Optimal Selection of Calibration and Validation Test Samples under Uncertainty.
Abstract not provided.
Urbina, Angel↗
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Results for “Optimization Under Uncertainty”
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Optimal Selection of Calibration and Validation Test Samples under Uncertainty.
Abstract not provided.
Urbina, Angel↗
Optimal PMU Placement for State Estimation with Grid Parameter Uncertainty
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Engineering - Electronic and electrical engineerin↗
Optimization of Medium Frequency Transformers with Practical Considerations
A method to design and optimize a Medium Frequency Transformer (MFT) based on commercially available components and semiconductor and converter constraints is presented. The optimization algorithm is used to redesign the transformer for a scaled-down electric vehicle (EV) fast charger using a three-level resonant circuit topology. The main consideration of this paper is the uncertainty caused by modeling assumptions in optimization algorithms. To reduce this uncertainty, space mapping is used to create an optimized design point. Lastly, a comparison of the designs found using the original optimization algorithm and the space mapping technique are compared and analyzed. For simplicity, only a single objective optimization routine is employed.
42 ENGINEERING↗
Optimal Control for X-Ray Mircroscopes
In this article, a systematic framework for designing the control for fine positioning (scanning) stages of X-ray microscopes is presented. This framework facilitates designs that simultaneously achieve specifications on positioning resolution and tracking bandwidth while guaranteeing robustness of the closed loop device to unmodeled uncertainties. We use robust optimal control techniques for modeling, quantifying design objectives and system-specific challenges, and designing the control laws. The control designs were implemented on a three degree of freedom piezoactuated flexure stages dedicated for fine positioning of X-ray optics. Experimental results demonstrate significant improvements in positioning performance of 134%, 150%, and 132% in tracking bandwidths along the lateral (X), vertical (Y), and beam (Z) directions, respectively, when compared to proportional-integral-derivative controller designs. This was achieved while keeping similar or better positioning resolution and robustness measures. Fast scanning for X-ray imaging was demonstrated in both the step scan and flyscan modes, where bandwidth was improved by over 450 times with flyscan compared to the step scan.
42 ENGINEERING↗
Experimental Validation of Approximate Dynamic Programming Based Optimization and Convergence on Microgrid Applications
Stochastic optimization can better address uncertainties in power system problems. However, when state space and action space become large, many existing approaches become computationally expensive and even infeasible. Approximate dynamic programming (ADP) attracts researchers’ attention as a powerful tool for solving power system optimization problems with reduced computational cost. In this paper, in light of the existing literature, we investigate how the ADP approach with post-decision value function approximation converges to the nearly optimal solution with improved computational speed and experimentally validate the performance of the approach for a microgrid energy optimization problem. The approximation error versus the number of iteration is studied for convergence analysis of the post-decision ADP. A flowchart is provided to illustrate the proposed ADP algorithm for a microgrid energy optimization problem. The performance of ADP and dynamic programming (DP) is compared in terms of optimization error and computational time. It has found that the post-decision ADP approach can achieve competitive optimality with improved computational speed compared to the traditional DP.
Das, Avijit↗
Risk Analysis for Resource Planning Optimization
This paper describes a systems engineering approach to resource planning by integrating mathematical modeling and constrained optimization, empirical simulation, and theoretical analysis techniques to generate an optimal task plan in the presence of uncertainties.
optimization↗
Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering
This poster highlights uncertainty and technical risk reduction capabilities in CCSI2, with a focus on robust optimization. It presents recent advances of the two-stage robust optimization (RO) solver PyROS and applications to advanced energy systems optimization. To demonstrate the computational performance and reliability of PyROS, a benchmarking study on a library of over 8,500 small-scale RO problems is presented. Further, PyROS is used to obtain robust system designs of a MEA-based CO2 absorber under uncertainty in the thermodynamic property models for a variety of CO2 capture rate threshold requirements. Overall, the results demonstrate that the PyROS solver, including recent extensions to multi-stage RO settings, provides a reliable avenue to optimize the design and operation of advanced energy systems subject to various sources of parametric uncertainty.
Sherman, Jason↗
Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering
This poster highlights uncertainty and technical risk reduction capabilities in CCSI2, with a focus on robust optimization. It presents recent advances of the two-stage robust optimization (RO) solver PyROS and applications to advanced energy systems optimization. To demonstrate the computational performance and reliability of PyROS, a benchmarking study on a library of over 8,500 small-scale RO problems is presented. Further, PyROS is used to obtain robust system designs of a MEA-based CO2 absorber under uncertainty in the thermodynamic property models for a variety of CO2 capture rate threshold requirements. Overall, the results demonstrate that the PyROS solver, including recent extensions to multi-stage RO settings, provides a reliable avenue to optimize the design and operation of advanced energy systems subject to various sources of parametric uncertainty.
Sherman, Jason↗
MO-E-BRE-01: Determination, Minimization and Communication of Uncertainties in Radiation Therapy
Medical Physicists have a general understanding of uncertainties in the radiation treatment process, both with respect to dosimetry and geometry. However, there is a desire to be more quantitative about uncertainty estimation. A recent International Atomic Energy Agency (IAEA) report (about to be published) recommends that we should be as “accurate as reasonably achievable, technical and biological factors being taken into account”. Thus, a single recommendation as a goal for accuracy in radiation therapy is an oversimplification. That report also suggests that individual clinics should determine their own level of uncertainties for their specific treatment protocols. The question is “how do we implement this in clinical practice”? AAPM Monograph 35 (2011 AAPM Summer School) addressed many specific aspects of uncertainties in each of the steps of a course of radiation treatment. The intent of this symposium is: (1) to review uncertainty considerations in the entire radiation treatment process including uncertainty determination for each step and uncertainty propagation for the total process, (2) to consider aspects of robust optimization which optimizes treatment plans while protecting them against uncertainties, and (3) to describe various methods of displaying uncertainties and communicating uncertainties to the relevant professionals. While the theoretical and research aspects will also be described, the emphasis will be on the practical considerations for the medical physicist in clinical practice. Learning Objectives: To review uncertainty determination in the overall radiation treatment process. To consider uncertainty modeling and uncertainty propagation. To highlight the basic ideas and clinical potential of robust optimization procedures to generate optimal treatment plans that are not severely affected by uncertainties. To describe methods of uncertainty communication and display.
60 APPLIED LIFE SCIENCES↗
Classical-Quantum Algorithm for Solving Stochastic Programs
Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.
97 MATHEMATICS AND COMPUTING↗
NREL Variability and Reserves Analysis for the Western Interconnect (Presentation)
Additional variability and uncertainty increase reserve requirements. In this light, this presentation discusses how use of generation reserves can be optimized for managing variability and uncertainty.
17 WIND ENERGY↗
Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems
Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.
Chowdhary, Abhijit↗
Low Activity Waste Glass Optimization with Property Models from Machine Learning, Part 2: Experimental Validation and Active Learning
The United States Department of Energy is responsible for managing legacy nuclear waste stored in underground tanks at the Hanford Site. To treat the waste, it is planned as the current baseline to separately vitrify low-activity waste (LAW) and high-level waste fractions. Previously, machine learning (ML) based glass property models (e.g., chemical durability, viscosity, electrical conductivity and SO3 solubility) were developed with prediction uncertainties. A waste glass optimization approach was then established to enable the capability of using these ML models in LAW glass formulation. In this study, the previous ML models were first experimentally validated, and the results were incorporated back into the database to update the ML models. The updated models and formulations showed increased waste loading while reducing the failure rate, demonstrating improved predictive accuracy, reduced uncertainties, and the effectiveness of active learning in guiding high-dimensional, nonlinear LAW glass design. This represents the first experimental validation of ML based LAW glass formulation, with practical benefits such as higher waste loading, shorter mission duration, and lower operational risk.
Lu, Xiaonan (ORCID:0000000179708148)↗
Stochastic DG Placement for Conservation Voltage Reduction Based on Multiple Replications Procedure
Conservation voltage reduction (CVR) and distributed-generation (DG) integration are popular strategies implemented by utilities to improve energy efficiency. This paper investigates the interactions between CVR and DG placement to minimize load consumption in distribution networks, while keeping the lowest voltage level within the predefined range. The optimal placement of DG units is formulated as a stochastic optimization problem considering the uncertainty of DG outputs and load consumptions. A sample average approximation algorithm-based technique is developed to solve the formulated problem effectively. A multiple replications procedure is developed to test the stability of the solution and calculate the confidence interval of the gap between the candidate solution and optimal solution. The proposed method has been applied to the IEEE 37-bus distribution test system with different scenarios. The numerical results indicate that the implementations of CVR and DG, if combined, can achieve significant energy savings.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Calibration of energy density functionals with deformed nuclei
Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Sensitivity and Uncertainty Quantification of Transition Scenario Simulations
This report documents the first collective attempt at developing and applying capabilities to quantify uncertainties, assess parametric sensitivities, and optimize multiple parameters and metrics in fuel cycle simulations generated by the SA&I Campaign. To do this, external codes that were designed to perform sensitivity analysis and uncertainty quantification (SA&UQ) needed to be coupled to the SA&I Campaign’s nuclear fuel cycle simulators (NFCS). In FY20, two approaches were pursued: 1) coupling Cyclus to an ORNL-internal code called MOT (Metaheuristic Optimization Tool) and 2) coupling DYMOND to the opensource SA&UQ tool kit Dakota. The primary objective of having these NFCS/SA&UQ coupled capabilities is to better inform DOE-NE and other stakeholders on the results generated from the NFCS. For a given set of fuel cycle strategies, policies, and technology assumptions that make up a fuel cycle scenario, these NFCS have traditionally been used by the SA&I Campaign to provide quantitative answers in terms of year-by-year mass flows, infrastructure requirements, costs, etc. With these newly developed coupled capabilities, the SA&I Campaign can now efficiently simulate hundreds or thousands of these scenarios, sample large ranges of parameters and assumptions, and use the unique features of the SA&UQ tools to process the data. This enables providing answers with known and propagated uncertainties, determining the sensitivity of important metrics to different parameters and assumptions, quantifying how much fuel cycle and technology parameters impact each other, and producing optimized fuel cycle strategies for single and multiple variables. To demonstrate these new capabilities, the Cyclus/MOT was used to model several scenarios ranging from simple fleet retirements to transitions to advanced reactors. Specifically, for a transition scenario from LWRs to SFRs and advanced LWRs, uncertainty quantification, sensitivity analysis, and optimization studies were applied to cases involving single and multiple parameter (input) and single and multiple metric (output) variations. In addition, a similar transition scenario was modeled to demonstrate how to optimize the reprocessing capacity parameter to minimize two performance metrics while taking into account uncertainties from two other parameters. Lastly, a depletion module based on SCALE/ORIGEN was added in Cyclus to simulate the third scenario that was designed to quantify the impact of the modeling assumption that all LWR used nuclear fuel have the same burnup. The newly developed DYMOND/Dakota capability was also applied to a transition scenario from the existing fleet to small modular reactors and fast reactors. This particular scenario involves not only explicit isotopic depletion via ORIGEN-2, but also includes multirecycling and utilizing the criticality search feature to determine the fresh fuel composition of recycled fuel, a feature unique to the DYMOND NFCS. A large database of simulations were run with 4 main parameters that were sampled: start date of reprocessing, reprocessing capacity, energy demand growth rate, and advanced reactor share of the fleet. The 4 main metrics were uranium consumption, enrichment requirements, waste generation, and levelized cost of electricity using data from the Cost Basis Report. The demonstrated SA&UQ results include those that inform on how to choose parameters to avoid “failed” scenarios, Sobol’ indices that inform on the importance of various parameters individually and synergistically, and Analysis of Variance (ANOVA) studies that decompose parameter ranges into groups and informs on whether variations are statistically significant.
Feng, B.↗
Dakota uncertainty quantification methods applied to the NEK-5000 SAHEX model.
This report summarizes the results of a NEAMS project focused on the use of uncertainty and sensitivity analysis methods within the NEK-5000 and Dakota software framework for assessing failure probabilities as part of probabilistic risk assessment. NEK-5000 is a software tool under development at Argonne National Laboratory to perform computational fluid dynamics calculations for applications such as thermohydraulics of nuclear reactor cores. Dakota is a software tool developed at Sandia National Laboratories containing optimization, sensitivity analysis, and uncertainty quantification algorithms. The goal of this work is to demonstrate the use of uncertainty quantification methods in Dakota with NEK-5000.
Weirs, V. Gregory↗