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Field-Assisted Embedding of Fiber Bragg Gratings with Compressive Strain for Sensing at High Temperatures
This document summarizes embedding of fiber Bragg grating sensors and temperature sensing. This document is for the Advanced Sensors and Instrumentation (ASI) program Spring 2025 Newsletter.
Enhanced Tensor Completion Based Approaches for State Estimation in Distribution Systems
Grid state estimation is essential for effective control and management of distribution systems. While weighted least squares has been the conventional method for state estimation, sparsity-aware methods have become popular due to their superior performance with limited data. Matrix completion and compressed sensing-based state estimation approaches exploit the underlying smoothness in the state variables. However, classic matrix completion methods do not take into account the temporal correlation of system states. Compressed sensing methods, on the other hand, require an appropriate choice of sparsifying basis that may not be easy to identify. This paper proposes a blocktensor completion based framework which uses an alternative approach to estimate voltage phasor, power injections and branch currents. This approach utilizes the temporal correlation of the system states in a tensor trace-norm minimization formulation with power flow equations as constraints. Herein, feature scaling is introduced in the problem formulation to benefit from the improved sensitivity of the tensor trace norm to the matrix columns in the scaled unfoldings of the tensor. Weighted tensor norm is utilized to exploit the structures of the different unfoldings of the state measurement tensor to improve the voltage estimation. The estimation accuracy is further improved by alternatively estimating the tensor columns and increasing the available data at each stage in the tensor completion process. The proposed methods are evaluated on the IEEE-33, 37 test systems and a 100- node test system. The proposed methods are shown to provide significant performance gains relative to the classic matrix and tensor completion based approaches.
Generative Patch Priors for Practical Compressive Image Recovery
In this work, we propose the generative patch prior (GPP) that defines a generative prior for compressive image recovery, based on patch-manifold models. Unlike learned, image-level priors that are restricted to the range space of a pre-trained generator, GPP can recover a wide variety of natural images using a pre-trained patch generator. Additionally, GPP retains the benefits of generative priors like high reconstruction quality at extremely low sensing rates, while also being much more generally applicable. We show that GPP outperforms several unsupervised and supervised techniques on three different sensing models – linear compressive sensing with known, and unknown calibration settings, and the non-linear phase retrieval problem. Finally, we propose an alternating optimization strategy using GPP for joint calibration-and-reconstruction which performs favorably against several baselines on a real world, uncalibrated compressive sensing dataset. The code and models for GPP are available on github.
An investigative study of multispectral data compression for remotely-sensed images using vector quantization and difference-mapped shift-coding
A study is conducted to investigate the effects and advantages of data compression techniques on multispectral imagery data acquired by NASA's airborne scanners at the Stennis Space Center. The first technique used was vector quantization. The vector is defined in the multispectral imagery context as an array of pixels from the same location from each channel. The error obtained in substituting the reconstructed images for the original set is compared for different compression ratios. Also, the eigenvalues of the covariance matrix obtained from the reconstructed data set are compared with the eigenvalues of the original set. The effects of varying the size of the vector codebook on the quality of the compression and on subsequent classification are also presented. The output data from the Vector Quantization algorithm was further compressed by a lossless technique called Difference-mapped Shift-extended Huffman coding. The overall compression for 7 channels of data acquired by the Calibrated Airborne Multispectral Scanner (CAMS), with an RMS error of 15.8 pixels was 195:1 (0.41 bpp) and with an RMS error of 3.6 pixels was 18:1 (.447 bpp). The algorithms were implemented in software and interfaced with the help of dedicated image processing boards to an 80386 PC compatible computer. Modules were developed for the task of image compression and image analysis. Also, supporting software to perform image processing for visual display and interpretation of the compressed/classified images was developed.
Study and simulation of low rate video coding schemes
The semiannual report is included. Topics covered include communication, information science, data compression, remote sensing, color mapped images, robust coding scheme for packet video, recursively indexed differential pulse code modulation, image compression technique for use on token ring networks, and joint source/channel coder design.
Analysis of sparse recovery for Legendre expansions using envelope bound
We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using ℓ 1 minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form m ≳ Θ 2 s x log factors have been relied on to determine the minimum number of samples m that guarantees successful reconstruction of s-sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound Θ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. Here, in this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for s-sparse Legendre expansions, m ≳ Θs 2 x log factors, which is independent of Θ. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in Bourgain and Chkifa et al., to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average.
On the Strong Convergence of Forward-Backward Splitting in Reconstructing Jointly Sparse Signals
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work (Daubechies et al., Pure Appl. Math. 57(11), 1413–1457, 2004), where the single vector signal can be infinite-dimensional, and (Fornasier and Rauhut, SIAM J. Numer. Anal. 46(2), 577613, 2008), which extends the aforementioned work to the joint sparse recovery of finite number of infinite-dimensional vectors. In our case, to take account of the joint sparsity and promote the coupling of nonvanishing components, we employ a convex relaxation approach with mixed norm penalty ℓ 2,1 . This paper discusses the computation of the solutions of linear inverse problems with such relaxation by a forward-backward splitting algorithm. However, since the solution matrix possesses infinitely many columns, the arguments of Daubechies et al. (Pure Appl. Math. 57(11), 1413–1457, 2004) no longer apply. As such, we establish new strong convergence results for the algorithm, in particular when the set of jointly sparse vectors is infinite.
Sparse adaptive basis set methods for solution of the time dependent Schrodinger equation
Scalable numerical solutions to the time dependent Schrodinger equation remain an outstanding goal in theoretical chemistry. Here we present a method which utilises recent breakthroughs in signal processing to consistently adapt a dictionary of basis functions to the dynamics of the system. Further, we show that for two low-dimensional model problems the size of the basis set does not grow quickly with time and appears only weakly dependent on dimensionality. The generality of this finding remains to be seen. The method primarily uses energies and gradients of the potential, opening the possibility for its use in on-the-fly ab initio quantum wavepacket dynamics.
Numerical characterization of support recovery in sparse regression with correlated design
Sparse regression is employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data is the presence of correlations between predictive features. These correlations hamper both feature selection and estimation and jeopardize conclusions drawn from estimated models. On the other hand, theoretical results on sparsity-inducing regularized regression have largely addressed conditions for selection consistency via asymptotics, and disregard the problem of model selection, whereby regularization parameters are chosen. In this numerical study, we address these issues through exhaustive characterization of the performance of several regression estimators, coupled with a range of model selection strategies. These estimators and selection criteria were examined across correlated regression problems with varying degrees of signal to noise, distributions of non-zero model coefficients, and model sparsity. Our results reveal a fundamental tradeoff between false positive and false negative control in all regression estimators and model selection criteria examined. Additionally, we numerically explore a transition point modulated by the signal-to-noise ratio and spectral properties of the design covariance matrix at which the selection accuracy of all considered algorithms degrades. Overall, we find that SCAD coupled with BIC or empirical Bayes model selection performs the best feature selection across the regression problems considered.
A Hybrid Framework Combining Model-Based and Data-Driven Methods for Hierarchical Decentralized Robust Dynamic State Estimation
This paper combines model-based and data-driven methods to develop a hierarchical, decentralized, robust dynamic state estimator (DSE). A two-level hierarchy is proposed, where the lower level consists of robust, model-based, decentralized DSEs. The state estimates sent from the lower level are received at the upper level, where they are filtered by a robust data-driven DSE after a principled sparse selection. This selection allows us to shrink the dimension of the problem at the upper level and hence significantly speed up the computational time. The proposed hybrid framework does not depend on the centralized infrastructure of the control centers; thus it can be completely embedded into the wide-area measurement systems. This feature will ultimately facilitate the placement of hierarchical decentralized control schemes at the phasor data concentrator locations. Also, the network model is not necessary; thus, a topology processor is not required. Finally, there is no assumption on the dynamics of the electric loads. The proposed framework is tested on the 2,000-bus synthetic Texas system, and shown to be capable of reconstructing the dynamic states of the generators with high accuracy, and of forecasting in the advent of missing data.
Universal Noiseless Coding Subroutines
Software package consists of FORTRAN subroutines that perform universal noiseless coding and decoding of integer and binary data strings. Purpose of this type of coding to achieve data compression in sense that coded data represents original data perfectly (noiselessly) while taking fewer bits to do so. Routines universal because they apply to virtually any "real-world" data source.
Magnetosonic ULF Waves With Anomalous Plasma–Magnetic Field Correlations: Standing Waves and Inhomogeneous Plasmas
Ultra-low frequency (ULF) wave observations across the heliosphere often rely on the sign of correlations between plasma (density/pressure) and magnetic field perturbations to distinguish between fast and slow magnetosonic modes. However, the assumptions behind this magnetohydrodynamic result are not always valid, particularly within the magnetosphere which is inhomogeneous and supports standing waves along the geomagnetic field. Through theory and a global simulation, we find both effects can result in anomalous plasma–magnetic field correlations. The interference pattern in standing waves can lead both body and surface magnetosonic waves to have different cross-phases than their constituent propagating waves. Furthermore, if the scale of gradients in the background are shorter than the wavelength or the waves are near-incompressible, then advection by the wave of inhomogeneities can overcome the wave's inherent sense of compression. These effects need to be allowed for and taken into account when applying the typical diagnostic to observations.
High-Dimensional Compressive Scanning Transmission Electron Microscopy
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Real-time and post-hoc compression for data from Distributed Acoustic Sensing
Distributed Acoustic Sensing (DAS) is an emerging sensing technology that records the strain-rate along fiber optic cables at high spatial and temporal resolution. This technique is becoming a popular tool in seismology, hydrology, and other subsurface monitoring applications. However, due to the large coverage (10’s of km) and high density of measurements (1m spacing at 100’s of Hz), a DAS installation could produce terabytes of data records per day. Because many DAS instruments are deployed in remote locations, this large data size poses significant challenges to its transfer and storage. In this paper, we explore lossless compression methods to reduce the storage requirement in both real-time and post-hoc scenarios. Here we propose a two-stage compression method to improve the compression ratio and compression speed. This two-stage compression method could reduce the storage requirement by 40%, which is 20% more than other lossless methods, such as ZSTD. We demonstrate that the compression method could complete its operation well before the DAS instrument needs to output the next file, making it suitable for real-time DAS acquisition. We also implement a parallel compression method for a post-hoc scenario and demonstrate that our method could effectively utilize a parallel computer. With 256 CPU cores, our parallel compression method achieves the speed of 26GB/second.
Self-Regulating Water-Separator System for Fuel Cells
proposed system would perform multiple coordinated functions in regulating the pressure of the oxidant gas (usually, pure oxygen) flowing to a fuelcell stack and in removing excess product water that is generated in the normal fuel-cell operation. The system could function in the presence or absence of gravitation, and in any orientation in a gravitational field. Unlike some prior systems for removing product water, the proposed system would not depend on hydrophobicity or hydrophilicity of surfaces that are subject to fouling and, consequently, to gradual deterioration in performance. Also unlike some prior systems, the proposed system would not include actively controlled electric motors for pumping; instead, motive power for separation and pumping away of product water would be derived primarily from the oxidant flow and perhaps secondarily from the fuel flow. The net effect of these and other features would be to make the proposed system more reliable and safer, relative to the prior systems. The proposed system (see figure) would include a pressure regulator and sensor in the oxidant supply just upstream from an ejector reactant pump. The pressure of the oxidant supply would depend on the consumption flow. In one of two control subsystems, the pressure of oxidant flowing from the supply to the ejector would be sensed and used to control the speed of a set of a reciprocating constant-displacement pump so that the volumetric flow of nominally incompressible water away from the system would slightly exceed the rate at which water was produced by the fuel cell(s). The two-phase (gas/liquid water) outlet stream from the fuel cell(s) would enter the water separator, a turbinelike centrifugal separator machine driven primarily by the oxidant gas stream. A second control subsystem would utilize feedback derived from the compressibility of the outlet stream: As the separator was emptied of liquid water, the compressibility of the pumped stream would increase. The compressibility would be sensed, and an increase in compressibility beyond a preset point (signifying a decrease in water content below an optimum low level) would cause the outflow from the reciprocating pump to be diverted back to the separator to recycle some water.