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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Automated extraction of knowledge for model-based diagnostics

The concept of accessing computer aided design (CAD) design databases and extracting a process model automatically is investigated as a possible source for the generation of knowledge bases for model-based reasoning systems. The resulting system, referred to as automated knowledge generation (AKG), uses an object-oriented programming structure and constraint techniques as well as internal database of component descriptions to generate a frame-based structure that describes the model. The procedure has been designed to be general enough to be easily coupled to CAD systems that feature a database capable of providing label and connectivity data from the drawn system. The AKG system is capable of defining knowledge bases in formats required by various model-based reasoning tools.

Gonzalez, Avelino J.↗
NASA NTRS2013

Autonomous Control of Space Nuclear Reactors

Nuclear reactors to support future robotic and manned missions impose new and innovative technological requirements for their control and protection instrumentation. Long-duration surface missions necessitate reliable autonomous operation, and manned missions impose added requirements for failsafe reactor protection. There is a need for an advanced instrumentation and control system for space-nuclear reactors that addresses both aspects of autonomous operation and safety. The Reactor Instrumentation and Control System (RICS) consists of two functionally independent systems: the Reactor Protection System (RPS) and the Supervision and Control System (SCS). Through these two systems, the RICS both supervises and controls a nuclear reactor during normal operational states, as well as monitors the operation of the reactor and, upon sensing a system anomaly, automatically takes the appropriate actions to prevent an unsafe or potentially unsafe condition from occurring. The RPS encompasses all electrical and mechanical devices and circuitry, from sensors to actuation device output terminals. The SCS contains a comprehensive data acquisition system to measure continuously different groups of variables consisting of primary measurement elements, transmitters, or conditioning modules. These reactor control variables can be categorized into two groups: those directly related to the behavior of the core (known as nuclear variables) and those related to secondary systems (known as process variables). Reliable closed-loop reactor control is achieved by processing the acquired variables and actuating the appropriate device drivers to maintain the reactor in a safe operating state. The SCS must prevent a deviation from the reactor nominal conditions by managing limitation functions in order to avoid RPS actions. The RICS has four identical redundancies that comply with physical separation, electrical isolation, and functional independence. This architecture complies with the safety requirements of a nuclear reactor and provides high availability to the host system. The RICS is intended to interface with a host computer (the computer of the spacecraft where the reactor is mounted). The RICS leverages the safety features inherent in Earth-based reactors and also integrates the wide range neutron detector (WRND). A neutron detector provides the input that allows the RICS to do its job. The RICS is based on proven technology currently in use at a nuclear research facility. In its most basic form, the RICS is a ruggedized, compact data-acquisition and control system that could be adapted to support a wide variety of harsh environments. As such, the RICS could be a useful instrument outside the scope of a nuclear reactor, including military applications where failsafe data acquisition and control is required with stringent size, weight, and power constraints.

Merk, John↗
NASA NTRS2001

Using Multiple Space Assests with In-Situ Measurements to Track Flooding in Thailand

Increasing numbers of space assets can enable coordinated measurements of flooding phenomena to enhance tracking of extreme events. We describe the use of space and ground measurements to target further measurements as part of a flood monitoring system in Thailand. We utilize rapidly delivered MODIS data to detect major areas of flooding and the target the Earth Observing One Advanced Land Imager sensor to acquire higher spatial resolution data. Automatic surface water extent mapping products delivered to interested parties. We are also working to extend our network to include in-situ sensing networks and additional space assets.

flooding↗
NASA NTRS1995

Adaptive data rate SSMA system for personal and mobile satellite communications

An adaptive data rate SSMA (spread spectrum multiple access) system is proposed for mobile and personal multimedia satellite communications without the aid of system control earth stations. This system has a constant occupied bandwidth and has variable data rates and processing gains to mitigate communication link impairments such as fading, rain attenuation and interference as well as to handle variable data rate on demand. Proof of concept hardware for 6MHz bandwidth transponder is developed, that uses offset-QPSK (quadrature phase shift keying) and MSK (minimum shift keying) for direct sequence spread spectrum modulation and handle data rates of 4k to 64kbps. The RS422 data interface, low rate voice and H.261 video codecs are installed. The receiver is designed with coherent matched filter technique to achieve fast code acquisition, AFC (automatic frequency control) and coherent detection with minimum hardware losses in a single matched filter circuit. This receiver structure facilitates variable data rate on demand during a call. This paper shows the outline of the proposed system and the performance of the prototype equipment.

Ikegami, Tetsushi↗
NASA NTRS2010

Automatic Identification of Solar X-Ray Bright Points in Hinode X-Ray Data

We have automated a method that is used to find point sources in Chandra X-ray telescope data, to identify solar bright points in Hinode X-ray data. This tool, called lextrct, first identifies candidate sources that are brighter than the surrounding background. The algorithm also allows selected pixels to be excluded from the source-finding, thus allowing saturated pixels (from flares and/or active regions) to be ignored. We then use lextrct to fit the sources to two-dimensional, elliptical Gaussians. The size and orientation give an approximation of the shape of the bright points. We are in the process of analyzing observations through the Al_poly filter with a four-second exposure time, to obtain a catalogue of bright points, which will include their sizes, lifetimes, intensities, and position on the solar disk

Adams, M. L.↗
NASA NTRS2011

Split-screen display system and standardized methods for ultrasound image acquisition and multi-frame data processing

A standardized acquisition methodology assists operators to accurately replicate high resolution B-mode ultrasound images obtained over several spaced-apart examinations utilizing a split-screen display in which the arterial ultrasound image from an earlier examination is displayed on one side of the screen while a real-time "live" ultrasound image from a current examination is displayed next to the earlier image on the opposite side of the screen. By viewing both images, whether simultaneously or alternately, while manually adjusting the ultrasound transducer, an operator is able to bring into view the real-time image that best matches a selected image from the earlier ultrasound examination. Utilizing this methodology, dynamic material properties of arterial structures, such as IMT and diameter, are measured in a standard region over successive image frames. Each frame of the sequence has its echo edge boundaries automatically determined by using the immediately prior frame's true echo edge coordinates as initial boundary conditions. Computerized echo edge recognition and tracking over multiple successive image frames enhances measurement of arterial diameter and IMT and allows for improved vascular dimension measurements, including vascular stiffness and IMT determinations.

Selzer, Robert H.↗
NASA NTRS2005

Radiation Dosimetry via Automated Fluorescence Microscopy

A developmental instrument for assessment of radiation-induced damage in human lymphocytes includes an automated fluorescence microscope equipped with a one or more chargecoupled- device (CCD) video camera(s) and circuitry to digitize the video output. The microscope is also equipped with a three-axis translation stage that includes a rotation stage, and a rotary tray that holds as many as thirty specimen slides. The figure depicts one version of the instrument. Once the slides have been prepared and loaded into the tray, the instrument can operate unattended. A computer controls the operation of the stage, tray, and microscope, and processes the digital fluorescence-image data to recognize and count chromosomes that have been broken, presumably by radiation. The design and method of operation of the instrument exploit fluorescence in situ hybridization (FISH) of metaphase chromosome spreads, which is a technique that has been found to be valuable for monitoring the radiation dose to circulating lymphocytes. In the specific FISH protocol used to prepare specimens for this instrument, metaphase lymphocyte cultures are chosen for high mitotic index and highly condensed chromosomes, then several of the largest chromosomes are labeled with three of four differently colored whole-chromosome-staining dyes. The three dyes, which are used both individually and in various combinations, are fluorescein isothiocyanate (FITC), Texas Red (or equivalent), and Cy5 (or equivalent); The fourth dye 4',6-diamidino- 2-phenylindole (DAPI) is used as a counterstain. Under control by the computer, the microscope is automatically focused on the cells and each slide is scanned while the computer analyzes the DAPI-fluorescence images to find the metaphases. Each metaphase field is recentered in the field of view and refocused. Then a four-color image (more precisely, a set of images of the same view in the fluorescent colors of the four dyes) is acquired. By use of pattern-recognition software developed specifically for this instrument, the images in the various colors are processed to recognize the metaphases and count the chromosome fragments of each color within the metaphases. The intermediate results are then further processed to estimate the proportion of cells that have suffered genetic damage. The prototype instrument scans at an average areal rate of 4.7 mm2/h in unattended operation, finding about 14 metaphases per hour. The false-alarm rate is typically less than 3 percent, and the metaphase-miss rate has been estimated to be less than 5 percent. The counts of chromosomes and fragments thereof are 50 to 70 percent accurate.

Castleman, Kenneth R.↗
NASA NTRS2000

BOREAS RSS-3 Atmospheric Measurements from a Helicopter-Mounted Sunphotometer

The BOREAS RSS-3 team collected and processed helicopter-based measurements of atmospheric conditions to estimates of aerosol optical thickness and atmospheric water vapor. The automatic sun-tracking photometer for helicopters was deployed during all three 1994 IFCs at numerous tower and auxiliary sites in both the NSA and the SSA. Six spectral channels (440, 540, 613, 670, 870, and 1030 nm) were chosen to span the visible and NIR wavelengths and to avoid gaseous absorption. One additional channel, 940 nm, was selected to measure the water column abundance above the helicopter platform. The data are stored in tabular ASCII files.

Hall, Forrest G.↗
NASA NTRS2010

Use of Business Intelligence Tools in the DSN

JPL has operated the Deep Space Network (DSN) on behalf of NASA since the 1960's. Over the last two decades, the DSN budget has generally declined in real-year dollars while the aging assets required more attention, and the missions became more complex. As a result, the DSN budget has been increasingly consumed by Operations and Maintenance (O&M), significantly reducing the funding wedge available for technology investment and for enhancing the DSN capability and capacity. Responding to this budget squeeze, the DSN launched an effort to improve the cost-efficiency of the O&M. In this paper we: elaborate on the methodology adopted to understand "where the time and money are used"-surprisingly, most of the data required for metrics development was readily available in existing databases-we have used commercial Business Intelligence (BI) tools to mine the databases and automatically extract the metrics (including trends) and distribute them weekly to interested parties; describe the DSN-specific effort to convert the intuitive understanding of "where the time is spent" into meaningful and actionable metrics that quantify use of resources, highlight candidate areas of improvement, and establish trends; and discuss the use of the BI-derived metrics-one of the most fascinating processes was the dramatic improvement in some areas of operations when the metrics were shared with the operators-the visibility of the metrics, and a self-induced competition, caused almost immediate improvement in some areas. While the near-term use of the metrics is to quantify the processes and track the improvement, these techniques will be just as useful in monitoring the process, e.g. as an input to a lean-six-sigma process.

Metrics↗
NASA NTRS1975

Instruction manual, optical effects module electronic controller and processor, model OEMCP

The OEM-1 electronic module is discussed; it is comprised of four subsystems: the signal processing and display; the stepper motor controls; the chopper controls; and the dc-dc invertor. The OEM-1 module controls the sample wheel so that the relative transmittance of the samples can be compared to the clear aperture position. The 3-1/2 digit digital voltmeter displays the clear aperture signal level as well as the ratio of the remaining sample positions relative to the clear aperture position. The sample wheel position is decoded so that the signals and ratios can be correlated to the data. The OEM is automatically reset to the I sub o on initial turn-on and can be reset to the '0' position by actuating a front panel switch. The sample wheel can be interrupted to change samples or induce a longer integration time if desired by a front panel command. Integration times from 1 - 50 seconds are provided at the front panel, and BCD data for external interfacing is provided.

Source record↗
NASA NTRS1999

Microgravity Transport Phenomena Experiment (MTPE) Overview

The Microgravity Transport Phenomena Experiment (MTPE) is a fluids experiment supported by the Fundamentals in Biotechnology program in association with the Human Exploration and Development of Space (BEDS) initiative. The MTP Experiment will investigate fluid transport phenomena both in ground based experiments and in the microgravity environment. Many fluid transport processes are affected by gravity. Osmotic flux kinetics in planar membrane systems have been shown to be influenced by gravimetric orientation, either through convective mixing caused by unstably stratified fluid layers, or through a stable fluid boundary layer structure that forms in association with the membrane. Coupled transport phenomena also show gravity related effects. Coefficients associated with coupled transport processes are defined in terms of a steady state condition. Buoyancy (gravity) driven convection interferes with the attainment of steady state, and the measurement of coupled processes. The MTP Experiment measures the kinetics of molecular migration that occurs in fluids, in response to the application of various driving potentials. Three separate driving potentials may be applied to the MTP Experiment fluids, either singly or in combination. The driving potentials include chemical potential, thermal potential, and electrical potential. Two separate fluid arrangements are used to study membrane mediated and bulk fluid transport phenomena. Transport processes of interest in membrane mediated systems include diffusion, osmosis, and streaming potential. Bulk fluid processes of interest include coupled phenomena such as the Soret Effect, Dufour Effect, Donnan Effect, and thermal diffusion potential. MTP Experiments are performed in the Microgravity Transport Apparatus (MTA), an instrument that has been developed specifically for precision measurement of transport processes. Experiment fluids are contained within the MTA fluid cells, designed to create a one dimensional flow geometry of constant cross sectional area, and to facilitate fluid filling and draining operations in microgravity. The fluid cells may be used singly for bulk solutions, or in a Stokes diaphragm configuration to investigate membrane mediated phenomena. Thermal and electrical driving potentials are applied to the experiment fluids through boundary plates located at the ends of the fluid cells. In the ground based instrument, two constant temperature baths circulate through reservoirs adjacent to the boundary plates, and establish the thermal environment within the fluid cells. The boundary plates also serve as electrodes for measurement and application of electrical potentials. The Fluid Manipulation System associated with the MTA is a computer controlled system that enables storage and transfer of experiment fluids during on orbit operations. The system is used to automatically initiate experiments and manipulate fluids by orchestrating pump and valve operations through scripted sequences. Unique technologies are incorporated in the MTA for measurement of fluid properties. Volumetric Flow Sensors have been developed for precision measurement of total fluid volume contained within the fluid cells over time. This data is most useful for measuring the kinetics of osmosis, where fluid is transported from one fluid cell to another through a semipermeable membrane. The MicroSensor Array has been designed to perform in situ measurement of several important fluid parameters, providing simultaneous measurement of solution composition at multiple locations within the experiment fluids. Micromachined sensors and interface electronics have been developed to measure temperature, electrical conductivity, pH, cation activity, and anion activity. The Profile Refractometer uses a laser optical system to directly image the fluid Index of Refraction profile that exists along the MTA fluid cell axis. A video system acquires images of the RI profile over time, and records the transport kinetics that occur upon application of chemical, thermal, or electrical driving potentials. Image processing algorithms have been developed to analyze the refractometer images on a pixel by pixel basis, calibrating and scaling the measured Index of Refraction profile to correlated solution properties of interest such as density, concentration, and temperature. Additional software has been developed to compile the processed images into a three dimensional matrix that contains fluid composition data as a function of experiment time and position in the fluid cell. These data are combined with data from the other sensor systems, and analyzed in the context of transport coefficients associated with the various transport phenomena. Analysis protocols have been developed to measure the transient kinetics, and steady state distribution of fluid components that occur in response to the applied driving potentials. The results are expressed in terms of effective transport coefficients. Experiments have been performed using a variety of solutes, and results generated are that are in agreement with published transport coefficient values.

Mason, Larry W.↗
NASA NTRS1974

Automated land-use mapping from spacecraft data

The author has identified the following significant results. In response to the need for a faster, more economical means of producing land use maps, this study evaluated the suitability of using ERTS-1 computer compatible tape (CCT) data as a basis for automatic mapping. Significant findings are: (1) automatic classification accuracy greater than 90% is achieved on categories of deep and shallow water, tended grass, rangeland, extractive (bare earth), urban, forest land, and nonforested wet lands; (2) computer-generated printouts by target class provide a quantitative measure of land use; and (3) the generation of map overlays showing land use from ERTS-1 CCTs offers a significant breakthrough in the rate at which land use maps are generated. Rather than uncorrected classified imagery or computer line printer outputs, the processing results in geometrically-corrected computer-driven pen drawing of land categories, drawn on a transparent material at a scale specified by the operator. These map overlays are economically produced and provide an efficient means of rapidly updating maps showing land use.

Chase, P. E.↗
NASA NTRS1994

Simplifying operations with an uplink/downlink integration toolkit

The Operations Engineering Lab (OEL) at JPL has developed a simple, generic toolkit to integrate the uplink/downlink processes, (often called closing the loop), in JPL's Multimission Ground Data System. This toolkit provides capabilities for integrating telemetry verification points with predicted spacecraft commands and ground events in the Mission Sequence Of Events (SOE) document. In the JPL ground data system, the uplink processing functions and the downlink processing functions are separate subsystems that are not well integrated because of the nature of planetary missions with large one-way light times for spacecraft-to-ground communication. Our new closed-loop monitoring tool allows an analyst or mission controller to view and save uplink commands and ground events with their corresponding downlinked telemetry values regardless of the delay in downlink telemetry and without requiring real-time intervention by the user. An SOE document is a time-ordered list of all the planned ground and spacecraft events, including all commands, sequence loads, ground events, significant mission activities, spacecraft status, and resource allocations. The SOE document is generated by expansion and integration of spacecraft sequence files, ground station allocations, navigation files, and other ground event files. This SOE generation process has been automated within the OEL and includes a graphical, object-oriented SOE editor and real-time viewing tool running under X/Motif. The SOE toolkit was used as the framework for the integrated implementation. The SOE is used by flight engineers to coordinate their operations tasks, serving as a predict data set in ground operations and mission control. The closed-loop SOE toolkit allows simple, automated integration of predicted uplink events with correlated telemetry points in a single SOE document for on-screen viewing and archiving. It automatically interfaces with existing real-time or non real-time sources of information, to display actual values from the telemetry data stream. This toolkit was designed to greatly simplify the user's ability to access and view telemetry data, and also provide a means to view this data in the context of the commands and ground events that are used to interpret it. A closed-loop system can prove especially useful in small missions with limited resources requiring automated monitoring tools. This paper will discuss the toolkit implementation, including design trade-offs and future plans for enhancing the automated capabilities.

Murphy, Susan C.↗
NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗
NASA NTRS1993

The NASA/industry Design Analysis Methods for Vibrations (DAMVIBS) program: Sikorsky Aircraft: Advances toward interacting with the airframe design process

A short history is traced of the work done at Sikorsky Aircraft under the NASA/industry DAMVIBS program. This includes both work directly funded by the program as well as work which was internally funded but which received its initial impetus from DAMVIBS. The development of a finite element model of the UH-60A airframe having a marked improvement in vibration-predicting ability is described. A new program, PAREDYM, developed at Sikorsky, which automatically adjusts an FEM so that its modal characteristics match test values, is described, as well as the part this program played in the improvement of the UH-60A model. Effects of the bungee suspension system on the shake test data used for model verification are described. The impetus given by the modeling improvement, as well as the recent availability of PAREDYM, has brought for the first time the introduction of low-vibration design into the design cycle at Sikorsky.

Twomey, William J.↗
NASA NTRS2000

Use Computer-Aided Tools to Parallelize Large CFD Applications

Porting applications to high performance parallel computers is always a challenging task. It is time consuming and costly. With rapid progressing in hardware architectures and increasing complexity of real applications in recent years, the problem becomes even more sever. Today, scalability and high performance are mostly involving handwritten parallel programs using message-passing libraries (e.g. MPI). However, this process is very difficult and often error-prone. The recent reemergence of shared memory parallel (SMP) architectures, such as the cache coherent Non-Uniform Memory Access (ccNUMA) architecture used in the SGI Origin 2000, show good prospects for scaling beyond hundreds of processors. Programming on an SMP is simplified by working in a globally accessible address space. The user can supply compiler directives, such as OpenMP, to parallelize the code. As an industry standard for portable implementation of parallel programs for SMPs, OpenMP is a set of compiler directives and callable runtime library routines that extend Fortran, C and C++ to express shared memory parallelism. It promises an incremental path for parallel conversion of existing software, as well as scalability and performance for a complete rewrite or an entirely new development. Perhaps the main disadvantage of programming with directives is that inserted directives may not necessarily enhance performance. In the worst cases, it can create erroneous results. While vendors have provided tools to perform error-checking and profiling, automation in directive insertion is very limited and often failed on large programs, primarily due to the lack of a thorough enough data dependence analysis. To overcome the deficiency, we have developed a toolkit, CAPO, to automatically insert OpenMP directives in Fortran programs and apply certain degrees of optimization. CAPO is aimed at taking advantage of detailed inter-procedural dependence analysis provided by CAPTools, developed by the University of Greenwich, to reduce potential errors made by users. Earlier tests on NAS Benchmarks and ARC3D have demonstrated good success of this tool. In this study, we have applied CAPO to parallelize three large applications in the area of computational fluid dynamics (CFD): OVERFLOW, TLNS3D and INS3D. These codes are widely used for solving Navier-Stokes equations with complicated boundary conditions and turbulence model in multiple zones. Each one comprises of from 50K to 1,00k lines of FORTRAN77. As an example, CAPO took 77 hours to complete the data dependence analysis of OVERFLOW on a workstation (SGI, 175MHz, R10K processor). A fair amount of effort was spent on correcting false dependencies due to lack of necessary knowledge during the analysis. Even so, CAPO provides an easy way for user to interact with the parallelization process. The OpenMP version was generated within a day after the analysis was completed. Due to sequential algorithms involved, code sections in TLNS3D and INS3D need to be restructured by hand to produce more efficient parallel codes. An included figure shows preliminary test results of the generated OVERFLOW with several test cases in single zone. The MPI data points for the small test case were taken from a handcoded MPI version. As we can see, CAPO's version has achieved 18 fold speed up on 32 nodes of the SGI O2K. For the small test case, it outperformed the MPI version. These results are very encouraging, but further work is needed. For example, although CAPO attempts to place directives on the outer- most parallel loops in an interprocedural framework, it does not insert directives based on the best manual strategy. In particular, it lacks the support of parallelization at the multi-zone level. Future work will emphasize on the development of methodology to work in a multi-zone level and with a hybrid approach. Development of tools to perform more complicated code transformation is also needed.

Jin, H.↗
NASA NTRS1990

Adaptive pattern recognition by mini-max neural networks as a part of an intelligent processor

In this decade and progressing into 21st Century, NASA will have missions including Space Station and the Earth related Planet Sciences. To support these missions, a high degree of sophistication in machine automation and an increasing amount of data processing throughput rate are necessary. Meeting these challenges requires intelligent machines, designed to support the necessary automations in a remote space and hazardous environment. There are two approaches to designing these intelligent machines. One of these is the knowledge-based expert system approach, namely AI. The other is a non-rule approach based on parallel and distributed computing for adaptive fault-tolerances, namely Neural or Natural Intelligence (NI). The union of AI and NI is the solution to the problem stated above. The NI segment of this unit extracts features automatically by applying Cauchy simulated annealing to a mini-max cost energy function. The feature discovered by NI can then be passed to the AI system for future processing, and vice versa. This passing increases reliability, for AI can follow the NI formulated algorithm exactly, and can provide the context knowledge base as the constraints of neurocomputing. The mini-max cost function that solves the unknown feature can furthermore give us a top-down architectural design of neural networks by means of Taylor series expansion of the cost function. A typical mini-max cost function consists of the sample variance of each class in the numerator, and separation of the center of each class in the denominator. Thus, when the total cost energy is minimized, the conflicting goals of intraclass clustering and interclass segregation are achieved simultaneously.

Szu, Harold H.↗
NASA NTRS1990

Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Arnold, Steven M.↗