Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical 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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Computational issues in optimal tuning and placement of passive dampers

The effectiveness of viscous elements in introducing damping in a structure is a function of several variables including their number, their location in the structure, and their physical properties. In this paper, the optimal damper placement and tuning problem is posed to optimize these variables. Both discrete and continuous optimization problems are formulated and solved corresponding, respectively, to the problems of placement of passive elements and to the tuning of their parameters. The paper particularly emphasizes the critical computational issues resulting from the optimization formulations. Numerical results involving a lightly damped testbed structure are presented.

Chu, C. C.↗
NASA NTRS1999

Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations

The derivation of storage explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, 16 ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been assessed using the differential equation testing code DETEST, and with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be pearl), matched while still saving two to three registers of memory.

Kennedy, Chistopher A.↗
NASA NTRS2000

Discontinuous dual-primal mixed finite elements for elliptic problems

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Bottasso, Carlo L.↗
NASA NTRS2010

Simulation of Propellant Loading System Senior Design Implement in Computer Algorithm

Propellant loading from the Storage Tank to the External Tank is one of the very important and time consuming pre-launch ground operations for the launch vehicle. The propellant loading system is a complex integrated system involving many physical components such as the storage tank filled with cryogenic fluid at a very low temperature, the long pipe line connecting the storage tank with the external tank, the external tank along with the flare stack, and vent systems for releasing the excess fuel. Some of the very important parameters useful for design purpose are the prediction of pre-chill time, loading time, amount of fuel lost, the maximum pressure rise etc. The physics involved for mathematical modeling is quite complex due to the fact the process is unsteady, there is phase change as some of the fuel changes from liquid to gas state, then conjugate heat transfer in the pipe walls as well as between solid-to-fluid region. The simulation is very tedious and time consuming too. So overall, this is a complex system and the objective of the work is student's involvement and work in the parametric study and optimization of numerical modeling towards the design of such system. The students have to first become familiar and understand the physical process, the related mathematics and the numerical algorithm. The work involves exploring (i) improved algorithm to make the transient simulation computationally effective (reduced CPU time) and (ii) Parametric study to evaluate design parameters by changing the operational conditions

Bandyopadhyay, Alak↗
NASA NTRS1983

An algorithm for the empirical optimization of antenna arrays

A numerical technique is presented to optimize the performance of arbitrary antenna arrays under realistic conditions. An experimental-computational algorithm is formulated in which n-dimensional minimization methods are applied to measured data obtained from the antenna array. A numerical update formula is used to induce partial derivative information without requiring special perturbations of the array parameters. The algorithm provides a new design for the antenna array, and the method proceeds in an iterative fashion. Test case results are presented showing the effectiveness of the algorithm.

Blank, S.↗
NASA NTRSDate not supplied

Scaled Aeroelastic Wind Tunnel Model Design with Topology Optimization

The goal of this work is to use numerical aeroelastic topology optimization to design flutter models to be tested in the Transonic Dynamics Tunnel, as part of an envisioned validation experiment for transonic flutter. The topological design develops the structural details of a variable-thickness aluminum plate located at the camber line of a scaled transport aircraft model, in order to satisfy the various conflicting design requirements, including a prescribed flutter boundary, flutter frequency, and static stress levels. Four designs are demonstrated here, where it is shown that the simultaneous design of a cylindrical tip store can help ease the conflict between low stiffness (to allow a wing to flutter in the tunnel envelope) and high strength (to ensure safe structural response). The tip store complicates the geometrical features of the wing, however, and is generally undesirable from the vantage point of a validation experiment.

Aeroelasticity↗
NASA NTRS2022

Stability Analysis of Streaks Induced by Optimized Vortex Generators

Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.

Boundary layer transition↗
NASA NTRS2022

Stability Analysis of Streaks Induced By Optimized Vortex Generators

Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.

Boundary layer transition↗
NASA NTRS1991

Optimal discrete-time dynamic output-feedback design - A w-domain approach

An alternative method for optimal digital control design is described in this paper. The method is based on the usage of the w-transform and has many attractive design features. One of these is its immediate connection with frequency loop-shaping techniques that are now popular and effective for multivariable control synthesis in continuous-time domain. Furthermore, any design algorithms originally developed for continuous-time systems can now be immediately extended to the discrete-time domain. The main results presented in this paper are the exact problem formulation and solution of an optimal discrete-time dynamic output-feedback design in the w-domain involving a quadratic performance index to random disturbances. In addition, necessary conditions for optimality are obtained for the numerical solution of the optimal output-feedback compensator design. A numerical example is presented illustrating its application to the design of a low-order dynamic compensator in a stability augmentation system of a commercial transport.

Ha, Cheolkeun↗
NASA NTRS1990

Numerical approach of collision avoidance and optimal control on robotic manipulators

Collision-free optimal motion and trajectory planning for robotic manipulators are solved by a method of sequential gradient restoration algorithm. Numerical examples of a two degree-of-freedom (DOF) robotic manipulator are demonstrated to show the excellence of the optimization technique and obstacle avoidance scheme. The obstacle is put on the midway, or even further inward on purpose, of the previous no-obstacle optimal trajectory. For the minimum-time purpose, the trajectory grazes by the obstacle and the minimum-time motion successfully avoids the obstacle. The minimum-time is longer for the obstacle avoidance cases than the one without obstacle. The obstacle avoidance scheme can deal with multiple obstacles in any ellipsoid forms by using artificial potential fields as penalty functions via distance functions. The method is promising in solving collision-free optimal control problems for robotics and can be applied to any DOF robotic manipulators with any performance indices and mobile robots as well. Since this method generates optimum solution based on Pontryagin Extremum Principle, rather than based on assumptions, the results provide a benchmark against which any optimization techniques can be measured.

Wang, Jyhshing Jack↗
NASA NTRS1990

AI/OR computational model for integrating qualitative and quantitative design methods

A theoretical framework for integrating qualitative and numerical computational methods for optimally-directed design is described. The theory is presented as a computational model and features of implementations are summarized where appropriate. To demonstrate the versatility of the methodology we focus on four seemingly disparate aspects of the design process and their interaction: (1) conceptual design, (2) qualitative optimal design, (3) design innovation, and (4) numerical global optimization.

Agogino, Alice M.↗
DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗
NASA NTRS1991

User's guide for NETS/PROSSS

Expensive analysis programs are often combined with optimization procedures to solve engineering problems. To obtain an optimal solution requires numerous iterations between the analysis program and the optimizer. This often becomes prohibitive due to the cost and amount of computer time needed to converge to an optimal solution. NETS/PROSSS was developed to address this problem. The purpose of this paper is to serve as a user's guide for NETS/PROSSS. The key features include the neural network, determining the training pairs for the neural network, and the approximated analysis/optimization process. A small problem is given to serve as an example of how to apply the system.

Rogers, James L.↗
NASA NTRS1991

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

Taasan, Shlomo↗
NASA NTRS2008

Signal Analysis Algorithms for Optimized Fitting of Nonresonant Laser Induced Thermal Acoustics Damped Sinusoids

This study seeks a numerical algorithm which optimizes frequency precision for the damped sinusoids generated by the nonresonant LITA technique. It compares computed frequencies, frequency errors, and fit errors obtained using five primary signal analysis methods. Using variations on different algorithms within each primary method, results from 73 fits are presented. Best results are obtained using an AutoRegressive method. Compared to previous results using Prony s method, single shot waveform frequencies are reduced approx.0.4% and frequency errors are reduced by a factor of approx.20 at 303K to approx. 0.1%. We explore the advantages of high waveform sample rates and potential for measurements in low density gases.

Balla, R. Jeffrey↗