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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

The NASA Meter Class Autonomous Telescope: Ascension Island

The Meter Class Autonomous Telescope (MCAT) is the newest optical sensor dedicated to NASA s mission to characterize the space debris environment. It is the successor to a series of optical telescopes developed and operated by the JSC Orbital Debris Program Office (ODPO) to monitor and assess the debris environment in (1) Low Earth Orbit (LEO), (2) Medium Earth Orbit (MEO), and (3) Geosynchronous Orbit (GEO), with emphasis on LEO and GEO altitudes. A joint NASA-Air Force Research Labs project, MCAT is a 1.3m optical telescope dedicated to debris research. Its optical path and sensor yield a large survey fence at the cutting edge of current detector performance. It has four primary operational observing modes, two of which were not computationally feasible a decade ago. Operations are supported by a sophisticated software suite that monitors clouds and weather conditions, and controls everything from data collection to dome rotation to processing tens of GB of imagery data nightly. With fainter detection limits, precision detection, acquisition and tracking of targets, multi-color photometry, precision astrometry, automated reacquisition capability, and the ability to process all data at the acquisition rate, MCAT is capable of producing and processing a volume and quality of data far in excess of any current (or prior) ODPO operations. This means higher fidelity population inputs and eliminating the multi-year backlog from acquisition-to-product typical of optical campaigns. All of this is possible given a suitable observing location. Originally planned for the island of Legan, part of the Kwajalein Atoll Islands, recent developments have led to a change in venue. Specifically, the Ground-based Electro-Optical Deep Space Surveillance, or GEODSS, System of telescopes is the United States major tracking system for deep space. This network consists of telescopes in Maui, Hawaii; Diego Garcia (Indian Ocean), and Socorro, New Mexico. A fourth optical telescope, though smaller in size, has been operating in conjunction with this effort until recently in M.ron, Spain. With the M.ron site closing, a significant gap in longitude exists between the New Mexico and Diego Garcia sites. This longitudinal gap is well covered by placing a telescope on Ascension Island (7degrees 58'20" S, 14degrees 24'4"W), in the Atlantic Ocean. Ascension Island offers the benefits of both location and weather. The near equatorial location affords the opportunity to access under-sampled low-inclination orbits and new GEO longitudes, while simultaneously filling in the GEODSS longitudinal gap. Ascension Island is a volcanic, desert island, receiving only 7" of rain per year on average. With consistent trade winds blowing from the SSE direction off Africa, the combination of an island location with consistent winds will create the smooth laminar flow sought after by all astronomical sites, which creates stable atmospheric ('seeing') conditions. Finally, this low population island has minimal lighting, resulting in very dark skies, ideal for an observatory.

Lederer, S. M.↗
NASA NTRS1988

Technology transfer: Imaging tracker to robotic controller

The transformation of an imaging tracker to a robotic controller is described. A multimode tracker was developed for fire and forget missile systems. The tracker locks on to target images within an acquisition window using multiple image tracking algorithms to provide guidance commands to missile control systems. This basic tracker technology is used with the addition of a ranging algorithm based on sizing a cooperative target to perform autonomous guidance and control of a platform for an Advanced Development Project on automation and robotics. A ranging tracker is required to provide the positioning necessary for robotic control. A simple functional demonstration of the feasibility of this approach was performed and described. More realistic demonstrations are under way at NASA-JSC. In particular, this modified tracker, or robotic controller, will be used to autonomously guide the Man Maneuvering Unit (MMU) to targets such as disabled astronauts or tools as part of the EVA Retriever efforts. It will also be used to control the orbiter's Remote Manipulator Systems (RMS) in autonomous approach and positioning demonstrations. These efforts will also be discussed.

Otaguro, M. S.↗
NASA NTRS2008

Assessment and Mission Planning Capability For Quantitative Aerothermodynamic Flight Measurements Using Remote Imaging

High resolution calibrated infrared imagery of vehicles during hypervelocity atmospheric entry or sustained hypersonic cruise has the potential to provide flight data on the distribution of surface temperature and the state of the airflow over the vehicle. In the early 1980 s NASA sought to obtain high spatial resolution infrared imagery of the Shuttle during entry. Despite mission execution with a technically rigorous pre-planning capability, the single airborne optical system for this attempt was considered developmental and the scientific return was marginal. In 2005 the Space Shuttle Program again sponsored an effort to obtain imagery of the Orbiter. Imaging requirements were targeted towards Shuttle ascent; companion requirements for entry did not exist. The engineering community was allowed to define observation goals and incrementally demonstrate key elements of a quantitative spatially resolved measurement capability over a series of flights. These imaging opportunities were extremely beneficial and clearly demonstrated capability to capture infrared imagery with mature and operational assets of the US Navy and the Missile Defense Agency. While successful, the usefulness of the imagery was, from an engineering perspective, limited. These limitations were mainly associated with uncertainties regarding operational aspects of data acquisition. These uncertainties, in turn, came about because of limited pre-flight mission planning capability, a poor understanding of several factors including the infrared signature of the Shuttle, optical hardware limitations, atmospheric effects and detector response characteristics. Operational details of sensor configuration such as detector integration time and tracking system algorithms were carried out ad hoc (best practices) which led to low probability of target acquisition and detector saturation. Leveraging from the qualified success during Return-to-Flight, the NASA Engineering and Safety Center sponsored an assessment study focused on increasing the probability of returning spatially resolved scientific/engineering thermal imagery. This paper provides an overview of the assessment task and the systematic approach designed to establish confidence in the ability of existing assets to reliably acquire, track and return global quantitative surface temperatures of the Shuttle during entry. A discussion of capability demonstration in support of a potential Shuttle boundary layer transition flight test is presented. Successful demonstration of a quantitative, spatially resolved, global temperature measurement on the proposed Shuttle boundary layer transition flight test could lead to potential future applications with hypersonic flight test programs within the USAF and DARPA along with flight test opportunities supporting NASA s project Constellation.

Horvath, Thomas↗
NASA NTRS2001

AVIRIS Inflight Calibration Experiments, Analysis, and Results in 2000

The NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) measures spectra from 370 to 2500 nm with nominally 10-nm sampling and resolution. The spectra are acquired as images with an 11 km width and up to 800 km length from the ER-2 platform or 2.1 km width and 160 km length from the Twin Otter platform. AVIRIS measurements are used for a range of Earth science research and application objectives. The molecular absorption and particle scattering properties expressed in the calibrated AVIRIS measurements are used. For both science research and application objectives, calibration of the AVIRIS spectra is required to produce useful results. Each year prior to the flight season AVIRIS is calibrated in the laboratory. However, the temperature, pressure, vibration, and observational geometry, as well as mechanical, electrical, and operational interfaces of the laboratory are different than the environment on board the airborne platform. To validate the calibration of AVIRIS in the flight environment, an inflight calibration experiment is orchestrated at the beginning of each flight season. In most years additional inflight calibration experiments occur towards the middle and end of the flight season as well. For an inflight calibration experiment, AVIRIS acquires airborne data over a designated calibration target. In concert with the airborne data acquisition, surface and atmospheric properties at the calibration target are measured in situ. These in situ measurements are used to constrain a radiative transfer code and predict the radiance incident at the AVIRIS instrument from the calibration target. This prediction is compared with the AVIRIS-measured radiance to validate the calibration of AVIRIS in the flight environment. Additional properties (such as the AVIRIS inflight measurement precision) are determined as well. This paper presents measurements, analyses, and results from the inflight calibration experiment held on the dry lake bed surface of Rogers Dry Lake, California, on June 5, 2000.

Green, Robert O.↗
DOE OSTI2026

Increasing Power Generation at the Patua Nevada Geothermal Field through Targeted and Adaptive EGS

In 2020, Patua Acquisition Company LLC, submitted the proposal “Increasing Power Generation at the Patua Nevada Geothermal Field through Targeted and Adaptive EGS”, in response to the DOE’s Geothermal Wells of Opportunity Funding Opportunity Announcement. The primary goal of the project was to convert an idle well, Patua 16-29, to an active producer and generate at least an additional 5 MWe at the Patua plant. The project was intended to provide an example of a reproducible methodology for well stimulation in Enhanced Geothermal Systems The project was proposed to be performed in three phases over a period of performance of four years. A first project go/no-go decision was made at the end of Phase 1 based on feasibility of the wellbore, site, and ability to realize a 5 MWe benefit from the project. Several factors were recognized that led to a no-go decision at this phase: • Electrical needs for placing the stimulated well on production were not considered in the initial scoping. Costs of pipeline costs were also underestimated in the original cost share. Easements and rights-of-way to establish a geothermal pipeline underneath or across an interstate highway were also found to be intractable on the time scale of the project. • The plant is injection limited, and no design or cost estimate was in place to handle the additional production needed to realize a 5 Mwe benefit. A new injection well would need to be drilled in addition to the other facility improvements to bring in the stimulated well. Patau Acquisition Company attempted to locate additional wells of opportunity that could realize the SOPOs goals, but was unsuccessful. As a result, this project is being terminated at the end of Phase 1.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Current Status of the Finite-Element Fluid Solver (COFFE) within HPCMP CREATE™-AV Kestrel

COFFE is the finite-element flow solver within HPCMP CREATE-AV™ Kestrel. Kestrel supports a range of flow solver fidelity options to support the DoD acquisition community, and COFFE targets the need for high-fidelity flow solutions. The COFFE solver, like all components of Kestrel, is under continual development as part of the CREATE-AV program. This paper documents the usage of COFFE on several workshop cases, which demonstrate new Kestrel capabilities and exercise features unique to COFFE. It concludes with a brief discussion of upcoming features in development for COFFE.

Holst, Kevin R.↗
NASA NTRS2011

Flight Dynamics Operations: Methods and Lessons Learned from Space Shuttle Orbit Operations

The Flight Dynamics Officer is responsible for trajectory maintenance of the Space Shuttle. This paper will cover high level operational considerations, methodology, procedures, and lessons learned involved in performing the functions of orbit and rendezvous Flight Dynamics Officer and leading the team of flight dynamics specialists during different phases of flight. The primary functions that will be address are: onboard state vector maintenance, ground ephemeris maintenance, calculation of ground and spacecraft acquisitions, collision avoidance, burn targeting for the primary mission, rendezvous, deorbit and contingencies, separation sequences, emergency deorbit preparation, mass properties coordination, payload deployment planning, coordination with the International Space Station, and coordination with worldwide trajectory customers. Each of these tasks require the Flight Dynamics Officer to have cognizance of the current trajectory state as well as the impact of future events on the trajectory plan in order to properly analyze and react to real-time changes. Additionally, considerations are made to prepare flexible alternative trajectory plans in the case timeline changes or a systems failure impact the primary plan. The evolution of the methodology, procedures, and techniques used by the Flight Dynamics Officer to perform these tasks will be discussed. Particular attention will be given to how specific Space Shuttle mission and training simulation experiences, particularly off-nominal or unexpected events such as shortened mission durations, tank failures, contingency deorbit, navigation errors, conjunctions, and unexpected payload deployments, have influenced the operational procedures and training for performing Space Shuttle flight dynamics operations over the history of the program. These lessons learned can then be extended to future vehicle trajectory operations.

Cutri-Kohart, Rebecca M.↗
NASA NTRS2016

A Model-Model and Data-Model Comparison for the Early Eocene Hydrological Cycle

A range of proxy observations have recently provided constraints on how Earth's hydrological cycle responded to early Eocene climatic changes. However, comparisons of proxy data to general circulation model (GCM) simulated hydrology are limited and inter-model variability remains poorly characterised. In this work, we undertake an intercomparison of GCM-derived precipitation and P - E distributions within the extended EoMIP ensemble (Eocene Modelling Intercomparison Project; Lunt et al., 2012), which includes previously published early Eocene simulations performed using five GCMs differing in boundary conditions, model structure, and precipitation-relevant parameterisation schemes. We show that an intensified hydrological cycle, manifested in enhanced global precipitation and evaporation rates, is simulated for all Eocene simulations relative to the preindustrial conditions. This is primarily due to elevated atmospheric paleo-CO2, resulting in elevated temperatures, although the effects of differences in paleogeography and ice sheets are also important in some models. For a given CO2 level, globally averaged precipitation rates vary widely between models, largely arising from different simulated surface air temperatures. Models with a similar global sensitivity of precipitation rate to temperature (dP=dT ) display different regional precipitation responses for a given temperature change. Regions that are particularly sensitive to model choice include the South Pacific, tropical Africa, and the Peri-Tethys, which may represent targets for future proxy acquisition. A comparison of early and middle Eocene leaf-fossil-derived precipitation estimates with the GCM output illustrates that GCMs generally underestimate precipitation rates at high latitudes, although a possible seasonal bias of the proxies cannot be excluded. Models which warm these regions, either via elevated CO2 or by varying poorly constrained model parameter values, are most successful in simulating a match with geologic data. Further data from low-latitude regions and better constraints on early Eocene CO2 are now required to discriminate between these model simulations given the large error bars on paleoprecipitation estimates. Given the clear differences between simulated precipitation distributions within the ensemble, our results suggest that paleohydrological data offer an independent means by which to evaluate model skill for warm climates.

Boundary conditions↗
NASA NTRS1991

Coherent Doppler lidar for automated space vehicle rendezvous, stationkeeping and capture

The inherent spatial resolution of laser radar makes ladar or lidar an attractive candidate for Automated Rendezvous and Capture application. Previous applications were based on incoherent lidar techniques, requiring retro-reflectors on the target vehicle. Technology improvements (reduced size, no cryogenic cooling requirement) have greatly enhanced the construction of coherent lidar systems. Coherent lidar permits the acquisition of non-cooperative targets at ranges that are limited by the detection capability rather than by the signal-to-noise ratio (SNR) requirements. The sensor can provide translational state information (range, velocity, and angle) by direct measurement and, when used with any array detector, also can provide attitude information by Doppler imaging techniques. Identification of the target is accomplished by scanning with a high pulse repetition frequency (dependent on the SNR). The system performance is independent of range and should not be constrained by sun angle. An initial effort to characterize a multi-element detection system has resulted in a system that is expected to work to a minimum range of 1 meter. The system size, weight and power requirements are dependent on the operating range; 10 km range requires a diameter of 3 centimeters with overall size at 3 x 3 x 15 to 30 cm, while 100 km range requires a 30 cm diameter.

Bilbro, James A.↗
NASA NTRS1974

Multiple target tracking and target attitude determination with a scanning laser radar

A scanning laser radar that can acquire and track single or multiple targets has recently been developed. Scan patterns have been designed for acquisition and tracking of one or more targets using a narrow laser beam. A synchronously scanned transmitter-receiver is used to acquire and track targets anywhere in a 376 x 376 element raster covering a 30 x 30 deg field. All scan patterns are electronically programmed, and the system automatically acquires and tracks the target or targets without the aid of an operator. The maximum tracking rate is 1.0 deg/sec (10.0 deg/sec) when used with a 1 kHz (10 kHz) scan rate. The estimated free space range against passive cooperative targets (corner cube reflectors) is 30 nautical miles. The laser radar has an accuracy of 10 cm (range) and 0.05 deg (angle). The developmental system is relatively small (1.5 cu ft), lightweight (60 lbs) and low-power-consuming (60 W).

Flom, T.↗
NASA NTRS1994

Evaluation of GPS position and attitude determination for automated rendezvous and docking missions

The use of the Global Positioning System for position and attitude determination is evaluated for an automated rendezvous and docking mission. The typical mission scenario involves the chaser docking with the target for resupply or repair purposes, and is divided into three sections. During the homing phase, the chaser utilizes coarse acquisition pseudorange data to approach the target; guidance laws for this stage are investigated. In the second phase, differential carrier phase positioning is utilized. The chaser must maintain a quasiconstant distance from the target, in order to resolve the initial integer ambiguities. Once the ambiguities are determined, the terminal phase is entered, and the rendezvous is completed with continuous carrier phase tracking. Attitude knowledge is maintained in all phases through the use of the carrier phase observable. A Kalman filter is utilized to estimate all states from the noisy measurement data. The effects of selective availability and cycle slips are also investigated.

Diprinzio, Marc D.↗
DOE OSTI2023

Elucidating Mechanisms of Rust Pathogenesis for Engineering Resistance in Poplar

The overall objective of this research was to elucidate the molecular basis for the virulence of Melampsora larici-populina towards Populus spp. in order to address the formidable challenge of engineering durable resistance in poplar against leaf rust. Our original research plan was built on the technically innovative approach of using dual host systems and known host defense proteins and pathogen avirulent effectors along with genome-wide approaches to identify key pathogenesis effectors of Melampsora larici-populina that target poplar defense and nutrient acquisition. Our efforts focused on developing high-throughput experimental approaches and systems to enable us to address our overarching hypothesis that rust effectors with homology to other fungal effectors will either bypass the poplar immune system and/or suppress effector-triggered immunity through conserved mechanisms, and that an analysis of these interaction networks would provide for new approaches to develop rust-resistant poplar. Three main objectives were originally proposed: (1) mine key rust effectors that suppress host immunity; (2) elucidate interaction networks in poplar targeted by key rust effectors; (3) generate transgenic poplar resources for identification of genes involved in pathogen infection or host defense triggered by rust. Generally, we worked towards all three objectives by developing and applying complementary molecular, genomic, biochemical and plant transformation approaches.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

The ARADS Project as an Astrobiological Survey Mission Prototype

An astrobiological survey prior to human arrival will be important for preservation of signs of any existing or past evidence of Martian life, to reduce the risk of unintentional forward contamination of Martian environments in which terrestrial microbes might be able to gain a foothold (e.g., [1]), and to potentially protect the health of any human crews and enable their safe return to Earth. Evaluating for the presence of life and biosignatures may become a critical-path Mars exploration precursor in the not-so-far future, circa 2030-35. The near-subsurface, with its potential combination of volatiles, vapor exchange with the surface, and shelter from surface radiation, will be a primary initial target for in-situ astrobiological investigation. Sample acquisition, drilling and sample handling are key elements of robotic missions that target the subsurface [2], as well as near-surface ground ice deposits. In the mid 2000s, the Mars Astrobiology Field Laboratory (AFL) was proposed as a follow-on mission concept to the Mars Science Laboratory (MSL)/Curiosity rover mission [3]. The AFL would have included precision drilling to 2m, automated sample handling and remote processing of cores. However, the AFL concept needed further development and maturation. The Atacama Rover Astrobiology Drilling Studies (ARADS) project concept [4] was in part AFL-inspired. The 2014 ARADS concept included a medium sized rover, with habitability instruments, including the Phoenix Wet Chemistry Laboratory (WCL) [5], and an enhanced version of the ExoMars Mars Organic Molecule Analyzer (MOMA) Laser Desorption-Linear Ion Trap Mass Spectrometer (LITMS) [6]. ARADS likewise included two biosignature detection instruments -- the Signs of Life Detector (SOLID) immunoassay instrument [7,8] and the Chemical Laptop-derived [9] Planetary In-Situ Capillary Electrophoresis System (PISCES), while mitigating Planetary Protection-relevant contamination issues [10]. ARADS project objectives were to demonstrate the potential science return for such a mission in the context of the search for evidence of life, and technically to demonstrate the feasibility of roving with drilling missions to Mars. ARADS technology goals targeted analog-site demonstrations of automated drilling and sampling, integrated with its mobile habitability and biosignature detection instruments. And ARADS science operations goals developed remote science, contamination mitigation, and communications methods to enable simulating AFL-like science operations with time delays, directed by a remote science team[11]. Five subsequent Mars analog site field demonstrations (in Chile’s hyperarid Atacama Desert, 2016-19) provided a step-by-step development pathway for the ARADS platform’s science capabilities and systems integration, culminating in an integrated remote roving mission simulation in the final ARADS year (2019).

biosignatures↗
NASA NTRS1984

Ku-Band rendezvous radar performance computer simulation model

All work performed on the Ku-band rendezvous radar performance computer simulation model program since the release of the preliminary final report is summarized. Developments on the program fall into three distinct categories: (1) modifications to the existing Ku-band radar tracking performance computer model; (2) the addition of a highly accurate, nonrealtime search and acquisition performance computer model to the total software package developed on this program; and (3) development of radar cross section (RCS) computation models for three additional satellites. All changes in the tracking model involved improvements in the automatic gain control (AGC) and the radar signal strength (RSS) computer models. Although the search and acquisition computer models were developed under the auspices of the Hughes Aircraft Company Ku-Band Integrated Radar and Communications Subsystem program office, they have been supplied to NASA as part of the Ku-band radar performance comuter model package. Their purpose is to predict Ku-band acquisition performance for specific satellite targets on specific missions. The RCS models were developed for three satellites: the Long Duration Exposure Facility (LDEF) spacecraft, the Solar Maximum Mission (SMM) spacecraft, and the Space Telescopes.

Magnusson, H. G.↗
NASA NTRS1987

The high resolution imaging spectrometer (HIRIS) for EOS

The HIRIS is designed to acquire images in 196 spectral bands simultaneously in the 0.4-2.5 micron wavelength region. HIRIS is a targeting rather than a continuous acquisition instrument and obtains high spatial and spectral resolution images in a 23 km swath with a 30 m GIFOV in vertical viewing. Gimbal pointing is proposed which will allow image acquisition at -30 + 60 deg down-track and + or - 25 deg cross-track. The raw data rate of the instrument is 393 Mbs. The high spectral resolution will make it possible to directly identify surficial materials such as rocks, soils, and suspended matter in water, and HIRIS opens up the possibility of studying biogeochemical processes in vegetation canopies. HIRIS will be used in conjunction with MODIS as a multistage sampling system.

Goetz, Alexander F. H.↗
NASA NTRS1989

The high resolution imaging spectrometer (HIRIS) for EOS

The high resolution imaging spectrometer (HIRIS) designed for the Earth Observing System (EOS) is designed to acquire images in 192 spectral bands simultaneously in the 0.4-2.5-micron wavelength region. HIRIS is a targeting rather than a continuous acquisition instrument and obtains high-spatial- and spectral-resolution images in a 30-km swath with a 30-m ground instantaneous field of view (GIFOV) in vertical viewing. Pointing will allow image acquisition at -30 to +60 deg along-track and +/-24 deg cross-track. The raw data rate of the instrument is 512 Mbs. The high spectral resolution will make it possible to identify many surficial materials such as rocks, soils, and suspended matter in water directly. HIRIS also offers the possibility of studying biochemical process in vegetation canopies.

Goetz, Alexander F. H.↗
NASA NTRS1993

Head-Up Auditory Displays for Traffic Collision Avoidance System Advisories: A Preliminary Investigation

The advantage of a head-up auditory display was evaluated in a preliminary experiment designed to measure and compare the acquisition time for capturing visual targets under two auditory conditions: standard one-earpiece presentation and two-earpiece three-dimensional (3D) audio presentation. Twelve commercial airline crews were tested under full mission simulation conditions at the NASA-Ames Man-Vehicle Systems Research Facility advanced concepts flight simulator. Scenario software generated visual targets corresponding to aircraft that would activate a traffic collision avoidance system (TCAS) aural advisory; the spatial auditory position was linked to the visual position with 3D audio presentation. Results showed that crew members using a 3D auditory display acquired targets approximately 2.2 s faster than did crew members who used one-earpiece head- sets, but there was no significant difference in the number of targets acquired.

Begault, Durand R.↗
NASA NTRS2000

A Probabilistic Framework for the Validation and Certification of Computer Simulations

The paper presents a methodology for quantifying, propagating, and managing the uncertainty in the data required to initialize computer simulations of complex phenomena. The purpose of the methodology is to permit the quantitative assessment of a certification level to be associated with the predictions from the simulations, as well as the design of a data acquisition strategy to achieve a target level of certification. The value of a methodology that can address the above issues is obvious, specially in light of the trend in the availability of computational resources, as well as the trend in sensor technology. These two trends make it possible to probe physical phenomena both with physical sensors, as well as with complex models, at previously inconceivable levels. With these new abilities arises the need to develop the knowledge to integrate the information from sensors and computer simulations. This is achieved in the present work by tracing both activities back to a level of abstraction that highlights their commonalities, thus allowing them to be manipulated in a mathematically consistent fashion. In particular, the mathematical theory underlying computer simulations has long been associated with partial differential equations and functional analysis concepts such as Hilbert spares and orthogonal projections. By relying on a probabilistic framework for the modeling of data, a Hilbert space framework emerges that permits the modeling of coefficients in the governing equations as random variables, or equivalently, as elements in a Hilbert space. This permits the development of an approximation theory for probabilistic problems that parallels that of deterministic approximation theory. According to this formalism, the solution of the problem is identified by its projection on a basis in the Hilbert space of random variables, as opposed to more traditional techniques where the solution is approximated by its first or second-order statistics. The present representation, in addition to capturing significantly more information than the traditional approach, facilitates the linkage between different interacting stochastic systems as is typically observed in real-life situations.

Ghanem, Roger↗