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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 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

A Formal Approach to Requirements-Based Programming

No significant general-purpose method is currently available to mechanically transform system requirements into a provably equivalent model. The widespread use of such a method represents a necessary step toward high-dependability system engineering for numerous application domains. Current tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The "gap" unfilled by such tools and methods is that the formal models cannot be proven to be equivalent to the requirements. We offer a method for mechanically transforming requirements into a provably equivalent formal model that can be used as the basis for code generation and other transformations. This method is unique in offering full mathematical tractability while using notations and techniques that are well known and well trusted. Finally, we describe further application areas we are investigating for use of the approach.

Hinchey, Michael G.↗
NASA NTRS2007

Two Mathematical Models of Nonlinear Vibrations

Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.

Brugarolas, Paul↗
NASA NTRS2011

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Cacio, Emanuela↗
NASA NTRS1976

Effects of edge-rounding on geodesic lenses

A method that eliminates the need for a mathematical model is described for measuring the absolute light intensity radiated from volume chemiluminescent and fluorescent sources. This technique applies to a uniform cylindrical luminous volume, which is the geometry most often practical for the study of flowing chemiluminescent and fluorescent fluids. In this method, the necessary integration over a luminous volume is carried out experimentally, using a calibrated piston source that has as its head a disk of uniform luminosity. The relatively small total error in absolute light intensity measurements with the piston source technique represents a significant improvement over competing comparison methods. The construction of a piston source to fit the cross section of a particular cylindrical volume is straightforward, and its calibration against a standard source can be readily made while exercising normal precautions.

Wood, V. E.↗
NASA NTRSDate not supplied

Controls Algorithms, Models, and Stability Assessments of the RCS and TVC systems on Mars Ascent Vehicle

This paper presents a control systems overview of the Mars Ascent Vehicle (MAV) control design and stability analysis with two separate control methods: Thrust Vector Control (TVC) based control using main engine thrust and Reaction Control System (RCS) via thrusters. A pole-placement TVC controller is proposed to address quickly peaking thrust produced by the MAV solid propulsion engine. The controllerutilizes real-time parameter estimation to calculate control gains using an online pole-placement method. The pole-placement technique allows the controller to maintain constant stability margins throughout the flight under changing parameters and rapidly peaking thrust. A mathematical stability proof via Lyapunov inequality and Nichols method is demonstrated to support the stability of the method. In addition to the TVC control, a phase-plane based RCS control logic is applied to the vehicle for roll control during ascent and all axes during coast phases of flight. The logic implemented is an on-off type logic that applies pre-determined thrusters firings in reference to boundary parameters of pointing and rate error chosen to balance desired pointing with stability. A describing function methodology is applied to the non-linear phase plane loop response to determine linear stability across all flight phases. The controller additionally applies command alteration logic to output signals to account for RCS hardware limitations. The following paper will provide the methodology for controller implementation of the TVC and RCS, and provide a summary of results of the MAV performance applying the aforementioned control design.

Han Woong Bae↗
NASA NTRSDate not supplied

A Numerical Method for Computing the State Transition Matrix Using Poincare Integral Invariants

The Poincare integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a new numerical procedure for obtaining the state transition matrix (STM), which can be applied to both conservative and nonconservative systems. The method is analogous to a finite difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. We discuss the mathematical similarities between this new STM and existing methods, show numerical results for orbital motion and uncertainty propagation, and discuss new insights afforded by the Hamiltonian properties of phase flow.

state transition matrix↗
NASA NTRS2001

Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science

Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.

Ransom, Jonathan B.↗
NASA NTRS1979

Development of analytical orbit propagation technique with drag

Two orbit computation methods were used: (1) numerical method- The solution to the satellite differential equations were solved in a step-by-step manner, using a mathematical algorithm taken from numerical analysis; and (2) analytical method - The solution was expressed by explicit functions of the independent variable. Analytical drag modules, tesseral terms initialization module, second order and long period terms module, and verification testing of the ASOP program were also considered.

Source record↗
NASA NTRS2006

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

Hrinda, Glenn A.↗
DOE OSTI2025

Weak Form Scientific Machine Learning: Test Function Construction for System Identification

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

FOS: Computer and information sciences↗
DOE OSTI2024

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1970

COPTRAN - A method of optimum communication systems design

Single set of mathematical expressions describes system cost and probability of error of data transmission in terms of four basic parameters in the link equation. A Lagrange multiplier sets up equations whose solutions yield the optimum values for system design considerations and weight and cost values.

Brinkman, K. L.↗
NASA NTRS2017

Point-Mass Aircraft Trajectory Prediction Using a Hierarchical, Highly-Adaptable Software Design

A highly adaptable and extensible method for predicting four-dimensional trajectories of civil aircraft has been developed. This method, Behavior-Based Trajectory Prediction, is based on taxonomic concepts developed for the description and comparison of trajectory prediction software. A hierarchical approach to the "behavioral" layer of a point-mass model of aircraft flight, a clear separation between the "behavioral" and "mathematical" layers of the model, and an abstraction of the methods of integrating differential equations in the "mathematical" layer have been demonstrated to support aircraft models of different types (in particular, turbojet vs. turboprop aircraft) using performance models at different levels of detail and in different formats, and promise to be easily extensible to other aircraft types and sources of data. The resulting trajectories predict location, altitude, lateral and vertical speeds, and fuel consumption along the flight path of the subject aircraft accurately and quickly, accounting for local conditions of wind and outside air temperature. The Behavior-Based Trajectory Prediction concept was implemented in NASA's Traffic Aware Planner (TAP) flight-optimizing cockpit software application.

Karr, David A.↗
DOE OSTI2024

Gray-Box Modeling for Distribution Systems With Inverter-Based Resources: Integrating Physics-Based and Data-Driven Approaches

Here, in this paper, we develop a novel gray-box modeling approach for distribution systems with inverter-based resources (IBRs). The proposed gray-box modeling method aims to improve estimation accuracy by taking advantages of both physics-based (white-box) and data-driven (black-box) modeling approaches. To this end, we utilize partial physical knowledge of the system, including the inverters’ structures and control diagrams, as well as the equivalent network model simplified through Kron reduction. The white-box model containing unknown parameters is then constructed with mathematical equations and an optimization-based method is subsequently employed to identify these unknown parameters within the white-box model. Next, the graybox modeling framework is then constructed by embedding the output variables of the white-box model into the input vector of a black-box model (represented using a neural network). Finally, the black-box section is trained using the collected input-output datasets and the gray-box model is then obtained. Furthermore, case studies demonstrate that our gray-box modeling approach effectively improves estimation accuracy compared to purely physics-based or data-driven methods.

42 ENGINEERING↗
NASA NTRS1999

A Textbook for a First Course in Computational Fluid Dynamics

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Zingg, D. W.↗
NASA NTRS1991

Aerodynamic sensitivity analysis methods for the compressible Euler equations

This study presents a mathematical formulation developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible 2D Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. The finite difference approach and the quasi-analytical approach are used to determine the aerodynamic sensitivity coefficients. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flowfield solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.

Baysal, Oktay↗
NASA NTRS1984

Investigation of the equatorial orographic-dynamic mechanism applying the bounded derivative method

A system of equations which describe the motion of a barotropic fluid in the presence of bottom topography are presented. The mathematical expression for orography is developed and the bounded derivative initialization method is applied to suppress gravitational oscillations. A stationary orographic trough is simulated. The geopotential and zonal motion have maximum deviation from the mean state at the top of the mountain. Regarding meridional speed, outflow occurs on the windward slope and inflow on the leeward slope. Divergence of order (10(-6)s(-1) is found on the windward slope while convergence of the same order of magnitude resides on the leeward slope. This outcome may have interesting implications regarding real climatology occurring over the equatorial regions of continental land masses.

Semazzi, F. H. M.↗