Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms
Abstract Not Provided
Astrophysics,ASTRO, GRQC↗
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Generation of high-resolution thermal scattering laws for solid moderators using fast Fourier transforms
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Nuclear Science & Technology↗
Improved motional Stark effect signal processing using fast Fourier transform spectral analysis
A Fast Fourier Transform (FFT) based method has been developed, which improves the frequency response of the Motional Stark Effect (MSE) system by about a factor of 10 over the conventional analog lock-in method. The method uses fits to rigorously derived analytic expressions for the FFT spectral components of the MSE signal to accurately obtain the amplitudes and phases of the 2f1 and 2f2 photo-elastic modulator (PEM) frequencies that encode the polarization angle. Since no frequency filtering is used in the FFT method, the frequency response is limited by fundamental measurement properties: the frequency response of the detector, photon statistics, sample rate, and the ability to resolve the spectral components. In contrast, the frequency response of the analog lock-in is limited by a low pass filter with a cutoff of around 500 Hz. In the case of the DIII-D MSE system, the output of the photo-multiplier tube detector was sampled at 500 kHz and FFTs with as few as 100 points were used to obtain the amplitudes of the 2f1 and 2f2 PEM frequency components. This corresponds to a frequency response of 5 kHz, about ten times faster than the analog lock-in amplifier system. Details of the FFT method will be presented and compared to those of the analog lock-in system.
Makowski, M. A.↗
Fast Fourier Transform for multivariate aggregate claims
The Fast Fourier Transform provides an alternative approximate method to evaluate the distribution of aggregate losses in insurance and finance. The efficiency of this method has already been proved for univariate and bivariate insurance models; therefore, in this paper, we extend it to a multivariate setting by considering its application to a particular model that includes losses of different types and dependency between them. Since the Fourier transform method works with truncated claims distributions, it can generate aliasing errors by wrapping around the probability mass that lies at the truncation point below this point. To eliminate this problem, we also discuss a suitable change of measure called exponential tilting that forces the tail of the distribution to decrease at exponential rate. Other possible errors are also discussed. We also illustrate the method on several numerical examples.
97 MATHEMATICS AND COMPUTING↗
Optimizing the Fast Fourier Transform Using Mixed Precision on Tensor Core Hardware
The Fast Fourier Transform is a fundamental tool in scientific and technical computation. The highly parallelizable nature of the algorithm makes it a suitable candidate for GPU acceleration. This paper focuses on exploiting the speedup due to using the half precision multiplication capability of the latest GPUs' tensor core hardware without significantly degrading the precision of the Fourier Transform result. We develop an algorithm that dynamically splits the input single precision dataset into two half precision sets at the lowest level, uses half precision multiplication, and recombines the result at a later step. This work paves the way for using tensor cores for high precision inputs.
Sorna, Anumeena↗
A generalizable machine learning-assisted fast Fourier transform algorithm to simulate the large strain phenomena in polycrystalline materials
Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.
36 MATERIALS SCIENCE↗
Elasto-viscoplastic fast Fourier transform modeling framework for assessing microstructural effects on stress intensity factors characterizing fracture toughness
A large-strain elasto-viscoplastic fast Fourier transform (LS-EVPFFT) model with non-periodic (NP) velocity-based boundary conditions is adapted to simulate the sensitivity of stress intensity factors on microstructure for 304L stainless steel. The material was characterized via electron backscattered diffraction (EBSD) serial-sectioning to obtain a measured 3-D microstructural cell to perform simulations. The NP-LS-EVPFFT model, including the simulation setup and boundary conditions, was verified using a crystal plasticity finite element (CPFE) model. To this end, the generation of meshes of notched specimens was developed, which involved creating Python scripts for mesh “cutting” in Abaqus, and Sculpt scripts in Cubit for meshing of the measured microstructural cell processed with DREAM.3D. The complexity of the mesh preparation highlighted the advantages of the FFT-based model, which circumvents the mesh generation process. Given the efficiency of the FFT-based model, statistical distribution of stress intensity factors in function of crystal orientation at the crack tip, grain structure, and crystallographic texture surrounding the crack tip were predicted. Further, the distributions reveal about 10% variation of stress intensity factors with microstructure with the most significant sensitivity found to be the crystal orientation at the crack tip. The methodology developed in this work is discussed as a practical simulation tool for predicting the sensitivity of stress intensity factors on microstructural variability in metallic materials.
36 MATERIALS SCIENCE↗
Recursive Use of the Short-Time Fast Fourier Transform for Signature Analysis in Continuous Processes
Although a nuclear reactor is a hostile environment for sensing and electrical communications, the reactor core is amenable to acoustic communication. An acoustic measurement infrastructure (AMI) has been installed in the Advanced Test Reactor (ATR) to record acoustic signals that can capture its different operating regimes. AMI uses coolant pumps as continuous signal sources, coolant and structural components as transmission lines, and accelerometers to capture system motion. A recursive signal processing technique based on the short-time fast Fourier transform (STFFT) for continuous processes provides unique signatures for diagnostic and prognostic analyses from the system motion data. Here this article presents a recursive STFFT methodology that processes acoustic signals from continuous industrial processes. The article first discusses the initial STFFT use with simulated data to elucidate the basic principles necessary to understand and interpret the STFFT results from actual pump vibration data. Each repetitive use of the STFFT on pump vibration data using the results from the prior STFFT processing will generate additional complimentary time-frequency-based signatures. These signatures are generated by the coolant pumps operating under different process conditions. After each use of the STFFT, the resulting signatures provide exemplary examples of the diversity and intuitive nature of recursively using the STFFT. This article focuses on recursively using the STFFT to provide numerous complimentary and diverse signatures that will ultimately be inputs for machine learning algorithms that provide predictive data analytics. The intuitive nature of the information and signatures from recursive STFFT processing will also bring intuitive interpretation capabilities to machine learning and predictive data analytic techniques.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Coolant Pump Predictive Data Analytics from Signatures Generated by the Recursive Short Time Fast Fourier Transform
Although a nuclear reactor is a hostile environment for sensors and signal transmissions, the reactor core is amenable to acoustic communication. An acoustic measurement infrastructure installed at the Advanced Test Reactor (ATR) nozzle trench area records acoustic signals that can capture reactor operating states. The distinct states produce unique signatures that can be identified and tracked using data processing and data analytics. The infrastructure relies on acoustic transmission through ATR in-pile structural components, piping, and coolant that transmit acoustically modified signals generated by the coolant pumps. This paper will discuss results from using the Recursive Short Time Fast Fourier Transform (RSTFFT) technique used to process acoustic signals and provide signatures that are identified and monitored by analytics. The RSTFFT is applied to ATR data to understand the vibration levels and signatures for different operating regimes as displayed by the spectrogram. The combination of coolant pumps for normal and high-power operation generate unique signatures. These acoustic signatures are used to develop machine learning approaches to automatically classify operating regimes. Two machine-learning models, Support Vector Machines and Linear Discriminant Analysis, were developed to classify two event classes. Class 1 is a normal steady-state operation, and Class 2 is any event that is due to start up, shut down, or other actions. Both types of machine learning models had over a 96% prediction accuracy for the two classes. These results lay the foundation for predictive analytic frameworks that can be leveraged by ATR to optimize operations and maintenance.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Model-less Source Location for Forced Oscillation based on Synchrophasor and Moving Fast Fourier Transformation
Forced oscillations in power systems occur when the grid is driven by an external and periodic force. To quickly detect and locate the source of the forced oscillation is critical in terms of ensuring the reliability of an interconnected power grid. This paper explores the electromechanical wave propagation theory and the Fast Fourier Transformation to analyze the forced oscillations. It proposes a model-less, adaptive, fast, and accurate source location algorithm. The proposed algorithm is extensively evaluated through simulation data from a 70k-bus U.S. Eastern Interconnection test system and field-collected synchrophasor data from the distribution-level wide-area monitoring system, FNET/GridEye. The evaluation results demonstrate the correctness and effectiveness of the proposed model-less forced oscillation source location algorithm.
Wang, Weikang↗
SBIR Phase I Final Report Commercialization of Large-Scale Distributed Heterogeneous Fast Fourier Transform
Explore the source record for details and available documents.
97 MATHEMATICS AND COMPUTING↗
The Dark Energy Spectroscopic Instrument: one-dimensional power spectrum from first Ly α forest samples with Fast Fourier Transform
ABSTRACT We present the one-dimensional Ly α forest power spectrum measurement using the first data provided by the Dark Energy Spectroscopic Instrument (DESI). The data sample comprises 26 330 quasar spectra, at redshift z > 2.1, contained in the DESI Early Data Release and the first 2 months of the main survey. We employ a Fast Fourier Transform (FFT) estimator and compare the resulting power spectrum to an alternative likelihood-based method in a companion paper. We investigate methodological and instrumental contaminants associated with the new DESI instrument, applying techniques similar to previous Sloan Digital Sky Survey (SDSS) measurements. We use synthetic data based on lognormal approximation to validate and correct our measurement. We compare our resulting power spectrum with previous SDSS and high-resolution measurements. With relatively small number statistics, we successfully perform the FFT measurement, which is already competitive in terms of the scale range. At the end of the DESI survey, we expect a five times larger Ly α forest sample than SDSS, providing an unprecedented precise one-dimensional power spectrum measurement.
79 ASTRONOMY AND ASTROPHYSICS↗
DESI DR1 Ly α 1D power spectrum: the Fast Fourier Transform estimator measurement
Here, we present the one-dimensional Lyman-α forest power spectrum measurement derived from the data release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI). The measurement of the Lyman-α forest power spectrum along the line of sight from high-redshift quasar spectra provides information on the shape of the linear matter power spectrum, neutrino masses, and the properties of dark matter. In this work, we use a Fast Fourier Transform (FFT)-based estimator, which is validated on synthetic data in a companion paper. Compared to the FFT measurement performed on the DESI early data release, we improve the noise characterization with a cross-exposure estimator and test the robustness of our measurement using various data splits. We also refine the estimation of the uncertainties and now present an estimator for the covariance matrix of the measurement. Furthermore, we compare our results to previous high-resolution and eBOSS measurements. In another companion paper, we present the same DR1 measurement using the Quadratic Maximum Likelihood Estimator (QMLE). These two measurements are consistent with each other and constitute the most precise one-dimensional power spectrum measurement to date, while being in good agreement with results from the DESI early data release.
Lyman alpha forest↗
Coupled chemo-mechanical modeling of point-defect diffusion in a crystal plasticity fast Fourier transform framework
Below the yield strength and at moderate-to-high homologous temperatures, the inelastic deformation of metals is mostly governed/rate-controlled by vacancy diffusion-mediated processes. As a function of grain size, stress, temperature and dislocation content, vacancies (or atoms) can adopt preferential diffusion paths across grain interiors, along grain boundaries, or towards and along dislocations, resulting in climb and self-climb. In the steady state and under constant load, grain boundary and grain bulk vacancy diffusion-mediated plasticity have been described in seminal works by Coble and by Nabarro and Herring, respectively. Yet, the interplay between all aforementioned potential diffusion pathways has not been comprehensively mapped. This work presents a thermodynamically-consistent full-field model integrated within a voxel-based elasto-viscoplastic fast Fourier transform framework, which considers the coupling between the diffusion-mediated plasticity mechanisms. In the proposed approach, the kinetics and kinematics of plastic deformation due to vacancy diffusion along grain boundaries and grain bulk, as well as the exchange between grain boundaries and bulk are described explicitly. A homogenization approach at the voxel level is further introduced to simultaneously consider bulk and grain boundary diffusion in a numerically efficient fashion. The new formulation predicts the expected strain rate dependencies and the scaling of the steady-state creep rate with respect to grain size, temperature, and stress. Finally, the model predicts the transition from grain bulk to grain boundary-dominated diffusion with reduction in grain size, a significant step towards capturing transitions in deformation behavior without any phenomenological or ad-hoc adjustments.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
tomoCAM : fast model-based iterative reconstruction via GPU acceleration and non-uniform fast Fourier transforms
X-ray-based computed tomography is a well established technique for determining the three-dimensional structure of an object from its two-dimensional projections. In the past few decades, there have been significant advancements in the brightness and detector technology of tomography instruments at synchrotron sources. These advancements have led to the emergence of new observations and discoveries, with improved capabilities such as faster frame rates, larger fields of view, higher resolution and higher dimensionality. These advancements have enabled the material science community to expand the scope of tomographic measurements towards increasingly in situ and in operando measurements. In these new experiments, samples can be rapidly evolving, have complex geometries and restrictions on the field of view, limiting the number of projections that can be collected. In such cases, standard filtered back-projection often results in poor quality reconstructions. Iterative reconstruction algorithms, such as model-based iterative reconstructions (MBIR), have demonstrated considerable success in producing high-quality reconstructions under such restrictions, but typically require high-performance computing resources with hundreds of compute nodes to solve the problem in a reasonable time. Here, tomoCAM , is introduced, a new GPU-accelerated implementation of model-based iterative reconstruction that leverages non-uniform fast Fourier transforms to efficiently compute Radon and back-projection operators and asynchronous memory transfers to maximize the throughput to the GPU memory. The resulting code is significantly faster than traditional MBIR codes and delivers the reconstructive improvement offered by MBIR with affordable computing time and resources. tomoCAM has a Python front-end, allowing access from Jupyter -based frameworks, providing straightforward integration into existing workflows at synchrotron facilities.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NEUTRON-IRRADIATION–INDUCED DAMAGE ASSESSMENT IN CONCRETE USING COMBINED PHASE CHARACTERIZATION AND NONLINEAR FAST FOURIER TRANSFORM SIMULATION
Understanding irradiation effects in concrete cavities of light water reactors is critical to the long-term operation (60+ years) of US nuclear power plants. Susceptibility of concrete to neutron irradiation greatly varies as a function of its constituents: coarse aggregates, sand, and hardened cement paste (hcp). In particular, higher irradiation–susceptibility of aggregates was found to be a direct function of radiation-induced volumetric expansion (RIVE), or the propensity of aggregates to swell as a function of mineral contents, structures and textures. Irradiation-induced amorphization is accompanied by significant swelling, especially in silicates. For example, the maximum volumetric expansions of quartz and feldspars have been shown to be as large as ≈ 18% and ≈ 8%, respectively, while the change of density in calcite remains rather low (≈ 0.3–0.5%). High swelling is associated with a high number of covalent bonds (Si–O) and a high degree of polymerization of [SiO4] tetrahedrons. Differential RIVEs between rock-forming minerals cause high stresses and may potentially develop cracking within the aggregates at the interface between aggregates and the hcp and within the hcp. Modeling neutron-irradiation effects in concrete requires addressing the problem at a scale that captures both the details of the aggregates’ mineralogy and texture, which is <~ 100 μm, and the representative size of concrete, which is ~ 10 cm. This requires high-resolution, large mapping capabilities. To this end, the US Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program developed an original tool suite called Microstructure Oriented Scientific Analysis of Irradiated Concrete (MOSAIC) in which Nonlinear 2D-fast Fourier transform (FFT) techniques are employed to model mechanical or irradiation-induced cracking of high-resolution complex microstructures derived from combined mapping techniques, including micro x-ray fluorescence (m-XRF), energy-dispersive x-ray spectroscopy (EDS), electron backscatter diffraction (EBSD), ellipsometry, and scanning electron microscopy (SEM). Irradiated mineral properties are derived from the Irradiated Minerals, Aggregate and Concrete (IMAC) database, which includes available relevant literature data. Rigorous coupled damage-creep simulations are obtained through sequential linear analysis. Illustrations of actual accelerated irradiation-damage propagation in a complex microstructures are presented herein.
Le Pape, Yann↗
Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations
We review two crystal plasticity methodologies based on Green’s functions for the prediction of microstructure-property relations in polycrystalline aggregates. The first, known as the viscoplastic self-consistent (VPSC) formulation, is a mean-field theory. The second, known as the viscoplastic fast Fourier transform-based (VPFFT) formulation, is a full-field method. Finally, the assumptions and main equations of these Green’s function-based crystal plasticity formulations are presented using a unified notation, pointing out their similarities and differences and cross-validating their predictions.
36 MATERIALS SCIENCE↗
Micropolar Elastoplasticity Using a Fast Fourier Transform‐Based Solver
ABSTRACT This work presents a micromechanical spectral formulation for obtaining the full‐field and homogenized response of elastoplastic micropolar composites. A closed‐form radial‐return mapping is derived from thermodynamics‐based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size‐dependent material response and micro‐plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.
42 ENGINEERING↗