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NASA NTRS2002

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Lorenzo, Carl F.↗
NASA NTRS1997

Cooperative Data Sharing: Simple Support for Clusters of SMP Nodes

Libraries like PVM and MPI send typed messages to allow for heterogeneous cluster computing. Lower-level libraries, such as GAM, provide more efficient access to communication by removing the need to copy messages between the interface and user space in some cases. still lower-level interfaces, such as UNET, get right down to the hardware level to provide maximum performance. However, these are all still interfaces for passing messages from one process to another, and have limited utility in a shared-memory environment, due primarily to the fact that message passing is just another term for copying. This drawback is made more pertinent by today's hybrid architectures (e.g. clusters of SMPs), where it is difficult to know beforehand whether two communicating processes will share memory. As a result, even portable language tools (like HPF compilers) must either map all interprocess communication, into message passing with the accompanying performance degradation in shared memory environments, or they must check each communication at run-time and implement the shared-memory case separately for efficiency. Cooperative Data Sharing (CDS) is a single user-level API which abstracts all communication between processes into the sharing and access coordination of memory regions, in a model which might be described as "distributed shared messages" or "large-grain distributed shared memory". As a result, the user programs to a simple latency-tolerant abstract communication specification which can be mapped efficiently to either a shared-memory or message-passing based run-time system, depending upon the available architecture. Unlike some distributed shared memory interfaces, the user still has complete control over the assignment of data to processors, the forwarding of data to its next likely destination, and the queuing of data until it is needed, so even the relatively high latency present in clusters can be accomodated. CDS does not require special use of an MMU, which can add overhead to some DSM systems, and does not require an SPMD programming model. unlike some message-passing interfaces, CDS allows the user to implement efficient demand-driven applications where processes must "fight" over data, and does not perform copying if processes share memory and do not attempt concurrent writes. CDS also supports heterogeneous computing, dynamic process creation, handlers, and a very simple thread-arbitration mechanism. Additional support for array subsections is currently being considered. The CDS1 API, which forms the kernel of CDS, is built primarily upon only 2 communication primitives, one process initiation primitive, and some data translation (and marshalling) routines, memory allocation routines, and priority control routines. The entire current collection of 28 routines provides enough functionality to implement most (or all) of MPI 1 and 2, which has a much larger interface consisting of hundreds of routines. still, the API is small enough to consider integrating into standard os interfaces for handling inter-process communication in a network-independent way. This approach would also help to solve many of the problems plaguing other higher-level standards such as MPI and PVM which must, in some cases, "play OS" to adequately address progress and process control issues. The CDS2 API, a higher level of interface roughly equivalent in functionality to MPI and to be built entirely upon CDS1, is still being designed. It is intended to add support for the equivalent of communicators, reduction and other collective operations, process topologies, additional support for process creation, and some automatic memory management. CDS2 will not exactly match MPI, because the copy-free semantics of communication from CDS1 will be supported. CDS2 application programs will be free to carefully also use CDS1. CDS1 has been implemented on networks of workstations running unmodified Unix-based operating systems, using UDP/IP and vendor-supplied high- performance locks. Although its inter-node performance is currently unimpressive due to rudimentary implementation technique, it even now outperforms highly-optimized MPI implementation on intra-node communication due to its support for non-copy communication. The similarity of the CDS1 architecture to that of other projects such as UNET and TRAP suggests that the inter-node performance can be increased significantly to surpass MPI or PVM, and it may be possible to migrate some of its functionality to communication controllers.

DiNucci, David C.↗
NASA NTRS2001

Comparison of 250 MHz R10K Origin 2000 and 400 MHz Origin 2000 Using NAS Parallel Benchmarks

This report describes results of benchmark tests on Steger, a 250 MHz Origin 2000 system with R10K processors, currently installed at the NASA Ames National Advanced Supercomputing (NAS) facility. For comparison purposes, the tests were also run on Lomax, a 400 MHz Origin 2000 with R12K processors. The BT, LU, and SP application benchmarks in the NAS Parallel Benchmark Suite and the kernel benchmark FT were chosen to measure system performance. Having been written to measure performance on Computational Fluid Dynamics applications, these benchmarks are assumed appropriate to represent the NAS workload. Since the NAS runs both message passing (MPI) and shared-memory, compiler directive type codes, both MPI and OpenMP versions of the benchmarks were used. The MPI versions used were the latest official release of the NAS Parallel Benchmarks, version 2.3. The OpenMP versions used were PBN3b2, a beta version that is in the process of being released. NPB 2.3 and PBN3b2 are technically different benchmarks, and NPB results are not directly comparable to PBN results.

Turney, Raymond D.↗
NASA NTRS2002

Performance Evaluation of Remote Memory Access (RMA) Programming on Shared Memory Parallel Computers

The purpose of this study is to evaluate the feasibility of remote memory access (RMA) programming on shared memory parallel computers. We discuss different RMA based implementations of selected CFD application benchmark kernels and compare them to corresponding message passing based codes. For the message-passing implementation we use MPI point-to-point and global communication routines. For the RMA based approach we consider two different libraries supporting this programming model. One is a shared memory parallelization library (SMPlib) developed at NASA Ames, the other is the MPI-2 extensions to the MPI Standard. We give timing comparisons for the different implementation strategies and discuss the performance.

Jin, Hao-Qiang↗
NASA NTRS2001

Bitsy Thinks Big

AeroAstro, of Herndon, Virginia, developed a nanospacecraft core module capable of developing recyclable spacecraft designs using standard interfaces. From this core module, known as the Bitsy(TM) kernel, custom spacecraft are able to connect mission-specific instruments and subsystems for variation in mission usage. The nanospacecraft core module may be used in conjunction with an existing microsatellite bus or customized to meet specific requirements. Building on this premise, AeroAstro has developed a line of satellite communications equipment, sun sensors, and Lithium-Ion batteries which are all incorporated in its complete line of mission-specific nanospacecraft. The Bitsy technology is also a key component in AeroAstro#s satellite inspection products and orbital transfer services. In the future, AeroAstro plans to market an even less expensive version of the Bitsy technology. The plan, which is targeted to universities, markets a sort of "satellite in a kit," for less than $1 million. This technology would allow universities to build true space hardware for a fraction of the cost of launching a regular satellite.

Source record↗
NASA NTRS1996

Simulation Software

Various NASA Small Business Innovation Research grants from Marshall Space Flight Center, Langley Research Center and Ames Research Center were used to develop the 'kernel' of COMCO's modeling and simulation software, the PHLEX finite element code. NASA needed it to model designs of flight vehicles; one of many customized commercial applications is UNISIM, a PHLEX-based code for analyzing underground flows in oil reservoirs for Texaco, Inc. COMCO's products simulate a computational mechanics problem, estimate the solution's error and produce the optimal hp-adapted mesh for the accuracy the user chooses. The system is also used as a research or training tool in universities and in mechanical design in industrial corporations.

Source record↗
NASA NTRS2003

Detailed Vibration Analysis of Pinion Gear with Time-Frequency Methods

In this paper, the authors show a detailed analysis of the vibration signal from the destructive testing of a spiral bevel gear and pinion pair containing seeded faults. The vibration signal is analyzed in the time domain, frequency domain and with four time-frequency transforms: the Short Time Frequency Transform (STFT), the Wigner-Ville Distribution with the Choi-Williams kernel (WV-CW), the Continuous Wavelet' Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels and damage conditions, are analyzed using these methods. A new metric for automatic anomaly detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the time-frequency transforms, as well as time and frequency representations, on this data set. Analysis with the CWT detects changes in the signal at low torque levels not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic anomaly detection and to develop fault detection methods for the metric.

Mosher, Marianne↗
NASA NTRS2002

Evaluation and Characterization Study of Dual Pulse Laser-Induced Spark (DPLIS) For Rocket Engine Ignition System Application

This paper addresses the progress of technology development of a laser ignition system at NASA Marshall Space Flight Center (MSFC). Initial hot-fire tests in a small-scale rocket chamber at MSFC have demonstrated the DPLIS concept having two main advantages over existing laser ignition concepts. First, the DPLIS can be potentially optimized its laser pulse format to maximize the initial plasma volume, the plasma lifetime, as well as the flame kernel growth rate. Characterization studies of the laser pulse format are now underway with experiments of igniting gaseous hydrogen/air in a Hencken burner. Once ignition is achieved, the flame is open to the atmosphere. This open environment allows easy access for diagnostics of the ignition phenomenon. The quick turn-around time of conducting experiments on this burner make it more amenable for conducting a large number of experiments for statistical analysis of the sensitivity of the test parameters. The results from these experiments will help optimize the laser format for future testing in an H2/O2 subscale rocket chamber.

Trinh, Huu P.↗
NASA NTRS2003

Optimal Area Profiles for Ideal Single Nozzle Air-Breathing Pulse Detonation Engines

The effects of cross-sectional area variation on idealized Pulse Detonation Engine performance are examined numerically. A quasi-one-dimensional, reacting, numerical code is used as the kernel of an algorithm that iteratively determines the correct sequencing of inlet air, inlet fuel, detonation initiation, and cycle time to achieve a limit cycle with specified fuel fraction, and volumetric purge fraction. The algorithm is exercised on a tube with a cross sectional area profile containing two degrees of freedom: overall exit-to-inlet area ratio, and the distance along the tube at which continuous transition from inlet to exit area begins. These two parameters are varied over three flight conditions (defined by inlet total temperature, inlet total pressure and ambient static pressure) and the performance is compared to a straight tube. It is shown that compared to straight tubes, increases of 20 to 35 percent in specific impulse and specific thrust are obtained with tubes of relatively modest area change. The iterative algorithm is described, and its limitations are noted and discussed. Optimized results are presented showing performance measurements, wave diagrams, and area profiles. Suggestions for future investigation are also discussed.

Paxson, Daniel E.↗
NASA NTRS2003

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Brenner, Martin J.↗
NASA NTRS2003

Meter-Scale 3-D Models of the Martian Surface from Combining MOC and MOLA Data

We have extended our previous efforts to derive through controlled photoclinometry, accurate, calibrated, high-resolution topographic models of the martian surface. The process involves combining MGS MOLA topographic profiles and MGS MOC Narrow Angle images. The earlier work utilized, along with a particular MOC NA image, the MOLA topographic profile that was acquired simultaneously, in order to derive photometric and scattering properties of the surface and atmosphere so as to force the low spatial frequencies of a one-dimensional MOC photoclinometric model to match the MOLA profile. Both that work and the new results reported here depend heavily on successful efforts to: 1) refine the radiometric calibration of MOC NA; 2) register the MOC to MOLA coordinate systems and refine the pointing; and 3) provide the ability to project into a common coordinate system, simultaneously acquired MOC and MOLA with a single set of SPICE kernels utilizing the USGS ISIS cartographic image processing tools. The approach described in this paper extends the MOC-MOLA integration and cross-calibration procedures from one-dimensional profiles to full two-dimensional photoclinometry and image simulations. Included are methods to account for low-frequency albedo variations within the scene.

Soderblom, Laurence A.↗
NASA NTRS2003

Performance Analysis of a Hybrid Overset Multi-Block Application on Multiple Architectures

This paper presents a detailed performance analysis of a multi-block overset grid compu- tational fluid dynamics app!ication on multiple state-of-the-art computer architectures. The application is implemented using a hybrid MPI+OpenMP programming paradigm that exploits both coarse and fine-grain parallelism; the former via MPI message passing and the latter via OpenMP directives. The hybrid model also extends the applicability of multi-block programs to large clusters of SNIP nodes by overcoming the restriction that the number of processors be less than the number of grid blocks. A key kernel of the application, namely the LU-SGS linear solver, had to be modified to enhance the performance of the hybrid approach on the target machines. Investigations were conducted on cacheless Cray SX6 vector processors, cache-based IBM Power3 and Power4 architectures, and single system image SGI Origin3000 platforms. Overall results for complex vortex dynamics simulations demonstrate that the SX6 achieves the highest performance and outperforms the RISC-based architectures; however, the best scaling performance was achieved on the Power3.

Djomehri, M. Jahed↗
NASA NTRS2003

The Updated Umkehr Ozone Retrieval Algorithm and its Validation against Satellite Data

Improvements to the Umkehr ozone profile retrieval algorithm have been developed and are now being evaluated. The updated algorithm is able to simulate observations more accurately and provides data output that is easier to analyze. Among the new diagnostic capabilities that the updated algorithm provides is the averaging kernel (AK) method. The AK approach allows studying how the algorithm responds when a small perturbation is made in a particular layer of the atmosphere [Rodgers 1976, 1990]. We will use the AK method to define precisely what Umkehr should measure given a set of profiles measured by other platforms. This method allows us to compare trends and offsets in data more accurately than it has been done in the past. The updated Umkehr retrievals will be validated against SAGE II ozone profiles as well as SSBUV ozone profile data. We will discuss possible reasons for offset between data and differences in derived ozone profile trends. Considerable variability of the ozone profile within the 10-degree latitude envelope creates noise in the SAGE matching dataset and makes comparisons difficult. To eliminate this problem, the SAGE and Umkehr data had been previously de-seasonalized by subtracting the latitude/season dependent ozone climatology. However, the remaining noise in the ozone residuals was still considerably high for trend analysis and was attributed to longitude variability of SAGE sampling. The new ozone climatology (Labow, NASA) that has longitude dependent ozone variability will be used to minimize contribution of sampling noise in comparisons of satellite and ground station. The comparison of zenith-sky radiances (Umkehr N-value measurements) synthesized for a given set of SAGE profiles will be used to determine whether SAGE-derived N-values agree with the Umkehr-measured N-values. The instrumental effects will be discussed. Both the Umkehr data and SAGE II measurements will be analyzed for their information about ozone variability and loss and recovery rates at the mid- and upper (40 km) levels. The updated long-term Umkehr dataset can be used to provide high quality information for identifying signs of ozone recovery. The long Umkehr historical record can provide additional information for separating the dynamic and chemical mechanisms of depletion, and can help the community better understand climate change effects.

Petropavlovskikh, I.↗
NASA NTRS2003

Flutter and Divergence Analysis using the Generalized Aeroelastic Analysis Method

The Generalized Aeroelastic Analysis Method (GAAM) is applied to the analysis of three well-studied checkcases: restrained and unrestrained airfoil models, and a wing model. An eigenvalue iteration procedure is used for converging upon roots of the complex stability matrix. For the airfoil models, exact root loci are given which clearly illustrate the nature of the flutter and divergence instabilities. The singularities involved are enumerated, including an additional pole at the origin for the unrestrained airfoil case and the emergence of an additional pole on the positive real axis at the divergence speed for the restrained airfoil case. Inconsistencies and differences among published aeroelastic root loci and the new, exact results are discussed and resolved. The generalization of a Doublet Lattice Method computer code is described and the code is applied to the calculation of root loci for the wing model for incompressible and for subsonic flow conditions. The error introduced in the reduction of the singular integral equation underlying the unsteady lifting surface theory to a linear algebraic equation is discussed. Acknowledging this inherent error, the solutions of the algebraic equation by GAAM are termed 'exact.' The singularities of the problem are discussed and exponential series approximations used in the evaluation of the kernel function shown to introduce a dense collection of poles and zeroes on the negative real axis. Again, inconsistencies and differences among published aeroelastic root loci and the new 'exact' results are discussed and resolved. In all cases, aeroelastic flutter and divergence speeds and frequencies are in good agreement with published results. The GAAM solution procedure allows complete control over Mach number, velocity, density, and complex frequency. Thus all points on the computed root loci can be matched-point, consistent solutions without recourse to complex mode tracking logic or dataset interpolation, as in the k and p-k solution methods.

Edwards, John W.↗
NASA NTRS2003

Investigation of Impinging Stream Vortex Chamber Concepts for Liquid Rocket Engine Applications

This paper addresses the progress of technology development of a laser ignition system at NASA Marshall Spac Flight Center (MSFC). Initial hot-fire tests in a small-scale rocket chamber at MSFC have demonstrated the dual pulse laser-induced spark (DPLIS) technique, which has an advantage over existing single-pulse laser ignition techniques in that it can be optimized in its laser pulse format to maximize the initial plasma volume, the plasm: lifetime, as well as the flame kernel growth rate. The distribution of the total laser energy into two separate pulse also lowers the peak power that would need to be sent through fiber optics to the combustion chamber, making the implementation of this technique more practical than other single-pulse techniques. A first generation prototype of an optic fiber-coupled laser ignition system will be tested a rocket chamber with RP-1/GOX and GH2/GOX propellants systems. Other relevant technology, such as optical windows, flight-qualified laser system etc. will be discussed in this paper.

Trinh, Huu P.↗
NASA NTRS1999

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Rauch, Kevin P.↗
NASA NTRS2004

Virtual Sensors: Using Data Mining to Efficiently Estimate Spectra

Detecting clouds within a satellite image is essential for retrieving surface geophysical parameters, such as albedo and temperature, from optical and thermal imagery because the retrieval methods tend to be valid for clear skies only. Thus, routine satellite data processing requires reliable automated cloud detection algorithms that are applicable to many surface types. Unfortunately, cloud detection over snow and ice is difficult due to the lack of spectral contrast between clouds and snow. Snow and clouds are both highly reflective in the visible wavelen,ats and often show little contrast in the thermal Infrared. However, at 1.6 microns, the spectral signatures of snow and clouds differ enough to allow improved snow/ice/cloud discrimination. The recent Terra and Aqua Moderate Resolution Imaging Spectro-Radiometer (MODIS) sensors have a channel (channel 6) at 1.6 microns. Presently the most comprehensive, long-term information on surface albedo and temperature over snow- and ice-covered surfaces comes from the Advanced Very High Resolution Radiometer ( AVHRR) sensor that has been providing imagery since July 1981. The earlier AVHRR sensors (e.g. AVHRR/2) did not however have a channel designed for discriminating clouds from snow, such as the 1.6 micron channel available on the more recent AVHRR/3 or the MODIS sensors. In the absence of the 1.6 micron channel, the AVHRR Polar Pathfinder (APP) product performs cloud detection using a combination of time-series analysis and multispectral threshold tests based on the satellite's measuring channels to produce a cloud mask. The method has been found to work reasonably well over sea ice, but not so well over the ice sheets. Thus, improving the cloud mask in the APP dataset would be extremely helpful toward increasing the accuracy of the albedo and temperature retrievals, as well as extending the time-series of albedo and temperature retrievals from the more recent sensors to the historical ones. In this work, we use data mining methods to construct a model of MODIS channel 6 as a function of other channels that are common to both MODIS and AVHRR. The idea is to use the model to generate the equivalent of MODIS channel 6 for AVHRR as a function of the AVHRR equivalents to MODIS channels. We call this a Virtual Sensor because it predicts unmeasured spectra. The goal is to use this virtual channel 6. to yield a cloud mask superior to what is currently used in APP . Our results show that several data mining methods such as multilayer perceptrons (MLPs), ensemble methods (e.g., bagging), and kernel methods (e.g., support vector machines) generate channel 6 for unseen MODIS images with high accuracy. Because the true channel 6 is not available for AVHRR images, we qualitatively assess the virtual channel 6 for several AVHRR images.

Srivastava, Ashok↗
NASA NTRS2004

Explanation Constraint Programming for Model-based Diagnosis of Engineered Systems

We can expect to see an increase in the deployment of unmanned air and land vehicles for autonomous exploration of space. In order to maintain autonomous control of such systems, it is essential to track the current state of the system. When the system includes safety-critical components, failures or faults in the system must be diagnosed as quickly as possible, and their effects compensated for so that control and safety are maintained under a variety of fault conditions. The Livingstone fault diagnosis and recovery kernel and its temporal extension L2 are examples of model-based reasoning engines for health management. Livingstone has been shown to be effective, it is in demand, and it is being further developed. It was part of the successful Remote Agent demonstration on Deep Space One in 1999. It has been and is being utilized by several projects involving groups from various NASA centers, including the In Situ Propellant Production (ISPP) simulation at Kennedy Space Center, the X-34 and X-37 experimental reusable launch vehicle missions, Techsat-21, and advanced life support projects. Model-based and consistency-based diagnostic systems like Livingstone work only with discrete and finite domain models. When quantitative and continuous behaviors are involved, these are abstracted to discrete form using some mapping. This mapping from the quantitative domain to the qualitative domain is sometimes very involved and requires the design of highly sophisticated and complex monitors. We propose a diagnostic methodology that deals directly with quantitative models and behaviors, thereby mitigating the need for these sophisticated mappings. Our work brings together ideas from model-based diagnosis systems like Livingstone and concurrent constraint programming concepts. The system uses explanations derived from the propagation of quantitative constraints to generate conflicts. Fast conflict generation algorithms are used to generate and maintain multiple candidates whose consistency can be tracked across multiple time steps.

Narasimhan, Sriram↗