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At least 433 records · Page 24

Applications of computer algebra to distributed parameter systems

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Storch, Joel A.↗

Rocket Engine Turbine Blade Surface Pressure Distributions Experiment and Computations

Understanding the unsteady aspects of turbine rotor flow fields is critical to successful future turbine designs. A technology program was conducted at NASA's Marshall Space Flight Center to increase the understanding of unsteady environments for rocket engine turbines. The experimental program involved instrumenting turbine rotor blades with miniature surface mounted high frequency response pressure transducers. The turbine model was then tested to measure the unsteady pressures on the rotor blades. The data obtained from the experimental program is unique in two respects. First, much more unsteady data was obtained (several minutes per set point) than has been possible in the past. Also, an extensive steady performance database existed for the turbine model. This allowed an evaluation of the effect of the on-blade instrumentation on the turbine's performance. A three-dimensional unsteady Navier-Stokes analysis was also used to blindly predict the unsteady flow field in the turbine at the design operating conditions and at +15 degrees relative incidence to the first-stage rotor. The predicted time-averaged and unsteady pressure distributions show good agreement with the experimental data. This unique data set, the lessons learned for acquiring this type of data, and the improvements made to the data analysis and prediction tools are contributing significantly to current Space Launch Initiative turbine airflow test and blade surface pressure prediction efforts.

Hudson, Susan T.↗

Measurements over distributed high performance computing and storage systems

Requirements are carefully described in descriptions of systems to be acquired but often there is no requirement to provide measurements and performance monitoring to ensure that requirements are met over the long term after acceptance. A set of measurements for various UNIX-based systems will be available at the 1992 Goddard Conference on Mass Storage Systems and Technologies. The authors invite others to contribute to the set of measurements. The framework for presenting the measurements of supercomputers, workstations, file servers, mass storage systems, and the networks that interconnect them are given. Production control and database systems are also included. Though other applications and third party software systems are not addressed, it is important to measure them as well. The capability to integrate measurements from all these components from different vendors, and from the third party software systems was recognized and there are efforts to standardize a framework to do this. The measurement activity falls into the domain of management standards. Standards work is ongoing for Open Systems Interconnection (OSI) systems management; AT&T, Digital, and Hewlett-Packard are developing management systems based on this architecture even though it is not finished. Another effort is in the UNIX International Performance Management Working Group. In addition, there are the Open Systems Foundation's Distributed Management Environment and the Object Management Group. A paper comparing the OSI systems management model and the Object Management Group model has been written. The IBM world has had a capability for measurement for various IBM systems since the 1970's and different vendors were able to develop tools for analyzing and viewing these measurements. Since IBM was the only vendor, the user groups were able to lobby IBM for the kinds of measurements needed. In the UNIX world of multiple vendors, a common set of measurements will not be as easy to get.

Williams, Elizabeth↗

Computation of spanwise distribution of circulation and lift coefficient for flapped wings of arbitrary planform

The question of the effect of distribution and magnitude of spanwise circulation and shed vorticity from an airplane wing on the distribution pattern of agricultural products distributed from an airplane was studied. The first step in an analysis of this question is the determination of the actual distribution of lift along an airplane wing, from which the pattern of shed vorticity can be determined. A procedure is developed to calculate the span loading for flapped and unflapped wings of arbitrary aspect ratio and taper ratio. The procedure was programmed on a small programmable calculator, the Hewlett Packard HP-97, and also was programmed in BASIC language. They could be used to explore the variations in span loading that can be secured by variable flap deflections or the effect of flying at varying air speeds at different airplane gross weights. Either an absolute evaluation of span loading can be secured or comparative span loading can be evaluated to determine their effect on swath width and swath distribution pattern. The programs are intended to assist the user in evaluating the effect of a given spanload distribution.

Razak, K.↗

Computational-experimental pressure distributions on a transonic, low-aspect-ratio wing

A generic, transonic, supercritical, low aspect-ratio wing was tested at design incidence of 5 deg at Mach numbers from 0.25 to 0.96. Oil-flow studies at the design Mach number of 0.85 showed local-flow separation, which, in retrospect, might have been avoided. At Mach 0.82 with unseparated flow, the surface-flow angles were less than 10 deg. Predictions with the FLO22 transonic potential code are good. Lift interference is strong without tunnel-wall suction. Evidence from this study shows that wings that are optimized for mild shock waves and pressure-recovery gradients generally have small, three-dimensional flow at conditions for unseparated flow.

Keener, E. R.↗

Human-computer interaction in distributed supervisory control tasks

An overview of activities concerned with the development and applications of the Operator Function Model (OFM) is presented. The OFM is a mathematical tool to represent operator interaction with predominantly automated space ground control systems. The design and assessment of an intelligent operator aid (OFMspert and Ally) is particularly discussed. The application of OFM to represent the task knowledge in the design of intelligent tutoring systems, designated OFMTutor and ITSSO (Intelligent Tutoring System for Satellite Operators), is also described. Viewgraphs from symposia presentations are compiled along with papers addressing the intent inferencing capabilities of OFMspert, the OFMTutor system, and an overview of intelligent tutoring systems and the implications for complex dynamic systems.

Mitchell, Christine M.↗

Measurements over distributed high performance computing and storage systems

A strawman proposal is given for a framework for presenting a common set of metrics for supercomputers, workstations, file servers, mass storage systems, and the networks that interconnect them. Production control and database systems are also included. Though other applications and third part software systems are not addressed, it is important to measure them as well.

Williams, Elizabeth↗

The alignment-distribution graph

Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.

Chatterjee, Siddhartha↗

The alignment-distribution graph

Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment-distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.

Chatterjee, Siddhartha↗

Application of a distributed network in computational fluid dynamic simulations

A general-purpose 3-D, incompressible Navier-Stokes algorithm is implemented on a network of concurrently operating workstations using parallel virtual machine (PVM) and compared with its performance on a CRAY Y-MP and on an Intel iPSC/860. The problem is relatively computationally intensive, and has a communication structure based primarily on nearest-neighbor communication, making it ideally suited to message passing. Such problems are frequently encountered in computational fluid dynamics (CDF), and their solution is increasingly in demand. The communication structure is explicitly coded in the implementation to fully exploit the regularity in message passing in order to produce a near-optimal solution. Results are presented for various grid sizes using up to eight processors.

Deshpande, Manish↗

Effects of Spatial Gradients on Electron Runaway Acceleration

The runaway process is known to accelerate electrons in many laboratory plasmas and has been suggested as an acceleration mechanism in some astrophysical plasmas, including solar flares. Current calculations of the electron velocity distributions resulting from the runaway process are greatly restricted because they impose spatial homogeneity on the distribution. We have computed runaway distributions which include consistent development of spatial gradients in the energetic tail. Our solution for the electron velocity distribution is presented as a function of distance along a finite length acceleration region, and is compared with the equivalent distribution for the infinitely long homogenous system (i.e., no spatial gradients), as considered in the existing literature. All these results are for the weak field regime. We also discuss the severe restrictiveness of this weak field assumption.

MacNeice, Peter↗

A Comparative Study on Computation of Cumulative Distribution Function in Predicting Time of Failure of Engineering Systems

Estimating accurate Time-of-Failure (ToF) of a system is key in making the decisions that impact operational safety and optimize cost. In this context, it is interesting to note that different approaches have been explored to tackle the problem of estimating ToF. The difference is in part characterized by different definitions of the hazard zones. The conventional definition for the cumulative distribution function (CDF) calculation is assumed to have well-defined hazard zones, that is, hazard zones defined as a function of the system state trajectory. An alternate method suggests the use of hazard zones defined as a function of the system state at time , instead of hazard zones defined as a function of system state up to and including time k (Acuna and Orchard 2018, 2017). This paper explores these differences and their impact on ToF estimation. Results for the conventional CDF definition indicated that, (i) the cumulative distribution function is always an increasing function of time, even when realizations of the degradation process are not monotonic, (ii) the sum of all probabilities is always 1 and does not need to be normalized, and (iii) all probabilities are positive and less than or equal to 1. Similar results are not observed for CDF calculation with hazard zones defined as a function only of the system state at time . Results for ToF estimation using Acuna's definition differ, suggesting that there is an underlying assumption of independence in the hazard zone definition. Therefore, we present an alternate definition of hazard zone which guarantees the properties of a well-defined CDF with a more straightforward ToF definition.

Hazard Zone↗

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Principal Component Analysis↗

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Computational Fluid Dynamics↗