Tamasco, Cynthia M
06 August 2011
This thesis presents the development and implementation of a generalized optimization framework for use in sheet-stamping process simulation by finite element analysis. The generic framework consists of three main elements: a process simulation program, an optimization code, and a response filtering program. These elements can be filled by any combination of applicable software packages. Example sheet-stamping process simulations are presented to demonstrate the usage of the framework in various forming scenarios. Each of the example simulations is presented with a sensitivity analysis. These examples include analysis of a 2-dimensional single-stage forming, a 2-dimensional multi-stage forming, and two different 3-dimensional single-stage forming processes. A forming limit diagram is used to define failure in the 3-dimensional process simulations. Optimization results are presented using damage minimization, thinning minimization, and springback minimization with aluminum alloy 6061-T6 blanks.
Alternative Methods for Operational Optimization of Hydro Power Plants / Alternativa Metoder för Driftoptimering av VattenkraftverkAlmgrund, Jonas January 2019 (has links)
The aim of this thesis is to optimize hydro power plants with data generated from observations and field tests at the plants. The output is optimal production tables and curves in order to operate and plan hydro power plants in an optimized way concerning power output, efficiency and distribution of water. The thesis is performed in collaboration with Vattenfall AB, which currently use an internal optimization program called SEVAP. Two alternative methods have been selected, employed and compared with the current optimization program, these are Interior-Point Method and Sequential Quadratic Programming. Three start-point strategies are created to increase the probability of finding a global optima. A heuristic rule is used for selection of strategy in order to prevent rapid changes in load distribution for small variations in dispatched water. The optimization is performed at three plants in Sweden with different size and setup. The results of this evaluation showed marginally better results for the employed methods in comparison to the currently used optimization. Further, the developed program is more flexible and compatible to integrate with future digitalization projects. / Syftet med detta examensarbete är att optimera vattenkraftverk med data som genererats från indextester vid kraftverken. Resultatet är optimala produktionstabeller och kurvor för drift och planering av vattenkraftverk. Dessa är baserade på att optimalt fördela vattnet mellan aggregaten för att maximera uteffekt och verkningsgrad. Detta arbete har utförts i samarbete med Vattenfall AB, som för närvarande använder ett internt optimeringsprogram som heter SEVAP. Två optimeringsmetoder har valts, implementerats och jämförts med det nuvarande optimeringsprogrammet. Dessa metoder är inrepunktsmetoden (IPM) och sekventiell kvadratiskt programmering (SQP). Tre startpunktsstrategier har används för att öka sannolikheten att hitta ett globalt optima. För att förhindra hastiga förändringar i lastfördelning för små variationer av avsänt vatten har en heuristisk regel används. Optimeringen har utförts på tre stationer med olika uppsättning och storlek. Resultatet av detta examensarbete visar marginellt bättre resultat för de använda metoderna i jämförelse med den nuvarande optimeringen. Det utvecklade programmet är flexibelt och kompatibelt att integrera med framtida digitaliseringsprojekt.
OPTIMAL DISTRIBUTED GENERATION SIZING AND PLACEMENT VIA SINGLE- AND MULTI-OBJECTIVE OPTIMIZATION APPROACHESDarfoun, Mohamed 09 July 2013 (has links)
Numerous advantages attained by integrating Distributed Generation (DG) in distribution systems. These advantages include decreasing power losses and improving voltage profiles. Such benefits can be achieved and enhanced if DGs are optimally sized and located in the systems. In this thesis, the optimal DG placement and sizing problem is investigated using two approaches. First, the optimization problem is treated as single-objective optimization problem, where the system’s active power losses are considered as the objective to be minimized. Secondly, the problem is tackled as a multi-objective one, focusing on DG installation costs. These problems are formulated as constrained nonlinear optimization problems using the Sequential Quadratic Programming method. A weighted sum method and a fuzzy decision-making method are presented to generate the Pareto optimal front and also to obtain the best compromise solution. Single and multiple DG installation cases are studied and compared to a case without DG, and a 15-bus radial distribution system and 33-bus meshed distribution system are used to demonstrate the effectiveness of the proposed methods.
2009 December 1900
Technology scaling has been the most obvious choice of designers and chip manufacturing companies to improve the performance of analog and digital circuits. With the ever shrinking technological node, process variations can no longer be ignored and play a significant role in determining the performance of nanoscaled devices. By choosing a worst case design methodology, circuit designers have been very munificent with the design parameters chosen, often manifesting in pessimistic designs with significant area overheads. Significant work has been done in estimating the impact of intra-die process variations on circuit performance, pertinently, noise margin and standby leakage power, for fixed transistor channel dimensions. However, for an optimal, high yield, SRAM cell design, it is absolutely imperative to analyze the impact of process variations at every design point, especially, since the distribution of process variations is a statistically varying parameter and has an inverse correlation with the area of the MOS transistor. Furthermore, the first order analytical models used for optimization of SRAM memories are not as accurate and the impact of voltage and its inclusion as an input, along with other design parameters, is often ignored. In this thesis, the performance parameters of a nano-scaled 6-T SRAM cell are modeled as an accurate, yield aware, empirical polynomial predictor, in the presence of intra-die process variations. The estimated empirical models are used in a constrained non-linear, robust optimization framework to design an SRAM cell, for a 45 nm CMOS technology, having optimal performance, according to bounds specified for the circuit performance parameters, with the objective of minimizing on-chip area. This statistically aware technique provides a more realistic design methodology to study the trade off between performance parameters of the SRAM. Furthermore, a dual optimization approach is followed by considering SRAM power supply and wordline voltages as additional input parameters, to simultaneously tune the design parameters, ensuring a high yield and considerable area reduction. In addition, the cell level optimization framework is extended to the system level optimization of caches, under both cell level and system level performance constraints.
Parameter identification problems for elastic large deformations - Part I: model and solution of the inverse problemMeyer, Marcus 20 November 2009 (has links) (PDF)
In this paper we discuss the identification of parameter functions in material models for elastic large deformations. A model of the the forward problem is given, where the displacement of a deformed material is found as the solution of a n onlinear PDE. Here, the crucial point is the definition of the 2nd Piola-Kirchhoff stress tensor by using several material laws including a number of material parameters. In the main part of the paper we consider the identification of such parameters from measured displacements, where the inverse problem is given as an optimal control problem. We introduce a solution of the identification problem with Lagrange and SQP methods. The presented algorithm is applied to linear elastic material with large deformations.
Design of a large-scale constrained optimization algorithm and its application to digital human simulationNicholson, John Corbett 01 May 2017 (has links)
A new optimization algorithm, which can efficiently solve large-scale constrained non-linear optimization problems and leverage parallel computing, is designed and studied. The new algorithm, referred to herein as LASO or LArge Scale Optimizer, combines the best features of various algorithms to create a computationally efficient algorithm with strong convergence properties. Numerous algorithms were implemented and tested in its creation. Bound-constrained, step-size, and constrained algorithms have been designed that push the state-of-the-art. Along the way, five novel discoveries have been made: (1) a more efficient and robust method for obtaining second order Lagrange multiplier updates in Augmented Lagrangian algorithms, (2) a method for directly identifying the active constraint set at each iteration, (3) a simplified formulation of the penalty parameter sub-problem, (4) an efficient backtracking line-search procedure, (5) a novel hybrid line-search trust-region step-size calculation method. The broader impact of these contributions is that, for the first time, an Augmented Lagrangian algorithm is made to be competitive with state-of-the-art Sequential Quadratic Programming and Interior Point algorithms. The present work concludes by showing the applicability of the LASO algorithm to simulate one step of digital human walking and to accelerate the optimization process using parallel computing.
A Comparative Analysis of an Interior-point Method and a Sequential Quadratic Programming Method for the Markowitz Portfolio Management ProblemXiao, Zhifu 12 August 2016 (has links)
No description available.
Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential EquationsOliveira, I.B., Patera, Anthony T. 01 1900 (has links)
The solution of a single optimization problem often requires computationally-demanding evaluations; this is especially true in optimal design of engineering components and systems described by partial differential equations. We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of partial differential equations with affine parameter dependence. The critical ingredients of the method are: (i) reduced-basis techniques for dimension reduction in computational requirements; (ii) an "off-line/on-line" computational decomposition for the rapid calculation of outputs of interest and respective sensitivities in the limit of many queries; (iii) a posteriori error bounds for rigorous uncertainty and feasibility control; (iv) Interior Point Methods (IPMs) for efficient solution of the optimization problem; and (v) a trust-region Sequential Quadratic Programming (SQP) interpretation of IPMs for treatment of possibly non-convex costs and constraints. / Singapore-MIT Alliance (SMA)
In this thesis, optimization approaches for intensity-modulated radiation therapy are developed and evaluated with focus on numerical efficiency and treatment delivery aspects. The first two papers deal with strategies for solving fluence map optimization problems efficiently while avoiding solutions with jagged fluence profiles. The last two papers concern optimization of step-and-shoot parameters with emphasis on generating treatment plans that can be delivered efficiently and accurately. In the first paper, the problem dimension of a fluence map optimization problem is reduced through a spectral decomposition of the Hessian of the objective function. The weights of the eigenvectors corresponding to the p largest eigenvalues are introduced as optimization variables, and the impact on the solution of varying p is studied. Including only a few eigenvector weights results in faster initial decrease of the objective value, but with an inferior solution, compared to optimization of the bixel weights. An approach combining eigenvector weights and bixel weights produces improved solutions, but at the expense of the pre-computational time for the spectral decomposition. So-called iterative regularization is performed on fluence map optimization problems in the second paper. The idea is to find regular solutions by utilizing an optimization method that is able to find near-optimal solutions with non-jagged fluence profiles in few iterations. The suitability of a quasi-Newton sequential quadratic programming method is demonstrated by comparing the treatment quality of deliverable step-and-shoot plans, generated through leaf sequencing with a fixed number of segments, for different number of bixel-weight iterations. A conclusion is that over-optimization of the fluence map optimization problem prior to leaf sequencing should be avoided. An approach for dynamically generating multileaf collimator segments using a column generation approach combined with optimization of segment shapes and weights is presented in the third paper. Numerical results demonstrate that the adjustment of leaf positions improves the plan quality and that satisfactory treatment plans are found with few segments. The method provides a tool for exploring the trade-off between plan quality and treatment complexity by generating a sequence of deliverable plans of increasing quality. The final paper is devoted to understanding the ability of the column generation approach in the third paper to find near-optimal solutions with very few columns compared to the problem dimension. The impact of different restrictions on the generated columns is studied, both in terms of numerical behaviour and convergence properties. A bound on the two-norm of the columns results in the conjugate-gradient method. Numerical results indicate that the appealing properties of the conjugate-gradient method on ill-conditioned problems are inherited in the column generation approach of the third paper. / QC 20100709
Distributed parameter systems (DPS) comprise an important class of engineering systems ranging from "traditional" such as tubular reactors, to cutting edge processes such as nano-scale coatings. DPS have been studied extensively and significant advances have been noted, enabling their accurate simulation. To this end a variety of tools have been developed. However, extending these advances for systems design is not a trivial task . Rigorous design and operation policies entail systematic procedures for optimisation and control. These tasks are "upper-level" and utilize existing models and simulators. The higher the accuracy of the underlying models, the more the design procedure benefits. However, employing such models in the context of conventional algorithms may lead to inefficient formulations. The optimisation and control of DPS is a challenging task. These systems are typically discretised over a computational mesh, leading to large-scale problems. Handling the resulting large-scale systems may prove to be an intimidating task and requires special methodologies. Furthermore, it is often the case that the underlying physical phenomena span various temporal and spatial scales, thus complicating the analysis. Stiffness may also potentially be exhibited in the (nonlinear) models of such phenomena. The objective of this work is to design reliable and practical procedures for the optimisation and control of DPS. It has been observed in many systems of engineering interest that although they are described by infinite-dimensional Partial Differential Equations (PDEs) resulting in large discretisation problems, their behaviour has a finite number of significant components , as a result of their dissipative nature. This property has been exploited in various systematic model reduction techniques. Of key importance in this work is the identification of a low-dimensional dominant subspace for the system. This subspace is heuristically found to correspond to part of the eigenspectrum of the system and can therefore be identified efficiently using iterative matrix-free techniques. In this light, only low-dimensional Jacobians and Hessian matrices are involved in the formulation of the proposed algorithms, which are projections of the original matrices onto appropriate low-dimensional subspaces, computed efficiently with directional perturbations.The optimisation algorithm presented employs a 2-step projection scheme, firstly onto the dominant subspace of the system (corresponding to the right-most eigenvalues of the linearised system) and secondly onto the subspace of decision variables. This algorithm is inspired by reduced Hessian Sequential Quadratic Programming methods and therefore locates a local optimum of the nonlinear programming problem given by solving a sequence of reduced quadratic programming (QP) subproblems . This optimisation algorithm is appropriate for systems with a relatively small number of decision variables. Inequality constraints can be accommodated following a penalty-based strategy which aggregates all constraints using an appropriate function , or by employing a partial reduction technique in which only equality constraints are considered for the reduction and the inequalities are linearised and passed on to the QP subproblem . The control algorithm presented is based on the online adaptive construction of low-order linear models used in the context of a linear Model Predictive Control (MPC) algorithm , in which the discrete-time state-space model is recomputed at every sampling time in a receding horizon fashion. Successive linearisation around the current state on the closed-loop trajectory is combined with model reduction, resulting in an efficient procedure for the computation of reduced linearised models, projected onto the dominant subspace of the system. In this case, this subspace corresponds to the eigenvalues of largest magnitude of the discretised dynamical system. Control actions are computed from low-order QP problems solved efficiently online.The optimisation and control algorithms presented may employ input/output simulators (such as commercial packages) extending their use to upper-level tasks. They are also suitable for systems governed by microscopic rules, the equations of which do not exist in closed form. Illustrative case studies are presented, based on tubular reactor models, which exhibit rich parametric behaviour.
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