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8th World Congress on Intelligent Control and Automation (WCICA)

作者： Yang Hong Liu Jianxin Ding Qiaolin N China Elect Power Univ Sch Elect & Elect Engn Baoding 071003 Hebei Province Peoples R China

ISBN: (纸本)9781424467129

WPP(Wind Power Penetration) is an important indicator to ensure wind power system security. It is with great practical significance for knowing probability distribution of WPP. There were two types of method to calculate probability distribution of WPP in the past. One type of method which used statistic theory to calculate were fast but had to know simple function relationship between WPP and load. Another type of method which used stochastic simulation to calculate could be fit for complex relationship between WPP and load but were very slow. To solve the problem, a flexibility method is given in the paper. Firstly, a piecewise linear function is given to express the relationship of WPP and load, and then a formula of calculating probability density of WPP is derived by applying the probability theory. The given method for calculating probability distribution of WPP is not only clear, simple, but also fast in speed. It is an ideal method. A practical calculation example shows that the method of this paper is effective and significance.

关键词： Wind Power Penetration Probability Distribution piecewise linear function

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Simulation of telescopic shock absorber outer characteristic with piecewise maths function

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2009年第1期7卷 8-14页

作者： Zhou, Changcheng Zhang, Xueyi Meng, Jie Zhao, Leilei Shandong Univ Technol Sch Transport & Vehicle Engn 12 Zhangzhou Rd Zibo 255049 Shandong Peoples R China

The pathway throttle and local throttle loss of oil fluxion of telescopic shock absorber were analysed and the curves of pathway loss coefficient and equivalent length of piston hole vs. shock absorber velocity are shown. According to the thickness and the pre-deformation of throttle slice, and the throttle hole area, the velocity points of valve opening were analysed by the relation of flux to the velocity, and pressure to the deformation of throttle slice, and the analytic formulas of shock absorber velocity during valve openings were given. On the basis of the velocity points, the outer characteristic model of shock absorber was established by piecewise linear function. A practical example of simulation of shock absorber outer characteristic was given, and the performance test was conducted. The results show that the model of outer simulation is correct, the simulation values coincide with test values, and it has important reference value for telescope shock absorber design and characteristic analysis.

关键词： characteristic modelling characteristic simulation piecewise linear function telescopic shock absorber

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Absolute exponential stability of recurrent neural networks with generalized activation function

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2008年第6期19卷 1075-1089页

作者： Xu, Jun Cao, Yong-Yan Sun, Youxian Tang, Jinshan Alcorn State Univ Syst Res Inst Alcorn State MS 39096 USA Alcorn State Univ Dept Adv Technol Alcorn State MS 39096 USA Jiangxi Univ Finance & Econ Sch Informat Technol Nanchang 330013 Peoples R China Wuhan Univ Sci & Technol Dept Automat Wuhan 430081 Peoples R China Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China Alcorn State Univ Syst Res Inst Image Proc & Bioimaging Res Lab Dept Adv Technol Alcorn State MS 39096 USA

In this paper, the recurrent neural networks (RNNs) with a generalized activation function class is proposed. In this proposed model, every component of the neuron's activation function belongs to a convex hull which is bounded by two odd symmetric piecewise linear functions that are convex or concave over the real space. All of the convex hulls are composed of generalized activation function classes. The novel activation function class is not only with a more flexible and more specific description of the activation functions than other function classes but it also generalizes some traditional activation function classes. The absolute exponential stability (AEST) of the RNN with a generalized activation function class is studied through three steps. The first step is to demonstrate the global exponential stability (GES) of the equilibrium point of original RNN with a generalized activation function being equivalent to that of RNN under all vertex functions of convex hull. The second step transforms the RNN under every vertex activation function into neural networks under an array of saturated linear activation functions. Because the GES of the equilibrium point of three systems are equivalent, the next stability analysis focuses on the GES of the equilibrium point of RNN system under an array of saturated linear activation functions. The last step is to study both the existence of equilibrium point and the GES of the RNN under saturated linear activation functions using the theory of M-matrix. In the end, a two-neuron RNN with a generalized activation function is constructed to show the effectiveness of our results.

关键词： absolute exponential stability (AEST) convex hull generalized activation function class piecewise linear function recurrent neural networks (RNNs)

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A modal learning adaptive function neural network applied to handwritten digit recognition

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INFORMATION SCIENCES 2008年第20期178卷 3802-3812页

作者： Kang, Miao Palmer-Brown, Dominic Univ E London Sch Comp & Technol London E16 2RD England

A novel combination of the adaptive function neural network (ADFUNN) and on-line snap-drift learning is presented in this paper and applied to optical and pen-based recognition of handwritten digits [E. Alpaydin, F. Alimoglu for Optical Recognition of Handwritten Digits and E. Alpaydin, C. Kaynak for Pen-Based Recognition of Handwritten Digits http://***/similar to mlearn/databases/optdigits/ http://***/similar to mlearn/databases/pendigits/]. Snap-drift [S.W. Lee, D. Palmer-Brown, C.M. Roadknight, Performance-guided neural network for rapidly self-organising active network management (invited Paper), journal of Neurocomputing, 61 C, 2004, pp. 5-20] employs the complementary concepts of common (intersection) feature learning (called snap) and LVQ (drift towards the input patterns) learning, and is a fast, unsupervised method suitable for on-line learning and non-stationary environments where new patterns are continually introduced. ADFUNN [M. Kang, D. Palmer-Brown, An adaptive function neural network (ADFUNN) for phrase recognition, in: The International joint Conference on Neural Networks (IJCNN05), Montreal, Canada, 2005, D. Palmer-Brown, M. Kang, ADFUNN: An adaptive function neural network, in: The 7th International Conference on Adaptive and Natural Computing Algorithms (ICAN-NGA05), Coimbra, Portugal, 2005] is based on a linear piecewise neuron activation function that is modified by a novel gradient descent supervised learning algorithm. It has recently been applied to the Iris dataset, and a natural language phrase recognition problem, exhibiting impressive generalisation classification ability with no hidden neurons. The unsupervised single layer snap-drift is effective in extracting distinct features from the complex cursive-letter datasets, and the supervised single layer ADFUNN is capable of solving linearly inseparable problems rapidly. In combination within one network (SADFUNN), these two methods are more powerful and yet simple

关键词： modal learning adaptive function neural network snap-drift neural network handwritten digits recognition piecewise linear function

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The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces

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Science China Mathematics 2008年第7期51卷 1243-1256页

作者： ZHENG XiYin YANG XiaoQi Department of Mathematics Yunnan UniversityKunming 650091China Department of Applied Mathematics the Hong Kong Polytechnic UniversityHung HumKowloonHong KongChina

In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.

关键词： piecewise linear function weak Pareto solution connectedness normed space 90C29 90C30 90C31

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Non-linear Modeling of Transformer Using Hammerstein Method

Non-linear Modeling of Transformer Using Hammerstein Method

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2nd International Power and Energy Conference (PECon 2008)

作者： Yazdanpanahi, H. Hejazi, M. A. Gharehpetian, G. B. Amir Kabir Univ Technol Dept Elect Engn Tehran 15914 Iran

ISBN: (纸本)9781424424047

This paper presents the nonlinear model of transformer which is based on Hammerstein method and describes the procedure of the parameter identification for the suggested model. In this procedure, a point slope parameterization of the static nonlinearity has been used which results in a computationally tractable optimization problem. The identification method simultaneously approximates the linear dynamic and nonlinear static blocks of the Hammerstein method.

关键词： Hammerstein Non-linearity Parameter identification piecewise linear function Transformer

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An Approach to The functions Approximation Problems by Mamdani Fuzzy System

An Approach to The Functions Approximation Problems by Mamda...

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10th International Conference on Control, Automation, Robotics and Vision

作者： Bui Cong Cuong Hoang Viet Long Vietnamese Acad Sci & Technol Inst Math 18 Hoang Quoc Viet Rd Hanoi 10307 Vietnam Univ Transport & Commun Lang Thuong Fac Basis Sci Hanoi Vietnam

ISBN: (纸本)9781424422869

In this paper, we introduce a class of piecewise multilinear models for Mamdani fuzzy system and investigate their approximation capabilities to integrable functions with LP-norm. Specially, by extending fuzzy system to stochastic one, the approximation capability of the stochastic Mamdani system to a class of random processes is analyzed. A result on the approximation of regular function is given showing that fuzzy system may keep their semantic structure while approximating to any degree of accuracy not only sufficiently regular functions, but also their derivatives

关键词： piecewise linear function piecewise multilinear function stochastic fuzzy system piecewise multilinear interpolation

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ON DISCRETE LIMITS OF SEQUENCES OF piecewise linear functionS

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REAL ANALYSIS EXCHANGE 2007年第1期33卷 107-110页

作者： Grande, Zbigniew Kazimierz Wielki Univ Inst Math Plac Weyssenhoffa 11 PL-85072 Bydgoszcz Poland

In this article we characterize the discrete limits of sequences of piece-wise linear functions. A function f : [0, 1] -> R is the discrete limit of a sequence of piecewise linear functions iff there are closed set... 详细信息

关键词： discrete convergence sequence of functions piecewise linear function

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Modified sum-product algorithms for decoding low-density parity-check codes

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IET COMMUNICATIONS 2007年第3期1卷 294-300页

作者： Papaharalabos, S. Sweeney, P. Evans, B. G. Mathiopoulos, P. T. Albertazzi, G. Vanelli-Coralli, A. Corazza, G. E. Natl Observ Athens Metaxa & Vas ISARS GR-15236 Athens Greece Univ Surrey CCSR Dept Elect Engn Guildford GU2 7XH Surrey England Univ Bologna DEIS Dept Elect Comp Sci & Syst I-40136 Bologna Italy

The authors deal with the sum-product algorithm (SPA) based on the hyperbolic tangent (tanh) rule when it is applied for decoding low-density parity-check (LDPC) codes. Motivated by the finding that, because of the large number of multiplications required by the algorithm, an overflow in the decoder may occur, two novel modifications of the tanh function (and its inverse) are proposed. By means of computer simulations, both methods are evaluated using random-based LDPC codes with binary phase shift keying (BPSK) signals transmitted over the additive white Gaussian noise (AWGN) channel. It is shown that the proposed modifications improve the bit error rate (BER) performance up to 1 dB with respect to the conventional SPA. These results have also shown that the error floor is removed at BER lower than 10(-6). Furthermore, two novel approximations are presented to reduce the computational complexity of the tanh function (and its inverse), based on either a piecewise linear function or a quantisation table. It is shown that the proposed approximations can slightly improve the BER performance (up to 0.13 dB) in the former case, whereas small BER performance degradation is observed (<0.25 dB) in the latter case. In both cases, however, the decoding complexity is reduced significantly.

关键词： quantisation table random codes computer simulation BER AWGN channels phase shift keying random-based LDPC codes approximation theory parity check codes piecewise linear techniques binary phase shift keying error statistics decoding channel coding additive white Gaussian noise channel bit error rate hyperbolic tangent rule low-density parity-check code sum-product algorithm piecewise linear function SPA

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On a new class of function systems of Faber-Schauder type

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MATHEMATICAL NOTES 2007年第5-6期82卷 575-582页

作者： Aubakirov, T. U. Bokaev, N. A. Buketov State Univ Karaganda Kazakhstan

In this paper, we introduce a new class of function systems generalizing the classical Faber-Schauder system. Under the condition that the generating sequence is bounded, we show that systems of such a class constitute bases in the space of continuous functions and prove some properties of series expansions of functions in these systems.

关键词： Faber-Schauder function system piecewise linear function Vandermonde determinant modulus of continuity modulus of smoothness

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