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Chatter classification by entropy functions and morphological processing in cylindrical traverse grinding

PRECISION ENGINEERING-JOURNAL OF THE AMERICAN SOCIETY FOR PRECISION ENGINEERING 1996年第2-3期18卷 110-117页

作者： Fu, JC Troy, CA Mori, K Industrial Engineering Department Da-Yeh Institute of Technology Dah-Tsuen Chang-Hwa Taiwan Industrial Engineering Department Da-Yeh Institute of Technology Dah-Tsuen Chang-Hwa 51505 112 Shah-Jeau Rd. Taiwan

During cylindrical traverse grinding processes, two types of regenerative chatter-workpiece and grinding wheel-may degrade the accuracy of the surface finish. To maintain productivity and quality, a closed-loop vibration control system should be provided for the grinding system. An algorithm for automated classification by type is essential in developing such a system. In cylindrical traverse grinding, the chaffer vibration signals display unstable dynamic characteristics, which makes the task of chatter classification especially difficult. This paper introduces an approach that combines entropy techniques with morphological preprocessing to classify traverse grinding regenerative chatter by type based on the vibration spectrum. Experimental data analysis is used to demonstrate that the proposed method can effectively distinguish workpiece regenerative chatter from wheel regenerative chatter. Because both the entropy function and morphological processing are computationally easy, this method is not only readily understood.

关键词： cylindrical traverse grinding regenerative chatter classification machining process monitoring entropy functions morphological processing

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Dualities between entropy functions and network codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第10期54卷 4470-4487页

作者： Chan, Terence Grant, Alex Univ S Australia Inst Telecommun Res Adelaide SA 5095 Australia

In communications networks, the capacity region of multisource network coding is given in terms of the set of entropy functions Gamma*. More broadly, determination of Gamma* would have an impact on converse theorems for multi-terminal problems in information theory. This paper provides several new dualities between entropy functions and network codes. Given a function g >= 0 defined on all subsets of N random variables, we provide a construction for a network multicast problem which is "solvable" if and only if g is the entropy function of a set of quasi-uniform random variables. The underlying network topology is fixed and the multicast problem depends on g only through link capacities and source rates. A corresponding duality is developed for linear network codes, where the constructed multicast problem is linearly solvable if and only if g is linear group characterizable. Relaxing the requirement that the domain of g be subsets of random variables, we obtain a similar duality between polymatroids and the linear programming bound. These duality results provide an alternative proof of the insufficiency of linear (and abelian) network codes, and demonstrate the utility of non-Shannon inequalities to tighten outer bounds on network coding capacity regions.

关键词： duality entropy functions Ingleton's inequality LP bounds network codes polymatroids pseudovariables

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Dualities between entropy functions and network codes

Dualities between entropy functions and network codes

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4th Workshop on Network Coding, Theory and Applications

作者： Chan, Terence Grant, Alex Univ S Australia Inst Telecommun Res Adelaide SA 5095 Australia

ISBN: (纸本)9781424416899

关键词： duality entropy functions Ingleton's inequality LP bounds network codes polymatroids pseudovariables

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Family of additive entropy functions out of thermodynamic limit

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Physical Review E 2003年第1期67卷 016104-016104页

作者： Alexander N. Gorban Iliya V. Karlin []Institute of Computational Modeling RAS 660036 Krasnoyarsk Russia

We derive a one-parametric family of entropy functions that respect the additivity condition, and which describe effects of finiteness of statistical systems, in particular, distribution functions with long tails. This one-parametric family is different from the Tsallis entropies, and is a convex combination of the Boltzmann-Gibbs-Shannon entropy and the entropy function proposed by Burg. An example of how longer tails are described within the present approach is worked out for the canonical ensemble. We also discuss a possible origin of a hidden statistical dependence, and give explicit recipes on how to construct corresponding generalizations of the master equation.

关键词： .convex entropy functions discuss canonical subsystems thermodynamic limit entropies distribution functions master equation one-parametric Family of additive family of entropy additivity effects of niteness long tails Tsallis entropy

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LOCAL EXTREMA OF entropy functions UNDER TENSOR PRODUCTS

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QUANTUM INFORMATION & COMPUTATION 2011年第11-12期11卷 1028-1044页

作者： Friedland, Shmuel Gour, Gilad Roy, Aidan Univ Illinois Dept Math Stat & Comp Sci Chicago IL 60607 USA Univ Calgary Inst Quantum Informat Sci Calgary AB T2N 1N4 Canada Univ Calgary Dept Math & Stat Calgary AB T2N 1N4 Canada Univ Waterloo Inst Quantum Comp Waterloo ON N2L 3G Canada

We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed ... 详细信息

关键词： Quantum channels entropy functions local additivity

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On the Use of entropy functions for Identification of Dynamic Systems

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IFAC Proceedings Volumes 1982年第4期15卷 725-729页

作者： K. Henning Institut für Regelungstechnik der RWTH Aachen Federal Republic of Germany

Methods of information theory can be used for analysis and modeling of dynamic systems in order to describe information transfer between input and output signals. The dynamic system may include nonlinearities and disturbances. Using so-called entropy functions identification is also possible, when input and output can only be described by non-technical processes. The results show that the description of dynamic nonlinear systems with deadtime and disturbances is possible by this method. The results may be obtained without any limitation of the type of the distribution function.

关键词： Information theory entropy functions system identification

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Generalised Entropies for Decision Trees in Classification Under Monotonicity Constraints

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EXPERT SYSTEMS 2025年第4期42卷

作者： Khalaf, Oumaima Garcia, Salvador Ben Ishak, Anis Univ Tunis Inst Super Gest BESTMOD LR99ES04 Le Bardo Tunisia Univ Granada Dept Comp Sci & Artificial Intelligence Granada Spain Andalusian Res Inst Data Sci & Computat Intelligen Dept Comp Sci & Artificial Intelligence Granada Spain Univ Tunis Inst Super Gest Dept Methodes Quantitat Le Bardo Tunisia Univ Manouba ESCT QuAnLab LR244ES21 Campus Univ Manouba Tunisia

Several decision-making approaches involve ordinal labelling between feature values and decision outcomes. These issues refer to ordinal classification under monotonicity constraints. Recently, some machine learning approaches have been designed to deal with these kinds of problems. Indeed, numerous experiments have shown that these algorithms are widely used in real-life applications because of their flexibility and efficiency in terms of interpretation and predictions. In this paper, we introduce novel approaches for measuring feature quality and information quantity, called R & eacute;nyi-Tsallis Monotonic Tree (RTMT), which uses the advantages of R & eacute;nyi and Tsallis entropies while incorporating monotonicity constraints through an optimisation framework. Moreover, we introduce Mono-CART, a variant of the CART approach adapted for monotonic classification. New decision tree algorithms are designed on the basis of aforementioned entropies while considering the monotonicity constraints within an optimisation system. The experiments conducted using some benchmark datasets demonstrate the superiority of the proposed approaches compared to existing methods.

关键词： classification tree entropy functions monotonic classification R & eacute nyi-Tsallis Monotonic Tree

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Analysis of Stochastic Chemical Reaction Networks with a Hierarchy of Timescales

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JOURNAL OF STATISTICAL PHYSICS 2025年第3期192卷 1-31页

作者： Laurence, Lucie Robert, Philippe INRIA Paris 48 rue BarraultCS 61534 F-75647 Paris France

We investigate a class of stochastic chemical reaction networks with n >= 1 chemical species S-1, ..., S-n, and whose complexes are only of the form k(i)S(i), i=1,..., n, where (k(i)) are integers. The time evolution of these CRNs is driven by the kinetics of the law of mass action. A scaling analysis is done when the rates of external arrivals of chemical species are proportional to a large scaling parameter N. A natural hierarchy of fast processes, a subset of the coordinates of (X-i(t)), is determined by the values of the mapping i bar right arrow k(i). We show that the scaled vector of coordinates i such that k(i) =1 and the scaled occupation measure of the other coordinates are converging in distribution to a deterministic limit as N gets large. The proof of this result is obtained by establishing a functional equation for the limiting points of the occupation measure, by an induction on the hierarchy of timescales and with relative entropy functions.

关键词： Chemical reaction networks Multi-timescales entropy functions

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Capacity Bounds for Networks With Correlated Sources and Characterisation of Distributions by Entropies

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第6期63卷 3540-3553页

作者： Thakor, Satyajit Chan, Terence Grant, Alex IIT Mandi Sch Comp & Elect Engn Mandi 175005 India Univ South Australia Inst Telecommun Res Adelaide SA 5001 Australia Myriota Pty Ltd Adelaide SA 5005 Australia

Characterising the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterising all information inequalities. The majority of computable outer bounds in the literature are relaxations of the linear programming bound, which involves entropy functions of random variables related to the sources and link messages. When sources are not independent, the problem is even more complicated. Extension of linear programming bounds to networks with correlated sources is largely open. Source dependence is usually specified through a joint probability distribution, and one of the main challenges in extending linear program bounds is the difficulty (or impossibility) of characterising arbitrary dependences via entropy functions. This paper tackles the problem by answering the question of how well entropy functions can characterise correlation among sources. We show that by using carefully chosen auxiliary random variables, the characterisation can be fairly "accurate". Using such auxiliary random variables, we also give implicit and explicit outer bounds on the capacity of networks with correlated sources. The characterisation of correlation or joint distribution via Shannon entropy functions is also applicable to other information measures, such as Renyi entropy and Tsallis entropy.

关键词： Correlated sources joint distribution entropy functions LP bound cut-set bounds network coding capacity outer bounds

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DISSIPATIVE entropy AND GLOBAL SMOOTH SOLUTIONS IN RADIATION HYDRODYNAMICS AND MAGNETOHYDRODYNAMICS

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MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES 2008年第12期18卷 2151-2174页

作者： Rohde, Christian Yong, Wen-An Univ Stuttgart Inst Angew Anal & Numer Simulat D-70569 Stuttgart Germany Tsinghua Univ Zhou Pei Yuan Ctr Appl Math Beijing 100084 Peoples R China

The equations of ideal radiation magnetohydrodynamics (RMHD) serve as a fundamental mathematical model in many astrophysical applications. It is well known that radiation can have a damping effect on solutions of associated initial-boundary-value problems. In other words, singular solutions like shocks can be prohibited. In this paper, we consider discrete-ordinate approximations of the RMHD-system for general equations of state. If the magnetic fields are absent (i.e. if we consider radiation hydrodynamics), we prove the existence of global-in-time classical solutions for the Cauchy problem in one space dimension under an appropriate smallness condition on the inital data. We also show that counterparts of the compressive shock waves for the full RHD case and counterparts of the slow and fast MHD shock waves for the full RMHD-system can have structures in the presence of radiation if the amplitude is sufficiently small. Moreover, a new entropy function for the RMHD-system is presented.

关键词： Radiative MHD entropy functions dissipation shock structures

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