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At least 541 records · Page 30

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

Madyastha, Raghavendra K.↗

Multidisciplinary design integration system for a supersonic transport aircraft

An aircraft preliminary design system which provides the multidisciplinary communications and couplings between several engineering disciplines is described. A primary benefit of this system is to demonstrate advanced technology multidisciplinary design integration methodologies. The current version includes the disciplines of aerodynamics and structures. Contributing engineering disciplines are coupled using the Global Sensitivity Equation approach to influence the global design optimization problem. A high speed civil transport configuration is used for configuration trade studies. Forty four independent design variables are used to control the cross-sectional areas of wing rib and spar caps and the thicknesses of wingskincover panels. A total of 300 stress, strain, buckling and displacement behavioral constraints and minimum gages on the design variables were used to optimize the idealized wing structure. The goal of the designs to resize the wing cover panels and internal structure for minimum mass.

Dovi, A. R.↗

Modal identification using single-mode projection filters and comparison with ERA and MLE results

The Single-Mode Projection Filter (SPF) is a newly developed algorithm for eigensystem parameter identification from both analytical results and test data. The SPF is formulated with a single mode only and practical for parallel processing implementation. Explicit formulations of SPF are derived for the multi-input multi-output (MIMO) system by using the orthogonal matrices of the controllability and observability matrices in the general sense. The modal parameters of SPF are initially obtained from an analytical model in modal space. The experimental data are then processed through SPF to update its modal parameters and to minimize a cost function defined by the norm of an error matrix. The updated modal parameters represent the characteristics of the test data. A two-dimensional global minimum optimization algorithm is developed and applied for the filter update by using the interval analysis method. The SPF is developed based on a single-mode subsystem and identifies only one modal frequency and one modal damping within a specified region. For an n-modes structure, n SPF can be implemented for parallel processing to reduce the computational burden. The SPF is applied to analyze the simulated data for the MAST beam structure. The estimated modal parameters are comparable to those from the Eigensystem Realization Algorithm (ERA) and repeated modal frequencies are identified. The modal analysis of the Spacecraft Control Laboratory Experiment (SCOLE) data is also performed by using the ERA and the Maximum Likelihood Estimate (MLE). The result shows that the first five modal frequencies are very close from ERA and MLE. However, there are slight disparities in the damping rates and the computational burdens are quite different among these two algorithms.

Huang, Jen-Kuang↗

Constrained minimization of smooth functions using a genetic algorithm

The use of genetic algorithms for minimization of differentiable functions that are subject to differentiable constraints is considered. A technique is demonstrated for converting the solution of the necessary conditions for a constrained minimum into an unconstrained function minimization. This technique is extended as a global constrained optimization algorithm. The theory is applied to calculating minimum-fuel ascent control settings for an energy state model of an aerospace plane.

Moerder, Daniel D.↗

Stochastic Methods for Aircraft Design

The global stochastic optimization method, simulated annealing (SA), was adapted and applied to various problems in aircraft design. The research was aimed at overcoming the problem of finding an optimal design in a space with multiple minima and roughness ubiquitous to numerically generated nonlinear objective functions. SA was modified to reduce the number of objective function evaluations for an optimal design, historically the main criticism of stochastic methods. SA was applied to many CFD/MDO problems including: low sonic-boom bodies, minimum drag on supersonic fore-bodies, minimum drag on supersonic aeroelastic fore-bodies, minimum drag on HSCT aeroelastic wings, FLOPS preliminary design code, another preliminary aircraft design study with vortex lattice aerodynamics, HSR complete aircraft aerodynamics. In every case, SA provided a simple, robust and reliable optimization method which found optimal designs in order 100 objective function evaluations. Perhaps most importantly, from this academic/industrial project, technology has been successfully transferred; this method is the method of choice for optimization problems at Northrop Grumman.

Pelz, Richard B.↗

AVHRR-Based Polar Pathfinder Products: Evaluation, Enhancement and Transition to MODIS

Study of the environment has historically been done with observations and measurements in relatively few local areas. While some of these have been done over long time spans, most have not. The NOAA/NASA Pathfinder project was initiated to complement these data sets with satellite data that can provide information over larger spatial areas and longer time spans. The AVHRR Polar Pathfinder (APR) program was part of this project. The APR was to supply data from the NOAA AVHRR instruments that was consistently generated in a format usable to a wide range of scientific investigators. A grant was obtained from the NASA Research Announcement 97-MTPE-03 to evaluate the APP products, to provide any enhancements, and to compare with products from the new MODIS instrument. There was about a two year overlap between the projects, and this validation effort had several impacts on the APP products. The APP products are derived from the instruments aboard 4 NOAA satellites, NOAA-7, 9, 11, and 14. Initial validation efforts compared the thermal calibrations of these instruments, and differences are found. Calibration has undergone many revisions and techniques have changed since the satellites were launched. The first calibration methods were optimized for global ocean temperatures, as this was one of the primary and important uses of the AVHRR instruments. As the APP program started, newer methods that provided more accurate temperature retrievals over a wider range of temperatures were being developed. The calibration of a wider range of temperatures were necessary because of the extremely low values in the polar regions. These methods were also designed so that calibrated data was also consistent between all the NOAA satellites. These newer calibration methods were then adopted primarily because of the initial finding of this validation effort.

Fowler, Charles↗

From Basking Ridge to the Jupiter Trojans

This presentation describes the activities of the Global Trajectory Optimization Lab, a subdivision of the Navigation and Mission Design Branch at NASA GSFC. The students will learn the basics of interplanetary trajectory optimization and then, as an example, the Lucy mission to the Jupiter Trojans will be described from both a science and engineering perspective.

trajectory design↗

Low Thrust Mission Trajectories to Near Earth Asteroids

The discovery of 2016 HO3 and its classification as a quasi-satellite has sparked a stronger interest towards Near Earth Asteroids (NEAs). This work presents low-thrust low-power mission designs to various NEAs using an EELV Secondary Payload Adapter (ESPA). A global trajectory optimizer (EMTG) was used to generate mission solutions to a select 13 NEAs using a 200 watt BHT-200 thruster as a proof of concept. The missions presented here demonstrate that a low-cost electric propulsion ESPA mission to NEAs is a feasible concept for many asteroids.

Asteroid↗

Modeling Spectralon's Bidirectional Reflectance for In-Flight Calibration of Earth-Orbiting Sensors

This paper describes the results of a model inversion which was conducted using measured Spectralon BRDF data at several illumination angles. We can describe the bidirectional reflectance of the Spectralon and in paticular its slight anisotrophy with a physically-based model. The root mean square difference between the model and the observations is currently of the order of the noise in the data (+/-1%). It is expected that meaningful corrections to account for the anisotrophy of the Spectralon panels will be achieved in the next few years and will improve the calibration of the MISR instrument.

EOS↗

Optimal Design of Grid-Stiffened Composite Panels Using Global and Local Buckling Analysis

A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. The design optimization process is adapted to identify the lightest-weight stiffening configuration and pattern for grid stiffened composite panels given the overall panel dimensions, design in-plane loads, material properties, and boundary conditions of the grid-stiffened panel.

Ambur, Damodar R.↗

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗

Optimal Design of General Stiffened Composite Circular Cylinders for Global Buckling with Strength Constraints

A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and strength constraints was developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory was used for the global analysis. Local buckling of skin segments were assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments were also assessed. Constraints on the axial membrane strain in the skin and stiffener segments were imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study were the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence and stiffening configuration, where stiffening configuration is a design variable that indicates the combination of axial, transverse and diagonal stiffener in the grid-stiffened cylinder. The design optimization process was adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configurations.

Jaunky, N.↗

Optimal Design of General Stiffened Composite Circular Cylinders for Global Buckling with Strength Constraints

A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and, strength constraints is developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory is used for the global analysis. Local buckling of skin segments are assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments are also assessed. Constraints on the axial membrane strain in the skin and stiffener segments are imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study are the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence, and stiffening configuration, where herein stiffening configuration is a design variable that indicates the combination of axial, transverse, and diagonal stiffener in the grid-stiffened cylinder. The design optimization process is adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads, and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configuration.

Jaunky, Navin↗

Minimum Landing Error Powered-Descent Guidance for Planetary Missions

An algorithm improves the accuracy with which a lander can be delivered to the surface of Mars. The main idea behind this innovation is the use of a lossless convexification, which converts an otherwise non-convex constraint related to thruster throttling to a convex constraint, enabling convex optimization to be used. The convexification leads directly to an algorithm that guarantees finding the global optimum of the original nonconvex optimization problem with a deterministic upper bound on the number of iterations required for convergence. In this innovation, previous work in powered-descent guidance using convex optimization is extended to handle the case where the lander must get as close as possible to the target given the available fuel, but is not required to arrive exactly at the target. The new algorithm calculates the minimum-fuel trajectory to the target, if one exists, and calculates the trajectory that minimizes the distance to the target if no solution to the target exists. This approach poses the problem as two Second-Order Cone Programs, which can be solved to global optimality with deterministic bounds on the number of iterations required.

Blackmore, Lars↗

A general Bayesian algorithm for the autonomous alignment of beamlines

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

47 OTHER INSTRUMENTATION↗

Dynamic Price Vector Formation Model-Based Automatic Demand Response Strategy for PV-Assisted EV Charging Stations

A real-time price (RTP)-based automatic demand response (ADR) strategy for PV-assisted electric vehicle (EV) Charging Station (PVCS) without vehicle to grid is proposed. The charging process is modeled as a dynamic linear program instead of the normal day-ahead and real-time regulation strategy, to capture the advantages of both global and real-time optimization. Different from conventional price forecasting algorithms, a dynamic price vector formation model is proposed based on a clustering algorithm to form an RTP vector for a particular day. A dynamic feasible energy demand region (DFEDR) model considering grid voltage profiles is designed to calculate the lower and upper bounds. A deduction method is proposed to deal with the unknown information of future intervals, such as the actual stochastic arrival and departure times of EVs, which make the DFEDR model suitable for global optimization. Finally, both the comparative cases articulate the advantages of the developed methods and the validity in reducing electricity costs, mitigating peak charging demand, and improving PV self-consumption of the proposed strategy are verified through simulation scenarios.

14 SOLAR ENERGY↗

A new mathematical approach to finding global solutions of the magnetic structure determination problem

Abstract Determination of magnetic structure is an important analytical procedure utilized in various fields ranging from fundamental condensed-matter physics and chemistry to advanced manufacturing. It is typically performed using a neutron diffraction technique; however, finding global solutions of the magnetic structure optimization problem represents a significant challenge. Generally, it is not possible to mathematically prove that the obtained magnetic structure is a truly global solution and that no solution exists when no acceptable structure is found. In this study, the global optimization technique called semidefinite relaxation of quadratic optimization, which has attracted much interest in the field of applied mathematics, is proposed to use as a new analytical method for the determination of magnetic structure, followed by the application of polarized neutron diffraction data. This mathematical approach allows avoiding spurious local solutions, decreasing the amount of time required to find a tentative solution and finding multiple solutions when they exist.

97 MATHEMATICS AND COMPUTING↗