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NASA NTRS2010

Improving Global Mass Flux Solutions from Gravity Recovery and Climate Experiment (GRACE) Through Forward Modeling and Continuous Time Correlation

We describe Earth's mass flux from April 2003 through November 2008 by deriving a time series of mas cons on a global 2deg x 2deg equal-area grid at 10 day intervals. We estimate the mass flux directly from K band range rate (KBRR) data provided by the Gravity Recovery and Climate Experiment (GRACE) mission. Using regularized least squares, we take into account the underlying process dynamics through continuous space and time-correlated constraints. In addition, we place the mascon approach in the context of other filtering techniques, showing its equivalence to anisotropic, nonsymmetric filtering, least squares collocation, and Kalman smoothing. We produce mascon time series from KBRR data that have and have not been corrected (forward modeled) for hydrological processes and fmd that the former produce superior results in oceanic areas by minimizing signal leakage from strong sources on land. By exploiting the structure of the spatiotemporal constraints, we are able to use a much more efficient (in storage and computation) inversion algorithm based upon the conjugate gradient method. This allows us to apply continuous rather than piecewise continuous time-correlated constraints, which we show via global maps and comparisons with ocean-bottom pressure gauges, to produce time series with reduced random variance and full systematic signal. Finally, we present a preferred global model, a hybrid whose oceanic portions are derived using forward modeling of hydrology but whose land portions are not, and thus represent a pure GRACE-derived signal.

Sabaka, T. J.↗

NASA NTRS2015

Global Optimization of Interplanetary Trajectories in the Presence of Realistic Mission Contraints

Interplanetary missions are often subject to difficult constraints, like solar phase angle upon arrival at the destination, velocity at arrival, and altitudes for flybys. Preliminary design of such missions is often conducted by solving the unconstrained problem and then filtering away solutions which do not naturally satisfy the constraints. However this can bias the search into non-advantageous regions of the solution space, so it can be better to conduct preliminary design with the full set of constraints imposed. In this work two stochastic global search methods are developed which are well suited to the constrained global interplanetary trajectory optimization problem.

Design↗

NASA NTRS2026

Deep RL for Fast Long-Horizon Operations Scheduling on NASA's Carruthers Geocorona Observatory Mission

Spacecraft operations scheduling is a highly constrained, long-horizon combinatorial optimization problem that traditionally relies on heuristics, constraint programming, or manual planning. We present a scalable deep reinforcement learning framework developed and deployed for NASA’s Carruthers Geocorona Observatory mission. Our framework introduces a macro-action abstraction known as activity blocks coupled with dynamic action-masking to navigate the intractably large search space and strictly enforce complex power, thermal, and instrument constraints. The resulting architecture generates globally feasible schedules with overwhelming probability, establishes operational trust, and executes a full training cycle in under six hours, circumventing the need for policy robustness by enabling rapid, on-demand retraining. Further, resulting schedules outperform baseline heuristics in scheduled science quality. The deep reinforcement learning framework was deployed as the default operational scheduler for the Carruthers Geocorona Observatory mission from the outset of the mission, demonstrating that deep reinforcement learning can be trusted for real spacecraft operations under complex, evolving constraints.

Geocorona↗

NASA NTRS1993

A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints

Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima.

Divelbiss, Adam↗

NASA NTRS1975

A triangular thin shell finite element: Linear analysis

The formulation of the linear stiffness matrix for a doubly-curved triangular thin shell element, using a modified potential energy principle, is described. The strain energy component of the potential energy is expressed in terms of displacements and displacement gradients by use of consistent Koiter strain-displacement equations. The element inplane and normal displacement fields are approximated by complete cubic polynomials. The interelement displacement admissibility conditions are met in the global representation by imposition of constraint conditions on the interelement boundaries; the constraints represent the modification of the potential energy. Errors due to the nonzero strains under rigid body motion are shown to be of small importance for practical grid refinements through performance of extensive comparison analyses.

Thomas, G. R.↗

NASA NTRS1976

Stratospheric measurement requirements and satellite-borne remote sensing capabilities

The capabilities of specific NASA remote sensing systems to provide appropriate measurements of stratospheric parameters for potential user needs were assessed. This was used to evaluate the capabilities of the remote sensing systems to perform global monitoring of the stratosphere. The following conclusions were reached: (1) The performance of current remote stratospheric sensors, in some cases, compares quite well with identified measurement requirements. Their ability to measure other species has not been demonstrated. (2) None of the current, in-situ methods have the capability to satisfy the requirements for global monitoring and the temporal constraints derived from the users needs portion of the study. (3) Existing, non-remote techniques will continue to play an important role in stratospheric investigations for both corroboration of remotely collected data and in the evolutionary development of future remote sensors.

Carmichael, J. J.↗

NASA NTRS1994

Vertical transport rates in the statosphere in 1993 from observations of CO2, N2O, and CH4

Measurements of CO2, N2O, and CH4 are analyzed to define hemispheric average vertical exchange rates in the lower stratosphere from November 1992 to October 1993. Effective vertical diffusion coefficients were small in summer, less than or equal to 1 sq m/s at altitudes below 25 km; values were similar near the tropopause in winter, but increased markedly with altitude. The analysis suggests possible longer residence times for exhaust from stratospheric aircraft, and more efficient transport from 20 km to the middle stratosphere, than predicted by many current models. Seasonally-resolved measurements of stratospheric CO2 and N2O provide significant new constraints on rates for global-scale vertical transport.

Wofsy, Steven C.↗

NASA NTRS1996

A General-Purpose Optimization Engine for Multi-Disciplinary Design Applications

A general purpose optimization tool for multidisciplinary applications, which in the literature is known as COMETBOARDS, is being developed at NASA Lewis Research Center. The modular organization of COMETBOARDS includes several analyzers and state-of-the-art optimization algorithms along with their cascading strategy. The code structure allows quick integration of new analyzers and optimizers. The COMETBOARDS code reads input information from a number of data files, formulates a design as a set of multidisciplinary nonlinear programming problems, and then solves the resulting problems. COMETBOARDS can be used to solve a large problem which can be defined through multiple disciplines, each of which can be further broken down into several subproblems. Alternatively, a small portion of a large problem can be optimized in an effort to improve an existing system. Some of the other unique features of COMETBOARDS include design variable formulation, constraint formulation, subproblem coupling strategy, global scaling technique, analysis approximation, use of either sequential or parallel computational modes, and so forth. The special features and unique strengths of COMETBOARDS assist convergence and reduce the amount of CPU time used to solve the difficult optimization problems of aerospace industries. COMETBOARDS has been successfully used to solve a number of problems, including structural design of space station components, design of nozzle components of an air-breathing engine, configuration design of subsonic and supersonic aircraft, mixed flow turbofan engines, wave rotor topped engines, and so forth. This paper introduces the COMETBOARDS design tool and its versatility, which is illustrated by citing examples from structures, aircraft design, and air-breathing propulsion engine design.

Patnaik, Surya N.↗

NASA NTRS1994

Vertical Transport Rates in the Stratosphere in 1993 from Observations of CO2, N2O and CH4

Measurements of CO2, N2O and CH4 are analyzed to define hemispheric average vertical exchange rates in the lower stratosphere from November 1992 to October 1993. Effective vertical diffusion coefficients were small in summer, less than or equal to 1 m(exp 2)/sec at altitudes below 25 km; values were similar near the tropopause in winter, but increased markedly with altitude. The analysis suggests possibly longer residence times for exhaust from stratospheric aircraft, and more efficient transport from 20 km to the middle stratosphere, than predicted by many current models. Seasonally-resolved measurements of stratospheric CO2 and N2O provide significant new constraints on rates for global-scale vertical transport.

Wofsy, Steven C.↗

NASA NTRS2001

Constraints Pb-210 and Be-7 on Wet Deposition and Transport in a Global Three-Dimensional Chemical Tracer Model Driven by Assimilated Meteorological Fields

The atmospheric distributions of the aerosol tracers Pb-210 and Be-7 are simulated with a global three-dimensional model driven by assimilated meteorological observations for 1991-1996 from the NASA Goddard Earth Observing System (GEOSl). The combination of terrigenic Pb-210 and cosmogenic Be-7 provides a sensitive test of wet deposition and vertical transport in the model. Our simulation of moist transport and removal includes scavenging in wet convective updrafts (40% scavenging efficiency per kilometer of updraft), midlevel entrainment and detrainment, first-order rainout and washout from both convective anvils and large-scale precipitation, and cirrus precipitation. Observations from surface sites in specific years are compared to model results for the corresponding meteorological years, and observations from aircraft missions over the Pacific are compared to model results for the days of the flights. Initial simulation of Be-7 showed that cross-tropopause transport in the GEOSl meteorological fields is too fast by a factor of 3-4. We adjusted the stratospheric Be-7 source to correct the tropospheric simulation. Including this correction, we find that the model gives a good simulation of observed Pb-210 and Be-7 concentrations and deposition fluxes at surface sites worldwide, with no significant global bias and with significant success in reproducing the observed latitudinal and seasonal distributions. We achieve several improvements over previous models; in particular, we reproduce the observed Be-7 minimum in the tropics and show that its simulation is sensitive to rainout from convective anvils. Comparisons with aircraft observations up to 12-km altitude suggest that cirrus precipitation could be important for explaining the low concentrations in the middle and upper troposphere.

Liu, Hong-Yu↗

NASA NTRS2016

Constraints from Airborne (210)Pb Observations on Aerosol Scavenging and Lifetime in a Global Chemical Transport Model

Lead-210 distribution and lifetime in the atmosphere are not sensitive to ice in-cloud scavenging in convective updraft. Ice in-cloud scavenging in stratiform clouds reduce tropospheric (210)Pb lifetime by approximately 1 day and results in better agreements with observed surface observations and aircraft measured profiles. However, the process results in significant underestimate of (210)Pb in UT/LS.

Zhang, Bo↗

NASA NTRS1994

A new look at the simultaneous analysis and design of structures

The minimum weight optimization of structural systems, subject to strength and displacement constraints as well as size side constraints, was investigated by the Simultaneous ANalysis and Design (SAND) approach. As an optimizer, the code NPSOL was used which is based on a sequential quadratic programming (SQP) algorithm. The structures were modeled by the finite element method. The finite element related input to NPSOL was automatically generated from the input decks of such standard FEM/optimization codes as NASTRAN or ASTROS, with the stiffness matrices, at present, extracted from the FEM code ANALYZE. In order to avoid ill-conditioned matrices that can be encountered when the global stiffness equations are used as additional nonlinear equality constraints in the SAND approach (with the displacements as additional variables), the matrix displacement method was applied. In this approach, the element stiffness equations are used as constraints instead of the global stiffness equations, in conjunction with the nodal force equilibrium equations. This approach adds the element forces as variables to the system. Since, for complex structures and the associated large and very sparce matrices, the execution times of the optimization code became excessive due to the large number of required constraint gradient evaluations, the Kreisselmeier-Steinhauser function approach was used to decrease the computational effort by reducing the nonlinear equality constraint system to essentially a single combined constraint equation. As the linear equality and inequality constraints require much less computational effort to evaluate, they were kept in their previous form to limit the complexity of the KS function evaluation. To date, the standard three-bar, ten-bar, and 72-bar trusses have been tested. For the standard SAND approach, correct results were obtained for all three trusses although convergence became slower for the 72-bar truss. When the matrix displacement method was used, correct results were still obtained, but the execution times became excessive due to the large number of constraint gradient evaluations required. Using the KS function, the computational effort dropped, but the optimization seemed to become less robust. The investigation of this phenomenon is continuing. As an alternate approach, the code MINOS for the optimization of sparse matrices can be applied to the problem in lieu of the Kreisselmeier-Steinhauser function. This investigation is underway.

Striz, Alfred G.↗

NASA NTRS1993

Synthesis of global thematic mapping, Venus: Geologic correlations/questions for the Magellan gravity mission

An important characteristic of the Magellan mission and the resulting data is that it is both global in coverage as well as extremely high in resolution. As a result, global questions may be addressed based on the constraints of extremely detailed geological evidence. An important first step in the task of interpreting the global geological record will be a synthesis of the primary geological characteristics and their relationship to significant questions. The following is a brief synthesis based on a comparison of mapped distributions, initial interpretations, and some questions that these results raise.

Crumpler, L. S.↗

NASA NTRS2005

A Design Comparison of Atmospheric Flight Vehicles for the Exploration of Titan

Titan, the largest moon of Saturn, is one of the most scientifically interesting locations in the Solar System. With a very cold atmosphere that is five times as dense as Earth s, and one and a half times the surface pressure, it also provides one of the most aeronautically fascinating environments known to humankind. While this may seem the ideal place to attempt atmospheric flight, many challenges await any vehicle attempting to navigate through it. In addition to these physical challenges, any scientific exploration mission to Titan will most likely have several operational constraints. One difficult constraint is the desire for a global survey of the planet and thus, a long duration flight within the atmosphere. Since many of the scientific measurements that would be unique to a vehicle flying through the atmosphere (as opposed to an orbiting spacecraft) desire near-surface positioning of their associated instruments, the vehicle must also be able to fly within the first scale height of the atmosphere. Another difficult constraint is that interaction with the surface, whether by landing or dropped probe, is also highly desirable from a scientific perspective. Two common atmospheric flight platforms that might be used for this mission are the airplane and airship. Under the assumption of a mission architecture that would involve an orbiting relay spacecraft delivered via aerocapture and an atmospheric flight vehicle delivered via direct entry, designs were developed for both platforms that are unique to Titan. Consequently, after a viable design was achieved for each platform, their advantages and disadvantages were compared. This comparison included such factors as deployment risk, surface interaction capability, mass, and design heritage. When considering all factors, the preferred candidate platform for a global survey of Titan is an airship.

Gasbarre, Joseph F.↗

NASA NTRS2002

High-Resolution Gravity and Time-Varying Gravity Field Recovery using GRACE and CHAMP

This progress report summarizes the research work conducted under NASA's Solid Earth and Natural Hazards Program 1998 (SENH98) entitled High Resolution Gravity and Time Varying Gravity Field Recovery Using GRACE (Gravity Recovery and Climate Experiment) and CHAMP (Challenging Mini-satellite Package for Geophysical Research and Applications), which included a no-cost extension time period. The investigation has conducted pilot studies to use the simulated GRACE and CHAMP data and other in situ and space geodetic observable, satellite altimeter data, and ocean mass variation data to study the dynamic processes of the Earth which affect climate change. Results from this investigation include: (1) a new method to use the energy approach for expressing gravity mission data as in situ measurements with the possibility to enhance the spatial resolution of the gravity signal; (2) the method was tested using CHAMP and validated with the development of a mean gravity field model using CHAMP data, (3) elaborate simulation to quantify errors of tides and atmosphere and to recover hydrological and oceanic signals using GRACE, results show that there are significant aliasing effect and errors being amplified in the GRACE resonant geopotential and it is not trivial to remove these errors, and (4) quantification of oceanic and ice sheet mass changes in a geophysical constraint study to assess their contributions to global sea level change, while the results improved significant over the use of previous studies using only the SLR (Satellite Laser Ranging)-determined zonal gravity change data, the constraint could be further improved with additional information on mantle rheology, PGR (Post-Glacial Rebound) and ice loading history. A list of relevant presentations and publications is attached, along with a summary of the SENH investigation generated in 2000.

Shum, C. K.↗

NASA NTRS2021

Observational Constraint on Cloud Feedbacks Suggests Moderate Climate Sensitivity

Global climate models (GCMs) predict warming in response to increasing greenhouse gases, partly due to decreased tropical low-level cloud cover and reflectance. We use satellite observations that discriminate stratocumulus (Sc) from shallow cumulus (Cu) clouds to separately evaluate their sensitivity to warming and constrain the tropical contribution to low-cloud feedback. We find an observationally inferred low-level feedback two times smaller than a previous estimate. Cu are insensitive to warming whereas GCMs exhibit a large positive cloud feedback in Cu regions. In contrast, Sc show sensitivity to warming and the tropical inversion layer strength, controlled by the tropical Pacific SST gradient. Models fail to reproduce the historical SST gradient trends and therefore changes in inversion strength, generating an overestimate of the positive Sc cloud feedback. Continued weak east-Pacific warming would therefore produce a weaker low-cloud feedback and imply a more moderate climate sensitivity (3.47  0.33 K) than many models predict.

Cloud feedback↗

NASA NTRS2012

Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems

In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.

planetary soft landing↗

NASA NTRS1989

A complete spherical harmonic approach to luni-solar tides

In this work a spherical harmonic theory of ocean tides is presented. The theory is based on Laplace tide equations modified to include turbulence with constant eddy viscosity, linearized bottom friction, and oceanic loading and self-gravitation. Variable bathymetry is also treated in harmonic terms, and no-flow boundary conditions are applied at continental coastlines. The tide and boundary constraint equations are reduced to matrix form and solved by a weighted least-squares procedure. Five zonal luni-solar tides, ranging in period from 14 days to 18.6 yr, are investigated using the theory; such tides have typically been difficult to compute using traditional numerical approaches. The polar motion and changes in the length of day induced by these long-period tides are calculated. Tidal solutions are compared extensively with results from other tidal theories and from recent satellite and sea-level observations. The greatest limitation to accurate prediction of zonal tides - for any theory - appears to be the marginal failure of all tide theories to conserve mass globally; the use of additional mass constraints may be warranted.

Dickman, S. R.↗