a second breakthrough, like the introduction of circuit simulators 40 years ago! Users can now conveniently analyse all the problems (discover, quantify, verify), and even exploit them, for example for optimization purposes. Most designers are caught up on everyday problems, so we fit that "wild bunch" into a systematic approach for variation-aware design, a designer's field guide and more. That is where this book can help! Circuit Design: Anticipate, Analyze, Exploit Variations starts with best-practise manual methods and links them tightly to up-to-date automation algorithms. We provide many tractable examples and explain key techniques you have to know. We then enable you to select and setup suitable methods for each design task - knowing their prerequisites, advantages and, as too often overlooked, their limitations as well. The good thing with computers is that you yourself can often verify amazing things with little effort, and you can use software not only to your direct advantage in solving a specific problem, but also for becoming a better skilled, more experienced engineer. Unfortunately, EDA design environments are not good at all to learn about advanced numerics. So with this book we also provide two apps for learning about statistic and optimization directly with circuit-related examples, and in real-time so without the long simulation times. This helps to develop a healthy statistical gut feeling for circuit design. The book is written for engineers, students in engineering and CAD / methodology experts. Readers should have some background in standard design techniques like entering a design in a schematic capture and simulating it, and also know about major technology aspects

Circuit Design

Circuit Design = Science + Art! Designers need a skilled "gut feeling" about circuits and related analytical techniques, plus creativity, to solve all problems and to adhere to the specifications, the written and the unwritten ones. You must anticipate a large number of influences, like temperature effects, supply voltages changes, offset voltages, layout parasitics, and numerous kinds of technology variations to end up with a circuit that works. This is challenging for analog, custom-digital, mixed-signal or RF circuits, and often researching new design methods in relevant journals, conference proceedings and design tools unfortunately gives the impression that just a "wild bunch" of "advanced techniques" exist. On the other hand, state-of-the-art tools nowadays indeed offer a good cockpit to steer the design flow, which include clever statistical methods and optimization techniques.Actually, this almost presents a second breakthrough, like the introduction of circuit simulators 40 years ago! Users can now conveniently analyse all the problems (discover, quantify, verify), and even exploit them, for example for optimization purposes. Most designers are caught up on everyday problems, so we fit that "wild bunch" into a systematic approach for variation-aware design, a designer's field guide and more. That is where this book can help! Circuit Design: Anticipate, Analyze, Exploit Variations starts with best-practise manual methods and links them tightly to up-to-date automation algorithms. We provide many tractable examples and explain key techniques you have to know. We then enable you to select and setup suitable methods for each design task - knowing their prerequisites, advantages and, as too often overlooked, their limitations as well. The good thing with computers is that you yourself can often verify amazing things with little effort, and you can use software not only to your direct advantage in solving a specific problem, but also for becoming a better skilled, more experienced engineer. Unfortunately, EDA design environments are not good at all to learn about advanced numerics. So with this book we also provide two apps for learning about statistic and optimization directly with circuit-related examples, and in real-time so without the long simulation times. This helps to develop a healthy statistical gut feeling for circuit design. The book is written for engineers, students in engineering and CAD / methodology experts. Readers should have some background in standard design techniques like entering a design in a schematic capture and simulating it, and also know about major technology aspects

Scalable String and Suffix Sorting: Algorithms, Techniques, and Tools

This dissertation focuses on two fundamental sorting problems: string sorting and suffix sorting. The first part considers parallel string sorting on shared-memory multi-core machines, the second part external memory suffix sorting using the induced sorting principle, and the third part distributed external memory suffix sorting with a new distributed algorithmic big data framework named Thrill.Comment: 396 pages, dissertation, Karlsruher Instituts f\"ur Technologie (2018). arXiv admin note: text overlap with arXiv:1101.3448 by other author

Forward uncertainty quantification with special emphasis on a Bayesian active learning perspective

Uncertainty quantification (UQ) in its broadest sense aims at quantitatively studying all sources of uncertainty arising from both computational and real-world applications. Although many subtopics appear in the UQ field, there are typically two major types of UQ problems: forward and inverse uncertainty propagation. The present study focuses on the former, which involves assessing the effects of the input uncertainty in various forms on the output response of a computational model. In total, this thesis reports nine main developments in the context of forward uncertainty propagation, with special emphasis on a Bayesian active learning perspective. The first development is concerned with estimating the extreme value distribution and small first-passage probabilities of uncertain nonlinear structures under stochastic seismic excitations, where a moment-generating function-based mixture distribution approach (MGF-MD) is proposed. As the second development, a triple-engine parallel Bayesian global optimization (T-PBGO) method is presented for interval uncertainty propagation. The third contribution develops a parallel Bayesian quadrature optimization (PBQO) method for estimating the response expectation function, its variable importance and bounds when a computational model is subject to hybrid uncertainties in the form of random variables, parametric probability boxes (p-boxes) and interval models. In the fourth research, of interest is the failure probability function when the inputs of a performance function are characterized by parametric p-boxes. To do so, an active learning augmented probabilistic integration (ALAPI) method is proposed based on offering a partially Bayesian active learning perspective on failure probability estimation, as well as the use of high-dimensional model representation (HDMR) technique. Note that in this work we derive an upper-bound of the posterior variance of the failure probability, which bounds our epistemic uncertainty about the failure probability due to a kind of numerical uncertainty, i.e., discretization error. The fifth contribution further strengthens the previously developed active learning probabilistic integration (ALPI) method in two ways, i.e., enabling the use of parallel computing and enhancing the capability of assessing small failure probabilities. The resulting method is called parallel adaptive Bayesian quadrature (PABQ). The sixth research presents a principled Bayesian failure probability inference (BFPI) framework, where the posterior variance of the failure probability is derived (not in closed form). Besides, we also develop a parallel adaptive-Bayesian failure probability learning (PA-BFPI) method upon the BFPI framework. For the seventh development, we propose a partially Bayesian active learning line sampling (PBAL-LS) method for assessing extremely small failure probabilities, where a partially Bayesian active learning insight is offered for the classical LS method and an upper-bound for the posterior variance of the failure probability is deduced. Following the PBAL-LS method, the eighth contribution finally obtains the expression of the posterior variance of the failure probability in the LS framework, and a Bayesian active learning line sampling (BALLS) method is put forward. The ninth contribution provides another Bayesian active learning alternative, Bayesian active learning line sampling with log-normal process (BAL-LS-LP), to the traditional LS. In this method, the log-normal process prior, instead of a Gaussian process prior, is assumed for the beta function so as to account for the non-negativity constraint. Besides, the approximation error resulting from the root-finding procedure is also taken into consideration. In conclusion, this thesis presents a set of novel computational methods for forward UQ, especially from a Bayesian active learning perspective. The developed methods are expected to enrich our toolbox for forward UQ analysis, and the insights gained can stimulate further studies