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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

High-Order/Low-Dissipation Chain-Rule Flux Solution Reconstruction Schemes in FUN3D

In this paper, we report progress in the development of economically high-order flux-solution-reconstruction (FSR) schemes, which are second-order accurate on general unstructured grids but achieve high-order accuracy when a grid is regular, i.e., has the same stencil (with the same spacing) throughout the domain. Two variants of the FSR schemes are discussed: chain-rule-flux-solution reconstruction (CFSR) and quadratic-form-flux-solution reconstruction (QFSR), where the former is based on the chain rule and the latter on the flux reconstruction expressed as a function of solution variables. These schemes are tested for flows with shock waves with a limiter incorporated in the flux and solution reconstructions. Improved results, compared with second-order methods are demonstrated for inviscid and viscous flows with smooth grids.

high-order↗
NASA NTRS1991

Flux-vector splitting algorithm for chain-rule conservation-law form

A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems.

Shih, T. I.-P.↗
NASA NTRS1985

An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures.

Derose, T. D.↗
NASA NTRS2008

Algorithm Optimally Orders Forward-Chaining Inference Rules

People typically develop knowledge bases in a somewhat ad hoc manner by incrementally adding rules with no specific organization. This often results in a very inefficient execution of those rules since they are so often order sensitive. This is relevant to tasks like Deep Space Network in that it allows the knowledge base to be incrementally developed and have it automatically ordered for efficiency. Although data flow analysis was first developed for use in compilers for producing optimal code sequences, its usefulness is now recognized in many software systems including knowledge-based systems. However, this approach for exhaustively computing data-flow information cannot directly be applied to inference systems because of the ubiquitous execution of the rules. An algorithm is presented that efficiently performs a complete producer/consumer analysis for each antecedent and consequence clause in a knowledge base to optimally order the rules to minimize inference cycles. An algorithm was developed that optimally orders a knowledge base composed of forwarding chaining inference rules such that independent inference cycle executions are minimized, thus, resulting in significantly faster execution. This algorithm was integrated into the JPL tool Spacecraft Health Inference Engine (SHINE) for verification and it resulted in a significant reduction in inference cycles for what was previously considered an ordered knowledge base. For a knowledge base that is completely unordered, then the improvement is much greater.

James, Mark↗
NASA NTRS1999

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Green, Lawrence↗
NASA NTRS1993

An on-line expert system for diagnosing environmentally induced spacecraft anomalies using CLIPS

A new rule-based, expert system for diagnosing spacecraft anomalies is under development. The knowledge base consists of over two-hundred rules and provide links to historical and environmental databases. Environmental causes considered are bulk charging, single event upsets (SEU), surface charging, and total radiation dose. The system's driver translates forward chaining rules into a backward chaining sequence, prompting the user for information pertinent to the causes considered. The use of heuristics frees the user from searching through large amounts of irrelevant information (varying degrees of confidence in an answer) or 'unknown' to any question. The expert system not only provides scientists with needed risk analysis and confidence estimates not available in standard numerical models or databases, but it is also an effective learning tool. In addition, the architecture of the expert system allows easy additions to the knowledge base and the database. For example, new frames concerning orbital debris and ionospheric scintillation are being considered. The system currently runs on a MicroVAX and uses the C Language Integrated Production System (CLIPS).

Lauriente, Michael↗
NASA NTRS1994

Diagnosing anomalies of spacecraft for space maintenance and servicing

Very often servicing of satellites is necessary to replace components which are responsible for anomalous behavior of satellite operations due to adverse interactions with the natural space environment. A major difficulty with this diagnosis is that those responsible for diagnosing these anomalies do not have the tools to assess the role of the space environment causing the anomaly. To address this issue, we have under development a new rule-based, expert system for diagnosing spacecraft anomalies. The knowledge base consists of over two-hundred rules and provides links to historical and environmental databases. Environmental causes considered are bulk charging, single event upsets (SEU), surface charging, and total radiation dose. The system's driver translates forward chaining rules into a backward chaining sequence, prompting the user for information pertinent to the causes considered. When the user selects the novice mode, the system automatically gives detailed explanations and descriptions of terms and reasoning as the session progresses, in a sense teaching the user. As such it is an effective tutoring tool. The use of heuristics frees the user from searching through large amounts of irrelevant information and allows the user to input partial information (varying degrees of confidence in an answer) or 'unknown' to any question. The system is available on-line and uses C Language Integrated Production System (CLIPS), an expert shell developed by the NASA Johnson Space Center AI Laboratory in Houston.

Lauriente, Michael↗
NASA NTRS1993

An Intelligent computer-aided tutoring system for diagnosing anomalies of spacecraft in operation

A new rule-based, expert system for diagnosing spacecraft anomalies is under development. The knowledge base consists of over two-hundred (200) rules and provides links to historical and environmental databases. Environmental causes considered are bulk charging, single event upsets (SEU), surface charging, and total radiation dose. The system's driver translates forward chaining rules into a backward chaining sequence, prompting the user for information pertinent to the causes considered. When the user selects the novice mode, the system automatically gives detailed explanations and descriptions of terms and reasoning as the session progresses, in a sense teaching the user. As such it is an effective tutoring tool. The use of heuristics frees the user from searching through large amounts of irrelevant information and allows the user to input partial information (varying degrees of confidence in an answer) or 'unknown' to any question. The system is available on-line and uses C Language Integrated Production System (CLIPS), an expert shell developed by the NASA Johnson Space Center AI Laboratory in Houston.

Rolincik, Mark↗
NASA NTRS1992

An expert system for diagnosing environmentally induced spacecraft anomalies

A new rule-based, machine independent analytical tool was designed for diagnosing spacecraft anomalies using an expert system. Expert systems provide an effective method for saving knowledge, allow computers to sift through large amounts of data pinpointing significant parts, and most importantly, use heuristics in addition to algorithms, which allow approximate reasoning and inference and the ability to attack problems not rigidly defined. The knowledge base consists of over two-hundred (200) rules and provides links to historical and environmental databases. The environmental causes considered are bulk charging, single event upsets (SEU), surface charging, and total radiation dose. The system's driver translates forward chaining rules into a backward chaining sequence, prompting the user for information pertinent to the causes considered. The use of heuristics frees the user from searching through large amounts of irrelevant information and allows the user to input partial information (varying degrees of confidence in an answer) or 'unknown' to any question. The modularity of the expert system allows for easy updates and modifications. It not only provides scientists with needed risk analysis and confidence not found in algorithmic programs, but is also an effective learning tool, and the window implementation makes it very easy to use. The system currently runs on a Micro VAX II at Goddard Space Flight Center (GSFC). The inference engine used is NASA's C Language Integrated Production System (CLIPS).

Rolincik, Mark↗
NASA NTRS1990

Developing an Intelligent Computer-Aided Trainer

The Payload-assist module Deploys/Intelligent Computer-Aided Training (PD/ICAT) system was developed as a prototype for intelligent tutoring systems with the intention of seeing PD/ICAT evolve and produce a general ICAT architecture and development environment that can be adapted by a wide variety of training tasks. The proposed architecture is composed of a user interface, a domain expert, a training session manager, a trainee model and a training scenario generator. The PD/ICAT prototype was developed in the LISP environment. Although it has been well received by its peers and users, it could not be delivered toe its end users for practical use because of specific hardware and software constraints. To facilitate delivery of PD/ICAT to its users and to prepare for a more widely accepted development and delivery environment for future ICAT applications, we have ported this training system to a UNIX workstation and adopted use of a conventional language, C, and a C-based rule-based language, CLIPS. A rapid conversion of the PD/ICAT expert system to CLIPS was possible because the knowledge was basically represented as a forward chaining rule base. The resulting CLIPS rule base has been tested successfully in other ICATs as well. Therefore, the porting effort has proven to be a positive step toward our ultimate goal of building a general purpose ICAT development environment.

Hua, Grace↗
DOE OSTI2026

Development of a Framework and Methodology for an Advanced Reactor Materials Environmental Effects Design Guide

Advanced non-light-water reactor components may operate at elevated temperature while experiencing cyclic loading, significant neutron irradiation, and exposure to reactor coolant. ASME Boiler and Pressure Vessel Code, Section III, Division 5, provides design rules for elevated-temperature service but does not include specific procedures to account for environmental effects on material properties. This report develops an initial framework and methodology for an Environmental Effects Design Guide (EEDG) focused on neutron irradiation; coolant-environment effects are reserved for future work. The proposed approach treats irradiation as a property-based overlay on the existing Division 5 design process, with two routes: a sparse-data route applying two reduction factors — FCR on creep-rupture strength and FF on fatigue life — for the creep-fatigue evaluations that typically control the design of advanced high-temperature reactor components, and a fuller framework developing the property-to-rule chain across the four Division 5 checks (primary load, strain limits and ratcheting, creep-fatigue, and buckling), together with swelling and weldments as scope items. Both routes are scoped by an in-pile qualification that restricts the use of post-irradiation-examination-derived properties in regimes where an in-pile mechanism could control the design outcome. Illustrative outputs derived on a compiled annealed Type 316 database — FCR ≈ 0.78–0.86 and FF ≈ 0.4 — demonstrate the calculation method within that specific dataset. The framework is an initial, testable design-rule concept; it identifies a practical path for preliminary design evaluations under sparse data and the material data and testing needed to develop the framework further.

Barua, Bipul (ORCID:0000000247184113)↗
DOE OSTI2021

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

A Trajectory-Driven Algorithm for Differentiating SRB Measures on Unstable Manifolds

Sinai-Ruelle-Bowen (SRB) measures are limiting stationary distributions describing the statistical behavior of chaotic dynamical systems. Directional derivatives of SRB measure densities conditioned on unstable manifolds are critical in the sensitivity analysis of hyperbolic chaos. These derivatives, known as the SRB density gradients, are by-products of the regularization of Lebesgue integrals appearing in the original linear response expression. In this paper, we propose a novel trajectory- driven algorithm for computing the SRB density gradient defined for systems with high-dimensional unstable manifolds. We apply the concept of measure preservation together with the chain rule on smooth manifolds. Due to the recursive one-step nature of our derivations, the proposed procedure is memory-efficient and can be naturally integrated with existing Monte Carlo schemes widely used in computational chaotic dynamics. Here, we numerically show the exponential convergence of our scheme, analyze the computational cost, and present its use in the context of Monte Carlo integration.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

The geopotential in nonsingular orbital elements

Singularities are eliminated from the geopotential and its partial derivatives for zero eccentricity and inclination, and an expression for the geopotential expansion based entirely on nonsingular orbital elements is developed. The argument relies on the treatments of the geopotential function given by Izsak (1964), Allan (1965) and Kaula (1966); the geopotential expansion developed does not involve mixed variables, and therefore does not require the chain rule to formulate the Lagrange planetary equations. The need for recursion relations to be used in conjunction with the nonsingular version of the geopotential expansion is also mentioned.

Nacozy, P. E.↗
NASA NTRS1981

The algebraic theory of latent projectors in lambda matrices

Multivariable systems such as a finite-element model of vibrating structures, control systems, and large-scale systems are often formulated in terms of differential equations which give rise to lambda matrices. The present investigation is concerned with the formulation of the algebraic theory of lambda matrices and the relationship of latent roots, latent vectors, and latent projectors to the eigenvalues, eigenvectors, and eigenprojectors of the companion form. The chain rule for latent projectors and eigenprojectors for the repeated latent root or eigenvalues is given.

Denman, E. D.↗
NASA NTRS1987

Slew maneuver dynamics of the Spacecraft Control Laboratory experiment

Mathematical expressions for slew maneuver dynamics are presented. The total kinetic energy expression of the system is given as T = T(0) + T(1) + T(2), where T(0), T(1), and T(2) refer to the kinetic energies of the shuttle, the flexible beam, and the tip mass (the reflector), respectively. The specific equations for each of these are defined and integrated into the total energy expression. Using the chain rule in the Lagrange equations and an expression allowing the transformation of the orbiter angular velocity from the inertial frame to the body-fixed frame, the rotational equations are obtained. Finally, the vibration equations for the beam are derived, again using the Lagrange equations.

Kakad, Y. P.↗
NASA NTRS1987

Design sensitivity analysis for an aeroelastic optimization of a helicopter blade

The sensitivity of vibratory hub loads of a four-bladed hingeless rotor with respect to blade design parameters is investigated using a finite element formulation in space and time. Design parameters include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity from aerodynamic center, blade bending stiffnesses (flap, lag and torsion). Hub loads selected are 4/rev vertical hub shear and 3/rev hub moment in the rotating reference frame. The sensitivity derivatives of vertical hub loads with respect to blade design parameters are compared using two approaches, finite difference scheme and analytical approach using chain rule differentiation. The analytical derivative approach developed as an integral part of response solution (finite element in time) is a powerful method for an aeroelastic optimization of a helicopter rotor.

Lim, Joon↗