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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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NASA NTRS2015

Global Precipitation Measurement Cold Season Precipitation Experiment (GCPEx): For Measurement Sake Let it Snow

As a component of the Earth's hydrologic cycle, and especially at higher latitudes,falling snow creates snow pack accumulation that in turn provides a large proportion of the fresh water resources required by many communities throughout the world. To assess the relationships between remotely sensed snow measurements with in situ measurements, a winter field project, termed the Global Precipitation Measurement (GPM) mission Cold Season Precipitation Experiment (GCPEx), was carried out in the winter of 2011-2012 in Ontario, Canada. Its goal was to provide information on the precipitation microphysics and processes associated with cold season precipitation to support GPM snowfall retrieval algorithms that make use of a dual-frequency precipitation radar and a passive microwave imager on board the GPM core satellite,and radiometers on constellation member satellites. Multi-parameter methods are required to be able to relate changes in the microphysical character of the snow to measureable parameters from which precipitation detection and estimation can be based. The data collection strategy was coordinated, stacked, high-altitude and in-situ cloud aircraft missions with three research aircraft sampling within a broader surface network of five ground sites taking in-situ and volumetric observations. During the field campaign 25 events were identified and classified according to their varied precipitation type, synoptic context, and precipitation amount. Herein, the GCPEx fieldcampaign is described and three illustrative cases detailed.

GCPEx↗
NASA NTRS2009

An Empirical Approach to Ocean Color Data: Reducing Bias and the Need for Post-Launch Radiometric Re-Calibration

A new empirical approach is developed for ocean color remote sensing. Called the Empirical Satellite Radiance-In situ Data (ESRID) algorithm, the approach uses relationships between satellite water-leaving radiances and in situ data after full processing, i.e., at Level-3, to improve estimates of surface variables while relaxing requirements on post-launch radiometric re-calibration. The approach is evaluated using SeaWiFS chlorophyll, which is the longest time series of the most widely used ocean color geophysical product. The results suggest that ESRID 1) drastically reduces the bias of ocean chlorophyll, most impressively in coastal regions, 2) modestly improves the uncertainty, and 3) reduces the sensitivity of global annual median chlorophyll to changes in radiometric re-calibration. Simulated calibration errors of 1% or less produce small changes in global median chlorophyll (less than 2.7%). In contrast, the standard NASA algorithm set is highly sensitive to radiometric calibration: similar 1% calibration errors produce changes in global median chlorophyll up to nearly 25%. We show that 0.1% radiometric calibration error (about 1% in water-leaving radiance) is needed to prevent radiometric calibration errors from changing global annual median chlorophyll more than the maximum interannual variability observed in the SeaWiFS 9-year record (+/- 3%), using the standard method. This is much more stringent than the goal for SeaWiFS of 5% uncertainty for water leaving radiance. The results suggest ocean color programs might consider less emphasis of expensive efforts to improve post-launch radiometric re-calibration in favor of increased efforts to characterize in situ observations of ocean surface geophysical products. Although the results here are focused on chlorophyll, in principle the approach described by ESRID can be applied to any surface variable potentially observable by visible remote sensing.

Gregg, Watson W.↗
NASA NTRS2005

Calibration and Characterization of the NASA EOS Terra and Aqua MODIS Instruments

The Moderate Resolution Imaging Spectroradiometer (MODIS) instrument is operating on both of the Terra and Aqua missions within the NASA Earth Observing System (EOS). The Terra MODIS instrument began taking observations in February 2000 and the Aqua MODIS instrument began taking observations in June of 2002 and both continue to operate successfully up to the present time. The MODIS instrument scans the entire Earth every 24 hours at nominal spatial resolutions between 250 and 1000 meters. It has 36 spectral bands spanning the electromagnetic spectrum from the visible wavelengths mar 400 micrometers to the emissive thermal infrared wavelengths at 15 micrometers. The MODIS instruments produce approximately 40 geophysical products devoted to observing land, ocean, and atmospheric processes and trends. To meet the scientific objectives associated with the NASA Earth sciences efforts the MODIS instruments must be and have been carefully calibrated and the performance characterized to meet specifications and goals such as five percent radiance and two percent relative to the sun accuracy in the twenty bands providing reflected solar radiation observations and one percent radiance accuracy in the sixteen bands observing in the thermal infrared. Over the time spanning instrument development and the pre-launch calibration and characterization of the instrument through the years of operation in space, the performance of the MODIS instruments have changed in multiple ways and appropriate adjustments made in relevant algorithms and look-up tables necessary to produce observations that meet the scientific objectives and requirements. The changes have been quantified and accounted for through careful use of on-board calibration devices such as the Spectro-Radiometric Calibration Assembly (SRCA), the Solar Diffuser (SD) and its companion Solar Diffuser Stability Monitor (SDSM), deep-space and lunar observations, and calibration targets on the Earth's surface. The strictest and most difficult challenges have come in trying to meet the requirements for observing Ocean color and related ocean biology processes over time and space. Overall the MODIS observations have been very successful in providing valuable scientific and applications results. The essential capabilities of MODIS are to be provided in the future by the Visible and Infrared Imaging Radiometer Suite (VIIRS) on the National Polar Orbiting Environmental Satellite Series (NPOESS).

Salomonson, Vincent V.↗
NASA NTRS1993

Telerobotic control of a mobile coordinated robotic server, executive summary

This interim report continues with the research effort on advanced adaptive controls for space robotics systems. In particular, previous results developed by the principle investigator and his research team centered around fuzzy logic control (FLC) in which the lack of knowledge of the robotic system as well as the uncertainties of the environment are compensated for by a rule base structure which interacts with varying degrees of belief of control action using system measurements. An on-line adaptive algorithm was developed using a single parameter tuning scheme. In the effort presented, the methodology is further developed to include on-line scaling factor tuning and self-learning control as well as extended to the multi-input, multi-output (MIMO) case. Classical fuzzy logic control requires tuning input scale factors off-line through trial and error techniques. This is time-consuming and cannot adapt to new changes in the process. The new adaptive FLC includes a self-tuning scheme for choosing the scaling factors on-line. Further the rule base in classical FLC is usually produced by soliciting knowledge from human operators as to what is good control action for given circumstances. This usually requires full knowledge and experience of the process and operating conditions, which limits applicability. A self-learning scheme is developed which adaptively forms the rule base with very limited knowledge of the process. Finally, a MIMO method is presented employing optimization techniques. This is required for application to space robotics in which several degrees-of-freedom links are commonly used. Simulation examples are presented for terminal control - typical of robotic problems in which a desired terminal point is to be reached for each link. Future activities will be to implement the MIMO adaptive FLC on an INTEL microcontroller-based circuit and to test the algorithm on a robotic system at the Mars Mission Research Center at North Carolina State University.

Lee, Gordon↗
NASA NTRS2005

Effect of Forest Canopy on Remote Sensing Soil Moisture at L-band

Global maps of soil moisture are needed to improve understanding and prediction of the global water and energy cycles. Accuracy requirements imply the use of lower frequencies (L-band) to achieve adequate penetration into the soil and to minimize attenuation by the vegetation canopy and effects of surface roughness. Success has been demonstrated over agricultural areas, but canopies with high biomass (e.g. forests) still present a challenge. Examples from recent measurements over forests with the L-band radiometer, 2D-STAR, and its predecessor, ESTAR, will be presented to illustrate the problem. ESTAR and 2D-STAR are aircraft-based synthetic aperture radiometers developed to help resolve both the engineering and algorithm issues associated with future remote sensing of soil moisture. ESTAR, which does imaging across track, was developed to demonstrate the viability of aperture synthesis for remote sensing. The instrument has participated several soil moisture experiments (e.g. at the Little Washita Watershed in 1992 and the Southern Great Plains experiments in 1997 and 1999). In addition, measurements have been made at a forest site near Waverly, VA which contains conifer forests with a variety of biomass. These data have demonstrated the success of retrieving soil moisture at L-band over agricultural areas and the response of passive observations at L-band to biomass over forests. 2D-STAR is a second generation instrument that does aperture synthesis in two dimensions (along track and cross track) and is dual polarized. This instrument has the potential to provide measurements at L-band that simulate the measurements that will be made by the two L-band sensors currently being developed for future remote sensing of soil moisture from space: Hydros (conical scan and real aperture) and SMOS (multiple incidence angle and synthetic aperture). 2D-STAR participated in the SMEX-03 soil moisture experiment, providing images from the NASA P-3 aircraft. Preliminary results include images of the experiment site area near Huntsville, AL that included a mixture of forest and agriculture. Changes during a rain event further illustrate the issues presented by forests. Work is continuing to reduce the 2D-STAR data and to support the two future remote sensing missions. Among the goals is to process the 2D-STAR data to create multiple looks (at the same pixel) with different incidence angles. Data in this format can be used to test algorithms for retrieving soil moisture and biomass such as are planned for SMOS. Also, the data are being processed to provide images at constant incidence angles such as will be obtained by Hydros. Although Hydros will have only one incidence angle, it will also carry an L-band radar, The goal is to use the radar to improve spatial resolution, an issue for remote sensing from space at the long wavelengths. Simultaneous observations with active and passive sensors also offers interesting prospects for treating areas of high biomass (forests) and irregular terrain and may be the challenge for the future.

LeVine, D. M.↗
DOE OSTI2025

GMFOLD: Subgraph matching for high-throughput DNA-aptamer secondary structure classification and machine learning interpretability

Aptamers are oligonucleotide receptors that bind to their targets with high affinity. Here, we consider aptamers comprised of single-stranded DNA that undergo target-binding-induced conformational changes, giving rise to unique secondary and tertiary structures. Given a specific aptamer primary sequence, there are well-established computational tools (notably mfold) to predict the secondary structure via free energy minimization algorithms. While mfold generates secondary structures for individual sequences, there is a need for a high-throughput process whereby thousands of DNA structures can be predicted in real-time for use in an interactive setting, when combined with aptamer selections that generate candidate pools that are too large to be experimentally interrogated. We developed a new Python code for high-throughput aptamer secondary structure determination (GMfold). GMfold uses subgraph matching methods to group aptamer candidates by secondary structure similarities. We also improve an open-source code, SeqFold, to incorporate subgraph matching concepts. We represent each secondary structure as a lowest-energy bipartite subgraph matching of the DNA graph to itself. These new tools enable thousands of DNA sequences to be compared based on their secondary structures, using machine-learning algorithms. This process is advantageous when analyzing sequences that arise from aptamer selections via systematic evolution of ligands by exponential enrichment (SELEX). This work is a building block for future machine-learning-informed DNA-aptamer selection processes to identify aptamers with improved target affinity and selectivity and advance aptamer biosensors and therapeutics.

Aptamer↗
NASA NTRS2001

The Contribution of TOMS and UARS Data to Our Understanding of Ozone Change

Both TOMS (Total Ozone Mapping Spectrometer) and UARS (Upper Atmosphere Research Satellite) have operated over an extended period, and generated data sets of sufficient accuracy to be of use in determining ozone change (TOMS) and some of the underlying causes (UARS). The basic scientific products have been used for model validation and assimilation to extend our understanding of stratospheric processes. TOMS on Nimbus-7, Earth-Probe, and QuikTOMS, and UARS have led to the next generation of instruments onboard the EOS platforms. Algorithms used for TOMS and UARS are being applied to the new data sets and extended to analysis of European satellite data (e.g., GOME)

Bhartia, Pawan K.↗
NASA NTRS2008

Closing the Certification Gaps in Adaptive Flight Control Software

Over the last five decades, extensive research has been performed to design and develop adaptive control systems for aerospace systems and other applications where the capability to change controller behavior at different operating conditions is highly desirable. Although adaptive flight control has been partially implemented through the use of gain-scheduled control, truly adaptive control systems using learning algorithms and on-line system identification methods have not seen commercial deployment. The reason is that the certification process for adaptive flight control software for use in national air space has not yet been decided. The purpose of this paper is to examine the gaps between the state-of-the-art methodologies used to certify conventional (i.e., non-adaptive) flight control system software and what will likely to be needed to satisfy FAA airworthiness requirements. These gaps include the lack of a certification plan or process guide, the need to develop verification and validation tools and methodologies to analyze adaptive controller stability and convergence, as well as the development of metrics to evaluate adaptive controller performance at off-nominal flight conditions. This paper presents the major certification gap areas, a description of the current state of the verification methodologies, and what further research efforts will likely be needed to close the gaps remaining in current certification practices. It is envisioned that closing the gap will require certain advances in simulation methods, comprehensive methods to determine learning algorithm stability and convergence rates, the development of performance metrics for adaptive controllers, the application of formal software assurance methods, the application of on-line software monitoring tools for adaptive controller health assessment, and the development of a certification case for adaptive system safety of flight.

Jacklin, Stephen A.↗
NASA NTRS2019

A Segmentation Algorithm for Characterizing Rise and Fall Segments in Seasonal Cycles: An Application to XCO2 to Estimate Benchmarks and Assess Model Bias

There is more useful information in the time series of satellite-derived column-averaged carbon dioxide (XCO2) than is typically characterized. Often, the entire time series is treated at once without considering detailed features at shorter timescales, such as nonstationary changes in signal characteristics – amplitude, period and phase. In many instances, signals are visually and analytically differentiable from other portions in a time series. Each rise (increasing) and fall (decreasing) segment in the seasonal cycle is visually discernable in a graph of the time series. The rise and fall segments largely result from seasonal differences in terrestrial ecosystem production, which means that the segment's signal characteristics can be used to establish observational benchmarks because the signal characteristics are driven by similar underlying processes. We developed an analytical segmentation algorithm to characterize the rise and fall segments in XCO2 seasonal cycles. We present the algorithm for general application of the segmentation analysis and emphasize here that the segmentation analysis is more generally applicable to cyclic time series. We demonstrate the utility of the algorithm with specific results related to the comparison between satellite- and model-derived XCO2 seasonal cycles (2009–2012) for large bioregions across the globe. We found a seasonal amplitude gradient of 0.74–0.77 ppm for every 10∘ of latitude in the satellite data, with similar gradients for rise and fall segments. This translates to a south–north seasonal amplitude gradient of 8 ppm for XCO2, about half the gradient in seasonal amplitude based on surface site in situ CO2 data (∼19 ppm). The latitudinal gradients in the period of the satellite-derived seasonal cycles were of opposing sign and magnitude (−9 d per 10∘ latitude for fall segments and 10 d per 10∘ latitude for rise segments) and suggest that a specific latitude (∼2∘ N) exists that defines an inversion point for the period asymmetry. Before (after) the point of asymmetry inversion, the periods of rise segments are lesser (greater) than the periods of fall segments; only a single model could reproduce this emergent pattern. The asymmetry in amplitude and the period between rise and fall segments introduces a novel pattern in seasonal cycle analyses, but, while we show these emergent patterns exist in the data, we are still breaking ground in applying the information for science applications. Maybe the most useful application is that the segmentation analysis allowed us to decompose the model biases into their correlated parts of biases in amplitude, period and phase independently for rise and fall segments. We offer an extended discussion on how such information about model biases and the emergent patterns in satellite-derived seasonal cycles can be used to guide future inquiry and model development.

Calle, Leonardo↗
NASA NTRS2019

A Segmentation Algorithm for Characterizing Rise and Fall Segments in Seasonal Cycles: an Application to Xco2 to Estimate Benchmarks and Assess Model Bias

There is more useful information in the time series of satellite-derived column-averaged carbon dioxide (XCO2) than is typically characterized. Often, the entire time series is treated at once without considering detailed features at shorter timescales, such as nonstationary changes in signal characteristics – amplitude, period and phase. In many instances, signals are visually and analytically differentiable from other portions in a time series. Each rise (increasing) and fall (decreasing) segment in the seasonal cycle is visually discernable in a graph of the time series. The rise and fall segments largely result from seasonal differences in terrestrial ecosystem production, which means that the segment's signal characteristics can be used to establish observational benchmarks because the signal characteristics are driven by similar underlying processes. We developed an analytical segmentation algorithm to characterize the rise and fall segments in XCO2 seasonal cycles. We present the algorithm for general application of the segmentation analysis and emphasize here that the segmentation analysis is more generally applicable to cyclic time series. We demonstrate the utility of the algorithm with specific results related to the comparison between satellite- and model-derived XCO2 seasonal cycles (2009–2012) for large bioregions across the globe. We found a seasonal amplitude gradient of 0.74–0.77 ppm for every 10∘ of latitude in the satellite data, with similar gradients for rise and fall segments. This translates to a south–north seasonal amplitude gradient of 8 ppm for XCO2, about half the gradient in seasonal amplitude based on surface site in situ CO2 data (∼19 ppm). The latitudinal gradients in the period of the satellite-derived seasonal cycles were of opposing sign and magnitude (−9 d per 10∘ latitude for fall segments and 10 d per 10∘ latitude for rise segments) and suggest that a specific latitude (∼2∘ N) exists that defines an inversion point for the period asymmetry. Before (after) the point of asymmetry inversion, the periods of rise segments are lesser (greater) than the periods of fall segments; only a single model could reproduce this emergent pattern. The asymmetry in amplitude and the period between rise and fall segments introduces a novel pattern in seasonal cycle analyses, but, while we show these emergent patterns exist in the data, we are still breaking ground in applying the information for science applications. Maybe the most useful application is that the segmentation analysis allowed us to decompose the model biases into their correlated parts of biases in amplitude, period and phase independently for rise and fall segments. We offer an extended discussion on how such information about model biases and the emergent patterns in satellite-derived seasonal cycles can be used to guide future inquiry and model development.

segmentation algorithm↗
NASA NTRS2015

The Ocean Colour Climate Change Initiative: I. A Methodology for Assessing Atmospheric Correction Processors Based on In-Situ Measurements

The Ocean Colour Climate Change Initiative intends to provide a long-term time series of ocean colour data and investigate the detectable climate impact. A reliable and stable atmospheric correction procedure is the basis for ocean colour products of the necessary high quality. In order to guarantee an objective selection from a set of four atmospheric correction processors, the common validation strategy of comparisons between in-situ and satellite derived water leaving reflectance spectra, is extended by a ranking system. In principle, the statistical parameters such as root mean square error, bias, etc. and measures of goodness of fit, are transformed into relative scores, which evaluate the relationship of quality dependent on the algorithms under study. The sensitivity of these scores to the selected database has been assessed by a bootstrapping exercise, which allows identification of the uncertainty in the scoring results. Although the presented methodology is intended to be used in an algorithm selection process, this paper focusses on the scope of the methodology rather than the properties of the individual processors.

Climate Change↗
NASA NTRS1976

Design of structures for optimum geometry

A general method is proposed for geometric optimization of finite element structures on the assumption that a reasonable initial geometry is specified. The number of finite elements, number of joints, and the element-joint relationships are specified and are not changed during the optimization process. The structure may be statically indeterminate and may support multiple loading conditions. Design variables include geometric and member sizing parameters. Design objectives may be minimum weight or cost, and constraints include strength and stiffness limitations. The optimization procedure is a general mathematical programming approach. An iterative design algorithm is outlined, and the method is specialized for truss structures. Design examples are given.

Vanderplaats, G. N.↗
NASA NTRS2017

Reusing JPSS Ground System Components to Process Aura Ozone Monitoring Instrument Science Products

New Earth observation instruments are planned to enable advancements in Earth science research over the next decade. Diversity of Earth observing instruments and their observing platforms will continue to increase as new instrument technologies emerge and are deployed as part of National programs such as Joint Polar Satellite System (JPSS), Geostationary Operational Environmental Satellite system (GOES), Landsat as well as the potential for many CubeSat and aircraft missions. The practical use and value of these observational data often extends well beyond their original purpose. The practicing community needs intuitive and standardized tools to enable quick unfettered development of tailored products for specific applications and decision support systems. However, the associated data processing system can take years to develop and requires inherent knowledge and the ability to integrate increasingly diverse data types from multiple sources. This paper describes the adaptation of a large-scale data processing system built for supporting JPSS algorithm calibration and validation (CalVal) node to a simplified science data system for rapid application. The new configurable data system reuses scalable JAVA technologies built for the JPSS Government Resource for Algorithm Verification, Independent Test, and Evaluation (GRAVITE) system to run within a laptop environment and support product generation and data processing of AURA Ozone Monitoring Instrument (OMI) science products. Of particular interest are the root requirements necessary for integrating experimental algorithms and Hierarchical Data Format (HDF) data access libraries into a science data production system. This study demonstrates the ability to reuse existing Ground System technologies to support future missions with minimal changes.

Science Data Systems↗
DOE OSTI2024

Robustness of neutron star merger simulations to changes in neutrino transport and neutrino-matter interactions

Binary neutron star mergers play an important role in nuclear astrophysics: Their gravitational wave and electromagnetic signals carry information about the equation of state of cold matter above nuclear saturation density, and they may be one of the main sources of r-process elements in the Universe. Neutrino-matter interactions during and after merger impact the properties of these electromagnetic signals and the relative abundances of the produced r-process elements. Existing merger simulations are, however, limited in their ability to realistically model neutrino transport and neutrino-matter interactions. Here, we perform a comparison of the impact of the use of state-of-the art two-moment or Monte Carlo transport schemes on the outcome of merger simulations, for a single binary neutron star system with a short-lived neutron star remnant [(5–10) ms]. We also investigate the use of different reaction rates in the simulations. While the best transport schemes generally agree well on the qualitative impact of neutrinos on the system, differences in the behavior of the high-density regions can significantly impact the collapse time and the properties of the hot tidal arms in this metastable merger remnant. The chosen interaction rates and transport algorithm as well as recent improvements by Radice et al. to the two-moment algorithms can all contribute to changes at the (10–30)% level in the global properties of the merger remnant and outflows. Furthermore, the limitations of previous moment schemes fixed by Radice et al. also appear sufficient to explain the large difference that we observed in the production of heavy-lepton neutrinos in a previous comparison of Monte Carlo and moment schemes in the context of a low-mass binary neutron star system.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

LandScan Global 2023: Silver Edition

For a quarter of a century, the LandScan Global (LSG) project has annually released a global, high-resolution gridded population dataset representing the ambient or unwarned population at a 30 arcsecond resolution. LSG supports a range of applications such as emergency management, disaster response, and human health and security for understanding populations at risk. The 2023 release of LSG, the LandScan Silver Edition, represents a major methodological leap forward while also leveraging previous knowledge—the previous year was the baseline for the current annual update carrying forward valuable knowledge of the built environment for the past quarter century—to train the machine learning models. Compared with annual releases over the past 24years, multiple advancements were made to different aspects of the methodology to achieve reproducibility, transparency, and consistent global propagation of solutions to modeling or population distribution issues identified during the review process. These novel changes include incorporation of the latest available geospatial inputs across the globe, machine learning models instead of manual modifications, population feature importance analysis, open-source solutions vs. proprietary software, generation of multiple global versions, analytic validations, and human-in-the-loop revisions to produce the final version. Additionally, algorithms—such as anomaly detection—were introduced to quickly identify areas of focus to develop a new and robust systematic review. Significant changes in modeled population distributions were observed between the 2022 and 2023 releases, largely attributable to improvements in data and methods and discussed thoroughly within this report. In summation, the LandScan Silver Edition leverages the best of the past quarter century of LSG legacy knowledge and continues a tradition of applying cutting-edge enhancements to serve as a new benchmark for accurate, actionable gridded population data

Lebakula, Viswadeep↗
NASA NTRS1979

Performability evaluation of the SIFT computer

Performability modeling and evaluation techniques are applied to the SIFT computer as it might operate in the computational evironment of an air transport mission. User-visible performance of the total system (SIFT plus its environment) is modeled as a random variable taking values in a set of levels of accomplishment. These levels are defined in terms of four attributes of total system behavior: safety, no change in mission profile, no operational penalties, and no economic process whose states describe the internal structure of SIFT as well as relavant conditions of the environment. Base model state trajectories are related to accomplishment levels via a capability function which is formulated in terms of a 3-level model hierarchy. Performability evaluation algorithms are then applied to determine the performability of the total system for various choices of computer and environment parameter values. Numerical results of those evaluations are presented and, in conclusion, some implications of this effort are discussed.

Meyer, J. F.↗
NASA NTRS1995

Millimeter-wave imaging radiometer data processing and development of water vapor retrieval algorithms

This document describes the current status of Millimeter-wave Imaging Radiometer (MIR) data processing and the technical development of the first version of a water vapor retrieval algorithm. The algorithm is being used by NASA/GSFC Microwave Sensors Branch, Laboratory for Hydrospheric Processes. It is capable of a three dimensional mapping of moisture fields using microwave data from airborne sensor of MIR and spaceborne instrument of Special Sensor Microwave/T-2 (SSM/T-2).

Chang, L. Aron↗
NASA NTRS1997

Optimal Approximation of Quadratic Interval Functions

Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

Koshelev, Misha↗