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NASA NTRS1982

Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems

A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.

Mukhopadhyay, V.↗

NASA NTRS1988

Statistical analysis of effective singular values in matrix rank determination

A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

Konstantinides, Konstantinos↗

NASA NTRS1989

A survey on the structured singular value

The structured singular value, U, is an important linear algebra tool to study a class of matrix perturbation problems. It is useful for analyzing the robustness of stability and performance of uncertain, (nominally) linear systems. Computation of (M) is difficult, and usually, upper and lower bounds are all that can be reliably computed. Upper bounds give conservative estimates of the sizes of allowable perturbations. The maximum singular value of a matrix M is an upper bound for (M). As an upper bound, it can be improved by finding a transformations to the data (i.e. M) which do not change the structured singular value, but do reduce the maximum singular value. Typically, upper bound algorithms involve searches over sets of transformations to yield the tightest bound. Lower bound algorithms are intelligent searches for minimum-norm solutions to multivariable polynomial equations, and are based on various optimality conditions that hold at the global (and, unfortunately, some local) minima. The current methods to compute both of these types of bounds are reviewed. Theoretical justification and extensive numerical experience with the various algorithms are covered.

Packard, Andy↗

NASA NTRS1992

Extreme value statistics analysis of fracture strengths of a sintered silicon nitride failing from pores

Statistical analysis and correlation between pore-size distribution and fracture strength distribution using the theory of extreme-value statistics is presented for a sintered silicon nitride. The pore-size distribution on a polished surface of this material was characterized, using an automatic optical image analyzer. The distribution measured on the two-dimensional plane surface was transformed to a population (volume) distribution, using the Schwartz-Saltykov diameter method. The population pore-size distribution and the distribution of the pore size at the fracture origin were correllated by extreme-value statistics. Fracture strength distribution was then predicted from the extreme-value pore-size distribution, usin a linear elastic fracture mechanics model of annular crack around pore and the fracture toughness of the ceramic. The predicted strength distribution was in good agreement with strength measurements in bending. In particular, the extreme-value statistics analysis explained the nonlinear trend in the linearized Weibull plot of measured strengths without postulating a lower-bound strength.

Chao, Luen-Yuan↗

NASA NTRS1991

Applications of singular value analysis and partial-step algorithm for nonlinear orbit determination

An adaptive method in which cruise and nonlinear orbit determination problems can be solved using a single program is presented. It involves singular value decomposition augmented with an extended partial step algorithm. The extended partial step algorithm constrains the size of the correction to the spacecraft state and other solve-for parameters. The correction is controlled by an a priori covariance and a user-supplied bounds parameter. The extended partial step method is an extension of the update portion of the singular value decomposition algorithm. It thus preserves the numerical stability of the singular value decomposition method, while extending the region over which it converges. In linear cases, this method reduces to the singular value decomposition algorithm with the full rank solution. Two examples are presented to illustrate the method's utility.

Ryne, Mark S.↗

NASA NTRS1950

The application of the statistical theory of extreme values to gust-load problems

An analysis is presented which indicates that the statistical theory of extreme values is applicable to the problems of predicting the frequency of encountering the larger gust loads and gust velocities for both specific test conditions as well as commercial transport operations. The extreme-value theory provides an analytic form for the distributions of maximum values of gust load and velocity. Methods of fitting the distribution are given along with a method of estimating the reliability of the predictions. The theory of extreme values is applied to available load data from commercial transport operations. The results indicate that the estimates of the frequency of encountering the larger loads are more consistent with the data and more reliable than those obtained in previous analyses. (author)

Press, Harry↗

NASA NTRS1991

Canonical multi-valued input Reed-Muller trees and forms

There is recently an increased interest in logic synthesis using EXOR gates. The paper introduces the fundamental concept of Orthogonal Expansion, which generalizes the ring form of the Shannon expansion to the logic with multiple-valued (mv) inputs. Based on this concept we are able to define a family of canonical tree circuits. Such circuits can be considered for binary and multiple-valued input cases. They can be multi-level (trees and DAG's) or flattened to two-level AND-EXOR circuits. Input decoders similar to those used in Sum of Products (SOP) PLA's are used in realizations of multiple-valued input functions. In the case of the binary logic the family of flattened AND-EXOR circuits includes several forms discussed by Davio and Green. For the case of the logic with multiple-valued inputs, the family of the flattened mv AND-EXOR circuits includes three expansions known from literature and two new expansions.

Perkowski, M. A.↗

NASA NTRS1995

NASA/DOD Aerospace Knowledge Diffusion Research Project. Paper 47: The value of computer networks in aerospace

This paper presents data on the value of computer networks that were obtained from a national survey of 2000 aerospace engineers that was conducted in 1993. Survey respondents reported the extent to which they used computer networks in their work and communication and offered their assessments of the value of various network types and applications. They also provided information about the positive impacts of networks on their work, which presents another perspective on value. Finally, aerospace engineers' recommendations on network implementation present suggestions for increasing the value of computer networks within aerospace organizations.

Bishop, Ann Peterson↗

NASA NTRS1995

Completed Beltrami-Michell formulation for analyzing mixed boundary value problems in elasticity

In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.

Patnaik, Surya N.↗

NASA NTRS1997

Accurate D0 Values for SiF and SiF+

Highly accurate D0 values are determined for SiF and SiF+ using the CCSD(T) approach in conjunction with basis set extrapolation. The results include the effect of spin-orbit coupling and core-valence correlation. Our best DO estimates for SiF and SiF+ are 141.5 and 159.7 kcal/mol, respectively, which we estimate to have an uncertainty of +/- 1.0 kcal/mol. For SiF, the value is significantly larger than the older experiments and only slightly larger than the most recent experiment. Our value is slightly larger than previous calculations. For SiF+ our best estimate is in good agreement with previous calculations and slightly smaller than the experimental value.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1999

Advanced Life Support System Value Metric

The NASA Advanced Life Support (ALS) Program is required to provide a performance metric to measure its progress in system development. Extensive discussions within the ALS program have reached a consensus. The Equivalent System Mass (ESM) metric has been traditionally used and provides a good summary of the weight, size, and power cost factors of space life support equipment. But ESM assumes that all the systems being traded off exactly meet a fixed performance requirement, so that the value and benefit (readiness, performance, safety, etc.) of all the different systems designs are exactly equal. This is too simplistic. Actual system design concepts are selected using many cost and benefit factors and the system specification is then set accordingly. The ALS program needs a multi-parameter metric including both the ESM and a System Value Metric (SVM). The SVM would include safety, maintainability, reliability, performance, use of cross cutting technology, and commercialization potential. Another major factor in system selection is technology readiness level (TRL), a familiar metric in ALS. The overall ALS system metric that is suggested is a benefit/cost ratio, [SVM + TRL]/ESM, with appropriate weighting and scaling. The total value is the sum of SVM and TRL. Cost is represented by ESM. The paper provides a detailed description and example application of the suggested System Value Metric.

Jones, Harry W.↗

NASA NTRS1999

Advanced Life Support System Value Metric

The NASA Advanced Life Support (ALS) Program is required to provide a performance metric to measure its progress in system development. Extensive discussions within the ALS program have led to the following approach. The Equivalent System Mass (ESM) metric has been traditionally used and provides a good summary of the weight, size, and power cost factors of space life support equipment. But ESM assumes that all the systems being traded off exactly meet a fixed performance requirement, so that the value and benefit (readiness, performance, safety, etc.) of all the different systems designs are considered to be exactly equal. This is too simplistic. Actual system design concepts are selected using many cost and benefit factors and the system specification is defined after many trade-offs. The ALS program needs a multi-parameter metric including both the ESM and a System Value Metric (SVM). The SVM would include safety, maintainability, reliability, performance, use of cross cutting technology, and commercialization potential. Another major factor in system selection is technology readiness level (TRL), a familiar metric in ALS. The overall ALS system metric that is suggested is a benefit/cost ratio, SVM/[ESM + function (TRL)], with appropriate weighting and scaling. The total value is given by SVM. Cost is represented by higher ESM and lower TRL. The paper provides a detailed description and example application of a suggested System Value Metric and an overall ALS system metric.

Jones, Harry W.↗

NASA NTRS2010

An Extreme-Value Approach to Anomaly Vulnerability Identification

The objective of this paper is to present a method for importance analysis in parametric probabilistic modeling where the result of interest is the identification of potential engineering vulnerabilities associated with postulated anomalies in system behavior. In the context of Accident Precursor Analysis (APA), under which this method has been developed, these vulnerabilities, designated as anomaly vulnerabilities, are conditions that produce high risk in the presence of anomalous system behavior. The method defines a parameter-specific Parameter Vulnerability Importance measure (PVI), which identifies anomaly risk-model parameter values that indicate the potential presence of anomaly vulnerabilities, and allows them to be prioritized for further investigation. This entails analyzing each uncertain risk-model parameter over its credible range of values to determine where it produces the maximum risk. A parameter that produces high system risk for a particular range of values suggests that the system is vulnerable to the modeled anomalous conditions, if indeed the true parameter value lies in that range. Thus, PVI analysis provides a means of identifying and prioritizing anomaly-related engineering issues that at the very least warrant improved understanding to reduce uncertainty, such that true vulnerabilities may be identified and proper corrective actions taken.

Everett, Chris↗

NASA NTRS2011

Coding for Parallel Links to Maximize the Expected Value of Decodable Messages

When multiple parallel communication links are available, it is useful to consider link-utilization strategies that provide tradeoffs between reliability and throughput. Interesting cases arise when there are three or more available links. Under the model considered, the links have known probabilities of being in working order, and each link has a known capacity. The sender has a number of messages to send to the receiver. Each message has a size and a value (i.e., a worth or priority). Messages may be divided into pieces arbitrarily, and the value of each piece is proportional to its size. The goal is to choose combinations of messages to send on the links so that the expected value of the messages decodable by the receiver is maximized. There are three parts to the innovation: (1) Applying coding to parallel links under the model; (2) Linear programming formulation for finding the optimal combinations of messages to send on the links; and (3) Algorithms for assisting in finding feasible combinations of messages, as support for the linear programming formulation. There are similarities between this innovation and methods developed in the field of network coding. However, network coding has generally been concerned with either maximizing throughput in a fixed network, or robust communication of a fixed volume of data. In contrast, under this model, the throughput is expected to vary depending on the state of the network. Examples of error-correcting codes that are useful under this model but which are not needed under previous models have been found. This model can represent either a one-shot communication attempt, or a stream of communications. Under the one-shot model, message sizes and link capacities are quantities of information (e.g., measured in bits), while under the communications stream model, message sizes and link capacities are information rates (e.g., measured in bits/second). This work has the potential to increase the value of data returned from spacecraft under certain conditions.

Klimesh, Matthew A.↗

NASA NTRSDate not supplied

Visualizations to Aid Decision-Making in the ACCP Value Framework

The Aerosols, Clouds, Convection, and Precipitation Value Framework is used to introduce structure, transparency, and traceability into the decision-making process for a study formulating and assessing potential observing system concepts to respond to the 2017-2027 Decadal Survey for Earth Science and Applications. Within the Value Framework, visualizations play an important role in presenting information and structuring conversations around that information. This paper describes three guiding principles that were applied to the design of the visualizations of the Value Framework, presents examples of visualizations that serve at least one of several functions (structuring communication, facilitating elicitation and aggregation of data, and summarizing complex information), and identifies lessons learned from the development and implementation of those visualizations. The guiding principles and lessons learned have not only contributed to the success of the Value Framework and the ACCP study, but also can be applied in other decision-making activities.

Christopher A. Jones↗

NASA NTRSDate not supplied

Visualizations to Aid Decision-Making in the ACCP Value Framework

Christopher A Jones↗

NASA NTRS2004

Making the most of missing values : object clustering with partial data in astronomy

We demonstrate a clustering analysis algorithm, KSC, that a) uses all observed values and b) does not discard the partially observed objects. KSC uses soft constraints defined by the fully observed objects to assist in the grouping of objects with missing values. We present an analysis of objects taken from the Sloan Digital Sky Survey to demonstrate how imputing the values can be misleading and why the KSC approach can produce more appropriate results.

clustering↗

NASA NTRS2022

Life Support Baseline Values and Assumptions Document

The Life Support Baseline Values and Assumptions Document (BVAD) provides analysts, modelers, and other life support researchers with a common set of values and assumptions which can be used as a baseline in their studies. This baseline, in turn, provides a common point of origin from which many studies in the community may depart, making research results easier to compare and providing researchers with reasonable values to assume for areas outside their experience. With the ability to accurately compare different technologies’ performance for the same function, managers will be able to make better decisions regarding technology development.

ECLSS↗