Solving Functional Inverse Problems using Alpert Multi-Wavelets
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Salloum, Maher↗
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Wavelet Transform and Hidden Markov Model Application for Unsupervised Clustering of Microseismic Events from CO2 Injection
ARMA conference poster for a year-round grad intern from CSM
Willis, Rachel Marie↗
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↗
Detecting multi‐scale riverine topographic variability and its influence on Chinook salmon habitat selection
Abstract Quantifying geomorphic conditions that impact riverine ecosystems is critical in river management due to degraded riverine habitat, changing flow and thermal conditions, and increasing anthropogenic pressure. Geomorphic complexity at different scales directly impacts habitat heterogeneity and affects aquatic biodiversity resilience. Here we showed that the combination of continuous spatial survey at high resolution, topobathymetric light detection and ranging (LiDAR), and continuous wavelet analysis can help identify and characterize that complexity. We used a continuous wavelet analysis on 1‐m resolution topobathymetry in three rivers in the Salmon River Basin, Idaho (USA), to identify different scales of topographic variability and the potential effects of this variability on salmonid redd site selection. On each river, wavelet scales characterized the topographic variability by portraying repeating patterns in the longitudinal profile. We found three major representative spatial wavelet scales of topographic variability in each river: a small wavelet scale associated with local morphology such as pools and riffles, a mid‐wavelet scale that identified larger channel unit features, and a large wavelet scale related to valley‐scale controls. The small wavelet scale was used to identify pools and riffles along the entire lengths of each river as well as areas with differing riffle‐pool development. Areas along the rivers with high local topographic variability (high wavelet power) at all wavelet scales contained the largest features (i.e., deepest or longest pools) in the systems. By comparing the wavelet power for each wavelet scale to Chinook salmon redd locations, we found that higher small‐scale wavelet power, which is related to pool‐riffle topography, is important for redd site selection. The continuous wavelet methodology objectively identified scales of topographic variability present in these rivers, performed efficient channel‐unit identification, and provided geomorphic assessment without laborious field surveys.
Duffin, Jenna↗
Quantized Constant-Q Gabor Atoms for Sparse Binary Representations of Cyber-Physical Signatures
Increased data acquisition by uncalibrated, heterogeneous digital sensor systems such as smartphones present new challenges. Binary metrics are proposed for the quantification of cyber-physical signal characteristics and features, and a standardized constant-Q variation of the Gabor atom is developed for use with wavelet transforms. Two different continuous wavelet transform (CWT) reconstruction formulas are presented and tested under different signal to noise ratio (SNR) conditions. A sparse superposition of Nth order Gabor atoms worked well against a synthetic blast transient using the wavelet entropy and an entropy-like parametrization of the SNR as the CWT coefficient-weighting functions. The proposed methods should be well suited for sparse feature extraction and dictionary-based machine learning across multiple sensor modalities.
46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
Coarse-grain cluster analysis of tensors with application to climate biome identification
A tensor provides a concise way to codify the interdependence of complex data. Treating a tensor as a d-way array, each entry records the interaction between the different indices. Clustering provides a way to parse the complexity of the data into more readily understandable information. Clustering methods are heavily dependent on the algorithm of choice, as well as the chosen hyperparameters of the algorithm. However, their sensitivity to data scales is largely unknown. In this work, we apply the discrete wavelet transform to analyze the effects of coarse-graining on clustering tensor data. We are particularly interested in understanding how scale affects clustering of the Earth's climate system. The discrete wavelet transform allows classification of the Earth's climate across a multitude of spatial-temporal scales. The discrete wavelet transform is used to produce an ensemble of classification estimates, as opposed to a single classification. Each element of the ensemble is a clustering at a different spatial-temporal scale. Information theoretic approaches are used to identify important scale lengths in clustering the L15 Climate Datset. We also discover a sub-collection of the ensemble that spans the majority of the variance observed, allowing for efficient consensus clustering techniques that can be used to identify climate biomes.
54 ENVIRONMENTAL SCIENCES↗
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↗
Multiscale Flow for robust and optimal cosmological analysis
We propose Multiscale Flow, a generative Normalizing Flow that creates samples and models the field-level likelihood of two-dimensional cosmological data such as weak lensing. Multiscale Flow uses hierarchical decomposition of cosmological fields via a wavelet basis and then models different wavelet components separately as Normalizing Flows. The log-likelihood of the original cosmological field can be recovered by summing over the log-likelihood of each wavelet term. This decomposition allows us to separate the information from different scales and identify distribution shifts in the data such as unknown scale-dependent systematics. The resulting likelihood analysis can not only identify these types of systematics, but can also be made optimal, in the sense that the Multiscale Flow can learn the full likelihood at the field without any dimensionality reduction. We apply Multiscale Flow to weak lensing mock datasets for cosmological inference and show that it significantly outperforms traditional summary statistics such as power spectrum and peak counts, as well as machine learning–based summary statistics such as scattering transform and convolutional neural networks. We further show that Multiscale Flow is able to identify distribution shifts not in the training data such as baryonic effects. Finally, we demonstrate that Multiscale Flow can be used to generate realistic samples of weak lensing data.
79 ASTRONOMY AND ASTROPHYSICS↗
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↗
A Novel Fault Diagnosis Approach for Rolling Bearing Based on CWT and Adaptive Sparse Representation
Extraction and enhancement of weak impulse signature is the key of rolling bearing fault prognostics in which case the features are often weak and covered by noise. Tunable Q-factor wavelet transform (TQWT), as an emerging wavelet construction theory developed in a frequency domain explicitly, has the advantages of matching with the specific oscillation behavior of signal components. In this article, an adaptive sparse representation (ASR) method is proposed, which integrates the sparse code shrinkage (SCS) and parameter optimization into TQWT. However, direct application of ASR is difficult to extract fault signatures at the early stage or low-speed operation due to weak fault symptoms and background noise. A novel fault diagnosis strategy based on continuous wavelet transform (CWT) and ASR is investigated. CWT owns significant advantages on multiscale subdivision and weak signal detection. The results of simulated and experimental vibration signal analyses verify the effectiveness of the proposed method in accurately extracting weak impulse features from the noise environment.
Yuan, Xing↗
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↗
A case study of denoising microseismic data in the Farnsworth, TX CO 2 EOR site
As geologic carbon sequestration projects begin to be funded with a higher degree of frequency, microseismic monitoring will become more necessary to establish caprock integrity and induced seismicity risk. The Farnsworth, TX site, which hosts enhanced oil recovery operations, provides an ideal laboratory to test essential components of microseismic monitoring such as surface station placement, denoising, and different autopicker methods. We find that despite careful optimization, the surface station placement at the Farnsworth site was insufficient given the high level of background noise from the industrial operations at the oil field. Thus, we use only borehole geophone data in our processing. Two denoising techniques were examined: the DeepDenoiser and the continuous wavelet transform. The continuous wavelet transform was shown to be a valuable tool in converting between raw waveforms to processed denoised waveforms for microseismic monitoring. In the case of the noisy waveforms, only ten detections are found, compared with 90 in the denoised data for a two-hour window. The DeepDenoiser suffered from the fact that the training data was regional earthquake data. In addition, the PhaseNet machine-learning autopicker was applied to both the noisy and the denoised data, and this algorithm detected thousands of more arrivals in the data denoised with the continuous wavelet transform technique.
58 GEOSCIENCES↗
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↗
Software-Defined Ultrasonic Communication System Based on Time-reversal Signal Processing
Ultrasonic communication through solid channels suffers from channel dispersion, attenuation, and multipath effect. For example, in elbow shape pipes or complex structures, the elastic waves are reflected and reverberated in multipath resulting in a major dispersion of the signals. In solid channels such as flat bar, multipath propagation is the main reason for bit-wavelet spreading and intersymbol interference (ISI). The conventional modulation method like OOK (on-off-keying) or PSK (phase-shift-keying) fails to provide a useful Signal-to-Noise Ratio (SNR). Time-reversal (TR) signal processing method is a promising technique that can compress the spreading of the bit-wavelet and strengthen the peak signal energy on the receiver. In this study, Finite Element Analysis (FEA) using ABAQUS software tools is used to characterize the bit-wavelet spreading effect caused by dispersive communication channels. Also, this study presents the impact of TR ultrasonic communication as a function of excitation pulse width, channel length, and carrier frequency through a flat-bar channel. A Software-Defined System-on-Chip (SD-SoC) platform is examined as a viable solution for the low-complexity and energy-efficient ultrasonic communication system. The proposed TR based SD-SoC ultrasonic communication system can make full use of signal dispersion for peak performance by minimizing the ISI within a dispersive and reverberant metal channel.
FEM simulation↗
Tidal frequencies and quasiperiodic subsurface water level variations dominate redox dynamics in a salt marsh system
Salt marshes are hotspots of nutrient processing en route to sensitive coastal environments. Whilst our understanding of these systems has improved over the years, we still have limited knowledge of the spatiotemporal variability of critical biogeochemical drivers within salt marshes. Sea-level rise will continue to force change on salt marsh functioning, highlighting the urgency of filling this knowledge gap. Our study was conducted in a central California estuary experiencing extensive marsh drowning and relative sea-level rise, making it a model system for such an investigation. Here we instrumented three marsh positions subjected to different degrees of tidal inundation (6.7%, 8.9%, and 11.2% of the time for the upper, middle, and lower marsh positions, respectively), providing locations with varied biogeochemical characteristics and hydrological interactions at the site. We continuously monitored redox potential (Eh) at depths of 0.1, 0.3, and 0.5 m, subsurface water levels (WL), and temperature at 0.7 m depth at each marsh position. To understand how drivers of subsurface biogeochemical processes fluctuate across tidal cycles, we used wavelet analyses to explain the interactions between Eh and WL. We found that tidal forcing significantly affects key drivers of biogeochemical processes by imparting controls on Eh variability, likely driving subsurface hydro-biogeochemistry of the salt marsh. Wavelet coherence showed that the Eh-WL relationship is nonlinear, and their lead–lag relationship is variable. We found that precipitation events perturb Eh at depth over timescales of hours, even though WL shows relatively minimal change during events. Furthermore, this work highlights the importance of high frequency in situ measurements, such as Eh, to help explain factors that govern subsurface biogeochemistry and hydrological processes in salt marshes.
54 ENVIRONMENTAL SCIENCES↗
Preliminary study of radio frequency waves in hypervelocity impact plasma
Orbital debris and meteoroids can cause mechanical and electrical anomalies by impacting spacecraft. Although mechanical damage tends to occur only from particles with masses >10 –3 g, electrical damage can be a result of hypervelocity (> 10 km/s) impacts (HVI) even with smaller particles. In HVI, the projectile speed exceeds the speed of sound in the material and has enough energy to create plasma by ionizing the material near the surface, which can then emit radio frequency (RF) waves. In this paper, we conduct a preliminary study on the characteristics of impact-generated RF emission with the ultimate goal of building an RF predictive model for risk assessment of HVI electrical effects that can damage spacecraft. First, we introduce wavelet analysis as a method for denoising and quantifying the total RF signal energy. An appropriate mother wavelet and the number of decomposition levels are selected using a synthetic signal. Second, the total energy of the RF emission is calculated using Parseval’s theorem. Results suggest that the total RF signal energy is proportional to the energy flux of the impactor. Lastly, spectrograms of the RF emission are analyzed to characterize features that can be used in the future to predict impacts that can cause electrical damage to satellites.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Deep neural operators can predict the real-time response of floating offshore structures under irregular waves
The use of neural operators in a digital twin model of an offshore floating structure holds the potential for a significant shift in the prediction of structural responses and health monitoring, offering valuable real-time control insights. In this work, we investigate the effectiveness of three neural operators, namely the deep operator network (DeepONet), the Fourier neural operator (FNO), and the Wavelet neural operator (WNO), to accurately capture the responses of a floating structure under six different sea state codes (3 − 8) based on the wave characteristics described by the World Meteorological Organization (WMO). To further enhance the accuracy of the vanilla architecture of the neural operators, novel extensions, such as wavelet-DeepONet and self-adaptive WNO, are proposed in this paper. The results demonstrate that these high-precision neural operators can deliver structural responses more efficiently, up to two orders of magnitude faster than a dynamic analysis using conventional numerical solvers. Additionally, compared to gated recurrent units (GRUs), a commonly used recurrent neural network for time-series estimation, neural operators are both more accurate and efficient, especially in situations with limited data availability. Taken together, our study shows that FNO outperforms all other operators for approximating the mapping of one input functional space to the output space as well as for responses that have small bandwidth of the frequency spectrum. Conversely, DeepONet, with historical states, proves most accurate in learning the mapping of multiple input functions to the output space and capturing responses within a broad frequency spectrum.
97 MATHEMATICS AND COMPUTING↗
Towards automated and real-time multi-object detection of anguilliform fishes from sonar data using YOLOv8 deep learning algorithm
Eels (Anguilla spp.), including American eels (Anguilla rostrata), European eels (Anguilla anguilla), and Japanese eels (Anguilla japonica), are species of critical management and regulatory concern due to their vulnerability to various stressors during downstream migrations. Accurate and efficient detection of migrating eels can improve our understanding of fish behaviors and fish-hydraulic structure interactions, thereby facilitating the design, operation, and optimization of more effective downstream passage facilities from both biological and economic perspectives. However, a real-time, automated framework for detecting migrating eels in real-world applications is currently lacking. Leveraging imaging sonar as a reliable technology for fish passage monitoring, field data are acquired using imaging sonar and then converted to single sonar frames/images for subsequent analysis. In this study, a framework based on the You Only Look Once Version 8 (YOLOv8)-based convolutional neural network is proposed for multi-object detection of eels and non-eel fish using the sonar images after image subtraction and additional wavelet denoising. The results from both training and testing phases demonstrate that the framework's ability can successfully detect both eels and non-eel fish in preprocessed sonar images, achieving F1-scores and mAP@0.50 exceeding 0.84. Additionally, the incorporation of wavelet denoising during preprocessing slightly improve detection performance. Furthermore, the transferability of this framework from eel to lamprey detection is demonstrated to be feasible given the similar morphological characteristics of these two species. Overall, the proposed framework achieves accurate and efficient detection of migrating eels, providing reliable and real-time information that can help conserve vulnerable eel and eel-like populations.
Deep learning↗