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Results for “Optimization Under Uncertainty”

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DOE OSTI2018

Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

Here, a massively parallel method to build large transition rate matrices from temperature-accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher-scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature acceleration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Sandia Fracture Challenge 3: detailing the Sandia Team Q failure prediction strategy

The third Sandia Fracture Challenge illustrated the geometric and material uncertainties presented by modern additive manufacturing techniques. Tasked with the challenge of predicting failure of a complex additively-manufactured geometry made of 316L stainless steel, we combined a rigorous material calibration scheme with a number of statistical assessments of problem uncertainties. Particularly, we used optimization techniques to calibrate a rate-dependent and anisotropic Hill plasticity model to represent material deformation coupled with a damage model driven by void growth and nucleation. Through targeted simulation studies we assessed the influence of internal voids and surface flaws on the specimens of interest in the challenge which guided our material modeling choices. Employing the Kolmogorov–Smirnov test statistic, we developed a representative suite of simulations to account for the geometric variability of test specimens and the variability introduced by material parameter uncertainty. This method allowed the team to successfully predict the failure mode of the experimental test population as well as the global response with a high degree of accuracy.

316L stainless steel↗

DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Renewable electricity capacity planning with uncertainty at multiple scales

Abstract We formulate and compare optimization models of investment in renewable generation using a suite of social planning models that compute optimal generation capacity investments for a hydro-dominated electricity system where inflow uncertainty results in a risk of energy shortage. The models optimize the expected cost of capacity expansion and operation allowing for investments in hydro, geothermal, solar, wind, and thermal plant, as well as battery storage for smoothing load profiles. A novel feature is the integration of uncertain seasonal hydroelectric energy supply and short-term variability in renewable supply in a two-stage stochastic programming framework. The models are applied to data from the New Zealand electricity system and used to estimate the costs of moving to a 100% renewable electricity system by 2035. We also explore the outcomes obtained when applying different forms of CO 2 constraint that limit respectively non-renewable capacity, non-renewable generation, and CO 2 emissions on average, almost surely, or in a chance-constrained setting, and show how our models can be used to investigate the merits of a proposed pumped-hydro scheme in New Zealand’s South Island.

Ferris, Michael C.↗

DOE OSTI2017

The impacts of oceanic deep temperature perturbations in the North Atlantic on decadal climate variability and predictability

Decadal climate predictability in the North Atlantic is largely related to ocean low frequency variability, whose sensitivity to initial conditions is not very well understood. Recently, three-dimensional oceanic temperature anomalies optimally perturbing the North Atlantic Mean Temperature (NAMT) have been computed via an optimization procedure using a linear adjoint to a realistic ocean general circulation model. The spatial pattern of the identified perturbations, localized in the North Atlantic, has the largest magnitude between 1000 and 4000 m depth. In the present study, the impacts of these perturbations on NAMT, on the Atlantic meridional overturning circulation (AMOC), and on climate in general are investigated in a global coupled model that uses the same ocean model as was used to compute the three-dimensional optimal perturbations. In the coupled model, these perturbations induce AMOC and NAMT anomalies peaking after 5 and 10 years, respectively, generally consistent with the ocean-only linear predictions. To further understand their impact, their magnitude was varied in a broad range. For initial perturbations with a magnitude comparable to the internal variability of the coupled model, the model response exhibits a strong signature in sea surface temperature and precipitation over North America and the Sahel region. The existence and impacts of these ocean perturbations have important implications for decadal prediction: they can be seen either as a source of predictability or uncertainty, depending on whether the current observing system can detect them or not. In fact, comparing the magnitude of the imposed perturbations with the uncertainty of available ocean observations such as Argo data or ocean state estimates suggests that only the largest perturbations used in this study could be detectable. This highlights the importance for decadal climate prediction of accurate ocean density initialisation in the North Atlantic at intermediate and greater depths.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗

DOE OSTI2014

WE-G-16A-01: Evolution of Radiation Treatment Planning

Welcome and Introduction - Lawrence N. Rothenberg This symposium is one a continuing series of presentations at AAPM Annual Meetings on the historical aspects of medical physics, radiology, and radiation oncology that have been organized by the AAPM History Committee. Information on previous presentations including “Early Developments in Teletherapy” (Indianapolis 2013), “Historical Aspects of Cross-Sectional Imaging” (Charlotte 2012), “Historical Aspects of Brachytherapy” (Vancouver 2011), “50 Years of Women in Medical Physics” (Houston 2008), and “Roentgen's Early Investigations” (Minneapolis 2007) can be found in the Education Section of the AAPM Website. The Austin 2014 History Symposium will be on “Evolution of Radiation Treatment Planning.” Overview - Radhe Mohan Treatment planning is one of the most critical components in the chain of radiation therapy of cancers. Treatment plans of today contain a wide variety of sophisticated information conveying the potential clinical effectiveness of the designed treatment to practitioners. Examples of such information include dose distributions superimposed on three- or even four-dimensional anatomic images; dose volume histograms, dose, dose-volume and dose-response indices for anatomic structures of interest; etc. These data are used for evaluating treatment plans and for making treatment decisions. The current state-of-the-art has evolved from the 1940s era when the dose to the tumor and normal tissues was estimated approximately by manual means. However, the symposium will cover the history of the field from the late-1950's, when computers were first introduced for treatment planning, to the present state involving the use of high performance computing and advanced multi-dimensional anatomic, functional and biological imaging, focusing only on external beam treatment planning. The symposium will start with a general overview of the treatment planning process including imaging, structure delineation, assignment of dose requirements, consideration of uncertainties, selection of beam configurations and shaping of beams, and calculations, optimization and evaluation of dose distributions. This will be followed by three presentations covering the evolution of treatment planning, which parallels the evolution of computers, availability of advanced volumetric imaging and the development of novel technologies such as dynamic multi-leaf collimators and online image guidance. This evolution will be divided over three distinct periods - prior to 1970's, the 2D era; from 1980 to the mid-1990's, the 3D era; and from the mid 1990's to today, the IMRT era. When the World was Flat: The Two-Dimensional Radiation Therapy Era” - Jacob Van Dyk In the 2D era, anatomy was defined with the aid of solder wires, special contouring devices and projection x-rays. Dose distributions were calculated manually from single field, flat surface isodoses on transparencies. Precalculated atlases of generic dose distributions were produced by the International Atomic Energy Agency. Massive time-shared main frames and mini-computers were used to compute doses at individual points or dose distributions in a single plane. Beam shapes were generally rectangular, with wedges, missing tissue compensators and occasional blocks to shield critical structures. Dose calculations were measurement-based or they used primary and scatter calculations based on scatter-air ratio methodologies. Dose distributions were displayed on line printers as alpha-numeric character maps or isodose patterns made with pen plotters. More than Pretty Pictures: 3D Treatment Planning and Conformal Therapy - Benedick A. Fraass The introduction of computed tomography allowed the delineation of anatomy three-dimensionally and, supported partly by contracts from the National Cancer Institute, made possible the introduction and clinical use of 3D treatment planning, leading to development and use of 3D conformal therapy in the 1980's. 3D computer graphics and 3D anatomical structure definitions made possible Beam's Eye View (BEV) displays, making conformal beam shaping and much more sophisticated beam arrangements possible. These conformal plans significantly improved target dose coverage as well as normal tissue sparing. The use of dose volume histograms, gross/clinical/planning target volumes, MRI and PET imaging, multileaf collimators, and computer-controlled treatment delivery made sophisticated planning approaches practical. The significant improvements in dose distributions and analysis achievable with 3D conformal therapy made possible formal dose escalation and normal tissue tolerance clinical studies that set new and improved expectations for improved local control and decreasing complications in many clinical sites. From the Art to the State of the Art: Inverse Planning and IMRT - Thomas R. Bortfeld While the potential of intensity modulation was recognized in the mid- 1980's, intensity-modulated radiotherapy (IMRT) did not become a reality until the mid-1990's. Broad beams of photons could be sub-divided into narrow beamlets whose intensities could be determined using sophisticated optimization algorithms to appropriately balance tumor dose with normal tissue sparing. The development of dynamic multi-leaf collimators (on conventional linear accelerators as well as in helical delivery devices) enabled the efficient delivery of IMRT. The evolution of IMRT planning is continuing in the form of Volumetric Modulated Arc Therapy (VMAT) and through advanced optimization tools, such as multi-criteria optimization, automated IMRT planning, and robust optimization to protect dose distributions against uncertainties. IMRT also facilitates “dose painting” in which different sub-volumes of the target are prescribed different doses. Clearly, these advancements are being made possible by the increasing power and lower cost of computers and developments in other fields such as imaging and operations research. Summary - Radhe Mohan The history does not end here. The advancement of treatment planning is expected to continue, leading to further automation and improvements in conformality and robustness of dose distributions, particularly in the area of particle therapy. Radiobiological modeling will gain emphasis as part of the planning process. Learning Objectives: The scope of changes in technology and the capabilities of radiation treatment planning The impact of these changes in the quality of treatment plans and optimality of dose distributions The impact of development in other fields (imaging, computers, operations research, etc.) on the evolution of radiation treatment planning.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination

The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Learning and Fast Adaptation for Grid Emergency Control via Deep Meta Reinforcement Learning

As power systems are undergoing a significant transformation with more uncertainties, less inertia and closer to operation limits, there is increasing risk of large outages. Thus, there is an imperative need to enhance grid emergency control to maintain system reliability and security. Towards this end, great progress has been made in developing deep reinforcement learning (DRL) based grid control solutions in recent years. However, existing DRL-based solutions have two main limitations: 1) they cannot handle well with a wide range of grid operation conditions, system parameters, and contingencies; 2) they generally lack the ability to fast adapt to new grid operation conditions, system parameters, and contingencies, limiting their applicability for real-world applications. Here, in this paper, we mitigate these limitations by developing a novel deep meta-reinforcement learning (DMRL) algorithm. The DMRL combines the meta strategy optimization together with DRL, and trains policies modulated by a latent space that can quickly adapt to new scenarios. We test the developed DMRL algorithm on the IEEE 300-bus system. We demonstrate fast adaptation of the meta-trained DRL polices with latent variables to new operating conditions and scenarios using the proposed method, which achieves superior performance compared to the state-of-the-art DRL and model predictive control (MPC) methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Isotherm modeling and techno-economic analysis of a TSA moving bed process using a tetraamine-appended MOF for NGCC applications

Tetraamine-appended metal-organic frameworks (MOF) are a new family of amine-functionalized MOF materials that show potential for CO 2 capture from flue gas conditions relevant to natural gas combined cycle (NGCC) power plants. This work presents isotherm modeling of the tetraamine-appended MOF Mg 2 (dobpdc)(3-4-3)(dobpdc 4- =4,4'-dioxidobiphenyl-3,3'dicarboxylate;3-4-3=N,N'bis(3-aminopropyl)-1,4-diaminobutane), process modeling, scale up, and a techno-economic optimization of a moving bed Temperature Swing Adsorption (TSA) process for carbon capture using this sorbent. This MOF exhibits a unique two-step CO 2 adsorption profile in three different pressure ranges. Thus, arctangent-based logistic functions and, quadratic and Langmuir models were employed to represent such isotherm behavior. The results of the isotherm model show good fitting vs the experimental data with an RMSE of 0.41. Here, to model the carbon capture process, the isotherm model was embedded into a moving bed contactor model, and this was used to simulate a TSA CO 2 capture cycle and evaluate cost-optimal designs considering flue gas from a -650 MWe NGCC power plant. The capital cost model consists of CAPEX correlations for reactors, compressors, ducting, etc., while the operating costs include steam, water, chemicals, and electricity (following NETL's quality guidelines for energy systems studies). A techno-economic optimization of the capture system was performed by using NETL's Framework for the Optimization and Quantification of Uncertainty and Surrogates tool (FOQUS). Results suggest that a moving bed carbon capture system with tetraamine-appended MOF can be competitive compared to conventional MEA solvent-based capture processes for NGCC plants, when a heat recovery efficiency of at least 40% is achieved, and MOF materials can be produced at a cost below -$9/kg.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Data-Driven Optimization of Pixelated CdZnTe Spectrometers for Uranium Enrichment Assay

Here, in recent work [Vavrek et al. (2025)], we developed the performance optimization framework spectre-ml for gamma spectrometers with variable performance across many readout channels. The framework uses non-negative matrix factorization (NMF) and clustering to learn groups of similarly-performing channels and sweep through various learned channel combinations to optimize the performance tradeoff of including worse-performing channels for better total efficiency. In this work, we integrate the pyGEM uranium enrichment assay code with our spectre-ml framework, and show that the U-235 enrichment relative uncertainty can be directly used as an optimization target. We find that this optimization reduces relative uncertainties after a 30 -minute measurement by an average of 20%, as tested on six different H3D M400 CdZnTe spectrometers, which can significantly improve uranium non-destructive assay measurement times in nuclear safeguards contexts. Additionally, this work demonstrates that the spect re-ml optimization framework can accommodate arbitrary end-user spectroscopic analysis code and performance metrics, enabling future optimizations for complex Pu spectra.

Gamma-ray detection↗

DOE OSTI2024

Multistage Stochastic optimization for mid-term integrated generation and maintenance scheduling of cascaded hydroelectric system with renewable energy uncertainty

The uncertainties resulting from the escalating penetration of renewable energy resources pose severe challenges to the efficient operation of modern power systems. Hydroelectricity is characterized by its flexibility, controllability, and reliability, and thus becomes one of the most ideal energy resources to hedge against such uncertainties. This paper studies the mid-term integrated generation and maintenance scheduling of a cascaded hydroelectric system (CHS) consisting of multiple cascaded reservoirs and hydroelectric units. To precisely describe the mid-term water regulation policies, the hydraulic coupling relationship and water-energy nexus of CHS are incorporated into the proposed optimization model. The uncertainties of natural water inflow and the power outputs of wind/solar energy generation are taken into consideration and captured via a stochastic process modeled by a scenario tree. A multistage stochastic optimization (MSO) approach is developed to coordinate the complementary operations of multiple energy resources, by optimizing the mid-term water resource management, generation scheduling, and maintenance scheduling of CHS. The proposed MSO model is formulated as a large-scale mixed-integer linear program that presents significant computational intractability. To address this issue, a tailored Benders decomposition algorithm is developed. Two real-world case studies are conducted to demonstrate the capability and characteristics of the proposed model and algorithm. The computational results show that the proposed MSO model can exploit the flexibility of hydroelectricity to efficiently respond to variable wind and solar power, and reserve water resources for the generation in peak months to reduce the consumption of fossil fuel. Furthermore, the proposed solution approach also exhibits promising computational efficiency when handling large-scale models.

13 HYDRO ENERGY↗

DOE OSTI2014

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Optimal Scheduling of an Isolated Microgrid With Battery Storage Considering Load and Renewable Generation Uncertainties

By modeling the uncertainty of spinning reserves provided by energy storage with probabilistic constraints, a new optimal scheduling mode is proposed in this paper for minimizing the operating costs of an isolated microgrid (MG) by using chance-constrained programming. The model is transformed into a readily solvable mixed integer linear programming formulation in general algebraic modeling system (GAMS) via a proposed discretized step transformation approach and finally solved by applying the CPLEX solver. By properly setting the confidence levels of the spinning reserve probability constraints, the MG operation can achieve a tradeoff between reliability and economy. The test results on the modified Oak Ridge National Laboratory Distributed Energy Control and Communication lab MG test system reveal that the proposal significantly exceeds the commonly used hybrid intelligent algorithm with much better and more stable optimization results and significantly reduced calculation times.

Li, Yang↗

DOE OSTI2024

Projective Integral Updates for High-Dimensional Variational Inference

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. Furthermore, this integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.

Gaussian mean-field↗

DOE OSTI2016

Managing Wind Power Uncertainty Through Strategic Reserve Purchasing

With the rapidly increasing penetration of wind power, wind producers are becoming increasingly responsible for the deviation of the wind power output from the forecast. Such uncertainty results in revenue losses to the wind power producers (WPPs) due to penalties in ex-post imbalance settlements. This paper explores the opportunities available for WPPs if they can purchase or schedule some reserves to offset part of their deviation rather than being fully penalized in the real time market. The revenue for WPPs under such mechanism is modeled. The optimal strategy for managing the uncertainty of wind power by purchasing reserves to maximize the WPP's revenue is analytically derived with rigorous optimality conditions. The amount of energy and reserves that should be bid in the market are explicitly quantified by the probabilistic forecast and the prices of the energy and reserves. A case study using the price data from ERCOT and wind power data from NREL is performed to verify the effectiveness of the derived optimal bidding strategy and the benefits of reserve purchasing. Additionally, the proposed bidding strategy can also reduce the risk of variations on WPP's revenue.

17 WIND ENERGY↗

NASA NTRSDate not supplied

Desensitized Aerocapture Guidance

Mission design flexibility can be increased using an aerocapture maneuver to capture into an orbit around a planet from a hyperbolic trajectory. In past work, bang-bang control has been shown as an optimal guidance solution that minimizes the $\Delta{V}$ required to get into a desired orbit using bank modulation. This work revisits aerocapture using a bank modulation problem to search for an optimal solution using a direct collocation method. Previous studies have shown that aerocapture performance is sensitive to atmospheric density. In the literature, several studies have used a desensitized control approach to make the optimal guidance more robust to uncertainties in the model. To this end, this work aims to develop a desensitized aerocapture guidance robust to uncertainty in atmospheric density. Furthermore, this work compares the robustness of the open-loop desensitized aerocapture guidance with optimal aerocapture guidance with an aerocapture application at Earth.

Pardha Sai Chadalavada↗

NASA NTRSDate not supplied

Desensitized Aerocapture Guidance

Desensitized↗