Search NASA⌕ Search

SEARCH · Search NASA

Results for “penalty methods”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Automation of reverse engineering process in aircraft modeling and related optimization problems

During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for quadratic programming problems.

Li, W.↗
NASA NTRS1975

A steepest descents method for reentry optimization

A steepest descents optimization program is applied to the problem of a lifting vehicle entering the earth's atmosphere. The program employs penalty functions representing terminal conditions and inflight inequality constraints. During each iteration, it reduces a single performance measure which is the sum of the performance index and the penalty functions. Therefore, only one set of adjoint equations must be integrated per iteration. Values of weight factors, multiplying the penalty functions, are automatically adjusted before each iteration in order that the penalty functions will approach acceptable values. This method is shown to be a form of the classical Lagrange multiplier methods.

Andrus, J. F.↗
NASA NTRS1976

On implementation of the extended interior penalty function

The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.

Cassis, J. H.↗
NASA NTRS1990

A computational efficient modelling of laminar separation bubbles

In predicting the aerodynamic characteristics of airfoils operating at low Reynolds numbers, it is often important to account for the effects of laminar (transitional) separation bubbles. Previous approaches to the modelling of this viscous phenomenon range from fast but sometimes unreliable empirical correlations for the length of the bubble and the associated increase in momentum thickness, to more accurate but significantly slower displacement-thickness iteration methods employing inverse boundary-layer formulations in the separated regions. Since the penalty in computational time associated with the more general methods is unacceptable for airfoil design applications, use of an accurate yet computationally efficient model is highly desirable. To this end, a semi-empirical bubble model was developed and incorporated into the Eppler and Somers airfoil design and analysis program. The generality and the efficiency was achieved by successfully approximating the local viscous/inviscid interaction, the transition location, and the turbulent reattachment process within the framework of an integral boundary-layer method. Comparisons of the predicted aerodynamic characteristics with experimental measurements for several airfoils show excellent and consistent agreement for Reynolds numbers from 2,000,000 down to 100,000.

Dini, Paolo↗
NASA NTRS1993

Advanced Multi-Phase Flow CFD Model Development for Solid Rocket Motor Flowfield Analysis

It is known that the simulations of solid rocket motor internal flow field with AL-based propellants require complex multi-phase turbulent flow model. The objective of this study is to develop an advanced particulate multi-phase flow model which includes the effects of particle dynamics, chemical reaction and hot gas flow turbulence. The inclusion of particle agglomeration, particle/gas reaction and mass transfer, particle collision, coalescence and breakup mechanisms in modeling the particle dynamics will allow the proposed model to realistically simulate the flowfield inside a solid rocket motor. The Finite Difference Navier-Stokes numerical code FDNS is used to simulate the steady-state multi-phase particulate flow field for a 3-zone 2-D axisymmetric ASRM model and a 6-zone 3-D ASRM model at launch conditions. The 2-D model includes aft-end cavity and submerged nozzle. The 3-D model represents the whole ASRM geometry, including additional grain port area in the gas cavity and two inhibitors. FDNS is a pressure based finite difference Navier-Stokes flow solver with time-accurate adaptive second-order upwind schemes, standard and extended k-epsilon models with compressibility corrections, multi zone body-fitted formulations, and turbulence particle interaction model. Eulerian/Lagrangian multi-phase solution method is applied for multi-zone mesh. To simulate the chemical reaction, penalty function corrected efficient finite-rate chemistry integration method is used in FDNS. For the AL particle combustion rate, the Hermsen correlation is employed. To simulate the turbulent dispersion of particles, the Gaussian probability distribution with standard deviation equal to (2k/3)(exp 1/2) is used for the random turbulent velocity components. The computational results reveal that the flow field near the juncture of aft-end cavity and the submerged nozzle is very complex. The effects of the turbulent particles affect the flow field significantly and provide better prediction of the ASRM performance. The multi-phase flow analysis using the FDNS code in the present research can be used as a design tool for solid rocket motor applications.

Liaw, Paul↗
NASA NTRS2002

Penalty-Based Finite Element Interface Technology for Analysis of Homogeneous and Composite Structures

An effective and robust interface element technology able to connect independently modeled finite element subdomains has been developed. This method is based on the use of penalty constraints and allows coupling of finite element models whose nodes do not coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. A significant effort has been directed toward identifying those model characteristics (element geometric properties, material properties, and loads) that most strongly affect the required penalty parameter, and subsequently to developing simple 'formulae' for automatically calculating the proper penalty parameter for each interface constraint. This task is especially critical in composite materials and structures, where adjacent sub-regions may be composed of significantly different materials or laminates. This approach has been validated by investigating a variety of two-dimensional problems, including composite laminates.

Averill, Ronald C.↗
NASA NTRS1999

Optimization of Aerospace Structure Subject to Damage Tolerance Criteria

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers. It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages. A common method for topology optimization is that of compliance minimization which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system. Sherrnan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this. SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗
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↗
DOE OSTI2025

The electronic structure, crystal fields, and magnetic anisotropy in RECo 5 magnets

The current progress in describing rare-earth-based magnets' electronic structure and magnetic properties is discussed. We use several currently popular electronic structure methods to show the typical values of critical parameters that define the physics of RECo 5 (RE = rare earth atom) materials. The magnetic moments and magnetic anisotropy of 4f atoms are obtained using several approaches, including anisotropic 4f-charge density-constrained DFT and DFT+HI methods. We also suggest the introduction of "penalty" functional for obtaining correct variational total energy in the traditional Hund's rule-constrained DFT-based techniques. The applicability and future extensions are discussed. The proposed combination of methods is potentially suitable for high-throughput computational searches of new rare-earth-containing magnetic materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1967

GREMEX-A new management training concept

Goddard Research Engineering Management Exercise provides experience in R&D project decision making from a management rather than technological view. The participant directs a hypothetical project presented in the management simulation technique. He uses old or new methods without concern for rewards or penalties existing in real life.

Denault, M. F.↗
NASA NTRS1974

A comparison of two types of structural optimization procedures for satisfying flutter requirements

A comparison is made of results obtained from mathematical programming and optimality criteria procedures for the minimum-mass design of typical aircraft wing structures to satisfy prescribed flutter requirements. The mathematical programming method is based on an interior penalty function approach. A rigorous optimality criterion and an intuitive optimality criterion based on uniform strain energy density are considered. An intuitive resizing procedure is used for both optimality criterion solutions. All results are calculated using the same computer program, changing only the optimization procedure. Both high- and low-aspect-ratio wings are examined. Finite elements are used for structural modeling, and the generalized coordinates for the flutter solution are based on the natural vibration modes of the structure.

Haftka, R. T.↗
NASA NTRS1984

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗
NASA NTRS1985

The performance characteristics of simulated ice on rotorcraft airfoils

Attention is given to the results of NASA-sponsored rotorcraft icing research which was aimed at the formulation of a predictive method for the computation of performance penalties due to rotor and airfoil icing. Parametric simulated ice test results obtained in wind tunnels are compared with those of other investigations. These comparisons indicate that proper design of simulated ice shapes can adequately represent ice on airfoil sections, with incremental lift, drag, and pitching moments matching those generated in icing wind tunnels.

Flemming, R. J.↗
NASA NTRS1988

Turbofan forced mixer lobe flow modeling. Part 3: Application to augment engines

Military engines frequently need large quantities of thrust for short periods of time. The addition of an augmentor can provide such thrust increases but with a penalty of increased duct length and engine weight. The addition of a forced mixer to the augmentor improves performance and reduces the penalty, as well as providing a method for siting the required flame holders. In this report two augmentor concepts are investigated: a swirl-mixer augmentor and a mixer-flameholder augmentor. Several designs for each concept are included and an experimental assessment of one of the swirl-mixer augmentors is presented.

Barber, T.↗
NASA NTRS1993

Optimal design of imperfect, anisotropic, ring-stiffened cylinders under combined loads

Development of an algorithm to perform the optimal sizing of buckling resistant, imperfect, anisotropic ring-stiffened cylinders subjected to axial compression, torsion, and internal pressure is presented. The enforcement of stability constraints is treated in a way that does not require any eigenvalue analysis. Assumption of criticality of these stability constraints during the optimal sizing of the cylinders produced designs that nevertheless satisfied all of the stress constraints as well as the stability constraints. Case studies performed using a combination of penalty function and feasible direction optimization methods indicate that the presence of the axisymmetric initial imperfection in the cylinder wall can significantly affect the optimal designs. Weight savings associated with the addition of two rings to the unstiffened cylinder and/or the addition of internal pressure is substantial when torsion makes up a significant fraction of the combined load state.

Ley, Robert P.↗
NASA NTRS2015

Comparative Habitability of Transiting Exoplanets

Exoplanet habitability is traditionally assessed by comparing a planet’s semimajor axis to the location of its host star’s “habitable zone,” the shell around a star for which Earth-like planets can possess liquid surface water. The Kepler space telescope has discovered numerous planet candidates near the habitable zone, and many more are expected from missions such as K2, TESS, and PLATO. These candidates often require significant follow-up observations for validation, so prioritizing planets for habitability from transit data has become an important aspect of the search for life in the universe. We propose a method to compare transiting planets for their potential to support life based on transit data, stellar properties and previously reported limits on planetary emitted flux. For a planet in radiative equilibrium, the emitted flux increases with eccentricity, but decreases with albedo. As these parameters are often unconstrained, there is an “eccentricity-albedo degeneracy” for the habitability of transiting exoplanets. Our method mitigates this degeneracy, includes a penalty for large-radius planets, uses terrestrial mass–radius relationships, and, when available, constraints on eccentricity to compute a number we call the “habitability index for transiting exoplanets” that represents the relative probability that an exoplanet could support liquid surface water. We calculate it for Kepler objects of interest and find that planets that receive between 60% and 90% of the Earth’s incident radiation, assuming circular orbits, are most likely to be habitable. Finally, we make predictions for the upcoming TESS and James Webb Space Telescope missions.

Planet and satellite surfaces↗
DOE OSTI2024

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗
DOE OSTI2025

Beam optics ramping in underconstrained lattice design: Application to Electron-Ion Collider hadron storage ring cooling section

This paper presents the lattice design and optics ramping strategy for the cooling section of the hadron storage ring at the electron-ion collider. The main challenge is that available tuning knobs exceed beam-optics constraints. Independently optimized injection and top-energy optics often yield disconnected solutions, making interpolation impossible. To address this, we propose two new methods. The first is an intermediate-penalty scheme that ensures ramping path continuity by penalizing constraint violations at intermediate states. The second is a continuation-based approach that adapts high-energy optics to low energy, guided by an adaptive weighting scheme to balance injection and ramping constraints. The solutions meet all beam dynamics and hardware limits. The two methods offer a general strategy for ramping in systems where the solution space is under-constrained and the starting and target configurations are far apart.

43 PARTICLE ACCELERATORS↗