Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Determining Spacecraft Reaction Wheel Friction Parameters

Software was developed to characterize the drag in each of the Cassini spacecraft's Reaction Wheel Assemblies (RWAs) to determine the RWA friction parameters. This tool measures the drag torque of RWAs for not only the high spin rates (greater than 250 RPM), but also the low spin rates (less than 250 RPM) where there is a lack of an elastohydrodynamic boundary layer in the bearings. RWA rate and drag torque profiles as functions of time are collected via telemetry once every 4 seconds and once every 8 seconds, respectively. Intermediate processing steps single-out the coast-down regions. A nonlinear model for the drag torque as a function of RWA spin rate is incorporated in order to characterize the low spin rate regime. The tool then uses a nonlinear parameter optimization algorithm based on the Nelder-Mead simplex method to determine the viscous coefficient, the Dahl friction, and the two parameters that account for the low spin-rate behavior.

Sarani, Siamak↗
NASA NTRS2011

Uncertainty Analysis via Failure Domain Characterization: Unrestricted Requirement Functions

This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. The methods developed herein, which are based on nonlinear constrained optimization, are applicable to requirement functions whose functional dependency on the uncertainty is arbitrary and whose explicit form may even be unknown. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the assumed uncertainty model (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.

Crespo, Luis G.↗
NASA NTRS2012

Wavefront Sensing for WFIRST with a Linear Optical Model

In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.

Jurling, Alden S.↗
NASA NTRS2015

Aerodynamic Shape Optimization of a Dual-Stream Supersonic Plug Nozzle

Aerodynamic shape optimization was performed on an isolated axisymmetric plug nozzle sized for a supersonic business jet. The dual-stream concept was tailored to attenuate nearfield pressure disturbances without compromising nozzle performance. Adjoint-based anisotropic mesh refinement was applied to resolve nearfield compression and expansion features in the baseline viscous grid. Deformed versions of the adapted grid were used for subsequent adjoint-driven shape optimization. For design, a nonlinear gradient-based optimizer was coupled to the discrete adjoint formulation of the Reynolds-averaged Navier- Stokes equations. All nozzle surfaces were parameterized using 3rd order B-spline interpolants and perturbed axisymmetrically via free-form deformation. Geometry deformations were performed using 20 design variables shared between the outer cowl, shroud and centerbody nozzle surfaces. Interior volume grid deformation during design was accomplished using linear elastic mesh morphing. The nozzle optimization was performed at a design cruise speed of Mach 1.6, assuming core and bypass pressure ratios of 6.19 and 3.24, respectively. Ambient flight conditions at design were commensurate with 45,000-ft standard day atmosphere.

shape optimization↗
NASA NTRSDate not supplied

Analytical Partial Derivatives of the Q-Law Guidance Algorithm

One method of producing low-thrust trajectories is the closed-loop Q-Law guidance algorithm. This work wraps Q-Law inside a nonlinear programming problem to search for locally optimal gain combinations and enforce nonlinear constraints on the initial state. Gradient-based trajectory optimization has been shown to benefit greatly when analytical partial derivatives are supplied to the optimizer. This paper presents the Q-Law optimization problem setup and derives the Q-Law thrust vector partial derivatives for the State Transition Matrix required by standard nonlinear optimization software.

Jackson L Shannon↗
NASA NTRS1978

Alternatives for jet engine control

General goals of the research were classified into two categories. The first category involves the use of modern multivariable frequency domain methods for control of engine models in the neighborhood of a quiescent point. The second category involves the use of nonlinear modelling and optimization techniques for control of engine models over a more extensive part of the flight envelope. In the frequency domain category, works were published in the areas of low-interaction design, polynomial design, and multiple setpoint studies. A number of these ideas progressed to the point at which they are starting to attract practical interest. In the nonlinear category, advances were made both in engine modelling and in the details associated with software for determination of time optimal controls. Nonlinear models for a two spool turbofan engine were expanded and refined; and a promising new approach to automatic model generation was placed under study. A two time scale scheme was developed to do two-dimensional dynamic programming, and an outward spiral sweep technique has greatly speeded convergence times in time optimal calculations.

Leake, R. J.↗
NASA NTRS2003

Nonlinear Resonant Oscillations of Gas in Optimized Acoustical Resonators and the Effect of Central Blockage

Optimizing resonator shapes for maximizing the ratio of maximum to minimum gas pressure at an end of the resonator is investigated numerically. It is well known that the resonant frequencies and the nonlinear standing waveform in an acoustical resonator strongly depend on the resonator geometry. A quasi-Newton type scheme was used to find optimized axisymmetric resonator shapes achieving the maximum pressure compression ratio with an acceleration of constant amplitude. The acoustical field was solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects were obtained through an automation scheme based on continuation method. Results are presented for optimizing three types of geometry: a cone, a horn-cone and a half cosine-shape. For each type, different optimized shapes were found when starting with different initial guesses. Further, the one-dimensional model was modified to study the effect of an axisymmetric central blockage on the nonlinear standing wave.

Li, Xiaofan↗
NASA NTRS2003

Nonlinear Resonant Oscillations of Gas in Optimized Acoustical Resonators and the Effect of Central Blockage

Optimizing resonator shapes for maximizing the ratio of maximum to minimum gas pressure at an end of the resonator is investigated numerically. It is well known that the resonant frequencies and the nonlinear standing waveform in an acoustical resonator strongly depend on the resonator geometry. A quasi-Newton type scheme was used to find optimized axisymmetric resonator shapes achieving the maximum pressure compression ratio with an acceleration of constant amplitude. The acoustical field was solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects were obtained through an automation scheme based on continuation method. Results are presented for optimizing three types of geometry: a cone, a horn-cone and a half cosine- shape. For each type, different optimized shapes were found when starting with different initial guesses. Further, the one-dimensional model was modified to study the effect of an axisymmetric central blockage on the nonlinear standing wave.

Li, Xiao-Fan↗
NASA NTRS1990

Optimal finite-thrust spacecraft trajectories using collocation and nonlinear programming

A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed optimization technique which uses a piecewise polynomial representation for the state and controls, and collocation, thus converting the optimal control problem into a nonlinear programming problem, which is solved numerically. This technique has been modified to provide efficient handling of those portions of the trajectory which can be determined analytically, i.e., the coast arcs. Among the problems that have been solved using this method are optimal rendezvous and transfer (including multirevolution cases) and optimal multiburn orbit insertion from hyperbolic approach.

Enright, Paul J.↗
NASA NTRS1992

The detrimental effect of friction on space microgravity robotics

The authors present an analysis of why control systems are ineffective in compensating for acceleration disturbances due to Coulomb friction. Linear arguments indicate that the effects of Coulomb friction on a body are most difficult to reject when the control actuator is separated from the body of compliance. The linear arguments were illustrated in a nonlinear simulation of optimal linear tracking control in the presence of nonlinear friction. The results of endpoint acceleration measurements for four robot designs are presented and are compared with simulation and to equivalent measurements on a human. It is concluded that Coulomb friction in common bearings and transmission induces unacceptable levels of endpoint acceleration, that these accelerations cannot be adequately attenuated by control, and that robots for microgravity work will require special design considerations for inherently low friction.

Newman, Wyatt S.↗
NASA NTRS1980

Alternatives for jet engine control

Alternatives to linear quadratic regulator theory in the linear case are examined along with nonlinear modelling and optimization approaches for global control. Context for the studies has been set by the DYNGEN digital simulator and by models generated for various phases of the F100 Multivariable Control Synthesis Program. With respect to the linear alternatives, the multivariable frequency domain is stressed. Progress is reported in both the direct algebraic approach to exact model matching, by means of stimulating work on the basic computational issues, and in the indirect generalized Nyquist approach. With respect to nonlinear modelling and optimization, the emphasis is twofold: the development of analytical nonlinear models of the jet engine and the use of these models in conjunction with techniques of mathematical programming in order to study global control over nonincremental portions of the flight envelope. The possibility of using tensor methods is explored.

Sain, M. K.↗
NASA NTRS1986

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗
DOE OSTI2022

The optimal beam-loading in two-bunch nonlinear plasma wakefield accelerators

Abstract Due to the highly nonlinear nature of the beam-loading, it is currently not possible to analytically determine the beam parameters needed in a two-bunch plasma wakefield accelerator for maintaining a low energy spread. Therefore in this paper, by using the Broyden–Fletcher–Goldfarb–Shanno algorithm for the parameter scanning with the code QuickPIC and the polynomial regression together with k -fold cross-validation method, we obtain two fitting formulas for calculating the parameters of tri-Gaussian electron beams when minimizing the energy spread based on the beam-loading effect in a nonlinear plasma wakefield accelerator. One formula allows the optimization of the normalized charge per unit length of a trailing beam to achieve the minimal energy spread, i.e. the optimal beam-loading. The other one directly gives the transformer ratio when the trailing beam achieves the optimal beam-loading. A simple scaling law for charges of drive beams and trailing beams is obtained from the fitting formula, which indicates that the optimal beam-loading is always achieved for a given charge ratio of the two beams when the length and separation of two beams and the plasma density are fixed. The formulas can also help obtain the optimal plasma densities for the maximum accelerated charge and the maximum acceleration efficiency under the optimal beam-loading respectively. These two fitting formulas will significantly enhance the efficiency for designing and optimizing a two-bunch plasma wakefield acceleration stage.

Physics↗
NASA NTRS1984

Development of a turbomachinery design optimization procedure using a multiple-parameter nonlinear perturbation method

An investigation was carried out to complete the preliminary development of a combined perturbation/optimization procedure and associated computational code for designing optimized blade-to-blade profiles of turbomachinery blades. The overall purpose of the procedures developed is to provide demonstration of a rapid nonlinear perturbation method for minimizing the computational requirements associated with parametric design studies of turbomachinery flows. The method combines the multiple parameter nonlinear perturbation method, successfully developed in previous phases of this study, with the NASA TSONIC blade-to-blade turbomachinery flow solver, and the COPES-CONMIN optimization procedure into a user's code for designing optimized blade-to-blade surface profiles of turbomachinery blades. Results of several design applications and a documented version of the code together with a user's manual are provided.

Stahara, S. S.↗
NASA NTRS1989

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Lan, C. Edward↗