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DOE OSTI2017

Fuzzy Euclidean wormholes in de Sitter space

Here, we investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. Furthermore, we prefer wormholes for some parameters, rather than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

Design and implementation of fuzzy logic controllers

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. We first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic values, term sets, fuzzy rule base, inference methods, and defuzzification methods. Second, we introduce a four-step fuzzy logic control system design procedure. The design procedure is illustrated via four examples, showing the capabilities and robustness of fuzzy logic control systems. This is followed by a tuning procedure that we developed from our design experience. Third, we present two Lyapunov based techniques for stability analysis. Finally, we present our design and implementation of a fuzzy logic controller for a linear actuator to be used to control the direction of the Free Flight Rotorcraft Research Vehicle at LaRC.

Abihana, Osama A.↗

NASA NTRS2005

Fuzzy Logic Engine

The Fuzzy Logic Engine is a software package that enables users to embed fuzzy-logic modules into their application programs. Fuzzy logic is useful as a means of formulating human expert knowledge and translating it into software to solve problems. Fuzzy logic provides flexibility for modeling relationships between input and output information and is distinguished by its robustness with respect to noise and variations in system parameters. In addition, linguistic fuzzy sets and conditional statements allow systems to make decisions based on imprecise and incomplete information. The user of the Fuzzy Logic Engine need not be an expert in fuzzy logic: it suffices to have a basic understanding of how linguistic rules can be applied to the user's problem. The Fuzzy Logic Engine is divided into two modules: (1) a graphical-interface software tool for creating linguistic fuzzy sets and conditional statements and (2) a fuzzy-logic software library for embedding fuzzy processing capability into current application programs. The graphical- interface tool was developed using the Tcl/Tk programming language. The fuzzy-logic software library was written in the C programming language.

Howard, Ayanna↗

NASA NTRS1997

ASICs Approach for the Implementation of a Symmetric Triangular Fuzzy Coprocessor and Its Application to Adaptive Filtering

This paper discusses the implementation of a fuzzy logic system using an ASICs design approach. The approach is based upon combining the inherent advantages of symmetric triangular membership functions and fuzzy singleton sets to obtain a novel structure for fuzzy logic system application development. The resulting structure utilizes a fuzzy static RAM to store the rule-base and the end-points of the triangular membership functions. This provides advantages over other approaches in which all sampled values of membership functions for all universes must be stored. The fuzzy coprocessor structure implements the fuzzification and defuzzification processes through a two-stage parallel pipeline architecture which is capable of executing complex fuzzy computations in less than 0.55us with an accuracy of more than 95%, thus making it suitable for a wide range of applications. Using the approach presented in this paper, a fuzzy logic rule-base can be directly downloaded via a host processor to an onchip rule-base memory with a size of 64 words. The fuzzy coprocessor's design supports up to 49 rules for seven fuzzy membership functions associated with each of the chip's two input variables. This feature allows designers to create fuzzy logic systems without the need for additional on-board memory. Finally, the paper reports on simulation studies that were conducted for several adaptive filter applications using the least mean squared adaptive algorithm for adjusting the knowledge rule-base.

Starks, Scott↗

NASA NTRS1992

Fuzzy set approach to quality function deployment: An investigation

The final report of the 1992 NASA/ASEE Summer Faculty Fellowship at the Space Exploration Initiative Office (SEIO) in Langley Research Center is presented. Quality Function Deployment (QFD) is a process, focused on facilitating the integration of the customer's voice in the design and development of a product or service. Various input, in the form of judgements and evaluations, are required during the QFD analyses. All the input variables in these analyses are treated as numeric variables. The purpose of the research was to investigate how QFD analyses can be performed when some or all of the input variables are treated as linguistic variables with values expressed as fuzzy numbers. The reason for this consideration is that human judgement, perception, and cognition are often ambiguous and are better represented as fuzzy numbers. Two approaches for using fuzzy sets in QFD have been proposed. In both cases, all the input variables are considered as linguistic variables with values indicated as linguistic expressions. These expressions are then converted to fuzzy numbers. The difference between the two approaches is due to how the QFD computations are performed with these fuzzy numbers. In Approach 1, the fuzzy numbers are first converted to their equivalent crisp scores and then the QFD computations are performed using these crisp scores. As a result, the output of this approach are crisp numbers, similar to those in traditional QFD. In Approach 2, all the QFD computations are performed with the fuzzy numbers and the output are fuzzy numbers also. Both the approaches have been explained with the help of illustrative examples of QFD application. Approach 2 has also been applied in a QFD application exercise in SEIO, involving a 'mini moon rover' design. The mini moon rover is a proposed tele-operated vehicle that will traverse and perform various tasks, including autonomous operations, on the moon surface. The output of the moon rover application exercise is a ranking of the rover functions so that a subset of these functions can be targeted for design improvement. The illustrative examples and the mini rover application exercise confirm that the proposed approaches for using fuzzy sets in QFD are viable. However, further research is needed to study the various issues involved and to verify/validate the methods proposed.

Masud, Abu S. M.↗

NASA NTRS1993

Fuzzy control of small servo motors

To explore the benefits of fuzzy logic and understand the differences between the classical control methods and fuzzy control methods, the Togai InfraLogic applications engineering staff developed and implemented a motor control system for small servo motors. The motor assembly for testing the fuzzy and conventional controllers consist of servo motor RA13M and an encoder with a range of 4096 counts. An interface card was designed and fabricated to interface the motor assembly and encoder to an IBM PC. The fuzzy logic based motor controller was developed using the TILShell and Fuzzy C Development System on an IBM PC. A Proportional-Derivative (PD) type conventional controller was also developed and implemented in the IBM PC to compare the performance with the fuzzy controller. Test cases were defined to include step inputs of 90 and 180 degrees rotation, sine and square wave profiles in 5 to 20 hertz frequency range, as well as ramp inputs. In this paper we describe our approach to develop a fuzzy as well as PH controller, provide details of hardware set-up and test cases, and discuss the performance results. In comparison, the fuzzy logic based controller handles the non-linearities of the motor assembly very well and provides excellent control over a broad range of parameters. Fuzzy technology, as indicated by our results, possesses inherent adaptive features.

Maor, Ron↗

NASA NTRS1994

A fuzzy classifier system for process control

A fuzzy classifier system that discovers rules for controlling a mathematical model of a pH titration system was developed by researchers at the U.S. Bureau of Mines (USBM). Fuzzy classifier systems successfully combine the strengths of learning classifier systems and fuzzy logic controllers. Learning classifier systems resemble familiar production rule-based systems, but they represent their IF-THEN rules by strings of characters rather than in the traditional linguistic terms. Fuzzy logic is a tool that allows for the incorporation of abstract concepts into rule based-systems, thereby allowing the rules to resemble the familiar 'rules-of-thumb' commonly used by humans when solving difficult process control and reasoning problems. Like learning classifier systems, fuzzy classifier systems employ a genetic algorithm to explore and sample new rules for manipulating the problem environment. Like fuzzy logic controllers, fuzzy classifier systems encapsulate knowledge in the form of production rules. The results presented in this paper demonstrate the ability of fuzzy classifier systems to generate a fuzzy logic-based process control system.

Karr, C. L.↗

NASA NTRS1990

Genetic algorithm based fuzzy control of spacecraft autonomous rendezvous

The U.S. Bureau of Mines is currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic allows for the uncertainty inherent in most control problems to be incorporated into conventional expert systems. Although fuzzy logic based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective decision. High performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of spacecraft are learned using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions learned by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the authors for the rendezvous problem. Thus, genetic algorithms are potentially an effective and structured approach for learning fuzzy membership functions.

Karr, C. L.↗

NASA NTRS1993

Fuzzy logic mode switching in helicopters

The application of fuzzy logic to a wide range of control problems has been gaining momentum internationally, fueled by a concentrated Japanese effort. Advanced Research & Development within the Engineering Department at Sikorsky Aircraft undertook a fuzzy logic research effort designed to evaluate how effective fuzzy logic control might be in relation to helicopter operations. The mode switching module in the advanced flight control portion of Sikorsky's motion based simulator was identified as a good candidate problem because it was simple to understand and contained imprecise (fuzzy) decision criteria. The purpose of the switching module is to aid a helicopter pilot in entering and leaving coordinated turns while in flight. The criteria that determine the transitions between modes are imprecise and depend on the varied ranges of three flight conditions (i.e., simulated parameters): Commanded Rate, Duration, and Roll Attitude. The parameters were given fuzzy ranges and used as input variables to a fuzzy rulebase containing the knowledge of mode switching. The fuzzy control program was integrated into a real time interactive helicopter simulation tool. Optimization of the heading hold and turn coordination was accomplished by interactive pilot simulation testing of the handling quality performance of the helicopter dynamic model. The fuzzy logic code satisfied all the requirements of this candidate control problem.

Sherman, Porter D.↗

NASA NTRS1992

Encoding spatial images: A fuzzy set theory approach

As the use of fuzzy set theory continues to grow, there is an increased need for methodologies and formalisms to manipulate obtained fuzzy subsets. Concepts involving relative position of fuzzy patterns are acknowledged as being of high importance in many areas. In this paper, we present an approach based on the concept of dominance in fuzzy set theory for modelling relative positions among fuzzy subsets of a plane. In particular, we define the following spatial relations: to the left (right), in front of, behind, above, below, near, far from, and touching. This concept has been implemented to define spatial relationships among fuzzy subsets of the image plane. Spatial relationships based on fuzzy set theory, coupled with a fuzzy segmentation, should therefore yield realistic results in scene understanding.

Sztandera, Leszek M.↗

NASA NTRS1992

Comparison between the performance of two classes of fuzzy controllers

This paper presents an application comparison between two classes of fuzzy controllers: the Clearness Transformation Fuzzy Controller (CTFC) and the CRI-based Fuzzy Controller. The comparison is performed by studying the application of the controllers to simulation examples of nonlinear systems. The CTFC is a new approach for the organization of fuzzy controllers based on a cognitive model of parameter driven control, the notion of fuzzy patterns to represent fuzzy knowledge and the Clearness Transformation Rule of Inference (CTRI) for approximate reasoning. The approach facilitates the implementation of the basic modules of the controller: the fuzzifier, defuzzifier, and the control protocol in a rule-based architecture. The CTRI scheme for approximate reasoning does not require the formation of fuzzy relation matrices yielding improved performance in comparison with the traditional organization of fuzzy controllers.

Janabi, T. H.↗

NASA NTRS1997

Simulation of the Predictive Control Algorithm for Container Crane Operation using Matlab Fuzzy Logic Tool Box

This research has investigated the use of fuzzy logic, via the Matlab Fuzzy Logic Tool Box, to design optimized controller systems. The engineering system for which the controller was designed and simulate was the container crane. The fuzzy logic algorithm that was investigated was the 'predictive control' algorithm. The plant dynamics of the container crane is representative of many important systems including robotic arm movements. The container crane that was investigated had a trolley motor and hoist motor. Total distance to be traveled by the trolley was 15 meters. The obstruction height was 5 meters. Crane height was 17.8 meters. Trolley mass was 7500 kilograms. Load mass was 6450 kilograms. Maximum trolley and rope velocities were 1.25 meters per sec. and 0.3 meters per sec., respectively. The fuzzy logic approach allowed the inclusion, in the controller model, of performance indices that are more effectively defined in linguistic terms. These include 'safety' and 'cargo swaying'. Two fuzzy inference systems were implemented using the Matlab simulation package, namely the Mamdani system (which relates fuzzy input variables to fuzzy output variables), and the Sugeno system (which relates fuzzy input variables to crisp output variable). It is found that the Sugeno FIS is better suited to including aspects of those plant dynamics whose mathematical relationships can be determined.

Richardson, Albert O.↗

DOE OSTI2018

A fuzzy logistic regression model based on the least squares estimation

To construct the relationship between fuzzy inputs and fuzzy output described by linguistic variable, we develop a fuzzy logistic regression model, which can be applied for various problems, such as clinical research, risk investment and decision making. In this regard, we introduce the integral calculation of distance of cut sets and a fuzzy adjustment term which could prevent a large fuzzy error for a fuzzy output caused by the output degenerating into crisp number when the independent variables are crisp numbers. The parameters of the fuzzy logistic regression model are derived by means of the least squares method. We adopt three criteria involving mean square error, Kim and Bishu criterion and capability index and also perform two ways of prediction including the in-sample forecast as well as the one-leave-out cross validation. The comparisons with five existing methods show that our proposed method has satisfactory performance and the results are illustrated in some case studies.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Applications of fuzzy theories to multi-objective system optimization

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis.

Rao, S. S.↗

NASA NTRS1992

Design issues of a reinforcement-based self-learning fuzzy controller for petrochemical process control

Fuzzy logic controllers have some often-cited advantages over conventional techniques such as PID control, including easier implementation, accommodation to natural language, and the ability to cover a wider range of operating conditions. One major obstacle that hinders the broader application of fuzzy logic controllers is the lack of a systematic way to develop and modify their rules; as a result the creation and modification of fuzzy rules often depends on trial and error or pure experimentation. One of the proposed approaches to address this issue is a self-learning fuzzy logic controller (SFLC) that uses reinforcement learning techniques to learn the desirability of states and to adjust the consequent part of its fuzzy control rules accordingly. Due to the different dynamics of the controlled processes, the performance of a self-learning fuzzy controller is highly contingent on its design. The design issue has not received sufficient attention. The issues related to the design of a SFLC for application to a petrochemical process are discussed, and its performance is compared with that of a PID and a self-tuning fuzzy logic controller.

Yen, John↗

NASA NTRS1992

WARP: Weight Associative Rule Processor. A dedicated VLSI fuzzy logic megacell

During the last five years Fuzzy Logic has gained enormous popularity in the academic and industrial worlds. The success of this new methodology has led the microelectronics industry to create a new class of machines, called Fuzzy Machines, to overcome the limitations of traditional computing systems when utilized as Fuzzy Systems. This paper gives an overview of the methods by which Fuzzy Logic data structures are represented in the machines (each with its own advantages and inefficiencies). Next, the paper introduces WARP (Weight Associative Rule Processor) which is a dedicated VLSI megacell allowing the realization of a fuzzy controller suitable for a wide range of applications. WARP represents an innovative approach to VLSI Fuzzy controllers by utilizing different types of data structures for characterizing the membership functions during the various stages of the Fuzzy processing. WARP dedicated architecture has been designed in order to achieve high performance by exploiting the computational advantages offered by the different data representations.

Pagni, A.↗

NASA NTRS1992

An experimental methodology for a fuzzy set preference model

A flexible fuzzy set preference model first requires approximate methodologies for implementation. Fuzzy sets must be defined for each individual consumer using computer software, requiring a minimum of time and expertise on the part of the consumer. The amount of information needed in defining sets must also be established. The model itself must adapt fully to the subject's choice of attributes (vague or precise), attribute levels, and importance weights. The resulting individual-level model should be fully adapted to each consumer. The methodologies needed to develop this model will be equally useful in a new generation of intelligent systems which interact with ordinary consumers, controlling electronic devices through fuzzy expert systems or making recommendations based on a variety of inputs. The power of personal computers and their acceptance by consumers has yet to be fully utilized to create interactive knowledge systems that fully adapt their function to the user. Understanding individual consumer preferences is critical to the design of new products and the estimation of demand (market share) for existing products, which in turn is an input to management systems concerned with production and distribution. The question of what to make, for whom to make it and how much to make requires an understanding of the customer's preferences and the trade-offs that exist between alternatives. Conjoint analysis is a widely used methodology which de-composes an overall preference for an object into a combination of preferences for its constituent parts (attributes such as taste and price), which are combined using an appropriate combination function. Preferences are often expressed using linguistic terms which cannot be represented in conjoint models. Current models are also not implemented an individual level, making it difficult to reach meaningful conclusions about the cause of an individual's behavior from an aggregate model. The combination of complex aggregate models and vague linguistic preferences has greatly limited the usefulness and predictive validity of existing preference models. A fuzzy set preference model that uses linguistic variables and a fully interactive implementation should be able to simultaneously address these issues and substantially improve the accuracy of demand estimates. The parallel implementation of crisp and fuzzy conjoint models using identical data not only validates the fuzzy set model but also provides an opportunity to assess the impact of fuzzy set definitions and individual attribute choices implemented in the interactive methodology developed in this research. The generalized experimental tools needed for conjoint models can also be applied to many other types of intelligent systems.

Turksen, I. B.↗

NASA NTRS1992

A genetic algorithms approach for altering the membership functions in fuzzy logic controllers

Through previous work, a fuzzy control system was developed to perform translational and rotational control of a space vehicle. This problem was then re-examined to determine the effectiveness of genetic algorithms on fine tuning the controller. This paper explains the problems associated with the design of this fuzzy controller and offers a technique for tuning fuzzy logic controllers. A fuzzy logic controller is a rule-based system that uses fuzzy linguistic variables to model human rule-of-thumb approaches to control actions within a given system. This 'fuzzy expert system' features rules that direct the decision process and membership functions that convert the linguistic variables into the precise numeric values used for system control. Defining the fuzzy membership functions is the most time consuming aspect of the controller design. One single change in the membership functions could significantly alter the performance of the controller. This membership function definition can be accomplished by using a trial and error technique to alter the membership functions creating a highly tuned controller. This approach can be time consuming and requires a great deal of knowledge from human experts. In order to shorten development time, an iterative procedure for altering the membership functions to create a tuned set that used a minimal amount of fuel for velocity vector approach and station-keep maneuvers was developed. Genetic algorithms, search techniques used for optimization, were utilized to solve this problem.

Shehadeh, Hana↗