Quantitative Object Reconstruction using Abel Transform Tomography and Mixed Variable Optimization

Researchers at the Los Alamos National Laboratory (LANL) are interested in quantitatively reconstructing an object using Abel transform x-ray tomography. Specifically, they obtain a radiograph by x-raying an object and attempt to quantitatively determine the number and types of materials and the thicknesses of each material layer. Their current methodologies either fail to provide a quantitative description of the object or are generally too slow to be useful in practice. As an alternative, the problem is modeled here as a mixed variable programming (MVP) problem, in which some variables are nonnumeric and for which no derivative information is available. The generalized pattern search (GPS) algorithm for linearly constrained MVP problems is applied to the x-ray tomography problem, by means of the NOMADm MATLAB® software package. Numerical results are provided for several test configurations of cylindrically symmetrical objects and show that, while there are difficulties to be overcome by researchers at LANL, this method is promising for solving x-ray tomography object reconstruction problems in practice

On the Use of Surrogate Functions for Mixed Variable Optimization of Simulated Systems

This research considers the efficient numerical solution of linearly constrained mixed variable programming (MVP) problems, in which the objective function is a black-box stochastic simulation, function evaluations may be computationally expensive, and derivative information is typically not available. MVP problems are those with a mixture of continuous, integer, and categorical variables, the latter of which may take on values only from a predefined list and may even be non-numeric. Mixed Variable Generalized Pattern Search with Ranking and Selection (MGPS-RS) is the only existing, provably convergent algorithm that can be applied to this class of problems. Present in this algorithm is an optional framework for constructing and managing less expensive surrogate functions as a means to reduce the number of true function evaluations that are required to find approximate solutions. In this research, the NOMADm software package, an implementation of pattern search for deterministic MVP problems, is modified to incorporate a sequential selection with memory (SSM) ranking and selection procedure for handling stochastic problems. In doing so, the underlying algorithm is modified to make the application of surrogates more efficient. A second class of surrogates based on the Nadaraya-Watson kernel regression estimator is also added to the software. Preliminary computational testing of the modified software is performed to characterize the relative efficiency of selected surrogate functions for mixed variable optimization in simulated systems

Optimal Periodic Inspection of a Stochastically Degrading System

This thesis develops and analyzes a procedure to determine the optimal inspection interval that maximizes the limiting average availability of a stochastically degrading component operating in a randomly evolving environment. The component is inspected periodically, and if the total observed cumulative degradation exceeds a fixed threshold value, the component is instantly replaced with a new, statistically identical component. Degradation is due to a combination of continuous wear caused by the component\u27s random operating environment, as well as damage due to randomly occurring shocks of random magnitude. In order to compute an optimal inspection interval and corresponding limiting average availability, a nonlinear program is formulated and solved using a direct search algorithm in conjunction with numerical Laplace transform inversion. Techniques are developed to significantly decrease the time required to compute the approximate optimal solutions. The mathematical programming formulation and solution techniques are illustrated through a series of increasingly complex example problems

Improving Mixed Variable Optimization of Computational and Model Parameters Using Multiple Surrogate Functions

This research focuses on reducing computational time in parameter optimization by using multiple surrogates and subprocess CPU times without compromising the quality of the results. This is motivated by applications that have objective functions with expensive computational times at high fidelity solutions. Applying, matching, and tuning optimization techniques at an algorithm level can reduce the time spent on unprofitable computations for parameter optimization. The objective is to recover known parameters of a flow property reference image by comparing to a template image that comes from a computational fluid dynamics simulation, followed by a numerical image registration and comparison process. Mixed variable pattern search and mesh adaptive direct search methods were applied using surrogate functions in the search step to produce solutions within a tolerance level of experimental observations. The surrogate functions are based on previous function values and computational times of those values. The use of multiple surrogates at each search step provides parameter selections that lead to improved solutions of an objective function evaluation with less computational time. Previously computed values for the objective function and computation time were used to compute a time cut-off parameter that allows termination during an objective function evaluation if the computational time exceeded a threshold or a divergent template image was created. This approach was tested using DACE and radial basis function surrogates within the NOMADm MATLAB® software. The numerical results are presented

Air Force Institute of Technology Research Report 2004

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, and Engineering Physics

Multi-Objective Optimization of Mixed-Variable, Stochastic Systems Using Single-Objective Formulations

Many problems exist where one desires to optimize systems with multiple, often competing, objectives. Further, these problems may not have a closed form representation, and may also have stochastic responses. Recently, a method expanded mixed variable generalized pattern search/ranking and selection (MVPS-RS) and Mesh Adaptive Direct Search (MADS) developed for single-objective, stochastic problems to the multi-objective case by using aspiration and reservation levels. However, the success of this method in approximating the true Pareto solution set can be dependent upon several factors. These factors include the experimental design and ranges of the aspiration and reservation levels, and the approximation quality of the nadir point. Additionally, a termination criterion for this method does not yet exist. In this thesis, these aspects are explored. Furthermore, there may be alternatives or additions to this method that can save both computational time and function evaluations. These include the use of surrogates as approximating functions and the expansion of proven singleobjective formulations. In this thesis, two new approaches are developed that make use of all of these previous existing methods in combination

Air Force Institute of Technology Research Report 2006

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physics

Microgrid modelling and online management

Modern power network owners have to respond to a number of challenges such as significant load changes and growth in the geographical distribution of the customers. On the other hand, the environmental policy and economic requirements from the market are constantly growing. The presence of these problems has led to an increased interest in the local renewable energy generation at the distribution level. The Microgrid (MG) concept assumes a cluster of loads and microsources operating as a single controllable system that provides both power and heat to its local area. Not much is known about Microgrid behavior as a whole system. Some models exist which describe the components of the Microgrid. This thesis aims to model Microgrids at steady state and study their transient responses to changing inputs. Currently models of a Diesel Engine, a Fuel Cell, a Microturbine, a Windturbine, a Photovoltaic cell, and Battery storage have been developed. In this thesis, a generalized formulation is introduced to determine the optimal operating strategy, the goal to minimize the operating costs as well as the reduction of the emission costs and level for a MicroGrid. To solve such a management problem it is first formulated as a nonlinear constrained cost optimization problem. Since the management problem poses a number of simultaneous objectives and constraints a Multiobjective optimization problem is formulated by considering the emission level reduction. A daily income from sold power and cost to be paid to the utility of the purchased power is added to the problem. The model takes also into consideration the reduction of emissions caused by NOx, SO2 and CO2. The optimization is aimed to minimize the operating costs of the system, while constraints are adjusted to meet the customer demand and the safety of the system. Different optimization techniques are applied to solve the problem, such as Mesh Adaptive Direct Search, Sequential Quadratic Programming, Genetic Algorithms, and Game Theory. Test cases provide comparison and evidence of the efficiency of the proposed methods.reviewe