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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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At least 37 records · Page 2
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DOE OSTI2018

A Müntz wavelets collocation method for solving fractional differential equations

In this paper, we introduce a new set of wavelets, namely Müntz wavelets. These wavelets are defined based on Müntz Legendre polynomials which have the property of orthogonality. We stabilize the wavelet coefficients by utilizing Jacobi polynomials to construct the modified Müntz wavelets. Next, we present a collocation scheme based on Müntz wavelets for solving fractional differential equations. The fractional derivative is described in the Caputo sense. Some error estimates are given and numerical examples are included to demonstrate the applicability and accuracy of the proposed method. This includes the elastic-dissipative mathematical model of linear mechanical devices known as Boltzman operator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach

In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficient orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test different choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Magnetoacoustic waves propagating along a dense slab and Harris current sheet and their wavelet spectra

Currently, there is a common endeavor to detect magnetoacoustic waves in solar flares. This paper contributes to this topic using an approach of numerical simulations. We studied a spatial and temporal evolution of impulsively generated fast and slow magnetoacoustic waves propagating along the dense slab and Harris current sheet using two-dimensional magnetohydrodynamic numerical models. Wave signals computed in numerical models were used for computations of the temporal and spatial wavelet spectra for their possible comparison with those obtained from observations. It is shown that these wavelet spectra allow us to estimate basic parameters of waveguides and perturbations. It was found that the wavelet spectra of waves in the dense slab and current sheet differ in additional wavelet components that appear in association with the main tadpole structure. These additional components are new details in the wavelet spectrum of the signal. While in the dense slab this additional component is always delayed after the tadpole head, in the current sheet this component always precedes the tadpole head. It could help distinguish a type of the waveguide in observed data. We present a technique based on wavelets that separates wave structures according to their spatial scales. This technique shows not only how to separate the magnetoacoustic waves and waveguide structure in observed data, where the waveguide structure is not known, but also how propagating magnetoacoustic waves would appear in observations with limited spatial resolutions. The possibilities detecting these waves in observed data are mentioned.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Wavelet Denoising of Radio Observations of Rotating Radio Transients (RRATs): Improved Timing Parameters for Eight RRATs

Rotating radio transients (RRATs) are sporadically emitting pulsars detectable only through searches for single pulses. While over 100 RRATs have been detected, only a small fraction (roughly 20%) have phase-connected timing solutions, which are critical for determining how they relate to other neutron star populations. Detecting more pulses in order to achieve solutions is key to understanding their physical nature. Astronomical signals collected by radio telescopes contain noise from many sources, making the detection of weak pulses difficult. Applying a denoising method to raw time series prior to performing a single-pulse search typically leads to a more accurate estimation of their times of arrival (TOAs). Taking into account some features of RRAT pulses and noise, we present a denoising method based on wavelet data analysis, an image-processing technique. Assuming that the spin period of an RRAT is known, we estimate the frequency spectrum components contributing to the composition of RRAT pulses. This allows us to suppress the noise, which contributes to other frequencies. We apply the wavelet denoising method including selective wavelet reconstruction and wavelet shrinkage to the de-dispersed time series of eight RRATs with existing timing solutions. The signal-to-noise ratio (S/N) of most pulses are improved after wavelet denoising. Compared to the conventional approach, we measure 12%–69% more TOAs for the eight RRATs. The new timing solutions for the eight RRATs show 16%–90% smaller estimation error of most parameters. Thus, we conclude that wavelet analysis is an effective tool for denoising RRATs signal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Evaluating the Efficacy of Wavelet Configurations on Turbulent-Flow Data

I/O is increasingly becoming a significant constraint for simulation codes and visualization tools on modern supercomputers. Data compression is an attractive workaround, and, in particular, wavelets provide a promising solution. However, wavelets can be applied in multiple configurations, and the variations in configuration impact accuracy, storage cost, and execution time. While the variation in these factors over wavelet configurations have been explored in image processing, they are not well understood for visualization and analysis of scientific data. To illuminate this issue, we evaluate multiple wavelet configurations on turbulent-flow data. Our approach is to repeat established analysis routines on uncompressed and lossy-compressed versions of a data set, and then quantitatively compare their outcomes. Our findings show that accuracy varies greatly based on wavelet configuration, while storage cost and execution time vary less. Overall, our study provides new insights for simulation analysts and visualization experts, who need to make tradeoffs between accuracy, storage cost, and execution time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Adaptive Multilinear Tensor Product Wavelets

Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how to generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. In conclusion, we focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical solution of systems of fractional delay differential equations using a new kind of wavelet basis

In the present paper, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet basis and their properties are utilized to obtain their operational matrix of fractional integration in the Riemann–Liouville sense and delay operational matrix. Convergence and error bound of the expansion by this kind of wavelet functions are investigated. Then, these operational matrices along with the Galerkin approach have been implemented to solve systems of fractional delay differential equations (SFDDEs). The main superiority of the proposed technique is that it reduces SFDDEs to a system of algebraic equations. Moreover, accuracy and efficiency of the suggested Chelyshkov wavelet approach are verified through some linear and nonlinear SFDDEs. Finally, the obtained numerical results are compared with those previously reported in the literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

The use of wavelet filters for reducing noise in posterior fossa Computed Tomography images

Wavelet transform based de-noising like wavelet shrinkage, gives the good results in CT. This procedure affects very little the spatial resolution. Some applications are reconstruction methods, while others are a posteriori de-noising methods. De-noising after reconstruction is very difficult because the noise is non-stationary and has unknown distribution. Therefore, methods which work on the sinogram-space don’t have this problem, because they always work over a known noise distribution at this point. On the other hand, the posterior fossa in a head CT is a very complex region for physicians, because it is commonly affected by artifacts and noise which are not eliminated during the reconstruction procedure. This can leads to some false positive evaluations. The purpose of our present work is to compare different wavelet shrinkage de-noising filters to reduce noise, particularly in images of the posterior fossa within CT scans in the sinogram-space. This work describes an experimental search for the best wavelets, to reduce Poisson noise in Computed Tomography (CT) scans. Results showed that de-noising with wavelet filters improved the quality of posterior fossa region in terms of an increased CNR, without noticeable structural distortions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra

We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the discrete wavelet transform (DWT) to the input signal, ‘shrinking’ certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by ‘trial and error’, which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the ‘Haar’ wavelet basis, which we found to provide excellent filtering for 1D stellar spectra, at a low computational cost. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. Finally, we expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SU-F-J-27: Segmentation of Prostate CBCT Images with Implanted Calypso Transponders Using Double Haar Wavelet Transform

Purpose: Segmentation of prostate CBCT images is an essential step towards real-time adaptive radiotherapy. It is challenging For Calypso patients, as more artifacts are generated by the beacon transponders. We herein propose a novel wavelet-based segmentation algorithm for rectum, bladder, and prostate of CBCT images with implanted Calypso transponders. Methods: Five hypofractionated prostate patients with daily CBCT were studied. Each patient had 3 Calypso transponder beacons implanted, and the patients were setup and treated with Calypso tracking system. Two sets of CBCT images from each patient were studied. The structures (i.e. rectum, bladder, and prostate) were contoured by a trained expert, and these served as ground truth. For a given CBCT, the moving window-based Double Haar transformation is applied first to obtain the wavelet coefficients. Based on a user defined point in the object of interest, a cluster algorithm based adaptive thresholding is applied to the low frequency components of the wavelet coefficients, and a Lee filter theory based adaptive thresholding is applied to the high frequency components. For the next step, the wavelet reconstruction is applied to the thresholded wavelet coefficients. A binary/segmented image of the object of interest is therefore obtained. DICE, sensitivity, inclusiveness and ΔV were used to evaluate the segmentation result. Results: Considering all patients, the bladder has the DICE, sensitivity, inclusiveness, and ΔV ranges of [0.81–0.95], [0.76–0.99], [0.83–0.94], [0.02–0.21]. For prostate, the ranges are [0.77–0.93], [0.84–0.97], [0.68–0.92], [0.1–0.46]. For rectum, the ranges are [0.72–0.93], [0.57–0.99], [0.73–0.98], [0.03–0.42]. Conclusion: The proposed algorithm appeared effective segmenting prostate CBCT images with the present of the Calypso artifacts. However, it is not robust in two scenarios: 1) rectum with significant amount of gas; 2) prostate with very low contrast. Model based algorithm might improve the segmentation in these two scenarios.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Stress analysis using direct-S wavelets produced by a vertical vibrator

We have determined how to extract the azimuth of maximum horizontal stress (SHmax) in deep rocks by doing a simple 360° mathematical rotation of a downgoing direct-S wavelet generated at the baseplate of a surface-based vertical vibrator. We worked with direct-S wavelets that travel through stressed rocks to a deep horizontal vertical seismic profile (VSP) geophone. We find that the azimuth where a polarity reversal occurs in mathematical rotations of this downgoing direct-S wavelet defines the azimuth of the SHmax in the overlying rocks. We tested this direct-S wavelet rotation method for determining the SHmax azimuth at a site in the Illinois Basin using legacy VSP data acquired in 2013. SHmax azimuths indicated by this simple wavelet-rotation method were determined when vertical vibrators were stationed at zero offset, at far offset, and at different azimuths around a VSP receiver well. These VSP-based SHmax azimuths agreed with the azimuth of the SHmax found by traditional minifrac tests in the VSP receiver well. This simple VSP data analysis procedure for detecting the azimuth of maximum horizontal stress has never, to our knowledge, been reported or discussed in the geophysical literature. This technical finding should be of interest to the worldwide geophysical community, especially to people who need to monitor how stress fields shift when fluids are injected into, or extracted from, deep porous reservoirs.

Geochemistry & Geophysics↗
DOE OSTI2018

Relativistic Hydrodynamics with Wavelets

Methods to solve the relativistic hydrodynamic equations are important in a large number of astrophysical simulations, which may be very dynamic and involve multiscale features. This requires computational methods that are highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge across the computational domain and over many temporal scales. While this has been historically accomplished with adaptive-mesh-refinement-based methods, alternatives using wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. The current work presents a new method, extending the wavelet adaptive multiresolution representation method, for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulation. We note the wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to the fluid flow while providing good conservation of fluid quantities. The resulting implementation, OAHU , is applied to a series of demanding 1D and 2D problems that explore high Lorentz factor outflows and the formation of several instabilities, including the Kelvin–Helmholtz instability and the Rayleigh–Taylor instability.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Standardized Software for Wind Load Forecast Error Analyses and Predictions Based on Wavelet-ARIMA Models - Applications at Multiple Geographically Distributed Wind Farms

Given the multi-scale variability and uncertainty of wind generation and forecast errors, it is a natural choice to use time-frequency representation (TFR) as a view of the corresponding time series represented over both time and frequency. Here we use wavelet transform (WT) to expand the signal in terms of wavelet functions which are localized in both time and frequency. Each WT component is more stationary and has consistent auto-correlation pattern. We combined wavelet analyses with time series forecast approaches such as ARIMA, and tested the approach at three different wind farms located far away from each other. The prediction capability is satisfactory -- the day-ahead prediction of errors match the original error values very well, including the patterns. The observations are well located within the predictive intervals. Integrating our wavelet-ARIMA (‘stochastic’) model with the weather forecast model (‘deterministic’) will improve our ability significantly to predict wind power generation and reduce predictive uncertainty.

uncertainty analysis, wind generation forecast, wa↗
DOE OSTI2018

An efficient approach for solving Klein–Gordon equation arising in quantum field theory using wavelets

A new approach for the solution of Klein–Gordon equation using Legendre wavelet-based approximation method is presented. The properties of Legendre wavelets are used to reduce the problem to the solution of system of algebraic equations. Usually 2{sup (k−1)}M{sup 2} connection coefficients are required to solve the Klein–Gordon equation by Legendre wavelets method as mentioned in the literature. But, our proposed method based on Legendre wavelets and algebraic polynomials require only 2{sup (k−1)}M connection coefficients instead of 2{sup (k−1)}M{sup 2} . Also the convergence analysis and error estimation for the proposed function approximation through the truncated series have been discussed and approved with the exact solution. Illustrative examples are discussed to demonstrate the validity and applicability of the technique with lesser computational effort.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Parallel adaptive wavelet collocation method for PDEs

A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A wavelet-based computational method for solving stochastic Itô–Volterra integral equations

This paper presents a computational method based on the Chebyshev wavelets for solving stochastic Itô–Volterra integral equations. First, a stochastic operational matrix for the Chebyshev wavelets is presented and a general procedure for forming this matrix is given. Then, the Chebyshev wavelets basis along with this stochastic operational matrix are applied for solving stochastic Itô–Volterra integral equations. Convergence and error analysis of the Chebyshev wavelets basis are investigated. To reveal the accuracy and efficiency of the proposed method some numerical examples are included.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Non-stationary dynamics in the bouncing ball: A wavelet perspective

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Non parametric denoising methods based on wavelets: Application to electron microscopy images in low exposure time

The 3D reconstruction of the Cryo-Transmission Electron Microscopy (Cryo-TEM) and Energy Filtering TEM images (EFTEM) hampered by the noisy nature of these images, so that their alignment becomes so difficult. This noise refers to the collision between the frozen hydrated biological samples and the electrons beam, where the specimen is exposed to the radiation with a high exposure time. This sensitivity to the electrons beam led specialists to obtain the specimen projection images at very low exposure time, which resulting the emergence of a new problem, an extremely low signal-to-noise ratio (SNR). This paper investigates the problem of TEM images denoising when they are acquired at very low exposure time. So, our main objective is to enhance the quality of TEM images to improve the alignment process which will in turn improve the three dimensional tomography reconstructions. We have done multiple tests on special TEM images acquired at different exposure time 0.5s, 0.2s, 0.1s and 1s (i.e. with different values of SNR)) and equipped by Golding beads for helping us in the assessment step. We herein, propose a structure to combine multiple noisy copies of the TEM images. The structure is based on four different denoising methods, to combine the multiple noisy TEM images copies. Namely, the four different methods are Soft, the Hard as Wavelet-Thresholding methods, Bilateral Filter as a non-linear technique able to maintain the edges neatly, and the Bayesian approach in the wavelet domain, in which context modeling is used to estimate the parameter for each coefficient. To ensure getting a high signal-to-noise ratio, we have guaranteed that we are using the appropriate wavelet family at the appropriate level. So we have chosen âĂIJsym8âĂİ wavelet at level 3 as the most appropriate parameter. Whereas, for the bilateral filtering many tests are done in order to determine the proper filter parameters represented by the size of the filter, the range parameter and the spatial parameter respectively. The experiments reported in this paper demonstrate the performance of the Bilateral Filtering and the Bayesian approaches in terms of improving the SNRout and the image quality. Taken together, these results suggest that the Bayesian process has a potential to outperform all the used methods, where in the multiple noisy copies structure it gave us the best SNRout without change of the golden beads diameter. The Bayesian approach yielded enhanced average image without needing a huge amount of copies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗