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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 775 records · Page 43
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NASA NTRS1998

Development and Integration of Control System Models

The computer simulation tool, TREETOPS, has been upgraded and used at NASA/MSFC to model various complicated mechanical systems and to perform their dynamics and control analysis with pointing control systems. A TREETOPS model of Advanced X-ray Astrophysics Facility - Imaging (AXAF-1) dynamics and control system was developed to evaluate the AXAF-I pointing performance for Normal Pointing Mode. An optical model of Shooting Star Experiment (SSE) was also developed and its optical performance analysis was done using the MACOS software.

Kim, Young K.↗
NASA NTRS2004

Fire Detection Organizing Questions

Verified models of fire precursor transport in low and partial gravity: a. Development of models for large-scale transport in reduced gravity. b. Validated CFD simulations of transport of fire precursors. c. Evaluation of the effect of scale on transport and reduced gravity fires. Advanced fire detection system for gaseous and particulate pre-fire and fire signaturesa: a. Quantification of pre-fire pyrolysis products in microgravity. b. Suite of gas and particulate sensors. c. Reduced gravity evaluation of candidate detector technologies. d. Reduced gravity verification of advanced fire detection system. e. Validated database of fire and pre-fire signatures in low and partial gravity.

Source record↗
NASA NTRS2010

Bird Migration Under Climate Change - A Mechanistic Approach Using Remote Sensing

The broad-scale reductions and shifts that may be expected under climate change in the availability and quality of stopover habitat for long-distance migrants is an area of increasing concern for conservation biologists. Researchers generally have taken two broad approaches to the modeling of migration behaviour to understand the impact of these changes on migratory bird populations. These include models based on causal processes and their response to environmental stimulation, "mechanistic models", or models that primarily are based on observed animal distribution patterns and the correlation of these patterns with environmental variables, i.e. "data driven" models. Investigators have applied the latter technique to forecast changes in migration patterns with changes in the environment, for example, as might be expected under climate change, by forecasting how the underlying environmental data layers upon which the relationships are built will change over time. The learned geostatstical correlations are then applied to the modified data layers.. However, this is problematic. Even if the projections of how the underlying data layers will change are correct, it is not evident that the statistical relationships will remain the same, i.e. that the animal organism may not adapt its' behaviour to the changing conditions. Mechanistic models that explicitly take into account the physical, biological, and behaviour responses of an organism as well as the underlying changes in the landscape offer an alternative to address these shortcomings. The availability of satellite remote sensing observations at multiple spatial and temporal scales, coupled with advances in climate modeling and information technologies enable the application of the mechanistic models to predict how continental bird migration patterns may change in response to environmental change. In earlier work, we simulated the impact of effects of wetland loss and inter-annual variability on the fitness of migratory shorebirds in the central fly ways of North America. We demonstrated the phenotypic plasticity of a migratory population of Pectoral sandpipers consisting of an ensemble of 10,000 individual birds in response to changes in stopover locations using an individual based migration model driven by remotely sensed land surface data, climate data and biological field data. With the advent of new computing capabilities enabled hy recent GPU-GP computing paradigms and commodity hardware, it now is possible to simulate both larger ensemble populations and to incorporate more realistic mechanistic factors into migration models. Here, we take our first steps use these tools to study the impact of long-term drought variability on shorebird survival.

Smith, James A.↗
NASA NTRS2017

UAV Trajectory Modeling Using Neural Networks

Large amount of small Unmanned Aerial Vehicles (sUAVs) are projected to operate in the near future. Potential sUAV applications include, but not limited to, search and rescue, inspection and surveillance, aerial photography and video, precision agriculture, and parcel delivery. sUAVs are expected to operate in the uncontrolled Class G airspace, which is at or below 500 feet above ground level (AGL), where many static and dynamic constraints exist, such as ground properties and terrains, restricted areas, various winds, manned helicopters, and conflict avoidance among sUAVs. How to enable safe, efficient, and massive sUAV operations at the low altitude airspace remains a great challenge. NASA's Unmanned aircraft system Traffic Management (UTM) research initiative works on establishing infrastructure and developing policies, requirement, and rules to enable safe and efficient sUAVs' operations. To achieve this goal, it is important to gain insights of future UTM traffic operations through simulations, where the accurate trajectory model plays an extremely important role. On the other hand, like what happens in current aviation development, trajectory modeling should also serve as the foundation for any advanced concepts and tools in UTM. Accurate models of sUAV dynamics and control systems are very important considering the requirement of the meter level precision in UTM operations. The vehicle dynamics are relatively easy to derive and model, however, vehicle control systems remain unknown as they are usually kept by manufactures as a part of intellectual properties. That brings challenges to trajectory modeling for sUAVs. How to model the vehicle's trajectories with unknown control system? This work proposes to use a neural network to model a vehicle's trajectory. The neural network is first trained to learn the vehicle's responses at numerous conditions. Once being fully trained, given current vehicle states, winds, and desired future trajectory, the neural network should be able to predict the vehicle's future states at next time step. A complete 4-D trajectory are then generated step by step using the trained neural network. Experiments in this work show that the neural network can approximate the sUAV's model and predict the trajectory accurately.

Neural Networks↗
NASA NTRSDate not supplied

Database Design Strategies for Coordinated Simulation and Testing in Additive Manufacturing

The qualification and certification (Q&C) process presents a significant challenge for widespread adoption of additive manufacturing (AM) materials and processes for aerospace applications. A relational database framework will be presented as a tool for data curation of coordinated experimental and computational materials modeling research activities. A comparison of relational and hierarchical data structures in this domain will be emphasized through the evolution of a database design strategy. This framework’s mission is to support the advancement of computational materials-informed Q&C by providing the necessary data infrastructure to trace reliability and reproducibility measures through unified AM materials simulation and experimental testing. FAIR (findable, accessible, interoperable, and reusable) data will be highlighted as a necessary precursor for automation of specific actions, which ultimately reduces the time and expense burden for Q&C. The discussion will be mostly limited to back-end design elements, though a few front-end user experience examples will also be shared.

Qualification↗
NASA NTRS2019

Analyzing Machine Learning Predictions of Passive Microwave Brightness Temperature Spectral Difference Over Snow-Covered Terrain in High Mountain Asia

Snow is an important component of the terrestrial freshwater budget in high mountainAsia (HMA) and contributes to the runoff in Himalayan rivers through snowmelt. Despitethe importance of snow in HMA, considerable spatiotemporal uncertainty exists across the different estimates of snow water equivalent for this region. In order to better estimate snow water equivalent, radiative transfer models are often used in conjunction with microwave brightness temperature measurements. In this study, the efficacy of support vector machines (SVMs), a machine learning technique, to predict passive microwave brightness temperature spectral difference (1Tb) as a function of geophysical variables (snow water equivalent, snow depth, snow temperature, and snow density) is explored through a sensitivity analysis. The use of machine learning (as opposed to radiative transfer models) is a relatively new and novel approach for improving snow water equivalent estimates. The Noah-MP land surface model within the NASALand Information System framework is used to simulate the hydrologic cycle over HMA and model geophysical variables that are then used for SVM training. The SVMsserve as a nonlinear map between the geophysical space (modeled in Noah-MP) andthe observation space (1Tb as measured by the radiometer). Advanced MicrowaveScanning Radiometer-Earth Observing System measured passive microwave brightness temperatures over snow-covered locations in the HMA region are used as training data during the SVM training phase. Sensitivity of well-trained SVMs to each Noah-MP modeled state variable is assessed by computing normalized sensitivity coefficients. Sensitivity analysis results generally conform with the known first-order physics. Input states that increase volume scattering of microwave radiation, such as snow density and snow water equivalent, exhibit a plurality of positive normalized sensitivity coefficients. In general, snow temperature was the most sensitive input to the SVM predictions. The sensitivity of each state is location and time dependent. The signs of normalized sensitivity coefficients that indicate physical irrationality are ascribed to significant cross-correlation between Noah-MP simulated states and decreased SVM prediction capability at specific locations due to insufficient training data. SVM prediction pitfalls do exist that serve to highlight the limitations of this particular machine learning algorithm.

high mountain Asia↗
NASA NTRS2020

Overview of Coupon Testing of an IM7/8552 Composite Required to Characterize High-Energy Impact Dynamic Material Models

As part of NASA’s Advanced Composites Project (ACP), a significant research effort was established to develop and mature analysis methods for composite materials particularly applicable to high-energy dynamic impact applications. An overall goal was to develop and advance analysis methods that can be characterized using fundamental coupon level tests. Based on this fundamental characterization, simulations at the higher levels of a building block approach can be purely predictive. The tests described in this report were performed on a unidirectional carbon fiber polymer matrix composite, IM7/8552 tape, as this material system is representative of a modern aerospace grade carbon fiber tape system. These tests were chosen to provide fundamental material characterization data for three representative progressive damage and failure analysis material models available within the LS-DYNA commercial transient dynamic finite element code for use in the simulation of the dynamic and impact response of composite materials. Two of the material models, MAT162 and MAT261, are well established material models within LS-DYNA. The third material model, MAT213, is under active development. Testing consisted primarily of ASTM-type standard tests, and the tests that were performed were consistent with the needs of all three models. Additionally, coupon level tests were performed that can be used to characterize a delamination model (e.g., cohesive zone or tie-break contact). While, the tests described in this report provide fundamental material characterization data for all three of the material models mentioned above, the data is applicable to additional material models not discussed.

Justusson, Brian P.↗
NASA NTRS2005

Collaborative Mission Design at NASA Langley Research Center

NASA Langley Research Center (LaRC) has developed and tested two facilities dedicated to increasing efficiency in key mission design processes, including payload design, mission planning, and implementation plan development, among others. The Integrated Design Center (IDC) is a state-of-the-art concurrent design facility which allows scientists and spaceflight engineers to produce project designs and mission plans in a real-time collaborative environment, using industry-standard physics-based development tools and the latest communication technology. The Mission Simulation Lab (MiSL), a virtual reality (VR) facility focused on payload and project design, permits engineers to quickly translate their design and modeling output into enhanced three-dimensional models and then examine them in a realistic full-scale virtual environment. The authors were responsible for envisioning both facilities and turning those visions into fully operational mission design resources at LaRC with multiple advanced capabilities and applications. In addition, the authors have created a synergistic interface between these two facilities. This combined functionality is the Interactive Design and Simulation Center (IDSC), a meta-facility which offers project teams a powerful array of highly advanced tools, permitting them to rapidly produce project designs while maintaining the integrity of the input from every discipline expert on the project. The concept-to-flight mission support provided by IDSC has shown improved inter- and intra-team communication and a reduction in the resources required for proposal development, requirements definition, and design effort.

Gough, Kerry M.↗
NASA NTRS2018

Modeling Principles Using the Relation Between Lagrange Multipliers and Bond Graphs

Final document is attached. Modeling dynamic systems by bond graphs has become state of the art technology since hundreds of researchers around the world have incorporated the technology in many fields of engineering and science. The legacy of its invertor Prof. Henry Paynter at MIT in 1959 is now a fundamental and practical technique to understand reality by building computer models. This paper addresses a particular aspect of this technology when modeling of mechanical systems require relaxation of constraints by means of Lagrange principles. Lagrange's equations are a useful means of describing and solving systems with kinematic constraints. Lagrange multipliers are variables used in equations to find the extremes of multivariate functions. Here we explore the relation of Lagrange multipliers to solve modeling difficulties of a space vehicle with equations with dependent derivatives. Lagrange multipliers were used in conjunction with bond graphs to simulate a system where joints of kinematic linkages produce dependent derivatives. NASA's Morpheus Project lunar lander was used as a case study. The Morpheus Project is a terrestrial test vehicle designed to fly the terminal descent trajectory of a lunar lander to advance the Autonomous Landing Hazard Avoidance Technology (ALHAT). An objective of this study is to apply the modeling approach herein to capture the dynamic movement of the lander as the propellant is sloshed and consumed. This paper expands further the analysis presented by (Granda, J J. Nguyen, L, Carlson, T, Sahragard-Monfared, G., Fornalski, E., Brocker 2016). Using an automated approach bond graph models of state space equations were generated using the Computer Aided Modeling Program (CAMPG). Integral causality models and derivative causality models were considered in order to find the simpler solution for the mathematical dependencies produced in modeling this vehicle.

Granda, Jose J.↗
NASA NTRS1991

A simplified wind vector algorithm for satellite scatterometers

A simplified algorithm is derived for retrieving wind vectors from microwave scatterometer observations. The azimuthal dependence of the sea-surface radar cross section is modeled by a double-cosine function, rather than the traditional second-order cosine expansion. The algorithm is tested using the aircraft scatterometer observations obtained during the AAFE-RADSCAT Experiment in 1975 and 1976. There is little difference between the performance of the simplified algorithm and the more involved least-squares searching algorithm. The AAFE-RADSCAT aircraft observations are sampled so as to simulate the three-look satellite scatterometer NSCAT that will be launched on the Japanese Advanced Earth Observing Satellite. The results of the retrievals indicate that it is probably not possible to uniquely determine the wind direction using just NSCAT observations because of a 180 degree ambiguity. However, if forecast models can predict the wind direction to an accuracy of +/- 90 deg, thereby eliminating the ambiguity, then the results indicate that NSCAT can determine the wind direction to an accuracy of about +/- 20 deg. Better performance is obtained when the three observations are the same polarization (either v-pol or h-pol), as compared to using a mix of v-pol and h-pol observations.

Wentz, Frank J.↗
NASA NTRS2014

Development and Performance Evaluations of HfO2-Si and Rare Earth-Si Based Environmental Barrier Bond Coat Systems for SiC/SiC Ceramic Matrix Composites

Ceramic environmental barrier coatings (EBC) and SiCSiC ceramic matrix composites (CMCs) will play a crucial role in future aircraft propulsion systems because of their ability to significantly increase engine operating temperatures, improve component durability, reduce engine weight and cooling requirements. Advanced EBC systems for SiCSiC CMC turbine and combustor hot section components are currently being developed to meet future turbine engine emission and performance goals. One of the significant material development challenges for the high temperature CMC components is to develop prime-reliant, high strength and high temperature capable environmental barrier coating bond coat systems, since the current silicon bond coat cannot meet the advanced EBC-CMC temperature and stability requirements. In this paper, advanced NASA HfO2-Si based EBC bond coat systems for SiCSiC CMC combustor and turbine airfoil applications are investigated. The coating design approach and stability requirements are specifically emphasized, with the development and implementation focusing on Plasma Sprayed (PS) and Electron Beam-Physic Vapor Deposited (EB-PVD) coating systems and the composition optimizations. High temperature properties of the HfO2-Si based bond coat systems, including the strength, fracture toughness, creep resistance, and oxidation resistance were evaluated in the temperature range of 1200 to 1500 C. Thermal gradient heat flux low cycle fatigue and furnace cyclic oxidation durability tests were also performed at temperatures up to 1500 C. The coating strength improvements, degradation and failure modes of the environmental barrier coating bond coat systems on SiCSiC CMCs tested in simulated stress-environment interactions are briefly discussed and supported by modeling. The performance enhancements of the HfO2-Si bond coat systems with rare earth element dopants and rare earth-silicon based bond coats are also highlighted. The advanced bond coat systems, when integrated with advanced EBC top coats, showed promise to achieve 1500 C temperature capability, helping enable next generation turbine engines with significantly improved engine component temperature capability and long-term durability.

HfO2-Si bond coat↗
NASA NTRSDate not supplied

Next Generation Exercise Device (NGED): Advancing Exercise Capabilities for Future Space Missions Through Biomechanical Modeling

BACKGROUND As space exploration extends to long-duration missions on the Moon and Mars, maintaining astronaut health and fitness becomes increasingly critical. The Next Generation Exercise Device (NGED), developed and tested by the HumanWorks Lab in NASA Johnson Space Center's (JSC) Software, Robotics, and Simulation Division, aims to address this challenge through innovative approaches. This study presents the development and evaluation of an NGED system, focusing on its adaptability to various mission scenarios, including prospective use in a Lunar Pressurized Rover (LPR). Central to this project is the application of biomechanical modeling to optimize exercise efficacy and safety in microgravity and partial gravity environments. The project is a collaborative effort with the Human Health and Performance group at Johnson Space Center, ensuring a comprehensive approach to astronaut well-being that integrates biomechanical principles with practical exercise solutions. The NGED represents the next generation of exercise capabilities for missions in space, on the Moon and Mars, with a specific focus on applications such as the LPR. METHODS AND RESULTS Data collection for NGED development was conducted with two motor-driven Beyond Power Voltra I [1] systems and a custom test structure to allow placement of the cable-based devices on the ground, at shoulder height, and overhead. The collection was performed in JSC’s Prototype Immersive Technology (PIT) Lab, utilizing an OptiTrack motion capture system and AMTI force platform, to enable detailed biomechanical analysis via OpenSim [2,3]. Motion capture data were collected for three subjects representing different body types and statures. The marker set used was an enhanced version of the full-body Plug-in Gait marker set [4], with additional markers strategically placed for the primary objective of informing exercise volume requirements. Subjects performed a series of 17 exercises, carefully selected to engage various muscle groups, including novel spaceflight exercises such as skiing (ergometer style), lateral pulldowns, wood chops, triceps extensions, and flies, with load variations ranging from 10 to 90 pounds to maintain kinematic form. This comprehensive approach allowed for a thorough evaluation of the NGED's performance across a wide range of motions and loads. The biomechanical modeling and analysis were conducted using a modified OpenSim Full Body Rajagopal Model [4,5] and also scaled to the maximum and minimum anthropometry provided in NASA-STD-3001 [6]. Volumetric convex hulls were generated based on model marker trajectories and aggregated into geometric assemblies. These can be placed in models of vehicle designs to assess fit to protect for exercise as well as to adapt NGED exercise to fit available space. Preliminary findings from the collection indicate that the NGED prototype demonstrates significant adaptability across varying user anthropometrics and exercise types. The device showed consistent performance in load-bearing exercises, with subjects able to perform exercises effectively while maintaining proper biomechanical form. CONCLUSION NGED represents a forward-looking advancement in exercise capabilities for future space missions. In the future, this system can be used to capture valuable metrics (e.g., isometric mid-thigh pull for force output measurements, assessments of postural muscle strength, overall isometric strength). Its versatility in accommodating various exercises and user physiques, coupled with the ability to provide targeted biomechanical loading, makes it a promising approach for maintaining astronaut health during long-duration missions to the Moon and Mars. Future work will focus on refining the NGED based on initial biomechanical findings, leveraging the detailed insights provided by motion capture and analysis techniques. Particular emphasis will be placed on optimizing its use within the confined spaces of a LPR and other space habitats. This work contributes significantly to NASA's goals of supporting human health and performance in deep space exploration, paving the way for sustainable long-term presence beyond Low Earth Orbit through advanced, biomechanically-informed exercise solutions.

C Wang↗
NASA NTRS2011

Spatial and Temporal Signatures of Flux Transfer Events in Global Simulations of Magnetopause Dynamics

Flux transfer events (FTEs) were originally identified by transient bipolar variations of the magnetic field component normal to the nominal magnetopause centered on enhancements in the total magnetic field strength. Recent Cluster and THEMIS multi-point measurements provided a wide range of signatures that are interpreted as evidence for FTE passage (e.g., crater FTE's, traveling magnetic erosion regions). We use the global magnetohydrodynamic (MHD) code BATS-R-US developed at the University of Michigan to model the global three-dimensional structure and temporal evolution of FTEs during multi-spacecraft magnetopause crossing events. Comparison of observed and simulated signatures and sensitivity analysis of the results to the probe location will be presented. We will demonstrate a variety of observable signatures in magnetic field profile that depend on space probe location with respect to the FTE passage. The global structure of FTEs will be illustrated using advanced visualization tools developed at the Community Coordinated Modeling Center

Kuznetsova, Maria M.↗
NASA NTRS2003

Rough-Wall Channel Analysis Using Suboptimal Control Theory

The original aim of this work was to shed some light on the physics of turbulence over rough walls using large-eddy simulations and the suboptimal-control wall boundary conditions introduced by Nicoud et al. It was hoped that, if that algorithm was used to fit the mean velocity profile of the simulations to that of a rough-walled channel, instead of to a smooth one, the wall stresses introduced by the control algorithm would give some indication of what aspects of rough walls are most responsible for the modification of the flow in real turbulence. It was similarly expected that the structure of the resulting velocity fluctuations would share some of the characteristics of rough-walled flows, thus again suggesting what is intrinsic and what is accidental in the effect of geometric wall roughness. A secondary goal was to study the effect of 'unphysical' boundary conditions on the outside flow by observing how a relatively major change of the target velocity profile, and therefore presumably of the applied wall stresses, modifies properties such as the dominant length scales of the velocity fluctuations away from the wall. As will be seen below, this secondary goal grew more important during the course of the study, which was carried out during a short summer visit of the first two authors to the CTR. It became clear that there are open questions about the way in which the control algorithm models the boundary conditions, even for smooth walls, and that these questions make the physical interpretation of the results difficult. Considerable more work in that area seems to be needed before even relatively advanced large-eddy simulations, such as these, can be used to draw conclusions about the physics of wall-bounded turbulent flows. The numerical method is the same as in Nicoud et al. The modifications introduced in the original code are briefly described in section 2, but the original paper should be consulted for a full description of the algorithm. The results are presented in section 3 and summarized in section 4. The elementary properties of turbulence over rough walls which are used in the text have been taken from recent reviews such as Raupach et al. or Jimenez.

Flores, O.↗
NASA NTRS1984

Periodic control of the individual-blade-control helicopter rotor

Results of an investigation into methods of controller design for an individual helicopter rotor blade in the high forward-flight speed regime are described. This operating condition poses a unique control problem in that the perturbation equations of motion are linear with coefficients that vary periodically with time. The design of a control law was based on extensions to modern multivariate synthesis techniques and incorporated a novel approach to the reconstruction of the missing system state variables. The controller was tested on both an electronic analog computer simulation of the out-of-plane flapping dynamics, and on a four foot diameter single-bladed model helicopter rotor in the M.I.T. 5x7 subsonic wind tunnel at high levels of advance ratio. It is shown that modal control using the IBC concept is possible over a large range of advance ratios with only a modest amount of computational power required.

Mckillip, R. M., Jr.↗
NASA NTRS1985

Elevated temperature crack growth

The purpose is to determine the ability of currently available P-I integrals to correlate fatigue crack propagation under conditions that simulate the turbojet engine combustor liner environment. The utility of advanced fracture mechanics measurements will also be evaluated during the course of the program. To date, an appropriate specimen design, a crack displacement measurement method, and boundary condition simulation in the computational model of the specimen were achieved. Alloy 718 was selected as an analog material based on its ability to simulate high temperature behavior at lower temperatures. Tensile and cyclic tests were run at several strain rates so that an appropriate constitutive model could be developed. Suitable P-I integrals were programmed into a finite element post-processor for eventual comparison with experimental data.

Malik, S. N.↗
NASA NTRS1992

Dynamic simulation of compressor and gas turbine performance

Dynamic simulation of compressor and gas turbine performance is useful in a variety of design, analysis, and test applications. Mathematical models employing estimated or experimentally-derived component characteristics have been widely used, especially for near-design-point studies of acceleration and deceleration transients and control strategies. With recent progress in simulation methods and computational power, it has become possible to build models with detail at the stage level, and with fundamental fluid mechanics input. Such models are more useful because of the ability to study the details of inter-component flow property behavior during machine transients, even including stall and surge. Dynamic performance simulation models are discussed with emphasis on the fundamental principles of the models and the methods used to represent component and stage flow characteristics. Results of several simulations of the dynamic behavior of multistage compressors are shown with comparisons to experimental data. Possibilities for advanced computational techniques for near-real-time simulations of compressors and gas turbines are reviewed.

Walter F O'Brien↗
NASA NTRS1994

An incremental database access method for autonomous interoperable databases

We investigated a number of design and performance issues of interoperable database management systems (DBMS's). The major results of our investigation were obtained in the areas of client-server database architectures for heterogeneous DBMS's, incremental computation models, buffer management techniques, and query optimization. We finished a prototype of an advanced client-server workstation-based DBMS which allows access to multiple heterogeneous commercial DBMS's. Experiments and simulations were then run to compare its performance with the standard client-server architectures. The focus of this research was on adaptive optimization methods of heterogeneous database systems. Adaptive buffer management accounts for the random and object-oriented access methods for which no known characterization of the access patterns exists. Adaptive query optimization means that value distributions and selectives, which play the most significant role in query plan evaluation, are continuously refined to reflect the actual values as opposed to static ones that are computed off-line. Query feedback is a concept that was first introduced to the literature by our group. We employed query feedback for both adaptive buffer management and for computing value distributions and selectivities. For adaptive buffer management, we use the page faults of prior executions to achieve more 'informed' management decisions. For the estimation of the distributions of the selectivities, we use curve-fitting techniques, such as least squares and splines, for regressing on these values.

Roussopoulos, Nicholas↗