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Continuum covariance propagation for understanding variance loss in advective systems

At the heart of modern data assimilation schemes is covariance propagation.Loss of variance experienced in large-scale applications such as numerical weather prediction is problematic, and the development of auxiliary methods to mitigate this issue is an active research area. The focus of this work is to understand the root causes of variance loss and show that for advective dynamics, the covariance propagation by itself typically causes significant, spurious loss of variance, even at full rank. To demonstrate this, we first study continuum covariance propagation by analyzing the covariance evolution equation for advective dynamics. The behavior of this evolution equation changes abruptly as the correlation length tends to zero, for example in the vicinity of sharp gradients in the advection field. This happens because the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments then confirm that the variance lost during numerical propagation greatly exceeds that due to numerical dissipation alone. The variance loss is driven primarily by inaccurate variance propagation resulting from standard, full-rank covariance propagation schemes, which have difficulty capturing the abrupt change in dynamics as the correlation length tends to zero. These results suggest that developing local covariance propagation methods may prove useful in ameliorating the variance loss observed in data assimilation schemes

Covariance Propagation↗

NASA NTRS1995

Studies of the draping and flaring angles of the Mars and Earth magnetotails

Observations of the Mars tail by the spacecraft have been used to estimate the draping angle of the magnetic field within the tail and the boundary flaring angle. The boundary of the tail is defined by the sudden disappearance of the proton flux by the TAUS ion spectrometer. Solar wind measurements by the TAUS instrument are used to calculate the approximate solar wind dynamic pressure when the spacecraft is within the tail boundary. The average draping angle (Acrsin((square root of (B(sub y)(exp 2) + B(sub z)(exp 2)))/B(sub T))) is found to be 27.2 deg +/- 1.4 deg. The draping angle magnitude depends on the solar wind dynamic pressure, but is quite variable. The flaring angle of the tail boundary at X = -2.5 R(sub M) has also been calculated from the balance of pressure between the lobe of the Martian tail and the component pressures of the solar wind. The flaring angle depends strongly on the solar wind dynamic pressure, and this dependence is identical to that obtained at the Earth by Petrinec and Russell. However, the magnitude of the flaring angle at Mars X = -2.5 R(sub M) is one-half the value obtained at Earth for -22.5 R(sub E) is less than or equal to X -10 R(sub E).

Zhang, T.-L.↗

NASA NTRS2003

Viscoelastic Vibration Dampers for Turbomachine Blades

Simple viscoelastic dampers have been invented for use on the root attachments of turbomachine blades. These dampers suppress bending- and torsion-mode blade vibrations, which are excited by unsteady aerodynamic forces during operation. In suppressing vibrations, these dampers reduce fatigue (thereby prolonging blade lifetimes) while reducing noise. These dampers can be installed in new turbomachines or in previously constructed turbomachines, without need for structural modifications. Moreover, because these dampers are not exposed to flows, they do not affect the aerodynamic performances of turbomachines. Figure 1 depicts a basic turbomachine rotor, which includes multiple blades affixed to a hub by means of dovetail root attachments. Prior to mounting of the blades, thin layers of a viscoelastic material are applied to selected areas of the blade roots. Once the blades have been installed in the hub and the rotor is set into rotation, centrifugal force compresses these layers between the mating load-bearing surfaces of the hub and the blade root. The layers of viscoelastic material provide load paths through which the vibration energy of the blade can be dissipated. The viscoelasticity of the material converts mechanical vibration energy into shear strain energy and then from shear strain energy to heat. Of the viscoelastic materials that have been considered thus far for this application, the one of choice is a commercial polyurethane that is available in tape form, coated on one side with an adhesive that facilitates bonding to blade roots. The thickness of the tape can be chosen to suit the specific application. The typical thickness of 0.012 in. (.0.3 mm) is small enough that the tape can fit in the clearance between the mating blade-root and hub surfaces in a typical turbomachine. In an experiment, a blade was mounted in a test fixture designed to simulate the blade-end conditions that prevail in a turbocompressor. Vibrations were excited in the blade by use of an impact hammer, and damping of the vibrations was measured by use of a dynamic signal analyzer. Tests were performed without and with viscoelastic dampers installed in the dovetail root attachment. The results of the measurements, some of which are presented in Figure 2, show that the viscoelastic dampers greatly increased the rate of damping of vibrations. Accordingly, dynamic stresses on rotor blades were significantly reduced, as shown in Figure 2.

Nguyen, Nhan↗

NASA NTRS1976

An analytical study and wind tunnel tests of an aeromechanical gust-alleviation system for a light airplane

The results of an analytical study of a system using stability derivatives determined in static wind tunnel tests of a 1/6 scale model of a popular, high wing, light airplane equipped with the gust alleviation system are reported. The longitudinal short period mode dynamics of the system are analyzed, and include the following: (1) root loci, (2) airplane frequency responses to vertical gusts, (3) power spectra of the airplane responses in a gust spectrum, (4) time history responses to vertical gusts, and (5) handling characteristics. The system reduces the airplane's normal acceleration response to vertical gusts while simultaneously increasing the pitching response and reducing the damping of the longitudinal short period mode. The normal acceleration response can be minimized by using the proper amount of static alleviation and a fast response system with a moderate amount of damping. The addition of a flap elevator interconnect or a pitch damper system further increases the alleviation while moderating the simultaneous increase in pitching response. The system provides direct lift control and may reduce the stick fixed longitudinal static stability.

Stewart, E. C.↗

NASA NTRS1980

The hammer QSD-quick stop device for high speed machining and rubbing

A quick stop device (QSD) was designed for use in orthogonal machining and rubbing experiments. QSD's are used to obtain chip root samples that are representative of the deformation taking place during dynamic (actual) cutting conditions. These 'frozen' specimens are helpful in examining the plastic deformation that occurs in the regions of compression and shear which form the chip; the secondary shear at the tool-chip interface; and the nose ploughing/flank rubbing action which operates on the newly machined surface. The Hammer QSD employs a shear pin mechanism, broken by a flying hammer, which is traveling at the same velocity as the workpiece. The device has been successfully tested up to 6000 sfpm (30.48 m/sec).

Black, J. T.↗

NASA NTRS1987

Response of stiffened panels for applications to acoustic fatigue

The surface protection systems of aerospace and aircraft structures are often constructed from discretely stiffened panels. This paper presents an analytical study on dynamic stress response of these structures to random surface flow and acoustic loads. To account for aerodynamic heating of high speed flow, thermal effects are included in the structural model. A generalized transfer matrix procedure is developed to obtain the required dynamic response solutions. Numerical results include spectral densities of stress, response root mean square values and fatigue damage for a variety of loading and thermal conditions.

Vaicaitis, R.↗

NASA NTRS1988

Helicopter stability and control modeling improvements and verification on two helicopters

A linearized model of helicopter flight dynamics is developed which includes the flapping, lead-lag, and dynamic inflow degrees of freedom (DOF). The model is a combination of analytical terms and numerically determined stability derivatives, and is used to investigate the importance of the rotor DOF to stability and control modeling. The results show that the rotor DOF can have a significant impact on some of the natural modes in a linear model. The flap and dynamic inflow DOF show the greatest influence. Flapping exhibits strong coupling to the body, dynamic inflow, and to lead-lag to a lesser extent. Dynamic inflow tends to damp the high-frequency flapping modes, and reduces the damping on coupled body-flap motion. Dynamic inflow also couples to the flapping motion to produce complex roots. With body-flap and lag regressing modes as exceptions, the results show essentially similar behavior for most modes of articulated and hingeless rotor helicopters.

Schrage, D. P.↗

NASA NTRS2012

Joint Chance-Constrained Dynamic Programming

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.

Ono, Masahiro↗

NASA NTRS2025

Effect of Strict Head Down Tilt Bedrest on Pituitary Gland Height

BACKGROUND Pituitary gland deformity and loss of pituitary height have been identified in astronauts postflight, hypothesized to be related to increased intracranial pressure or intracranial pressure pulsatility exposure from prolonged weightlessness. Microgravity-induced chronic headward fluid shift has been suggested as a root cause of intracranial compliance changes leading to altered intracranial pressure dynamics. Elevated intracranial pressure or pressure pulsatility is theorized to promote the development of an arachnoid diverticulum, which herniates into the pituitary fossa via a defect in the diaphragma sellae compressing the pituitary gland. We aimed to determine if chronic headward fluid induced by strict head-down tilt bed rest (HDTBR) can cause similar quantitative changes in pituitary gland height. METHODS Control group data from two 6-degree HDTBR studies were analyzed (SANS CM and AGBRESA). The AGBRESA study collected MRI data at Baseline, 14 days into HDTBR (HDTBR-14), 52 days into HDTBR (HDTBR-52), and three days into Recovery (R+ 3) and included eight healthy adults (2 women), age = 33 ± 8 years. The SANS CM collected MRI data at Baseline, 15 days into HDTBR (HDTBR-15), 29 days into HDTBR (HDTBR-29), and 12 days into Recovery (R+12) and included twelve healthy adults (4 women), age = 34 ± 9 years. Pituitary gland height was evaluated using a sagittal, 3D T1-MPRAGE sequence obtained on a dedicated 3T Siemens Biograph MRI scanner using a 32-channel head coil. Following the reconstruction of a true orthogonal sagittal plane of the pituitary gland using a 3D multiplanar reconstruction tool (Horosproject.org), the anterior pituitary mid-gland height at the pituitary stalk level was quantified according to the methodology described by Kramer et al. . A paired t-test was used to evaluate changes from the baseline measurements. FINDINGS The mean height of the pituitary gland at baseline was 6.5 ± 1.7 mm (AGBRESA) and 5.7 ± 1.6 mm (SANS CM). From baseline measurements, the SANS CM STUDY data showed a decrease in mean pituitary height of 0.3 mm (p=.011) at HDTBR-15, 0.5 mm at HDTBR-29 (p<.001) and 0.2 mm at R+12 (p=.02). From baseline measurements, the AGBRESA data showed a decrease in mean pituitary height of 0.3 mm (p=.06) at HDTBR-14, 0.6 mm at HDTBR-52 (p<.002) and 0.2 mm at R+3 (p=.13). CONCLUSION HDTBR results in progressive loss of pituitary height, which is most severe with the longest HDTBR exposure. Early pituitary height loss was the same at HDTBR-14 (AGBRESA) and HDTBR-15 (SANS CM). Residual pituitary height loss was the same at R+12 and R+3 but only significant in the latter (SANS CM). The degree of pituitary height loss at HDTBR-52 replicates the 0.6 mm height loss found in long-duration astronauts after approximately six months of microgravity exposure (p<.01, preflight mean height=5.9 mm). The hormonal effects of pituitary height loss are unknown in astronauts and HDTBR subjects and should be investigated in future studies. Future work will examine the individual variability in the loss of pituitary gland height and whether those changes are associated with other SANS findings, such as optic disc edema.

L A Kramer↗

NASA NTRS2024

On the Use of SMAP Soil Moisture for Forecasting NDVI Over CONUS Cropland Regions

Vegetation health forecasting (NDVI as a proxy) informs decision-makers about the end of season crop yield productivity but is not well-documented. This study tests improvements in vegetation health forecasting by developing a data-driven Dynamic Agricultural Productivity Indicator ( DAPI ), which simultaneously incorporates satellite-based root zone soil moisture (RZSM) and satellite-based NDVI data. RZSM is estimated via data assimilation of satellite based SMAP SM dataset. We employ the proposed DAPI forecast across four cropland types in CONUS, including corn, cotton, soybeans, and wheat. Results demonstrate superior performance of the DAPI forecasts compared to climatology-based NDVI forecasts, with the largest improvements in water-limited regions. DAPI shows particularly good performance during hydrologic disturbances such as floods and droughts. To this end, the DAPI approach is useful in estimating future vegetation health for identifying potential food-insecure areas, predicting crop price changes, and projecting expected commodities market trends.

Manh Le↗

NASA NTRS2021

Robust Control Methodology Via Loop Shaping, Root Locus, and Model Reference Control

The paper describes the development of a robust control methodology that can tolerate large uncertainties in plant dynamics in terms of proportional gain variations as well as frequencies and damping. For this to be accomplished, the methodology starts by designing a feedback controller based on a loop shaping technique. The design is then improved by employing a root locus control design approach. Finally, the response of the feedback system is further improved by augmenting the control design using model reference control. The design approach also takes into consideration the speed of the process actuator for a fast response and for high disturbance rejection. Results from two control design examples covered in the paper show that this control approach can tolerate plant proportional gain uncertainty of approximately ± two orders of magnitude with relatively large variations in plant frequencies and damping.

Control Systems↗

NASA NTRS2001

Spatiotemporal relationships between growth and microtubule orientation as revealed in living root cells of Arabidopsis thaliana transformed with green-fluorescent-protein gene construct GFP-MBD

Arabidopsis thaliana plants were transformed with GFP-MBD (J. Marc et al., Plant Cell 10: 1927-1939, 1998) under the control of a constitutive (35S) or copper-inducible promoter. GFP-specific fluorescence distributions, levels, and persistence were determined and found to vary with age, tissue type, transgenic line, and individual plant. With the exception of an increased frequency of abnormal roots of 35S GFP-MBD plants grown on kanamycin-containing media, expression of GFP-MBD does not appear to affect plant phenotype. The number of leaves, branches, bolts, and siliques as well as overall height, leaf size, and seed set are similar between wild-type and transgenic plants as is the rate of root growth. Thus, we conclude that the transgenic plants can serve as a living model system in which the dynamic behavior of microtubules can be visualized. Confocal microscopy was used to simultaneously monitor growth and microtubule behavior within individual cells as they passed through the elongation zone of the Arabidopsis root. Generally, microtubules reoriented from transverse to oblique or longitudinal orientations as growth declined. Microtubule reorientation initiated at the ends of the cell did not necessarily occur simultaneously in adjacent neighboring cells and did not involve complete disintegration and repolymerization of microtubule arrays. Although growth rates correlated with microtubule reorientation, the two processes were not tightly coupled in terms of their temporal relationships, suggesting that other factor(s) may be involved in regulating both events. Additionally, microtubule orientation was more defined in cells whose growth was accelerating and less stringent in cells whose growth was decelerating, indicating that microtubule-orienting factor(s) may be sensitive to growth acceleration, rather than growth per se.

NASA Discipline Plant Biology↗

NASA NTRS2020

Synergistic Use of SMAP and OCO-2 Data in Assessing the Responses of Ecosystem Productivity to the 2018 U.S. Drought

Soil moisture and gross primary productivity (GPP) estimates from the Soil Moisture Active Passive (SMAP) and solar-induced chlorophyll fluorescence (SIF) from the Orbiting Carbon Observatory-2 (OCO-2) provide new opportunities for understanding the relationship between soil moisture and terrestrial photosynthesis over large regions. Here we explored the potential of the synergistic use of SMAP and OCO-2 based data for monitoring the responses of ecosystem productivity to drought. We used complementary observational information on root-zone soil moisture and GPP (9 km) from SMAP and fine-resolution SIF (0.05°; GOSIF) derived from OCO-2 SIF soundings. We compared the spatial pattern and temporal evolution of anomalies of these variables over the conterminous U.S. during the 2018 drought, and examined to what extent they could characterize the drought-induced variations of flux tower GPP and crop yield data. Our results showed that SMAP GPP and GOSIF could well capture the spatial extent and dynamics of drought indicated by the U.S. Drought Monitor maps and the SMAP root-zone soil moisture deficit. Over the U.S. Southwest, monthly anomalies of soil moisture showed significant positive correlations with those of SMAP GPP (R2=0.44, p<0.001) and GOSIF (R2=0.76, p<0.001), demonstrating strong water availability constraints on plant productivity across dryland ecosystems. We further found that SMAP GPP and GOSIF captured the impact of drought on tower GPP and crop yield. Our results suggest that synergistic use of SMAP and OCO-2 data products can reveal the drought evolution and its impact on ecosystem productivity and carbon uptake at multiple spatial and temporal scales, and demonstrate the value of SMAP and OCO-2 for studying ecosystem function, carbon cycling, and climate change.

Soil Moisture Active Passive↗

NASA NTRS2002

Cryo Cooler Induced Micro-Vibration Disturbances to the Hubble Space Telescope

This paper presents an overview of the Hubble Space Telescope (HST) Near Infrared Camera and Multi-Object Spectrometer (NICMOS) Cryo Cooler (MCC) system, a description of the micro-vibration characterization testing performed, and a discussion of the simulated performance. The NCC is a reverse Brayton cycle system that employs micro turbo-machinery to provide cooling to the NICMOS instrument. Extensive testing was conducted to quantify the expected on-orbit disturbances caused by the micro turbo-machinery and provide input to a flexible-body dynamic simulation to demonstrate compliance with the HST 7 milli-arcsecond root mean square jitter requirement.

Jedrich, Nick↗

NASA NTRS2003

Ultrasail

Ultrasail is a complete sail system for the launch, deployment, stabilization and control of very large solar sails enabling reduced mission times for interplanetary and deep space spacecraft. Ultrasail is an innovative, non-traditional approach to propulsion technology achieved by combining propulsion and control systems developed for formation-flying microsatellites with an innovative solar sail architecture to achieve sq km-class controllable sail areas, sail subsystem area densities of 1 gm per sq m, and thrust levels equivalent to 400 kW ion thruster systems used for comparable deep space missions. Ultrasail can conceivably even achieve outer planetary rendezvous, a deep space capability now reserved for high-mass nuclear and chemical systems. Ultrasail is a Delta IV-launched multi-blade spin-stabilized system with blade lengths as long as 50 km, reminiscent of the MacNeal Heliogyro. The primary innovation is the near-elimination of sail supporting structures by attaching the sail tip to a rigid formation-flying microsatellite truss which deploys the sail blade, and which then articulates the blade to provide attitude control, including spin stabilization and precession of the spin axis. These tip microsatellites are controlled by a solar-powered 3-axis microthruster system (electric or cold gas) to maintain proper sail film tension during deployment and spin-up. The satellite mass also provides a stabilizing centrifugal force on the blade while in rotation. Understanding the dynamics of individual blades is key to the overall dynamics of Ultrasail. Forces and torques that must be modeled include those due to solar pressure, those generated by the microsatellite at the blade tip and by torques applied at the blade root. Centrifugal forces also play a significant role in the deployment and maintenance of the sail configuration. To capture the dynamics of the overall system, the equations of motion for the blades have been derived. Using these differential equations, a control law will be derived to maneuver Ultrasail. This law involves the pitching of the individual blades thereby moving the distribution of the radiation pressure on each individual blade and inducing a resultant torque on the system. The direction of the angular momentum vector and its rate of precession can be controlled through the pitch angle of the blades. The Ultrasail trajectory is also being studied. Optimal or near-optimal trajectories are being generated to showcase Ultrasail performance. Various missions, e.g. outer planet and solar polar missions for observation of the Sun, are currently being investigated to demonstrate the performance enhancements generated by Ultrasail technology. Calculus-of-variations-based optimization software is used to produce optimal Ultrasail trajectories. The performance of these trajectories is being compared to optimal results generated with other propulsion models, including chemical propulsion, ion propulsion, and competing solar sail concepts. Results of these studies will quantify the performance of Ultrasail compared to existing solar sail concepts for high energy missions.

Burton, R.↗

NASA NTRS2001

Dynamic Deformation Measurements of an Aeroelastic Semispan Model

The techniques used to acquire, reduce, and analyze dynamic deformation measurements of an aeroelastic semispan wind tunnel model are presented. Single-camera, single-view video photogrammetry (also referred to as videogrammetric model deformation, or VMD) was used to determine dynamic aeroelastic deformation of the semispan 'Models for Aeroelastic Validation Research Involving Computation' (MAVRIC) model in the Transonic Dynamics Tunnel at the NASA Langley Research Center. Dynamic deformation was determined from optical retroreflective tape targets at five semispan locations located on the wing from the root to the tip. Digitized video images from a charge coupled device (CCD) camera were recorded and processed to automatically determine target image plane locations that were then corrected for sensor, lens, and frame grabber spatial errors. Videogrammetric dynamic data were acquired at a 60-Hz rate for time records of up to 6 seconds during portions of this flutter/Limit Cycle Oscillation (LCO) test at Mach numbers from 0.3 to 0.96. Spectral analysis of the deformation data is used to identify dominant frequencies in the wing motion. The dynamic data will be used to separate aerodynamic and structural effects and to provide time history deflection data for Computational Aeroelasticity code evaluation and validation.

Graves, Sharon S.↗

NASA NTRS2010

Solving Component Structural Dynamic Failures Due to Extremely High Frequency Structural Response on the Space Shuttle Program

For many years, the capabilities to determine the root-cause failure of component failures have been limited to the analytical tools and the state of the art data acquisition systems. With this limited capability, many anomalies have been resolved by adding material to the design to increase robustness without the ability to determine if the design solution was satisfactory until after a series of expensive test programs were complete. The risk of failure and multiple design, test, and redesign cycles were high. During the Space Shuttle Program, many crack investigations in high energy density turbomachines, like the SSME turbopumps and high energy flows in the main propulsion system, have led to the discovery of numerous root-cause failures and anomalies due to the coexistences of acoustic forcing functions, structural natural modes, and a high energy excitation, such as an edge tone or shedding flow, leading the technical community to understand many of the primary contributors to extremely high frequency high cycle fatique fluid-structure interaction anomalies. These contributors have been identified using advanced analysis tools and verified using component and system tests during component ground tests, systems tests, and flight. The structural dynamics and fluid dynamics communities have developed a special sensitivity to the fluid-structure interaction problems and have been able to adjust and solve these problems in a time effective manner to meet budget and schedule deadlines of operational vehicle programs, such as the Space Shuttle Program over the years.

Frady, Greg↗

NASA NTRS1991

Aeroelastic modal characteristics of mistuned blade assemblies: Mode localization and loss of eigenstructure

An investigation of the effects of small mistuning on the aeroelastic modes of bladed disk assemblies with aerodynamic coupling between blades is presented. The cornerstone of the approach is the use and development of perturbation methods that exhibit the crucial role of the interblade coupling and yield general findings regarding mistuning effects. It is shown that blade assemblies with weak aerodynamic interblade coupling are highly sensitive to small blade mistuning, and that their dynamics is quantitatively altered in the following ways: the regular pattern that characterizes the root locus of the tuned aeroelastic eigenvalues in the complex plane is totally lost; the aeroelastic mode shapes becomes severely localized to only a few blades of the assembly and lose their constant interblade phase angle feature; and curve veering phenomena take place when the eigenvalues are plotted versus a mistuning parameter.

Pierre, Christophe↗