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At least 1,369 records · Page 76

A method for nonlinear optimization with discrete design variables

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.

Olsen, Gregory R.↗

Development of BEM for ceramic composites

It is evident that for proper micromechanical analysis of ceramic composites, one needs to use a numerical method that is capable of idealizing the individual fibers or individual bundles of fibers embedded within a three-dimensional ceramic matrix. The analysis must be able to account for high stress or temperature gradients from diffusion of stress or temperature from the fiber to the ceramic matrix and allow for interaction between the fibers through the ceramic matrix. The analysis must be sophisticated enough to deal with the failure of fibers described by a series of increasingly sophisticated constitutive models. Finally, the analysis must deal with micromechanical modeling of the composite under nonlinear thermal and dynamic loading. This report details progress made towards the development of a boundary element code designed for the micromechanical studies of an advanced ceramic composite. Additional effort has been made in generalizing the implementation to allow the program to be applicable to real problems in the aerospace industry.

Henry, D. P.↗

Analytical Modeling of the High Strain Rate Deformation of Polymer Matrix Composites

The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.

Goldberg, Robert K.↗

MACOS Version 3.31

Version 3.31 of Modeling and Analysis for Controlled Optical Systems (MACOS) has been released. MACOS is an easy-to-use computer program for modeling and analyzing the behaviors of a variety of optical systems, including systems that have large, segmented apertures and are aligned with the technology of wavefront sensing and control. Two previous versions were described in "Improved Software for Modeling Controlled Optical Systems" (NPO-19841) NASA Tech Briefs, Vol. 21, No. 12 (December 1997), page 42 and "Optics Program Modified for Multithreaded Parallel Computing" (NPO-40572) NASA Tech Briefs, Vol. 30, No. 1 (January 2006) page 13a. The present version incorporates the following enhancements over prior versions: a) A powerful system-optimization facility includes algorithms for linear, nonlinear, unconstrained, and constrained optimization of optical systems under a variety of settings. b) There is now enhanced capability to perturb optical components individually and on subsystem levels, and to optimize system performance by adjusting selected individual components as well as subsystems. c) Capabilities for modeling a variety of new optical aperture types have been added. d) Effects of multilayer thin-film coats on optical surfaces can now be taken into account when tracing polarized rays. e) Major software-engineering work was performed to make MACOS more reliable, flexible, and manageable for purposes of maintenance and further development.

Redding, David↗

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗

THERMAL DIAGNOSTICS WITH THE ATMOSPHERIC IMAGING ASSEMBLY ON BOARD THE SOLAR DYNAMICS OBSERVATORY: A VALIDATED METHOD FOR DIFFERENTIAL EMISSION MEASURE INVERSIONS

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized Gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a nonlinear force-free field, and (3) thermodynamic models from a fully compressible, 3D MHD simulation of active region (AR) corona formation following magnetic flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and Hinode X-ray Telescope data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.

79 ASTRONOMY AND ASTROPHYSICS↗

FY2014 FES (Fusion Energy Sciences) Theory & Simulation Performance Target, Final Report

We report here the work done for the FY14 OFES Theory Performance Target as given below: "Understanding alpha particle confinement in ITER, the world's first burning plasma experiment, is a key priority for the fusion program. In FY 2014, determine linear instability trends and thresholds of energetic particle-driven shear Alfven eigenmodes in ITER for a range of parameters and profiles using a set of complementary simulation models (gyrokinetic, hybrid, and gyrofluid). Carry out initial nonlinear simulations to assess the effects of the unstable modes on energetic particle transport". In the past year (FY14), a systematic study of the alpha-driven Alfven modes in ITER has been carried out jointly by researchers from six institutions involving seven codes including the transport simulation code TRANSP (R. Budny and F. Poli, PPPL), three gyrokinetic codes: GEM (Y. Chen, Univ. of Colorado), GTC (J. McClenaghan, Z. Lin, UCI), and GYRO (E. Bass, R. Waltz, UCSD/GA), the hybrid code M3D-K (G.Y. Fu, PPPL), the gyro-fluid code TAEFL (D. Spong, ORNL), and the linear kinetic stability code NOVA-K (N. Gorelenkov, PPPL). A range of ITER parameters and profiles are specified by TRANSP simulation of a hybrid scenario case and a steady-state scenario case. Based on the specified ITER equilibria linear stability calculations are done to determine the stability boundary of alpha-driven high-n TAEs using the five initial value codes (GEM, GTC, GYRO, M3D-K, and TAEFL) and the kinetic stability code (NOVA-K). Both the effects of alpha particles and beam ions have been considered. Finally, the effects of the unstable modes on energetic particle transport have been explored using GEM and M3D-K.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electrostatic analysis of charge-coupled structures

An analysis is presented which is based upon a numerical solution of Gauss's law for the multiple dielectric semiconductor and electrode structure. The formulation resulted in a large set of equations, usually nonlinear, which were solved by an iterative scheme based upon the Gauss-Seidel method employing a relaxation parameter. Proper consideration of the nonlinearity of the space-charge in the semiconductor allowed convergent solutions which can give reasonable approximations to the channel potential profiles though not as good for estimating the space charge itself. The results of this work, which are three computer programs, are listed. None of the programs give the electric field explicitly as output data. However, when this information is desired, the programs can be expanded to include field estimations based on a polynominal fit to the potential field, or they may serve as subprograms for main programs dealing with general aspects of charge transfer.

Gassaway, J. D.↗

Accelerated convergence of structured banded systems using constrained corrections

An efficient iterative method for solving a structured banded system of equations is described. The method was developed for a full potential flow program and uses a basic interation step, a dynamic relation step, and a multigrid concept of constraining iterative corrections. The solution of a large linear system of equations is examined. Efficient iterative methods have become attractive for large problems. In the nonlinear cases, these iterations may be effectively merged to improve convergence rates.

Kneile, K.↗

V/STOL propulsion control technology

Results of a NASA sponsored study of V/STOL Propulsion Control Analysis are presented. The study involved propulsion control requirements, design concepts and procedures, and control designs for supersonic V/STOL. A variable cycle engine with a remote augmented lift system was used as a basis for establishing typical operating requirements and control concepts, and a nonlinear engine model was developed for control development as a precursor to a real-time simulation capability. A simplified aircraft model was also used to investigate transition requirements, and a long-range technology plan was developed to define subsequent program requirements for achieving a real-time piloted simulation capability.

Brown, H.↗

Global/local methods for probabilistic structural analysis

A probabilistic global/local method is proposed to reduce the computational requirements of probabilistic structural analysis. A coarser global model is used for most of the computations with a local more refined model used only at key probabilistic conditions. The global model is used to establish the cumulative distribution function (cdf) and the Most Probable Point (MPP). The local model then uses the predicted MPP to adjust the cdf value. The global/local method is used within the advanced mean value probabilistic algorithm. The local model can be more refined with respect to the g1obal model in terms of finer mesh, smaller time step, tighter tolerances, etc. and can be used with linear or nonlinear models. The basis for this approach is described in terms of the correlation between the global and local models which can be estimated from the global and local MPPs. A numerical example is presented using the NESSUS probabilistic structural analysis program with the finite element method used for the structural modeling. The results clearly indicate a significant computer savings with minimal loss in accuracy.

Millwater, H. R.↗

A History of Full-Scale Aircraft and Rotorcraft Crash Testing and Simulation at NASA Langley Research Center

This paper summarizes 2-1/2 decades of full-scale aircraft and rotorcraft crash testing performed at the Impact Dynamics Research Facility (IDRF) located at NASA Langley Research Center in Hampton, Virginia. The IDRF is a 240-ft.-high steel gantry that was built originally as a lunar landing simulator facility in the early 1960's. It was converted into a full-scale crash test facility for light aircraft and rotorcraft in the early 1970 s. Since the first full-scale crash test was preformed in February 1974, the IDRF has been used to conduct: 41 full-scale crash tests of General Aviation (GA) aircraft including landmark studies to establish baseline crash performance data for metallic and composite GA aircraft; 11 full-scale crash tests of helicopters including crash qualification tests of the Bell and Sikorsky Advanced Composite Airframe Program (ACAP) prototypes; 48 Wire Strike Protection System (WSPS) qualification tests of Army helicopters; 3 vertical drop tests of Boeing 707 transport aircraft fuselage sections; and, 60+ crash tests of the F-111 crew escape module. For some of these tests, nonlinear transient dynamic codes were utilized to simulate the impact response of the airframe. These simulations were performed to evaluate the capabilities of the analytical tools, as well as to validate the models through test-analysis correlation. In September 2003, NASA Langley closed the IDRF facility and plans are underway to demolish it in 2007. Consequently, it is important to document the contributions made to improve the crashworthiness of light aircraft and rotorcraft achieved through full-scale crash testing and simulation at the IDRF.

Jackson, Karen E.↗

International Space Station 2A Array Modal Analysis

On December 9th 2009, the International Space Station (ISS) 2A solar array mast experienced prolonged longeron shadowing during a Soyuz undocking. Analytical reconstruction of induced thermal and dynamic structural loads showed an exceedance of the mast buckling limit. Possible structural damage to the solar array mast could have occurred during this event. A Low fidelity video survey of the 2A mast showed no obvious damage of the mast longerons or battens. The decision was made to conduct an on-orbit dynamic test of the 2A array on December 18th, 2009. The test included thruster pluming on the array while photogrammetry data was recorded. The test was similar to other Dedicated Thruster Firings (DTFs) that were performed to measure structural frequency and damping of a solar array. Results of the DTF indicated lower frequency mast modes than model predictions, thus leading to speculation of mast damage. A detailed nonlinear analysis was performed on the 2A array model to assess possible solutions to modal differences. The setup of the parametric nonlinear trade study included the use of a detailed array model and the reduced mass and stiffness matrices of the entire ISS being applied to the array interface. The study revealed that the array attachment structure is nonlinear and thus was the source of error in the model prediction of mast modes. In addition, a detailed study was performed to determine mast mode sensitivity to mast longeron damage. This sensitivity study was performed to assess if the ISS program has sufficient instrumentation for mast damage detection.

Laible, Michael↗

Electric Field Conjugation in the Presence of Model Uncertainty

The Wide-Field Infrared Survey Telescope (WFIRST) is a 2.4-meter-diameter space telescope NASA program. The payload will include a coronagraph instrument (CGI). The CGI designs under development use deformable mirrors (DM) to create a point spread function (PSF) with a dark region around the obscured star object. Electric field conjugation (EFC) is an iterative nonlinear optimization procedure that uses measurements of the electric field at the image to determine the DM displacements to modify the PSF to create the region of high contrast in the image. EFC requires a numerical model of the coronagraph to calculate the Jacobian of the system, which is used, along with regularization, to solve for the DM displacements for each iteration of the nonlinear optimization. Ideally, the coronagraph is aligned and calibrated, and the calibration data are used in the numerical model for calculating the Jacobian. However, calibration and alignment measurements always contain uncertainty resulting in calibration error. Therefore, the Jacobian calculated from the numerical model is not an exact representation of the physical coronagraph, and the resulting DM solution for an EFC iteration does not have the exact impact on the electric field of the coronagraph as predicted by the EFC. The result is slow convergence, and, as will be shown, drives the use of more restrictive regularization. Using Monte Carlo trials, we investigate the effect of calibration error on EFC convergence and regulatization. Comparison to results from the High Contrast Imaging Testbed Hybrid Lyot Coronagraph are also presented.

Marx, David↗

Highlights of the 2016 Summer Laboratory Student Intern Program at Sandia National Labs [Slides]

Combined picosecond (10 -12 s) and femtosecond (10 -15 s) laser pulses can give sensitive, low-noise measurements of important quantities in reacting flows, such as species concentrations and temperature. Emmanuel’s work focused on the development of an instrument for tailoring the time profile of picosecond laser pulses for use in nonlinear optical spectroscopic methods created from broad bandwidth femtosecond pulses. In addition to constructing the device, Emmanuel produced a LabView-based automation code, building off skills he developed in a previous CCI internship at Sandia.

42 ENGINEERING↗

Static actuator-sharing algorithm for concurrent control of multiple plasma properties

Simultaneous regulation of multiple properties in next-generation tokamaks like ITER and fusion pilot plant may require the integration of different plasma control algorithms. Such integration requires the conversion of individual controller commands into physical actuator requests while accounting for the coupling between different plasma properties. This work proposes a tokamak and scenario-agnostic actuator-sharing algorithm (ASA) to perform the above-mentioned command-request conversion and, hence, integrate multiple plasma controllers. The proposed algorithm implicitly solves a quadratic programming (QP) problem formulated to account for the saturation limits and the relation between the controller commands and physical actuator requests. Since the constraints arising in the QP program are linear, the proposed ASA is highly computationally efficient and can be implemented in the tokamak plasma control system in real time. Furthermore, the proposed algorithm is designed to handle real-time changes in the control objectives and actuators’ availability. Nonlinear simulations carried out using the Control Oriented Transport SIMulator illustrate the effectiveness of the proposed algorithm in achieving multiple control objectives simultaneously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Importance of helicopter dynamics to the mathematical model of the helicopter

A mathematical model of the helicopter requires appropriate representation of the constituent elements of rotor dynamics. General-purpose programs that model a variety of configurations for a broad range of operating conditions result in varying and incompatible levels of sophistication. Analysis of specific dynamic problems facilitates the identification of configuration parameters which determine system behavior. For the present analysis, the nonlinear equations of a torsionally rigid hingeless rotor are linearized about an equilibrium condition to determine flap-lag stability characteristics in hover. A collocation method was used to obtain the coupled natural frequencies and modes. These modes allow exact treatment of the effect of elastic coupling which more than compensates for the destabilizing inertial coupling. The sensitivity of damping to the number of modes was found to be small, and reasonable accuracy was obtained the first flapwise and edgewise coupled modes. The range of destabilizing precone was found to be small.

White, W. F., Jr.↗

Model verification of large structural systems

A computer program for the application of parameter identification on the structural dynamic models of space shuttle and other large models with hundreds of degrees of freedom is described. Finite element, dynamic, analytic, and modal models are used to represent the structural system. The interface with math models is such that output from any structural analysis program applied to any structural configuration can be used directly. Processed data from either sine-sweep tests or resonant dwell tests are directly usable. The program uses measured modal data to condition the prior analystic model so as to improve the frequency match between model and test. A Bayesian estimator generates an improved analytical model and a linear estimator is used in an iterative fashion on highly nonlinear equations. Mass and stiffness scaling parameters are generated for an improved finite element model, and the optimum set of parameters is obtained in one step.

Lee, L. T.↗