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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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NASA NTRS1996

Design of Multi-Parameter Steerable Functions Using Cascade Basis Reduction

A new cascade basis reduction method of computing the optimal least-squares set of basis functions steering a given function is presented. The method combines the Lie group-theoretic and the singular value decomposition approaches in such a way that their respective strengths complement each other. Since the Lie group-theoretic approach is used, the set of basis and steering functions computed can be expressed analytically. Because the singular value decomposition method is used, this set of basis and steering functions is optimal in the least-squares sense. Furthermore, the computational complexity in designing basis functions for transformation groups with large numbers of parameters is significantly reduced. The efficiency of the cascade basis reduction method is demonstrated by designing a set of basis functions that steers a Gabor function under the four-parameter linear transformation group.

Teo, P.↗

NASA NTRS1999

Design Optimization of Stiffened Panels with Postbuckling Constraints

The funding provided by the grant is used to complete the final stages of the development of a geometrically nonlinear analysis and design capability for the static response of compressively loaded prismatic plate structures. The analysis is based on the nonlinear finite strip method and is applicable for structures, such as stiffened panels or box columns, that can be modeled as assemblages of finite length plate strips. In an effort to reduce the computational cost of the nonlinear finite strip method, thus making it suitable for use in the design optimization environment, reduced basis techniques as described in various references by Noor are used in conjunction with the finite strip method. In addition, an efficient scheme for tracing the nonlinear equilibrium paths through highly nonlinear response curves was implemented. The new scheme, which is referred to as the normal flow algorithm, is based on homotopy methods, and is capable of negotiating highly nonlinear limit point instabilities with a reduced computational cost compared to the popular Ricks/Wempner and Chrisfield algorithms.

Guerdal, Zafer↗

NASA NTRS1996

Low-Dimensional Dynamical Models of Thermal Convection

A low-dimensional dynamic model for transitional buoyancy-driven flow in a differentially heated tall enclosure is presented. The full governing partial differential equations with the associated boundary conditions are solved by a spectral element method for a cavity of aspect ratio A=20. Proper orthogonal decomposition is applied to the oscillatory solution at Prandtl number Pr=P tau (omega) = 0.71 and Grashof number G tau (omega) = 3.2 x 10 (exp 4) to construct empirical eigenfunctions. Using the four most energetic empirical eigenfunctions for the velocity and temperature as basis functions and applying Galerkin's method, a reduced model consisting of eight nonlinear ordinary differential equations is obtained. Close to the 'design' conditions (P tau(omega) G tau(omega)), the low-order model (LOM) predictions are in excellent agreement with the predictions of the full model. In particular, the critical Grashof number at the onset of the first temporal flow instability (Hopf bifurcation) was well as the frequency and amplitude of oscillations at supercritical conditions are in excellent agreement with the predictions of the full model. Far from the 'design' conditions, the LOM predicts the existence of multiple stable steady solutions at large values of G tau, and a unique stable steady solution at small values of G tau, and exhibits hysteretic behavior that is qualitatively similar to that observed in direct numerical simulations based on the full model.

Liakopoulos, Anthony↗

NASA NTRS1975

Structural reanalysis via a mixed method

A study is made of the approximate structural reanalysis technique based on the use of Taylor series expansion of response variables in terms of design variables in conjunction with the mixed method. In addition, comparisons are made with two reanalysis techniques based on the displacement method. These techniques are the Taylor series expansion and the modified reduced basis. It is shown that the use of the reciprocals of the sizing variables as design variables (which is the natural choice in the mixed method) can result in a substantial improvement in the accuracy of the reanalysis technique. Numerical results are presented for a space truss structure.

Noor, A. K.↗

DOE OSTI2025

Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks

The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.

42 ENGINEERING↗

DOE OSTI2020

A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations

Here, we investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

"embedded" basis↗

DOE OSTI2021

Estimating basis functions in massive fields under the spatial mixed effects model

Abstract Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation–maximization algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.

Pazdernik, Karl↗

DOE OSTI2020

Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets

We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller–Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn–Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn–Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.

Morales, Miguel A. (ORCID:0000000263893067)↗

DOE OSTI2024

Adaptive Methods for Radial Basis Functions

Radial basis functions (RBFs) are a powerful tool for constructing high-order accurate reduced representations of scattered data in arbitrary dimension and on manifolds. We present a method of constructing data approximations in which we utilize a functional tail to capture a global background profile and a RBF neural network (NN) to capture the smaller-scale features. In the RBF NN the RBF centers, matrix shape parameters were selected adaptively for each RBF. We also utilized a geodesic notion of distance on the manifold on which the data lies, e.g., the spherical geodesic for data on the sphere. Although each of these ideas have been been investigated separately in previous works, their combination into a single algorithm is novel. We defined a machine learning problem in which these properties are learned to minimize the data reduction error. We demonstrate the algorithm for applications of scattered data reduction in the plane and on the sphere.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Structural response reconstruction using a system-equivalent singular vector basis

Here, this paper develops a novel method for reconstructing the full-field response of structural dynamic systems using sparse measurements. The singular value decomposition is applied to a frequency response matrix relating the structural response to physical loads, base motion, or modal loads. The left singular vectors form a non-physical reduced basis that can be used for response reconstruction with far fewer sensors than existing methods. The contributions of the singular vectors to measured response are termed singular-vector loads (SVLs) and are used in a regularized Bayesian framework to generate full-field response estimates and confidence intervals. The reconstruction framework is applicable to the estimation of single data records and power spectral densities from multiple records. Reconstruction is successfully performed in configurations where the number of SVLs to identify is less than, equal to, and greater than the number of sensors used for reconstruction. In a simulation featuring a seismically excited shear structure, SVL reconstruction significantly outperforms modal FRF-based reconstruction and successfully estimates full-field responses with as few as two uniaxial accelerometers. SVL reconstruction is further verified in a simulation featuring an acoustically excited cylinder. Finally, response reconstruction and uncertainty quantification are performed on an experimental structure with three shaker inputs and 27 triaxial accelerometer outputs.

42 ENGINEERING↗

DOE OSTI2021

Using computational singular perturbation as a diagnostic tool in ODE and DAE systems: a case study in heterogeneous catalysis

We have extended the computational singular perturbation (CSP) method to differential algebraic equation (DAE) systems and demonstrated its application in a heterogeneous-catalysis problem. The extended method obtains the CSP basis vectors for DAEs from a reduced Jacobian matrix that takes the algebraic constraints into account. Here we use a canonical problem in heterogeneous catalysis, the transient continuous stirred tank reactor (T-CSTR), for illustration. The T-CSTR problem is modelled fundamentally as an ordinary differential equation (ODE) system, but it can be transformed to a DAE system if one approximates typically fast surface processes using algebraic constraints for the surface species. We demonstrate the application of CSP analysis for both ODE and DAE constructions of a T-CSTR problem, illustrating the dynamical response of the system in each case. We also highlight the utility of the analysis in commenting on the quality of any particular DAE approximation built using the quasi-steady state approximation (QSSA), relative to the ODE reference case.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Initial postbuckling analysis of elastoplastic thin-shear structures

The design of thin shell structures with respect to elastoplastic buckling requires an extended analysis of the influence of initial imperfections. For conservative design, the most critical defect should be assumed with the maximum allowable magnitude. This defect is closely related to the initial postbuckling behavior. An algorithm is given for the quasi-static analysis of the postbuckling behavior of structures that exhibit multiple buckling points. the algorithm based upon an energy criterion allows the computation of the critical perturbation which will be employed for the definition of the critical defect. For computational efficiency, the algorithm uses the reduced basis technique with automatic update of the modal basis. The method is applied to the axisymmetric buckling of cylindrical shells under axial compression, and conclusions are given for future research.

E G Carnoy↗

NASA NTRS1984

On reduced matrix inversion for operator splitting methods

The element-splitting heat-conduction algorithm of Hughes et al. (1983) is modified using the dual-basis approach of Flanagan and Belytschko (1981). The size of the system to be solved is reduced, and the formulation of a stiffness matrix is avoided. The 2D application is demonstrated, and the feasibility of a 3D implementation is indicated.

Belytschko, T.↗

NASA NTRS1974

Application of optimality criteria in structural synthesis

The rational use of optimality criteria was investigated for a class of structural synthesis problems where materials, configuration and applied load conditions are specified, and the minimum weight design is to be determined. The potential of hybrid methods of structural optimization for dealing with relatively large design problems involving practical complexity was explored. The reduced basis concept in design space was used to decrease the number of generalized design variables dealt with by the mathematical programming algorithm. Optimality criteria methods for obtaining design vectors associated with displacement, system buckling and natural frequency constraints are presented. A stress ratio method was used to generate a basis design vector representing the stress constraints. The finite element displacement method was used as the basic structural analysis tool. Results for several examples of truss systems subject to stress, displacement and minimum size constraints are presented. An assessment of these results indicates the effectiveness of the hybrid method developed.

Terai, K.↗

DOE OSTI2023

Cost analysis of hydrogen production by high-temperature solid oxide electrolysis

In this study, we estimate construction and operation costs of gigawatt-scale solid oxide electrolysis (SOE) facilities for producing high purity hydrogen gas from water. Manufacturing and assembly costs for two types of SOE cell stacks are estimated using a detailed design for manufacture and assembly (DFMA®) analysis. Modular balance of plant (BOP) process equipment is designed and sized with Aspen®, and cost estimated using equipment vendor quotes. Factory and on-site assembly and installation costs for SOEC stack and BOP equipment integration into modular SOE process units are calculated using a simplified DFMA® method. Total stack costs on a stack input power (SIP) basis reduce to <$100/kW e DC SIP for >500 MW e DC SIP /year production rates with electrode cermet, interconnects, and high-temperature heat treatments dominating the total cost. Integration of stacks with larger BOP equipment operating at higher pressures offers ~36% cost reduction in total facility capital cost due to an economies of physical scale effect since BOP equipment comprises >50% of facility costs. Optimized H 2 prices decrease from ~$\$$4/kgH 2 to ~$\$$2/kgH 2 for 1 GWe DCSIP facilities using $\$$0.025/kWh electricity price. All costs are reported in 2021 US dollars.

08 HYDROGEN↗

DOE OSTI2023

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Here in this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining the technique of oversampling, one makes use of the information of the current residuals to adaptively construct basis functions in the online stage to reduce the error of multiscale approximation. A complete analysis of the method is presented, which shows the proposed online enrichment leads to a fast convergence from multiscale approximation to the fine-scale solution. The error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Further, the convergence rate of the enrichment algorithm depends on a factor of exponential decay regarding the number of oversampling layers and a user-defined parameter. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed online adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2018

Optimal Control Prediction Method for Control Allocation

This paper proposes a novel prediction method for online optimal control allocation that extends the volume of moments achievable with the Moore-Penrose generalized inverse to the entire Attainable Moment Set. This method formulates the control allocation problem using selected basis vectors and associated gains which reduces the optimization problem dimensions and provides physical insight into the resulting optimal solutions. The proposed algorithm finds the entire family of unique optimal control solutions along the desired moment vector from the origin to the boundary of the Attainable Moment Set. Numerical results for the Moore-Penrose prediction method show that the unique minimal controls obtained yield the desired moment with near machine precision accuracy while maintaining control effectors within specified position limits. This method has been fully validated against the unique solution obtained on the boundary of the Attainable Moment Set using the Durham Direct Allocation method. Minimal control solutions obtained for moments in the interior of the Attainable Moment Set, similarly yield the desired moment to near machine precision while providing control solutions that are smaller (i.e. 2-norm) than solutions found with traditional control allocation algorithms (e.g. interior point methods) applied to the minimal control problem. Numerical simulations using a Matlab® autocoded executable (MEX) for the representative real world problem of 3-moments with 20 individual control effectors and prescribed control position limits show a mean computation speed of approximately 125 Hz which is sufficient to enable real-time flight allocation.

Acheson, Michael J.↗

NASA NTRS1975

Geometric analysis and restitution of digital multispectral scanner data arrays

An investigation was conducted to define causes of geometric defects within digital multispectral scanner (MSS) data arrays, to analyze the resulting geometric errors, and to investigate restitution methods to correct or reduce these errors. Geometric transformation relationships for scanned data, from which collinearity equations may be derived, served as the basis of parametric methods of analysis and restitution of MSS digital data arrays. The linearization of these collinearity equations is presented. Algorithms considered for use in analysis and restitution included the MSS collinearity equations, piecewise polynomials based on linearized collinearity equations, and nonparametric algorithms. A proposed system for geometric analysis and restitution of MSS digital data arrays was used to evaluate these algorithms, utilizing actual MSS data arrays. It was shown that collinearity equations and nonparametric algorithms both yield acceptable results, but nonparametric algorithms possess definite advantages in computational efficiency. Piecewise polynomials were found to yield inferior results.

Baker, J. R.↗