Optimal procedures for stochastically failing equipment
Optimal procedures for stochastically failing equipment
OPTIMAL CONTROL↗
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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.
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Aeroservoelastic Optimization under Stochastic Gust Constraints
This work considers the aeroservoelastic optimization of a highly flexible transport aircraft wingbox with several control surfaces distributed along the trailing edge. The steady deflections of the control surfaces are designed to alleviate static maneuver loads, while the unsteady deflections are designed to alleviate stochastic continuous gust disturbances. Spatially-detailed unsteady stochastic stress and panel buckling constraints are formulated via modal acceleration, and by methods to locate the most-probable failure point along an equal-probability hypersurface. For the case considered here, it is found that the inclusion of such gust constraints during optimization presents a sizable structural mass penalty. In some cases, this mass penalty can be completely recovered with controlled gust load alleviation.
Stanford, Bret K.↗
Improved performance of stellarator coil design optimization
Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Enhancing flexibility for climate change using seasonal energy storage (aquifer thermal energy storage) in distributed energy systems
Long-term energy storage is expected to play a vital role in the deep decarbonization of building energy sectors, while enhancing the flexibility of buildings to withstand future climate variations. However, it is challenging to design distributed multi-energy systems (DMES) while taking into account the uncertainties introduced by climate change, since stochastic optimization of such systems is difficult. The present study introduces a stochastic optimization model to address this bottleneck, taking into account DMES including aquifer thermal energy storage (ATES) as the long-term thermal storage. For the first time, a novel optimization algorithm links ATES with the DMES optimization model with the support of a simplified geotechnical model. Subsequently, a case study was conducted, focusing on a residential district in Chicago where the impact of future climate condition, energy demand, and solar and wind energy potentials were evaluated using Weather Research and Forecasting (WRF) data (up to 2080) and the EnergyPlus model. The study revealed that ATES is an attractive way to improve the renewable energy penetration level and minimize the dependence on fossil fuels with reasonable support from the grid to assist the fluctuations in both demand and generation. Furthermore, ATES notably reduces fuel consumption and dependence while greatly enhancing the flexibility of the energy system to withstand fluctuations in demand and renewable energy generation brought by future climate variations. These qualities will make ATES an important part of distributed energy systems, even though it is not currently the lowest cost alternative due to lack of technology maturity. Furthermore, the design platform introduced in the present study can be used to design DMES enhancing flexibility to accommodate future climate variations.
25 ENERGY STORAGE↗
A stochastic constrained optimization technique and its application to detector array processing.
A stochastic projected gradient algorithm is proposed which can be used for finding a constrained optimum point for a concave or convex objective function subject to nonlinear constraints which form a connected region even when only a noisy estimate of the objective function is available. For a constraint described by a single linear equation, convergence to the constrained optimum value is proved, and the rate of convergence of the algorithm to the constrained optimum value is determined. The algorithm is applied to the nonlinear problem of obtaining automatically an array of detectors which forms a beam in a desired direction in space in the presence of interfering noise so as to maximize the SNR subject to a constraint on the super-gain ratio.
Winkler, L. P.↗
Sufficient conditions for the optimality of a stochastic control.
Sufficient conditions for optimal stochastic control of diffusion processes governed by vector equations satisfying local Lipschitz conditions
OPTIMAL CONTROL↗
A backward SDE method for uncertainty quantification in deep learning
Here, we develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.
97 MATHEMATICS AND COMPUTING↗
Risk-averse optimal control of semilinear elliptic PDEs
In this paper, we consider the optimal control of semilinear elliptic PDEs with random inputs. These problems are often nonconvex, infinite-dimensional stochastic optimization problems for which we employ risk measures to quantify the implicit uncertainty in the objective function. In contrast to previous works in uncertainty quantification and stochastic optimization, we provide a rigorous mathematical analysis demonstrating higher solution regularity (in stochastic state space), continuity and differentiability of the control-to-state map, and existence, regularity and continuity properties of the control-to-adjoint map. Our proofs make use of existing techniques from PDE-constrained optimization as well as concepts from the theory of measurable multifunctions. We illustrate our theoretical results with two numerical examples motivated by the optimal doping of semiconductor devices.
97 MATHEMATICS AND COMPUTING↗
A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers
We present Q-SASS, a quasi-Newton method for unconstrained stochastic optimization that does not rely on common random numbers. Most existing quasi-Newton approaches leverage common random numbers to construct second-order updates. However, motivated by challenges in variational quantum algorithms—where such coordination is not possible—we consider the setting in which function values and gradients are accessible only through noisy probabilistic zeroth- and first-order oracles, and no common random numbers can be exploited. We derive high-probability tail bounds on the iteration complexity of our algorithm for nonconvex, convex, and strongly convex (more generally, those satisfying the PL condition) objective functions. Finally, we demonstrate the empirical benefits of our quasi-Newton updating scheme on both synthetic and quantum chemistry problems.
Complexity bound↗
Demand Driven Cycamore Archetypes
Future nuclear fuel cycle options may present advantages over today’s once-through fuel cycle. Nuclear fuel cycle simulation tools assess the performance of those fuel cycles as well as the dynamics of long-term technology transitions. In many nuclear fuel cycle simulation tools, it has historically been the responsibility of the user to manually define facility deployment schemes and all facility parameters. While this is straightforward in simple fuel cycles, transitions from one fuel cycle to another can be more complex. In particular, deployment schemes for supportive fuel cycle facilities beyond the reactor become complex if the analyst desires to avoid gaps in the nuclear fuel and power supply chain during those transition scenarios. As nuclear fuel cycle analysis approaches questions regarding the feasibility and performance of the deployment schemes and technology choices during technology transition, automation of this historically manual process is necessary. The main objective of this work was to develop and demonstrate Cyclus automation capabilities toward key nuclear fuel cycle transition scenarios. While deploying reactors to meet power demand is trivial, and existed in the earliest versions of CYCLUS, automated, predictive deployment and decommissioning of other facilities is more complex. These include mining, milling, enrichment, fuel fabrication, reprocessing, and others. For example, a balanced closed fuel cycle may require ensuring that there is enough fast reactor fuel for their operation and may drive deployment of a fleet of light water reactors. This concern comprises the main challenge that drove the project effort. The Demand-Driven Cycamore Archetype project (NEUP-FY16-10512) aimed to develop CYCAMORE demand-driven deployment capabilities and thereby automate transition scenario definition. The developed software package, d3ploy, in the form of a CYCLUS Institution agent, deploys Facilities to meet the front-end and back-end demands of the fuel cycle. The University of South Carolina and the University of Illinois applied multiple algorithmic approaches to this challenge. This project developed an in situ demand-driven development schedule calculation through non-optimizing, deterministic-optimizing, and stochastic-optimizing algorithms as CYCLUS archetypes and demonstrated these new archetypes in program-supporting fuel cycle transition scenarios. Both objectives were achieved. This report documents the results and deliverables obtained toward these achievements in detail.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
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↗
Limiting performance of dynamic systems subject to random inputs
The problem of determining the limiting performance characteristics of mechanical systems subject to random input is studied. A review is presented of the classical work in the optimal design of stochastic systems. Some recent results of stochastic optimal control theory are employed. The solution to the limiting performance problem is formulated in both the frequency and time domains. Both formulations require substantial, burdensome computations when applied to large scale systems.
Pilkey, W. D.↗
On stochastic control and optimal measurement strategies
The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.
Kramer, L. C.↗
Open-loop-feedback-optimal adaptive stochastic control of linear systems
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.
Ku, R.↗
Fleet Assignment Using Collective Intelligence
Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).
Antoine, Nicolas E.↗
Evaluation and Optimization of Well Completion Options for the Utah FORGE Site
Orientation and completion for well pairs that have been subjected to multi-zonal stimulation play a critical role in the long-term performance of an Enhanced Geothermal Reservoir. Enhanced geothermal systems often rely on preferential flow along fractures between well injection and production locations. Modeling this preferential flow using discrete fracture networks (DNF) relies on stochastic realizations of the DFN based on geological sampling. Here we present the development of a stochastic optimization methodology to determine well completion options in a discrete fracture network based on using parallel subset simulation. Stochastic optimization will provide insight into regions where placements of the injection and production wells are optimal. An example optimization of well-pair location optimization based on a deterministic-stochastic DFN model representing FORGE follows a discussion of the theory.
15 GEOTHERMAL ENERGY↗
Optimal Control of Biomass Feedstock Processing System Under Uncertainty in Biomass Quality
Planning of biorefinery operations is complicated by the stochastic nature of physical and chemical characteristics of biomass feedstock, such as, moisture level and carbohydrate content. Biomass characteristics affect the performance of the equipment which feed the reactor and the efficiency of the conversion process in a biorefinery. We propose a stochastic optimization model to identify a blend of feedstocks, inventory levels, and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor while meeting the requirements of the biochemical conversion process. We propose a sample average approximation (SAA) of the model, and develop an efficient algorithm to solve the SAA model. A feedstock preprocessing process consists of two-stage grinding and pelleting is used to develop a case study. Extensive numerical analysis are conducted which lead to a number of observations. Our main observation is that sequencing bales based on moisture level and carbohydrate content leads to robust solutions that improve processing time and processing rate of the reactor. We provide a number of managerial insights that facilitate the implementation of the model proposed. Note to Practitioners—This paper is motivated by the challenges faced in the bioenergy industry. The focus of this paper is on plants which use the biochemical conversion process to generate liquid fuels. It has been observed that variations in biomass characteristics, such as moisture content, cause variations in feeding of the system which lead to under-utilization of equipment. A requirement of biochemical conversion process is to maintain the carbohydrate content of biomass processed by the reactor, larger than a threshold. We propose a model that identifies the inventory levels and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor. The goal is to improve equipment utilization while satisfying the requirements of the conversion process. The model is tested using real-life data. We found out that by sequencing bales based on moisture level and carbohydrate content, a plant can reduce variability in the system leading to improved system reliability, higher processing rates of the reactor, and higher throughput.
09 BIOMASS FUELS↗
Data-Driven Compositional Optimization in Misspecified Regimes
With a manifold growth in the scale and intricacy of systems, the challenges of parametric misspecification become pronounced. These concerns are further exacerbated in compositional settings, which emerge in problems complicated by modeling risk and robustness. In “Data-Driven Compositional Optimization in Misspecified Regimes,” the authors consider the resolution of compositional stochastic optimization problems, plagued by parametric misspecification. In considering settings where such misspecification may be resolved via a parallel learning process, the authors develop schemes that can contend with diverse forms of risk, dynamics, and nonconvexity. They provide asymptotic and rate guarantees for unaccelerated and accelerated schemes for convex, strongly convex, and nonconvex problems in a two-level regime with extensions to the multilevel setting. Surprisingly, the nonasymptotic rate guarantees show no degradation from the rate statements obtained in a correctly specified regime and the schemes achieve optimal (or near-optimal) sample complexities for general T-level strongly convex and nonconvex compositional problems.
Business & Economics↗