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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Convergence of Weak-SINDy Surrogate Models

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Separation analysis, a tool for analyzing multigrid algorithms

The separation of vectors by multigrid (MG) algorithms is applied to the study of convergence and to the prediction of the performance of MG algorithms. The separation operator for a two level cycle algorithm is derived. It is used to analyze the efficiency of the cycle when mixing of eigenvectors occurs. In particular cases the separation analysis reduces to Fourier type analysis. The separation operator of a two level cycle for a Schridubger eigenvalue problem, is derived and analyzed in a Fourier basis. Separation analysis gives information on how to choose performance relaxations and inter-level transfers. Separation analysis is a tool for analyzing and designing algorithms, and for optimizing their performance.

Costiner, Sorin↗
NASA NTRS2019

Structural Analysis of Test Flight Vehicles with Multifunctional Energy Storage

Under the NASA Aeronautics Research Mission Directorate (ARMD) Convergent Aeronautical Solutions (CAS) project, NASA Glenn Research Center has been leading Multifunctional Structures for High Energy Lightweight Load-bearing Storage (M-SHELLS) research efforts. The technology of integrating load-carrying structures with electrical energy storage capacity has the potential to reduce the overall weight of future electric aircraft. The proposed project goals were to develop M-SHELLS in the form of honeycomb coupons and subcomponents, integrate them into the structure, and conduct low-risk flight tests onboard a remotely piloted small aircraft. Experimental M-SHELLS energy-storing coupons were fabricated and tested in the laboratory for their electrical and mechanical properties. In this paper, finite element model development and structural analyses of two small test aircraft candidates are presented. The finite element analysis of the initial two-spar wing is described for strain, deflection, and weight estimation. After a test aircraft Tempest was acquired, a load- deflection test of the wing was conducted. A finite element model of the Tempest was then developed based on the test aircraft dimensions and construction detail. The component weight analysis from the finite element model and test measurements were correlated. Structural analysis results with multifunctional energy storage panels in the fuselage of the test vehicle are presented. Although the flight test was cancelled because of programmatic reasons and time constraints, the structural analysis results indicate that the mid-fuselage floor composite panel could provide structural integrity with minimal weight penalty while supplying electrical energy. To explore potential future applications of the multifunctional structure, analyses of the NASA X-57 Maxwell electric aircraft and a NASA N+3 Technology Conventional Configuration (N3CC) fuselage are presented. Secondary aluminum structure in the fuselage sub-floor and cargo area were partially replaced with reinforced five-layer composite panels with M-SHELLS honeycomb core. The N3CC fuselage weight reduction associated with each design without risking structural integrity are described. The structural analysis and weight estimation with the application of composite M-SHELLS panels to the N3CC fuselage indicate a 3.2% reduction in the fuselage structural weight, prior to accounting for the additional weight of core material required to complete the energy storage functionality.

Mukhopadhyay, Vivek↗
NASA NTRSDate not supplied

Safety Assessment of a Machine Learning-Based Aircraft Emergency Braking System: A Case Study

Machine Learning (ML) is revolutionizing many technological fields, but its use in aviation remains restricted due to stringent certification requirements. Efforts by the aviation community to establish standards for certifying ML-based systems are progressing, yet challenges persist, particularly with safety assessment methods for ML-based systems. This research addresses these challenges through a case study of an autonomous emergency braking system utilizing a computer vision deep neural network (DNN). We demonstrate a safety assessment process tailored to ML-specific concerns, such as low integrity and performance variability in quantitative safety analysis. This study can serve as an illustrative example to facilitate the discussion and convergence on certification aspects for ML-based systems within the aviation community.

Safety certification↗
NASA NTRS1995

Separation of crack extension modes in orthotropic delamination models

In the analysis of an interface crack between dissimilar elastic materials, the mode of crack extension is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. This behavior currently limits the applicability of interfacial fracture mechanics as a means to predict composite delamination. The Virtual Crack Closure Technique (VCCT) is a method used to extract mode 1 and mode 2 energy release rates from numerical fracture solutions. The mode of crack extension extracted from an oscillatory solution using the VCCT is not unique due to the dependence of mode on the virtual crack extension length, Delta. In this work, a method is presented for using the VCCT to extract Delta-independent crack extension modes for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior. Instead, it is argued that physically reasonable, Delta-independent modes of crack extension can be extracted from oscillatory solutions. Knowledge of near-tip fields is used to determine the explicit Delta dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Delta. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Delta-independent modes of crack extension result. The modified technique has potential as a consistent method for extracting crack extension modes from numerical solutions. The Delta-independent modes extracted using this technique can also serve as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.

Beuth, Jack L.↗
DOE OSTI2021

Kinetic equilibrium reconstruction and the impact on stability analysis of KSTAR plasmas

High fidelity kinetic plasma equilibrium reconstructions are an essential requirement for accurate stability and disruption prediction analyses to support continuous operation of high beta tokamak plasmas. The present kinetic equilibrium reconstructions of plasmas in the KSTAR device include plasma density and temperature profiles from Thomson scattering and ion temperature from charge exchange spectroscopy diagnostics, and allowance for fast particle pressure. In addition, up to 25 channels of motional Stark effect diagnostic data are used to constrain the magnetic field pitch angle profile in the plasma to produce a reliable computation of the safety factor, q, profile. In this work, H-mode plasmas exhibit clear pedestal characteristics in the reconstructed pressure profile compared to internal transport barrier or L-mode plasmas. The plasma configuration and vertical position of inner strike points are validated by CCD and infrared camera images. Ideal and resistive magnetohydrodynamic (MHD) stability analyses using the DCON and resistive DCON codes utilize these kinetic equilibrium reconstructions to compare to experimental plasma stability. Equilibria with sufficiently low convergence error can provide reliable computation of ideal and resistive MHD stability analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1984

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗
NASA NTRS1985

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗
DOE OSTI2020

A coupled multipoint stress–multipoint flux mixed finite element method for the Biot system of poroelasticity

In this work, we present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure–displacement system on simplicial and quadrilateral grids. A mixed stress–displacement–rotation formulation for elasticity with weak stress symmetry is coupled with a mixed velocity–pressure Darcy formulation. The spatial discretization is based on combining the multipoint stress mixed finite element (MSMFE) method for elasticity and the multipoint flux mixed finite element (MFMFE) method for Darcy flow. It uses the lowest order Brezzi–Douglas–Marini mixed finite element spaces for the poroelastic stress and Darcy velocity, piecewise constant displacement and pressure, and continuous piecewise linear or bilinear rotation. A vertex quadrature rule is applied to the velocity, stress, and stress–rotation bilinear forms, which block-diagonalizes the corresponding matrices and allows for local velocity, stress, and rotation elimination. This leads to a cell-centered positive-definite system for pressure and displacement at each time step. We perform error analysis for the semidiscrete and fully discrete formulations, establishing first order convergence for all variables in their natural norms. The numerical tests confirm the theoretical convergence rates and illustrate the locking-free property of the method.

42 ENGINEERING↗
DOE OSTI2022

Practical guide to replica exchange transition interface sampling and forward flux sampling

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Here, focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Decay Dose Shielding Analysis with Hybrid Unstructured Mesh/Constructive Solid Geometry Monte Carlo Calculation and ADVANTG Acceleration

The Oak Ridge National Laboratory (ORNL) Second Target Station (STS) neutron production facility is an accelerator driven pulsed neutron source that is currently being actively developed at ORNL. The neutrons are produced by proton-induced spallation reactions. A proton beam of 700 kW power is delivered to a spallation target in short, less than 1 µs long pulses, with 15 Hz repetition rate. The spallation target of ORNL STS is a rotating water-cooled tungsten target with tantalum cladding housed in a stainless-steel shroud. It is divided into 21 segments. These segments become highly activated due to spallation reactions or nuclei transmutation by the emitted neutrons. The radioactive nuclides continue to decay after ceasing operation. The decay dose rates generated from the target segments once they are removed from their operational location within the core vessel must be accurately quantified to determine the shielding configurations of remote handling tools and transport casks and to aid in planning maintenance events. To determine the shielding configurations needed for an activated target segment after ceasing operation, both the hybrid unstructured mesh (UM)/constructive solid geometry (CSG) approach that was previously utilized for STS analyses [1] and the ADVANTG code [2] were used. Even though the ADVANTG code does not include UM capability, the utilization of its advanced variance reduction technique was crucial to accelerate the extremely difficult final photon transport calculation in this analysis. This paper also describes the procedures taken to mitigate the convergence issues that occur when ADVANTG uses a source definition that does not match the source of the final Monte Carlo (MC) calculation. These convergence issues often occur because of inconsistencies between source and transport biasing parameters.

Ibrahim, Ahmad↗
NASA NTRS1986

Optimal application of Morrison's iterative noise removal for deconvolution

Morrison's iterative method of noise removal can be applied for both noise removal alone and noise removal prior to deconvolution. This method is applied to noise of various noise levels added to determine the optimum use of the method. The phase shift method of migration and modeling is evaluated and the results are compared to Stolt's approach. A method is introduced by which the optimum iterative number for deconvolution can be found. Statistical computer simulation is used to describe the optimum use of two convergent iterative techniques for seismic data. The Always-Convergent deconvolution technique was applied to data recorded during the quantitative analysis of materials through NonDestructive Evaluation (NDE) in which ultrasonic signals were used to detect flaws in substances such as composites.

Ioup, George E.↗
NASA NTRS1988

The N2-P3 complex of the evoked potential and human performance

The N2-P3 complex and other endogenous components of human evoked potential provide a set of tools for the investigation of human perceptual and cognitive processes. These multidimensional measures of central nervous system bioelectrical activity respond to a variety of environmental and internal factors which have been experimentally characterized. Their application to the analysis of human performance in naturalistic task environments is just beginning. Converging evidence suggests that the N2-P3 complex reflects processes of stimulus evaluation, perceptual resource allocation, and decision making that proceed in parallel, rather than in series, with response generation. Utilization of these EP components may provide insights into the central nervous system mechanisms modulating task performance unavailable from behavioral measures alone. The sensitivity of the N2-P3 complex to neuropathology, psychopathology, and pharmacological manipulation suggests that these components might provide sensitive markers for the effects of environmental stressors on the human central nervous system.

Odonnell, Brian F.↗
NASA NTRS1991

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

Graf, Wiley E.↗
NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problem

Most finite element schemes for solving the Navier-Stokes equations can be categorized into the Galerkin mixed method and the penalty method. The mixed method leads to a saddle-point problem. In order to guarantee the existence of a solution, the combination of velocity and pressure interpolations requires satisfaction of the Ladyzhenskaya Babuska Brezzi (LBB) consistency condition which precludes the use of equal order interpolations and many seemingly natural pairs of velocity and pressure elements. In a previous paper a least-squares finite element method based on the first order velocity-pressure-vorticity formulation for the Stokes problem was proposed. This method leads to a minimization problem. The choice of combination of elements is thus not subject to the LBB condition. The numerical experiments exhibit the optimal rate of convergence for all variables with equal order interpolations. A theoretical error analysis supports the numerical results. In this paper the least-squares finite element method is extended to solving the incompressible Navier-Stokes problem.

Jiang, Bonan↗
NASA NTRS2004

Jupiter's Atmospheric Temperatures: From Voyager IRIS to Cassini CIRS

Retrievals run on Cassini Composite Infrared Spectrometer data obtained during the distant Jupiter flyby have been used to generate global temperature maps of the planet in the troposphere and stratosphere. Similar retrievals were performed on Voyager 1 IRIS data and have provided the first detailed IRIS map of the stratosphere. In both data sets, high latitude troposphere temperatures are presented for the first time, and the meridional gradients indicate the presence of circumpolar jets. Thermal winds were calculated for each data set and show strong vertical shears in the zonal winds at low latitudes. The temperatures retrieved from the two spacecraft were also compared with yearly ground-based data obtained over the intervening two decades. Tropospheric temperatures reveal gradual changes at low latitudes, with little obvious seasonal or short-term variation (Orton et al. 1994). Stratospheric temperatures show much more complicated behavior over short timescales, consistent with quasi-quadrennial oscillations at low latitudes, as suggested in prior analyses of shorter intervals of ground- based data (Orton et al. 1991, Friedson 1999). A scaling analysis indicates that meridional motions, mechanically forced by wave or eddy convergence, play an important role in modulating the temperatures and winds in the upper troposphere and stratosphere on seasonal and shorter time scales. At latitudes away from the equator, the mechanical forcing can be derived simply from a temporal record of temperature and its vertical derivative. Ground-based observations with improved vertical resolution and/or long-term monitoring from spacecraft are required for this purpose.

Simon-Miller, Amy A.↗
NASA NTRS1998

Computational Analysis of Shock Layer Emission Measurements in an Arc-Jet Facility

This paper reports computational analysis of radiation emission experiments in a high enthalpy arc-jet wind tunnel at NASA Ames Research Center. Recently, as part of ongoing arc-jet characterization work, spectroscopic radiation emission experiments have been conducted at the 20 MW NASA Ames arc-jet facility. The emission measurements were obtained from the arc-jet freestream and from a shock layer formed in front of flatfaced models. Analysis of these data is expected to provide valuable information about the thermodynamic state of the gas in the arc-jet freestream and in the shock layer as well as thermochemical equilibration processes behind the shock in arc-jet flows. Knowledge of the thermodynamic state of the gas in arc-jet test flows and especially within the shock layer is essential to interpret the heat transfer measurements such as in surface catalysis experiments. The present work is a continuation of previous work and focuses on analysis of the emission data obtained at relatively low-pressure conditions for which the arc-jet shock layer is expected to be in thermal and chemical nonequilibrium. Building blocks of the present computational analysis are: (1) simulation of nonequilibrium expanding flow in the converging-diverging conical nozzle and supersonic jet; (2) simulation of nonequilibrium shock layer formed in front of the flat-faced cylinder model; and (3) prediction of line-of-sight radiation from the computed flowfield. For computations of the nonequilibrium flow in the conical nozzle and shock layer, multi-temperature nonequilibrium codes with the axisymmetric formulation are used. For computations of line-of-sight radiation. a nonequilibrium radiation code (NEQAIR) is used to predict emission spectra from the computed flowfield. Computed line-of-sight averaged flow properties such as vibrational and rotational temperatures, species number densities within the shock layer will be compared with those deduced from the experimental spectra. Detailed comparisons of computational and experimental spectra will also be presented.

Gokcen, Tahir↗
DOE OSTI2022

Design and execution of a verification, validation, and uncertainty quantification plan for a numerical model of left ventricular flow after LVAD implantation

Left ventricular assist devices (LVADs) are implantable pumps that act as a life support therapy for patients with severe heart failure. Despite improving the survival rate, LVAD therapy can carry major complications. Particularly, the flow distortion introduced by the LVAD in the left ventricle (LV) may induce thrombus formation. While previous works have used numerical models to study the impact of multiple variables in the intra-LV stagnation regions, a comprehensive validation analysis has never been executed. The main goal of this work is to present a model of the LV-LVAD system and to design and follow a verification, validation and uncertainty quantification (VVUQ) plan based on the ASME V&V40 and V&V20 standards to ensure credible predictions. The experiment used to validate the simulation is the SDSU cardiac simulator, a bench mock-up of the cardiovascular system that allows mimicking multiple operation conditions for the heart-LVAD system. The numerical model is based on Alya, the BSC’s in-house platform for numerical modelling. Alya solves the Navier-Stokes equation with an Arbitrary Lagrangian-Eulerian (ALE) formulation in a deformable ventricle and includes pressure-driven valves, a 0D Windkessel model for the arterial output and a LVAD boundary condition modeled through a dynamic pressure-flow performance curve. The designed VVUQ plan involves: (a) a risk analysis and the associated credibility goals; (b) a verification stage to ensure correctness in the numerical solution procedure; (c) a sensitivity analysis to quantify the impact of the inputs on the four quantities of interest (QoIs) (average aortic root flow $Q^{avg}_{Ao}$, maximum aortic root flow $Q^{max}_{Ao}$, average LVAD flow $Q^{avg}_{VAD}$, and maximum LVAD flow $Q^{max}_{VAD}$; (d) an uncertainty quantification using six validation experiments that include extreme operating conditions. Numerical code verification tests ensured correctness of the solution procedure and numerical calculation verification showed a grid convergence index (GCI)95% <3.3%. The total Sobol indices obtained during the sensitivity analysis demonstrated that the ejection fraction, the heart rate, and the pump performance curve coefficients are the most impactful inputs for the analysed QoIs. The Minkowski norm is used as validation metric for the uncertainty quantification. It shows that the midpoint cases have more accurate results when compared to the extreme cases. The total computational cost of the simulations was above 100 [core-years] executed in around three weeks time span in Marenostrum IV supercomputer. This work details a novel numerical model for the LV-LVAD system, that is supported by the design and execution of a VVUQ plan created following recognised international standards. We present a methodology demonstrating that stringent VVUQ according to ASME standards is feasible but computationally expensive.

59 BASIC BIOLOGICAL SCIENCES↗