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NASA NTRS1991

Measuring uncertainty by extracting fuzzy rules using rough sets

Despite the advancements in the computer industry in the past 30 years, there is still one major deficiency. Computers are not designed to handle terms where uncertainty is present. To deal with uncertainty, techniques other than classical logic must be developed. The methods are examined of statistical analysis, the Dempster-Shafer theory, rough set theory, and fuzzy set theory to solve this problem. The fundamentals of these theories are combined to possibly provide the optimal solution. By incorporating principles from these theories, a decision making process may be simulated by extracting two sets of fuzzy rules: certain rules and possible rules. From these rules a corresponding measure of how much these rules is believed is constructed. From this, the idea of how much a fuzzy diagnosis is definable in terms of a set of fuzzy attributes is studied.

Worm, Jeffrey A.↗

NASA NTRS1992

DecisionMaker software and extracting fuzzy rules under uncertainty

Knowledge acquisition under uncertainty is examined. Theories proposed in deKorvin's paper 'Extracting Fuzzy Rules Under Uncertainty and Measuring Definability Using Rough Sets' are discussed as they relate to rule calculation algorithms. A data structure for holding an arbitrary number of data fields is described. Limitations of Pascal for loops in the generation of combinations are also discussed. Finally, recursive algorithms for generating all possible combination of attributes and for calculating the intersection of an arbitrary number of fuzzy sets are presented.

Walker, Kevin B.↗

NASA NTRS1992

Uncertainty management by relaxation of conflicting constraints in production process scheduling

Mathematical-analytical methods as used in Operations Research approaches are often insufficient for scheduling problems. This is due to three reasons: the combinatorial complexity of the search space, conflicting objectives for production optimization, and the uncertainty in the production process. Knowledge-based techniques, especially approximate reasoning and constraint relaxation, are promising ways to overcome these problems. A case study from an industrial CIM environment, namely high-grade steel production, is presented to demonstrate how knowledge-based scheduling with the desired capabilities could work. By using fuzzy set theory, the applied knowledge representation technique covers the uncertainty inherent in the problem domain. Based on this knowledge representation, a classification of jobs according to their importance is defined which is then used for the straightforward generation of a schedule. A control strategy which comprises organizational, spatial, temporal, and chemical constraints is introduced. The strategy supports the dynamic relaxation of conflicting constraints in order to improve tentative schedules.

Dorn, Juergen↗

NASA NTRS1991

How to help intelligent systems with different uncertainty representations cooperate with each other

In order to solve a complicated problem one must use the knowledge from different domains. Therefore, if one wants to automatize the solution of these problems, one has to help the knowledge-based systems that correspond to these domains cooperate, that is, communicate facts and conclusions to each other in the process of decision making. One of the main obstacles to such cooperation is the fact that different intelligent systems use different methods of knowledge acquisition and different methods and formalisms for uncertainty representation. So an interface f is needed, 'translating' the values x, y, which represent uncertainty of the experts' knowledge in one system, into the values f(x), f(y) appropriate for another one. The problem of designing such an interface as a mathematical problem is formulated and solved. It is shown that the interface must be fractionally linear: f(x) = (ax + b)/(cx + d).

Kreinovich, Vladik YA.↗

NASA NTRS1993

Probabilistic sizing of laminates with uncertainties

A reliability based design methodology for laminate sizing and configuration for a special case of composite structures is described. The methodology combines probabilistic composite mechanics with probabilistic structural analysis. The uncertainties of constituent materials (fiber and matrix) to predict macroscopic behavior are simulated using probabilistic theory. Uncertainties in the degradation of composite material properties are included in this design methodology. A multi-factor interaction equation is used to evaluate load and environment dependent degradation of the composite material properties at the micromechanics level. The methodology is integrated into a computer code IPACS (Integrated Probabilistic Assessment of Composite Structures). Versatility of this design approach is demonstrated by performing a multi-level probabilistic analysis to size the laminates for design structural reliability of random type structures. The results show that laminate configurations can be selected to improve the structural reliability from three failures in 1000, to no failures in one million. Results also show that the laminates with the highest reliability are the least sensitive to the loading conditions.

Shah, A. R.↗

NASA NTRS1991

On robustness analysis with non-diagonally structured uncertainty

The authors study the structured singular value for a class of robustness analysis problems in which the uncertainty is allowed to be nondiagonally structured, and the norm of each block is individually considered. The results extend the previous work conducted for problems where each uncertainty block is assumed to be a scalar. Computations of this generalized notion via both the similarity and nonsimilarity scaling methods are investigated. It is shown in particular that under certain circumstances the structured singular value defined here coincides with a vector-induced norm.

Chen, Jie↗

NASA NTRS1991

The effect of model uncertainty on some optimal routing problems

The effect of model uncertainties on optimal routing in a system of parallel queues is examined. The uncertainty arises in modeling the service time distribution for the customers (jobs, packets) to be served. For a Poisson arrival process and Bernoulli routing, the optimal mean system delay generally depends on the variance of this distribution. However, as the input traffic load approaches the system capacity the optimal routing assignment and corresponding mean system delay are shown to converge to a variance-invariant point. The implications of these results are examined in the context of gradient-based routing algorithms. An example of a model-independent algorithm using online gradient estimation is also included.

Mohanty, Bibhu↗

NASA NTRS1992

Robust linear quadratic designs with respect to parameter uncertainty

The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

Douglas, Joel↗

NASA NTRS1993

The detectability of brown dwarfs - Predictions and uncertainties

In order to determine the likelihood for the detection of isolated brown dwarfs in ground-based observations as well as in future spaced-based astronomy missions, and in order to evaluate the significance of any detections that might be made, we must first know the expected surface density of brown dwarfs on the celestial sphere as a function of limiting magnitude, wavelength band, and Galactic latitude. It is the purpose of this paper to provide theoretical estimates of this surface density, as well as the range of uncertainty in these estimates resulting from various theoretical uncertainties. We first present theoretical cooling curves for low-mass stars that we have computed with the latest version of our stellar evolution code. We use our evolutionary results to compute theoretical brown-dwarf luminosity functions for a wide range of assumed initial mass functions and stellar birth rate functions. The luminosity functions, in turn, are utilized to compute theoretical surface density functions for brown dwarfs on the celestial sphere. We find, in particular, that for reasonable theoretical assumptions, the currently available upper bounds on the brown-dwarf surface density are consistent with the possibility that brown dwarfs contribute a substantial fraction of the mass of the Galactic disk.

Nelson, L. A.↗

NASA NTRS1993

Effects of location uncertainties on the observed distribution of gamma-ray bursts detected by BATSE

The Burst and Transient Source Experiment (BATSE) on NASA's Compton Gamma-Ray Observatory has shown that the sources of gamma-ray bursts have an angular distribution consistent with isotropy, yet the bursts are spatially inhomogeneous. Detection of a statistically significant deviation from isotropy in the burst distribution would provide a clue to the distance of the burst sources. BATSE's ability to detect slight deviations of the angular distribution from isotropy is, in part, dependent on the accuracy of the computed burst locations. Using bursts whose locations have been determined accurately and independently, we estimate BATSE's location uncertainties and incorporate them into 3D Monte Carlo simulations of the burst distributions to show that, despite individual burst location uncertainties of about 5 deg, the ability of BATSE to place stringent limits on the anisotropy present in the angular distribution of the gamma-ray bursts is not significantly degraded. Observational effects of possible galactic halo distributions of the burst sources are noted.

Horack, J. M.↗

NASA NTRS1993

The violent environment of the origin of life - Progress and uncertainties

Dating of terrestrial fossils and returned lunar samples reveals that the origin of life on Earth occurred not in a quiescent, peaceful environment, but rather in a violent, impact-ridden one. This realization has important consequences. On the one hand, sufficiently large and fast impactors can erode planetary atmospheres, and the very largest of these may have sterilized the surface of the Earth. In this regard, deep-sea hydrothermal vents become especially interesting for the history of early life, as they provide an environment protected against all but the greatest impact devastation. At the same time, impactors would have been delivering key biogenic elements (such as carbon and nitrogen) to Earth's surface, and (with much greater difficulty) intact organic molecules as well. Estimates of the various sources of prebiotic organics suggest that the heavy bombardment either produced or delivered quantities of organics comparable to those produced by other energy sources. However, substantial uncertainties exist. After reviewing the current understanding of the role of the heavy bombardment in the origins of life, a number of remaining key uncertainties are considered, and attempts are made to both quantify their magnitude and point to means of resolving them.

Chyba, Christopher F.↗

NASA NTRS1992

The Second International Workshop on Squeezed States and Uncertainty Relations

This conference publication contains the proceedings of the Second International Workshop on Squeezed States and Uncertainty Relations held in Moscow, Russia, on 25-29 May 1992. The purpose of this workshop was to study possible applications of squeezed states of light. The Workshop brought together many active researchers in squeezed states of light and those who may find the concept of squeezed states useful in their research, particularly in understanding the uncertainty relations. It was found at this workshop that the squeezed state has a much broader implication than the two-photon coherent states in quantum optics, since the squeeze transformation is one of the most fundamental transformations in physics.

D Han↗

NASA NTRS1993

Disturbance, the uncertainty principle and quantum optics

It is shown how a disturbance-type uncertainty principle can be derived from an uncertainty principle for joint measurements. To achieve this, we first clarify the meaning of 'inaccuracy' and 'disturbance' in quantum mechanical measurements. The case of photon number and phase is treated as an example, and it is applied to a quantum non-demolition measurement using the optical Kerr effect.

Martens, Hans↗

NASA NTRS1993

The legacy of uncertainty

An historical account is given of the circumstances whereby the uncertainty relations were introduced into physics by Heisenberg. The criticisms of QED on measurement-theoretical grounds by Landau and Peierls are then discussed, as well as the response to them by Bohr and Rosenfeld. Finally, some examples are given of how the new freedom to advance radical proposals, in part the result of the revolution brought about by 'uncertainty,' was implemented in dealing with the new phenomena encountered in elementary particle physics in the 1930's.

Brown, Laurie M.↗

NASA NTRS1993

Uncertainty relations, zero point energy and the linear canonical group

The close relationship between the zero point energy, the uncertainty relations, coherent states, squeezed states, and correlated states for one mode is investigated. This group-theoretic perspective enables the parametrization and identification of their multimode generalization. In particular the generalized Schroedinger-Robertson uncertainty relations are analyzed. An elementary method of determining the canonical structure of the generalized correlated states is presented.

Sudarshan, E. C. G.↗

NASA NTRS1993

Positive phase space distributions and uncertainty relations

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Kruger, Jan↗

NASA NTRS1992

Uncertainties in climate data sets

Climate diagnostics are constructed from either analyzed fields or from observational data sets. Those that have been commonly used are normally considered ground truth. However, in most of these collections, errors and uncertainties exist which are generally ignored due to the consistency of usage over time. Examples of uncertainties and errors are described in NMC and ECMWF analyses and in satellite observational sets-OLR, TOVS, and SMMR. It is suggested that these errors can be large, systematic, and not negligible in climate analysis.

Mcguirk, James P.↗

NASA NTRS1994

Experimental uncertainty and drag measurements in the national transonic facility

This report documents the results of a study which was conducted in order to establish a framework for the quantitative description of the uncertainty in measurements conducted in the National Transonic Facility (NTF). The importance of uncertainty analysis in both experiment planning and reporting results has grown significantly in the past few years. Various methodologies have been proposed and the engineering community appears to be 'converging' on certain accepted practices. The practical application of these methods to the complex wind tunnel testing environment at the NASA Langley Research Center was based upon terminology and methods established in the American National Standards Institute (ANSI) and the American Society of Mechanical Engineers (ASME) standards. The report overviews this methodology.

Batill, Stephen M.↗