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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem

This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

Optical Design of a Compact Imaging Spectrometer for Planetary Mineralogy

We present the design of a compact, wide-angle pushbroom imaging spectrometer suitable for exploration of solar system bodies from low orbit. The spectrometer is based on a single detector array with a broadband response that covers the range 400 to 3000 nm and provides a spectral sampling of 10 nm. The telescope has a 24-deg field of view with 600 spatially resolved elements (detector pixels). A specially designed convex diffraction grating permits optimization of the signal-to-noise ratio through the entire spectral band. Tolerances and design parameters permit the achievement of high uniformity of response through field and wavelength. The spectrometer performance is evaluated in terms of predicted spectral and spatial response functions and from the point of view of minimizing their variation through field and wavelength. The design serves as an example for illustrating the design principles specific to this type of system.

space optics↗
DOE OSTI2022

Market mechanism to enable grid-aware dispatch of Aggregators in radial distribution networks

This paper presents a market-based optimization framework wherein Aggregators can compete for nodal capacity across a distribution feeder and guarantee that allocated flexible capacity cannot cause overloads or congestion. This mechanism, thus, allows Aggregators with allocated capacity to pursue a number of services at the whole-sale market level to maximize revenue of flexible resources. Based on Aggregator bids of capacity (MW) and network access price ($/MW), the distribution system operator (DSO) formulates an optimization problem that prioritizes capacity to the different Aggregators across the network while implicitly considering AC network constraints. This grid-aware allocation is obtained by incorporating a convex inner approximation into the optimization framework that prioritizes hosting capacity to different Aggregators. We adapt concepts from transmission-level capacity market clearing, utility demand charges, and Internet-like bandwidth allocation rules to distribution system operations by incorporating nodal voltage and transformer constraints into the optimization framework. Simulation based results on IEEE distribution networks showcase the effectiveness of the approach.

Nazir, Mohammad Nawaf↗
DOE OSTI2020

Formulation and solution approach for calibrating activity-based travel demand model-system via microsimulation

This study addresses the problem of calibrating utility-maximizing nested logit activity-based travel demand model-systems. After estimation, it is common practice to use aggregate measurements to calibrate the estimated model-system’s parameters prior to their application in transportation planning, policy making, and operations. However, calibration of activity-based model-systems has received much less attention. Existing calibration approaches are myopic heuristics in the sense that they do not consider the fundamental inter-dependencies among choice-models and do not have a systematic way to adjust model parameters. Also, other purely simulation-based approaches do not perform well in large-scale applications. In this study, we focus on utility-maximizing nested logit activity-based model-systems and calibrating aggregate statistics such as activity shares, mode shares, time-dependent & mode-specific OD flows, and time-dependent & mode-specific sensor counts. We formulate the calibration problem as a simulation-based optimization problem and propose a stochastic gradient-based solution procedure to solve it. The solution procedure relies on microsimulation to calculate expectations of the aggregate statistics of interest to the calibration problem. Additionally, we derive approximate analytical expressions for the gradient of the objective function —that are evaluated through microsimulation on mini-batches of the population. The proposed solution procedure is sensitive to the fundamental structure of the activity-based model-system and is non-myopic in considering the dependencies across its model components. The formulated optimization problem is non-convex, highly nonlinear, and potentially has multiple-minima. Lastly, we show —through a real-world application— that the proposed solution procedure outperforms other state-of-the-art purely simulation-based optimization approaches in terms of computational efficiency, stability, and convergence. We also compare various gradient-based solution algorithms to determine the best algorithm to update the parameters. This work has the potential to facilitate wider and easier application of activity-based model-systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Abstract ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma–wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e. the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

Physics↗
DOE OSTI2021

Analysis of the ratio of ℓ 1 and ℓ 2 norms in compressed sensing

We study the ratio of ℓ 1 and ℓ 2 norms ( ℓ 1 / ℓ 2 ) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1 / ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1 / ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1 / ℓ 2 algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks

To fit sparse linear associations, a LASSO sparsity inducing penalty with a single hyperparameter provably allows to recover the important features (needles) with high probability in certain regimes even if the sample size is smaller than the dimension of the input vector (haystack). More recently learners known as artificial neural networks (ANN) have shown great successes in many machine learning tasks, in particular fitting nonlinear associations. Small learning rate, stochastic gradient descent algorithm and large training set help to cope with the explosion in the number of parameters present in deep neural networks. Yet few ANN learners have been developed and studied to find needles in nonlinear haystacks. Driven by a single hyperparameter, our ANN learner, like for sparse linear associations, exhibits a phase transition in the probability of retrieving the needles, which we do not observe with other ANN learners. To select our penalty parameter, we generalize the universal threshold of Donoho and Johnstone (Biometrika 81(3):425–455, 1994) which is a better rule than the conservative (too many false detections) and expensive cross-validation. In the spirit of simulated annealing, we propose a warm-start sparsity inducing algorithm to solve the high-dimensional, non-convex and non-differentiable optimization problem. We perform simulated and real data Monte Carlo experiments to quantify the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Peer-to-Peer Market-Based Control Strategy for a Smart Residential Community with Behind-the-Meter Distributed Energy Resources

This paper presents a distributed peer-to-peer market control strategy to manage and to enable resource sharing of behind-the-meter distributed energy resources in a residential community. In the proposed strategy, each consumer or prosumer determines the flexibility of their point of connection to the power network such that the obtained flexibility is network-feasible. Based on the feasible flexibility, the consumers and the prosumers trade power among each other at each time instance to fulfill their preferred load requirements while maximizing their payoffs and helping to regulate node voltages inside the community. Because the problem to be solved is non-convex, a distributed particle swarm optimization algorithm is used to coordinate the consumers/prosumers in a fully autonomous manner without any centralized or hierarchical coordination. Numerical simulations performed on a community of 48 homes demonstrate the efficacy of the proposed approach.

behind-the-meter↗
DOE OSTI2022

A Peer-to-Peer Market-Based Control Strategy for a Smart Residential Community with Behind-the-Meter Distributed Energy Resources: Preprint

This paper presents a distributed peer-to-peer market control strategy to manage and to enable resource sharing of behind-the-meter distributed energy resources in a residential community. In the proposed strategy, each consumer or prosumer determines the flexibility of their point of connection to the power network such that the obtained flexibility is network-feasible. Based on the feasible flexibility, the consumers and the prosumers trade power among each other at each time instance to fulfill their preferred load requirements while maximizing their payoffs and helping to regulate node voltages inside the community. Because the problem to be solved is non-convex, a distributed particle swarm optimization algorithm is used to coordinate the consumers/prosumers in a fully autonomous manner without any centralized or hierarchical coordination. Numerical simulations performed on a community of 48 homes demonstrate the efficacy of the proposed approach.

behind-the-meter↗
DOE OSTI2023

A Peer-to-Peer Market-Based Control Strategy for a Smart Residential Community with Behind-the-Meter Distributed Energy Resources

This paper presents a distributed peer-to-peer market control strategy to manage and to enable resource sharing of behind-the-meter distributed energy resources in a residential community. In the proposed strategy, each consumer or prosumer determines the flexibility of their point of connection to the power network such that the obtained flexibility is network-feasible. Based on the feasible flexibility, the consumers and the prosumers trade power among each other at each time instance to fulfil their preferred load requirements while maximizing their payoffs and helping to regulate node voltages inside the community. Because the problem to be solved is non-convex, a distributed particle swarm optimization algorithm is used to coordinate the consumers/prosumers in a fully autonomous manner without any centralized or hierarchical coordination. Numerical simulations performed on a community of 48 homes demonstrate the efficacy of the proposed approach.

distributed energy resource↗
DOE OSTI2020

Piecewise polyhedral formulations for a multilinear term

Herein, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex-hull representation. Based on the PPR’s solution, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on standard benchmark nonlinear programs (NLPs) with multilinear terms and compare with a traditional formulation that is built using recursive bilinear groupings of multilinear terms.

42 ENGINEERING↗
DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRSDate not supplied

Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗