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At least 577 records · Page 32

A Practical Approach to Uncertainty Quantification Using Probability Boxes

To date, while the use of CFD for aerospace vehicle design and development is prevalent, the documentation of uncertainties associated with the simulations are rare. Instead, the current state-of-the-art relies heavily on the experience of the CFD practitioner to estimate the uncertainty associated with their simulations through simple sensitivity studies or subject matter expertise. This practice will have to be replaced with a formal uncertainty quantification (UQ) process if CFD is to play an expanded role in the research and engineering design community, test and evaluation community, and ultimately certification for flight. Accounting for uncertainties in a formal manner is a tedious process. Moreover, the typical CFD practitioner is not likely to be familiar with formal UQ methods. These factors have prevented the adoption of UQ methods in the engineering design and development cycle. This presentation will outline a credible approach to UQ using Probability Boxes that is straightforward to apply, and can readily be automated using existing UQ tool sets such as the DAKOTA packaged developed at Sandia. The added expense incurred when moving away from a deterministic CFD process to a stochastic one that captures uncertainties to enable risk-informed decision making will be discussed, as well as effective ways to reduce the computational costs.

Uncertainty Quantification↗

Galaxy Correlation Function and Local Density from Photometric Redshifts Using the Stochastic Order Redshift Technique (SORT)

The stochastic order redshift technique (SORT) is a simple, efficient, and robust method to improve cosmological redshift measurements. The method relies upon having a small (∼10 per cent) reference sample of high-quality redshifts. Within pencil- beam-like sub-volumes surrounding each galaxy, we use the precise dN/dz distribution of the reference sample to recover new redshifts and assign them one-to-one to galaxies such that the original rank order of redshifts is preserved. Preserving the rank order is motivated by the fact that random variables drawn from Gaussian probability density functions with different means but equal standard deviations satisfy stochastic ordering. This process is repeated for sub-volumes surrounding each galaxy in the survey. This results in every galaxy being assigned multiple ‘recovered’ redshifts from which a new redshift estimate is determined. An earlier paper applied SORT to a mock Sloan Digital Sky Survey at z 0.2 and accurately recovered the two-point correlation function (2PCF) on scales > 4 h−1Mpc. In this paper, we test the performance of SORT in surveys spanning the redshift range 0.75 < z < 2.25. We used two mock surveys extracted from the Small MultiDark–Planck and Bolshoi–Planck N-body simulations with dark matter haloes that were populated by the Santa Cruz semi-analytic model. We find that SORT overall improves redshift estimates, accurately recovers the redshift-space 2PCF ξ (s) on scales > 2.5 h−1Mpc, and provides improved local density estimates in regions of average or higher density, which may allow for improved understanding of how galaxy properties relate to their environments.

James Kakos↗

A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution

Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.

97 MATHEMATICS AND COMPUTING↗

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗

A Fast, Two-dimensional Gaussian Process Method Based on Celerite: Applications to Transiting Exoplanet Discovery and Characterization

Gaussian processes (GPs) are commonly used as a model of stochastic variability in astrophysical time series. In particular, GPs are frequently employed to account for correlated stellar variability in planetary transit light curves. The efficient application of GPs to light curves containing thousands to tens of thousands of data points has been made possible by recent advances in GP methods, including the celerite method. Here we present an extension of the celerite method to two input dimensions where, typically, the second dimension is small. This method scales linearly with the total number of data points when the noise in each large dimension is proportional to the same celerite kernel and only the amplitude of the correlated noise varies in the second dimension. We demonstrate the application of this method to the problem of measuring precise transit parameters from multiwavelength light curves and show that it has the potential to improve transit parameters measurements by orders of magnitude. Applications of this method include transit spectroscopy and exomoon detection, as well a broader set of astronomical problems.

79 ASTRONOMY AND ASTROPHYSICS↗

Stochastic scheduling for commercial building cooling systems: considering uncertainty in zone temperature prediction

Here, this paper presents the first attempt to address the uncertainty in zone temperature prediction with stochastic optimization. The uncertain zone temperature is a process uncertainty and has not been considered in the existing stochastic optimization for building control. To fill this gap, we proposed a novel formulation of stochastic optimization to handle process uncertainty in building control. Specifically, we first examined the accuracy of a typical linear model for predicting zone temperature. We then formulated the scheduling of the building cooling system as a stochastic optimization problem over a 24-hour look-ahead period to minimize the electricity cost of the studied building cooling system. After that, we applied the proposed stochastic load scheduling (SLS) to a direct expansion (DX) cooling system that serves a medium office building. Through simulation with a detailed building energy simulation software, EnergyPlus, we evaluated the operational cost and the thermal comfort compared with a deterministic load scheduling. The operation cost of scheduling was found to vary with the level of zone temperature prediction uncertainty. The proposed SLS can mitigate the impacts of uncertain zone temperature predictions on both operational cost and thermal comfort. The evaluation results indicate that the proposed SLS works better when the uncertainty level is more significant.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Characterization of latent image of electron beam resist via critical-dimension resonant soft X-ray scattering

Metrology plays a crucial role in semiconductor manufacturing by providing accurate and precise measurement and characterization of critical parameters. With the development of high-resolution extreme ultraviolet lithography (EUVL) processes, critical dimensions are shrinking to sub-10 nm. Resist materials encounter the challenge of providing heightened sensitivity and a handle on exacerbating stochastic variations. A comprehensive understanding of the chemical profile of the latent image is pivotal for mitigating stochastic effects and optimizing pattern quality. However, the subtle differences in chemistry between the exposed and unexposed regions of the resists make it extremely challenging to characterize the latent images with sub-nanometer precision. Here, we develop the metrology with critical-dimension resonant soft X-ray scattering (CD-RSoXS) to probe the chemical profiles of latent images stored in resist after exposure. The combination of absorption spectroscopy and enhanced scattering contrast makes it possible to characterize the subtle structural and chemical variations in the latent image. Moreover, the results of the measurements are compared with the simulations with a finite element method–based Maxwell solver to extract a detailed profile of the latent and developed images. We demonstrate that the CD-RSoXS technique can provide valuable insights into the high spatial resolution and local chemical sensitivity simultaneously, which is crucial to understanding the resolution limits and stochastic effects in EUVL processes.

36 MATERIALS SCIENCE↗

Stochastic reconstruction of fracture network pattern using spatial point processes

Fracture spatial patterns can strongly affect fluid flow in the subsurface. Proximity and distribution of fractures control reservoir flow behavior over various length scales. In many studies, however, simplified geometrical patterns are generated for fractures which may lead to unrealistic subsurface models. Here we introduce a new method for characterization and modeling of fracture spatial patterns based on outcrop observations. We use Ripley's K-function to characterize the arrangement of fracture barycenters and intersection points over various length scales. In addition, we use semivariograms to quantify spatial correlation in fracture intensity maps. Using this information, we develop a stochastic algorithm that generates two-dimensional fracture network realizations with spatial properties similar to those of a real fracture network measured in the field. Numerical simulation models indicate that the generated fracture realizations exhibit similar flow behaviors as that of the original fracture network. Furthermore, such modeling tools expand and improve our capability in building representative fracture models and in quantification of uncertainty in naturally and hydraulically fractured reservoirs.

58 GEOSCIENCES↗

Raptor: A Python Library for Porosity Predictions in Additive Manufacturing

Raptor is an efficient Python library for simulating stochastic lack-of-fusion (sLoF) defects in additive manufacturing (AM) processes. These defects arise from stochastic variations in the melt pool boundary leading to undermelting from insufficient overlap between adjacent melt pools or successive layers (Grasso & Colosimo, 2017; Khairallah et al., 2016). Performance variability of AM parts is a pressing challenge in qualification and certification of AM parts; this is in part due to the poorly understood formation rate and statistics of sLoF defects. Raptor is designed to capture the explicit morphologies of sLoF defects and their statistics to accelerate qualification and certification efforts of AM parts in critical applications.

Subraveti, Vamsi [Vanderbilt University]↗

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗

Stochastic exciton-scattering theory of optical line shapes: Renormalized many-body contributions

Spectral line shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by broad-band pulsed laser stimulation, as distinguished from those for stationary phonon bath. In particular, we consider the contribution of pair-fluctuations arising from the full bosonic many-body Hamiltonian within a mean-field approximation, treating the coupling to the system as a stochastic noise term. Herein, using the Itô transformation, we consider two limiting cases for our model, which lead to a connection between the observed spectral fluctuations and the spectral density of the environment. In the first case, we consider a Brownian environment and show that this produces spectral dynamics that relax to form dressed excitonic states and recover an Anderson–Kubo-like form for the spectral correlations. In the second case, we assume that the spectrum is Anderson–Kubo like and invert to determine the corresponding background. Using the Jensen inequality, we obtain an upper limit for the spectral density for the background. The results presented here provide the technical tools for applying the stochastic model to a broad range of problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Processing Aleatory and Epistemic Uncertainties in Experimental Data From Sparse Replicate Tests of Stochastic Systems for Real-Space Model Validation

This paper presents a practical methodology for propagating and processing uncertainties associated with random measurement and estimation errors (that vary from test-to-test) and systematic measurement and estimation errors (uncertain but similar from test-to-test) in inputs and outputs of replicate tests to characterize response variability of stochastically varying test units. Also treated are test condition control variability from test-to-test and sampling uncertainty due to limited numbers of replicate tests. These aleatory variabilities and epistemic uncertainties result in uncertainty on computed statistics of output response quantities. The methodology was developed in the context of processing experimental data for “real-space” (RS) model validation comparisons against model-predicted statistics and uncertainty thereof. The methodology is flexible and sufficient for many types of experimental and data uncertainty, offering the most extensive data uncertainty quantification (UQ) treatment of any model validation method the authors are aware of. It handles both interval and probabilistic uncertainty descriptions and can be performed with relatively little computational cost through use of simple and effective dimension- and order-adaptive polynomial response surfaces in a Monte Carlo (MC) uncertainty propagation approach. A key feature of the progressively upgraded response surfaces is that they enable estimation of propagation error contributed by the surrogate model. Sensitivity analysis of the relative contributions of the various uncertainty sources to the total uncertainty of statistical estimates is also presented. Finally, the methodologies are demonstrated on real experimental validation data involving all the mentioned sources and types of error and uncertainty in five replicate tests of pressure vessels heated and pressurized to failure. Simple spreadsheet procedures are used for all processing operations.

97 MATHEMATICS AND COMPUTING↗

Random element method for numerical modeling of diffusional processes

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Ghoniem, A. F.↗

Observation of spatter-induced stochastic lack-of-fusion in laser powder bed fusion using in situ process monitoring

Material produced via additive manufacturing (AM) continues to exhibit variable mechanical properties despite apparent optimization of processing parameters, inhibiting qualification efforts and limiting use in critical applications. Stochastic lack-of-fusion flaws may help explain this variability, but the origin of these seemingly random defects has to this point remained unclear. In this work, we show that spatter particles, material ejected from the laser melt pool, are directly responsible for generating stochastic lack-of-fusion in laser-based powder bed fusion components through the application of spatial statistics. Herein a statistically significant, causal relationship between spatter particles and stochastic lack-of-fusion is established, and the spatial and morphological relationships between spatter and internal flaws are investigated. The occurrence of spatter-induced lack-of-fusion in relation to the inert gas flow and laser trajectory direction is also investigated, and recommendations for mitigating the occurrence of spatter are evaluated.

36 MATERIALS SCIENCE↗

Cross-Scale Observational Signatures of Magnetic Reconnection

Magnetic reconnection is a significant mechanism for energy release across many astrophysical applications. In the solar atmosphere, reconnection is considered a primary contributor of flare evolution and coronal heating. Directly observing reconnection occurring in the solar atmosphere, however, is not trivial considering that the scale size of the diffusion region is magnitudes smaller than the observational capabilities of current instrumentation, and coronal magnetic field measurements are not currently sufficient to capture the process. Meanwhile, reconnection occurring in the Earth's magnetosphere transfers energy from the solar wind through a comparable process, although on vastly different scales. Magnetospheric measurements are made in situ rather than remotely; ergo, comparison of observations between the two regimes allows for potentially significant insight into reconnection as a stochastic and possibly turbulent process. We will present a set of observations from long-duration solar events and compare them to in situ measurements from the magnetosphere.

Savage, Sabrina↗

Signal processing in a randomly time varying system.

Stochastic operators are applied to an analysis of some deterministic systems of signal transformation. The distribution of a random process at the output of a system is given through its distribution at the input and through a stochastic Green's function. A two-point correlation function is derived to obtain a solution to differential equations which contain coefficients, boundary conditions, or right-hand terms representing random processes.

Adomian, G.↗

Control of Complex Dynamic Systems by Neural Networks

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.

Spall, James C.↗

Microgrid energy scheduling under uncertain extreme weather: Adaptation from parallelized reinforcement learning agents

Microgrids are useful solutions for integrating renewable energy resources and providing seamless green electricity to minimize carbon footprint. In recent years, extreme weather events happened often worldwide and caused significant economic and societal losses. Such events bring uncertainties to the microgrid energy scheduling problems and increase the challenges of microgrid operation. Traditional optimization approaches suffer from the inaccuracy of the uncertain microgrid model and the unseen events. Existing reinforcement learning (RL) - based approaches are also hampered by the limited generalization and the increasing computational burden when stochastic formulations are required to accommodate the uncertainties. This paper proposes a new parallelized reinforcement learning (PRL) method based on the probabilistic events to handle the microgrid energy uncertainties. Specifically, several local learning agents are employed to interact with pertinent microgrid environments in a distributed manner and report outcomes to the global agent, which will optimize microgrid energy resources online during extreme events. The stochastic microgrid energy optimization problem is reformulated to include all possible scenarios with probabilities. The advantage estimate functions of learning agents are designed with a backward sweep to transfer the outcomes to the value function updating process. Two simulation studies, stochastic optimization and online testing, are performed to compare with several existing RL approaches. Results substantiate that the proposed PRL method can achieve up to 20% optimization performance improvement with 4 and 28 times less computation cost than Q-learning with experience replay and multi-agent Q-learning approaches, respectively.

24 POWER TRANSMISSION AND DISTRIBUTION↗