Uncertainty Evaluation of Computational Model Used to Support the Integrated Powerhead Demonstration Project

NASA and the U.S. Air Force are working on a joint project to develop a new hydrogen-fueled, full-flow, staged combustion rocket engine. The initial testing and modeling work for the Integrated Powerhead Demonstrator (IPD) project is being performed by NASA Marshall and Stennis Space Centers. A key factor in the testing of this engine is the ability to predict and measure the transient fluid flow during engine start and shutdown phases of operation. A model built by NASA Marshall in the ROCket Engine Transient Simulation (ROCETS) program is used to predict transient engine fluid flows. The model is initially calibrated to data from previous tests on the Stennis E1 test stand. The model is then used to predict the next run. Data from this run can then be used to recalibrate the model providing a tool to guide the test program in incremental steps to reduce the risk to the prototype engine. In this paper, they define this type of model as a calibrated model. This paper proposes a method to estimate the uncertainty of a model calibrated to a set of experimental test data. The method is similar to that used in the calibration of experiment instrumentation. For the IPD example used in this paper, the model uncertainty is determined for both LOX and LH flow rates using previous data. The successful use of this model is then demonstrated to predict another similar test run within the uncertainty bounds. The paper summarizes the uncertainty methodology when a model is continually recalibrated with new test data. The methodology is general and can be applied to other calibrated models

Caching Gaussians: Minimizing Total Correlation on the Gray–Wyner Network

We study a caching problem that resembles a lossy Gray–Wyner network: A source produces vector samples from a Gaussian distribution, but the user is interested in the samples of only one component. The encoder first sends a cache message without any knowledge of the user’s preference. Upon learning her request, a second message is provided in the update phase so as to attain the desired fidelity on that component. The cache is efficient if it exploits as much of the correlation in the source as possible, which connects to the notions of Wyner’s common information (for high cache rates) and Watanabe’s total correlation (for low cache rates). For the former, we extend known results for 2 Gaussians to multivariates by showing that common information is a simple linear program, which can be solved analytically for circulant correlation matrices. Total correlation in a Gaussian setting is less well-studied. We show that for bivariates and using Gaussian auxiliaries it is captured in the dominant eigenvalue of the correlation matrix. For multivariates the problem is a more difficult optimization over a non-convex domain, but we conjecture that circulant matrices may again be analytically solvable

Caching (a pair of) Gaussians

A source produces i.i.d. vector samples from a Gaussian distribution, but the user is interested in only one component. In the cache phase, not knowing which component the user is interested in, a first compressed description is produced. Upon learning the user’s choice, a second message is provided in the update phase so as to attain the desired fidelity on that component. We aim to find the cache strategy that minimizes the average update rate. We show that for Gaussian codebooks, the optimal strategy depends on whether or not the cache is large enough to make the vector conditionally independent. If it is, infinitely many equally optimal strategies exist. If it is not, we show that the encoder should project the source onto some subspace prior to coding. For a pair of Gaussians, we exactly characterize this projection vector

Total Correlation of Gaussian Vector Sources on the Gray–Wyner Network

We study a generalization of Wyner’s Common Information to Watanabe’s Total Correlation. The first minimizes the description size required for a variable that can make two other random variables conditionally independent. If independence is unattainable, Watanabe’s total (conditional) correlation is measure to check just how independent they have become. Following up on earlier work for scalar Gaussians, we discuss the minimization of total correlation for Gaussian vector sources. Using Gaussian auxiliaries, we show one should transform two vectors of length d into d independent pairs, after which a reverse water filling procedure distributes the minimization over all these pairs. Lastly, we show how this minimization of total conditional correlation fits a lossy coding problem by using the Gray–Wyner network as a model for a caching problem

Successive Refinement of Gaussian Projections

Successive refinement is a technique to encode a source iteratively, improving the distortion at each step. If the code rates of all steps combined can be as efficient as coding only for the final distortion in one go, then the source is said to be successively refinable. We turn our attention to vector sources and we propose to replace the high-distortion first stage by a projection to low-dimensional space. The goal remains the same: code the original, high-dimensional source afterwards by only a small addendum. We look at Gaussian sources subject to an MSE criterion as a first step in this direction. A coding scheme for this problem is developed by turning the projection into an estimator of the source. It is shown that Gaussian vector sources coded via a projection can be successively refinable. We derive a parametric description of distortion pairs that can achieve this state; this region exists for any projection matrix, but its size may vary

Endothelial Dysfunction Plays a Key Role in Increasing Cardiovascular Risk in Type 2 Diabetes The Hoorn Study

In the pathogenesis of cardiovascular events, interaction between risk factors has seldom been identified. However, endothelial dysfunction on the one hand and type 2 diabetes mellitus, impaired glucose metabolism (IGM), and insulin resistance on the other may act synergistically (ie, interact) in the development of cardiovascular disease. We therefore investigated the interaction between endothelial dysfunction and type 2 diabetes mellitus, IGM, and insulin resistance with regard to risk of cardiovascular events. In a prospective population-based cohort (n=445; 69 years; 55% women; 23% type 2 diabetes mellitus, 28% IGM [by design]), endothelial dysfunction (brachial artery flow-mediated dilatation), glucose tolerance (oral glucose tolerance test), and insulin sensitivity (homeostasis model assessment for insulin resistance [HOMA2-IR]) were determined. After a median follow-up of 7.6 years, 106 participants had had a cardiovascular event. After adjustments, 1 SD less flow-mediated dilatation was associated with cardiovascular events in type 2 diabetes mellitus (hazard ratio 1.69 [95% confidence interval, 1.14-2.52]) and IGM (1.50 [0.95-2.37]) and among those in the highest HOMA2-IR tertile (1.92 [1.42-2.60]), but not in normal glucose metabolism (0.85 [0.63-1.16]) or among those in the lower 2 HOMA2-IR tertiles combined (0.85 [0.65-1.12]). Interaction between flow-mediated dilatation and type 2 diabetes mellitus, IGM, or insulin resistance was present on an additive (relative excess risk caused by interaction >0) and on a multiplicative scale (P interactio

Local Stiffness of the Carotid and Femoral Artery Is Associated With Incident Cardiovascular Events and All-Cause Mortality The Hoorn Study

ObjectivesThis study sought to investigate the association of local and segmental arterial stiffness with incident cardiovascular events and all-cause mortality.BackgroundThe association of different stiffness indices, in particular of carotid, brachial, and femoral stiffness, with cardiovascular disease and mortality is currently unknown.MethodsIn a population-based cohort (n = 579, mean age 67 years, 50% women, 23% with type 2 diabetes [by design]), we assessed local stiffness of carotid, femoral, and brachial arteries (by ultrasonography), carotid-femoral pulse wave velocity (cfPWV), aortic augmentation index, and systemic arterial compliance.ResultsAfter a median follow-up of 7.6 years, 130 participants had a cardiovascular event and 96 had died. The hazard ratios (HRs) (95% confidence intervals [CIs]) per 1 SD for cardiovascular events and all-cause mortality, respectively, were HR: 1.22 (95% CI: 0.95 to 1.56) and 1.51 (95% CI: 1.11 to 2.06) for lower carotid distensibility; HR: 1.19 (95% CI: 1.00 to 1.41) and 1.28 (95% CI: 1.07 to 1.53) for higher carotid elastic modulus; HR: 1.08 (95% CI: 0.88 to 1.31) and 1.43 (95% CI: 1.10 to 1.86) for lower carotid compliance; HR: 1.39 (95% CI: 1.06 to 1.83) and 1.27 (95% CI: 0.90 to 1.79) for lower femoral distensibility; HR: 1.25 (95% CI: 0.96 to 1.63) and 1.47 (95% CI: 1.01 to 2.13) for lower femoral compliance; and HR: 1.56 (95% CI: 1.23 to 1.98) and 1.13 (95% CI: 0.83 to 1.54) for higher cfPWV. These results were adjusted for age, sex, mean arterial pressure, and cardiovascular risk factors. Mutual adjustments for each of the other stiffness indices did not materially change these results. Brachial stiffness, augmentation index, and systemic arterial compliance were not associated with cardiovascular events or mortality.ConclusionsCarotid and femoral stiffness indices are independently associated with incident cardiovascular events and all-cause mortality. The strength of these associations with events may differ per stiffness parameter

Numerical investigation of recirculation in the UTSI MHD combustor

Numerical studies were carried out to investigate the gross structure of flow in cylindrical combustors. The combustor configurations studied are variations of a working design used at the University of Tennessee Space Institute to burn pulverized coal at temperatures in excess of 3000K for generation of a plasma feeding a magnetohydrodynamic channel. The numerical studies were conducted for an isothermal fluid; the main objective of the calculations was to study the effect of the oxidant injection pattern on the gross structure of recirculating flows within the combustor. The calculations illustrate the basic features of the flow in combustors of this type and suggest implications for the injection of coal and oxidizer in this type of combustor

Three-Dimensional Flow Field Measurements in a Transonic Turbine Cascade

Three-dimensional flow field measurements are presented for a large scale transonic turbine blade cascade. Flow field total pressures and pitch and yaw flow angles were measured at an inlet Reynolds number of 1.0 x 10(exp 6) and at an isentropic exit Mach number of 1.3 in a low turbulence environment. Flow field data was obtained on five pitchwise/spanwise measurement planes, two upstream and three downstream of the cascade, each covering three blade pitches. Three-hole boundary layer probes and five-hole pitch/yaw probes were used to obtain data at over 1200 locations in each of the measurement planes. Blade and endwall static pressures were also measured at an inlet Reynolds number of 0.5 x 10(exp 6) and at an isentropic exit Mach number of 1.0. Tests were conducted in a linear cascade at the NASA Lewis Transonic Turbine Blade Cascade Facility. The test article was a turbine rotor with 136 deg of turning and an axial chord of 12.7 cm. The flow field in the cascade is highly three-dimensional as a result of thick boundary layers at the test section inlet and because of the high degree of flow turning. The large scale allowed for very detailed measurements of both flow field and surface phenomena. The intent of the work is to provide benchmark quality data for CFD code and model verification