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All sources NASA NTRS DOE OSTI

DOE OSTI2021

An Artificial Neural Network System for Photon-Based Active Interrogation Applications

Active interrogation (AI) is a promising technique to detect shielded special nuclear materials (SNMs). At the University of Michigan, we are developing a photon-based AI system that uses bremsstrahlung radiation from an electron linear accelerator (linac) as an ionizing source and stilbene organic scintillating detectors for neutron detection. Stilbene scintillators are sensitive to fast neutrons and photons and have excellent pulse shape discrimination (PSD) capabilities. The traditional charge integration (CI) method commonly used for PSD analysis eliminates piled-up pulses and relies on a particle discrimination line to separate neutrons and photons. The presence of the intense photon flux during AI creates a significant number of piled-up events in the stilbene scintillator, thereby posing a great challenge to the traditional CI method. Identifying true single neutron pulses becomes challenging due to the presence of a pile-up cloud and overlapping neutron, photon and pile-up clouds in the PSD analysis. To mitigate the effect of pulse pile up and identify true single neutron pulses from stilbene scintillators, an artificial neural network (ANN) system is developed. The developed ANN system identifies single neutron pulses and neutron-photon combinations from piled-up events. The results obtained from a 252Cf measurement in the presence of the intense photon flux show that the developed ANN system outperforms the traditional CI method. Since many piled-up events lie above the particle discrimination line, they get misclassified as neutrons by the traditional CI method resulting in 25% overestimation of the net neutron count rate during the linac pulse. The overall net neutron count rate (single and restored neutrons) during the linac pulse, estimated by the ANN system is 60% of the ground truth. Energy spectroscopy of the ANN attributed single neutron pulses further provides evidence on the detection of prompt fission neutrons from the 252Cf fission source.

42 ENGINEERING↗

NASA NTRS2013

Using NASA's Space Launch System to Enable Game Changing Science Mission Designs

NASA's Marshall Space Flight Center is directing efforts to build the Space Launch System (SLS), a heavy-lift rocket that will help restore U.S. leadership in space by carrying the Orion Multi-Purpose Crew Vehicle and other important payloads far beyond Earth orbit. Its evolvable architecture will allow NASA to begin with Moon fly-bys and then go on to transport humans or robots to distant places such as asteroids, Mars, and the outer solar system. Designed to simplify spacecraft complexity, the SLS rocket will provide improved mass margins and radiation mitigation, and reduced mission durations. These capabilities offer attractive advantages for ambitious missions such as a Mars sample return, by reducing infrastructure requirements, cost, and schedule. For example, if an evolved expendable launch vehicle (EELV) were used for a proposed mission to investigate the Saturn system, a complicated trajectory would be required with several gravity-assist planetary fly-bys to achieve the necessary outbound velocity. The SLS rocket, using significantly higher C3 energies, can more quickly and effectively take the mission directly to its destination, reducing trip times and cost. As this paper will report, the SLS rocket will launch payloads of unprecedented mass and volume, such as monolithic telescopes and in-space infrastructure. Thanks to its ability to co-manifest large payloads, it also can accomplish complex missions in fewer launches. Future analyses will include reviews of alternate mission concepts and detailed evaluations of SLS figures of merit, helping the new rocket revolutionize science mission planning and design for years to come.

Creech, Stephen D.↗

NASA NTRS2011

Policies and Procedures for Accessing Archived NASA Lunar Data via the Web

The National Space Science Data Center (NSSDC) was established by NASA to provide for the preservation and dissemination of scientific data from NASA missions. This paper describes the policies specifically related to lunar science data. NSSDC presently archives 660 lunar data collections. Most of these data (423 units) are stored offline in analog format. The remainder of this collection consists of magnetic tapes and discs containing approximately 1.7 TB of digital lunar data. The active archive for NASA lunar data is the Planetary Data System (PDS). NSSDC has an agreement with the PDS Lunar Data Node to assist in the restoration and preparation of NSSDC-resident lunar data upon request for access and distribution via the PDS archival system. Though much of NSSDC's digital store also resides in PDS, NSSDC has many analog data collections and some digital lunar data sets that are not in PDS. NSSDC stands ready to make these archived lunar data accessible to both the research community and the general public upon request as resources allow. Newly requested offline lunar data are digitized and moved to near-line storage devices called digital linear tape jukeboxes. The data are then packaged and made network-accessible via FTP for the convenience of a growing segment of the user community. This publication will 1) discuss the NSSDC processes and policies that govern how NASA lunar data is preserved, restored, and made accessible via the web and 2) highlight examples of special lunar data requests.

James, Nathan L.↗

NASA NTRS1989

A wide bandwidth electrostatic field sensor for lightning research

Data obtained from UHF radar observation of direct-lightning strikes to the NASA F-106B aircraft have indicated that most of the 690 strikes acquired during direct-strike lightning tests were triggered by the aircraft. As an aid in understanding the triggered lightning process, a wide bandwidth electric field measuring system was designed for the F-106B by implementing a clamped-detection signal processing concept originated at the Air Force Cambridge Research Lab in 1953. The detection scheme combines the signals from complementary stator pairs clamped to zero bolts at the exact moment when each stator pair is maximally shielded by the rotor, a process that restores the dc level lost by the charge amplifier. The system was implemented with four shutter-type field mills located at strategic points on the aircraft. The bandwidth of the system was determined in the laboratory to be from dc to over 100 Hz, whereas past designs had upper limits of 10 to 100 Hz. To obtain the undisturbed electric field vector and total aircraft charge, the airborne field mill system is calibrated by using techniques involving results from ground and flight calibrations of the F-106B, laboratory tests of a metallized model, and a finite difference time-domain electromagnetic computer code.

Zaepfel, Klaus P.↗

DOE OSTI2020

Voltage Restoration in Microgrids using Temporal Logic Specifications

This paper proposes an energy storage controller synthesis method for voltage restoration in microgrids with respect to temporal logic specifications (TLSs). TLSs is introduced in this paper as a formalism to control the voltage variation of a critical bus against an operational bounds over time. The power system with synchronous generator (SG) connected to a critical load bus is modeled as a set of differential-algebraic equations and a simplified analytical model is derived to describe the voltage variation of this critical bus. The control objective is to schedule an optimal control input signal from a supportive energy storage system (ESS) connected to the critical bus, such that the voltage variation of the latter satisfies the TLSs, such as a finite-time restoration. The proposed control is verified on a lumped distribution system model. With this control diagram, supportive controllers can be designed to make voltage behaviors comply with grid codes and avoid unnecessary relay actions.

Taousser, Fatima Zohra↗

NASA NTRS1983

Optimal trajectories for aeroassisted orbital transfer

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Miele, A.↗

DOE OSTI2021

Enabling Realistic Communications Evaluations for ADMS

Increasing penetration levels of inverter-based distributed energy resources (DERs) in distribution systems are creating challenges in system operation. Currently, wired or proprietary wireless communications are used by advanced distribution management systems (ADMS) to detect the state of the system and control the DERs for optimal operation. Wireless communications are an alternative solution that can enable connectivity between the dispersed assets used in distribution system applications. As demand for the seamless integration of distributed energy resources (DERs) continues to increase, proper networking and communications systems are becoming important to support the DER infrastructure. This report summarizes validation of a private wireless LTE network in a laboratory environment. The purpose of this work is to 1) demonstrate the effectiveness of private wireless LTE communication for grid applications and 2) provide a means of evaluating latency and overall performance of wireless communication in grid applications. First, private wireless LTE communication was validated in a direct transfer trip relaying scenario as an example of one-way communications using grid equipment. This study provided a baseline understanding of the variation in latency for seven different kinds of wireless scenarios shown in Figure A below. As expected, weak (attenuated) wireless signal-based communication yielded the widest ranges in latency. When higher priority was set for the trip signal communication, this resulted in lower latency in communication timing. In the final phase of this project, the private wireless LTE network was validated using two-way communications in an advanced distribution management system (ADMS) testbed which was developed in the ESIF at NREL. The purpose of this was to study the impact of wireless communication on grid performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Energy Storage as an Equity Asset

Abstract Purpose of Review This review offers a discussion on how energy storage deployment advances equitable outcomes for the power system. It catalogues the four tenets of the energy justice concept—distributive, recognition, procedural, and restorative—and shows how they relate to inequities in energy affordability, availability, due process, sustainability, and responsibility. Recent Findings Energy storage systems have been deployed to support grid reliability and renewable resource integration, but there is additional emerging value in considering the connections between energy storage applications and equity challenges in the power system. Through a thorough review of the energy justice and energy transitions literature, this paper offers the equity dimensions of storage project design and implementations. Summary Emerging energy programs and projects are utilizing energy storage in pursuit of improved equity outcomes. Future research and policy design should integrate energy justice principles to align storage penetration with desired equity outcomes.

25 ENERGY STORAGE↗

DOE OSTI2026

Post-Event Fault Identification with Machine Learning for Protection System Validation

Power system protection devices have transitioned over the past few decades from mechanical to analog devices, then to solid state and finally digital. Relays and their associated critical network of equipment have significantly increased in complexity. Even internally, relays have gained significant intricacy, with relatively simple overcurrent or differential functions now being assisted by a myriad of other functions. This is necessary as the grid becomes more complex, but it brings increased difficulty in monitoring and upkeep. Misoperation caused by accidental improper relay settings or deliberate malicious actions is a constant challenge faced by all utilities. These improper settings can be difficult to identify and may require exhaustive post-mortem analysis, typically after a major outage event has already occurred. A mechanism is needed for monitoring the behavior of protection systems to validate that their performance falls within expectations. Relays that fail to isolate a fault or trip when there is no system disturbance can be flagged for settings review in situations where this behavior may not have been noticed due to manual restoration or backup protection operations. This work presents a concept for a machine learning (ML) system capable of validating the performance of protection systems by identifying fault events and characterizing protection system responses based solely on available current and voltage measurements. As a first step in its development, an experimental dataset is generated, and a random forest model is implemented with high accuracy in distinguishing four power system scenarios.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2010

NASA Tech Briefs, March 2010

Topics covered include: Software Tool Integrating Data Flow Diagrams and Petri Nets; Adaptive Nulling for Interferometric Detection of Planets; Reducing the Volume of NASA Earth-Science Data; Reception of Multiple Telemetry Signals via One Dish Antenna; Space-Qualified Traveling-Wave Tube; Smart Power Supply for Battery-Powered Systems; Parallel Processing of Broad-Band PPM Signals; Inexpensive Implementation of Many Strain Gauges; Constant-Differential-Pressure Two-Fluid Accumulator; Inflatable Tubular Structures Rigidized with Foams; Power Generator with Thermo-Differential Modules; Mechanical Extraction of Power From Ocean Currents and Tides; Nitrous Oxide/Paraffin Hybrid Rocket Engines; Optimized Li-Ion Electrolytes Containing Fluorinated Ester Co-Solvents; Probabilistic Multi-Factor Interaction Model for Complex Material Behavior; Foldable Instrumented Bits for Ultrasonic/Sonic Penetrators; Compact Rare Earth Emitter Hollow Cathode; High-Precision Shape Control of In-Space Deployable Large Membrane/Thin-Shell Reflectors; Rapid Active Sampling Package; Miniature Lightweight Ion Pump; Cryogenic Transport of High-Pressure-System Recharge Gas; Water-Vapor Raman Lidar System Reaches Higher Altitude; Compact Ku-Band T/R Module for High-Resolution Radar Imaging of Cold Land Processes; Wide-Field-of-View, High-Resolution, Stereoscopic Imager; Electrical Capacitance Volume Tomography with High-Contrast Dielectrics; Wavefront Control and Image Restoration with Less Computing; Polarization Imaging Apparatus; Stereoscopic Machine-Vision System Using Projected Circles; Metal Vapor Arcing Risk Assessment Tool; Performance Bounds on Two Concatenated, Interleaved Codes; Parameterizing Coefficients of a POD-Based Dynamical System; Confidence-Based Feature Acquisition; Algorithm for Lossless Compression of Calibrated Hyperspectral Imagery; Universal Decoder for PPM of any Order; Algorithm for Stabilizing a POD-Based Dynamical System; Mission Reliability Estimation for Repairable Robot Teams; Processing AIRS Scientific Data Through Level 3; Web-Based Requesting and Scheduling Use of Facilities; AutoGen Version 5.0; Time-Tag Generation Script; PPM Receiver Implemented in Software; Tropospheric Emission Spectrometer Product File Readers; Reporting Differences Between Spacecraft Sequence Files; Coordinating "Execute" Data for ISS and Space Shuttle; Database for Safety-Oriented Tracking of Chemicals; Apparatus for Cold, Pressurized Biogeochemical Experiments; Growing B Lymphocytes in a Three-Dimensional Culture System; Tissue-like 3D Assemblies of Human Broncho-Epithelial Cells; Isolation of Resistance-Bearing Microorganisms; Oscillating Cell Culture Bioreactor; and Liquid Cooling/Warming Garment.

Source record↗

NASA NTRS2012

Update on Apollo Data Restoration by the NSSDC and the PDS Lunar Data Node

The Lunar Data Node (LDN) , under the auspices of the Geosciences Node of the Planetary Data System (PDS) and the National Space Science Data Center (NSSDC), is continuing its efforts to recover and restore Apollo science data. The data being restored are in large part archived with NSSDC on older media, but unarchived data are also being recovered from other sources. They are typically on 7- or 9-track magnetic tapes, often in obsolete formats, or held on microfilm, microfiche, or paper documents. The goal of the LDN is to restore these data from their current form, which is difficult for most researchers to access, into common digital formats with all necessary supporting data (metadata) and archive the data sets with PDS. Restoration involves reading the data from the original media, deciphering the data formats to produce readable digital data and converting the data into usable tabular formats. Each set of values in the table must then be understood in terms of the quantity measured and the units used. Information on instrument properties, operational history, and calibrations is gathered and added to the data set, along with pertinent references, contacts, and other ancillary documentation. The data set then undergoes a peer review and the final validated product is archived with PDS. Although much of this effort has concentrated on data archived at NSSDC in the 1970's, we have also recovered data and information that were never sent to NSSDC. These data, retrieved from various outside sources, include raw and reduced Gamma-Ray Spectrometer data from Apollos 15 and 16, information on the Apollo 17 Lunar Ejecta And Meteorites experiment, Dust Detector data from Apollos 11, 12, 14, and I5, raw telemetry tapes from the Apollo ALSEPs, and Weekly Status Reports for all the Apollo missions. These data are currently being read or organized, and supporting data is being gathered. We are still looking for the calibrated heat flow data from Apollos 15 and 17 for the period 1975-1977, any assistance or information on these data would be welcome. NSSDC has recently been tasked to release its hard-copy archive, comprising photography, microfilm, and microfiche. The details are still being discussed, but we are concentrating on recovering the valuable lunar data from these materials while they are still readily accessible. We have identified the most critical of these data and written a LASER proposal to fund their restoration. Included in this effort are data from the Apollo 15 and 16 Mass Spectrometers and the Apollo 17 Par-UV Spectrometer and ancillary information on the Apollo 17 Surface Electrical Properties Experiment.

Williams, David R.↗

NASA NTRS2013

Monitoring Regional Forest Disturbances across the US with near Real Time MODIS NDVI Products Resident to the ForWarn Forest Threat Early Warning System

Forest threats across the US have become increasingly evident in recent years. Sometimes these have resulted in regionally evident disturbance progressions (e.g., from drought, bark beetle outbreaks, and wildfires) that can occur across multiyear durations and have resulted in extensive forest overstory mortality. In addition to stand replacement disturbances, other forests are subject to ephemeral, sometimes yearly defoliation from various insects and varying types and intensities of ephemeral damage from storms. Sometimes, after prolonged severe disturbance, signs of recovery in terms of Normalized Difference Vegetation Index (NDVI) can occur. The growing prominence and threat of forest disturbances in part have led to the formation and implementation of the 2003 Healthy Forest Restoration Act which mandated that national forest threat early warning system be developed and deployed. In response, the US Forest Service collaborated with NASA, DOE Oakridge National Laboratory, and the USGS Eros Data Center to build and roll-out the near real time ForWarn early warning system for monitoring regionally evident forest disturbances. Given the diversity of disturbance types, severities, and durations, ForWarn employs multiple historical baselines that are used with current NDVI to derive a suite of six forest change products that are refreshed every 8 days. ForWarn employs daily quarter kilometer MODIS NDVI data from the Aqua and Terra satellites, including MOD13 data for deriving historical baseline NDVIs and eMODIS 7 NDVI for compiling current NDVI. In doing so, the Time Series Product Tool and the Phenological Parameters Estimation Tool are used to temporally de-noise, fuse, and aggregate current and historical MODIS NDVIs into 24 day composites refreshed every 8 days with 46 dates of products per year. The 24 day compositing interval enables disturbances to be detected, while minimizing the frequency of residual atmospheric contamination. Forest change products are computed versus the previous 1, previous 3, and all previous years in the MODIS record for a given 24 day interval. Other "weekly" forest change products include one computed using an adaptive length compositing method for quicker detection of disturbances, two others that adjust for seasonal fluctuations in normal vegetation phenology (e.g., early versus late springs). This overall approach enables forest disturbance dynamics from a variety of regionally evident biotic and abiotic forest disturbances to be viewed and assessed through the calendar year. The change products are also being utilized for forest change trend analysis and for developing regional forest overstory mortality products. ForWarn's forest change products are used to alert forest health specialists about new forest disturbances. Such alerts are also typically based on available Landsat, aerial, and ground data as well as communications with forest health specialists and previous experience. ForWarn products have been used to detect and track many types of regional disturbances to multiple forest types, including defoliation from caterpillars and severe storms, as well as mortality from both biotic and abiotic agents (e.g., bark beetles, drought, fire, anthropogenic clearing). ForWarn offers products that could be combined with other geospatial data on forest biomass to assess forest disturbance carbon impacts within the conterminous US.

Spruce, Joseph P.↗

DOE OSTI2025

Data-driven Community-centered Resilient Assessment and Planning Toolkit for Nexus of Energy and Water (DCRAPT-NEW)

Urban areas, including Detroit and Pittsburgh, have suffered significant dual outages of the electrical and water infrastructure in the past decade due, in part, to the increasing number of extreme weather events. With increasing temperatures and rainfall intensity, these regions need to prepare for increasing extreme events through community-based energy and water resilience analysis, planning, and enhancement. This project developed a suite of open-source, open-access, community-centered, data-driven assessment and distributed energy resource (DER) and planning tools for energy and water resilience enhancement in urban areas. Through establishing a multi-level community awareness and engagement mechanism and a comprehensive collection of power outage and flooding data, an innovative group of community energy and water resilience assessment and planning tools have been developed for a wide range of users with differing and variable sets of data available to them. The developed tools include (1) DOE EAGLE-I data-driven, deep-learning assisted resilience assessment and DER planning tools at the county level with socioeconomic factors incorporated; (2) Utility annual power outage data-driven tools for long term resilience assessment and DER planning and 15-min power outage data-driven tools for short term resilience assessment and planning; (3) Detailed engineering tools for energy and water systems resilience assessment and planning when the system topology and component fragility curves are available; (4) Alternative Resiliency Metric Calculation that extracts and separates outage and restoration processes; and (5) Co-optimization tools that evaluate the resilience of the power and sewage system and allow users to conduct joint planning with energy and wastewater systems. The developed tools provide planners, decision-makers, and stakeholders with powerful capabilities to systematically evaluate system/community resilience and optimal and actionable guidance for enhancing resilience while prioritizing DER investments. The tools have been used and validated in Detroit and Pittsburgh and can be used in other areas of the nation. In addition, this project will (1) advance the knowledge and applications of machine-learning methods in analyzing and fusing different layers of information and generating meaningful data points such as generating rare weather events; (2) significantly improve the energy and water resilience of the identified communities in Detroit and Pittsburgh and prepare for more frequent and severe weather conditions; (3) help communities assess extreme weather event impacts and address short-term and long-term resilience-related issues The developed tools have been made public via GitHub and demonstrated to community stakeholders and utility companies via the two annual workshops and numerous community engagement meetings. The project outcomes are also disseminated through publications in various journals and conference proceedings, and presentations at top conferences.

13 HYDRO ENERGY↗

NASA NTRS1981

Always-Convergent Iterative Noise Removal and Deconvolution for Image Data

Linear filtering techniques currently used for the restoration of noisy, blurred or otherwise degraded image data are discussed and new techniques related to the iterative techniques of Morrison and van Cittert are developed and implemented. Programs written for the implementation are discussed in the appendices. It is shown that the new techniques are convergent for any system response function, and they are applied to the task of restoring a severely blurred image.

Ioup, G. E.↗

DOE OSTI2022

Optically induced changes in the band structure of the Weyl charge-density-wave compound (TaSe 4 ) 2 I

Collective modes are responsible for the emergence of novel quantum phases in topological materials. In the quasi-one dimensional (1D) Weyl semimetal (TaSe 4 ) 2 I , a charge density wave (CDW) opens band gaps at the Weyl points, thus turning the system into an axionic insulator. Melting the CDW would restore the Weyl phase, but 1D fluctuations extend the gapped regime far above the 3D transition temperature (T CDW = 263 K), thus preventing the investigation of this topological phase transition with conventional spectroscopic methods. Here we use a non-equilibrium approach: we perturb the CDW phase by photoexcitation, and we monitor the dynamical evolution of the band structure by time- and angle-resolved photoelectron spectroscopy. We find that, upon optical excitation, electrons populate the linearly dispersing states at the Fermi level (E F ), and fill the CDW gap. The dynamics of both the charge carrier population and the band gap renormalization (BGR) show a fast component with a characteristic time scale of a few hundreds femtoseconds. However, the BGR also exhibits a second slow component on the µs time scale. The combination of an ultrafast response and of persistent changes in the spectral weight at E$_\mathrm{F}$, and the resulting sensitivity of the linearly dispersing states to optical excitations, may explain the high performances of (TaSe 4 ) 2 I as a material for broadband infrared photodetectors.

36 MATERIALS SCIENCE↗

NASA NTRS1975

Combined effect of flight factors

The effects of various combinations of space flight stresses are discussed. Included are weightlessness, acceleration, vibration, ionizing radiation, hypoxia, and ambient temperature. The problem of constructing mathematical models to describe the dynamics of biological systems, including those to analyze and predict adaptation and restoration processes following combined stresses, is also considered.

Antipov, V. V.↗

NASA NTRS1985

On the accuracy of modelling the dynamics of large space structures

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.

Diarra, C. M.↗

NASA NTRS1985

On the accuracy of modelling the dynamics of large space structures

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the Space Shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modelling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.

Diarra, C. M.↗