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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Performance of Compact Pulsed Thermal Imaging System for In-Service Applications. Pulsed thermal tomography nondestructive examination of additively manufactured reactor materials and components

Additive manufacturing (AM) is an emerging method for cost-efficient fabrication of complex topology nuclear reactor parts from high-strength corrosion resistance alloys, such as stainless steel and Inconel. AM of metallic structures for nuclear energy applications is currently based on laser powder bed fusion (LPBF) process, which has the capability of melting metallic powder and net shaping the structures with relatively high precision. Some of the challenges with using LPBF method for nuclear manufacturing include the possibility of introducing pores into metallic structures. Integrity of AM structures needs to be evaluated nondestructively because material flaws could lead to premature failures due to creep in high temperature nuclear reactor environment. Currently, there exist limited capabilities to evaluate actual AM structures nondestructively. Pulsed Thermography (PT) imaging provides a capability for non-destructive evaluation (NDE) of sub-surface defects in arbitrary size structures. The PT method is based on recording material surface temperature transients with infrared (IR) camera following thermal pulse delivered on material surface with flash light. The PT method has advantages for NDE of actual AM structures because the method involves one-sided non-contact measurements and fast processing of large sample areas captured in one image. The data cube of PT measurements consists of surface temperature taken at sequential time intervals T(x,y,t). Material defects can be detected either by analyzing the thermograms T(x,y,t) data cube, or by using thermal tomography (TT) algorithm to obtain 3D spatial reconstruction of thermal effusivity e(x,y,z). To reduce the cost and enable in-service NDE in spatially constrained environment, it is highly desirable to develop PT with compact and inexpensive IR camera. Following initial qualification of an AM component for deployment in a nuclear reactor, a compact PT system can also be used for in-service nondestructive evaluation (NDE) applications. However, data cube obtained with PT based on compact IR camera suffers from strong thermal noises and loss of features due to relatively low sampling rate. In this report we describe two unsupervised machine learning (ML) algorithms for enhancement of PT images obtained with compact IR camera. In one approach, we introduce Sparse Coding Discrete Cosine Transform (SC/DCT) algorithm to remove additive white Gaussian noise (AWGN) from spatial thermal effusivity reconstructions. In another approach we introduce a Spatial Temporal Denoised Thermal Source Separation (STDTSS) ML algorithm to process thermograms. The STDTSS algorithm consists of spatial and temporal denoising using Gaussian and Savitzky–Golay filtering, followed by the matrix decomposition using Principal Component Analysis (PCA), and Independent Component Analysis (ICA) to automatically detect flaws. In the work described in this report, we constructed a compact PT system using a relatively small and low-cost FLIR A65 camera, consisting on uncooled microbolometer detector. Performance of SC/DCT algorithm was demonstrated on enhancing TT images of Inconel 718 AM plate. Performance of the STDTSS methods was investigated using thermography data obtained from imaging stainless steel 316L specimens produced with LPBF method with imprinted calibrated porosity defects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Bringing randomized algorithms to mainstream numerical linear algebra

Numerical linear algebra (NLA) underpins huge swaths of computational science and engineering. For scientists and engineers to make the most of the DOE’s computing resources, it is essential that they have access to high-performance implementations of algorithms with best-in-class scalability and reliability. Despite this, prevailing NLA libraries have little to no support for breakthrough algorithms from the field of randomized numerical linear algebra (RandNLA) that have been developed over the past twenty years. The goal of this LDRD was to break a log-jam that had prevented broad adoption of RandNLA. Our work had two thrusts. The first was to develop RandBLAS: a trustworthy and high-performance C++ library for randomized dimension reduction (an operation widely known as sketching). The second was the development of a novel randomized algorithm for computing a challenging type of matrix decomposition known as Householder QR with column pivoting (Householder QRCP). In this one-year late-start LDRD we successfully delivered RandBLAS 1.0 and new CPU and GPU codes for Householder QRCP. RandBLAS has extensive documentation at https://randblas.readthedocs.io/en/stable/. Papers on RandBLAS and and our high-performance QRCP codes are forthcoming.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Data-scientific Noise-removal Method for Efficient Submillimeter Spectroscopy With Single-dish Telescopes

For submillimeter spectroscopy with ground-based single-dish telescopes, removing the noise contribution from the Earth’s atmosphere and the instrument is essential. For this purpose, here we propose a new method based on a data-scientific approach. The key technique is statistical matrix decomposition that automatically separates the signals of astronomical emission lines from the drift noise components in the fast-sampled (1–10 Hz) time-series spectra obtained by a position-switching (PSW) observation. Because the proposed method does not apply subtraction between two sets of noisy data (i.e., on-source and off-source spectra), it improves the observation sensitivity by a factor of √2. It also reduces artificial signals such as baseline ripples on a spectrum, which may also help to improve the effective sensitivity. We demonstrate this improvement by using the spectroscopic data of emission lines toward a high-redshift galaxy observed with a 2 mm receiver on the 50 m Large Millimeter Telescope. Since the proposed method is carried out offline and no additional measurements are required, it offers an instant improvement on the spectra reduced so far with the conventional method. It also enables efficient deep spectroscopy driven by the future 50 m class large submillimeter single-dish telescopes, where fast PSW observations by mechanical antenna or mirror drive are difficult to achieve.

47 OTHER INSTRUMENTATION↗
NASA NTRS1978

Reduction of matrix wavefront for NASTRAN

The three grid point resequencing algorithms most often run by NASTRAN users are compared for their ability to reduce matrix root-mean-square (rms) wavefront, which is the most critical parameter in determining matrix decomposition time in NASTRAN. The three algorithms are Cuthill-McKee (CM), Gibbs-Poole-Stockmeyer (GPS), and Levy. The first two (CM and GPS) are in the BANDIT program, and the Levy algorithm is in WAVEFRONT. Results are presented for a diversified collection of 30 test problems ranging in size from 59 to 2680 nodes. It is concluded that GPS is exceptionally fast and, for the conditions under which the test was made, the algorithm best able to reduce rms wavefront consistently well.

Everstine, G. C.↗
NASA NTRS1981

Mathematical specifications of the Onboard Navigation Package (ONPAC) simulator (revision 1)

The mathematical theory of the computational algorithms employed in the onboard navigation package system is described. This system, which simulates an onboard navigation processor, was developed to aid in the design and evaluation of onboard navigation software. The mathematical formulations presented include the factorized UDU(T) form of the extended Kalman filter, the equations of motion of the user satellite, the user clock equations, the observation equations and their partial derivatives, the coodinate transformations, and the matrix decomposition algorithms.

Dunham, J. B.↗
NASA NTRS1983

BANDIT in NASTRAN

BANDIT has been implemented into the NASTRAN April '83 release. It is now a permanent feature in NASTRAN and will be included in all future releases for all four computing machines (IBM, CDC, UNIVAC, and VAX). Originally BANDIT operated as a preprocessor of NASTRAN. It read the NASTRAN input cards and produced a set of resequencing (SEOGP) cards that would greatly reduce the computational time required by the matrix decomposition module of NASTRAN for a large structure. In the past, many computer centers had installed BANDIT in their systems together with the NASTRAN program. The user would run the BANDIT program and NASTRAN as if they were one program (or two separated programs depending on how the two programs were actually tied together in the computer systems). In some cases, the user was required to pass the input cards and the output SEQGP cards between the two programs, and n others, the data was manipulated through the use of cataloged disc files. Although there is nothing wrong with this BANDIT-NASTRAN arrangement, there are, however, several shortcomings which are mentioned in this paper. The BANDIT in the NASTRAN April '83 release has removed all the deficiencies, and it comes in one version applicable to the four computing machines.

Chan, G. C.↗
NASA NTRS1988

Recursive least squares estimation and Kalman filtering by systolic arrays

One of the most promising new directions for high-throughput-rate problems is that based on systolic arrays. In this paper, using the matrix-decomposition approach, a systolic Kalman filter is formulated as a modified square-root information filter consisting of a whitening filter followed by a simple least-squares operation based on the systolic QR algorithm. By proper skewing of the input data, a fully pipelined time and measurement update systolic Kalman filter can be achieved with O(n squared) processing cells, resulting in a system throughput rate of O (n).

Chen, M. J.↗
NASA NTRS1990

An efficient design sensitivity analysis of eigenvectors

Subspace iteration has been a major advance in solving large eigen problems when only a subset of eigen-pairs is required. The essence of this method is a transformation from displacement coordinates of an n-th order eigensystem to generalized coordinates of a smaller q-th order. The eigenvalue problem is then solved in the reduced space. The method was first developed by Clint and Jennings for real symmetric systems and was then called 'simultaneous iteration'. The success of the method prompted further research along this line and there have been many improved algorithms developed. This approach has been widely used by structural engineers for extracting the most useful natural frequencies and mode shapes of large-scale dynamic systems. This paper exploits into a new direction which is in the form of iterative process for simultaneously calculating eigenvector derivatives of many eigenvectors with respect to multi-variables. The method fully uses all the available information from preceding eigenvalue solution and, thus, effectively economizes computational efforts. It iterates through two equations derived from the first variation of the two fundamental equations used in subspace iteration method. There is no expensive large matrix decomposition required and the process converges to acceptable solution in a finite number of iterations. Therefore, the procedure increases its efficiency superiority over the others as the system size or the number of interested eigenvectors become larger and larger.

Ting, T.↗
DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗
NASA NTRS2015

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Leone, Frank A., Jr.↗
DOE OSTI2024

Assessment of Accelerated Stress Testing Data for Silicon Photovoltaics Using Tensor Decomposition Methods

In this work, we examine the use of high-order tensor decompositions to analyze degradation pathways emerging from accelerated stress testing of silicon photovoltaic (PV) modules. Matrix-based decompositions are powerful tools for studying two-dimensional data arrays and form the foundation of a host of classical data analysis techniques. Tensors are high-order extrapolations of matrices that are able to account for more parameter dimensions, and a variety of tensor decomposition methods have been developed that similarly seek to extend insights from matrix decompositions to higher dimensions. Applying and interpreting tensor decomposition methods to sequences of PV module image data, we seek to uncover and isolate different degradation modes occurring from accelerated stress testing procedures. Further, we consider the contributions of different modes to PV module performance degradations.

data analysis↗
NASA NTRS1976

On the computation and updating of the modified Cholesky decomposition of a covariance matrix

Methods for obtaining and updating the modified Cholesky decomposition (MCD) for the particular case of a covariance matrix when one is given only the original data are described. These methods are the standard method of forming the covariance matrix K then solving for the MCD, L and D (where K=LDLT); a method based on Householder reflections; and lastly, a method employing the composite-t algorithm. For many cases in the analysis of remotely sensed data, the composite-t method is the superior method despite the fact that it is the slowest one, since (1) the relative amount of time computing MCD's is often quite small, (2) the stability properties of it are the best of the three, and (3) it affords an efficient and numerically stable procedure for updating the MCD. The properties of these methods are discussed and FORTRAN programs implementing these algorithms are listed.

Vanrooy, D. L.↗
NASA NTRS1982

Assessing the quality of curvilinear coordinate meshes by decomposing the Jacobian matrix

An algebraic decomposition of the Jacobian matrix which relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. The decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. The analysis is applied to the solution of the full potential code TAIR, showing grid plots, carpet plots, and truncation error for a NACA 0012 airfoil.

Kerlick, G. D.↗
NASA NTRS1975

Analysis of multiloop, multirate sampled-data systems

Based upon new identities between z-transforms at a basis rate, z-transforms at faster rates, and modified z-transforms, the equivalence between the frequency decomposition method and the switch decomposition method is precisely presented so that results of one method are easily obtained from results of the other. Next, a method is developed for determining the closed loop transfer function of multiloop, multirate sampled-data systems with noninteger ratio sampling rates. Previously, this process involved solving a complex system of equations with rational polynomial coefficients. Herein, this is avoided by introducing a systematic decomposition of matrix operators which naturally arise from the switch decomposition method. The matrix operators are simplified by introducing the shifted transforms of signals sampled at one of the faster rates.

Boykin, W. H.↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2021

Sparsity of Radiating Characteristic Modes on Infinite Periodic Structures

Characteristic modes on infinite periodic structures are studied using spectral dyadic Green’s functions. This formulation demonstrates that, in contrast to the modal analysis of finite structures, the number of radiating characteristic modes is limited by unit cell size and incident wave vector (i.e., scan angle or phase shift per unit cell). Here, the reflection tensor is decomposed into modal contributions from radiating modes, indicating that characteristic modes are a predictably sparse basis in which to study reflection phenomena.

42 ENGINEERING↗
NASA NTRS2009

Effects of Tantalum on the Temporal Evolution of a Model Ni-Al-Cr Superalloy During Phase Decomposition

The effects of a 2.0 at.% addition of Ta to a model Ni-10.0Al-8.5Cr (at.%) superalloy aged at 1073 K are assessed using scanning electron microscopy and atom-probe tomography. The gamma'(Ll2)-precipitate morphology that develops as a result of gamma-(fcc)matrix phase decomposition is found to evolve from a bimodal distribution of spheroidal precipitates, to {001}-faceted cuboids and parallelepipeds aligned along the elastically soft {001}-type directions. The phase compositions and the widths of the gamma'-precipitate/gamma-matrix heterophase interfaces evolve temporally as the Ni-Al-Cr-Ta alloy undergoes quasi-stationary state coarsening after 1 h of aging. Tantalum is observed to partition preferentially to the gamma'-precipitate phase, and suppresses the mobility of Ni in the gamma-matrix sufficiently to cause an accumulation of Ni on the gamma-matrix side of the gamma'/gamma interface. Additionally, computational modeling, employing Thermo-Calc, Dictra and PrecipiCalc, is employed to elucidate the kinetic pathways that lead to phase decomposition in this concentrated Ni-Al-Cr-Ta alloy.

Booth, Morrison, Christopher↗