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The optimal control theory of stochastic linear systems is discussed in terms of the advantages of distributed-control systems, and the control of randomly-sampled systems. An optimal solution to longitudinal control is derived and applied to the F-8 DFBW aircraft. A randomly-sampled linear process model with additive process and noise is developed.
Extensive flight test data obtained from two recent performance tests of a UH 60A aircraft are reviewed. A power difference is calculated from the power balance equation and is used to examine power measurement errors. It is shown that the baseline measurement errors are highly non-Gaussian in their frequency distribution and are therefore influenced by additional, unquantified variables. Linear regression is used to examine the influence of other variables and it is shown that a substantial portion of the variance depends upon measurements of atmospheric parameters. Correcting for temperature dependence, although reducing the variance in the measurement errors, still leaves unquantified effects. Examination of the power difference over individual test runs indicates significant errors from drift, although it is unclear how these may be corrected. In an idealized case, where the drift is correctable, it is shown that the power measurement errors are significantly reduced and the error distribution is Gaussian. A new flight test program is recommended that will quantify the thermal environment for all torque measurements on the UH 60. Subsequently, the torque measurement systems will be recalibrated based on the measured thermal environment and a new power measurement assessment performed.
The paper presents a statistical method for extracting regional information on the radiative heat flux at the top of the atmosphere from a satellite-borne scanning radiometer. The radiative heat flux distribution is denoted by a double Fourier series with coefficients to be determined from measurements. The method determines, in the sense of minimum variance, the best linear estimator of the total flux over a region. The heat flux distribution is represented by a truncated series which is unbiased.
SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.
Abstract This study demonstrated using yttrium (Y) as an indicator to estimate the total rare earth element and Y contents (REY) in coal-associated samples and to facilitate selection of samples with high REY assays in a fast and inexpensive manner. More than 10 anthracite-associated samples were collected from each of three Pennsylvanian sites (sites B, J and C) based on Thorium gamma ray logging suggesting high REY content. Several samples from each site were analyzed by ICP-MS to determine the rare earth distribution patterns and to establish the site-specific linear equations of Y and REY. The Y contents of the remaining samples were measured by a portable X-ray fluorescence analyzer, and the REY values were estimated based on the site-specific linear equation developed earlier. R-squared values above 0.70 were obtained for all the estimation equations from all three sites on both a whole sample basis and an ash basis. Previously, ash content has been widely used as an indicator of high REY content. This may not be applicable for a specific site. Site B in this study is an example where ash contents could not be statistically correlated with REY, so using Y for estimation is more applicable. The demonstrated sample screening process is suitable for samples from sites that share more similar distribution patterns (either MREY or LREY or HREY) as well as for samples from sites that share multiple distribution patterns (LREY/MREY/HREY) depending on the desirable accuracy. The demonstrated process lowers the analytical cost from $70 to 80 dollars per sample to $10–15 per sample while significantly reducing the processing time and acid consumption for ICP digestion. This is particularly true when a relatively large sample size is involved, for example, 100 samples from one site analyzed by ICP-MS/OES.
A new method for performing Monte Carlo forecasts is introduced. The method, called dynamic stratification, selects initial perturbations based on a stratification of the error distribution. A simple implementation is presented in which the error distribution used for the stratification is estimated from a linear model derived from a large ensemble of 12-h forecasts with the full dynamic model. The stratification thus obtained is used to choose a small subsample of initial states with which to perform the dynamical Monte Carlo forecasts. Several test cases are studied using a simple two-level general circulation model with uncertain initial conditions. It is found that the method provides substantial reductions in the sampling error of the forecast mean and variance when compared to the more traditional approach of choosing the initial perturbations at random. The degree of improvement, however, is sensitive to the nature of the initial error distribution and to the base state. In practice the method may be viable only if the computational burden involved in obtaining an adequate estimate of the error distribution is shared with the data-assimilation procedure.
The transonic truss-braced wing (TTBW) concept is under consideration by the NASA Advanced Air Transport Technology (AATT) project due to its potential to reduce fuel consumption of transport aircraft. To properly evaluate the TTBW concept, detailed structural modeling and subsequent test planning is underway, which requires a simplified set of discrete applied loads that simulate the distributed aerodynamic pressures. Given the unique architecture of the TTBW and its intended operation in the transonic regime, computational fluid dynamics (CFD) is the ideal approach to employ to ensure the aerodynamics of this configuration are sufficiently captured. To convert aerodynamic results into input for structural models, application of a data transfer tool, Discrete Data Transfer Between Dissimilar Meshes (DDTBDM), is presented to resolve aerodynamic pressures from CFD into single load vectors at hardpoints along both the wing and the strut. Evaluation of mapping the aerodynamic forces to hardpoints at rib and spar intersections in a structural model is performed, and the results are also compared with a linear static aeroelastic analysis. The structural responses indicate that distributing forces along only the wing and strut forward spars is insufficient for simulating the distributed aerodynamic loads. Adding moments along the forward spars improved the global response of the wing, but the point moments created unrealistic local rotations within the structure. When distributing loads along both the forward and aft spars of the wing and strut, the global response was less sensitive to the inclusion of point moments, which indicated the arrangement of point forces alone was sufficient input for structural design work and testing and provided a more continuous loading profile.
The transonic truss-braced wing (TTBW) concept is under consideration by the NASA Advanced Air Transport Technology (AATT) project due to its potential to reduce fuel consumption of transport aircraft. To properly evaluate the TTBW concept, detailed structural modeling and subsequent test planning is underway, which requires a simplified set of discrete applied loads that simulate the distributed aerodynamic pressures. Given the unique architecture of the TTBW and its intended operation in the transonic regime, computational fluid dynamics (CFD) is the ideal approach to employ to ensure the aerodynamics of this configuration are sufficiently captured. To convert aerodynamic results into input for structural models, application of a data transfer tool, Discrete Data Transfer Between Dissimilar Meshes (DDTBDM), is presented to resolve aerodynamic pressures from CFD into single load vectors at hardpoints along both the wing and the strut. Evaluation of mapping the aerodynamic forces to hardpoints at rib and spar intersections in a structural model is performed, and the results are also compared with a linear static aeroelastic analysis. The structural responses indicate that distributing forces along only the wing and strut forward spars is insufficient for simulating the distributed aerodynamic loads. Adding moments along the forward spars improved the global response of the wing, but the point moments created unrealistic local rotations within the structure. When distributing loads along both the forward and aft spars of the wing and strut, the global response was less sensitive to the inclusion of point moments, which indicated the arrangement of point forces alone was sufficient input for structural design work and testing and provided a more continuous loading profile.
Achieving maximum electron beam brightness in photoinjectors requires detailed control of the 3D bunch shape and precise tuning of the beam focusing. Even in state-of-the-art designs, slice emittance growth due to nonlinear space charge forces and partial nonlaminarity often remains non-negligible. In this work, we introduce a new means to linearize the transverse slice phase space: a sacrificial portion of the bunch’s own charge distribution, formed into a wavebroken shock front by highly nonlinear space charge forces within the gun, whose downstream purpose is to dynamically linearize the desired bunch core. We show that linearization of an appropriately prepared bunch can be achieved via strongly nonlaminar focusing of the sacrificial shock front, while the inner core focuses laminarly. This leads to a natural spatial separation of the two distributions: a dense core surrounded by a diffuse halo of sacrificial charge that can be collimated. Multiobjective genetic algorithm optimizations of the ultracompact x-ray free electron laser injector employ this concept, and we interpret it with an analytic model that agrees well with the simulations. In simulation, we demonstrate a final bunch charge of 100 pC, peak current ∼ 30 A, and a sacrificial charge of 150 pC (250 pC total emitted from cathode) with normalized emittance growth of < 20 nm rad due to space charge. This implies a maximum achievable brightness approximately an order of magnitude greater than existing free electron laser injector designs. Published by the American Physical Society 2024
This paper reports a dispersion analysis of two wave packets simultaneously observed near the local proton gyrofrequency by the Parker Solar Probe. The observed wave event exhibits clear two-banded wave packets both propagating along the magnetic field, characterized by left-handed (L-mode) and right-handed (R-mode) polarizations simultaneously. By incorporating the Doppler shift effect into a linear dispersion analysis, we find two possible scenarios that explain these simultaneous opposite polarizations: (1) Two inherently L-mode waves in the plasma frame, propagate parallel and antiparallel to the solar wind velocity, with similar wave frequencies and wave numbers. The polarization of the antiparallel propagating wave reverses as it moves sunward in the plasma frame while still comoving with the solar wind in the stationary frame. This reversal manifests the polarization of the wave as an R-mode in the spacecraft frame. (2) Simultaneous L-mode and R-mode waves propagate parallel to the solar wind velocity, with different wave frequencies and wave numbers. Concurrent proton observations during the wave event reveal a dominant anisotropic ($T$⟂/$T$ ∥ > 1) core distribution with a drifting beam population. Estimation of the linear growth rate for both L-mode and R-mode waves suggests that both scenarios are plausible, indicating that the observation is near the wave-generation region. We explore the potential impact of these simultaneous waves on solar wind heating and scattering effects, hypothesizing that such waves might enhance efficiency compared to waves with a single wave packet, contingent upon the statistical significance of such waves.
The Proton Improvement Plan – II (PIP-II) is a superconducting linear accelerator being built at Fermilab that will provide 800 MeV proton beams for neutrino production. The Linac requires cooling at 40 K, 5 K, and 2 K temperatures, which will be provided by cryogenic helium produced by a Helium Cryoplant and distributed by a Cryogenic Distribution System (CDS). Based primarily on the Linac heat load requirements at each temperature and the allowable pressure drop, we have made a preliminary thermodynamic design of the CDS. The design also incorporates special requirements such as controlled and/or fast cooldown of the superconducting RF cavities and their dual maximum allowable working pressures. This paper presents the overall features of the PIP-II CDS, sizing of helium process circuits, different operating modes, and calculated mass flow capacities that cater to these operating modes.
Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.
This letter investigates a Branching Dueling Q-Network (BDQ) based online operation strategy for a microgrid with distributed battery energy storage systems (BESSs) operating under uncertainties. Additionally, the developed deep reinforcement learning (DRL) based microgrid online optimization strategy can achieve a linear increase in the number of neural network outputs with the number of distributed BESSs, which overcomes the curse of dimensionality caused by the charge and discharge decisions of multiple BESSs. Numerical simulations validate the effectiveness of the proposed method.
Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches-Optimization by Linear Decomposition and Collaborative Optimization-are based on bi-level optimization and reflect what we call a structural perspective. The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective. The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bi-level approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computational difficulties for optimization algorithms. The single-level alternative we discuss affords a more limited degree of autonomy than that of the bi-level approaches, but without the computational difficulties of the bi-level methods. Key Words: Autonomy, bi-level optimization, distributed optimization, multidisciplinary optimization, multilevel optimization, nonlinear programming, problem integration, system synthesis
Several proteins involved in the response to DNA double strand breaks (DSB) form microscopically visible nuclear domains, or foci, after exposure to ionizing radiation. Radiation-induced foci (RIF) are believed to be located where DNA damage is induced. To test this assumption, we analyzed the spatial distribution of 53BP1, phosphorylated ATM and gammaH2AX RIF in cells irradiated with high linear energy transfer (LET) radiation. Since energy is randomly deposited along high-LET particle paths, RIF along these paths should also be randomly distributed. The probability to induce DSB can be derived from DNA fragment data measured experimentally by pulsed-field gel electrophoresis. We used this probability in Monte Carlo simulations to predict DSB locations in synthetic nuclei geometrically described by a complete set of human chromosomes, taking into account microscope optics from real experiments. As expected, simulations produced DNA-weighted random (Poisson) distributions. In contrast, the distributions of RIF obtained as early as 5 min after exposure to high LET (1 GeV/amu Fe) were non-random. This deviation from the expected DNA-weighted random pattern can be further characterized by relative DNA image measurements. This novel imaging approach shows that RIF were located preferentially at the interface between high and low DNA density regions, and were more frequent in regions with lower density DNA than predicted. This deviation from random behavior was more pronounced within the first 5 min following irradiation for phosphorylated ATM RIF, while gammaH2AX and 53BP1 RIF showed very pronounced deviation up to 30 min after exposure. These data suggest the existence of repair centers in mammalian epithelial cells. These centers would be nuclear sub-domains where DNA lesions would be collected for more efficient repair.
The area under the receiver operating characteristic curve (AUC) is widely used in evaluating diagnostic performance for many clinical tasks. It is still challenging to evaluate the reading performance of distinguishing between positive and negative regions of interest (ROIs) in the nested-data problem, where multiple ROIs are nested within the cases. To address this issue, we identify two kinds of AUC estimators, within-cases AUC and between-cases AUC. We focus on the between-cases AUC estimator, since our main research interest is in patient-level diagnostic performance rather than location-level performance (the ability to separate ROIs with and without disease within each patient). Another reason is that as the case number increases, the number of between-cases paired ROIs is much larger than the number of within-cases ROIs. We provide estimators for the variance of the between-cases AUC and for the covariance when there are two readers. We derive and prove the above estimators’ theoretical values based on a simulation model and characterize their behavior using Monte Carlo simulation results. We also provide a real-data example. Moreover, we connect the distribution-based simulation model with the simulation model based on the linear mixed-effect model, which helps better understand the sources of variation in the simulated dataset.
The EXOS-B/Siple Station joint experiment on the triggering of VLF emissions by man-made signals causing some form of wave-particle interactions in the magnetosphere is presented, and results concerning wave-particle correlations are reported. In situ measurements of both energetic electron flux and VLF waves were made near the meridian connecting Siple Station, Antarctica with Roberval, Quebec, Canada in campaigns during July through September, 1979 and December 1979 through January 1980 at times of VLF transmission from Siple. Strong observed signals were found to be well correlated with a pancake pitch angle distribution of 0.3 to 6.9-keV electrons, and to exhibit a positive linear growth rate. Artificially stimulated emissions were observed to be accompanied by large electron fluxes in all energy channels in the equatorial interaction region, although the measured pitch angle distribution was not highly anisotropic. Results may be interpreted by the amplification of Siple signals by the cyclotron instability due to high pitch angle anisotropy (pancake distribution) and the triggering of emissions in the presence of high electron fluxes with some anisotropy and a sufficiently strong signal.
The detection of circular polarization in R Mon and NGC 2261 is reported. This detection implies that the mechanism responsible for the linear and circular polarization is most likely multiple scattering in a flattened distribution. It replaces the previously suggested scenario where dichroic extinction by elongated dust grains aligned by a toroidal magnetic field was producing the polarization. The multiple scattering interpretation of linear polarization maps also means that these maps now provide direct evidence for a circumstellar disk around R Mon and possibly around many other young stellar objects.