Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic methods”

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.

At least 1,171 records · Page 65

Indirect-to-direct band gap transition in relaxed and strained Ge{sub 1−x−y}Si{sub x}Sn{sub y} ternary alloys

Sn-containing group IV semiconductors create the possibility to independently control strain and band gap thus providing a wealth of opportunities to develop an entirely new class of low dimensional systems, heterostructures, and silicon-compatible electronic and optoelectronic devices. With this perspective, this work presents a detailed investigation of the band structure of strained and relaxed Ge{sub 1−x−y}Si{sub x}Sn{sub y} ternary alloys using a semi-empirical second nearest neighbors tight binding method. This method is based on an accurate evaluation of the deformation potential constants of Ge, Si, and α-Sn using a stochastic Monte-Carlo approach as well as a gradient based optimization method. Moreover, a new and efficient differential evolution approach is also developed to accurately reproduce the experimental effective masses and band gaps. Based on this, we elucidated the influence of lattice disorder, strain, and composition on Ge{sub 1−x−y}Si{sub x}Sn{sub y} band gap energy and directness. For 0 ≤ x ≤ 0.4 and 0 ≤ y ≤ 0.2, we found that tensile strain lowers the critical content of Sn needed to achieve a direct band gap semiconductor with the corresponding band gap energies below 0.76 eV. This upper limit decreases to 0.43 eV for direct gap, fully relaxed ternary alloys. The obtained transition to direct band gap is given by y > 0.605 × x + 0.077 and y > 1.364 × x + 0.107 for epitaxially strained and fully relaxed alloys, respectively. The effects of strain, at a fixed composition, on band gap directness were also investigated and discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Estimating the epidemic threshold on networks by deterministic connections

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computational Aspects of Single-Molecule Kinetics for Coupled Catalytic Cycles: A Spectral Analysis

Catalysis from single active sites is analyzed using methods developed from single molecule kinetics. Using a stochastic Markov state description, the observable properties of general catalytic networks of reactions are expressed using an eigenvalue decomposition of the transition matrix for the Markov process. By the use of a sensitivity analysis, the necessary eigenvalues and eigenvectors are related to the energies of controlling barriers and wells located along the reaction routes. A generalization of the energetic span theory allows the eigenvalues to be computed from several activation energies corresponding to distinct barrier-well pairings. The formalism is demonstrated accurately for model problems for a physically realistic mechanism for an alkene hydrogenation reaction on a single atom catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predictive drug dosage control through a Fokker–Planck observer

During the years, various techniques have been presented for optimal control of tumor growth for which its stochastic behavior has rarely been considered. This article uses the well-known Gompertz stochastic model, for describing tumor growth, and by receding horizon model predictive control (RH-MPC) scheme computes the drug dosage for minimizing the tumor-cell population. To do this, a predictive control problem is defined based on the difference between the probability density function of tumor-cell population and the desired probability density function. In the model, both the drug dosage limitation and the Fokker–Planck equation have been considered as constraints. By solving this problem, the drug dosage which is considered as an external input to tumor model, is computed. In this article, the Fokker–Planck equation is used (1) as a nonlinear observer of probability density function of tumor-cell population and (2) a mapping vehicle from stochastic to deterministic domain. The Fokker–Planck equation is written for the Gompertz stochastic model of tumor growth. The equation is then solved through the path integral method. In this way, the probability density function of tumor-cell population, which contains the entire stochastic characteristics of the tumor growth, is obtained for any instance of time. The simulation results have also been presented for the evaluation of the suggested approach. The results show that the tumor-cell population can be controlled within a number of time windows (15 time windows in our case study) if an appropriate desired PDF is selected.

97 MATHEMATICS AND COMPUTING↗

Probability of failure and risk assessment of propulsion structural components

The probabilistic structural analysis method (PSAM) was developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as the Space Shuttle Main Engine turbopump blades. Risk is calculated after expensive service experience. However, probabilistic structural analysis provides a rational alternative method to quantify uncertainties in the structural performance and durability. NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a probabilistic structural analysis computer code which integrates finite element methods and reliability algorithms, capable to predicting the probability distributions of structural response variables such as stress, displacement, natural frequencies, and buckling loads. This computer code is detailed.

Shiao, Michael C.↗

Stochastic averaging and sensitivity analysis for two scale reaction networks

In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate computations for obtaining estimates of expected values and sensitivities with respect to the steady state distribution. A two-time-scale formulation is used to establish bounds on the bias induced by the averaging method. Further, this formulation provides a framework to create an accelerated “averaged” version of most single-scale sensitivity estimation methods. In particular, we propose the use of a centered ergodic likelihood ratio method for steady state estimation and show how one can adapt it to accelerated simulations of multiscale systems. Lastly, we develop an adaptive “batch-means” stopping rule for determining when to terminate the micro-equilibration process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-element stochastic spectral projection for high quantile estimation

We investigate quantile estimation by multi-element generalized Polynomial Chaos (gPC) metamodel where the exact numerical model is approximated by complementary metamodels in overlapping domains that mimic the model’s exact response. The gPC metamodel is constructed by the non-intrusive stochastic spectral projection approach and function evaluation on the gPC metamodel can be considered as essentially free. Thus, large number of Monte Carlo samples from the metamodel can be used to estimate α-quantile, for moderate values of α. As the gPC metamodel is an expansion about the means of the inputs, its accuracy may worsen away from these mean values where the extreme events may occur. By increasing the approximation accuracy of the metamodel, we may eventually improve accuracy of quantile estimation but it is very expensive. A multi-element approach is therefore proposed by combining a global metamodel in the standard normal space with supplementary local metamodels constructed in bounded domains about the design points corresponding to the extreme events. To improve the accuracy and to minimize the sampling cost, sparse-tensor and anisotropic-tensor quadratures are tested in addition to the full-tensor Gauss quadrature in the construction of local metamodels; different bounds of the gPC expansion are also examined. The global and local metamodels are combined in the multi-element gPC (MEgPC) approach and it is shown that MEgPC can be more accurate than Monte Carlo or importance sampling methods for high quantile estimations for input dimensions roughly below N=8, a limit that is very much case- and α-dependent.

97 MATHEMATICS AND COMPUTING↗

Stochastic Optimal Control via Bellman's Principle

This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.

Crespo, Luis G.↗

Interaction picture density matrix quantum Monte Carlo

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SLFP: A stochastic linear fractional programming approach for sustainable waste management

Highlights: > A new fractional programming (SLFP) method is developed for waste management. > SLFP can solve ratio optimization problems associated with random inputs. > A case study of waste flow allocation demonstrates its applicability. > SLFP helps compare objectives of two aspects and reflect system efficiency. > This study supports in-depth analysis of tradeoffs among multiple system criteria. - Abstract: A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Improving Sensorimotor Function Using Stochastic Vestibular Stimulation

Astronauts experience sensorimotor changes during spaceflight, particularly during G-transition phases. Post flight sensorimotor changes may include postural and gait instability, spatial disorientation, and visual performance decrements, all of which can degrade operational capabilities of the astronauts and endanger the crew. Crewmember safety would be improved if these detrimental effects of spaceflight could be mitigated by a sensorimotor countermeasure and even further if adaptation to baseline could be facilitated. The goal of this research is to investigate the potential use of stochastic vestibular stimulation (SVS) as a technology to improve sensorimotor function. We hypothesize that low levels of SVS will improve sensorimotor performance through stochastic resonance (SR). The SR phenomenon occurs when the response of a nonlinear system to a weak input signal is optimized by the application of a particular nonzero level of noise. Two studies have been initiated to investigate the beneficial effects and potential practical usage of SVS. In both studies, electrical vestibular stimulation is applied via electrodes on the mastoid processes using a constant current stimulator. The first study aims to determine the repeatability of the effect of vestibular stimulation on sensorimotor performance and perception in order to better understand the practical use of SVS. The beneficial effect of low levels of SVS on balance performance has been shown in the past. This research uses the same balance task repeated multiple times within a day and across days to study the repeatability of the stimulation effects. The balance test consists of 50 sec trials in which the subject stands with his or her feet together, arms crossed, and eyes closed on compliant foam. Varying levels of SVS, ranging from 0-700 micro A, are applied across different trials. The subject-specific optimal SVS level is that which results in the best balance performance as measured by inertial measurement units placed on the upper and lower torso of the subjects. Additionally, each individual’s threshold for illusory motion perception of suprasensory electrical vestibular stimulation is measured multiple times within and across days to better understand how multiple SVS test methods compare. The second study aims to demonstrate stochastic resonance in the vestibular system using a perception based motion recognition task. This task measures an individual’s velocity threshold of motion recognition using a 6-degree of freedom Stewart platform and a 3-down/1-up staircase procedure. For this study, thresholds are determined using 150 trials in the upright, head-centered roll tilt motion direction at a 0.2 Hz frequency. We aim to demonstrate the characteristic bell shaped curve associated with stochastic resonance with each subject’s motion recognition thresholds at varying SVS levels ranging from 0 to 1500 micro A. The curve includes the individual’s baseline threshold with no SVS, optimal or minimal threshold at some mid-level of SVS, and finally degraded or increased threshold at a high SVS level. An additional aim is to formally retest each subject at his or her individual optimal SVS level on a different day than the original testing for additional validity. The overall purpose of this research is to further quantify the effects of SVS on various sensorimotor tasks and investigate the practical implications of its use in the context of human space flight so that it may be implemented in the future as a component of a comprehensive countermeasure plan for adaptation to G-transitions.

Galvan, R. C.↗

A Bayesian Approach for Estimating Uncertainty in Stochastic Economic Dispatch considering Wind Power Penetration

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in this stochastic economic dispatch problem for forecasting purposes, the conventional Monte-Carlo method is prohibitively time-consuming for practical applications. To overcome this problem, here we propose a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling as the computer experimental design, a Gaussian-process emulator is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated stochastic economic dispatch model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

17 WIND ENERGY↗

Correlation between human observer performance and model observer performance in differential phase contrast CT

Purpose: With the recently expanding interest and developments in x-ray differential phase contrast CT (DPC-CT), the evaluation of its task-specific detection performance and comparison with the corresponding absorption CT under a given radiation dose constraint become increasingly important. Mathematical model observers are often used to quantify the performance of imaging systems, but their correlations with actual human observers need to be confirmed for each new imaging method. This work is an investigation of the effects of stochastic DPC-CT noise on the correlation of detection performance between model and human observers with signal-known-exactly (SKE) detection tasks.Methods: The detectabilities of different objects (five disks with different diameters and two breast lesion masses) embedded in an experimental DPC-CT noise background were assessed using both model and human observers. The detectability of the disk and lesion signals was then measured using five types of model observers including the prewhitening ideal observer, the nonprewhitening (NPW) observer, the nonprewhitening observer with eye filter and internal noise (NPWEi), the prewhitening observer with eye filter and internal noise (PWEi), and the channelized Hotelling observer (CHO). The same objects were also evaluated by four human observers using the two-alternative forced choice method. The results from the model observer experiment were quantitatively compared to the human observer results to assess the correlation between the two techniques.Results: The contrast-to-detail (CD) curve generated by the human observers for the disk-detection experiments shows that the required contrast to detect a disk is inversely proportional to the square root of the disk size. Based on the CD curves, the ideal and NPW observers tend to systematically overestimate the performance of the human observers. The NPWEi and PWEi observers did not predict human performance well either, as the slopes of their CD curves tended to be steeper. The CHO generated the best quantitative agreement with human observers with its CD curve overlapping with that of human observer. Statistical equivalence between CHO and humans can be claimed within 11% of the human observer results, including both the disk and lesion detection experiments.Conclusions: The model observer method can be used to accurately represent human observer performance with the stochastic DPC-CT noise for SKE tasks with sizes ranging from 8 to 128 pixels. The incorporation of the anatomical noise remains to be studied.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Kinetic Monte Carlo simulation of dopant-defect systems under submicrosecond laser thermal processes

An innovative Kinetic Monte Carlo (KMC) code has been developed, which rules the post-implant kinetics of the defects system in the extremely far-from-the equilibrium conditions caused by the laser irradiation close to the liquid-solid interface. It considers defect diffusion, annihilation and clustering. The code properly implements, consistently to the stochastic formalism, the fast varying local event rates related to the thermal field T(r,t) evolution. This feature of our numerical method represents an important advancement with respect to current state of the art KMC codes. The reduction of the implantation damage and its reorganization in defect aggregates are studied as a function of the process conditions. Phosphorus activation efficiency, experimentally determined in similar conditions, has been related to the emerging damage scenario.

36 MATERIALS SCIENCE↗

Optimal Control of Differentially Private EV Charging: A Scalable Learning Approach Under Uncertainty

Internet of Things (IoT)-enabled electric vehicles (IoEVs) enable intelligent charging coordination that accounts for grid congestion. However, increased data exchange raises privacy concerns, as charging patterns can reveal sensitive driver behavior to grid operators. Here, we propose a differentially private (DP) EV charging framework that enables coordinated control while protecting driver data with theoretical privacy guarantees. Nevertheless, integrating DP inevitably introduces uncertainty into the control strategy for EVs, which can lead to infeasible solutions. To tackle this challenge, we develop a feasible and scalable control algorithm based on constrained reinforcement learning (CRL) and convex hulls. While our framework is designed to handle the uncertainty introduced by DP, it is general and also applicable to other sources of uncertainty in EV charging, such as the stochastic nature of driver behavior and renewable variability. This ensures feasible and privacy-preserving coordination of EV charging at scale. Our method constructs convex hulls within the action space to guarantee feasibility under stochastic constraints and incorporates constraint reduction techniques to improve scalability. Case studies based on IEEE benchmark systems demonstrate that the proposed approach effectively balances feasibility under uncertainty, scalability, and privacy in large-scale EV charging control.

Engineering - Power transmission and distribution↗