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A problem of choosing the best scaling function as a mathematical optimization problem is formulated and solved under different optimality criteria. A list of functions which are optimal under different criteria is presented which includes both the best functions empirically proved and new functions that may be worth trying.
We present an optimal preconditioning algorithm that is equally applicable to the dual (FETI) and primal (Balancing) Schur complement domain decomposition methods, and which successfully addresses the problems of subdomain heterogeneities including the effects of large jumps of coefficients. The proposed preconditioner is derived from energy principles and embeds a new coarsening operator that propagates the error globally and accelerates convergence. The resulting iterative solver is illustrated with the solution of highly heterogeneous elasticity problems.
A gradient-based shape optimization based on quasi-analytical sensitivities has been extended for practical three-dimensional aerodynamic applications. The flow analysis has been rendered by a fully implicit, finite-volume formulation of the Euler and Thin-Layer Navier-Stokes (TLNS) equations. Initially, the viscous laminar flow analysis for a wing has been compared with an independent computational fluid dynamics (CFD) code which has been extensively validated. The new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4 with coarse- and fine-grid based computations performed with Euler and TLNS equations. The influence of the initial constraints on the geometry and aerodynamics of the optimized shape has been explored. Various final shapes generated for an identical initial problem formulation but with different optimization path options (coarse or fine grid, Euler or TLNS), have been aerodynamically evaluated via a common fine-grid TLNS-based analysis. The initial constraint conditions show significant bearing on the optimization results. Also, the results demonstrate that to produce an aerodynamically efficient design, it is imperative to include the viscous physics in the optimization procedure with the proper resolution. Based upon the present results, to better utilize the scarce computational resources, it is recommended that, a number of viscous coarse grid cases using either a preconditioned bi-conjugate gradient (PbCG) or an alternating-direction-implicit (ADI) method, should initially be employed to improve the optimization problem definition, the design space and initial shape. Optimized shapes should subsequently be analyzed using a high fidelity (viscous with fine-grid resolution) flow analysis to evaluate their true performance potential. Finally, a viscous fine-grid-based shape optimization should be conducted, using an ADI method, to accurately obtain the final optimized shape.
This paper describes a computationally efficient nearly optimal Bayesian algorithm to estimate rain (and drop size distribution) profiles, given a radar reflectivity profile at a single attenuating wavelength. In addition to estimating the averages of all the mutually ambiguous combinations of rain parameters that can produce the data observed, the approach also calculates the n-ns uncertainty in its estimates (this uncertainty thus quantifies "the amount of ambiguity" in the "solution"). The paper also describes a more general approach that can make estimates based on a radar reflectivity profile together with an approximate measurement of the path-integrated attenuation, or a radar reflectivity profile and a set of passive microwave brightness temperatures. This more general "combined" algorithm is currently being adapted for the Tropical Rainfall Measuring Mission.
Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman Filter and Global Positioning System (GPS) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. Current techniques of Kalman filtering, however, still rely on manual tuning from analysts, and cannot help in optimizing autonomy without compromising accuracy and performance. This paper presents an approach to produce a high accuracy autonomous navigation system fully integrated with the flight system. The resulting system performs real-time state estimation by using an Extended Kalman Filter (EKF) implemented with high-fidelity state dynamics model, as does the GPS Enhanced Orbit Determination Experiment (GEODE) system developed by the NASA Goddard Space Flight Center. Augmented to the EKF is a sophisticated neural-fuzzy system, which combines the explicit knowledge representation of fuzzy logic with the learning power of neural networks. The fuzzy-neural system performs most of the self-tuning capability and helps the navigation system recover from estimation errors. The core requirement is a method of state estimation that handles uncertainties robustly, capable of identifying estimation problems, flexible enough to make decisions and adjustments to recover from these problems, and compact enough to run on flight hardware. The resulting system can be extended to support geosynchronous spacecraft and high-eccentricity orbits. Mathematical methodology, systems and operations concepts, and implementation of a system prototype are presented in this paper. Results from the use of the prototype to evaluate optimal control algorithms implemented are discussed. Test data and major control issues (e.g., how to define specific roles for fuzzy logic to support the self-learning capability) are also discussed. In addition, architecture of a complete end-to-end candidate flight system that provides navigation with highly autonomous control using data from GPS is presented.
Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer brightness temperature data in the 85 GHz channel (T85) reveal distinct local minima (T85min) in a regional map containing a Mesoscale Convective System (MCS). A map of surface rain rate for that region, deduced from simultaneous measurements made by the Precipitation Radar (PR) on board the TRMM satellite, reveals that these T85min, produced by scattering, correspond to local PR rain maxima. Utilizing the PR rain rate map as a guide, we have developed a TMI algorithm to retrieve convective and stratiform rain. In this algorithm, two parameters are used to classify three kinds of thunderstorms (Cbs) based on the T85 data: a) the magnitude of scattering depression deduced from local T85mi, and b) the mean horizontal gradient of T85 around such minima. Initially, the algorithm is optimized or tuned utilizing the PR and TMI data of a few MCS events. The areal distribution of light (1-10 mm/hr), moderate (10-20 mm/hr), and intense (greater than or equal to 20 mm/hr) rain rates are retrieved on the average with an accuracy of about 15%. Taking advantage of this ability of our retrieval method, one could derive the latent heat input into the atmosphere over the 760 km wide swath of the TMI radiometer in the tropics.
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
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The objective of this paper is to develop a statistically optimal assimilation algorithm which estimates the entire system state, i.e., vertical soil moisture and temperature profiles, from information which is only available for portion of the system (namely, the near-surface soil moisture and temperature).
We describe a computationally efficient nearly-optimal Bayesian algorithm to estimate rain profiles, given a radar reflectivity profile at a single attenuating wavelength.
The Jason Microwave Radiometer (JMR) is included on the Jason-1 ocean altimeter satellite to measure the wet tropospheric path delay (PD) experienced by the radar altimeter signal. JMR is nadir pointing and measures the radiometric brightness temperature (T(sub B)) at 18.7, 23.8 and 34.0 GHz. JMR is a Dicke radiometer and it is the first radiometer to be flown in space that uses noise diodes for calibration. Therefore, monitoring the long term stability of the noise diodes is essential. Each channel has three redundant noise diodes which are individually coupled into the antenna signal to provide an estimate of the gain. Two significant jumps in the JMR path delays, relative to ground truth, were observed around 300 and 700 days into the mission. Slow drifts in the retrieved products were also evident over the entire mission. During a recalibration effort, it was determined that a single set of calibration coefficients was not able to remove the calibration jumps and drifts, suggesting that there was a change in the hardware and time dependent coefficients would be required. To facilitate the derivation of time dependent coefficients, an optimal estimation based calibration system was developed which iteratively determines that set of calibration coefficients which minimize the RMS difference between the JMR TBs and on-Earth hot and cold absolute references. This optimal calibration algorithm was used to fine tune the front end path loss coefficients and derive a time series of the JMR noise diode brightness temperatures for each of the nine diodes. Jumps and drifts, on the order of 1% to 2%, are observed among the noise diodes in the first three years on-orbit.
We report on the development of position-sensitive transition-edge sensors (PoST's) for future x-ray astronomy missions such as the International X-ray Observatory (IXO), currently under study by NASA and ESA. PoST's consist of multiple absorbers each with a different thermal coupling to one or more transition-edge sensor (TES). This differential thermal coupling between absorbers and TES's results in different characteristic pulse shapes and allows position discrimination between the different pixels. The development of PoST's is motivated by a desire to achieve maximum focal-plane area with the least number of readout channels and as such. PoST's are ideally suited to provide a focal-plane extension to the Constellation-X microcalorimeter array. We report the first experimental results of our latest one and two channel PoST's, which utilize fast thermalizing electroplated Au/Bi absorbers coupled to low noise Mo/Au TES's - a technology already successfully implemented in our arrays of single pixel TES's. We demonstrate 6 eV energy resolution coupled with spatial sensitivity in the keV energy range. We also report on the development of signal processing algorithms to optimize energy and position sensitivity of our detectors.
Distributed approaches for conflict resolution rely on analyzing the behavior of each aircraft to ensure that system-wide safety properties are maintained. This paper presents the criteria method, which increases the quality and efficiency of a safety assurance analysis for distributed air traffic concepts. The criteria standard is shown to provide two key safety properties: safe separation when only one aircraft maneuvers and safe separation when both aircraft maneuver at the same time. This approach is complemented with strong guarantees of correct operation through formal verification. To show that an algorithm is correct, i.e., that it always meets its specified safety property, one must only show that the algorithm satisfies the criteria. Once this is done, then the algorithm inherits the safety properties of the criteria. An important consequence of this approach is that there is no requirement that both aircraft execute the same conflict resolution algorithm. Therefore, the criteria approach allows different avionics manufacturers or even different airlines to use different algorithms, each optimized according to their own proprietary concerns.
In the early problem-solution era of software programming, functional decompositions were mainly used to design and implement software solutions. In functional decompositions, functions and data are introduced as two separate entities during the design phase, and are followed as such in the implementation phase. Functional decompositions make use of refactoring through optimizing the algorithms, grouping similar functionalities into common reusable functions, and using abstract representations of data where possible; all these are done during the implementation phase. This paper advocates the usage of object-oriented methodologies and design patterns as the centerpieces of refactoring software solutions. Refactoring software is a method of changing software design while explicitly preserving its external functionalities. The combined usage of object-oriented methodologies and design patterns to refactor should also benefit the overall software life cycle cost with improved software.
A set of automated planning algorithms is the current operations baseline approach for the Intelligent Payload Module (IPM) of the proposed Hyper spectral Infrared Imager (HyspIRI) mission. For this operations concept, there are only local (e.g. non-depletable) operations constraints, such as real-time downlink and onboard memory, and the forward sweeping algorithm is optimal for determining which science products should be generated onboard and on ground based on geographical overflights, science priorities, alerts, requests, and onboard and ground processing constraints. This automated planning approach was developed for the HyspIRI IPM concept. The HyspIRI IPM is proposed to use an X-band Direct Broadcast (DB) capability that would enable data to be delivered to ground stations virtually as it is acquired. However, the HyspIRI VSWIR and TIR instruments will produce approximately 1 Gbps data, while the DB capability is 15 Mbps for a approx. =60X oversubscription. In order to address this mismatch, this innovation determines which data to downlink based on both the type of surface the spacecraft is overflying, and the onboard processing of data to detect events. For example, when the spacecraft is overflying Polar Regions, it might downlink a snow/ice product. Additionally, the onboard software will search for thermal signatures indicative of a volcanic event or wild fire and downlink summary information (extent, spectra) when detected, thereby reducing data volume. The planning system described above automatically generated the IPM mission plan based on requested products, the overflight regions, and available resources.
The OpenMDAO project is underway at NASA to develop a framework which simplifies the implementation of state-of-the-art tools and methods for multidisciplinary design, analysis and optimization. Foremost, OpenMDAO has been designed to handle variable problem formulations, encourage reconfigurability, and promote model reuse. This work demonstrates the concept of iteration hierarchies in OpenMDAO to achieve a flexible environment for supporting advanced optimization methods which include adaptive sampling and surrogate modeling techniques. In this effort, two efficient global optimization methods were applied to solve a constrained, single-objective and constrained, multiobjective version of a joint aircraft/engine sizing problem. The aircraft model, NASA's nextgeneration advanced single-aisle civil transport, is being studied as part of the Subsonic Fixed Wing project to help meet simultaneous program goals for reduced fuel burn, emissions, and noise. This analysis serves as a realistic test problem to demonstrate the flexibility and reconfigurability offered by OpenMDAO.
Hammering drills are effective in fracturing the drilled medium while rotary drills remove cuttings. The combination provides a highly effective penetration mechanism. Piezoelectric actuators were integrated into an adapter to produce ultrasonic percussion; augmenting rotary drilling. The drill is capable of operating at low power, low applied force and, with proper tuning, low noise. These characteristics are of great interest for future NASA missions and the construction/remodeling industry. The developed augmenter connects a commercially available drill and bit and was tested to demonstrate its capability. Input power to the drill was read using a multimeter and the augmenter received a separate input voltage. The drive frequency of the piezoelectric actuator was controlled by a hill climb algorithm that optimizes and records average power usage to operate the drill at resonating frequency. Testing the rotary drill and augmenter across a range of combinations with total power constant at 160 Watts has shown results in concrete and limestone samples that are as good as or better than the commercial drill. The drill rate was increased 1.5 to over 10 times when compared to rotation alone.
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.