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At least 145 records · Page 8

Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ 1 -regularization

We develop a new data-driven paradigm for efficient model reduction of a broad class of nonlinear dynamical systems. Our model reduction method directly enables the interpretation of key components of the dynamical system, unlike traditional projection-based model reduction methods that focus on reducing computational complexity more than interpretability. Our method is not application specific and is simple to implement on nonlinear dynamical systems arising from a variety of different fields. It requires minimal parameterization using a single parameter to trade-off between model complexity and estimation error. We use a data-driven paradigm to formulate model reduction as an efficient convex optimization problem that scales polynomially in the original size of the complex system, enabling systems with as many as thousands of components to be reduced in a matter of minutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ptychographic phase retrieval by proximal algorithms

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 10 4 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.

36 MATERIALS SCIENCE↗

SkyFACT: high-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods

We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), a new approach for studying, modeling and decomposing diffuse gamma-ray emission. Like most previous analyses, the approach relies on predictions from cosmic-ray propagation codes like GALPROP and DRAGON. However, in contrast to previous approaches, we account for the fact that models are not perfect and allow for a very large number (∼> 10{sup 5}) of nuisance parameters to parameterize these imperfections. We combine methods of image reconstruction and adaptive spatio-spectral template regression in one coherent hybrid approach. To this end, we use penalized Poisson likelihood regression, with regularization functions that are motivated by the maximum entropy method. We introduce methods to efficiently handle the high dimensionality of the convex optimization problem as well as the associated semi-sparse covariance matrix, using the L-BFGS-B algorithm and Cholesky factorization. We test the method both on synthetic data as well as on gamma-ray emission from the inner Galaxy, |ℓ|<90{sup o} and | b |<20{sup o}, as observed by the Fermi Large Area Telescope. We finally define a simple reference model that removes most of the residual emission from the inner Galaxy, based on conventional diffuse emission components as well as components for the Fermi bubbles, the Fermi Galactic center excess, and extended sources along the Galactic disk. Variants of this reference model can serve as basis for future studies of diffuse emission in and outside the Galactic disk.

79 ASTRONOMY AND ASTROPHYSICS↗

Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure

ABSTRACT A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous ‘dark core’ – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at $99{{\ \rm per\ cent}}$ confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

Price, M. A.↗

Estimation of many-body quantum Hamiltonians via compressive sensing

We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s sparse in a known basis. The classical postprocessing is a convex optimization problem on the total Hilbert space which is generally not scalable. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Network-Cognizant Design of Decentralized Volt/VAR Controllers

This paper considers the problem of designing decentralized Volt/VAR controllers for distributed energy resources (DERs). The voltage-reactive power characteristics of individual DERs are obtained by solving a convex optimization problem, where given performance objectives (e.g., minimization of the voltage deviations from a given profile) are specified and stability constraints are enforced. The resultant Volt/VAR characteristics are network-cognizant, in the sense that they embed information on the location of the DERs and, consequently, on the effect of reactive-power adjustments on the voltages throughout the feeder. Bounds on the maximum voltage deviation incurred by the controllers are analytically established. Numerical results are reported to corroborate the technical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Matrix Completion Using Alternating Minimization for Distribution System State Estimation

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power flow constraints has been shown to be effective in estimating voltage phasors under low-observability conditions using single-snapshot information. However, the method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems and if multiple-snapshot (time-series) information is used. This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. This algorithm is based on reformulating the matrix completion problem as a bilinear (non-convex) optimization problem, and applying the alternating minimization algorithm to solve this problem. This paper proves the summable convergence of the proposed algorithm, and demonstrates its efficacy and scalability via IEEE 123-bus system and a real utility feeder system. This paper also explores the value of adding more data from the history in terms of computation time and estimation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Resilient Reinforcement in Secure State Estimation against Sensor Attacks with a priori Information

This paper deals with the state estimation problem in the presence of malicious sensor attacks. Unlike the existing work, in this paper, we address the problem with a priori information of the state to be estimated. Specifically, we address three prior knowledge: the sparsity information, (alpha, n_0)-sparsity information, and side information, and in each scenario, we show that the state can be reconstructed even if more sensors are compromised. This implies that the prior information reinforces the system resilience against sensor attacks. Then, an estimator under sensor attacks considering the information is developed and, under a certain condition, the estimator can be relaxed into a tractable convex optimization problem. Further, we extend this analysis to systems in presence of measurement noises, and it is shown that the prior information reduces the state-estimation error caused by the noise. Here, the numerical simulations in a diffusion process finally illustrate the reinforcement and error-reduction results with the information.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Robustness Against Disturbances in Power Systems Under Frequency Constraints

The wide deployment of renewable generation and the gradual decrease in the overall system inertia make modern power grids more vulnerable to transient instabilities and unacceptable frequency fluctuations. Time-domain simulation based assessment of the system robustness against uncertain and stochastic disturbances is extremely time-consuming. In this paper, we develop an alternative approach, which has its roots in the input-output stability analysis for Lur'e systems. Our approach consists of a mathematically rigorous characterization of the external disturbances that the power system is transiently stable and the frequency constraints are not violated. As a result, the derived certificate is efficiently constructed via convex optimization and is shown to be non-conservative for different IEEE test cases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Resilience Analysis of DC Microgrids under Denial of Service Threats

This paper develops a resilience analysis framework to study the fault ride-through capability of direct current (DC) microgrids in unknown denial of service (DoS) cyber incidents. DoS can be a frequent threat to DC microgrids with advanced controllers that hinge on active information exchanges: it can paralyze data communications and cause control ineptness or even system instability. Furthermore, we show that temporal DoS incidents render the DC microgrid cyber-physical topology and parameters time-varying and cause them to jump between faulty conditions. As existing DC microgrid stability analysis results are primarily developed from time-invariant systems, they might not be valid for the DoS interrupted systems. In this paper, we seek to study whether a DC microgrid is resilient against time-varying unknown DoS incidents. The problem is formulated as a stability analysis problem for a system with randomly switching dynamics. Scalable conditions are developed to provide provable resilience guarantees. In addition, we exploit the special structure of the conditions to yield quantified resilience measure by convex optimization techniques. As a result, the measure can be used for the evaluation of the resilience of different DC microgrid design against DoS incidents. We demonstrate the effectiveness of the proposed work using simulation case studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Monitoring Long Term Voltage Instability due to Distribution & Transmission Interaction using Unbalanced μPMU & PMU Measurements

This research extends the idea of the Thevenin equivalent into unbalanced 3φ circuits and proposes a 3φ long-term voltage stability indicator (VSI), that can identify critical loads in a system. Furthermore, in order to identify whether the voltage stability limit is due to the transmission network or a distribution network, a transmission-distribution distinguishing index (TDDI) is proposed. The novelty in the proposed indices is that they can account for the unbalance in the lines and loads, enabling them to use unbalanced phasor measurements naturally. This is supported by mathematical derivations and numerical results. A convex optimization formulation to estimate the 3φ Thevenin equivalent using PMU & μPMU measurements is proposed, making it possible to calculate VSI and TDDI in an online model-free manner. Numerical simulations performed using co-simulation between Pypower and GridlabD are presented for the IEEE 9 bus and the 30 bus transmission networks combined with several modified IEEE 13 node and 37 node distribution networks. These case studies validate the proposed 3φ-VSI and TDDI over a wide range of scenarios and demonstrate the importance of μPMU measurements in identifying the regions causing long term voltage instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Learning Distribution Grid Topologies: A Tutorial

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. Here this tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The feasibility of a piecewise-linear dynamic bowtie filter

Purpose: The prepatient attenuator (or 'bowtie filter') in CT is used to modulate the flux as a function of fan angle of the x-ray beam incident on the patient. Traditional, static bowtie filters are tailored only for very generic scans and for the average patient. The authors propose a design for a dynamic bowtie that can produce a time-dependent piecewise-linear attenuation profile. This dynamic bowtie may reduce dynamic range, dose or scatter, but in this work they focus on its ability to reduce dynamic range, which may be particularly important for systems employing photon-counting detectors. Methods: The dynamic bowtie is composed of a set of triangular wedges. Each wedge is independently moved in order to produce a time-dependent piecewise-linear attenuation profile. Simulations of the bowtie are conducted to estimate the dynamic range reduction in six clinical datasets. The control of the dynamic bowtie is determined by solving a convex optimization problem, and the dose is estimated using Monte Carlo techniques. Beam hardening artifacts are also simulated. Results: The dynamic range is reduced by factors ranging from 2.4 to 27 depending on the part of the body studied. With a dynamic range minimization objective, the dose to the patient can be reduced from 6% to 33% while maintaining peak image noise. Further reduction in dose may be possible with a specific dose reduction objective. Beam hardening artifacts are suppressed with a two-pass algorithm. Conclusions: A dynamic bowtie producing a time-dependent, piecewise-linear attenuation profile is possible and can be used to modulate the flux of the scanner to the imaging task. Initial simulations show a large reduction in dynamic range. Several other applications are possible.

60 APPLIED LIFE SCIENCES↗

A general framework of noise suppression in material decomposition for dual-energy CT

Purpose: As a general problem of dual-energy CT (DECT), noise amplification in material decomposition severely reduces the signal-to-noise ratio on the decomposed images compared to that on the original CT images. In this work, the authors propose a general framework of noise suppression in material decomposition for DECT. The method is based on an iterative algorithm recently developed in their group for image-domain decomposition of DECT, with an extension to include nonlinear decomposition models. The generalized framework of iterative DECT decomposition enables beam-hardening correction with simultaneous noise suppression, which improves the clinical benefits of DECT. Methods: The authors propose to suppress noise on the decomposed images of DECT using convex optimization, which is formulated in the form of least-squares estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, the authors include the inverse of the estimated variance–covariance matrix of the decomposed images as the penalty weight in the least-squares term. Analytical formulas are derived to compute the variance–covariance matrix for decomposed images with general-form numerical or analytical decomposition. As a demonstration, the authors implement the proposed algorithm on phantom data using an empirical polynomial function of decomposition measured on a calibration scan. The polynomial coefficients are determined from the projection data acquired on a wedge phantom, and the signal decomposition is performed in the projection domain. Results: On the Catphan{sup ®}600 phantom, the proposed noise suppression method reduces the average noise standard deviation of basis material images by one to two orders of magnitude, with a superior performance on spatial resolution as shown in comparisons of line-pair images and modulation transfer function measurements. On the synthesized monoenergetic CT images, the noise standard deviation is reduced by a factor of 2–3. By using nonlinear decomposition on projections, the authors’ method effectively suppresses the streaking artifacts of beam hardening and obtains more uniform images than their previous approach based on a linear model. Similar performance of noise suppression is observed in the results of an anthropomorphic head phantom and a pediatric chest phantom generated by the proposed method. With beam-hardening correction enabled by their approach, the image spatial nonuniformity on the head phantom is reduced from around 10% on the original CT images to 4.9% on the synthesized monoenergetic CT image. On the pediatric chest phantom, their method suppresses image noise standard deviation by a factor of around 7.5, and compared with linear decomposition, it reduces the estimation error of electron densities from 33.3% to 8.6%. Conclusions: The authors propose a general framework of noise suppression in material decomposition for DECT. Phantom studies have shown the proposed method improves the image uniformity and the accuracy of electron density measurements by effective beam-hardening correction and reduces noise level without noticeable resolution loss.

60 APPLIED LIFE SCIENCES↗

MO-DE-207A-02: A Feature-Preserving Image Reconstruction Method for Improved Pancreaticlesion Classification in Diagnostic CT Imaging

Purpose: To develop a feature-preserving model based image reconstruction (MBIR) method that improves performance in pancreatic lesion classification at equal or reduced radiation dose. Methods: A set of pancreatic lesion models was created with both benign and premalignant lesion types. These two classes of lesions are distinguished by their fine internal structures; their delineation is therefore crucial to the task of pancreatic lesion classification. To reduce image noise while preserving the features of the lesions, we developed a MBIR method with curvature-based regularization. The novel regularization encourages formation of smooth surfaces that model both the exterior shape and the internal features of pancreatic lesions. Given that the curvature depends on the unknown image, image reconstruction or denoising becomes a non-convex optimization problem; to address this issue an iterative-reweighting scheme was used to calculate and update the curvature using the image from the previous iteration. Evaluation was carried out with insertion of the lesion models into the pancreas of a patient CT image. Results: Visual inspection was used to compare conventional TV regularization with our curvature-based regularization. Several penalty-strengths were considered for TV regularization, all of which resulted in erasing portions of the septation (thin partition) in a premalignant lesion. At matched noise variance (50% noise reduction in the patient stomach region), the connectivity of the septation was well preserved using the proposed curvature-based method. Conclusion: The curvature-based regularization is able to reduce image noise while simultaneously preserving the lesion features. This method could potentially improve task performance for pancreatic lesion classification at equal or reduced radiation dose. The result is of high significance for longitudinal surveillance studies of patients with pancreatic cysts, which may develop into pancreatic cancer. The Senior Author receives financial support from Siemens GmbH Healthcare.

60 APPLIED LIFE SCIENCES↗

A multiresolution spatial parametrization for the estimation of fossil-fuel carbon dioxide emissions via atmospheric inversions.

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. To that end, we construct a multiresolution spatial parametrization for fossil-fuel CO2 emissions (ffCO2), to be used in atmospheric inversions. Such a parametrization does not currently exist. The parametrization uses wavelets to accurately capture the multiscale, nonstationary nature of ffCO2 emissions and employs proxies of human habitation, e.g., images of lights at night and maps of built-up areas to reduce the dimensionality of the multiresolution parametrization. The parametrization is used in a synthetic data inversion to test its suitability for use in atmospheric inverse problem. This linear inverse problem is predicated on observations of ffCO2 concentrations collected at measurement towers. We adapt a convex optimization technique, commonly used in the reconstruction of compressively sensed images, to perform sparse reconstruction of the time-variant ffCO2 emission field. We also borrow concepts from compressive sensing to impose boundary conditions i.e., to limit ffCO2 emissions within an irregularly shaped region (the United States, in our case). We find that the optimization algorithm performs a data-driven sparsification of the spatial parametrization and retains only of those wavelets whose weights could be estimated from the observations. Further, our method for the imposition of boundary conditions leads to a 10 computational saving over conventional means of doing so. We conclude with a discussion of the accuracy of the estimated emissions and the suitability of the spatial parametrization for use in inverse problems with a significant degree of regularization.

Ray, Jaideep↗

Interpretable Net Load Forecasting Using Smooth Multiperiodic Features

We consider the problem of forecasting net load over a horizon such as one day, using a trailing window of past net load values as well as date and time. We focus on three variations on this problem: point forecasts, marginal quantile forecasts, and generating conditional samples of the future value. We propose a method that relies on linear regression using some custom engineered time-based features to capture multiple periodicities, such as daily, weekly, and seasonal, and their interactions. Our proposed models are readily interpretable, and rely on efficient and reliable convex optimization [1] to fit. We illustrate our method on four years worth of hourly net load data, comparing predictions made with various subsets of the features.

Ogut, Mehmet G↗

Time Dilated Bundt Cake Analysis of PV Output [Poster]

We present a novel method for modeling time-dependent statistics in the power signal generated by a photovoltaic (PV) system. Our white-box machine learning method is interpretable and auditable, based on principles of multiperiodic basis functions and convex optimization. Our proposed method of time dilating the daily signal to remove night time values results in a novel representation of PV power signals, evocative of a ‘Bundt cake’. The proposed model describes the marginal distribution of power output as a function of date and time. The resulting probabilistic model of a PV system can be used to perform a variety of tasks, and here, we demonstrate the application of clear sky detection.

14 SOLAR ENERGY↗