SEARCH · Engineering Papers

Results for “multilevel”

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.

SourceResearch connectionFrom yearThrough year

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

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1984

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Tiffany, S. H.↗

NASA NTRS1985

Structural optimization by generalized, multilevel optimization

In the present development history for both a general multilevel optimization capability and a three-level structural optimization, which is taken to be qualitatively equivalent to a multilevel implementation, a structure is partitioned into a number of substructuring levels where each substructure corresponds to a subsystem. The method is illustrated by a portal framework that decomposes into individual beams, each of which is a box that can be further decomposed into stiffened plates. Substructuring therefore spans three different levels. Since further extensions would only add to the intermediate substructuring levels, the three-level case is qualitatively complete.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1985

Theoretical and software considerations for general dynamic analysis using multilevel substructured models

The dynamic analysis of complex structural systems using the finite element method and multilevel substructured models is presented. The fixed-interface method is selected for substructure reduction because of its efficiency, accuracy, and adaptability to restart and reanalysis. This method is extended to reduction of substructures which are themselves composed of reduced substructures. The implementation and performance of the method in a general purpose software system is emphasized. Solution algorithms consistent with the chosen data structures are presented. It is demonstrated that successful finite element software requires the use of software executives to supplement the algorithmic language. The complexity of the implementation of restart and reanalysis porcedures illustrates the need for executive systems to support the noncomputational aspects of the software. It is shown that significant computational efficiencies can be achieved through proper use of substructuring and reduction technbiques without sacrificing solution accuracy. The restart and reanalysis capabilities and the flexible procedures for multilevel substructured modeling gives economical yet accurate analyses of complex structural systems.

Schmidt, R. J.↗

NASA NTRS1987

Practical implementation of an accurate method for multilevel design sensitivity analysis

Solution techniques for handling large scale engineering optimization problems are reviewed. Potentials for practical applications as well as their limited capabilities are discussed. A new solution algorithm for design sensitivity is proposed. The algorithm is based upon the multilevel substructuring concept to be coupled with the adjoint method of sensitivity analysis. There are no approximations involved in the present algorithm except the usual approximations introduced due to the discretization of the finite element model. Results from the six- and thirty-bar planar truss problems show that the proposed multilevel scheme for sensitivity analysis is more effective (in terms of computer incore memory and the total CPU time) than a conventional (one level) scheme even on small problems. The new algorithm is expected to perform better for larger problems and its applications on the new generation of computer hardwares with 'parallel processing' capability is very promising.

Nguyen, Duc T.↗

NASA NTRS1989

Fuzzy set applications in engineering optimization: Multilevel fuzzy optimization

A formulation for multilevel optimization with fuzzy objective functions is presented. With few exceptions, formulations for fuzzy optimization have dealt with a one-level problem in which the objective is the membership function of a fuzzy set formed by the fuzzy intersection of other sets. In the problem examined here, the goal set G is defined in a more general way, using an aggregation operator H that allows arbitrary combinations of set operations (union, intersection, addition) on the individual sets Gi. This is a straightforward extension of the standard form, but one that makes possible the modeling of interesting evaluation strategies. A second, more important departure from the standard form will be the construction of a multilevel problem analogous to the design decomposition problem in optimization. This arrangement facilitates the simulation of a system design process in which different components of the system are designed by different teams, and different levels of design detail become relevant at different time stages in the process: global design features early, local features later in the process.

Diaz, Alejandro R.↗

NASA NTRS1989

A multilevel approach to the design of dc-free line codes

A multilevel approach to the design of dc-free line codes is presented. The different levels can be used for different purposes; for example, to control the maximum accumulated charge or to guarantee a certain minimum distance. The advantages of codes designed by this method over similar codes are the improved run-length/accumulated-charge parameters, higher transmission rate, and the systematic nature of the code construction. The multilevel structure allows the redundancy in the signal selection procedure to be allocated efficiently among the different levels. It also allows the use of suboptimal staged decoding procedures that have performance/complexity advantages over maximum-likelihood decoding.

Calderbank, A. R.↗

NASA NTRS1991

An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

Rybicki, G. B.↗

NASA NTRS1990

New evidence favoring multilevel decomposition and optimization

A new multilevel optimization technique based on a global sensitivity matrix which uses behavior variables in addition to design variables and constraints to decompose the problem is proposed. The technique simplifies the decomposition of the design problem and the programming task and improves the convergence speed of multilevel optimization compared to conventional optimization. The technique is particularly well suited to problems with large numbers of design variables and with computationally expensive constraints.

Padula, Sharon L.↗

NASA NTRS1994

Nonresonant interaction of ultrashort electromagnetic pulses with multilevel quantum systems

Some features of the excitation of multilevel quantum systems under the action of electromagnetic pulses which are shorter than the inverse frequency of interlevel transitions are considered. It is shown that the interaction is characterized by a specific type of selectivity which is not connected with the resonant absorption of radiation. The simplest three-level model displays the inverse population of upper levels. The effect of an ultrashort laser pulse on a multilevel molecule was regarded as an instant reception of the oscillation velocity by the oscillator and this approach showed an effective excitation and dissociation of the molecule. The estimations testify to the fact that these effects can be observed using modern femtosecond lasers.

Belenov, E.↗

NASA NTRS1992

On the Retrieval and Analysis of Multilevel Clouds

An accurate satellite retrieval of cloud properties depends upon the detection and analysis of multilayered, overlapping cloud systems that surface observations show to be common. Multiple cloud layers are often found, for instance, in frontal situations, where cirrus overlays boundary layer convective cloud or low-to mid-level stratus cloud. Surface observers (Hahan et al., 1982) indicate that over ocean in the Northern Hemisphere between 30 deg. N and 60 deg. N, 51 percent of observations are of multilevel clouds. A satellite analysis by Coakley (1983) over the Pacific Ocean finds that more than 50 percent of 500 (250 sq km) frames exhibit evidence of multilayered cloud systems. The questions addressed in this study are the following: What error is introduced when inferring the cloud pressure from a Field-Of-View (FOV) that contains some arbitrary amount of transparent cloud overlaying a lower-level black cloud, such as stratus, by making the assumption that there is only a single cloud layer in the FOV, and what may be done to improve the cloud retrieval? The CO2 slicing methods (e.g. McCleese and Wilson, 1976; Smith and Platt, 1978; Chahine, 1974) have been shown to provide accurate means of inferring cirrus cloud altitude from passive infrared radiance measurements. The CO2 techniques have been applied to radiometric data from several instruments, notably the High Resolution Infrared Radiometric Sounder (HIRS/2, hereafter referred to as HIRS), the VISSR Atmospheric Sounder (VAS) (e.g., Menzel et al., 1983; Wylie and Menzel, 1989), and most recently to the High Resolution Interferometer Sounder (HIS) (Smith and Frey, 1990). The methods take advantage of the fact that infrared CO2 sounding channels spaced closely in wavenumber each have varying opacity to CO2, thereby causing each channel to be sensitive to a different level in the atmosphere. The techniques have been shown to be effective for single-layered, nonblack, mid- to high-level clouds such as cirrus, but are generally applied operationally to any given cloud occurrence. The CO2 slicing algorithms are most accurate for clouds than occur in a single, well-defined layer, or for multi-layered cloud cases in which the uppermost cloud layer is nearly black. Significant cloud height retrieval errors may ensue if the HIRS Field-Of-View (FOV) is cotaminated with low cloud. McCleese and Wilson (1976) have shown that the retrieved cloud height for the case of multiple cloud layers is a weighted average of the cloud heights actually present. The weight is approximately proportional to the product of the cloud heigt and the effective cloud amount. The effect of their result is that the uppermost cloud layer dominates the cloud pressure retrieval. Beyond stating that the higher cloud dominates the cloud pressure retrieval, there is no quantitative information to provide a way of estimating the errors in cloud pressure retrieval one should expect for certain common multilevel cloud situations or any suggestions on how to reduce the errors. In this paper we estimate the magnitude of the errors and use a simple algorithm to reduce the errors in optically thin cloud height retrival.

Baum, Bryan A.↗

NASA NTRS2001

Efficiency Improvements to the Displacement Based Multilevel Structural Optimization Algorithm

Multilevel Structural Optimization (MSO) continues to be an area of research interest in engineering optimization. In the present project, the weight optimization of beams and trusses using Displacement based Multilevel Structural Optimization (DMSO), a member of the MSO set of methodologies, is investigated. In the DMSO approach, the optimization task is subdivided into a single system and multiple subsystems level optimizations. The system level optimization minimizes the load unbalance resulting from the use of displacement functions to approximate the structural displacements. The function coefficients are then the design variables. Alternately, the system level optimization can be solved using the displacements themselves as design variables, as was shown in previous research. Both approaches ensure that the calculated loads match the applied loads. In the subsystems level, the weight of the structure is minimized using the element dimensions as design variables. The approach is expected to be very efficient for large structures, since parallel computing can be utilized in the different levels of the problem. In this paper, the method is applied to a one-dimensional beam and a large three-dimensional truss. The beam was tested to study possible simplifications to the system level optimization. In previous research, polynomials were used to approximate the global nodal displacements. The number of coefficients of the polynomials equally matched the number of degrees of freedom of the problem. Here it was desired to see if it is possible to only match a subset of the degrees of freedom in the system level. This would lead to a simplification of the system level, with a resulting increase in overall efficiency. However, the methods tested for this type of system level simplification did not yield positive results. The large truss was utilized to test further improvements in the efficiency of DMSO. In previous work, parallel processing was applied to the subsystems level, where the derivative verification feature of the optimizer NPSOL had been utilized in the optimizations. This resulted in large runtimes. In this paper, the optimizations were repeated without using the derivative verification, and the results are compared to those from the previous work. Also, the optimizations were run on both, a network of SUN workstations using the MPICH implementation of the Message Passing Interface (MPI) and on the faster Beowulf cluster at ICASE, NASA Langley Research Center, using the LAM implementation of UP]. The results on both systems were consistent and showed that it is not necessary to verify the derivatives and that this gives a large increase in efficiency of the DMSO algorithm.

Plunkett, C. L.↗

NASA NTRS2002

Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries

This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.

Aftosmis, M. J.↗

DOE OSTI2020

Estimating posterior quantity of interest expectations in a multilevel scalable framework

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large-scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element-agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state-of-the-art scalable AMG. To illustrate the applicability of this approach, numerical tests are performed on two 3D examples-a unit cube and an egg-shaped domain with an irregular boundary-where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Estimation of distributions via multilevel Monte Carlo with stratified sampling

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach

In this paper, we present a method combining multilevel Monte Carlo (MLMC) and a graph-based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph-based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Direct Power Control of Back to Back Modular Multilevel Converter with Advanced Grid Support Functions for Grid Forming Application

Possibility of using back-to-back modular multilevel converter system with a direct power control architecture has been investigated in this paper. The rectifier side is controlled to be in grid following mode whereas the inverter side is controlled in grid forming mode. Both the sides’ local controllers use Lyapunov energy function based architecture to accomplish the objective of active and reactive power control as well as maintaining a fixed user defined voltage over the dc bus on the rectifier side. Therefore, the proposed direct power control architecture has embedded dc bus control architecture to maintain fixed user defined value of the capacitors. Similar architecture is implemented on the inverter side to accomplish either voltage control during grid forming or power control during grid following. Advanced grid support functionalities based on IEEE-1547-2018 is implemented and utilized to generate the reference values for either the rectifier or the inverter sides. The overall system is modeled based on MATLAB/Simulink and PLECS domain and various important case studies to verify the efficacy of the overall system has been presented.

direct power control (DPC)↗

DOE OSTI2022

Control and Grid Support Function Evaluation for a Three-Phase Back-to-Back Modular Multilevel Converter System

This paper focuses on the evaluation of advanced inverter controls for a 500kW back-to-back (B2B), silicon carbide, multilevel modular converter (MMC) used as a direct-connected medium-voltage grid intertie. A decentralized hierarchical controller architecture for the MMC system is presented, which uses the main controller to implement higher level grid interconnection functions per the IEEE 1547–2018 standards and the local controllers to execute lower level closed-loop functionality of the MMC stages. This paper presents and elaborates on the grid functionalities are elaborated and presented. The back-to-back converter system is equipped with local controllers and their corresponding functionalities are presented. Case study results for the corresponding functionalities presented show the effectiveness of the proposed architecture. To enhance the operation capabilities of the system, a parameter update scheme has been implemented and utilized in unison with the controller.

decentralized control↗