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Results for “STEEPEST DESCENT METHOD”

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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
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 NTRS1986

Optimal block cosine transform image coding for noisy channels

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered.

Vaishampayan, V.↗
NASA NTRS1990

Optimal block cosine transform image coding for noisy channels

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimiaation of a scheme based on the 2-D block cosine transorm when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noise channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered.

Vaishampayan, Vinay A.↗
DOE OSTI2024

Gravitational production of heavy particles during and after inflation

Abstract We investigate the gravitational production of a scalar fieldχwith a mass exceeding the Hubble scale during inflationm χ ≳H I , employing both analytical and numerical approaches. We demonstrate that the steepest descent method effectively captures the epochs and yields of gravitational production in a compact and simple analytical framework. These analytical results align with the numerical solutions of the field equation. Our study covers three spacetime backgrounds: de Sitter, power-law inflation, and the Starobinsky inflation model. Within these models, we identify two distinct phases of particle production: during and after inflation. During inflation, we derive an accurate analytic expression for the particle production rate, accounting for a varying Hubble rate. After inflation, the additional burst of particle production depends on the inflaton mass around its minimum. When this mass is smaller than the Hubble scale during inflation,H I , there is no significant extra production. However, if the inflaton mass is larger, post-inflation production becomes the dominant contribution. Furthermore, we explore the implications of gravitationally produced heavy fields for dark matter abundance, assuming their cosmological stability.

Physics↗
NASA NTRS1973

DOPEX-1D2C: A one-dimensional, two-constraint radiation shield optimization code

A one-dimensional, two-constraint radiation sheild weight optimization procedure and a computer program, DOPEX-1D2C, is described. The DOPEX-1D2C uses the steepest descent method to alter a set of initial (input) thicknesses of a spherical shield configuration to achieve a minimum weight while simultaneously satisfying two dose-rate constraints. The code assumes an exponential dose-shield thickness relation with parameters specified by the user. Code input instruction, a FORTRAN-4 listing, and a sample problem are given. Typical computer time required to optimize a seven-layer shield is less than 1/2 minute on an IBM 7094.

Lahti, G. P.↗
NASA NTRS1973

Approximations in the minimum time-to-climb problem

The minimum time-to-climb problem is formulated as a third order system and three approximate solutions based on reduced order systems are presented. The first of these is the often used energy state, the second is the less frequently used two state and the third is a slightly altered form of the second, herein called the modified two state. These three approximations are discussed and compared both qualitatively and, by using a numerical example, quantitatively. The numerical example is also solved by the steepest descent method to provide a basis for comparison. It is concluded that the modified two state approximation is significantly better than the other two. This approximation is used to assess the sensitivity of climb performance to various vehicle parameters and it is found that, as expected, thrust and weight influence the time-to-climb most strongly.

Ardema, M. D.↗
NASA NTRS1976

Operations research investigations of satellite power stations

A systems model reflecting the design concepts of Satellite Power Stations (SPS) was developed. The model is of sufficient scope to include the interrelationships of the following major design parameters: the transportation to and between orbits; assembly of the SPS; and maintenance of the SPS. The systems model is composed of a set of equations that are nonlinear with respect to the system parameters and decision variables. The model determines a figure of merit from which alternative concepts concerning transportation, assembly, and maintenance of satellite power stations are studied. A hybrid optimization model was developed to optimize the system's decision variables. The optimization model consists of a random search procedure and the optimal-steepest descent method. A FORTRAN computer program was developed to enable the user to optimize nonlinear functions using the model. Specifically, the computer program was used to optimize Satellite Power Station system components.

Cole, J. W.↗
NASA NTRS1982

Effects of unsteady free-stream velocity and free-stream turbulence at a stagnation point

The combined effects of transient free stream velocity and turbulence at a stagnation point on a cylinder situated in a crossflow is investigated analytically, and a model is formulated for the eddy diffusivity induced by free-stream turbulence. The steepest descent method is used to integrate the governing momentum expression, and numerical solutions are given for the unsteady wall shear stress function for specific free-stream transients. It is found after correlation of the results by means of a new turbulence parameter that wall friction increases with increasing free-stream turbulence intensity, and that the friction factor increases with increasing reduced frequency of oscillation values.

Gorla, R. S. R.↗
NASA NTRS1984

Effects of unsteady free stream velocity and free stream turbulence on stagnation point heat transfer

The combined effects of transient free stream velocity and free stream turbulence on heat transfer at a stagnation point over a cylinder situated in a crossflow are studied. An eddy diffusivity model was formulated and the governing momentum and energy equations are integrated by means of the steepest descent method. The numerical results for the wall shear stress and heat transfer rate are correlated by a turbulence parameter. The wall friction and heat transfer rate increase with increasing free stream turbulence intensity.

Gorla, R. S. R.↗
NASA NTRS1984

Combined influence of unsteady free stream velocity and free stream turbulence on stagnation point heat transfer

An analysis is presented to study the combined effects of transient free stream velocity and free stream turbulence on heat transfer at a stagnation point over a cylinder situated in a crossflow. An expression for the eddy diffusivity has been formulated and the governing momentum and energy equations are integrated by means of the steepest descent method. The numerical results for the heat transfer rate are correlated by a turbulence parameter. It has been found that the stagnation point heat transfer rate increases with increasing free stream turbulence intensity.

Gorla, R. S. 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 NTRS1991

Airfoil optimization with efficient gradient calculations

The viscous airfoil design analysis code XFOIL was extended to allow optimization using conformal mapping coefficients as design variables. The optimization technique used was the Steepest Descent method applied to a Penalty Function. The gradients of the aerodynamic variables with respect to the design variables were cheaply calculated as by-products of XFOIL's integral boundary layer Newton solver. The speed of the optimization process further increased by updating the Newton system boundary layer variables after each optimization step using the available gradient information. Two examples are presented.

Sorensen, Thomas↗