Interval analysis Research Papers - Academia.edu (original) (raw)

Statistics: is the science of collection, organization, presentation, analysis, and reasonable interpretation of data. It also deals with methods and techniques that can be used to draw conclusions about the characteristics of a large number of data points--commonly called a population by using a smaller subset of the entire data.
Statistics is sometimes described as the science of decision making under uncertainty and can be divided into two broad areas as follows:
Descriptive Statistics Quantities and techniques used to describe a sample characteristic e.g. mean, standard deviation, box-plot.
Inferential Statistics which covers those statistical procedures used to help draw conclusions or inferences about a population on the basis of a sample of data collected from the population. Important areas inferential statistics include confidence intervals, hypothesis tests, regression analysis and experimental design. Underlying inferential statistics is the idea of probability and probability distributions.

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- Probability and statistics, Descriptive Statistics, Interval analysis, Trial

This paper presents a basic tutorial on epistemic uncertainty q uantification methods. Epistemic uncertainty, characterizing lack-of-knowledge, is often prevalent in engineering applications. However, the methods we have for analyzing and propagating epistemic uncertainty are not as nearly widely used or well-understood as methods to propagate aleatory uncertainty (e.g. inherent variability characterized by probability distributions). We examine three methods used in propagating epistemic uncertainties: interval analysis, Dempster-Shafer evidence theory, and second-order probability. We demonstrate examples of their use on a problem in structural dynamics.

- by Thomas Paez
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- Structural Dynamics, Model validation, Interval analysis, Second Order
- by Scott Ferson
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- Engineering, Probability Theory, Monte Carlo Simulation, Mathematical Sciences

In this paper, an efficient numerical approach is developed for solving the baseline problem with interval uncertainties. Interval arithmetic is also utilized for developing the proposed method in the presence of uncertainties with only lower and upper bounds of parameters. In the proposed method, the equation of motion, performance index, and boundary conditions are first changed into some algebraic equations. This process converts the problem into an optimization problem. The presented technique is based on an interval extension of Chebyshev polynomials where its coefficients are achieved by world cup optimization algorithm, as a new optimization algorithm. The proposed method approximates the control and state variables as a function of time. The proposed solution is based on state parameterization, such that the state variable is approximated by the proposed interval Chebyshev polynomials with unknown interval coefficients. Finally, by solving the baseline problem in the presence of interval uncertainties, the reliability and effectiveness of the proposed method are demonstrated.

- by Navid Razmjooy and +1
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- Optimal Control, Uncertainty, Interval analysis, WCO

A Turbo Pascal program for data acquisition and analysis is presented. The program detects incoming data as TTL pulses through the serial port of an IBM-PC and compatible computers and displays the instantaneous frequency plot and the interval histogram on-line. Novel features of this Pascal program are: (1) no special hardware requirements and (2) on-line analysis of more than one source at a time. No hardware additions to the supplied computer and easy operation make this program a valuable tool, directly useable in an IBM-PC and compatible computers.

- by Rosario Vega
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- Cognitive Science, Vestibular System, Software, Evoked Potentials
- by S. Tornil
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- Automatic Control, Parameter estimation, Interval analysis, Spectrum
- by Mohammad Movahhedy
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- Engineering, Fuzzy Logic, Mathematical Sciences, Interval analysis

A novel real-time patient-specific algorithm to predict epileptic seizures is proposed. The method is based on the analysis of the positive zero-crossing intervals in the scalp electroencephalogram (EEG), describing the brain dynamics. In a moving-window analysis, the histogram of these intervals in each EEG epoch is computed, and the distribution of the histogram value in specific bins, selected using interictal and preictal references, is estimated based on the values obtained from the current epoch and the epochs of the last 5 min. The resulting distribution for each selected bin is then compared to two reference distributions (interictal and preictal), and a seizure prediction index is developed. Comparing this index with a patient-specific threshold for all EEG channels, a seizure prediction alarm is finally generated. The algorithm was tested on approximately 15.5 hours of multichannel scalp EEG recordings from three patients with temporal lobe epilepsy, including 14 seizures....

- by Manouchehr Javidan and +1
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- Algorithms, Electroencephalography, Neurophysiology, Temporal Lobe

Scientists are, all the time, in a struggle with uncertainty which is always a threat to a trustworthy scientific knowledge. A very simple and natural idea, to defeat uncertainty, is that of enclosing uncertain measured values in real closed intervals. On the basis of this idea, interval arithmetic is constructed. The idea of calculating with intervals is not completely new in mathematics: the concept has been known since Archimedes, who used guaranteed lower and upper bounds to compute his constant Pi. Interval arithmetic is now a broad field in which rigorous mathematics is associated with scientific computing. This connection makes it possible to solve uncertainty problems that cannot be efficiently solved by floating-point arithmetic. Today, application areas of interval methods include electrical engineering, control theory, remote sensing, experimental and computational physics, chaotic systems, celestial mechanics, signal processing, computer graphics, robotics, and computer-assisted proofs. The purpose of this book is to be a concise but informative introduction to the theories of interval arithmetic as well as to some of their computational and scientific applications.

- by Hend Dawood
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- Applied Mathematics, Real Analysis, Computer Science, Computer Engineering
- by Gwen Littlewort
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- Set Theory, Parameter estimation, Interval analysis, Boundary Value Problems

This paper presents a basic tutorial on epistemic uncertainty quantification methods. Epistemic uncertainty, characterizing lack-of-knowledge, is often prevalent in engineering applications. However, the methods we have for analyzing and propagating epistemic uncertainty are not as nearly widely used or well-understood as methods to propagate aleatory uncertainty (e.g. inherent variability characterized by probability distributions). We examine three methods used in propagating

- by IOSR Journals
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- Wireless Communications, Optimization, Newton's method, Interval analysis

In this paper, a new interval version of Runge-Kutta methods is proposed for time discretization and solving of optimal control problems (OCPs) in the presence of uncertain parameters. A new technique based on interval arithmetic is introduced to achieve the confidence bounds of the system. The proposed method is based on the new forward representation of Hukuhara interval difference and combining it with Runge-Kutta method for solving the OCPs with interval uncertainties. To perform the proposed method on OCPs, the Lagrange multiplier method is first applied to achieve the necessary conditions and then, using some algebraic manipulations, they are converted to an ordinary differential equation to achieve the interval optimal solution for the considered OCP with uncertain parameters. Shooting method is also employed to cover the Runge-Kutta methods restrictions in solving the OCPs with boundary values. The simulation results are applied to some practical case studies for demonstrating the effectiveness of the proposed method.

- by Navid Razmjooy
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- Optimal Control, Runge-Kutta Methods, Interval analysis, Shooting Methods

This paper presents the kinematic analysis and the development of a 4-degree-of-freedom serial-parallel mechanism for large commercial vehicle driving simulators. The degrees of freedom are selected according to the target maneuvers and the structure of human motion perception organs. Several kinematic properties of parallel part of the mechanism under study are investigated, including the inverse and the forward kinematics problems, workspace determination, singularity, and kinematic sensitivity analysis. The workspace of the parallel part of the mechanism is obtained by interval analysis. Moreover, using elimination theory, a univariate expression representing the forward kinematics solution of the parallel part is obtained.

- by Branko Ristic and +1
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- Nonlinear dynamics, Multidisciplinary, Information Fusion, State Space
- by J. Peleman
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- Technology, Pepper, QTL mapping, Biological Sciences
- by Vessela Krasteva and +1
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- Algorithms, Biomedical Engineering, Signal Processing, Statistical Analysis
- by Peter Duchessi and +1
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- Artificial Intelligence, Information Technology, Machine Learning, Modeling
- by Agostinho Da Rosa
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- Psychology, Electroencephalography, Sleep Medicine, Autonomic Nervous System

Crystals were detected in glass bottles containing autoclaved (standard cycle: 1218 C, 17 lb/in2, for 20 min) tap water. Bottles were fitted with a sipper tube and stopper. Crystals were observed twice at approximately a 6-month interval. Analysis of crystals and crystal-laden water by transmission electron microscopy and inductively coupled plasma and energy X-ray analysis revealed that the crystals were silicon. Subsequently, procedures and processes involved with preparation of water bottles were analyzed to determine the source or factors involved with silicon contamination. Analyses of silicon concentrations were performed on samples of tap water (0.88 to 1.20 ppm), tap water autoclaved in polycarbonate (0.89 to 1.20 ppm) and glass water bottles (0.84 to 11.0 ppm), glass and polycarbonate bottles after purposeful contamination of tap water with various amounts of alkaline detergent (1.10 to 1.70 ppm), and on steam condensate from the autoclave (0.23 and 0.47 ppm) to ascertain t...

- by Jeffrey Lohmiller
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- Transmission Electron Microscopy, Biological Sciences, X Rays, Stainless Steel

1 Le Mésotonique Tempéré de Bach (texte extensif) Relaté à « Das wohltemperirte Clavier » Résumé Les battements d'harmoniques des quintes et tierces majeures de tempéraments historiques bien connus sont analysés. Il apparait que les battements d'harmoniques pourraient être le facteur réel et déterminant pour les tempéraments baroques, surtout parce que les battements d'harmoniques tiennent une grande importance pour le musicien interprète pour ce qui concerne l'harmonie et les affects musicaux possibles, et pour l'accordeur pour le confort et la qualité de l'accord. D'autre part, il n'est pas toujours clair si les rapports, cents ou commas publiés sont déduits à partir de calculs théoriques ou à partir de résultats concrets obtenus de mesures ou réglages faits au monocorde. L'importance révélée des caractéristiques des battements apporte des arguments supplémentaires pour l'acceptation de la proposition de Jobin relative au tempérament probable pratiqué par Bach, ou d'alternatives quasi identiques basées sur le calcul de battements. Une nouvelle hypothèse est proposée concernant les spirales dessinées sur la page de titre du « Clavier bien tempéré » de Jean Sebastien Bach. Mots clé Baroque ; bien tempéré ; mésotonique ; intervalle ; comma ; battement ; harmonique ; rapport ; cent ; Bach Mes plus sincères remerciements à Mr. A Calvet, qui a minutieusement vérifié, amélioré et corrigé la version française de ce texte, non seulement du point de vue linguistique, mais aussi de son point de vue en tant qu'accordeur professionnel. Symboles utilisés : Les symboles utilisés dans ce texte sont ceux généralement utilisés dans les publications anglophones : • Notes : les notes sont nommées selon pour l'octave qui contient la note A4, pour laquelle on a en général : ~ 415 < A4 < ~ 466 Hz. • Nombres décimaux : le point est utilisé comme séparateur entre les nombres entiers et les décimales.

- by Johan Broekaert
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- J S Bach, Tuning and Temperament, Interval analysis, Meantone Temperament

We propose an algorithm to compute the limit cycle set of uncertain non-rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a prescribed accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the prescribed accuracy. Moreover, for a prescribed accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non-rational example with nonlinear parametric dependencies. Copyright © 2005 John Wiley & Sons, Ltd.

- by Jayesh Barve
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- Mechanical Engineering, Applied Mathematics, Interval analysis, Nonlinear system
- by Laurent Hardouin
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- Engineering, Mathematical Sciences, Interval analysis, Boolean Satisfiability
- by Arnaud Clerentin
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- State Estimation, Interval analysis, Stereoscopic Vision

For the given arbitrary sequence of real numbers {xi} n i=1 we construct several lower and upper bound converging sequences. Our goal is to localize the absolute value of the sequence maximum. Also we can calculate the value of such numbers. Since the proposed algorithms are iterative, asymptotical convergence theorems are proved. The presented task seems to be pointless from

- by Natalia Andrianova
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- Matrix Analysis, Interval analysis, Convergence theorem, Data Processing
- by Diego Alvarez
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- Engineering, Order Statistics, Interval analysis
- by Hartono Hadjarati
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- Interval Training, Interval analysis

Interval analysis is a growing branch of computational mathematics where operations are carried out on intervals instead of real numbers. This paper presents the first application of this method to robotic mechanisms for the solution of inverse kinematics. As shown in this paper, it is possible to potentially compute all solutions of the inverse kinematics problem using this method. This paper describes the preliminaries of interval analysis, the numerical algorithm, the computational complexity, and illustrations with examples.

- by Asai Asaithambi
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- Mechanical Engineering, Robotics, Mathematics, Algorithms
- by Erin Wagner
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- Biology, Association study, Meat quality, Interval analysis

In this paper, we have proved the indispensable inequalities of classical analysis for interval value functions: Hölder, Cauchy-Schwarz and Carlson inequalities. Additionally, we achieved generalization for Carlson's inequality for... more

- by Necmettin Alp and +1
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- Mathematics, Interval analysis

We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in an n-dimensional Hilbert space, {\cal H}^n, n\ge 3 , to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in {\bb R}^n , on algorithms that single out those diagrams on which algebraic 0-1 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all four-dimensional KS vector systems containing up to 24 vectors were generated and described, all three-dimensional vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found.

- by Brendan McKay
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- Mathematical Sciences, Physical sciences, Interval analysis, Three Dimensional

In this paper, the interval nature of fuzzy numbers is revealed by showing that many interesting results from classical interval analysis transfer also into the fuzzy case. The paper deals with a solution of a fuzzy interval system of... more

- by Katerine Perez
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- Pure Mathematics, Interval analysis, Fuzzy Sets and Systems, Linear Equations

Map matching algorithms are used to integrate an initial estimated position with digital road network data for computing the vehicle position on a road map. In this paper, a map matching algorithm based on belief function theory is proposed. This method provides an accurate estimation of vehicle position relative to a digital road map using belief function theory and interval

- by Fahed Abdallah
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- Information Fusion, Sensor Fusion, Interval analysis, ROAD NETWORK

In the article we present an interval difference scheme for solving a general elliptic boundary value problem with Dirichlet’ boundary conditions. The obtained interval enclosure of the solution contains all possible numerical errors. A... more

The classification problem is concerned with categorizing observations into different groups. The performance of the classification process is dependent on how well the discriminant function for the specific problem performs. A... more

- by Jaideep Motwani
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- Neural Network, Mathematical Sciences, Classification, Interval analysis
- by Frederic Messine
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- Applied Mathematics, Global Optimization, Interval analysis, Branch and Bound
- by Shankar Krishnan
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- Engineering, Computational Geometry, Algorithm, Geometric model
- by Alex Nicolau
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- Computability Theory, Interval analysis, Equivalence Checking, Decision Problem

Interval arithmetic has been proved to be very subtle, reliable, and most fundamental in addressing uncertainty and imprecision. However, the theory of classical interval arithmetic and all its alternates suffer from algebraic anomalies, and all have difficulties with interval dependency. A theory of interval arithmetic that seems promising is the theory of parametric intervals. The theory of parametric intervals is presented in the literature with the zealous claim that it provides a radical solution to the long-standing dependency problem in the classical interval theory, along with the claim that parametric interval arithmetic, unlike Moore's classical interval arithmetic, has additive and multiplicative inverse elements, and satisfies the distributive law. So, does the theory of parametric intervals accomplish these very desirable objectives? Here it is argued that it does not.

- by Hend Dawood and +1
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- Numerical Analysis, Mathematical Logic, Computational Mathematics, Uncertainty

An Interval Partitioning Method (IPM) is proposed to solve the (nonconvex) Mixed Integer Nonlinear Programming Problem (MINLP). The MINLP is encountered in many application areas and solving this problem bears practical importance. This paper proposes an IPM where two tree search strategies (breadth first and mixed breadth/depth first) and three variable subdivision methods are implemented. Two proposed variable subdivision methods are novel and they proritize variables hierarchically according to several features. The IPM is implemented on a set of nonconvex MINLP instances extracted from the MINLP benchmarks and numerical results show that its performance is quite promising.

- by B. Nogarede
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- Engineering, Global Optimization, Physical sciences, Interval analysis