Calibration of Radiation-Induced Cancer Risk Models According to Random Data
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model calibration↗
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Probabilistic finite elements
In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.
Belytschko, Ted↗
Profiling Saturn's rings by radio occultation
The development of reconstruction algorithms that correct for diffraction effects in radio occultation measurements is described. The reciprocal Fresnel transform relationship between the complex amplitude of the observed coherent signal and the complex microwave transmittance of the rings is derived using the Huygens-Fresnel formulation of the diffraction problem. The effects of the finite data segment width, the uncertainties in the Fresnel scale, systematic phase errors in the kernel of the inverse transform, reference oscillator instabilities, and random noise measurements on the resolution of the reconstructed transmittance are analyzed. Examples of reconstructed opacity profiles for some regions of Saturn's rings derived by applying the reconstruction theory to Voyager 1 at Saturn data are presented.
Marouf, Essam A.↗
Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning
Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions.
Corbetta, Matteo↗
Implementation of Probabilistic Design Methodology at Tennessee State University
Engineering Design is one of the most important areas in engineering education. Deterministic Design Methodology (DDM) is the only design method that is taught in most engineering schools. This method does not give a direct account of uncertainties in design parameters. Hence, it is impossible to quantify the uncertainties in the response and the actual safety margin remains unknown. The desire for a design methodology tha can identify the primitive (random) variables that affect the structural behavior has led to a growing interest on Probabilistic Design Methodology (PDM). This method is gaining more recognition in industries than in educational institutions. Some of the reasons for the limited use of the PDM at the moment are that many are unaware of its potentials, and most of the software developed for PDM are very recent. The central goal of the PDM project at Tennessee State University is to introduce engineering students to the method. The students participating in the project learn about PDM and the computer codes that are available to the design engineer. The software being used of this project is NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) developed under NASA probabilistic structural analysis program. NESSUS has three different modules which make it a very comprehensive computer code for PDM. A research in technology transfer through course offering in PDM is in effect a Tennessee State University. The aim is to familiarize students with the problem of uncertainties in engineering design. Included in the paper are some projects on PDM carried out by some students and faculty. The areas this method is being applied at the moment include, Design of Gears (spur and worm); Design of Shafts; Design of Statistically Indeterminate Frame Structures; Design of Helical Springs; and Design of Shock Absorbers. Some of the current results of these projects are presented.
Onwubiko, Chinyere↗
Synthesis of a modern/classical controller for large space structures
The paper is concerned with wide-sense stationary random vibrations of a representative large space structure subject to nonwhite excitations, and with synthesis of its controller amid modeling uncertainties due to truncated modes. Dynamics is analyzed by residue calculus in frequency domain. Steady state variance of a modal coordinate is shown to depend on, among other things, power spectral density of excitation at the modal frequency. Modal cost analysis is performed for an order reduction with a performance objective of attitude, attitude rate and energy control. Optimal and suboptimal output feedback controllers are compared. By treating deleted modes as an additive and a multiplicative perturbation in an idealized transfer function, the low frequency modes omitted according to modal cost analysis are found to cause instability. Finally, the size of the idealized model is shown to be governed by light damping and stringency in performance and stability specifications.
Hablani, H. B.↗
Ultraviolet extinction differences within NGC 6530
Ultraviolet extinction curves are presented for 14 stars in the very young cluster NGC 6530. The variation of the short-wavelength extinction is consistent with that expected based on random errors alone, although the weakest extinction is found only toward the cluster center. Variations significantly larger than the measurement uncertainty are found in the area, width, and central peak position of the 2200 A extinction bump. These parameters are largest in the cluster center and decrease systematically outwards. Physical processes capable of modifying the grains in the H II region containing the cluster are discussed.
Boggs, Don↗
Stereo advantage for a peg-in-hole task using a force-feedback manipulator
An improved assessment methodology has been implemented at NOSC and tested using an instrumented peg-in-hole (PiH) taskboard. Several aspects of the methodology are discussed in light of their implications for future studies of manipulator performance. Using a simple (but high-fidelity) force-feedback manipulator, a group of 9 trained operators showed a consistent advantage for stereoscopic TV viewing over monoscopic TV viewing when performing the PiH task. To introduce a controlled element of spatial uncertainty into the testing procedure, taskboard orientation relative to the manipulator and remote video camera head was changed in a randomized order on a trial-by-trial basis. The stereoscopic advantage demonstrated by this study can reasonably be expected to be even more pronounced as the quality of the stereo TV interface is improved and force-feedback provided through the manipulator system is diminished and/or distorted.
Spain, Edward H.↗
Computation of vertical profiles of longwave radiative cooling over the equatorial Pacific
An important quantity whose magnitude has not been throughly examined is the vertical distribution of heating in the Tropics. The details of the vertical distribution of heating have a significant impact on a number of phenomena, including the 30-60 day oscillation, sometimes known as the intraseasonal oscillation. Prior attempts to establish the structure of the heating relied on limited field data or assimilated data, coupled with climatological radiative heating parameters. The availability of high quality global-scale datasets has made it possible to make more accurate calculations than were possible a few years ago. An important component of the apparent heat budget is the longwave radiative cooling, which in this paper is found by using the ECMWF/WCRP/TOGA Archive 2 and ISCCP C1 datasets, together with a well-established parameterization scheme. A method is developed that can be used to estimate the vertical structure of cloud amounts based on top-of-atmosphere cloud observations, and the results are used with a wide-band longwave parameterization to produce longwave cooling rates over the tropical Pacific Ocean. Outgoing longwave radiation is calculated and compared the ERBE results. The calculated values are generally higher than those from ERBE, though the spatial distributions are similar. Some significant problems exist with the ECMWF upper-tropospheric water vapor amounts, which could imply uncertainties of 0.5 C/day in the calculated cooling rates. This is comparable to the differences associated with the minimum or random overlap assumptions used to generate cloud profiles.
Ramsey, Perry G.↗
Studies of Error Sources in Geodetic VLBI
Achieving the goal of millimeter uncertainty in three dimensional geodetic positioning on a global scale requires significant improvement in the precision and accuracy of both random and systematic error sources. For this investigation we proposed to study errors due to instrumentation in Very Long Base Interferometry (VLBI) and due to the atmosphere. After the inception of this work we expanded the scope to include assessment of error sources in GPS measurements, especially as they affect the vertical component of site position and the measurement of water vapor in the atmosphere. The atmosphere correction 'improvements described below are of benefit to both GPS and VLBI.
Rogers, A. E. E.↗
Modeling Errors in Daily Precipitation Measurements: Additive or Multiplicative?
The definition and quantification of uncertainty depend on the error model used. For uncertainties in precipitation measurements, two types of error models have been widely adopted: the additive error model and the multiplicative error model. This leads to incompatible specifications of uncertainties and impedes intercomparison and application.In this letter, we assess the suitability of both models for satellite-based daily precipitation measurements in an effort to clarify the uncertainty representation. Three criteria were employed to evaluate the applicability of either model: (1) better separation of the systematic and random errors; (2) applicability to the large range of variability in daily precipitation; and (3) better predictive skills. It is found that the multiplicative error model is a much better choice under all three criteria. It extracted the systematic errors more cleanly, was more consistent with the large variability of precipitation measurements, and produced superior predictions of the error characteristics. The additive error model had several weaknesses, such as non constant variance resulting from systematic errors leaking into random errors, and the lack of prediction capability. Therefore, the multiplicative error model is a better choice.
Modeling↗
Turbulent and directed plasma motions in solar flares
An improved method for fitting asymmetric soft X-ray line profiles from solar flares is presented. A two-component model is used where one component represents the total emission from directed upflow plasma and the other the emission from the plasma at rest. Unlike previous methods, the width of the moving component is independent from that of the stationary component. Time variations of flare plasma characteristics (i.e., temperature, emission measure of moving and stationary plasma, upflow and turbulent velocities) are derived from the Ca XIX and Fe XXV spectra recorded by the Bent Crystal Spectrometer on the Solar Maximum Mission. The fitting technique provides a statistical estimation for the uncertainties in the fitting parameters. The relationship between the directed and turbulent motions has been studied, and a correlation of the random and directed motions has been found in some flares with intensive plasma upflows. Mean temperatures of the upflowing and stationary plasmas are compared for the first time from ratios of calcium to iron X-ray line intensities. Finally, evidence for turbulent motions and the possibility of plasma upflow late into the decay phase is presented and discussed.
Fludra, A.↗
Assessment of computational prediction of tail buffeting
Assessments of the viability of computational methods and the computer resource requirements for the prediction of tail buffeting are made. Issues involved in the use of Euler and Navier-Stokes equations in modeling vortex-dominated and buffet flows are discussed and the requirement for sufficient grid density to allow accurate, converged calculations is stressed. Areas in need of basic fluid dynamics research are highlighted: vorticity convection, vortex breakdown, dynamic turbulence modeling for free shear layers, unsteady flow separation for moderately swept, rounded leading-edge wings, vortex flows about wings at high subsonic speeds. An estimate of the computer run time for a buffeting response calculation for a full span F-15 aircraft indicates that an improvement in computer and/or algorithm efficiency of three orders of magnitude is needed to enable routine use of such methods. Attention is also drawn to significant uncertainties in the estimates, in particular with regard to nonlinearities contained within the modeling and the question of the repeatability or randomness of buffeting response.
Edwards, John W.↗
Uncertainty Quantification of the FUN3D-Predicted NASA CRM Flutter Boundary
A nonintrusive point collocation method is used to propagate parametric uncertainties of the flexible Common Research Model, a generic transport configuration, through the unsteady aeroelastic CFD solver FUN3D. A range of random input variables are considered, including atmospheric flow variables, structural variables, and inertial (lumped mass) variables. UQ results are explored for a range of output metrics (with a focus on dynamic flutter stability), for both subsonic and transonic Mach numbers, for two different CFD mesh refinements. A particular focus is placed on computing failure probabilities: the probability that the wing will flutter within the flight envelope.
Stanford, Bret K.↗
Self-Consistent Implementation of a Zero-Equation Transport Model Into a Predictive Model for a Hall Effect Thruster
The performance of an axisymmetric multi-fluid Hall thruster code that incorporates a self-consistent, data-driven closure model for the anomalous electron transport is investigated. Five different operating conditions of the H9 magnetically shielded Hall thruster are simulated with the Jet Propulsion Laboratory’s Hall2De. In order to capture the inherent uncertainty associated with the closure model, O(100) simulations are run for each condition, each of using a coefficient set sampled randomly from a probability distribution. The results of these simulations provide probabilistic predictions of thruster performance quantities including thrust, and discharge current, as well as several component efficiencies and centerline plasma properties. The model is found to yield converged solutions at all conditions, with large 10 kHzrange oscillations and performance trends with voltage and flow rate similar to experiment. The model under-predicts the thrust by 15-25% and over-predicts the discharge current by 20% on average compared to experiments at the same discharge voltage and mass flow rate. This performance discrepancy is due to lower beam utilization, mass utilization, and divergence efficiency than experiment, resulting from high Hall parameters in the acceleration region, which lead to a protracted ion acceleration region. The physical processes underlying this result are discussed in the context of future data-driven modeling efforts.
Jorns, Benjamin A.↗
Discovery of X-Ray Polarization Angle Rotation in the Jet From Blazar Mrk 421
The magnetic-field conditions in astrophysical relativistic jets can be probed by multiwavelength polarimetry, which has been recently extended to X-rays. For example, one can track how the magnetic field changes in the flow of the radiating particles by observing rotations of the electric vector position angle Ψ. Here we report the discovery of a ΨX rotation in the X-ray band in the blazar Markarian 421 at an average flux state. Across the 5 days of Imaging X-ray Polarimetry Explorer observations on 4–6 and 7–9 June 2022, ΨX rotated in total by ≥360°. Over the two respective date ranges, we find constant, within uncertainties, rotation rates (80 ± 9° per day and 91 ± 8° per day) and polarization degrees (ΠX = 10% ± 1%). Simulations of a random walk of the polarization vector indicate that it is unlikely that such rotation(s) are produced by a stochastic process. The X-ray-emitting site does not completely overlap the radio, infrared and optical emission sites, as no similar rotation of Ψ was observed in quasi-simultaneous data at longer wavelengths. We propose that the observed rotation was caused by a helical magnetic structure in the jet, illuminated in the X-rays by a localized shock propagating along this helix. The optically emitting region probably lies in a sheath surrounding an inner spine where the X-ray radiation is released.
Makarian 421↗
Simulation of Stochastic Processes by Coupled ODE-PDE
A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.
Zak, Michail↗
Terrestrial Single-Station Analog for Constraining the Martian Core and Deep Interior: Implications for InSight
We used a terrestrial single-station seismometer to quantify the uncertainty of InSight (INterior explorations using Seismic Investigations, Geodesy and Heat Transport) data for determining Martian core size. To mimic Martian seismicity, we formed a catalog using 917 terrestrial earthquakes, from which we randomly selected events. We stacked ScS amplitudes on modeled arrival times and searched for where ScS produced coherent seismic amplitudes. A core detection was defined by a coherent peak with small offset between predicted and user-selected arrival times. Iterating the detection algorithm with varying signal-to-noise (SNR) ranges and quantity of events determined the selection frequency of each model and quantified core depth uncertainty. Increasing the quantity of events reduced core depth uncertainty while increasing the recovery rate, while increasing event SNR had little effect. Including ScS2 multiples increased the recovery rate and reduced core depth uncertainty when we used low quantities of events. The most-frequent core depths varied by back azimuth, suggesting our method is sensitive to the presence of mantle heterogeneities. When we added 1° in source distance errors, core depth uncertainty increased by up to 11 km and recovery rates decreased by <5%. Altering epicentral distances by 25% added ~35 km of uncertainty and reduced recovery rates to <50% in some cases. From these experiments, we estimate that if InSight can detect five events with high location precision (<10% epicentral distance errors), that there is at least an 88% chance of core depth recovery using ScS alone with uncertainty in core depth approaching 18 km and decreasing as more events are located.
Marusiak, Angela G.↗