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At least 73 records · Page 4

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

Robust Real-Time Modeling of Distribution Systems with Data-Driven Grid-Wise Observability (Final Technical Report)

The overall objective of this project is to leverage existing and emerging sensor measurements to develop data-driven observability enhancement algorithms as well as robust state estimation and parameter identification techniques to enable real-time grid-wise monitoring and modeling of loads and distributed energy resources (DERs). The project resulted in a holistic framework with the following key components: 1) data-driven and machine learning-based grid-edge visibility enhancement, 2) robust branch-current-based state estimation (BCSE), and 3) robust real-time steady-state and dynamic-state modeling of loads and DERs. The research outcomes have provided utility companies better network visibility, higher-fidelity load/DER models, and more accurate assessment of DERs’ impacts, thus, facilitating the integration of renewable energy sources. The synergistic collaborative project among Iowa State University (ISU), Argonne National Laboratory (ANL), Electric Power Research Center (EPRC), SIEMENS Industry, Alliant Energy, Cedar Falls Utilities (CFU), and Maquoketa Valley Electric Cooperative (MVEC) to leverage the team’s extensive expertise and experience in power distribution systems, state estimation, online modeling and identification, and DER integrations. The proposed frameworks have been verified with industry adopted software and attempted integrated with existing tool wherever possible

24 POWER TRANSMISSION AND DISTRIBUTION↗

Time-Varying Output Delay Compensation-A Model-Free Approach and its Application on Cooperative On-Ramp Merging

This paper presents a model-free approach to compensate for time-varying output delay in networked control systems. The proposed architecture combines a model-free observer and the Smith predictor. The model-free observer estimates the current state while handling modeling errors and uncertainties of the system. The Smith predictor moves the effect of time delay outside the control closed-loop using the estimated delayed output and the actual output of the plant. The proposed method is applied to a cooperative on-ramp merging problem. First, an ultra-local model predictive control is implemented to provide a computationally efficient online speed planner agnostic to the vehicle dynamics. After that, a model-free observer is designed to estimate the current state. Finally, the proposed architecture is tested against a time-varying output delay with an upper bound of 200 milliseconds. The results demonstrate the effectiveness of the proposed method with improved tracking of intervehicle distance.

Waleed khan, Muhammad [The University of Texas at ↗

Master State Distributed Estimator (masde)

The MSE technology provides a distributed state estimation scheme for power utilities by making it a real time dynamic system, versus the static snapshot method used today. This will allow utilities to verify power grid readings and identify false data on the communication network. The prevailing method of estimation takes all the data from the system into a single load flow equation at the utilities command center. This becomes a large algorithm that is very time consuming to solve, providing the engineers only snap shots of the system. The MFD distributes an algorithm to devises that are already installed at various locations on the power grid. This allows for much faster computer times because the algorithms contain magnitudes less data. When each distributed estimator completes its calculation, it sends the results back to the master device to check against all other distributed estimators.

Reen, DylanW.↗

Large-scale Nonlinear Approaches for Inference of Reporting Dynamics and Unobserved SARS-CoV-2 Infections

This work focuses on estimation of unknown states and parameters in a discrete-time, stochastic, SEIR model using reported case counts and mortality data. An SEIR model is based on classifying individuals with respect to their status in regards to the progression of the disease, where S is the number individuals who remain susceptible to the disease, E is the number of individuals who have been exposed to the disease but not yet infectious, I is the number of individuals who are currently infectious, and R is the number of recovered individuals. For convenience, we include in our notation the number of infections or transmissions, T, that represents the number of individuals transitioning from compartment S to compartment E over a particular interval. Similarly, we use C to represent the number of reported cases.

59 BASIC BIOLOGICAL SCIENCES↗

Joint neutron/molecular dynamics vibrational spectroscopy reveals softening of HIV-1 protease upon binding of a tight inhibitor

Biomacromolecules are inherently dynamic, and their dynamics are interwoven into function. The fast collective vibrational dynamics in proteins occurs in the low picosecond timescale corresponding to frequencies of ~5-50 cm -1 . This sub-to-low THz frequency regime covers the low-amplitude collective breathing motions of a whole protein and vibrations of the constituent secondary structure elements, such as α-helices, β-sheets and loops. We have used inelastic neutron scattering experiments in combination with molecular dynamics simulations to demonstrate the vibrational dynamics softening of HIV-1 protease, a target of HIV/AIDS antivirals, upon binding of a tight clinical inhibitor darunavir. Changes in the vibrational density of states of matching structural elements in the two monomers of the homodimeric protein are not identical, indicating asymmetric effect of darunavir on the vibrational dynamics. Three of the 11 major secondary structure elements contribute over 40% to the overall changes in the vibrational density of states upon darunavir binding. Molecular dynamics simulations informed by experiments allowed us to estimate that the altered vibrational dynamics of the protease would contribute -3.6 kcal/mol -1 at 300 K, or 25%, to the free energy of darunavir binding. As HIV-1 protease drug resistance remains a concern, our results open a new avenue to help establish a direct quantitative link between protein vibrational dynamics and drug resistance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distributed State Estimation Over Time-Varying Graphs: Exploiting the Age-of-Information

Here, we study the problem of designing a distributed observer for an LTI system over a time-varying communication graph. The limited existing work on this topic imposes various restrictions either on the observation model or on the sequence of communication graphs. In contrast, we propose a single-time-scale distributed observer that works under mild assumptions. Specifically, our communication model only requires strong-connectivity to be preserved over non-overlapping, contiguous intervals that are even allowed to grow unbounded over time. We show that under suitable conditions that bound the growth of such intervals, joint observability is sufficient to track the state of any discrete-time LTI system exponentially fast, at any desired rate. We also develop a variant of our algorithm that is provably robust to worst-case adversarial attacks, provided the sequence of graphs is sufficiently connected over time. The key to our approach is the notion of a "freshness-index" that keeps track of the age-of-information being diffused across the network. Such indices enable nodes to reject stale estimates of the state, and, in turn, contribute to stability of the error dynamics.

42 ENGINEERING↗

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗

Whose Gas is it anyway? Differentiating the Source of a Large Soil Vapor Plume beneath Two Adjacent Waste Sites - 20487

DOE contractor CH2M Hill Plateau Remediation Company is currently responsible for conducting groundwater contamination monitoring at several RCRA treatment, storage, and disposal units located on the Hanford Site in Richland, Washington State. The Nonradioactive Dangerous Waste Landfill treatment, storage, and disposal unit presents a distinct groundwater monitoring problem because of a large multi-contaminant soil vapor plume beneath it that is a likely source of low-level volatile organic compound groundwater contamination. Adjacent to Nonradioactive Dangerous Waste Landfill is the Solid Waste Landfill. Volatile organic compounds are inventory components of both the Nonradioactive Dangerous Waste Landfill and the Solid Waste Landfill. Therefore, it is possible that both sites could be contributing to the soil vapor plume. For regulatory purposes, it is important to differentiate which site is the primary contributor of volatile organic compounds to the plume. An approach was developed to identify the primary volatile organic compound source of the soil vapor plume beneath Nonradioactive Dangerous Waste Landfill and Solid Waste Landfill. The site conceptual model hypothesis of vapor-phase volatile organic compound transport to the dissolved phase in groundwater was tested by a simple mathematical model of vapor/liquid equilibrium concentrations at the groundwater/air interface. Once it was shown that vapor-phase volatile organic compound transport to groundwater was a valid conceptual model for Nonradioactive Dangerous Waste Landfill and Solid Waste Landfill, spatial and statistical methods were used to determine the primary site contributing to the majority of volatile organic compounds to the soil vapor plume. Average groundwater chloroform, tetrachloroethene, and trichloroethene concentrations from Nonradioactive Dangerous Waste Landfill and Solid Waste Landfill monitoring network wells were plotted on maps of the facilities and immediate vicinities and compared to soil vapor sampling probe locations. Principal component analysis and mixing ratios were used to identify source contributions of each treatment, storage, and disposal unit to the plume. Results of the vapor/liquid equilibrium concentrations mathematical model showed that transport phenomena outweigh steady-state equilibria. Estimated vapor/liquid equilibrium concentrations were considerably lower than soil vapor measurements. The results indicate that dynamic vadose zone and groundwater factors such as decreased vapor concentrations with depth, vapor dilution from dispersion in the vadose zone, and advective and diffusional volatile organic compound dilution in groundwater result in groundwater volatile organic compound concentrations much less than would be measured under steady-state equilibrium conditions. Site source contribution differentiation by principal component analysis and mixing ratios was inconclusive using actual soil gas data because of the similarity in concentration values in both datasets for Nonradioactive Dangerous Waste Landfill and Solid Waste Landfill. Similar data populations suggest mixing of the vapor contributions from both sites by dispersion through the soil matrix pore spaces. However, when groundwater volatile organic compound data were compared between the Nonradioactive Dangerous Waste Landfill and Solid Waste Landfill monitoring networks, Solid Waste Landfill mean concentrations were higher, suggesting more vapor-phase volatile organic compound transport to groundwater at those locations. Simulated volatile organic compound soil vapor and groundwater datasets created to test the methods developed for this study show that the method can be successful in source differentiation when significantly different datasets are compared. This paper will describe a method of testing a conceptual model for vapor-phase contaminant transport to groundwater and for differentiating site sources of contaminants comprising a mixed-constituent soil vapor plume. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Getting lost tracking the carbon footprint of hydropower

In the transition to low-carbon electricity, well-quantified estimates of carbon dynamics are needed to ensure that emissions reduction targets are achieved. Here we review the state of the science on carbon accounting for hydropower reservoirs and identify limitations and future solutions. Nearly all research on reservoir greenhouse-gas (GHG) emissions has focused on individual reservoirs in isolation without considering their position in a freshwater network draining organic matter from upstream watersheds or the coordinated operation of reservoir cascades. Second, carbon inventories have extrapolated from a small, non-probabilistic sample of highly variable measurements of GHG emissions to unsampled reservoirs. A stronger statistical foundation is needed to estimate a global inventory and its uncertainty. Third, attribution to hydropower is based on ranks assigned to reservoir purpose. Instead, the physical influence of hydropower on carbon dynamics could be directly measured. Fourth, current carbon-accounting practices neglect time. A time-varying approach would quantify variation in emissions for electricity portfolios from changes in the fuel mix at different times and account for ancillary services, i.e., the ability to support the grid when variable renewables are not available without using natural gas. Reservoirs also sequester a significant portion of inflowing carbon in sediments and slow the carbon cycle by delaying the return of carbon to the atmosphere for decades to centuries. Together, these refinements would help to illuminate pathways toward meeting energy demand with the longest-possible delay in returning carbon to the atmosphere and without adding ancient sources to the pool of carbon cycling through aquatic ecosystems.

13 HYDRO ENERGY↗

Derivative-based SINDy (DSINDy): Addressing the challenge of discovering governing equations from noisy data

Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a predetermined basis in the states and finds the expansion coefficients through linear regression with sparsity constraints. This approach requires an accurate estimation of the state time derivatives, which is not necessarily possible in the high-noise regime without additional constraints. We present an approach called Derivative-based SINDy (DSINDy) that combines two novel methods to improve ODE recovery at high-noise levels. First, we denoise the state variables by applying a projection operator that leverages the assumed basis for the system dynamics. Second, we use a second order cone program (SOCP) to find the derivative and governing equations simultaneously. We derive theoretical results for the projection-based denoising step, which allow us to estimate the values of hyperparameters used in the SOCP formulation. This underlying theory helps limit the number of required user-specified parameters. Finally, we present results demonstrating that our approach leads to improved system recovery for the Van der Pol oscillator, the Duffing oscillator, the Rössler attractor, and the Lorenz 96 model.

97 MATHEMATICS AND COMPUTING↗

Integration of AI/ML with Data Assimilation for Earth System Prediction

Focal Area(s): Development of dynamically consistent AI/ML methods that can integrate with the data assimilation cycle to improve the efficiency and effectiveness of state estimation and prediction at short to medium range forecast horizons. Science Challenge: This white paper addresses a first step toward complete integration of AI/ML and DA. Here, we address model emulation and its application to simple coupled atmosphere-ocean dynamics for use in data assimilation applications.

54 ENVIRONMENTAL SCIENCES↗

Quantum simulations of excited states with active-space downfolded Hamiltonians

Many-body techniques based on the double unitary coupled cluster ansatz (DUCC) can be used to downfold electronic Hamiltonians into low-dimensional active spaces. It can be shown that the resulting dimensionality reduced Hamiltonians are amenable for quantum computing. Recent studies performed for several benchmark systems using quantum phase estimation (QPE) algorithms demonstrated that these formulations can recover a significant portion of ground-state dynamical correlation effects that stem from the electron excitations outside of the active space. These results have also been confirmed in studies of ground-state potential energy surfaces using quantum simulators. In this letter, we study the effectiveness of the DUCC formalism in describing excited states. We also emphasize the role of the QPE formalism and its stochastic nature in discovering/identifying excited states or excited-state processes in situations when the knowledge about the true configurational structure of a sought after excited state is limited or postulated (due to the specific physics driving excited-state processes of interest). In this context, we can view the QPE algorithm as an engine for verifying various hypotheses for excited-state processes and providing statistically meaningful results that correspond to the electronic state(s) with the largest overlap with a postulated configurational structure. We illustrate these ideas on examples of strongly cor- related molecular systems, characterized by small energy gaps and high density of quasi-degenerate states around the Fermi level.

quantum chemistry, quantum computing, computationa↗

Dynamic Queue Prediction at Signalized Intersections with Fusing Sensory Information and Connected Vehicles

Queue length is one of the most essential metrics for indicating traffic conditions at signalized intersections. Most existing studies mainly focus on queue length estimation in a retrieving way which cannot effectively predict the future state of vehicle in queue. This paper proposes an innovative dynamic queue prediction model in a vehicle-infrastructure cooperative way. The proposed dynamic queue predictor can customize the queue prediction using the trajectories of preceding vehicles from radar detection with varying information from loop detectors and connected vehicles (CVs). The dynamic queue prediction accuracy can be further improved with at least one present CV in the same cycle. With the accurate dynamic queue prediction, we present a case study of Queue-Aware Eco-Approach and Departure (QEAD) to provide an online optimal vehicle trajectory considering both the signal status and preceding vehicle's future status in queue. The proposed framework and algorithms are of pragmatic significance and one of its advanced features is the ability to work under low penetration rate of CVs. The test using Next Generation SIMulation (NGSIM) dataset and a case study in VISSIM microscopic simulation show promising results.

Ye, Fei↗

Optimization-Based Fast-Frequency Estimation and Control of Low-Inertia Microgrids

The lack of inertial response from non-synchronous, inverter-based generation in microgrids makes the power system vulnerable to a large rate of change of frequency (ROCOF) and frequency excursions. Energy storage systems (ESSs) can be utilized to provide fast-frequency support to prevent such large excursions in the system. However, fast-frequency support is a power-intensive application that has a significant impact on the ESS lifetime. In this paper, a framework that allows the ESS operator to provide fast-frequency support as a service is proposed. The framework maintains the desired quality-of-service (limiting the ROCOF and frequency) while taking into account the ESS lifetime and physical limits. The framework utilizes moving horizon estimation (MHE) to estimate the frequency deviation and ROCOF from noisy phase-locked loop (PLL) measurements. These estimates are employed by a model predictive control (MPC) algorithm that computes control actions by solving a finite-horizon, online optimization problem. Additionally, this approach avoids oscillatory behavior induced by delays that are common when using low-pass filters as with traditional derivative-based (virtual inertia) controllers. MATLAB/Simulink simulations on a test system from Cordova, Alaska, show the effectiveness of the MHE-MPC approach to reduce frequency deviations and ROCOF of a low-inertia microgrid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Correlation between Sensor Performance, Autonomy Performance and Fuel-Efficiency in Semi-Truck Platoons

Semi-trucks, specifically class-8 trucks, have recently become a platform of interest for autonomy systems. Platooning involves multiple trucks following each n close proximity, with only the lead truck being manually driven and the rest being controlled autonomously. This approach to semi-truck autonomy is easily integrated on existing platforms, reduces delivery times, and reduces green- house gas emissions via fuel economy benefits. Level 1 SAE fuel studies were performed on class-8 trucks operating with the Auburn Cooperative Adaptive Cruise Control (CACC) system, and fuel savings up to 10-12% were seen. Enabling platooning autonomy required the use of radar, global positioning systems (GPS), and wireless vehicle-to-vehicle (V2V) communication. Poor measurements and state estimates can lead to incorrect or missing positioning data, which can lead to unnecessary dynamics and finally wasted fuel. This is especially an issue if deceleration is applied in response to a bad measurement. In this study, a faulty radar was shown to cause a greater than 5% increase in fuel consumption. The mechanism of this fuel consumption increase is investigated and applied to other types of sensor failures to indicate their potential effects on fuel economy. This analysis indicates that poor GPS signals over short time can be largely filtered out, with no real gain or loss of fuel economy. V2V communications were intentionally limited by causing interference, which resulted in dropped communication packets over a small physical area, but not an appreciable impact on fuel economy.

vehicle platooning, sensor performance, semi-auton↗

PERSIANN Dynamic Infrared–Rain Rate Model (PDIR) for High-Resolution, Real-Time Satellite Precipitation Estimation

Precipitation measurements with high spatiotemporal resolution are a vital input for hydrometeorological and water resources studies; decision-making in disaster management; and weather, climate, and hydrological forecasting. Moreover, real-time precipitation estimation with high precision is pivotal for the monitoring and managing of catastrophic hydroclimate disasters such as flash floods, which frequently transpire after extreme rainfall. While algorithms that exclusively use satellite infrared data as input are attractive owing to their rich spatiotemporal resolution and near-instantaneous availability, their sole reliance on cloud-top brightness temperature (T b ) readings causes underestimates in wet regions and overestimates in dry regions—this is especially evident over the western contiguous United States (CONUS). We introduce an algorithm, the Precipitation Estimations from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) Dynamic Infrared–Rain rate model (PDIR), which utilizes climatological data to construct a dynamic (i.e., laterally shifting) T b –rain rate relationship that has several notable advantages over other quantitative precipitation-estimation algorithms and noteworthy skill over the western CONUS. Validation of PDIR over the western CONUS shows a promising degree of skill, notably at the annual scale, where it performs well in comparison to other satellite-based products. Analysis of two extreme landfalling atmospheric rivers show that solely IR-based PDIR performs reasonably well compared to other IR- and PMW-based satellite rainfall products, marking its potential to be effective in real-time monitoring of extreme storms. This research suggests that IR-based algorithms that contain the spatiotemporal richness and near-instantaneous availability needed for rapid natural hazards response may soon contain the skill needed for hydrologic and water resource applications.

54 ENVIRONMENTAL SCIENCES↗