Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convergence analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Thermal stress analysis of reusable surface insulation for shuttle

An iterative procedure for accurately determining tile stresses associated with static mechanical and thermally induced internal loads is presented. The necessary conditions for convergence of the method are derived. An user-oriented computer program based upon the present method of analysis was developed. The program is capable of analyzing multi-tiled panels and determining the associated stresses. Typical numerical results from this computer program are presented.

Ojalvo, I. U.↗
DOE OSTI2025

Spotlight: efficient automated global optimization in rietveld analysis of diffraction data

Performing reliable Rietveld analysis on tens or hundreds of powder diffraction datasets from parametric or time-resolved experiments often poses a bottleneck in extracting meaningful results from the data. While automated analysis of data has recently been demonstrated, high temperature annealing studies, during which phase transformations occur and lattice parameters may change due to repartitioning of elements, are prime examples where automation by a simple phase identification from a database of room temperature structures or automation by sequential refinements is likely to fail. To enable reliable, efficient, automated Rietveld analysis, we present a Python package named Spotlight , building on established Rietveld packages such as MAUD, GSAS , or GSAS-II , which extends the refinement of best fit parameters to a global optimization using an ensemble of optimizers leveraging hierarchical parallel execution on high-performance computing clusters. Spotlight further enables the efficient design of refinement plans through the iterative automated machine-learning of a surrogate for the refinement on which the global optimizations are performed until results from the surrogate converge to the response surface data. We demonstrate Spotlight with the analysis of uranium molybdenum and Ti–6Al–4V datasets, as well as in two open-source tutorials analyzing aluminium oxide and lead sulphate.

36 MATERIALS SCIENCE↗
DOE OSTI2017

NONPARAMETRIC EMPIRICAL BAYES ESTIMATION THROUGH DECONVOLUTION IN PROBABILISTIC RISK ANALYSIS

The advent of Markov Chain Monte Carlo (MCMC) simulations and availability of open source software made full hierarchical Bayesian analysis tractable and a popular choice in parameter estimation for Probabilistic Risk Assessment (PRA). However, despite its theoretical attractiveness, the hierarchical Bayesian analysis is not without its problems. Two of the most prominent practical difficulties in applying hierarchical Bayes analysis in practice to analyze source-to-source variability, for example, is its sensitivity to the selection of the first-stage prior and dependence of the rate of convergence on the selection of the first-stage prior. The first-stage prior in hierarchical Bayesian analysis is usually assumed having a parametric form, often conjugate to the likelihood function (aleatory model). To facilitate convergence for hierarchical Bayes models, the first-stage prior is frequently set through empirical Bayes estimate, which can use available historical data to find the parameters of the first-stage prior. The paper discusses a new nonparametric empirical Bayes estimation and compare it to several well-known parametric estimates such as method of moments and maximum likelihood. The new nonparametric technique exploits the prior predictive distribution as integral equation and proceeds to solve it with respect to prior assuming the sampling data distribution and aleatory model are available. The discussion covers topics such as selection of aleatory model for future data, selection of regularization parameter, and density estimation for historical data. For comparison, the paper is using contrived as well as real-world data from utilities. Utilities data represent failure data with Poisson distribution used for aleatory model.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Vertical and Horizontal Wind Structure Prior to and During the 1997/1998 ENSO Event

Analyses of ECMWF and satellite wind products are used to investigate low frequency fluctuations in the wind fields immediately preceding and during the 1997/1998 ENSO event. An extended EOF analysis of the horizontal and vertical wind structure that allows for the study of propagating features indicates that the dominant mode of variability established in the lower levels of the atmosphere is a convergence in the central tropical Pacific. At mid-levels, the westerlies increase with time over most of the equatorial Pacific, and there are closed cyclonic features on either side of the equator. At upper levels, the flow tends to become divergent across the equatorial Pacific, and there is a strong flow from the northwest Pacific across Indonesia that then turns to the west along the equator in the Indian Ocean. The addition of satellite data for improved surface wind estimates reveal that the Indian Ocean winds were anomalously strong during the winter preceding the initiation of the ENSO event. An analysis of the momentum convergence flux at the surface indicates a very strong anomaly 9 months prior to the ENSO event that begins in the western Indian Ocean and propagates to the east, arriving over the Pacific warm pool area coincident with the beginning of the El Nino. Changes in the near surface thermal and water vapor structure over the Indian Ocean during this period will also be discussed.

Adamec, David↗
NASA NTRS2009

New Flutter Analysis Technique for CFD-based Unsteady Aeroelasticity

This paper presents a flutter analysis technique for the transonic flight regime. The technique uses an iterative approach to determine the critical dynamic pressure for a given mach number. Unlike other CFD-based flutter analysis methods, each iteration solves for the critical dynamic pressure and uses this value in subsequent iterations until the value converges. This process reduces the iterations required to determine the critical dynamic pressure. To improve the accuracy of the analysis, the technique employs a known structural model, leaving only the aerodynamic model as the unknown. The aerodynamic model is estimated using unsteady aeroelastic CFD analysis combined with a parameter estimation routine. The technique executes as follows. The known structural model is represented as a finite element model. Modal analysis determines the frequencies and mode shapes for the structural model. At a given mach number and dynamic pressure, the unsteady CFD analysis is performed. The output time history of the surface pressure is converted to a nodal aerodynamic force vector. The forces are then normalized by the given dynamic pressure. A multi-input multi-output parameter estimation software, ERA, estimates the aerodynamic model through the use of time histories of nodal aerodynamic forces and structural deformations. The critical dynamic pressure is then calculated using the known structural model and the estimated aerodynamic model. This output is used as the dynamic pressure in subsequent iterations until the critical dynamic pressure is determined. This technique is demonstrated on the Aerostructures Test Wing-2 model at NASA's Dryden Flight Research Center.

Pak, Chan-gi↗
NASA NTRS1998

Asymptotic Spreading Rate of Initially Compressible Jets: Experiment and Analysis

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing "jet Mach number" M(sub J). Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the "potential core length" of the jet occurring with increasing M(sub J), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Zaman, K. B. M. Q.↗
NASA NTRS1998

Asymptotic Spreading Rate of Initially Compressible Jets-Experiment and Analysis

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing "jet Mach number" M(sub j). Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the "potential core length" of the jet occurring with increasing M(sub j), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Zaman, K. B. M. Q.↗
DOE OSTI2018

Communication: Approaching exact quantum chemistry by cluster analysis of full configuration interaction quantum Monte Carlo wave functions

We propose to accelerate convergence toward full configuration interaction (FCI) energetics by using the coupled-cluster approach, in which singly and doubly excited clusters, needed to determine the energy, are iterated in the presence of their three- and four-body counterparts extracted from FCI quantum Monte Carlo (FCIQMC) propagations. Finally, preliminary calculations for the water molecule at the equilibrium and stretched geometries show that we can accurately extrapolate the FCI energetics based on the early stages of FCIQMC propagations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Error analysis for spectral approximation of the Korteweg-De Vries equation

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Maday, Y.↗
NASA NTRS1994

Structural/aerodynamic Blade Analyzer (SAB) User's Guide, Version 1.0

The structural/aerodynamic blade (SAB) analyzer provides an automated tool for the static-deflection analysis of turbomachinery blades with aerodynamic and rotational loads. A structural code calculates a deflected blade shape using aerodynamic loads input. An aerodynamic solver computes aerodynamic loads using deflected blade shape input. The two programs are iterated automatically until deflections converge. Currently, SAB version 1.0 is interfaced with MSC/NASTRAN to perform the structural analysis and PROP3D to perform the aerodynamic analysis. This document serves as a guide for the operation of the SAB system with specific emphasis on its use at NASA Lewis Research Center (LeRC). This guide consists of six chapters: an introduction which gives a summary of SAB; SAB's methodology, component files, links, and interfaces; input/output file structure; setup and execution of the SAB files on the Cray computers; hints and tips to advise the user; and an example problem demonstrating the SAB process. In addition, four appendices are presented to define the different computer programs used within the SAB analyzer and describe the required input decks.

Morel, M. R.↗
DOE OSTI2024

Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

We introduce a safe extremum-seeking (Safe ES) algorithm which achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, “practical safety” is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time—semiglobally—if starting in safe set. The safety result of the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Acceleration of convergence and spectrum transformation of implicit finite difference operators associated with Navier-Stokes equations

Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.

Saleem, M.↗
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗
DOE OSTI2018

Fault Detection for Dynamical Systems using Differential Geometric and Concurrent Learning Approach

This paper presents a fault identification and estimation approach that brings together the differential geometric concept of observability codistribution with data driven concurrent learning. In order to identify faults in presence of unknown disturbances, we utilize the differential geometric approach to design a coordinate transformation, to find a subspace in which the effect of disturbances and system faults can be segregated. We then use concurrent learning to estimate magnitude of the constant fault. We illustrate the approach to fault isolation for a linear helicopter dynamics and a spherical pendulum dynamics. We use Lyapunov stability analysis to show that the fault estimate by concurrent learning converges to the actual fault value, and then illustrate the design of a recovery controller.

Fault detection and diagnosis↗
DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Computation of multi-region relaxed magnetohydrodynamic equilibria

We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Advancing the STS Neutron Moderator Design with an Automated Optimization Workflow and Unstructured Mesh Modeling

With the Second Target Station approaching its final design phase, a detailed neutronics evaluation of its critical components is necessary. Optimizing the dimensions of the two cold-source moderators that are at the heart of this facility presents a multi-objective optimization problem for which an accurate geometric description is crucial. We have applied a fully automated optimization workflow in which a detailed unstructured mesh geometry is automatically generated with Attila4MC, starting from a parametrized CREO geometry followed by preprocessing with SpaceClaim. With this geometry, a MCNP run is performed to calculate the brightness metrics, which are subsequently provided to the optimization algorithm in DAKOTA that provides new parameters and drives the optimization loop until convergence. In this paper, we show the results of the analysis that are used for the final design of the cylindrical and tube moderator. The optimization simulations provide a refinement to and confirmation of the conclusions of the previous design iteration. Additional to the optimization, a sensitivity study is performed to study the effect of minor geometry changes, which is important for the final engineering design. In conclusion, with these studies, we demonstrate that the automated workflow and high-fidelity unstructured mesh modeling are efficient tools for a thorough design evaluation.

DAKOTA↗