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Results for “Stochastic optimisation”

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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18 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Two-stage minimax stochastic unit commitment

The study proposes a stochastic optimisation approach based on discrete scenarios and the minimax criterion to deal with demand uncertainty in the two-stage unit commitment problem. To avoid making an over-conservative decision, the approach is designed to assign a probability-based weight to each demand scenario and provide a unit commitment schedule that minimises the maximum possible-weighted generation cost. Unit commitment is determined in the first stage and the economic dispatch under the scenario that corresponds to the maximum possible-weighted generation cost is determined in the second stage. The problem is formulated as a type of min-max-min mixed integer programming model. By introducing an auxiliary variable, the model is further transformed into a minimisation problem. A Benders decomposition algorithm is developed to solve the problem. The Benders master problem determines the unit commitment decision, while the Benders subproblem determines the dispatch decision. Multiple Benders feasibility cuts are constructed when the Benders subproblem is infeasible. Valid inequalities are derived to improve the lower bound provided by the Benders master problem. Numerical results show the performance of the algorithm.

Che, Ping↗
DOE OSTI2016

Parallel and interacting stochastic approximation annealing algorithms for global optimisation

We present the parallel and interacting stochastic approximation annealing (PISAA) algorithm, a stochastic simulation procedure for global optimisation, that extends and improves the stochastic approximation annealing (SAA) by using population Monte Carlo ideas. The efficiency of standard SAA algorithm crucially depends on its selfadjusting mechanism which presents stability issues in high dimensional or rugged optimisation problems. The proposed algorithm involves simulating a population of SAA chains that interact each other in a manner that significantly improves the stability of the self-adjusting mechanism and the search for the global optimum in the sampling space, as well as it inherits SAA desired convergence properties when a square-root cooling schedule is used. It can be implemented in parallel computing environments in order to mitigate the computational overhead. As a result, PISAA can address complex optimisation problems that it would be difficult for SAA to satisfactory address. We demonstrate the good performance of the proposed algorithm on challenging applications including Bayesian network learning and protein folding. Our numerical comparisons suggest that PISAA outperforms the simulated annealing, stochastic approximation annealing, and annealing evolutionary stochastic approximation Monte Carlo.

Local trap↗
DOE OSTI2017

Stochastic level-set method for shape optimisation

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical programming. The stochastic element of the algorithm is built on the methods of statistical mechanics and is designed so that the system explores a Boltzmann–Gibbs distribution of structures. In non-convex optimisation problems, the deterministic algorithm can get trapped in local optima: the stochastic generalisation enables sampling of multiple local optima, which aids the search for the globally-optimal structure. The method is demonstrated for several simple geometrical problems, and a proof-of-principle calculation is shown for a simple engineering structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A Stochastic Gradient Descent Approach for Stochastic Optimal Control

In this work, we introduce a stochastic gradient descent approach to solve the stochastic optimal control problem through stochastic maximum principle. The motivation that drives our method is the gradient of the cost functional in the stochastic optimal control problem is under expectation, and numerical calculation of such an expectation requires fully computation of a system of forward backward stochastic differential equations, which is computationally expensive. By evaluating the expectation with single-sample representation as suggested by the stochastic gradient descent type optimisation, we could save computational efforts in solving FBSDEs and only focus on the optimisation task which aims to determine the optimal control process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Utilising demand response for distribution service restoration to achieve grid resiliency against natural disasters

The increased frequency of power outages due to natural disasters in recent years has highlighted the urgency of enhancing distribution grid resilience. The effective distribution service restoration (DSR) is an important measure for a resilient distribution grid. In this work, the authors demonstrate that DSR can be significantly improved by leveraging the flexibility provided by the inclusion of demand response (DR). The authors propose a framework for this by considering integrated control of household-level flexible appliances to vary the load demand at the distribution-grid level to improve DSR. The overall framework of the proposed system is modelled as a three-step method considering three optimization problems to (i) calculate feasible controllable aggregated load range for each bus, (ii) determine candidate buses to perform DR and their target load demand, and (iii) maintain the load level in each house through home energy management during the DSR, considering uncertainties in load and solar generation sequentially. The optimization problems are formulated as linear programming, mixed-integer linear programming, and multistage stochastic programming (solved using the stochastic dual dynamic programming) models. Finally, case studies performed in the IEEE 123-node test feeder show improvements in resilience in terms of energy restored compared to the restoration process without DR.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

In this note, we present a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.

42 ENGINEERING↗
DOE OSTI2018

Closed‐loop hierarchical control strategies for connected and autonomous hybrid electric vehicles with random errors

This study presents a closed‐loop hierarchical control strategy for a group of connected and autonomous hybrid electric vehicles (HEVs) with the purpose of optimising fuel economy while guaranteeing traffic mobility and vehicle safety. In the hierarchical control architecture, a decentralised stochastic model predictive control (SMPC)‐based higher level controller incorporating signal phase and timing information is formulated to optimise the velocity profile of each vehicle, and an adaptive equivalent consumption minimisation strategy based lower level controller is employed for the energy management control of the HEVs. Creatively, random errors of the control variable are considered in the SMPC framework. The errors are discretised and modelled as a Markov process and the state transition matrix of the errors is generated randomly to capture the error transition dynamics. To solve the SMPC problem more efficiently, a scenario‐based SMPC is employed. Moreover, the propulsion and recuperation efficiencies of the lower level controller are calculated at each time step with measurable variables, and fed back to the higher level controller for velocity optimisation in next time step. Simulation results validate the control effectiveness and advantages of the proposed control architecture.

Qiu, Shaolin↗
DOE OSTI2023

Optimal white-noise stochastic forcing for linear models of turbulent channel flow

In the present study an optimisation problem is formulated to determine the forcing of an eddy-viscosity-based linearised Navier–Stokes model in channel flow at $Re_\tau \approx 5200$ ( $Re_\tau$ is the friction Reynolds number), where the forcing is white-in-time and spatially decorrelated. The objective functional is prescribed such that the forcing drives a response to best match a set of velocity spectra from direct numerical simulation (DNS), as well as remaining sufficiently smooth. Strong quantitative agreement is obtained between the velocity spectra from the linear model with optimal forcing and from DNS, but only qualitative agreement between the Reynolds shear stress co-spectra from the model and DNS. The forcing spectra exhibit a level of self-similarity, associated with the primary peak in the velocity spectra, but they also reveal a non-negligible amount of energy spent in phenomenologically mimicking the non-self-similar part of the velocity spectra associated with energy cascade. By exploiting linearity, the effect of the individual forcing components is assessed and the contributions from the Orr mechanism and the lift-up effect are also identified. Finally, the effect of the strength of the eddy viscosity on the optimisation performance is investigated. The inclusion of the eddy viscosity diffusion operator is shown to be essential in modelling of the near-wall features, while still allowing the forcing of the self-similar primary peak. In particular, reducing the strength of the eddy viscosity results in a considerable increase in the near-wall forcing of wall-parallel components.

Mechanics↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Minimum entropy filtering for a single output non-Gaussian stochastic system using state transformation

This paper presents a novel filter design for the single-output stochastic non-linear systems subjected to non-Gaussian noises and the proposed assumptions. Based on a state transformation, the unmeasurable states of the systems can be estimated where non-linear terms in the systems have been eliminated. It has been shown that the estimation error is linearly dynamical regarding to the presented vector-valued filter gain which can be optimised by minimising the entropy-based performance criterion. In addition, the convergence of the presented algorithm is analysed in mean-square sense and a numerical example is given to verify the effectiveness of the presented filtering algorithm. Meanwhile, the extended Kalman filter, unscented particle filter and minimum entropy filter are given for the comparisons of the filtering performance. Following the presented framework, some extensions of the presented filtering algorithm are discussed to indicate the flexibility of the filter design. The contribution of this paper can be summarised as establishing a novel minimum entropy filtering framework which consists of model transformation, entropy optimisation and convergence analysis.

42 ENGINEERING↗
DOE OSTI2017

Stochastic assessment of distributed generation hosting capacity and energy efficiency in active distribution networks

Active network management (ANM) aims to increase the capacity of variable distributed generation (DG), which can be connected to existing distribution networks. In this study, it is proposed to simultaneously consider the efficient use of energy resources when high shares of DG are procured through the ANM approach. To that end, a multi-period and multiobjective optimisation algorithm, based on the linearised optimal power flow, is formulated. The algorithm seeks to maximise the installed capacity of DG while minimising the energy losses and consumption of voltage-dependent loads. The objectives are optimised considering the coordinated operation of voltage regulators and on-load tap changers, and the management of DG generation curtailment and reactive power compensation from DG. Additionally, the effects of load and generation uncertainties are addressed through a two-stage stochastic programming formulation of the multiobjective problem. The result is a set of non-inferior solutions, which allows exploring the degree of conflict among the objectives. The proposed approach was tested on two IEEE test feeders and the solutions show a significant improvement in the system's energy efficiency with a low impact on the amount of connected DG.

Quijano, Darwin Alexis↗
DOE OSTI2018

Phenotypic switching of populations of cells in a stochastic environment

We report that in biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise-deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. Finally, we discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Optimisation of the Kaplan hydropower system via PID 2 and digital twin

Here, this paper proposes a proportional–integral-double–derivative (PID 2 ) optimisation method for the Kaplan hydropower system by building a digital twin. The study first uses one multilayer perceptron (MLP) to model the hydroturbine dynamic and then adopts three connected MLPs to model the generator dynamic, both in an open-loop fashion. Inspired by stochastic distribution control (SDC) theory, we regard the training of the turbine's neural network model as a process control problem, and we propose minimising entropy loss to update the network parameters. The next step is to build the digital twin by connecting the neural network models with a PID 2 controller and a lead-lag exciter and run the whole model in a closed-loop fashion. After that, a binary search approach is applied to optimise the PID 2 parameters based on the obtained digital twin model. The simulation results show that the proposed method can reduce the mean square tracking error by more than 90%. Furthermore, the method is extended to jointly optimise the PID 2 controller and excitation system gains through multiobjective optimisation, leveraging Pareto frontier analysis to balance active power and voltage tracking performance. Simulation results confirm the effectiveness of the proposed method, achieving a 83.46% reduction in relative mean square error of active power, a 47.13% reduction in terminal voltage tracking error, and an 82.78% improvement in the overall scalarized objective.

Hydropower system↗
DOE OSTI2022

Particle Swarm Optimisation for group structure optimization for radiotherapy shielding

Neutron transport simulations are ubiquitous in nuclear engineering because they allow one to model experimental systems and render a model platform for easy perturbation of experimental designs. In addition, simulations allow one to gain experimental insight without actually having to go through the trouble of building a physical experiment. Neutron transport simulations can be stochastic or deterministic based. Stochastic neutron transport simulations are typically simulated using the Monte Carlo method and yield very accurate solutions but are computationally expensive, while deterministic methods are typically faster but can be less accurate. Here we focus on optimizing the accuracy of deterministic neutron transport simulations for radiotherapy simulations. Deterministic neutron transport requires discretization of angle, energy, and space to appropriately analyze the system one is trying to model. Discretization of energy is challenging because of the highly variable neutron flux at certain neutron energies. Improper discretization of energy in the transport model can lead to erroneous results and therefore inaccurate interpretations of the solution. In this study, we evaluate Particle Swarm Optimization (PSO) as a mechanism for selecting optimal group structures for radiotherapy shielding. We tested the particle swarm optimization algorithm on radiotherapy shielding problems using Los Alamos National Laboratory's (LANL) main deterministic transport code PARTISN. Results show that the optimized energy group structures generated from the optimization algorithm outperformed LANL's standard energy group structures, and therefore demonstrate utility in using PSO to expedite computation times due to the increased accuracy obtained with a smaller but optimized group structure. (authors)

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

Phenotype heterogeneity in cancer cell populations

Phenotype heterogeneity in cancer cell populations, be it of genetic, epigenetic or stochastic origin, has been identified as a main source of resistance to drug treatments and a major source of therapeutic failures in cancers. The molecular mechanisms of drug resistance are partly understood at the single cell level (e.g., overexpression of ABC transporters or of detoxication enzymes), but poorly predictable in tumours, where they are hypothesised to rely on heterogeneity at the cell population scale, which is thus the right level to describe cancer growth and optimise its control by therapeutic strategies in the clinic. We review a few results from the biological literature on the subject, and from mathematical models that have been published to predict and control evolution towards drug resistance in cancer cell populations. We propose, based on the latter, optimisation strategies of combined treatments to limit emergence of drug resistance to cytotoxic drugs in cancer cell populations, in the monoclonal situation, which limited as it is still retains consistent features of cell population heterogeneity. The polyclonal situation, that may be understood as “bet hedging” of the tumour, thus protecting itself from different sources of drug insults, may lie beyond such strategies and will need further developments. In the monoclonal situation, we have designed an optimised therapeutic strategy relying on a scheduled combination of cytotoxic and cytostatic treatments that can be adapted to different situations of cancer treatments. Finally, we review arguments for biological theoretical frameworks proposed at different time and development scales, the so-called atavistic model (diachronic view relying on Darwinian genotype selection in the coursof billions of years) and the Waddington-like epigenetic landscape endowed with evolutionary quasi-potential (synchronic view relying on Lamarckian phenotype instruction of a given genome by reversible mechanisms), to represent evolution towards heterogeneity, possibly polyclonal, in cancer cell populations and propose innovative directions for therapeutic strategies based on such frameworks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Risk bases can complement dose bases for implementing and optimising a radiological protection strategy in urgent and transition emergency phases

Current radiological emergency response recommendations have been provided by the International Commission on Radiological Protection and adopted by the International Atomic Energy Agency in comprehensive Safety Standards. These standards provide dose-based guidance for decision making (e.g., on sheltering or relocation) via generic criteria in terms of effective dose in the range from 20 mSv per year, during transition from emergency to existing exposure situation, to 100 mSv, acute or annual, in the urgent phase of a nuclear accident. The purpose of this paper was to examine how such dose reference levels directly translate into radiation-related risks of the main stochastic detrimental health effects (cancer). Methodologies, provided by the World Health Organization after the Fukushima accident, for calculating the lifetime and 20 year cancer risks and for attributing relevant organ doses from effective doses, have been applied here for this purpose with new software, designed to be available for use immediately after a nuclear accident. A new feature in this software is a comprehensive accounting for uncertainty via simulation technique, so that the risks may now be presented with realistic confidence intervals. The types of cancer risks considered here are time-integrated over lifetime and the first 20 years after exposure for all solid cancers and either the most radiation-sensitive types of cancer, i.e., leukaemia and female breast cancer, or the most radiation-relevant type of cancer occurring early in life, i.e., thyroid. It is demonstrated here how reference dose levels translate differently into specific cancer risk levels (with varying confidence interval sizes), depending on age at exposure, gender, time-frame at-risk and type of cancer considered. This demonstration applies German population data and considers external exposures. Further work is required to comprehensively extend this methodology to internal exposures that are likely to be important in the early stages of a nuclear accident. A discussion is provided here on the potential for such risk-based information to be used by decision makers, in the urgent and transition phases of nuclear emergencies, to identify protective measures (e.g., sheltering, evacuation) in a differential way (i.e., for particularly susceptible sub-groups of a population).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Unified probabilistic energy flow analysis for electricity–gas coupled systems with integrated demand response

Under a multi-energy environment, the conventional demand response programmes in smart-grid will be evolving to the concept of integrated demand response (IDR). In order to examine such an effect, this study presents a new methodological framework to conduct the probabilistic energy flow (PEF) analysis of integrated energy systems, while considering the potential effects of IDR. For this aim, a new price-elasticity-based IDR model is developed. As distinct from existing works, this study explicitly focuses on the stochastic characteristics of IDR programme and a novel Z-number-based technique is introduced to handle the relevant uncertainties that involved. The proposed Z-number model can not only capture the inherent randomness in demand-side performance but also account for the potential impact of information availability/reliability on the representation of IDR. Since the presence of Z-numbers makes the authors model include different types of uncertain representations, the fuzzy expectation technique and centroid method are jointly used to make them manageable under the same framework. A comprehensive algorithm based on the cumulant method and an optimisation scheme is employed to solve this PEF problem with consideration of IDR. The proposed framework is illustrated through numerical studies and simulation results confirm its effectiveness in actual implementations.

Zeng, Bo↗