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NASA NTRS1998

Effects of magnetometer calibration and maneuvers on accuracies of magnetometer-only attitude-and-rate determination

Two different algorithms - a deterministic magnetic-field-only algorithm and a Kalman filter for gyroless spacecraft - are used to estimate the attitude and rates of the Rossi X-Ray Timing Explorer (RXTE) using only measurements from a three-axis magnetometer. The performance of these algorithms is examined using in-flight data from various scenarios. In particular, significant enhancements in accuracies are observed when' the telemetered magnetometer data are accurately calibrated using a recently developed calibration algorithm. Interesting features observed in these studies of the inertial-pointing RXTE include a remarkable sensitivity of the filter to the numerical values of the noise parameters and relatively long convergence time spans. By analogy, the accuracy of the deterministic scheme is noticeably lower as a result of reduced rates of change of the body-fixed geomagnetic field. Preliminary results show the filter-per-axis attitude accuracies ranging between 0.1 and 0.5 deg and rate accuracies between 0.001 deg/sec and 0.005 deg./sec, whereas the deterministic method needs a more sophisticated techniques for smoothing time derivatives of the measured geomagnetic field to clearly distinguish both attitude and rate solutions from the numerical noise. Also included is a new theoretical development in the deterministic algorithm: the transformation of a transcendental equation in the original theory into an 8th-order polynomial equation. It is shown that this 8th-order polynomial reduces to quadratic equations in the two limiting cases-infinitely high wheel momentum, and constant rates-discussed in previous publications.

Challa, M.↗

DOE OSTI2021

Evaluation of sequence tracking methods for Compton cameras based on CdZnTe arrays

In this study, the performance of sequence tracking methods for multiple interaction events in specific CdZnTe Compton imagers was evaluated using Monte Carlo simulations. The Compton imager consisted of a 6 × 6 array of virtual Frisch-grid CZT crystals, where the dimensions of each crystal were 5 × 5 × 12 mm 3 . The sequence tracking methods for another Compton imager that consists of two identical CZT crystals arrays were also evaluated. When 662 keV radiation was incident on the detectors, the percentages of the correct sequences determined by the simple comparison and deterministic methods for two sequential interactions were identical (~80 %), while those evaluated using the minimum squared difference method (55-59 %) and Three Compton method (45-55 %) for three sequential interactions, differed from each other. The reconstructed images of a 662 keV point source detected using single and double arrays were evaluated based on their angular resolution and signal-to-noise ratio, and the results showed that the double arrays outperformed single arrays.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Numerical Method Improvements in Griffin for Pebble Bed Reactors with a Focus on the Computation of Burnup

Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient multiphysics modeling of advanced reactors, has been used recently to model both high-temperature gas-cooled and fluoride-salt-cooled pebble bed reactors (PBRs). Griffin uses deterministic methods for solving neutron transport and an Eulerian approach to model pebble movement. An Eulerian approach is also used to directly compute burnup instead of using a pass approach like other tools such as VSOP or PANGU. This work discusses verification efforts and numerical method improvements related specifically to the Eulerian modeling approach implemented for directly computing pebble burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1996

The Study of the Relationship between Probabilistic Design and Axiomatic Design Methodology

The structural design, or the design of machine elements, has been traditionally based on deterministic design methodology. The deterministic method considers all design parameters to be known with certainty. This methodology is, therefore, inadequate to design complex structures that are subjected to a variety of complex, severe loading conditions. A nonlinear behavior that is dependent on stress, stress rate, temperature, number of load cycles, and time is observed on all components subjected to complex conditions. These complex conditions introduce uncertainties; hence, the actual factor of safety margin remains unknown. In the deterministic methodology, the contingency of failure is discounted; hence, there is a use of a high factor of safety. It may be most useful in situations where the design structures are simple. The probabilistic method is concerned with the probability of non-failure performance of structures or machine elements. It is much more useful in situations where the design is characterized by complex geometry, possibility of catastrophic failure, sensitive loads and material properties. Also included: Comparative Study of the use of AGMA Geometry Factors and Probabilistic Design Methodology in the Design of Compact Spur Gear Set.

Onwubiko, Chin-Yere↗

DOE OSTI2025

Optimizing the Smoothness and Thickness Uniformity of Thin-Film Parylene-N Vapor-Deposited Coatings for Inertial Confinement Fusion Experiments

Polymer coatings with submicrometer smoothness and constant thickness are a required component in a variety of inertial confinement fusion experiments. Smoothness is important for minimizing Rayleigh-Taylor-driven hydrodynamic instabilities, and uniform thickness is important for uniform shock propagation and shell convergence, both of which are critical phenomena that affect the experiment. The preferred polymer coating method is to vapor deposit the parylene-N polymer because it provides nominally smooth conformal coatings. As the coating thickness exceeds 5 µm, however, dome-shaped nodular growth defects develop and the thickness will vary by up to 17% over a distance of 3 cm. This study presents a deterministic method for achieving uniform film thicknesses with ±2% variability over 3 cm and a predictive method to control the thickness to within 5% of the desired value. A coating smoothness of ∼50 nm rms, measured over 40 000 µm 2 , was achieved by adding additional surfaces near the substrates. This additional area improved the thickness uniformity, an effect that is attributed to the low sticking coefficient of the parylene monomer.

chemical vapor deposition (CVD)↗

NASA NTRS2013

Alternate Methods in Refining the SLS Nozzle Plug Loads

Numerical analysis has shown that the SLS nozzle environmental barrier (nozzle plug) design is inadequate for the prelaunch condition, which consists of two dominant loads: 1) the main engines startup pressure and 2) an environmentally induced pressure. Efforts to reduce load conservatisms included a dynamic analysis which showed a 31% higher safety factor compared to the standard static analysis. The environmental load is typically approached with a deterministic method using the worst possible combinations of pressures and temperatures. An alternate probabilistic approach, utilizing the distributions of pressures and temperatures, resulted in a 54% reduction in the environmental pressure load. A Monte Carlo simulation of environmental load that used five years of historical pressure and temperature data supported the results of the probabilistic analysis, indicating the probabilistic load is reflective of a 3-sigma condition (1 in 370 probability). Utilizing the probabilistic load analysis eliminated excessive conservatisms and will prevent a future overdesign of the nozzle plug. Employing a similar probabilistic approach to other design and analysis activities can result in realistic yet adequately conservative solutions.

Burbank, Scott↗

NASA NTRS2010

Navier-Stokes Dynamics by a Discrete Boltzmann Model

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

Rubinstein, Robet↗

NASA NTRS2017

Dynamic Routing of Aircraft in the Presence of Adverse Weather Using a POMDP Framework

Each year weather-related airline delays result in hundreds of millions of dollars in additional fuel burn, maintenance, and lost revenue, not to mention passenger inconvenience. The current approaches for aircraft route planning in the presence of adverse weather still mainly rely on deterministic methods. In contrast, this work aims to deal with the problem using a Partially Observable Markov Decision Processes (POMDPs) framework, which allows for reasoning over uncertainty (including uncertainty in weather evolution over time) and results in solutions that are more robust to disruptions. The POMDP-based decision support system is demonstrated on several scenarios involving convective weather cells and is benchmarked against a deterministic planning system with functionality similar to those currently in use or under development.

Decision making↗

NASA NTRS1993

The application of structural reliability techniques to plume impingement loading of the Space Station Freedom Photovoltaic Array

A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design, during its 15 year life, is minute.

Yunis, Isam S.↗

NASA NTRS1993

The Application of Structural Reliability Techniques to Plume Impingement Loading of the Space Station Freedom Photovoltaic Array

Yunis, Isam S.↗

NASA NTRS2010

Exhaustive Versus Randomized Searchers for Nonlinear Optimization in 21st Century Computing: Solar Application

We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.

Sen, Syamal K.↗

DOE OSTI2017

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthal resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2011

Probabilistic Path Planning of Montgolfier Balloons in Strong, Uncertain Wind Fields

Lighter-than-air vehicles such as hot-air balloons have been proposed for exploring Saturn s moon Titan, as well as other bodies with significant atmospheres. For these vehicles to navigate effectively, it is critical to incorporate the effects of surrounding wind fields, especially as these winds will likely be strong relative to the control authority of the vehicle. Predictive models of these wind fields are available, and previous research has considered problems of planning paths subject to these predicted forces. However, such previous work has considered the wind fields as known a priori, whereas in practical applications, the actual wind vector field is not known exactly and may deviate significantly from the wind velocities estimated by the model. A probabilistic 3D path-planning algorithm was developed for balloons to use uncertain wind models to generate time-efficient paths. The nominal goal of the algorithm is to determine what altitude and what horizontal actuation, if any is available on the vehicle, to use to reach a particular goal location in the least expected time, utilizing advantageous winds. The solution also enables one to quickly evaluate the expected time-to-goal from any other location and to avoid regions of large uncertainty. This method is designed for balloons in wind fields but may be generalized for any buoyant vehicle operating in a vector field. To prepare the planning problem, the uncertainty in the wind field is modeled. Then, the problem of reaching a particular goal location is formulated as a Markov decision process (MDP) using a discretized space approach. Solving the MDP provides a policy of what actuation option (how much buoyancy change and, if applicable, horizontal actuation) should be selected at any given location to minimize the expected time-to-goal. The results provide expected time-to-goal values from any given location on the globe in addition to the action policy. This stochastic approach can also provide insights not accessible by deterministic methods; for example, one can evaluate variability and risk associated with different scenarios, rather than only viewing the expected outcome.

Wolf, Michael↗

DOE OSTI2017

Assessing the social sustainability contribution of an infrastructure project under conditions of uncertainty

Assessing the viability of a public infrastructure includes economic, technical and environmental aspects; however, on many occasions, the social aspects are not always adequately considered. This article proposes a procedure to estimate the social sustainability of infrastructure projects under conditions of uncertainty, based on a multicriteria deterministic method. The variability of the method inputs is contributed by the decision-makers. Uncertain inputs are treated through uniform and beta PERT distributions. The Monte Carlo method is used to propagate uncertainty in the method. A case study of a road infrastructure improvement in El Salvador is used to illustrate this treatment. The main results determine the variability of the short and long-term social improvement indices by infrastructure and the probability of the position in the prioritization of the alternatives. The proposed mechanism improves the reliability of the decision making early in infrastructure projects, taking their social contribution into account. The results can complement environmental and economic sustainability assessments. - Highlights: •Estimate the social sustainability of infrastructure projects under conditions of uncertainty •The method uses multicriteria and Monte Carlo techniques and beta PERT distributions •Determines variability of the short and long term social improvement •Determines probability in the prioritization of alternatives •Improves reliability of decision making considering the social contribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Multigroup Constant Calculation with Static α-Eigenvalue Monte Carlo for Time-Dependent Neutron Transport Simulations

Herein, multigroup constants for deterministic methods that preserve the time-dependent physics of the neutron transport equations are derived. Alternative multigroup constant weighting spectra are discussed: (1) the fundamental k-eigenfunction, (2) the fundamental α-eigenfunction, and (3) a composite of several α-modes. To generate the fundamental α-eigenfunction for calculating the multigroup constants, a static fundamental α-eigenvalue method is implemented into the open source Monte Carlo code OpenMC. Several static and kinetic problems are devised to verify the implementations and to investigate the relative performance of the alternative multigroup constant weighting spectra. Results emphasize that as a multigroup constant weighting spectrum, the fundamental α-eigenfunction offers physical characteristics that make it advantageous (in producing accurate solutions) over the typically used fundamental k-eigenfunction.

42 ENGINEERING↗

DOE OSTI2019

Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging

We present a formulation to simultaneously invert for a heterogeneous shear modulus field and traction boundary conditions in an incompressible linear elastic plane stress model. Our approach utilizes scalable deterministic methods, including adjoint-based sensitivities and quasi-Newton optimization, to reduce the computational requirements for large-scale inversion with partial differential equation (PDE) constraints. Here, we address the use of regularization for such formulations and explore the use of different types of regularization for the shear modulus and boundary traction. We apply this PDE-constrained optimization algorithm to a synthetic dataset to verify the accuracy in the reconstructed parameters, and to experimental data from a tissue-mimicking ultrasound phantom. In all of these examples, we compare inversion results from full-field and sparse data measurements.

42 ENGINEERING↗

DOE OSTI2026

Deterministic Quantum Trajectory via Imaginary Time Evolution

Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum trajectories also encode essential physical information. Prominent examples include measurement-induced phase transitions, where a pure quantum state corresponding to fixed measurement outcomes (trajectories) exhibits distinct entanglement phases, depending on the measurement rate. However, direct observation of this effect is hindered by an exponential postselection barrier, whereby the probability of realizing a specific trajectory is exponentially small. We propose a deterministic method to efficiently prepare quantum trajectories in polynomial time using imaginary time evolution and, thus, overcome this fundamental challenge. Here, we demonstrate that our method applies to a certain class of quantum states, and argue that universal approaches do not exist for any quantum trajectories. Our result paves the way for experimentally exploring the physics of individual quantum trajectories at scale and enables direct observation of certain postselection-dependent phenomena.

Mittal, Shivan [Los Alamos National Laboratory (LA↗