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NASA NTRS1991

Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Smith, Ralph C.↗

NASA NTRS1992

Parallel computation of geometry control in adaptive truss structures

The fast computation of geometry control in adaptive truss structures involves two distinct parts: the efficient integration of the inverse kinematic differential equations that govern the geometry control and the fast computation of the Jacobian, which appears on the right-hand-side of the inverse kinematic equations. This paper present an efficient parallel implementation of the Jacobian computation on an MIMD machine. Large speedup from the parallel implementation is obtained, which reduces the Jacobian computation to an O(M-squared/n) procedure on an n-processor machine, where M is the number of members in the adaptive truss. The parallel algorithm given here is a good candidate for on-line geometry control of adaptive structures using attached processors.

Ramesh, A. V.↗

NASA NTRS1984

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗

NASA NTRS1990

Mapping unstructured grid problems to the connection machine

We present a highly parallel graph mapping technique that enables one to solve unstructured grid problems on massively parallel computers. Many implicit and explicit methods for solving discretizated partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The time spent communicating can limit the high performance promised by massively parallel computing. To eliminate this bottleneck, we map the graph of the irregular problem to the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. We show that, in comparison to a naive assignment of processors, our heuristic mapping algorithm significantly reduces the communication time on the Connection Machine, CM-2.

Hammond, Steven W.↗

NASA NTRS2009

Steady-State ALPS for Real-Valued Problems

The two objectives of this paper are to describe a steady-state version of the Age-Layered Population Structure (ALPS) Evolutionary Algorithm (EA) and to compare it against other GAs on real-valued problems. Motivation for this work comes from our previous success in demonstrating that a generational version of ALPS greatly improves search performance on a Genetic Programming problem. In making steady-state ALPS some modifications were made to the method for calculating age and the method for moving individuals up layers. To demonstrate that ALPS works well on real-valued problems we compare it against CMA-ES and Differential Evolution (DE) on five challenging, real-valued functions and on one real-world problem. While CMA-ES and DE outperform ALPS on the two unimodal test functions, ALPS is much better on the three multimodal test problems and on the real-world problem. Further examination shows that, unlike the other GAs, ALPS maintains a genotypically diverse population throughout the entire search process. These findings strongly suggest that the ALPS paradigm is better able to avoid premature convergence then the other GAs.

Hornby, Gregory S.↗

NASA NTRS2015

Kodiak: An Implementation Framework for Branch and Bound Algorithms

Recursive branch and bound algorithms are often used to refine and isolate solutions to several classes of global optimization problems. A rigorous computation framework for the solution of systems of equations and inequalities involving nonlinear real arithmetic over hyper-rectangular variable and parameter domains is presented. It is derived from a generic branch and bound algorithm that has been formally verified, and utilizes self-validating enclosure methods, namely interval arithmetic and, for polynomials and rational functions, Bernstein expansion. Since bounds computed by these enclosure methods are sound, this approach may be used reliably in software verification tools. Advantage is taken of the partial derivatives of the constraint functions involved in the system, firstly to reduce the branching factor by the use of bisection heuristics and secondly to permit the computation of bifurcation sets for systems of ordinary differential equations. The associated software development, Kodiak, is presented, along with examples of three different branch and bound problem types it implements.

Smith, Andrew P.↗

NASA NTRS2012

Apparatus and methods for manipulation and optimization of biological systems

The invention provides systems and methods for manipulating, e.g., optimizing and controlling, biological systems, e.g., for eliciting a more desired biological response of biological sample, such as a tissue, organ, and/or a cell. In one aspect, systems and methods of the invention operate by efficiently searching through a large parametric space of stimuli and system parameters to manipulate, control, and optimize the response of biological samples sustained in the system, e.g., a bioreactor. In alternative aspects, systems include a device for sustaining cells or tissue samples, one or more actuators for stimulating the samples via biochemical, electromagnetic, thermal, mechanical, and/or optical stimulation, one or more sensors for measuring a biological response signal of the samples resulting from the stimulation of the sample. In one aspect, the systems and methods of the invention use at least one optimization algorithm to modify the actuator's control inputs for stimulation, responsive to the sensor's output of response signals. The compositions and methods of the invention can be used, e.g., to for systems optimization of any biological manufacturing or experimental system, e.g., bioreactors for proteins, e.g., therapeutic proteins, polypeptides or peptides for vaccines, and the like, small molecules (e.g., antibiotics), polysaccharides, lipids, and the like. Another use of the apparatus and methods includes combination drug therapy, e.g. optimal drug cocktail, directed cell proliferations and differentiations, e.g. in tissue engineering, e.g. neural progenitor cells differentiation, and discovery of key parameters in complex biological systems.

Ho, Chih-Ming↗

NASA NTRS1991

Mapping implicit spectral methods to distributed memory architectures

Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case.

Overman, Andrea L.↗

NASA NTRS1997

Analysis of Texture Using the Fractal Model

Properties such as the fractal dimension (FD) can be used for feature extraction and classification of regions within an image. The FD measures the degree of roughness of a surface, so this number is used to characterize a particular region, in order to differentiate it from another. There are two basic approaches discussed in the literature to measure FD: the blanket method, and the box counting method. Both attempt to measure FD by estimating the change in surface area with respect to the change in resolution. We tested both methods but box counting resulted computationally faster and gave better results. Differential Box Counting (DBC) was used to segment a collage containing three textures. The FD is independent of directionality and brightness so five features were used derived from the original image to account for directionality and gray level biases. FD can not be measured on a point, so we use a window that slides across the image giving values of FD to the pixel on the center of the window. Windowing blurs the boundaries of adjacent classes, so an edge-preserving, feature-smoothing algorithm is used to improve classification within segments and to make the boundaries sharper. Segmentation using DBC was 90.8910 accurate.

Navas, William↗

NASA NTRS1995

Multithreaded Model for Dynamic Load Balancing Parallel Adaptive PDE Computations

We present a multithreaded model for the dynamic load-balancing of numerical, adaptive computations required for the solution of Partial Differential Equations (PDE's) on multiprocessors. Multithreading is used as a means of exploring concurrency in the processor level in order to tolerate synchronization costs inherent to traditional (non-threaded) parallel adaptive PDE solvers. Our preliminary analysis for parallel, adaptive PDE solvers indicates that multithreading can be used an a mechanism to mask overheads required for the dynamic balancing of processor workloads with computations required for the actual numerical solution of the PDE's. Also, multithreading can simplify the implementation of dynamic load-balancing algorithms, a task that is very difficult for traditional data parallel adaptive PDE computations. Unfortunately, multithreading does not always simplify program complexity, often makes code re-usability not an easy task, and increases software complexity.

Chrisochoides, Nikos↗

NASA NTRS2003

Reliable Transport over SpaceWire for James Webb Space Telescope (JWST) Focal Plane Electronics (FPE) Network

NASA's James Webb Space Telescope (JWST) faces difficult technical and budgetary challenges to overcome before it is scheduled launch in 2010. The Integrated Science Instrument Module (ISIM), shares these challenges. The major challenge addressed in this paper is the data network used to collect, process, compresses and store Infrared data. A total of 114 Mbps of raw information must be collected from 19 sources and delivered to the two redundant data processing units across a twenty meter deployed thermally restricted interface. Further data must be transferred to the solid-state recorder and the spacecraft. The JWST detectors are kept at cryogenic temperatures to obtain the sensitivity necessary to measure faint energy sources. The Focal Plane Electronics (FPE) that sample the detector, generate packets from the samples, and transmit these packets to the processing electronics must dissipate little power in order to help keep the detectors at these cold temperatures. Separating the low powered front-end electronics from the higher-powered processing electronics, and using a simple high-speed protocol to transmit the detector data minimize the power dissipation near the detectors. Low Voltage Differential Signaling (LVDS) drivers were considered an obvious choice for physical layer because of their high speed and low power. The mechanical restriction on the number cables across the thermal interface force the Image packets to be concentrated upon two high-speed links. These links connect the many image packet sources, Focal Plane Electronics (FPE), located near the cryogenic detectors to the processing electronics on the spacecraft structure. From 12 to 10,000 seconds of raw data are processed to make up an image, various algorithms integrate the pixel data Loss of commands to configure the detectors as well as the loss of science data itself may cause inefficiency in the use of the telescope that are unacceptable given the high cost of the observatory. This combination of requirements necessitates a redundant, fault tolerant, high- speed, low mass, low power network with a low Bit error Rate(1E-9- 1E-12). The ISIM systems team performed many studies of the various network architectures that meeting these requirements. The architecture selected uses the Spacewire protocol, with the addition of a new transport and network layer added to implement end-to-end reliable transport. The network and reliable transport mechanism must be implemented in hardware because of the high average information rate and the restriction on the ability of the detectors to buffer data due to power and size restrictions. This network and transport mechanism was designed to be compatible with existing Spacewire links and routers so that existing equipment and designs may be leveraged upon. The transport layer specification is being coordinated with European Space Agency (ESA), Spacewire Working Group and the Consultative Committee for Space Data System (CCSDS) PlK Standard Onboard Interface (SOIF) panel, with the intent of developing a standard for reliable transport for Spacewire. Changes to the protocol presented are likely since negotiations are ongoing with these groups. A block of RTL VHDL that implements a multi-port Spacewire router with an external user interface will be developed and integrated with an existing Spacewire Link design. The external user interface will be the local interface that sources and sinks packets onto and off of the network (Figure 3). The external user interface implements the network and transport layer and handles acknowledgements and re-tries of packets for reliable transport over the network. Because the design is written in RTL, it may be ported to any technology but will initially be targeted to the new Actel Accelerator series (AX) part. Each link will run at 160 Mbps and the power will be about 0.165 Watt per link worst case in the Actel AX.

Rakow, Glenn↗

NASA NTRS2004

On Improving Efficiency of Differential Evolution for Aerodynamic Shape Optimization Applications

Differential Evolution (DE) is a simple and robust evolutionary strategy that has been provEn effective in determining the global optimum for several difficult optimization problems. Although DE offers several advantages over traditional optimization approaches, its use in applications such as aerodynamic shape optimization where the objective function evaluations are computationally expensive is limited by the large number of function evaluations often required. In this paper various approaches for improving the efficiency of DE are reviewed and discussed. Several approaches that have proven effective for other evolutionary algorithms are modified and implemented in a DE-based aerodynamic shape optimization method that uses a Navier-Stokes solver for the objective function evaluations. Parallelization techniques on distributed computers are used to reduce turnaround times. Results are presented for standard test optimization problems and for the inverse design of a turbine airfoil. The efficiency improvements achieved by the different approaches are evaluated and compared.

Madavan, Nateri K.↗

NASA NTRS1993

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗

NASA NTRSDate not supplied

IMUFDIR Tuning In Response To Structural Deformation Of The Orion Capsule

During system level Thermal Vacuum (TVAC) testing it was discovered that the pressure differential of the crew cabin in a vacuum would deflect the capsule slightly, causing significant misalignment of Orion’s three Inertial Measurement Units (IMUs). This phenomenon has been likened to a balloon expanding. When this misalignment was modeled in simulation as a function of atmospheric pressure, it was determined that the rate of deflection on reentry was significant enough to cause a mis-compare of the angular rates measured by the IMUs. This mis-comparison of the rates caused Orion’s Fault Detection Isolation and Recovery (FDIR) algorithm to falsely fail one of the IMUs. This manuscript will discuss how the IMUFDIR algorithm was detuned to be insensitive to these ballooning effects, while still meeting FDIR requirements to capture real faults in an IMU. All testing to validate this detuning was performed in a Six Degree of Freedom (6 DOF) Monte Carlo Simulation Environment.

Nicholas Rahaim↗

NASA NTRS2023

The Earth in Living Color - NASA’s Surface Biology and Geology Designated Observable

The Surface Biology and Geology (SBG) Designated Observable will transform our understanding of the global land surface, inland and coastal aquatic ecosystems through visible-to-shortwave infra-red imaging (VSWIR) spectroscopy and thermal infra-red (TIR) imaging. SBG is one of four high-priority observables recommended in the 2017 NASA Earth Science Decadal Survey t o address science questions on vegetation and aquatic ecosystem health, snow-cover dynamics, volcanic activity, and minerology. With a planned launch readiness date of 2028, SBG is currently in Pre-Phase A, with Level 1 requirements being developed for a two-spacecraft architecture, including an additional constellation pathfinder. The recommended architecture emerged from an extensive study (2018-2021) that engaged the research and applications community to consider the science questions and measurement objectives of the Decadal Survey. A Science and Applications Traceability Matrix was used as a basis for scoring candidate architectures, with inputs from four working groups that covered algorithms, applications, calibration and validation, and modeling. Two pathfinder studies, Modeling End-to-End Traceability in support of SBG (MEET-SBG) and Space-based Imaging Spectroscopy and Thermal pathfindER (SISTER) are providing pre-launch modeling tools and data for algorithm development to support science value trades. The architecture consists of one spacecraft hosting a wide-swath VSWIR imaging spectrometer providing 30-m ground-sample distance (GSD), a spectral range of 380-2500 nm (at 10 nm resolution), 16-day revisit with 400 signal-to-noise for VNIR and 250 for SWIR (at 25% reflectance). A separate spacecraft will host a wide swath thermal imager, with five to seven bands placed between 4-12 μm), with 60-m (GSD), 3- day revisit, and 0.2K noise-equivalent differential temperature (NeDT). A VNIR compact camera will be hosted on the TIR spacecraft to enable coincident TIR and VNIR observations. A constellation pathfinder will evaluate options for enabling VSWIR mission continuity using Small Sats or data buys. Partnerships with international space agencies contribute technology as well as improvements to temporal revisit. SBG, when launched, will be the first dedicated mission collecting the full spectra of the Earth’s ‘living color’ and will play a critical role in NASA’s Earth System Observatory.

David S Schimel↗

NASA NTRS1997

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

Chattopadhyay, Aditi↗

NASA NTRS2001

Configural Scoring of Simulator Sickness, Cybersickness and Space Adaptation Syndrome: Similarities and Differences?

From a survey of ten U.S. Navy flight simulators a large number (N > 1,600 exposures) of self-reports of motion sickness symptomatology were obtained. Using these data, scoring algorithms were derived, which permit examination of groups of individuals that can be scored either for 1) their total sickness experience in a particular device; or, 2) according to three separable symptom clusters which emerged from a Factor Analysis. Scores from this total score are found to be proportional to other global motion sickness symptom checklist scores with which they correlate (r = 0.82). The factors that surfaced from the analysis include clusters of symptoms referable as nausea, oculomotor disturbances, and disorientation (N, 0, and D). The factor scores may have utility in differentiating the source of symptoms in different devices. The present chapter describes our experience with the use of both of these types of scores and illustrates their use with examples from flight simulators, space sickness and virtual environments.

Kennedy, Robert S.↗

NASA NTRS1983

Close-mode identification performance of the ITD algorithm

Results of Monte Carlo numerical simulations conducted to study the close-mode performance of the Ibrahim Time-Domain (ITD) modal identification algorithm are presented. The ITD technique is a matrix eigensolution method for obtaining structural modal parameters directly from free-response test data without using the FFT. Thus, the well-known resolution and leakage limitations of the FFT procedure, that are particularly significant with short records, are avoided. As an example, one of several experimental data analyses where close modes have been accurately identified using very short records is shown. Although the identification scatter is found to increase as the square of reductions in frequency separation at small separations, the ability to differentiate modes spaced at fractions of the FFT resolution is substantiated.

Pappa, R. S.↗