Complex stochastic noise and modulation.
Distribution theory to represent stochastic modulation and noise processes as analytic time functions
Gupta, S. C.↗
SEARCH · Engineering Papers
Results for “STOCHASTIC PROCESSES”
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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Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics
The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted
Pohorille, Andrew↗
Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems
In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.
CPH systems↗
Development of a Physics-Based Combustion Model for Engine Knock Prediction
The objective of this project is to improve the prediction of engine knock by developing a new combustion modeling framework. Engine knock is a limiting factor to constrain the increase of fuel efficiency for spark ignition (SI) engines in most passenger cars. Efforts to increase fuel efficiency, increasing the compression ratio or downsizing, lead to the increase in the tendency of the knock occurrence. The knock is an undesired ignition of the end-gas, unburned fuel/air mixture ahead of the spark-ignited premixed flame, resulting in rapid in-cylinder pressure rises and engine damages. The combustion modeling framework developed in this project can consider turbulence-chemistry interactions during end-gas ignition, while using a reasonably detailed chemical mechanism developed for ignition and combustion reactions under engine relevant conditions, and the subtle characteristics of spark-ignited flame propagation. It is developed in the context of large eddy simulation (LES), which can capture stochastic in-cylinder processes. The developed model is incorporated into a commercial software for engine simulation, CONVERGE CFD, as a user defined function, and validated. Engine knock and knock-free experiments as well as direct numerical simulation (DNS) of end-gas ignition in homogeneous turbulence are performed to help model development and provide data sets for model validation. With further validation, the developed model is expected to advance the predictive capability for engine knock simulations and thus contribute to improving the fuel efficiency.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Processing Random and Systematic Experimental Uncertainties in Replicate Tests of Stochastic Phenomena for Real-Space Model Validation.
Abstract not provided.
Romero, Vicente J.↗
A coordination theory for intelligent machines
A formal model for the coordination level of intelligent machines is established. The framework of the coordination level investigated consists of one dispatcher and a number of coordinators. The model called coordination structure has been used to describe analytically the information structure and information flow for the coordination activities in the coordination level. Specifically, the coordination structure offers a formalism to (1) describe the task translation of the dispatcher and coordinators; (2) represent the individual process within the dispatcher and coordinators; (3) specify the cooperation and connection among the dispatcher and coordinators; (4) perform the process analysis and evaluation; and (5) provide a control and communication mechanism for the real-time monitor or simulation of the coordination process. A simple procedure for the task scheduling in the coordination structure is presented. The task translation is achieved by a stochastic learning algorithm. The learning process is measured with entropy and its convergence is guaranteed. Finally, a case study of the coordination structure with three coordinators and one dispatcher for a simple intelligent manipulator system illustrates the proposed model and the simulation of the task processes performed on the model verifies the soundness of the theory.
Wang, Fei-Yue↗
Arbitrarily accurate, nonparametric coarse graining with Markov renewal processes and the Mori–Zwanzig formulation
Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. However, summarizing and analyzing the results of such simulations is often challenging due to the high dimension in which simulations are carried out and, consequently, due to the very large amount of data that are typically generated. Coarse graining is a popular technique for addressing this problem by providing compact and expressive representations. Coarse graining, however, potentially comes at the cost of accuracy, as dynamical information is, in general, lost when projecting the problem in a lower-dimensional space. This article shows how to eliminate coarse-graining error using two key ideas. First, we represent coarse-grained dynamics as a Markov renewal process. Second, we outline a data-driven, non-parametric Mori–Zwanzig approach for computing jump times of the renewal process. Numerical tests on a small protein illustrate the method.
36 MATERIALS SCIENCE↗
Optimization of stochastic feature properties in laser powder bed fusion
Process parameter selection in laser powder bed fusion (LPBF) controls the as-printed dimensional tolerances, pore formation, surface quality and microstructure of printed metallic structures. Measuring the stochastic mechanical performance for a wide range of process parameters is cumbersome both in time and cost. As such, in this study, we overcome these hurdles by using high-throughput tensile (HTT) testing of over 250 dogbone samples to examine process-driven performance of strut-like small features, ~1 mm 2 in austenitic stainless steel (316 L). The output mechanical properties, porosity, surface roughness and dimensional accuracy were mapped across the printable range of laser powers and scan speeds using a continuous wave laser LPBF machine. Tradeoffs between ductility and strength are shown across the process space and their implications are discussed. While volumetric energy density deposited onto a substrate to create a melt-pool can be a useful metric for determining bulk properties, it was not found to directly correlate with output small feature performance.
316 L stainless steel↗
Uncertainty Quantification for Multiphase Computational Fluid Dynamics Closure Relations with a Physics-Informed Bayesian Approach
Multiphase Computational Fluid Dynamics (MCFD) based on the two-fluid model is considered a promising tool to model complex two-phase flow systems. MCFD simulation can predict local flow features without resolving interfacial information. As a result, the MCFD solver relies on closure relations to describe the interaction between the two phases. Those empirical or semi-mechanistic closure relations constitute a major source of uncertainty for MCFD predictions. In this paper, we leverage a physics-informed uncertainty quantification (UQ) approach to inversely quantify the closure relations’ model form uncertainty in a physically consistent manner. This proposed approach considers the model form uncertainty terms as stochastic fields that are additive to the closure relation outputs. Combining dimensionality reduction and Gaussian processes, the posterior distribution of the stochastic fields can be effectively quantified within the Bayesian framework with the support of experimental measurements. As this UQ approach is fully integrated into the MCFD solving process, the physical constraints of the system can be naturally preserved in the UQ results. Here, in a case study of adiabatic bubbly flow, we demonstrate that this UQ approach can quantify the model form uncertainty of the MCFD interfacial force closure relations, thus effectively improving the simulation results with relatively sparse data support.
42 ENGINEERING↗
Energy supply processes for magnetospheric substorms and solar flares - Tippy bucket model or pitcher model?
In the past, both magnetospheric substorms and solar flares have almost exclusively been discussed in terms of explosive magnetic reconnection. Such a model may conceptually be illustrated by the so-called 'tippy-bucket model', which causes sudden unloading processes, namely a sudden (catastrophic, stochastic, and unpredictable) conversion of stored magnetic energy. However, recent observations indicate that magnetospheric substorms can be understood as a result of a directly driven process which can conceptually be illustrated by the 'pitcher model' in which the output rate varies in harmony with the input rate. It is also possible that solar flare phenomena are directly driven by a photospheric dynamo. Thus, explosive magnetic reconnection may simply be an unworkable hypothesis and may not be a puzzle to be solved as the primary energy supply process for magnetospheric substorms and solar flares.
Akasofu, S.-I.↗
Transport of ions in presence of induced electric field and electrostatic turbulence - Source of ions injected into ring current
The transport of ions from the polar ionosphere to the inner magnetosphere during stormtime conditions has been computed using a Monte Carlo diffusion code. The effect of the electrostatic turbulence assumed to be present during the substorm expansion phase was simulated by a process that accelerated the ions stochastically perpendicular to the magnetic field with a diffusion coefficient proportional to the energization rate of the ions by the induced electric field. This diffusion process was continued as the ions were convected from the plasma sheet boundary layer to the double-spiral injection boundary. Inward of the injection boundary, the ions were convected adiabatically. By using as input an O(+) flux of 2.8 x 10 to the 8th per sq cm per s (w greater than 10 eV) and an H(+) flux of 5.5 x 10 to the 8th per sq cm per s (w greater than 0.63 eV), the computed distribution functions of the ions in the ring current were found to be in good agreement, over a wide range in L (4 to 8), with measurements made with the ISEE-1 satellite during a storm. This O(+) flux and a large part of the H(+) flux are consistent with the DE satellite measurements of the polar ionospheric outflow during disturbed times.
Cladis, J. B.↗
The polar ionosphere as a source of the storm time ring current
The transport of ions from the polar ionosphere to the inner magnetosphere during storm time conditions has been computed using a Monte Carlo diffusion code. The effect of the electrostatic turbulence assumed to be present during the substorm expansion phase was simulated by a process that accelerated the ions stochastically perpendicular to the magnetic field with a diffusion coefficient proportional to the rate of energization of the ions by the induced electric field. This diffusion process was continued as the ions were convected from the plasma sheet boundary layer to the double-spiral injection boundary. Inward of the injection boundary the ions were convected adiabatically. By using as input an O(+) flux of 2.8 x 10 to the 8th per sq cm per s (w greater than 10 eV) and an H(+) flux of 5.5 x 10 to the 8th per sq cm per s (w greater than .63 eV) the computed distribution functions of the ions in the ring current were found to be in good agreement, over a wide range in L (4-8), with measurements made with the ISEE 1 satellite during a storm. This O(+) flux and a large part of the H(+) flux appear to be consistent with the DE-1 and DE-2 satellite measurements of the polar ionospheric outflow during disturbed times.
Cladis, J. B.↗
Stochastic machine learning via sigma profiles to build a digital chemical space
This work establishes a different paradigm on digital molecular spaces and their efficient navigation by exploiting sigma profiles. To do so, the remarkable capability of Gaussian processes (GPs), a type of stochastic machine learning model, to correlate and predict physicochemical properties from sigma profiles is demonstrated, outperforming state-of-the-art neural networks previously published. The amount of chemical information encoded in sigma profiles eases the learning burden of machine learning models, permitting the training of GPs on small datasets which, due to their negligible computational cost and ease of implementation, are ideal models to be combined with optimization tools such as gradient search or Bayesian optimization (BO). Gradient search is used to efficiently navigate the sigma profile digital space, quickly converging to local extrema of target physicochemical properties. While this requires the availability of pretrained GP models on existing datasets, such limitations are eliminated with the implementation of BO, which can find global extrema with a limited number of iterations. A remarkable example of this is that of BO toward boiling temperature optimization. Holding no knowledge of chemistry except for the sigma profile and boiling temperature of carbon monoxide (the worst possible initial guess), BO finds the global maximum of the available boiling temperature dataset (over 1,000 molecules encompassing more than 40 families of organic and inorganic compounds) in just 15 iterations (i.e., 15 property measurements), cementing sigma profiles as a powerful digital chemical space for molecular optimization and discovery, particularly when little to no experimental data is initially available.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Identification of hot water end-use process of electric water heaters from energy measurements
This paper presents an algorithm for the identification of parameters for a stochastic hot water end-use process that drives a homogeneous population of thermostatically controlled electric water heaters (EWH). Usually, only metered interval consumption data (kWh) is collected and the hot water end-use process is unobservable to utility and aggregators. However, the availability of EWHs for demand response (DR) is closely coupled with the hot water end-use process. In this context, the hot water end-use process is modeled as a two-state Markov chain (Use / No use), which causes the thermostatic ON-OFF switching process to behave as a Markov renewal process (MRP). A set of first passage-time problems is developed to obtain the moments of the transition probability densities of the MRP. These problems are addressed by establishing a system of coupled partial differential equations characterizing the temperature evolution of the EWH population. A key quantity in the methodology for estimating the parameters is the total time an EWH is ON within a period of interest. It is referred to as the total busy time. Total busy time in this approach is a random variable for which analytical expressions of the moments are developed as a function of the metered window length. The latter expressions become the basis of a hot water demand model identification algorithm which is validated using agent-based simulations of EWHs.
42 ENGINEERING↗
Online Control of Process Variance Using Feedback
For many stochastic control problem formulations, design objectives typically include constraining the covariance of the outputs of the system. Recent engineering challenges have demonstrated an interest in controlling system output covariances to a setpoint. However, open-loop control of system output covariance can be exceptionally challenging when the system has significant plant uncertainties. This paper explores closed-loop control of the system’s output covariance using a windowed variance function. The stochastic nature of the windowed variance feedback means that root locus and other classical control design techniques cannot be immediately used. Expected value analysis is used to generate transfer functions for the average response of such systems, and the results are used to design controllers. Stochastic simulations are presented to verify the analytical results and make other observations concerning closed-loop variance control.
Bieniek, Mitchell↗
Sequential processing techniques for trajectory estimation
Sequential stochastic techniques for trajectory estimation
Berry, W. H.↗
Advancing process-based flood frequency analysis for assessing flood hazard and population flood exposure
Recent studies have showcased the use of process-based hydrological models with Stochastic Storm Transposition (SST) techniques to conduct Flood Frequency Analysis (FFA). This framework, referred hereby FFA-SST, has proved to be a robust strategy to estimate peak flows of specific annual exceedance probability (e.g., 100-year peak flow) that can reflect natural and anthropogenic disturbances, including changes in land use and meteorological patterns. With the objective of advancing the FFA-SST framework, this study presents for the first time the use of an Integrated Surface-Subsurface Hydrological Model (ISSHM) to conduct FFA-SST by extending the analysis from peak flow responses to flood extent, enabling a unique view and analysis of flood hazard and population flood exposure at the basin scale. As a proof-of-concept, we used the ISSHM, Advanced Terrestrial Simulator (Amanzi-ATS) model, and the SST model, RainyDay, to conduct FFA-SST by simulating the flood response to 5,000 annual synthetic storm events in a 2,227 $km^2$ Southeast Texas watershed. We demonstrate that ATS, without site-specific calibration, provides a robust process-based representation of peak flows, flood extent, streamflow, evapotranspiration, soil moisture content, and water storage changes. Our results and analyses, covering frequency curves up to a 500-year return period for peak flows, basin inundation fractions, and the number of people exposed to flooding, offer a unique perspective to analyze flood impacts across spatial scales. Overall, this study provides critical insights for flood risk management by extending the FFA-SST framework to include both flood hazard and population flood exposure analyses at the basin scale. Such an approach will empower stakeholders and disaster emergency agencies with a more comprehensive understanding of flood impacts across the entire basin domain, facilitating informed decision-making for flood risk assessment and management.
58 GEOSCIENCES↗
Stochasticity in the Switching of Nanodisks for Probabilistic Computing
Stochasticity in magnetic nanodevices is an essential characteristic for harnessing these devices to computing based on population coding or the building blocks of probabilistic computing, p-bits. A magnetic tunneling junction (MTJ) consisting of a patterned magnetic element is considered a promising computing unit in the concept of artificial neurons and p-bits. A comprehensive understanding of the stochasticity in the switching of patterned magnetic elements is crucial for realizing MTJ-based probabilistic computing technology. In the present work, the stochastic behavior in the switching process of a perpendicularly magnetized Co/Pt disk within an array was directly observed utilizing full-field soft X-ray microscopy. Within 50 repeated hysteretic cycles, the stochastic magnetization switching of individual Co/Pt disks within disk arrays is identified. We found that the stochasticity in the magnetization switching of disks considerably depends on the disk size. The stochasticity initially decreases as the disk radius gets bigger from 125 to 375 nm (region I), then increases with further enlarging the disk size to 625 nm (region II). The variance of thermal fluctuation relevant to the disk size and the multilevel switching within a disk are severely involved in the observed size-dependent stochasticity. Furthermore, this work provides the way for controlling the stochasticity in the switching of nanopatterned elements, which is a key aspect of MTJ-based probabilistic computing.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗