Framework for Extracting and Characterizing Load Profile Variability Based on a Comparative Study of Different Wavelet Functions
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24 POWER TRANSMISSION AND DISTRIBUTION↗
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Alpert multi-wavelets for functional inverse problems: direct optimization and deep learning
Computational engineering models often contain unknown entities (e.g. parameters, initial and boundary conditions) that require estimation from other measured observable data. Estimating such unknown entities is challenging when they involve spatio-temporal fields because such functional variables often require an infinite-dimensional representation. Here, we address this problem by transforming an unknown functional field using Alpert wavelet bases and truncating the resulting spectrum. Hence the problem reduces to the estimation of few coefficients that can be performed using common optimization methods. We apply this method on a one-dimensional heat transfer problem where we estimate the heat source field varying in both time and space. The observable data is comprised of temperature measured at several thermocouples in the domain. This latter is composed of either copper or stainless steel. The optimization using our method based on wavelets is able to estimate the heat source with an error between 5% and 7%. We analyze the effect of the domain material and number of thermocouples as well as the sensitivity to the initial guess of the heat source. Finally, we estimate the unknown heat source using a different approach based on deep learning techniques where we consider the input and output of a multi-layer perceptron in wavelet form. We find that this deep learning approach is more accurate than the optimization approach with errors below 4%.
97 MATHEMATICS AND COMPUTING↗
Planetary Boundary Layer Height derived from MPL data using Sawyer-Li method
Sawyer and Li (2013) developed a technique to derive the PBL height from micropulse lidar (MPL) backscatter measurements using combined wavelet covariance transform and iterative curve-fitting methods. The wavelet covariance transform method applies a Haar wavelet function to MPL backscatter signals (Brooks et al., 2003).
54 ENVIRONMENTAL SCIENCES↗
A multiresolution adaptive wavelet method for nonlinear partial differential equations
We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.
97 MATHEMATICS AND COMPUTING↗
Improving the Transportability of a Deep Learning Denoising Model Using Transfer Learning Techniques
The adoption of machine learning techniques in the seismology community has led to great performance improvements in several areas, including signal processing. Specifically, the development of deep learning–based seismic waveform denoising models has the potential to yield improvements in signal detection capabilities for networks operating in particularly noisy environments. Recent advancements in the design of these deep learning denoising models have included the incorporation of continuous and discrete wavelet transform functions into the network architecture to improve the learning capabilities and efficiency of said models. These wavelet transform–based seismic denoising models have shown improved denoising capabilities in regions where there is good agreement between the data features present in the training and evaluation datasets. However, questions remain about the overall transportability of these models to other monitoring regions. Here, in this study, we will determine the baseline transportability of a newly developed multilevel wavelet‐transform convolutional neural network (MWCNN) seismic denoising model. We accomplish this by taking a version of the MWCNN denoising model trained on data collected from the Utah region and evaluating its denoising performance on datasets collected from the neighboring Nevada region, which differ with regard to monitoring sensor types and event histories. We find that there is a notable variability in denoising performance related to the degree of similarity between the initial and new target datasets. The most notable difference in denoising performance is the ability of the denoising model to preserve accurate amplitude information associated with the signal energy present in the waveform data. Finally, we evaluate the ability of transfer learning techniques to improve the transportability of the MWCNN denoising model. We find that although there is still a performance gap present in the denoising results of the MWCNN model, transfer learning did yield improved results.
Quinones, Louis [Sandia National Laboratories (SNL↗
Detection of the significant impact of source clustering on higher order statistics with DES Year 3 weak gravitational lensing data
We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10 −3 (2.6σ) using third-order map moments and p = 3 × 10 −11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.
79 ASTRONOMY AND ASTROPHYSICS↗
Short‐Term Hourly Weather Forecasting Using PredRNN With Image Preprocessing
Global weather forecast models are vital tools with numerous applications, including public safety, agriculture, and transportation. Recent advancements in artificial intelligence (AI) and deep learning (DL) have shown the potential to enhance weather forecasting accuracy and speed. In this study, we developed a short-term hourly weather forecast framework with a wavelet transform function for data preprocessing and a spatiotemporal DL model, PredRNN, for predicting five surface atmospheric variables, including wind speed and direction, mean sea level pressure (MSLP), temperature, and precipitation. The framework demonstrated promising results. It produces global forecasts at 0.25° (∼25 km) with a 1-day lead time RMSE of 1.8 m/s for wind components, 180 Pa for MSLP, and 1.8 K for temperature. Although our model does not surpass state-of-the-art AI weather forecast models across all metrics, it outperforms these models in precipitation forecasting and wind prediction at short lead times and achieves comparable accuracy for MSLP. Its native hourly forecasting capability, together with training on widely accessible GPU hardware, contributes meaningfully to the advancement of accessible DL weather forecasting methods. Our work highlights the importance of integrating temporal components and data transformation techniques to improve the predictability and accuracy of weather forecasts.
Tran, Hoang [Pacific Northwest National Laboratory↗
Image Deconvolution and Point-spread Function Reconstruction with STARRED: A Wavelet-based Two-channel Method Optimized for Light-curve Extraction
We present starred, a point-spread function (PSF) reconstruction, two-channel deconvolution, and light-curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data is targeted rather than an infinite one, thereby minimizing deconvolution artifacts. In addition, starred performs a joint deconvolution of all available data, accounting for epoch-to-epoch variations of the PSF and decomposing the resulting deconvolved image into a point source and an extended source channel. The output is a high-signal-to-noise-ratio, high-resolution frame combining all data and the photometry of all point sources in the field of view as a function of time. Of note, starred also provides exquisite PSF models for each data frame. We showcase three applications of starred in the context of the imminent LSST survey and of JWST imaging: (i) the extraction of supernovae light curves and the scene representation of their host galaxy; (ii) the extraction of lensed quasar light curves for time-delay cosmography; and (iii) the measurement of the spectral energy distribution of globular clusters in the "Sparkler," a galaxy at redshift z = 1.378 strongly lensed by the galaxy cluster SMACS J0723.3-7327. starred is implemented in jax, leveraging automatic differentiation and graphics processing unit acceleration. This enables the rapid processing of large time-domain data sets, positioning the method as a powerful tool for extracting light curves from the multitude of lensed or unlensed variable and transient objects in the Rubin-LSST data, even when blended with intervening objects.
79 ASTRONOMY AND ASTROPHYSICS↗
Solving Functional Inverse Problems using Alpert Multi-Wavelets
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Salloum, Maher↗
Measuring nonlinearities of a cantilever beam using a low-cost efficient wireless intelligent sensor for strain (LEWIS-S)
In the context of experimental vibration data, strain gauges can obtain linear and nonlinear dynamic measurements. However, measuring strain can be disincentivizing and expensive due to the complexity of data acquisition systems, lack of portability, and high costs. This research introduces the use of a low-cost efficient wireless intelligent sensor for strain (LEWIS-S) that is based on a portable-sensor-design platform that streamlines strain sensing. Additionally, the softening behavior of a cantilever beam with geometric and inertial nonlinearities is characterized by the LEWIS-S based on high force level inputs. Two experiments were performed on a nonlinear cantilever beam with measurements obtained by the LEWIS-S sensor and an accelerometer. First, a sine sweep test was performed through the fundamental resonance of the system, then a ring-down test was performed from a large initial static deformation. Good agreement was revealed in quantities of interest such as frequency response functions, the continuous wavelet transforms, and softening behavior in the backbone curves.
42 ENGINEERING↗
Detecting Anomalies for Fire Prevention in Distribution Systems: Challenges and Analytical Techniques
Electric utilities in California have historically been linked to up to 10% of wildfires. To mitigate this risk, Southern California Edison has invested significantly in wildfire prevention strategies, including undergrounding cables and enhancing equipment inspections. This article explores a novel approach to fire prevention by detecting anomalies in the distribution system that may indicate potential fire hazards. The focus is on identifying arcing conditions through high-resolution point-on-wave (POW) measurements. Arcing, a precursor to fires, is challenging to detect due to its subtle transients and complex system topology. The article discusses the use of advanced signal processing and machine learning techniques, such as spectral correlation function and discrete wavelet transform, to extract features from POW data and accurately identify arcing events. The study demonstrates a high accuracy rate in detecting arcing, paving the way for improved fire prevention measures in electric distribution systems.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Convective and turbulent motions in non-precipitating Cu. Part 1: Method of separation of convective and turbulent motions
Atmospheric motions in clouds and cloud surroundings have a wide range of scales, from several kilometers to centimeters. These motions have different impacts on cloud dynamics and microphysics. Larger-scale motions (hereafter referred to as convective motions) are responsible for mass transport over distances comparable with cloud scale, while motions of smaller scales (hereafter referred to as turbulent motions) are stochastic and responsible for mixing and cloud dilution. This distinction substantially simplifies the analysis of dynamic and microphysical processes in clouds. The present research is Part I of the study aimed at describing the method for separating the motion scale into a convective component and a turbulent component. An idealized flow is constructed, which is a sum of an initially prescribed field of the convective velocity with updrafts in the cloud core and downdrafts outside the core, and a stochastic turbulent velocity field obeying the turbulent properties, including the -5/3 law and the 2/3 structure function law. A wavelet method is developed allowing separation of the velocity field into the convective and turbulent components, with parameter values being in a good agreement with those prescribed initially. The efficiency of the method is demonstrated by an example of a vertical velocity field of a cumulus cloud simulated using the System for Atmospheric Modeling (SAM) with bin microphysics and resolution of 10 m. It is shown that vertical velocity in clouds indeed can be represented as a sum of convective velocity (forming zone of cloud updrafts and subsiding shell) and a stochastic velocity obeying laws of homogeneous and isotropic turbulence.
54 ENVIRONMENTAL SCIENCES↗
Volumetric Rendering on Wavelet-Based Adaptive Grid
Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.
Vezolainen, Alexei V.↗
Estimating SHmax azimuth with P sources and vertical geophones: Use P-P reflection amplitudes or use SV-P reflection times?
We compared two methods for extracting the azimuth of maximum horizontal stress (SHmax) from 3D land-based seismic data generated by a P source and recorded with vertical geophones. In the first method, we used the direct-SV mode that is produced by all land-based P sources. P sources generate SV illumination that radiates in all azimuth directions from a source station and creates SV-P reflections that are recorded by vertical geophones. Unless stratigraphy has steep dip, SV-P raypaths recorded by vertical geophones are the reverse of P-SV raypaths recorded by horizontal geophones. Thus, SV-P data provide the same S-wave sensitivity to stress fields as popular P-SV data do. In the second method, we retrieved P-P reflections and then performed an amplitude-variation-with-azimuth (AVA) analysis of the amplitude-gradient behavior of P-P reflection wavelets. We did this analysis in narrow azimuth corridors to determine the gradient of reflection-wavelet amplitudes as a function of azimuth. This P-P AVA amplitude-gradient method has been of great interest in the reflection seismology community since it was introduced in the late 1990s. Each of these methods, AVA analysis of the gradient of P-P reflection amplitudes and azimuth-dependent arrival times of SV-P reflections, can be used to determine the azimuth of SHmax stress. We compare the results of the two methods with ground truth measurements of SHmax azimuth at a CO 2 sequestration site in the Michigan Basin. SHmax azimuths were determined from P-P and SV-P data at three major boundaries at depths of approximately 3500 ft (1067 m), 5500 ft (1676 m), and 7500 ft (2286 m). Two estimates of SHmax azimuth (one using SV-P data and one using P-P data) were made at each stacking bin inside a 24 mi 2 (62 km 2 ) image space. The result was approximately 98,000 estimates of SHmax azimuth across each of these three boundaries for each of these two prediction strategies. Histogram displays of PP AVA gradient estimates had peaks at correct azimuths of SHmax at all three depths, but the spread of the distributions widened with depth and split into two peaks at the deepest boundary. In contrast, each histogram of SHmax azimuth predicted by azimuth-dependent SV-P traveltimes had a single, definitive peak that was positioned at the correct SHmax azimuth at all three boundary depths.
Geochemistry & Geophysics↗
CODEX clusters
Context: Large area catalogs of galaxy clusters constructed from ROSAT All-Sky Survey provide the basis for our knowledge of the population of clusters thanks to long-term multiwavelength efforts to follow up observations of these clusters. Aims: The advent of large area photometric surveys superseding previous, in-depth all-sky data allows us to revisit the construction of X-ray cluster catalogs, extending the study to lower cluster masses and higher redshifts and providing modeling of the selection function. Methods: We performed a wavelet detection of X-ray sources and made extensive simulations of the detection of clusters in the RASS data. We assigned an optical richness to each of the 24 788 detected X-ray sources in the 10 382 square degrees of the Baryon Oscillation Spectroscopic Survey area using red sequence cluster finder redMaPPer version 5.2 run on Sloan Digital Sky Survey photometry. We named this survey COnstrain Dark Energy with X-ray (CODEX) clusters. Results: We show that there is no obvious separation of sources on galaxy clusters and active galactic nuclei (AGN) based on the distribution of systems on their richness. This is a combination of an increasing number of galaxy groups and their selection via the identification of X-ray sources either by chance or by groups hosting an AGN. To clean the sample, we use a cut on the optical richness at the level corresponding to the 10% completeness of the survey and include it in the modeling of the cluster selection function. We present the X-ray catalog extending to a redshift of 0.6. Conclusions: The CODEX suvey is the first large area X-ray selected catalog of northern clusters reaching fluxes of 10 –13 ergs s –1 cm –2 . We provide modeling of the sample selection and discuss the redshift evolution of the high end of the X-ray luminosity function (XLF). Our results on z < 0.3 XLF agree with previous studies, while we provide new constraints on the 0.3 < z < 0.6 XLF. We find a lack of strong redshift evolution of the XLF, provide exact modeling of the effect of low number statistics and AGN contamination, and present the resulting constraints on the flat ΛCDM.
79 ASTRONOMY AND ASTROPHYSICS↗
CNN-Based Phase Fault Classification in Real and Simulated Power Systems Data
This study proposes a convolutional neural network (CNN)–based two-step phase fault detection and identification method to classify anomalies in the power grid signal. Specifically, the first step checks the fault’s existence and determines the need for the second step. Subsequently, in the case of anomalies in the power grid signal, the second step identifies the type of fault, including line-to-line, single-line-to-ground, double-line-to-ground, and triple-line. Accordingly, the CNN architecture is both designed for the classification layers and trained with simulated data. To provide maximum prediction accuracy with minimum processing time, this study investigates the combinations of various feature extraction (FE) techniques, such as fast Fourier transform (FFT), amplitude and phase (AP), auto-correlation function, power spectral density, and wavelet transform (WT). Consequently, simulated and real-world results demonstrate that the proposed two-step method outperforms conventional one-step techniques, with the best performance obtained by using the combination of AP-AP, AP-WT, FFT-AP, and FFT-WT–based FE methods.
Alaca, Ozgur↗
Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed
Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Exploring metastable states in UO 2 using hybrid functionals and dynamical mean field theory
A detailed exploration of the f-atomic orbital occupancy space for UO2 is performed using a first principles approach based on density functional theory (DFT), employing a full hybrid functional within a systematic basis set. Specifically, the PBE0 functional is combined with an occupancy biasing scheme implemented in a wavelet-based algorithm which is adapted to large supercells. The results are compared with previous DFT + U calculations reported in the literature, while dynamical mean field theory is also performed to provide a further base for comparison. This work shows that the computational complexity of the energy landscape of a correlated f-electron oxide is much richer than has previously been demonstrated. The resulting calculations provide evidence of the existence of multiple previously unexplored metastable electronic states of UO 2 , including those with energies which are lower than previously reported ground states.
36 MATERIALS SCIENCE↗