13,562 research outputs found
An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems
This article presents a new approach to the real-time solution of inverse
problems on embedded systems. The class of problems addressed corresponds to
ordinary differential equations (ODEs) with generalized linear constraints,
whereby the data from an array of sensors forms the forcing function. The
solution of the equation is formulated as a least squares (LS) problem with
linear constraints. The LS approach makes the method suitable for the explicit
solution of inverse problems where the forcing function is perturbed by noise.
The algebraic computation is partitioned into a initial preparatory step, which
precomputes the matrices required for the run-time computation; and the cyclic
run-time computation, which is repeated with each acquisition of sensor data.
The cyclic computation consists of a single matrix-vector multiplication, in
this manner computation complexity is known a-priori, fulfilling the definition
of a real-time computation. Numerical testing of the new method is presented on
perturbed as well as unperturbed problems; the results are compared with known
analytic solutions and solutions acquired from state-of-the-art implicit
solvers. The solution is implemented with model based design and uses only
fundamental linear algebra; consequently, this approach supports automatic code
generation for deployment on embedded systems. The targeting concept was tested
via software- and processor-in-the-loop verification on two systems with
different processor architectures. Finally, the method was tested on a
laboratory prototype with real measurement data for the monitoring of flexible
structures. The problem solved is: the real-time overconstrained reconstruction
of a curve from measured gradients. Such systems are commonly encountered in
the monitoring of structures and/or ground subsidence.Comment: 24 pages, journal articl
Proportional Topology Optimization: A new non-gradient method for solving stress constrained and minimum compliance problems and its implementation in MATLAB
A new topology optimization method called the Proportional Topology
Optimization (PTO) is presented. As a non-gradient method, PTO is simple to
understand, easy to implement, and is also efficient and accurate at the same
time. It is implemented into two MATLAB programs to solve the stress
constrained and minimum compliance problems. Descriptions of the algorithm and
computer programs are provided in detail. The method is applied to solve three
numerical examples for both types of problems. The method shows comparable
efficiency and accuracy with an existing gradient optimality criteria method.
Also, the PTO stress constrained algorithm and minimum compliance algorithm are
compared by feeding output from one algorithm to the other in an alternative
manner, where the former yields lower maximum stress and volume fraction but
higher compliance compared to the latter. Advantages and disadvantages of the
proposed method and future works are discussed. The computer programs are
self-contained and publicly shared in the website www.ptomethod.org.Comment: 18 pages, 8 figures, and 2 appendices (MATLAB codes
Efficient Optimization and Robust Value Quantification of Enhanced Oil Recovery Strategies
With an increasing demand for hydrocarbon reservoir produces such as oil, etc., and difficulties in finding green oil fields, the use of Enhanced Oil Recovery (EOR) methods such as polymer, Smart water, and solvent flooding for further development of existing fields can not be overemphasized. For reservoir profitability and reduced environmental impact, it is crucial to consider appropriate well control settings of EOR methods for given reservoir characterization. Moreover, finding appropriate well settings requires solving a constrained optimization problem with suitable numerical solution methods. Conventionally, the solution method requires many iterations involving several computationally demanding function evaluations before convergence to the appropriate near optimum. The major subject of this thesis is to develop an efficient and accurate solution method for constrained optimization problems associated with EOR methods for their value quantifications and ranking in the face of reservoir uncertainties.
The first contribution of the thesis develops a solution method based on the inexact line search method (with Ensemble Based Optimization (EnOpt) for approximate gradient computation) for robust constrained optimization problems associated with polymer, Smart water, and solvent flooding. Here, the objective function is the expectation of the Net Present Value (NPV) function over given geological realizations. For a given set of well settings, the NPV function is defined based on the EOR simulation model, which follows from an appropriate extension of the black-oil model. The developed solution method is used to find the economic benefits and also the ranking of EOR methods for different oil reservoirs developed to mimic North Sea reservoirs.
Performing the entire optimization routine in a transformed domain along with truncations has been a common practice for handling simple linear constraints in reservoir optimization. Aside from the fact that this method has a negative impact on the quality of gradient computation, it is complicated to use for non-linear constraints. The second contribution of this thesis proposes a technique based on the exterior penalty method for handling general linear and non-linear constraints in reservoir optimization problems to improve gradient computation quality by the EnOpt method for efficient and improved optimization algorithm.
Because of the computationally expensive NPV function due to the costly reservoir simulation of EOR methods, the solution method for the underlying EOR optimization problem becomes inefficient, especially for large reservoir problems. To speedup the overall computation of the solution method, this thesis introduces a novel full order model (FOM)-based certified adaptive machine learning optimization procedures to locally approximate the expensive NPV function. A supervised feedforward deep neural network (DNN) algorithm is employed to locally create surrogate model. In the FOM-based optimization algorithm of this study, several FOM NPV function evaluations are required by the EnOpt method to approximate the gradient function at each (outer) iteration until convergence. To limit the number FOM-based evaluations, we consider building surrogate models locally to replace the FOM based NPV function at each outer iteration and proceed with an inner optimization routine until convergence. We adapt the surrogate model using some FOM-based criterion where necessary until convergence. The demonstration of methodology for polymer optimization problem on a benchmark model results in an improved optimum and found to be more efficient compared to using the full order model optimization procedures
Content Placement in Cache-Enabled Sub-6 GHz and Millimeter-Wave Multi-antenna Dense Small Cell Networks
This paper studies the performance of cache-enabled dense small cell networks
consisting of multi-antenna sub-6 GHz and millimeter-wave base stations.
Different from the existing works which only consider a single antenna at each
base station, the optimal content placement is unknown when the base stations
have multiple antennas. We first derive the successful content delivery
probability by accounting for the key channel features at sub-6 GHz and mmWave
frequencies. The maximization of the successful content delivery probability is
a challenging problem. To tackle it, we first propose a constrained
cross-entropy algorithm which achieves the near-optimal solution with moderate
complexity. We then develop another simple yet effective heuristic
probabilistic content placement scheme, termed two-stair algorithm, which
strikes a balance between caching the most popular contents and achieving
content diversity. Numerical results demonstrate the superior performance of
the constrained cross-entropy method and that the two-stair algorithm yields
significantly better performance than only caching the most popular contents.
The comparisons between the sub-6 GHz and mmWave systems reveal an interesting
tradeoff between caching capacity and density for the mmWave system to achieve
similar performance as the sub-6 GHz system.Comment: 14 pages; Accepted to appear in IEEE Transactions on Wireless
Communication
Learning and Management for Internet-of-Things: Accounting for Adaptivity and Scalability
Internet-of-Things (IoT) envisions an intelligent infrastructure of networked
smart devices offering task-specific monitoring and control services. The
unique features of IoT include extreme heterogeneity, massive number of
devices, and unpredictable dynamics partially due to human interaction. These
call for foundational innovations in network design and management. Ideally, it
should allow efficient adaptation to changing environments, and low-cost
implementation scalable to massive number of devices, subject to stringent
latency constraints. To this end, the overarching goal of this paper is to
outline a unified framework for online learning and management policies in IoT
through joint advances in communication, networking, learning, and
optimization. From the network architecture vantage point, the unified
framework leverages a promising fog architecture that enables smart devices to
have proximity access to cloud functionalities at the network edge, along the
cloud-to-things continuum. From the algorithmic perspective, key innovations
target online approaches adaptive to different degrees of nonstationarity in
IoT dynamics, and their scalable model-free implementation under limited
feedback that motivates blind or bandit approaches. The proposed framework
aspires to offer a stepping stone that leads to systematic designs and analysis
of task-specific learning and management schemes for IoT, along with a host of
new research directions to build on.Comment: Submitted on June 15 to Proceeding of IEEE Special Issue on Adaptive
and Scalable Communication Network
Current singularities in planar magnetic X points of finite compressibility
The formation of current singularities in nonresistive, line-tied magnetic X points is addressed. It is pointed out that, although gas pressure suppresses the current singularity development when strictly antiparallel, one-dimensional magnetic fields implode, the pressure is likely to be less effective in the more realistic case of two-dimensional magnetic fields. Detailed nonlinear relaxation computations at various levels of compressibility confirm that singularity is present even in the incompressible limit, but its strength, as determined by the amplitude and morphology of the current density, is considerably reduced. The singularity strength is quantified by computing the scalings of the peak current density with resolution. The scalings show that localized current structures can be expected only for negligible gas pressures. The numerical results imply that the inclusion of gas pressure effectively stalls fast magnetic reconnection in line-tied X-point geometries
- …