Stochastic compartmental analysis - Model and least squares estimation from time series data
Biomathematical model and least square estimation from time series data of discrete particle population in stochastic compartmental system
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Biomathematical model and least square estimation from time series data of discrete particle population in stochastic compartmental system
As weather-dependent renewable generation increases its share in the generation mix of most electric energy systems, a stochastic unit commitment becomes the natural day-ahead scheduling tool. However, such a tool is generally computationally intractable if a detailed uncertainty description is considered. Taking this into account, we proposed a learning method to make the stochastic unit commitment problem tractable. Here, recent advances in statistical learning and machine learning to address optimization problems can be advantageously applied to the rather intractable stochastic unit commitment problem. Considering these advances, we explore simple learning techniques to drastically reduce the size of a stochastic unit commitment problem without significantly altering its optimal solution. The considered stochastic unit commitment problem is formulated as a two-stage stochastic programming problem. The first stage represents commitment decisions, while the second one represents the operation conditions under different scenarios. Taking into account historical solved instances (or proxies for them), we reduce the size (measured by numbers of constraints and variables) of the stochastic unit commitment problem by (i) fixing unchanged binary variables and by (ii) eliminating inactive inequality constraints. Our numerical results show that the reduced problem generally requires significantly less time to solve while obtaining high-quality solutions, which are very close to or indistinguishable from the one obtained by solving the original problem. We use an Illinois 200-bus system to illustrate and characterize the performance of the proposed problem-reduction method.
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.
This talk goes into the algorithmic work done under the Forest project in order to solve expensive power grid models. We explore multiple fidelities of models that balance accuracy and computational expense. We use bundling strategies and progressive hedging in order to parallelize large stochastic programs.
We introduce a statistical data model and an associated optimization-based clustering algorithm which allows data vectors to belong to zero, one or several parent clusters.
The major goals of this project were: 1) to use field campaign measurements from DOE’s Atmospheric Radiation Measurement (ARM) program to characterize variability of important parameters describing properties of ice particles in the atmosphere; 2) based on this observational analysis, to develop a parameterization scheme for weather and climate models that stochastically varies these parameters, and implement the new scheme into a weather model called the Weather Research and Forecasting model (WRF); 3) to use WRF coupled with the new stochastic scheme to simulate ARM field campaign thunderstorm cases and analyze how accounting for this parameter variability affects the model simulations. This work was performed jointly between the National Center for Atmospheric Research, University of Oklahoma, and University of Utah. To accomplish these goals, we extended an approach previously developed to characterize the variability in the size distribution of ice particles to parameters that are explicitly represented in models (i.e., relationships between ice particle mass and size, and between particle fall velocity and size). Our project was, to our knowledge, the first to apply observationally-constrained estimates of this parameter variability describing mass-size and fall velocity-size in a modeling framework. Our results showed efficacy of the approach, evaluated using ARM observations. Similarly, to our knowledge, work in this project was the first to propose and evaluate in detail a stochastic approach for unresolved turbulent mixing in high-resolution model simulations against detailed, benchmark large eddy simulations and ARM observations. Results showed some promising behavior, particularly with increased mixing and dilution of air in thunderstorm cores with surrounding environmental air, bringing the stochastic simulations closer to the benchmark large eddy simulations; however, results were somewhat degraded using stochastic mixing compared to observations from the AMIE/DYNAMO field campaign. This project also further refined and applied a modeling methodology called “piggybacking” that can robustly separate dynamical and thermodynamic impacts of model changes, and comparison studies of different models based on cases developed from ARM observations. Finally, this project directly supported three graduate students who completed their PhDs as well as a postdoctoral research fellow.
A stochastic domination analysis model was developed to examine the effect that emerging carbon markets can have on the spatially varying returns and risk profiles of bioenergy crops relative to conventional crops. The code is written in MATLAB, and includes the calculated output. See the README file for instructions to run the code.
Deterministic pathway models that describe the biochemical interactions of a group of related proteins, their complexes, activation through kinase, etc. are often the basis for many systems biology models. Low dose radiation effects present a unique set of challenges to these models including the importance of stochastic effects due to the nature of radiation tracks and small number of molecules activated, and the search for infrequent events that contribute to cancer risks. We have been studying models of the ATM, TGF -Smad and WNT signaling pathways with the goal of applying pathway models to the investigation of low dose radiation cancer risks. Modeling challenges include introduction of stochastic models of radiation tracks, their relationships to more than one substrate species that perturb pathways, and the identification of a representative set of enzymes that act on the dominant substrates. Because several pathways are activated concurrently by radiation the development of modular pathway approach is of interest.
The dependable reporting of methane (CH 4 ) emissions from point sources, such as fugitive leaks from oil and gas infrastructure, is important for profit maximization (retaining more hydrocarbons), evaluating climate impacts, assessing CH 4 fees for regulatory programs, and validating CH 4 intensity in differentiated gas programs. Currently, there are disagreements between emissions reported by different quantification techniques for the same sources. It has been suggested that downwind CH 4 quantification methods using CH 4 measurements on the fence line of production facilities could be used to generate emission estimates from oil and gas operations at the site level, but it is currently unclear how accurate the quantified emissions are. To investigate the accuracy of downwind methods, this study uses fence-line simulated data collected during controlled-release experiments as input for a non-standard closed-path eddy covariance (EC), the Gaussian plume inverse model (GPIM), and the backward Lagrangian stochastic (bLs) model in a range of atmospheric conditions. This study's EC attempt was unsuccessful due to data collection and instrumentation issues, resulting in invalid results characterized by underestimated emissions, large negative fluxes, and cospectra/ogives that deviated from their ideal shapes. Consequently, the EC results could not be compared with the GPIM and bLS model. The bLs model demonstrated the highest accuracy for single-release single-point emissions, though it exhibited greater uncertainty than GPIM under multi-release conditions. Across the GPIM and bLs model, the most reliable quantification was achieved with 15 min averaging and a narrow 5° wind sector range. Although EC was limited in this context, future studies should consider employing a standard EC system and further optimizing GPIM and bLs approaches – particularly for complex multi-source scenarios – to enhance quantification accuracy and reduce uncertainty.
We use a statistical tropical cyclone (TC) model, the North Atlantic Stochastic Hurricane Model (NASHM), in combination with sea-surface temperature (SST) projections from climate models, to estimate regional changes in US TC activity into the 2030s. NASHM is trained on historical variations in TC characteristics with two SST indices: global-tropical mean SST and the difference between tropical North-Atlantic (NA) SST and the rest of the global tropics, often referred to as “relative SST.” Testing confirms the model’s ability to reproduce historical US TC activity, as well as to make skillful predictions. When NASHM is driven by SST projections into the 2030s, overall NA annual TC counts increase, and the fractional increase is the greatest at the highest wind intensities. However, an eastward anomaly in mean TC tracks and an eastward shift in TC formation region result in a geographically-varied signal in US coastal activity. Florida’s Gulf coast is projected to see significant increases in TC activity, compared to the long-term historical mean, and these increases are fractionally greatest at the highest intensities. By contrast, the northwestern US Gulf and the US East Coast will see little change.
Rapid expansion of wind energy development across the world has highlighted the need to better understand turbine-caused avian mortality. The risk to golden eagles (Aquila chrysaetos) is of particular concern due to their small population size and conservation status. Golden eagles subsidize their flight in part by soaring in orographic updrafts, which can place them in conflict with wind turbines utilizing the same low-altitude wind resource. Understanding the behavior of soaring raptors in varying atmospheric conditions can therefore be relevant to predicting and mitigating their risk of collision. We present a predictive movement model that simulates individual paths of golden eagles during directional flight (such as migration) that is subsidized by orographic updraft. We modeled eagles in a 50 km by 50 km study area in Wyoming containing three wind power plants with documented golden eagle collisions with turbines. The movement model is applicable to any region where ground elevation is known at turbine scale (50 m) and wind conditions are known at facility scale (3 km). For a given set of atmospheric conditions, the model simulates movements of thousands of orographic soaring eagles to produce a density map quantifying the relative probability of eagle presence. We validated the simulated tracks with GPS telemetry data showing four directional tracks made by golden eagles transiting through the area in 2019 and 2020. For each eagle track, validation was performed using the ratio of the model-simulated eagle presence likelihood with uniform eagle presence and the presence computed using directed random-walk movements. We found that the predictive performance of the model was significantly better (likelihood ratio 1) for low-altitude movements than high-altitude movements that can involve thermal-soaring. We employed the model to produce seasonal presence maps for migrating golden eagles. We found significant turbine-level variations in eagle presence between northerly and southerly migration routes through the study area. Overall, the proposed model offers a generalizable, probabilistic, and predictive tool to assist wind energy developers, ecologists, wildlife managers, and industry consultants in estimating the potential for conflict between soaring birds and wind turbines, thereby reducing the need for site-specific data on golden eagle movements.
A generalized Markov chain representation of fault dynamics is presented for the case that available modeling of fault growth physics and future environmental stresses can be represented by two independent stochastic process models. A contrived but representatively challenging example will be presented and analyzed, in which uncertainty in the modeling of fault growth physics is represented by a uniformly distributed dice throwing process, and a discrete random walk is used to represent uncertain modeling of future exogenous loading demands to be placed on the system. A finite horizon dynamic programming algorithm is used to solve for an optimal control policy over a finite time window for the case that stochastic models representing physics of failure and future environmental stresses are known, and the states of both stochastic processes are observable by implemented control routines. The fundamental limitations of optimization performed in the presence of uncertain modeling information are examined by comparing the outcomes obtained from simulations of an optimizing control policy with the outcomes that would be achievable if all modeling uncertainties were removed from the system.
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Producing and distributing COVID-19 vaccine during the pandemic is a major logistical challenge requiring careful planning and efficient execution. This report presents information on logistical, policy and technical issues relevant to rapidly fielding a COVID-19 vaccination program. For this study we (a) conducted literature review and subject matter expert elicitation to understand current vaccine manufacturing and distribution capabilities and vaccine allocation strategies, (b) designed a baseline vaccine distribution strategy and modeling strategy to provide insight into the potential for targeted distribution of limited initial vaccine supplies, and (c) developed parametric interfaces to enable vaccine distribution scenarios to be analyzed in depth with Sandias Adaptive Recovery Model that will allow us evaluate the additional sub- populations and alternative distribution scenarios from a public health benefit and associated economic disruption Principal issues, challenges, and complexities that complicate COVID-19 vaccine delivery identified in our literature and subject matter expert investigation include these items: The United States has not mounted an urgent nationwide vaccination campaign in recent history. The existing global manufacturing and distribution infrastructure are not able to produce enough vaccine for the population immediately. Vaccines, once available will be scarce resources. Prioritization for vaccine allocation will be built on existing distribution networks. Vaccine distribution may not have a universal impact on disease transmission and morbidity because of scarcity, priority population demographics, and underlying disease transmission rates. Considerations for designing a vaccine distribution strategy are discussed. A baseline distribution strategy is designed and tested using the Adaptive Recovery Model, which couples a deterministic compartmental epidemiological model and a stochastic network model. We show the impact of this vaccine distribution strategy on hospitalizations, mortality, and contact tracing requirements. This model can be used to quantitatively evaluate alternative distribution scenarios, guiding policy decisions as vaccine candidates are narrowed down.
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