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Optimal Design of Transonic Fan Blade Leading Edge Shape Using CFD and Simultaneous Perturbation Stochastic Approximation MethodXing, X.Q., Damodaran, Murali 01 1900 (has links)
Simultaneous Perturbation Stochastic Approximation method has attracted considerable application in many different areas such as statistical parameter estimation, feedback control, simulation-based optimization, signal & image processing, and experimental design. In this paper, its performance as a viable optimization tool is demonstrated by applying it first to a simple wing geometry design problem for which the objective function is described by an empirical formula from aircraft design practice and then it is used in a transonic fan blade design problem in which the objective function is not represented by any explicit function but is estimated at each design iteration by a computational fluid dynamics algorithm for solving the Navier-Stokes equations / Singapore-MIT Alliance (SMA)
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Efficient Solution Of Optimization Problems With Constraints And/or Cost Functions Expensive To EvaluateKurtdere, Ahmet Gokhan 01 January 2010 (has links) (PDF)
There are many optimization problems motivated by engineering applications, whose constraints and/or cost functions are computationally expensive to evaluate. What is more derivative information is usually not available or available at a considerable cost. For that reason, classical optimization methods, based on derivatives, are not applicable. This study presents a framework based on available methods in literature to overcome this important problem. First, a penalized model is constructed where the violation of the constraints are added to the cost function. The model is optimized with help of stochastic approximation algorithms until a point satisfying the constraints is obtained. Then, a sample point set satisfying the constraints is obtained by taking advantage of direct search algorithms based sampling strategies. In this context, two search direction estimation methods, convex hull based and estimated radius of curvature of the sample point set based methods can be applicable. Point set is used to create a barrier which imposes a large cost for points near to the boundary. The aim is to obtain convergence to local optima using the most promising direction with help of direct search methods. As regards to the evaluation of the cost function there are two directions to follow: a-) Gradient-based methods, b-) Non-gradient methods. In gradient-based methods, the gradient is approximated using the so-called stochastic approximation algorithms. In the latter case, direct search algorithms based sampling strategy is realized. This study is concluded by using all these ideas in the solution of complicated test problems where the cost and the constraint functions are costly to evaluate.
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同時摂動確率近似に基づくモデルフリー型制御器設計 / Model-Free Controller Design based on Simultaneous Perturbation Stochastic ApproximationMohd, Ashraf bin Ahmad 23 March 2015 (has links)
Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19125号 / 情博第571号 / 新制||情||100 / 32076 / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 杉江 俊治, 教授 石井 信, 教授 加納 学, 准教授 東 俊一 / 学位規則第4条第1項該当
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Radio frequency interference modeling and mitigation in wireless receiversGulati, Kapil 21 October 2011 (has links)
In wireless communication systems, receivers have generally been designed under the assumption that the additive noise in system is Gaussian. Wireless receivers, however, are affected by radio frequency interference (RFI) generated from various sources such as other wireless users, switching electronics, and computational platforms. RFI is well modeled using non-Gaussian impulsive statistics and can severely degrade the communication performance of wireless receivers designed under the assumption of additive Gaussian noise.
Methods to avoid, cancel, or reduce RFI have been an active area of research over the past three decades. In practice, RFI cannot be completely avoided or canceled at the receiver. This dissertation derives the statistics of the residual RFI and utilizes them to analyze and improve the communication performance of wireless receivers. The primary contributions of this dissertation are to (i) derive instantaneous statistics of co-channel interference in a field of Poisson and Poisson-Poisson clustered interferers, (ii) characterize throughput, delay, and reliability of decentralized wireless networks with temporal correlation, and (iii) design pre-filters to mitigate RFI in wireless receivers. / text
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Monte Carlo Methods for Stochastic Differential Equations and their ApplicationsLeach, Andrew Bradford, Leach, Andrew Bradford January 2017 (has links)
We introduce computationally efficient Monte Carlo methods for studying the statistics of stochastic differential equations in two distinct settings. In the first, we derive importance sampling methods for data assimilation when the noise in the model and observations are small. The methods are formulated in discrete time, where the "posterior" distribution we want to sample from can be analyzed in an accessible small noise expansion. We show that a "symmetrization" procedure akin to antithetic coupling can improve the order of accuracy of the sampling methods, which is illustrated with numerical examples. In the second setting, we develop "stochastic continuation" methods to estimate level sets for statistics of stochastic differential equations with respect to their parameters. We adapt Keller's Pseudo-Arclength continuation method to this setting using stochastic approximation, and generalized least squares regression. Furthermore, we show that the methods can be improved through the use of coupling methods to reduce the variance of the derivative estimates that are involved.
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Optimization under Uncertainty with Applications in Data-driven Stochastic Simulation and Rare-event EstimationZhang, Xinyu January 2022 (has links)
For many real-world problems, optimization could only be formulated with partial information or subject to uncertainty due to reasons such as data measurement error, model misspecification, or that the formulation depends on the non-stationary future. It thus often requires one to make decisions without knowing the problem's full picture. This dissertation considers the robust optimization framework—a worst-case perspective—to characterize uncertainty as feasible regions and optimize over the worst possible scenarios. Two applications in this worst-case perspective are discussed: stochastic estimation and rare-event simulation.
Chapters 2 and 3 discuss a min-max framework to enhance existing estimators for simulation problems that involve a bias-variance tradeoff. Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters in terms of the simulation budget can be readily established, the precise best values depend on model characteristics that are typically unknown in advance. We introduce a framework to construct new classes of estimators, based on judicious combinations of simulation runs on sequences of tuning parameter values, such that the estimators consistently outperform a given tuning parameter choice in the conventional approach, regardless of the unknown model characteristics. We argue the outperformance via what we call the asymptotic minimax risk ratio, obtained by minimizing the worst-case asymptotic ratio between the mean square errors of our estimators and the conventional one, where the worst case is over any possible values of the model unknowns. In particular, when the minimax ratio is less than 1, the calibrated estimator is guaranteed to perform better asymptotically. We identify this minimax ratio for general classes of weighted estimators and the regimes where this ratio is less than 1. Moreover, we show that the best weighting scheme is characterized by a sum of two components with distinct decay rates. We explain how this arises from bias-variance balancing that combats the adversarial selection of the model constants, which can be analyzed via a tractable reformulation of a non-convex optimization problem.
Chapters 4 and 5 discuss extreme event estimation using a distributionally robust optimization framework. Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter difficult bias-variance tradeoffs that exacerbates especially when data size is too small, deteriorating the reliability of the tail estimation. The chapters study a framework based on the recently surging literature of distributionally robust optimization. This approach can be viewed as a nonparametric alternative to conventional EVT, by imposing general shape belief on the tail instead of parametric assumption and using worst-case optimization as a resolution to handle the nonparametric uncertainty. We explain how this approach bypasses the bias-variance tradeoff in EVT. On the other hand, we face a conservativeness-variance tradeoff which we describe how to tackle. We also demonstrate computational tools for the involved optimization problems and compare our performance with conventional EVT across a range of numerical examples.
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Model-Free Controller Design based on Simultaneous Perturbation Stochastic Approximation / 同時摂動確率近似に基づくモデルフリー型制御器設計Mohd, Ashraf bin Ahmad 23 March 2015 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19125号 / 情博第571号 / 新制||情||100(附属図書館) / 32076 / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 杉江 俊治, 教授 石井 信, 教授 加納 学, 准教授 東 俊一 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM
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A Nonlinear Stochastic Optimization Framework For REDPatro, Rajesh Kumar 12 1900 (has links) (PDF)
No description available.
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On some problems in the simulation of flow and transport through porous mediaThomas, Sunil George 20 October 2009 (has links)
The dynamic solution of multiphase flow through porous media is of
special interest to several fields of science and engineering, such as petroleum,
geology and geophysics, bio-medical, civil and environmental, chemical engineering
and many other disciplines. A natural application is the modeling of
the flow of two immiscible fluids (phases) in a reservoir. Others, that are broadly
based and considered in this work include the hydrodynamic dispersion (as in
reactive transport) of a solute or tracer chemical through a fluid phase. Reservoir
properties like permeability and porosity greatly influence the flow of these
phases. Often, these vary across several orders of magnitude and can be discontinuous
functions. Furthermore, they are generally not known to a desired level
of accuracy or detail and special inverse problems need to be solved in order
to obtain their estimates. Based on the physics dominating a given sub-region
of the porous medium, numerical solutions to such flow problems may require
different discretization schemes or different governing equations in adjacent regions.
The need to couple solutions to such schemes gives rise to challenging
domain decomposition problems. Finally, on an application level, present day
environment concerns have resulted in a widespread increase in CO₂capture and
storage experiments across the globe. This presents a huge modeling challenge
for the future. This research work is divided into sections that aim to study various
inter-connected problems that are of significance in sub-surface porous media
applications. The first section studies an application of mortar (as well as nonmortar,
i.e., enhanced velocity) mixed finite element methods (MMFEM and
EV-MFEM) to problems in porous media flow. The mortar spaces are first
used to develop a multiscale approach for parabolic problems in porous media
applications. The implementation of the mortar mixed method is presented for
two-phase immiscible flow and some a priori error estimates are then derived
for the case of slightly compressible single-phase Darcy flow. Following this,
the problem of modeling flow coupled to reactive transport is studied. Applications
of such problems include modeling bio-remediation of oil spills and other
subsurface hazardous wastes, angiogenesis in the transition of tumors from a
dormant to a malignant state, contaminant transport in groundwater flow and
acid injection around well bores to increase the permeability of the surrounding
rock. Several numerical results are presented that demonstrate the efficiency
of the method when compared to traditional approaches. The section following
this examines (non-mortar) enhanced velocity finite element methods for solving
multiphase flow coupled to species transport on non-matching multiblock grids.
The results from this section indicate that this is the recommended method of
choice for such problems.
Next, a mortar finite element method is formulated and implemented
that extends the scope of the classical mortar mixed finite element method
developed by Arbogast et al [12] for elliptic problems and Girault et al [62] for
coupling different numerical discretization schemes. Some significant areas of
application include the coupling of pore-scale network models with the classical
continuum models for steady single-phase Darcy flow as well as the coupling
of different numerical methods such as discontinuous Galerkin and mixed finite
element methods in different sub-domains for the case of single phase flow [21,
109]. These hold promise for applications where a high level of detail and
accuracy is desired in one part of the domain (often associated with very small
length scales as in pore-scale network models) and a much lower level of detail at other parts of the domain (at much larger length scales). Examples include
modeling of the flow around well bores or through faulted reservoirs.
The next section presents a parallel stochastic approximation method
[68, 76] applied to inverse modeling and gives several promising results that
address the problem of uncertainty associated with the parameters governing
multiphase flow partial differential equations. For example, medium properties
such as absolute permeability and porosity greatly influence the flow behavior,
but are rarely known to even a reasonable level of accuracy and are very often
upscaled to large areas or volumes based on seismic measurements at discrete
points. The results in this section show that by using a few measurements of
the primary unknowns in multiphase flow such as fluid pressures and concentrations
as well as well-log data, one can define an objective function of the
medium properties to be determined, which is then minimized to determine the
properties using (as in this case) a stochastic analog of Newton’s method. The
last section is devoted to a significant and current application area. It presents a
parallel and efficient iteratively coupled implicit pressure, explicit concentration
formulation (IMPEC) [52–54] for non-isothermal compositional flow problems.
The goal is to perform predictive modeling simulations for CO₂sequestration
experiments.
While the sections presented in this work cover a broad range of topics
they are actually tied to each other and serve to achieve the unifying, ultimate
goal of developing a complete and robust reservoir simulator. The major results
of this work, particularly in the application of MMFEM and EV-MFEM
to multiphysics couplings of multiphase flow and transport as well as in the
modeling of EOS non-isothermal compositional flow applied to CO₂sequestration,
suggest that multiblock/multimodel methods applied in a robust parallel
computational framework is invaluable when attempting to solve problems as
described in Chapter 7. As an example, one may consider a closed loop control
system for managing oil production or CO₂sequestration experiments in huge
formations (the “instrumented oil field”). Most of the computationally costly activity occurs around a few wells. Thus one has to be able to seamlessly connect
the above components while running many forward simulations on parallel
clusters in a multiblock and multimodel setting where most domains employ an
isothermal single-phase flow model except a few around well bores that employ,
say, a non-isothermal compositional model. Simultaneously, cheap and efficient
stochastic methods as in Chapter 8, may be used to generate history matches of
well and/or sensor-measured solution data, to arrive at better estimates of the
medium properties on the fly. This is obviously beyond the scope of the current
work but represents the over-arching goal of this research. / text
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Analog Signal Processor for Adaptive Antenna ArraysHossu, Mircea January 2007 (has links)
An analog circuit for beamforming in a mobile Ku band satellite TV antenna array has been implemented. The circuit performs continuous-time gradient descent using simultaneous perturbation gradient estimation. Simulations were performed using Agilent ADS circuit simulator. Field tests were performed in a realistic scenario using a satellite signal. The results were comparable to the simulation predictions and to results obtained using a digital implementation of a similar stochastic approximation algorithm.
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