SEARCH · Engineering Papers
Results for “Stochastic optimization”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Sizing and Topology Design of an Aeroelastic Wingbox Under Uncertainty
The goals of this work are to use a nested optimizer to conduct simultaneous sizing (inner level) and topology (outer level) design of a wingbox, considering uncertainties in the safety factors used to define the aeroelastic constraints. These uncertainties, propagated via sampling-driven polynomial chaos, are explicitly introduced at the inner level of the method, during gradient-based sizing optimization, resulting in a stochastic optimal sizing distribution. Measures of robustness in the total structural mass are then passed to the outer level, where a global optimizer evolves the topology parameters. The results demonstrate design choices needed to improve robustness in the face of uncertain safety factors, and the various physical mechanisms driving this process.
A Multiobjective Optimization Framework for Stochastic Control of Complex Systems
This paper addresses the problem of minimizing the long-run expected average cost of a complex system consisting of subsystems that interact with each other and the environment. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems, and we show that the control policy yielding the Pareto optimal solution is an optimal control policy that minimizes the average cost criterion for the entire system. For practical situations with constraints consistent to those we study here, our results imply that the Pareto control policy may be of value in deriving online an optimal control policy in complex systems.
Optimization under Stochastic Ambiguity for Resilient Infrastructure Systems.
Abstract not provided.
Summary Report on Synthetic Time History Development and Deployment
This report summarizes research work performed at the Colorado School of Mines (CSM) and George Washington University (GWU) in support of the DOE Office of Nuclear Energy Integrated Energy Systems (IES) program. In particular, the work focuses on improving and strengthening two fundamental steps in the mathematical and computational framework that is currently being developed to optimize the economic performance of Integrated Energy Systems. One of the innovative approaches taken by the IES program is that, rather than optimizing the system for a specific year or week or day, the optimization is performed using stochastic synthetic data. Synthetic data is generated by training artificial intelligence (AI) using available but limited data sets. The synthetic data should possess the same patterns as the original set and the same statistical properties, but never repeat the same set of values exactly. The work from CSM focuses on this first step; namely, investigating a methodology to determine the quality of the synthetic data and the right settings for properly training the AI. Once a large set of trustworthy data can be generated the problem of stochastic optimization can be tackled. The optimal IES configuration is highly dependent on the rare high peaks or deep depths of the net demand (grid electricity demand less variable renewable energy [VRE] production). Using an unbiased random sampling of the synthetic data, these extremes are very difficult to generate and therefore the optimization can be unrepresentative and inaccurate. GWU has started an approach to increase the likelihood of generating these rare events with the proper associated probabilistic weight. Both of these projects represent a step forward in achieving the capability to properly size the IESs and to properly capture the value that these systems can provide to the grid by absorbing volatility of net demand without disproportionately increasing the cost of maintaining grid reliability.
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.
Lagrangian relaxation based heuristics for a chance-constrained optimization model of a hybrid solar-battery storage system
Here, we develop a stochastic optimization model for scheduling a hybrid solar-battery storage system. Solar power in excess of the promise can be used to charge the battery, while power short of the promise is met by discharging the battery. We ensure reliable operations by using a joint chance constraint. Models with a few hundred scenarios are relatively tractable; for larger models, we demonstrate how a Lagrangian relaxation scheme provides improved results. To further accelerate the Lagrangian scheme, we embed the progressive hedging algorithm within the subgradient iterations of the Lagrangian relaxation. Lastly, we investigate several enhancements of the progressive hedging algorithm, and find bundling of scenarios results in the best bounds.
Demand Response Under Stochastic, Price-Dependent User Behavior
This letter focuses on price-based demand response (DR) implemented through dynamic adjustments of electricity prices. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. We propose a stochastic, feedback-based pricing strategy to compensate for estimation errors and uncertainty in customer response, establish theoretical results demonstrating the stability and near-optimality of the proposed approach, and validate its effectiveness through numerical simulations.
Optimal control of saturating systems with stochastic inputs
Optimal control of nonlinear saturating systems with stochastic inputs
Reliability-Based Design Optimization of a Composite Airframe Component
A stochastic optimization methodology (SDO) has been developed to design airframe structural components made of metallic and composite materials. The design method accommodates uncertainties in load, strength, and material properties that are defined by distribution functions with mean values and standard deviations. A response parameter, like a failure mode, has become a function of reliability. The primitive variables like thermomechanical loads, material properties, and failure theories, as well as variables like depth of beam or thickness of a membrane, are considered random parameters with specified distribution functions defined by mean values and standard deviations.
Optimal Energy Management for Microgrid with Stationary and Mobile Storage
This paper studies energy management in a Microgrid (MG) with solar generation, Battery Energy Management System (BESS) and gridable (V2G) EVs. A two-stage stochastic optimization method is proposed to capture the intermittent solar generation and random EV user behaviors. It is subsequently formulated as a Mixed Integer Linear Programming (MILP) problem. To evalutate the proposed method, real solar generation, loads, BESS and EV data is used in Sample Average Approximation (SAA). Computational results show the correctness of the proposed method as well as steady and tightly bounded optimality gap. Comparisons demonstrate that the proposed stochastic method outperforms its deterministic counterpart at the expense of higher computational cost. It is also observed that moderate number of EVs helps to reduce the overall operational cost of the MG, which sheds light on future EV integration to the smart grid.
Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties
We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.
Exact and inexact subsampled Newton methods for optimization
Abstract The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear rate of convergence in expectation. The second part of the paper analyzes an inexact Newton method that solves linear systems approximately using the conjugate gradient (CG) method, and that samples the Hessian and not the gradient (the gradient is assumed to be exact). We provide a complexity analysis for this method based on the properties of the CG iteration and the quality of the Hessian approximation, and compare it with a method that employs a stochastic gradient iteration instead of the CG method. We report preliminary numerical results that illustrate the performance of inexact subsampled Newton methods on machine learning applications based on logistic regression.
Chance-Constrained Day-Ahead Hourly Scheduling in Distribution System Operation
This paper aims to propose a two-step approach for day-ahead hourly scheduling in a distribution system operation, which contains two operation costs, the operation cost at substation level and feeder level. In the first step, the objective is to minimize the electric power purchase from the day-ahead market with the stochastic optimization. The historical data of day-ahead hourly electric power consumption is used to provide the forecast results with the forecasting error, which is presented by a chance constraint and formulated into a deterministic form by Gaussian mixture model (GMM). In the second step, the objective is to minimize the system loss. Considering the nonconvexity of the three-phase balanced AC optimal power flow problem in distribution systems, the second-order cone program (SOCP) is used to relax the problem. Then, a distributed optimization approach is built based on the alternating direction method of multiplier (ADMM). The results shows that the validity and effectiveness method.
Stochastic time-optimal control problems
Two types of stochastic time-optimal controls in a one-dimensional setting are considered. Multidimensional problems, in the case of complete state information available and the system modeled by stochastic differential equations, are studied under the formulation of minimizing the expected transient-response time. The necessary condition of optimality is the satisfaction for the value function of a parabolic partial differential equation with boundary conditions. The sufficient condition of optimality is also provided, based on Dynkin's formula. Finally, three examples are given.
Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F{sub 2} using selected configuration interaction trial wavefunctions
The potential energy curve of the F{sub 2} molecule is calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction (CI)-type trial wavefunctions. To keep the number of determinants reasonable and thus make FN-DMC calculations feasible in practice, the CI expansion is restricted to those determinants that contribute the most to the total energy. The selection of the determinants is made using the CIPSI approach (Configuration Interaction using a Perturbative Selection made Iteratively). The trial wavefunction used in FN-DMC is directly issued from the deterministic CI program; no Jastrow factor is used and no preliminary multi-parameter stochastic optimization of the trial wavefunction is performed. The nodes of CIPSI wavefunctions are found to reduce significantly the fixed-node error and to be systematically improved upon increasing the number of selected determinants. To reduce the non-parallelism error of the potential energy curve, a scheme based on the use of a R-dependent number of determinants is introduced. Using Dunning’s cc-pVDZ basis set, the FN-DMC energy curve of F{sub 2} is found to be of a quality similar to that obtained with full configuration interaction/cc-pVQZ.