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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Engineering and Scientific Applications: Using MatLab(Registered Trademark) for Data Processing and Visualization

MatLab(TradeMark)(MATrix LABoratory) is a numerical computation and simulation tool that is used by thousands Scientists and Engineers in many countries. MatLab does purely numerical calculations, which can be used as a glorified calculator or interpreter programming language; its real strength is in matrix manipulations. Computer algebra functionalities are achieved within the MatLab environment using "symbolic" toolbox. This feature is similar to computer algebra programs, provided by Maple or Mathematica to calculate with mathematical equations using symbolic operations. MatLab in its interpreter programming language form (command interface) is similar with well known programming languages such as C/C++, support data structures and cell arrays to define classes in object oriented programming. As such, MatLab is equipped with most of the essential constructs of a higher programming language. MatLab is packaged with an editor and debugging functionality useful to perform analysis of large MatLab programs and find errors. We believe there are many ways to approach real-world problems; prescribed methods to ensure foregoing solutions are incorporated in design and analysis of data processing and visualization can benefit engineers and scientist in gaining wider insight in actual implementation of their perspective experiments. This presentation will focus on data processing and visualizations aspects of engineering and scientific applications. Specifically, it will discuss methods and techniques to perform intermediate-level data processing covering engineering and scientific problems. MatLab programming techniques including reading various data files formats to produce customized publication-quality graphics, importing engineering and/or scientific data, organizing data in tabular format, exporting data to be used by other software programs such as Microsoft Excel, data presentation and visualization will be discussed.

Sen, Syamal K.↗
NASA NTRS1990

Turbulent flow calculations using unstructured and adaptive meshes

A method of efficiently computing turbulent compressible flow over complex two dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow-field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of flow-field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly-stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady-state is achieved using an unstructured multigrid algorithm. Turbulence modeling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element airfoil geometries are computed and compared with experimental data.

Mavriplis, Dimitri J.↗
NASA NTRS2019

Approach for Propagating Radiometric Data Uncertainties Through NASA Ocean Color Algorithms

Spectroradiometric satellite observations of the ocean are commonly referred to as “ocean color” remote sensing. NASA has continuously collected, processed, and distributed ocean color datasets since the launch of the Sea-viewing Wide-field-of-view Sensor (SeaWiFS) in 1997. While numerous ocean color algorithms have been developed in the past two decades that derive geophysical data products from sensor-observed radiometry, few papers have clearly demonstrated how to estimate measurement uncertainty in derived data products. As the uptake of ocean color data products continues to grow with the launch of new and advanced sensors, it is critical that pixel-by-pixel data product uncertainties are estimated during routine data processing. Knowledge of uncertainties can be used when studying long-term climate records, or to assist in the development and performance appraisal of bio-optical algorithms. In this method paper we provide a comprehensive overview of how to formulate first-order first-moment (FOFM) calculus for propagating radiometric uncertainties through a selection of bio-optical models. We demonstrate FOFM uncertainty formulations for the following NASA ocean color data products: chlorophyll-a pigment concentration (Chl), the diffuse attenuation coefficient at 490 nm (K(sub d,490)), particulate organic carbon (POC), normalized fluorescent line height (nflh), and inherent optical properties (IOPs). Using a quality-controlled in situ hyperspectral remote sensing reflectance (R(sub rs,i)) dataset, we show how computationally inexpensive, yet algebraically complex, FOFM calculations may be evaluated for correctness using the more computationally expensive Monte Carlo approach. We compare bio-optical product uncertainties derived using our test R(sub rs) dataset assuming spectrally-flat, uncorrelated relative uncertainties of 1, 5, and 10%. We also consider spectrally dependent, uncorrelated relative uncertainties in R(sub rs). The importance of considering spectral covariances in R(sub rs), where practicable, in the FOFM methodology is highlighted with an example SeaWiFS image. We also present a brief case study of two POC algorithms to illustrate how FOFM formulations may be used to construct measurement uncertainty budgets for ecologically-relevant data products. Such knowledge, even if rudimentary, may provide useful information to end-users when selecting data products or when developing their own algorithms.

Bio-optics↗
DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗
NASA NTRS2003

Optimal Feedback Control of Thermal Networks

An improved approach to the mathematical modeling of feedback control of thermal networks has been devised. Heretofore software for feedback control of thermal networks has been developed by time-consuming trial-and-error methods that depend on engineers expertise. In contrast, the present approach is a systematic means of developing algorithms for feedback control that is optimal in the sense that it combines performance with low cost of implementation. An additional advantage of the present approach is that a thermal engineer need not be expert in control theory. Thermal networks are lumped-parameter approximations used to represent complex thermal systems. Thermal networks are closely related to electrical networks commonly represented by lumped-parameter circuit diagrams. Like such electrical circuits, thermal networks are mathematically modeled by systems of differential-algebraic equations (DAEs) that is, ordinary differential equations subject to a set of algebraic constraints. In the present approach, emphasis is placed on applications in which thermal networks are subject to constant disturbances and, therefore, integral control action is necessary to obtain steady-state responses. The mathematical development of the present approach begins with the derivation of optimal integral-control laws via minimization of an appropriate cost functional that involves augmented state vectors. Subsequently, classical variational arguments provide optimality conditions in the form of the Hamiltonian equations for the standard linear-quadratic-regulator (LQR) problem. These equations are reduced to an algebraic Riccati equation (ARE) with respect to the augmented state vector. The solution of the ARE leads to the direct computation of the optimal proportional- and integral-feedback control gains. In cases of very complex networks, large numbers of state variables make it difficult to implement optimal controllers in the manner described in the preceding paragraph.

Papalexandris, Miltiadis↗
DOE OSTI2025

Constructing the infrared conformal generators on the fuzzy sphere

We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how to extract these generators using the energy momentum tensor, which is complicated by the fact that one does not have a priori access to the energy momentum tensor of the CFT limit but rather must construct it numerically. We discuss and quantitatively analyze the main sources of corrections to the conformal generators due to the breaking of scale-invariance at finite energy, and develop efficient methods for removing these corrections. The resulting generators have matrix elements that match CFT predictions with accuracy varying from sub-percent level for the lowest-lying states up to several percent accuracy for states with dimension \sim 5 ∼ 5 with N=16 N = 16 fermions. We show that the generators can be used to accurately identify primary operators vs descendant operators in energy ranges where the spectrum is too dense to do the identification solely based on the approximate integer spacing within conformal multiplets.

Fardelli, Giulia (ORCID:0000000217998124)↗
DOE OSTI2025

Adaptive Algebraic Derivative Estimation for Battery Electric Buses Energy Consumption Forecasting

The limited service life of onboard batteries for EVs is a challenge, underscoring the need for real-time battery usage prediction. This paper proposes an adaptive Algebraic Derivative Estimation (ADE) approach for forecasting the energy consumption of battery electric buses. By dynamically adjusting the sliding window length, the adaptive ADE retains the fixed-length ADE’s key advantage—namely, operating online without reliance on extensive historical datasets—while substantially bolstering forecast accuracy by actively trading estimation bias off estimation variance. Comparative experiments against both the conventional ADE with a fixed length and a representative machine learning algorithm, XGBoost, were conducted, with performance evaluated via root mean square error, mean absolute error, and the coefficient of determination. The results demonstrate that the proposed approach significantly outperforms baseline methods.

Cui, Tianyang [The University of Texas at Dallas]↗
DOE OSTI2025

Surrogate-Based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different from those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP)-based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 7.6x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Cho, Younghyun↗
DOE OSTI2021

Object-space optimization of tomographic reconstructions for additive manufacturing

Volumetric 3D printing motivated by computed axial lithography enables rapid printing of homogeneous parts but requires a high dimensionality gradient-descent optimization to calculate image sets. Here we introduce a new, simpler approach to image-computation that algebraically optimizes a model of the printed object, significantly improving print accuracy of complex parts under imperfect material and optical precision by improving optical dose contrast between the target and surrounding regions. Quality metrics for volumetric printing are defined and shown to be significantly improved by the new algorithm. The approach is extended beyond binary printing to grayscale control of conversion to enable functionally graded materials. The flexibility of the technique is digitally demonstrated with realistic projector point spread functions, printing around occluding structures, printing with restricted angular range, and incorporation of materials chemistry such as inhibition. Finally, simulations show that the method facilitates new printing modalities such as printing into flat, rather than cylindrical packages to extend the applications of volumetric printing.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Convexity, Squeezing, and the Elekes-Szabó Theorem

Here, this paper explores the relationship between convexity and sum sets. In particular, we show that elementary number theoretical methods, principally the application of a squeezing principle, can be augmented with the Elekes-Szabó Theorem in order to give new information. Namely, if we let $A \subset \mathbb R$, we prove that there exist $a,a' \in A$ such that\[\left | \frac{(aA+1)^{(2)}(a'A+1)^{(2)}}{(aA+1)^{(2)}(a'A+1)} \right | \gtrsim |A|^{31/12}.\]We are also able to prove that\[\max \{|A+ A-A|, |A^2+A^2-A^2|, |A^3 + A^3 - A^3|\} \gtrsim |A|^{19/12}.\]Both of these bounds are improvements of recent results and takes advantage of computer algebra to tackle some of the computations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

The Design-To-Cost Manifold

Design-to-cost is a popular technique for controlling costs. Although qualitative techniques exist for implementing design to cost, quantitative methods are sparse. In the launch vehicle and spacecraft engineering process, the question whether to minimize mass is usually an issue. The lack of quantification in this issue leads to arguments on both sides. This paper presents a mathematical technique which both quantifies the design-to-cost process and the mass/complexity issue. Parametric cost analysis generates and applies mathematical formulas called cost estimating relationships. In their most common forms, they are continuous and differentiable. This property permits the application of the mathematics of differentiable manifolds. Although the terminology sounds formidable, the application of the techniques requires only a knowledge of linear algebra and ordinary differential equations, common subjects in undergraduate scientific and engineering curricula. When the cost c is expressed as a differentiable function of n system metrics, setting the cost c to be a constant generates an n-1 dimensional subspace of the space of system metrics such that any set of metric values in that space satisfies the constant design-to-cost criterion. This space is a differentiable manifold upon which all mathematical properties of a differentiable manifold may be applied. One important property is that an easily implemented system of ordinary differential equations exists which permits optimization of any function of the system metrics, mass for example, over the design-to-cost manifold. A dual set of equations defines the directions of maximum and minimum cost change. A simplified approximation of the PRICE H(TM) production-production cost is used to generate this set of differential equations over [mass, complexity] space. The equations are solved in closed form to obtain the one dimensional design-to-cost trade and design-for-cost spaces. Preliminary results indicate that cost is relatively insensitive to changes in mass and that the reduction of complexity, both in the manufacturing process and of the spacecraft, is dominant in reducing cost.

Dean, Edwin B.↗
NASA NTRS2011

Engineering and Scientific Applications: Using MatLab(Registered Trademark) for Data Processing and Visualization

MatLab(R) (MATrix LABoratory) is a numerical computation and simulation tool that is used by thousands Scientists and Engineers in many cou ntries. MatLab does purely numerical calculations, which can be used as a glorified calculator or interpreter programming language; its re al strength is in matrix manipulations. Computer algebra functionalities are achieved within the MatLab environment using "symbolic" toolbo x. This feature is similar to computer algebra programs, provided by Maple or Mathematica to calculate with mathematical equations using s ymbolic operations. MatLab in its interpreter programming language fo rm (command interface) is similar with well known programming languag es such as C/C++, support data structures and cell arrays to define c lasses in object oriented programming. As such, MatLab is equipped with most ofthe essential constructs of a higher programming language. M atLab is packaged with an editor and debugging functionality useful t o perform analysis of large MatLab programs and find errors. We belie ve there are many ways to approach real-world problems; prescribed methods to ensure foregoing solutions are incorporated in design and ana lysis of data processing and visualization can benefit engineers and scientist in gaining wider insight in actual implementation of their perspective experiments. This presentation will focus on data processing and visualizations aspects of engineering and scientific applicati ons. Specifically, it will discuss methods and techniques to perform intermediate-level data processing covering engineering and scientifi c problems. MatLab programming techniques including reading various data files formats to produce customized publication-quality graphics, importing engineering and/or scientific data, organizing data in tabu lar format, exporting data to be used by other software programs such as Microsoft Excel, data presentation and visualization will be discussed. The presentation will emphasize creating practIcal scripts (pro grams) that extend the basic features of MatLab TOPICS mclude (1) Ma trix and vector analysis and manipulations (2) Mathematical functions (3) Symbolic calculations & functions (4) Import/export data files (5) Program lOgic and flow control (6) Writing function and passing parameters (7) Test application programs

Sen, Syamal K.↗
NASA NTRS1990

Domain decomposition methods in aerodynamics

Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.

Venkatakrishnan, V.↗
NASA NTRS1982

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes decoupled. The transformation is easily computed by applying the new Riccati iteration. The iteration yields a solution to the nonsymmetric algebraic Riccati equation obtained by partitioning the original system matrix A. The numerical procedure is initiated with the trivial iterate L(0) = 0, and is globally convergent to the desired unique time scale decoupling solution. After transformation, the decoupled system may be used in controller design to achieve exact closed loop pole placement in the slow subsystem without altering the poles of the fast subsystem. The decoupled form may also be used to reduce system order by wetting a small parameter to zero. Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system. These methods are demonstrated using the 16th order linear model of a turbofan engine.

Anderson, L. R.↗
NASA NTRS1994

Advanced information processing system: Hosting of advanced guidance, navigation and control algorithms on AIPS using ASTER

This program demonstrated the integration of a number of technologies that can increase the availability and reliability of launch vehicles while lowering costs. Availability is increased with an advanced guidance algorithm that adapts trajectories in real-time. Reliability is increased with fault-tolerant computers and communication protocols. Costs are reduced by automatically generating code and documentation. This program was realized through the cooperative efforts of academia, industry, and government. The NASA-LaRC coordinated the effort, while Draper performed the integration. Georgia Institute of Technology supplied a weak Hamiltonian finite element method for optimal control problems. Martin Marietta used MATLAB to apply this method to a launch vehicle (FENOC). Draper supplied the fault-tolerant computing and software automation technology. The fault-tolerant technology includes sequential and parallel fault-tolerant processors (FTP & FTPP) and authentication protocols (AP) for communication. Fault-tolerant technology was incrementally incorporated. Development culminated with a heterogeneous network of workstations and fault-tolerant computers using AP. Draper's software automation system, ASTER, was used to specify a static guidance system based on FENOC, navigation, flight control (GN&C), models, and the interface to a user interface for mission control. ASTER generated Ada code for GN&C and C code for models. An algebraic transform engine (ATE) was developed to automatically translate MATLAB scripts into ASTER.

Brenner, Richard↗
NASA NTRS2013

Probabilistic Analysis for Comparing Fatigue Data Based on Johnson-Weibull Parameters

Leonard Johnson published a methodology for establishing the confidence that two populations of data are different. Johnson's methodology is dependent on limited combinations of test parameters (Weibull slope, mean life ratio, and degrees of freedom) and a set of complex mathematical equations. In this report, a simplified algebraic equation for confidence numbers is derived based on the original work of Johnson. The confidence numbers calculated with this equation are compared to those obtained graphically by Johnson. Using the ratios of mean life, the resultant values of confidence numbers at the 99 percent level deviate less than 1 percent from those of Johnson. At a 90 percent confidence level, the calculated values differ between +2 and 4 percent. The simplified equation is used to rank the experimental lives of three aluminum alloys (AL 2024, AL 6061, and AL 7075), each tested at three stress levels in rotating beam fatigue, analyzed using the Johnson- Weibull method, and compared to the ASTM Standard (E739 91) method of comparison. The ASTM Standard did not statistically distinguish between AL 6061 and AL 7075. However, it is possible to rank the fatigue lives of different materials with a reasonable degree of statistical certainty based on combined confidence numbers using the Johnson- Weibull analysis. AL 2024 was found to have the longest fatigue life, followed by AL 7075, and then AL 6061. The ASTM Standard and the Johnson-Weibull analysis result in the same stress-life exponent p for each of the three aluminum alloys at the median, or L(sub 50), lives

Vlcek, Brian L.↗
NASA NTRS1988

Developing integrated parametric planning models for budgeting and managing complex projects

The applicability of integrated parametric models for the budgeting and management of complex projects is investigated. Methods for building a very flexible, interactive prototype for a project planning system, and software resources available for this purpose, are discussed and evaluated. The prototype is required to be sensitive to changing objectives, changing target dates, changing costs relationships, and changing budget constraints. To achieve the integration of costs and project and task durations, parametric cost functions are defined by a process of trapezoidal segmentation, where the total cost for the project is the sum of the various project cost segments, and each project cost segment is the integral of a linearly segmented cost loading function over a specific interval. The cost can thus be expressed algebraically. The prototype was designed using Lotus-123 as the primary software tool. This prototype implements a methodology for interactive project scheduling that provides a model of a system that meets most of the goals for the first phase of the study and some of the goals for the second phase.

Etnyre, Vance A.↗
NASA NTRS1996

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Cai, Zhiqiang↗