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Results for “Approximate gradient descent”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2005

Kurtosis Approach Nonlinear Blind Source Separation

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Duong, Vu A.↗

NASA NTRS2005

Kurtosis Approach for Nonlinear Blind Source Separation

kurtosis↗

NASA NTRS1991

Inverse problems in diffraction

A two-dimensional problem of diffraction of a plane electromagnetic wave on a smooth 2 pi-periodic surface is considered. A numerical algorithm solving this problem is developed. An inverse problem of determination of the shape of 2 pi-periodic surface using the performance data of reverse scattering is considered. The inverse problem was solved by means of minimization of the residual functional with the help of the gradient descent method. The initial data were calculated with the help of the numerical method. On each step of the iterative method of minimization, the residual functional was calculated approximately with the help of the small slope method. The examples of the shape determination are considered.

Mikheev, Andrew G.↗

NASA NTRS1995

A General Method for Solving Systems of Non-Linear Equations

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Nachtsheim, Philip R.↗

NASA NTRS1987

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗

NASA NTRS1996

ATMOS/ATLAS-3 Observations of Long-Lived Tracers and Descent in the Antarctic Vortex in November 1994

Observations of the long-lived tracers N2O, CH4 and HF obtained by the Atmospheric Trace Molecule Spectroscopy (ATMOS) instrument in early November 1994 are used to estimate average descent rates during winter in the Antarctic polar vortex of 0.5 to 1.5 km/month in the lower stratosphere, and 2.5 to 3.5 km/month in the middle and upper stratosphere. Descent rates inferred from ATMOS tracer observations agree well with theoretical estimates obtained using radiative heating calculations. Air of mesospheric origin (N2O less than 5 ppbV) was observed at altitudes above about 25 km within the vortex. Strong horizontal gradients of tracer mixing ratios, the presence of mesospheric air in the vortex in early spring, and the variation with altitude of inferred descent rates indicate that the Antarctic vortex is highly isolated from midlatitudes throughout the winter from approximately 20 km to the stratopause. The 1994 Antarctic vortex remained well isolated between 20 and 30 km through at least mid-November.

Abrams, M. C.↗

NASA NTRS1994

Multigrid one shot methods for optimal control problems: Infinite dimensional control

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Arian, Eyal↗

NASA NTRS1981

Determination of atmospheric properties for STS-1 aerothermodynamic investigations

A procedure for determining an approximation to the freestream atmospheric properties along the Shuttle entry trajectory is presented. Meteorological data as input is obtained by rawinsondes from surface to 70 km, and meteorological spheres from 60-90 km, launched from Hawaii and California. The Langley Atmospheric Information Retrieval System (LAIRS) developed to approximate the atmospheric freestream properties along the flight path, is outlined, noting temperature and wind data are interpolated in altitude, while gradients and diurnal and semidiurnal coefficients are taken from the COSPAR reference atmosphere. The data are input to a model to project temperature profiles for the Shuttle descent, and the input atmospheric parameters are listed. Efforts are continuing in order to correct discrepancies in the generated profiles for regions below 3 km.

Price, J. M.↗

NASA NTRS1973

Optimal control of a variable spin speed CMG system for space vehicles

Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

Liu, T. C.↗

NASA NTRS2009

Optimization of OT-MACH Filter Generation for Target Recognition

An automatic Optimum Trade-off Maximum Average Correlation Height (OT-MACH) filter generator for use in a gray-scale optical correlator (GOC) has been developed for improved target detection at JPL. While the OT-MACH filter has been shown to be an optimal filter for target detection, actually solving for the optimum is too computationally intensive for multiple targets. Instead, an adaptive step gradient descent method was tested to iteratively optimize the three OT-MACH parameters, alpha, beta, and gamma. The feedback for the gradient descent method was a composite of the performance measures, correlation peak height and peak to side lobe ratio. The automated method generated and tested multiple filters in order to approach the optimal filter quicker and more reliably than the current manual method. Initial usage and testing has shown preliminary success at finding an approximation of the optimal filter, in terms of alpha, beta, gamma values. This corresponded to a substantial improvement in detection performance where the true positive rate increased for the same average false positives per image.

false alarm reduction↗

NASA NTRS1987

Maximum likelihood estimation of parameterized 3-D surfaces using a moving camera

A new approach is introduced to estimating object surfaces in three-dimensional space from a sequence of images. A surface of interest here is modeled as a 3-D function known up to the values of a few parameters. The approach will work with any parameterization. However, in work to date researchers have modeled objects as patches of spheres, cylinders, and planes - primitive objects. These primitive surfaces are special cases of 3-D quadric surfaces. Primitive surface estimation is treated as the general problem of maximum likelihood parameter estimation based on two or more functionally related data sets. In the present case, these data sets constitute a sequence of images taken at different locations and orientations. A simple geometric explanation is given for the estimation algorithm. Though various techniques can be used to implement this nonlinear estimation, researches discuss the use of gradient descent. Experiments are run and discussed for the case of a sphere of unknown location. These experiments graphically illustrate the various advantages of using as many images as possible in the estimation and of distributing camera positions from first to last over as large a baseline as possible. Researchers introduce the use of asymptotic Bayesian approximations in order to summarize the useful information in a sequence of images, thereby drastically reducing both the storage and amount of processing required.

Hung, Y.↗

NASA NTRS1988

In situ observations of ClO in the Antarctic: Evidence for chlorine catalyzed destruction of ozone

Results from a series of 12 ER-2 aircraft flights into the Antarctic polar vortex are summarized. These in situ data define the spatial and temporal distribution of ClO as the aircraft flew at an altitude of approx. 18 km from Punta Arenas (54 deg S latitude) to the base of the Palmer Peninsula (72 deg S latitude), executed a rapid descent to approx. 13 km, turned north and climbed bach to approximately 18 km, returning to Punta Arenas. A general pattern in the ClO distribution is reported: mixing ratios of approximately 10 ppt are found at altitude in the vicinity of 55 deg S increasing to 50 ppt at 60 degrees S. In the vicinity of 65 deg S latitude a steep gradient in the ClO mixing ratio is observed. At a fixed potential temperature, the ClO mixing ratio through this sharp transition increases by an order of magnitude within a very few degrees of latitude, thus defining the edge of the chemical containment vessel. From the edge of that containment vessel to the southern extension of the flights, 72 deg S, a dome of slowly increasing ClO best describes the distribution. Conclusion are drawn from the data.

Anderson, J. G.↗

NASA NTRS2013

Peak-Seeking Control For Reduced Fuel Consumption: Flight-Test Results For The Full-Scale Advanced Systems Testbed FA-18 Airplane

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. This presentation also focuses on the design of the flight experiment and the practical challenges of conducting the experiment.

flight optimization↗

NASA NTRS2013

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-Test Results

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

flight optimization↗

NASA NTRS2013

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-test Results

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

flight optimization↗

NASA NTRS1992

Learning and tuning fuzzy logic controllers through reinforcements

A new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. In particular, our Generalized Approximate Reasoning-based Intelligent Control (GARIC) architecture: (1) learns and tunes a fuzzy logic controller even when only weak reinforcements, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto, Sutton, and Anderson to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and has demonstrated significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Berenji, Hamid R.↗

NASA NTRS1992

Learning and tuning fuzzy logic controllers through reinforcements

This paper presents a new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system. In particular, our generalized approximate reasoning-based intelligent control (GARIC) architecture (1) learns and tunes a fuzzy logic controller even when only weak reinforcement, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward neural network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto et al. (1983) to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and demonstrates significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Berenji, Hamid R.↗

NASA NTRS1990

Optical neural network system for pose determination of spinning satellites

An optical neural network architecture and algorithm based on a Hopfield optimization network are presented for multitarget tracking. This tracker utilizes a neuron for every possible target track, and a quadratic energy function of neural activities which is minimized using gradient descent neural evolution. The neural net tracker is demonstrated as part of a system for determining position and orientation (pose) of spinning satellites with respect to a robotic spacecraft. The input to the system is time sequence video from a single camera. Novelty detection and filtering are utilized to locate and segment novel regions from the input images. The neural net multitarget tracker determines the correspondences (or tracks) of the novel regions as a function of time, and hence the paths of object (satellite) parts. The path traced out by a given part or region is approximately elliptical in image space, and the position, shape and orientation of the ellipse are functions of the satellite geometry and its pose. Having a geometric model of the satellite, and the elliptical path of a part in image space, the three-dimensional pose of the satellite is determined. Digital simulation results using this algorithm are presented for various satellite poses and lighting conditions.

Lee, Andrew↗