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NASA NTRS1988

Robustness margin calculation with dynamic and real parametric uncertainty

The problem of robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics, where the latter takes the form of one complex block dynamic uncertainty, is considered. A robustness margin Tm is defined with respect to such model uncertainty structure and robust stability is characterized in terms of it. An algorithm to calculate Tm and the closely related multivariable stability margin km and structured singular value mu measures of robust stability is developed. It is shown that other control problems, such as robust performance for real parametric uncertainty, can also be handled in this framework.

Sideris, Athanasios↗
NASA NTRS1988

Treatment of uncertainty in artificial intelligence

The present assessment of the development status of research efforts concerned with AI reasoning under conditions of uncertainty emphasizes the importance of appropriateness in the approach selected for both the epistemic and the computational levels. At the former level, attention is given to the form of uncertainty-representation and the fidelity of its reflection of actual problems' uncertainties; at the latter level, such issues as the availability of the requisite information and the complexity of the reasoning process must be considered. The tradeoff between these levels must always be the focus of AI system-developers' attention.

Berenji, Hamid R.↗
NASA NTRS1989

Evaluating Statistical Process Control (SPC) techniques and computing the uncertainty of force calibrations

In recent years there has been a push within NASA to use statistical techniques to improve the quality of production. Two areas where statistics are used are in establishing product and process quality control of flight hardware and in evaluating the uncertainty of calibration of instruments. The Flight Systems Quality Engineering branch is responsible for developing and assuring the quality of all flight hardware; the statistical process control methods employed are reviewed and evaluated. The Measurement Standards and Calibration Laboratory performs the calibration of all instruments used on-site at JSC as well as those used by all off-site contractors. These calibrations must be performed in such a way as to be traceable to national standards maintained by the National Institute of Standards and Technology, and they must meet a four-to-one ratio of the instrument specifications to calibrating standard uncertainty. In some instances this ratio is not met, and in these cases it is desirable to compute the exact uncertainty of the calibration and determine ways of reducing it. A particular example where this problem is encountered is with a machine which does automatic calibrations of force. The process of force calibration using the United Force Machine is described in detail. The sources of error are identified and quantified when possible. Suggestions for improvement are made.

Navard, Sharon E.↗
NASA NTRS1990

Bias and uncertainty in the absorption emission measurement of atomic sodium density in the SSME exit plane

The measurement of atomic sodium concentration in the TTB 019 firing of April 1990 is significant in that it represents the first measurement of density at the exit plane of the space shuttle main engine. The knowledge of the sodium density, combined with the certainty that the exit plane of the plume is optically thin at the sodium D-line wavelengths, provides essential information for evaluation of diagnostic techniques using sodium atoms, such as resonant Doppler velocimetry for temperature, pressure, and velocity through high resolution fluorescent lineshape analysis. The technique used for the sodium atom line transmission (SALT) measurements is that of resonant absorption emission using a hollow cathode lamp as the reference source. Through the use of two-dimensional kinetic (TDK) predictions of temperature and density for the flight engine case and radiative transfer calculations, this line-of-sight spectrally integrated transmission indicates a sodium atom concentration, i.e., mole fraction, of 0.91e-10. The subject of this paper is the assumptions and measurement uncertainties tied into the calculation. Because of the narrow shape of the source emission, the uncertainties in the absorption profile could introduce considerable bias in the measurement. The following were investigated: (1) the inclusion of hyperfine splitting of the D-lines in the calculation; (2) the use of the flight engine predictions of plume temperature and density versus those for the large throat engine; (3) the assumption of a Gaussian, i.e., Doppler, distribution for the source radiance with a temperature of 400 K; (4) the use of atomic collisional shift and width values for the work by Jongerius; and (5) a Doppler shift for a 7 degree outward velocity vector at the plume edge. Also included in the study was the bias introduced by an uncertainty in the measurement of the D1/D2 line ratio in the source.

Bauman, Leslie E.↗
NASA NTRS1991

Assessing damping uncertainty in space structures with fuzzy sets

NASA has been interested in the development of methods for evaluating the predictive accuracy of structural dynamic models. This interest stems from the use of mathematical models in evaluating the structural integrity of all spacecraft prior to flight. Space structures are often too large and too weak to be tested fully assembled in a ground test lab. The predictive accuracy of a model depends on the nature and extent of its experimental verification. The further the test conditions depart from in-service conditions, the less accurate the model will be. Structural damping is known to be one source of uncertainty in models. The uncertainty in damping is explored in order to evaluate the accuracy of dynamic models. A simple mass-spring-dashpot system is used to illustrate a comparison among three methods for propagating uncertainty in structural dynamics models: the First Order Method, the Numerical Simulation Method, and the Fuzzy Set Method. The Fuzzy Set Method is shown to bound the range of possible responses and thus to provide a valuable limiting check on the First Order Method near resonant conditions. Fuzzy Methods are a relative inexpensive alternative to numerical simulation.

Ross, Timothy J.↗
NASA NTRS1992

Sensitivity of wildlife habitat models to uncertainties in GIS data

Decision makers need to know the reliability of output products from GIS analysis. For many GIS applications, it is not possible to compare these products to an independent measure of 'truth'. Sensitivity analysis offers an alternative means of estimating reliability. In this paper, we present a CIS-based statistical procedure for estimating the sensitivity of wildlife habitat models to uncertainties in input data and model assumptions. The approach is demonstrated in an analysis of habitat associations derived from a GIS database for the endangered California condor. Alternative data sets were generated to compare results over a reasonable range of assumptions about several sources of uncertainty. Sensitivity analysis indicated that condor habitat associations are relatively robust, and the results have increased our confidence in our initial findings. Uncertainties and methods described in the paper have general relevance for many GIS applications.

Stoms, David M.↗
NASA NTRS1993

Effects of radiobiological uncertainty on shield design for a 60-day lunar mission

Some consequences of uncertainties in radiobiological risk due to galactic cosmic ray exposure are analyzed to determine their effect on engineering designs for a first lunar outpost - a 60-day mission. Quantitative estimates of shield mass requirements as a function of a radiobiological uncertainty factor are given for a simplified vehicle structure. The additional shield mass required for compensation is calculated as a function of the uncertainty in galactic cosmic ray exposure, and this mass is found to be as large as a factor of 3 for a lunar transfer vehicle. The additional cost resulting from this mass is also calculated. These cost estimates are then used to exemplify the cost-effectiveness of research.

Wilson, John W.↗
NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗
NASA NTRS1991

Uncertainty analysis for Ulysses safety evaluation report

As part of the effort to review the Ulysses Final Safety Analysis Report and to understand the risk of plutonium release from the Ulysses spacecraft General Purpose Heat Source-Radioisotope Thermal Generator, the Interagency Nuclear Safety Review Panel (INSRP) performed an integrated, quantitative analysis of the uncertainties of the calculated risk of plutonium release from Ulysses. Using state-of-art probabilistic risk assessment technology, the uncertainty analysis accounted for both variability and uncertainty of the key parameters of the risk analysis. The results show that INSRP had high confidence that risk of fatal cancers from potential plutonium release associated with calculated launch and deployment accident scenarios is low.

Frank, Michael V.↗
NASA NTRS1993

Quantification of uncertainties in composites

An integrated methodology is developed for computationally simulating the probabilistic composite material properties at all composite scales. The simulation requires minimum input consisting of the description of uncertainties at the lowest scale (fiber and matrix constituents) of the composite and in the fabrication process variables. The methodology allows the determination of the sensitivity of the composite material behavior to all the relevant primitive variables. This information is crucial for reducing the undesirable scatter in composite behavior at its macro scale by reducing the uncertainties in the most influential primitive variables at the micro scale. The methodology is computationally efficient. The computational time required by the methodology described herein is an order of magnitude less than that for Monte Carlo Simulation. The methodology has been implemented into the computer code PICAN (Probabilistic Integrated Composite ANalyzer). The accuracy and efficiency of the methodology/code are demonstrated by simulating the uncertainties in the heat-transfer, thermal, and mechanical properties of a typical laminate and comparing the results with the Monte Carlo simulation method and experimental data. The important observation is that the computational simulation for probabilistic composite mechanics has sufficient flexibility to capture the observed scatter in composite properties.

Liaw, D. G.↗
NASA NTRS1993

A practical approach to determining the uncertainty of a pressure measurement system

The pressure measurement systems located at three propulsion component test stands at the Marshall Space Flight Center (MSFC) were evaluated for their specific measurement uncertainty levels. An elemental error source evaluation was performed to provide an analytical estimate of uncertainty. Applied loads tests were also conducted at the different MSFC test sites to derive an empirical estimate of uncertainty for the measurement system process. The analytical results are compared to those obtained empirically. The data from MFSC was also compared to data reported from other comparable test facilities. Methods for acquiring and processing the data from calibration, acquisition, and reduction error sources are also addressed.

Fish, James E.↗
NASA NTRS1988

Uncertainties in large space systems

Uncertainties of a large space system (LSS) can be deterministic or stochastic in nature. The former may result in, for example, an energy spillover problem by which the interaction between unmodeled modes and controls may cause system instability. The stochastic uncertainties are responsible for mode localization and estimation errors, etc. We will address the effects of uncertainties on structural model formulation, use of available test data to verify and modify analytical models before orbiting, and how the system model can be further improved in the on-orbit environment.

Fuh, Jon-Shen↗
NASA NTRS1992

Probabilistic evaluation of uncertainties and risks in aerospace components

This paper summarizes a methodology developed at NASA Lewis Research Center which computationally simulates the structural, material, and load uncertainties associated with Space Shuttle Main Engine (SSME) components. The methodology was applied to evaluate the scatter in static, buckling, dynamic, fatigue, and damage behavior of the SSME turbo pump blade. Also calculated are the probability densities of typical critical blade responses, such as effective stress, natural frequency, damage initiation, most probable damage path, etc. Risk assessments were performed for different failure modes, and the effect of material degradation on the fatigue and damage behaviors of a blade were calculated using a multi-factor interaction equation. Failure probabilities for different fatigue cycles were computed and the uncertainties associated with damage initiation and damage propagation due to different load cycle were quantified. Evaluations on the effects of mistuned blades on a rotor were made; uncertainties in the excitation frequency were found to significantly amplify the blade responses of a mistuned rotor. The effects of the number of blades on a rotor were studied. The autocorrelation function of displacements and the probability density function of the first passage time for deterministic and random barriers for structures subjected to random processes also were computed. A brief discussion was included on the future direction of probabilistic structural analysis.

Shah, A. R.↗
NASA NTRS1993

On a Lagrange-Hamilton formalism describing position and momentum uncertainties

According to Heisenberg's uncertainty relation, in quantum mechanics it is not possible to determine, simultaneously, exact values for the position and the momentum of a material system. Calculating the mean value of the Hamiltonian operator with the aid of exact analytic Gaussian wave packet solutions, these uncertainties cause an energy contribution additional to the classical energy of the system. For the harmonic oscillator, e.g., this nonclassical energy represents the ground state energy. It will be shown that this additional energy contribution can be considered as a Hamiltonian function, if it is written in appropriate variables. With the help of the usual Lagrange-Hamilton formalism known from classical particle mechanics, but now considering this new Hamiltonian function, it is possible to obtain the equations of motion for position and momentum uncertainties.

Schuch, Dieter↗
NASA NTRS1993

Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states

We compute the quantum entropy for monomode and two-mode systems set in squeezed states. Thereafter, the quantum entropy is also calculated for angular momentum algebra when the system is either in a coherent or in an intelligent spin state. These values are compared with the corresponding values of the respective uncertainties. In general, quantum entropies and uncertainties have the same minimum and maximum points. However, for coherent and intelligent spin states, it is found that some minima for the quantum entropy turn out to be uncertainty maxima. We feel that the quantum entropy we use provides the right answer, since it is given in an essentially unique way.

Aragone, C.↗
NASA NTRS1993

Task planning with uncertainty for robotic systems

In a practical robotic system, it is important to represent and plan sequences of operations and to be able to choose an efficient sequence from them for a specific task. During the generation and execution of task plans, different kinds of uncertainty may occur and erroneous states need to be handled to ensure the efficiency and reliability of the system. An approach to task representation, planning, and error recovery for robotic systems is demonstrated. Our approach to task planning is based on an AND/OR net representation, which is then mapped to a Petri net representation of all feasible geometric states and associated feasibility criteria for net transitions. Task decomposition of robotic assembly plans based on this representation is performed on the Petri net for robotic assembly tasks, and the inheritance of properties of liveness, safeness, and reversibility at all levels of decomposition are explored. This approach provides a framework for robust execution of tasks through the properties of traceability and viability. Uncertainty in robotic systems are modeled by local fuzzy variables, fuzzy marking variables, and global fuzzy variables which are incorporated in fuzzy Petri nets. Analysis of properties and reasoning about uncertainty are investigated using fuzzy reasoning structures built into the net. Two applications of fuzzy Petri nets, robot task sequence planning and sensor-based error recovery, are explored. In the first application, the search space for feasible and complete task sequences with correct precedence relationships is reduced via the use of global fuzzy variables in reasoning about subgoals. In the second application, sensory verification operations are modeled by mutually exclusive transitions to reason about local and global fuzzy variables on-line and automatically select a retry or an alternative error recovery sequence when errors occur. Task sequencing and task execution with error recovery capability for one and multiple soft components in robotic systems are investigated.

Cao, Tiehua↗
NASA NTRS1993

NASA/DOD Aerospace Knowledge Diffusion Research Project. Report 15: Technical uncertainty and project complexity as correlates of information use by US industry-affiliated aerospace engineers and scientists: Results of an exploratory investigation

An exploratory study was conducted that investigated the influence of technical uncertainty and project complexity on information use by U.S. industry-affiliated aerospace engineers and scientists. The study utilized survey research in the form of a self-administered mail questionnaire. U.S. aerospace engineers and scientists on the Society of Automotive Engineers (SAE) mailing list served as the study population. The adjusted response rate was 67 percent. The survey instrument is appendix C to this report. Statistically significant relationships were found to exist between technical uncertainty, project complexity, and information use. Statistically significant relationships were found to exist between technical uncertainty, project complexity, and the use of federally funded aerospace R&D. The results of this investigation are relevant to researchers investigating information-seeking behavior of aerospace engineers. They are also relevant to R&D managers and policy planners concerned with transferring the results of federally funded aerospace R&D to the U.S. aerospace industry.

Pinelli, Thomas E.↗
NASA NTRS1993

Uncertainty analysis of diffuse-gray radiation enclosure problems: A hypersensitive case study

An uncertainty analysis of diffuse-gray enclosure problems is presented. The genesis was a diffuse-gray enclosure problem which proved to be hypersensitive to the specification of view factors. This genesis is discussed in some detail. The uncertainty analysis is presented for the general diffuse-gray enclosure problem and applied to the hypersensitive case study. It was found that the hypersensitivity could be greatly reduced by enforcing both closure and reciprocity for the view factors. The effects of uncertainties in the surface emissivities and temperatures are also investigated.

Taylor, Robert P.↗