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IEEE-Power-and-Energy-Society General Meeting (PESGM)

作者： Farrokhseresht, Mana Farrokhseresht, Nakisa Hesamzadeh, Mohammad Reza KTH Royal Inst Technol Elect Market Res Grp Stockholm Sweden

ISBN: (纸本)9781509041688

In this paper, a method for Reactive Power Planning (RPP) is proposed which ensures voltage stability in a system with cross-border electricity flows. One or more cross-border tie-lines connect the Source-area, containing cheap generation, to the Sink-area which is willing to import this cheap power. A mathematical method is used to maximize the economic benefit of the Sink-area with respect to the cost of the installed reactive compensators which maximize the Net Transfer Capacity (NTC) of the tie-lines. An analytic expression for the NTC does not exist and two methods are henceforth proposed to approximate the NTC: (1) approximation by a piecewise linear function and (2) by a polynomial obtained with statistical regression. The method is programmed in GAMS and formulated as a Mixed-Integer Non-linear Programming problem (MINLP).

关键词： Reactive Power Planning Voltage Stability Net Transfer Capacity Regression piecewise linear functions

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Pulp property development Part III: Fiber residence time and consistency profile impact on specific energy and pulp properties

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NORDIC PULP & PAPER RESEARCH JOURNAL 2016年第2期31卷 300-+页

作者： Karlstrom, Anders Hill, Jan Ferritsius, Olof Ferritsius, Rita Chalmers Univ Technol S-41296 Gothenburg Sweden QualTech AB Tyringe Sweden Mid Sweden Univ Stockholm Sweden

This paper focuses on the pulp properties obtained from ThermoMechanical Pulp (TMP) CD refiners. Undersampled pulp variables are expanded into an oversampled set of process data, which makes it possible to analyze pulp properties in a dynamic time frame. It is shown that, in order to gain deeper insight into the defibration/fibrillation at a specific energy input, one needs to know the fiber residence time and the consistency profile. Moreover, the fiber residence time in the flat zone (FZ) and conical zone (CD) are intertwined with the consistency out from FZ and CD. Together with an external variable (production), these internal variables are essential for predicting the pulp properties. It is also shown that internal process conditions from different test series can be manipulated in the operating window using a low-frequency gain description obtained from an ARX model. The same mapping procedure can be applied to pulp and handsheet properties (in this paper represented by the tensile index), and this opens for implementation of new optimization routines to find more energy efficient operating points while maintaining pre-specified pulp quality.

关键词： Pulp quality models TMP refiners piecewise linear functions

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When Does the Equality J（X＊） = J（X） Hold for a Two-dimensional Banach Space X ？

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Acta Mathematica Sinica,English Series 2015年第8期31卷 1303-1314页

作者： Kichi-Suke SAITO Masahiro SATO Ryotaro TANAKA Department of Mathematics Faculty of Science Niigata University Department of Mathematical Sciences Graduate School of Science and TechnologyNiigata University

In this paper, we consider the following problem about the James constant： When does the equality J（X＊） = J（X） hold for a Banach space X ？ It is known that the James constant of a Banach space does not coincide with that of its dual space in general. In fact, we already have counterexamples of two-dimensional normed spaces that are equipped with either symmetric or absolute norms. However,we show that if the norm on a two-dimensional space X is both symmetric and absolute, then the equality J（X＊） = J（X） holds. This provides a global answer to the problem in the two-dimensional case.

关键词： James constant symmetric absolute norms piecewise linear functions

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Least Squares Approximation to Lognormal Sum Distribution via piecewise linear functions

Least Squares Approximation to Lognormal Sum Distribution vi...

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4th IEEE Conference on Industrial Electronics and Applications

作者： Zhao, Lian Ding, Jiu Ryerson Univ Dept Elect & Comp Engn Toronto ON M5B 2K3 Canada Univ Southern Mississippi Dept Math Hattiesburg MS 39406 USA

ISBN: (纸本)9781424427994

In this paper, the least squares approximation via a piecewise linear function approach is applied to solve the approximation problem of a sum of lognormal random variables. A number of linear basis functions are applied and the corresponding coefficients are specified to form a piecewise linear approximation to the sum lognormal cumulative distribution function. By using the proposed approach, arbitrary precision of the approximation can be achieved by increasing the number of basis functions. The computation complexity shows no significant increase with the increase of the number of basis functions. Simulation results exhibit a desirable performance by using the proposed approximation method through piecewise linear basis functions.

关键词： Lognormal random variables L-2-norm least squares piecewise linear functions basis functions cumulative distribution functions (CDF)

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Chua's circuit and its characterization as a filter

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EUROPEAN JOURNAL OF PHYSICS 2014年第6期35卷

作者： Campos-Canton, I. Segura-Cisneros, O. A. Balderas-Navarro, R. E. Campos-Canton, E. UASLP Fac Ciencias San Luis Potosi Mexico UASLP Inst Invest Comunicac Opt San Luis Potosi 78000 Mexico IPICYT Div Matemat Aplicadas San Luis Potosi 78216 Mexico

This article deals with Chua's circuit characterization from the point of view of a filter based on the concept of piecewise linear functions. Furthermore, experiments are developed for teaching electronic systems that can be used for novel filtering concepts. The frequency range in which they are tested is from 20 Hz to 20 kHz, due to the audio spectrum comprised in this frequency range. The node associated with the capacitor and Chua's diode is used as input, and the node for another capacitor and the coil is used as output, thereby establishing one input-output relationship for each system case given by the piecewise linear functions. The experimental result shows that Chua's circuit behaves as a bandpass filter-amplifier, with a maximum frequency around 3 kHz and bandwidth between 1.5 kHz and 5.5 kHz. The results presented in this paper can motivate engineering students to pursue applications of novel electrical circuits based on topics that are of potential interest in their future research studies.

关键词： filters Chua's circuit piecewise linear functions analog electronics

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A reformulation framework for global optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第1期57卷 115-141页

作者： Lundell, Andreas Skjal, Anders Westerlund, Tapio Abo Akad Univ Ctr Excellence Optimizat & Syst Engn SF-20500 Turku Finland

In this paper, we present a global optimization method for solving nonconvex mixed integer nonlinear programming (MINLP) problems. A convex overestimation of the feasible region is obtained by replacing the nonconvex constraint functions with convex underestimators. For signomial functions single-variable power and exponential transformations are used to obtain the convex underestimators. For more general nonconvex functions two versions of the so-called alpha BB-underestimator, valid for twice-differentiable functions, are integrated in the actual reformulation framework. However, in contrast to what is done in branch-and-bound type algorithms, no direct branching is performed in the actual algorithm. Instead a piecewise convex reformulation is used to convexify the entire problem in an extended variable-space, and the reformulated problem is then solved by a convex MINLP solver. As the piecewise linear approximations are made finer, the solution to the convexified and overestimated problem will form a converging sequence towards a global optimal solution. The result is an easily-implementable algorithm for solving a very general class of optimization problems.

关键词： Global optimization Reformulation technique Convex underestimators Mixed integer nonlinear programming Twice-differentiable functions Signomial functions piecewise linear functions alpha BB-underestimator SGO-algorithm

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Non-iterative identification and model following control of Hammerstein systems with asymmetric dead-zone non-linearities

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IET CONTROL THEORY AND APPLICATIONS 2012年第1期6卷 84-89页

作者： Lv, X. Ren, X. Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

A novel non-iterative identification algorithm based on the parameterisation of unknown dead-zone non-linearity is proposed for control of Hammerstein systems in presence of asymmetric dead-zone input. A canonical representation for piecewise linear functions is employed to describe the dead-zone function such that a universal-type parametric model can be established to approximate the entire system. Both the dead-zone parameters (thresholds and slopes) and the coefficients in linear transfer function can be estimated simultaneously using the designed persistent exciting input. A modified model following control scheme is then designed in such a way that the plant output tracks the desired output with satisfactory performance. This method can be applied without a priori knowledge of the dead-zone non-linearity. Numerical simulations are presented to illustrate the effectiveness of the proposed scheme.

关键词： linear transfer function universal type parametric model control nonlinearities piecewise linear functions transfer functions numerical simulation Control system analysis and synthesis methods Nonlinear control systems numerical analysis unknown dead zone nonlinearity Hammerstein system control identification nonlinear control systems persistent exciting input plant output noniterative identification algorithm asymmetric dead zone input cascade control Simulation, modelling and identification dead zone function piecewise linear techniques parameterisation canonical representation

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Impact of using linear optimization models in dose planning for HDR brachytherapy

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MEDICAL PHYSICS 2012年第2期39卷 1021-1028页

作者： Holm, Asa Larsson, Torbjorn Tedgren, Asa Carlsson Linkoping Univ Dept Math SE-58183 Linkoping Sweden Linkoping Univ Dept Med & Hlth Sci IMH SE-58185 Linkoping Sweden Swedish Radiat Safety Author SE-17116 Stockholm Sweden

Purpose: Dose plans generated with optimization models hitherto used in high-dose-rate (HDR) brachytherapy have shown a tendency to yield longer dwell times than manually optimized plans. Concern has been raised for the corresponding undesired hot spots, and various methods to mitigate these have been developed. The hypotheses upon this work is based are (a) that one cause for the long dwell times is the use of objective functions comprising simple linear penalties and (b) that alternative penalties, as these are piecewise linear, would lead to reduced length of individual dwell times. Methods: The characteristics of the linear penalties and the piecewise linear penalties are analyzed mathematically. Experimental comparisons between the two types of penalties are carried out retrospectively for a set of prostate cancer patients. Results: When the two types of penalties are compared, significant changes can be seen in the dwell times, while most dose-volume parameters do not differ significantly. On average, total dwell times were reduced by 4.2%, with a reduction of maximum dwell times by 25%, when the alternative penalties were used. Conclusions: The use of linear penalties in optimization models for HDR brachytherapy is one cause for the undesired long dwell times that arise in mathematically optimized plans. By introducing alternative penalties, a significant reduction in dwell times can be achieved for HDR brachytherapy dose plans. Although various measures for mitigating the long dwell times are already available, the observation that linear penalties contribute to their appearance is of fundamental interest. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3676179]

关键词： brachytherapy optimization treatment planning linear programming piecewise linear functions

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Explicit hybrid model predictive control: discontinuous piecewise-affine approximation and FPGA implementation

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IFAC Proceedings Volumes 2011年第1期44卷 1350-1355页

作者： Tomaso Poggi Sergio Trimboli Alberto Bemporad Marco Storace Biophysical and Electronic Engineering Department University of Genoa Via Opera Pia 11a I-16145 Genova Italy Mechanical and Structural Engineering Department University of Trento Via Mesiano 77 I-38123 Trento Italy

Abstract In this paper we introduce a digital architecture implementing the explicit solution of a switched model predictive control problem. Given a mixed-logic dynamical system, we derive an explicit controller in the form of a possibly discontinuous piecewise-affine function. This function is then approximated by resorting to piecewise-affine simplicial functions, which can be implemented on a circuit by extending the representation capabilities of a previously proposed architecture to evaluate the control action. The architecture has been implemented on FPGA and validated on a benchmark example related to an air conditioning system.

关键词： piecewise linear functions nonlinear circuits digital architectures

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Set membership estimation theory for Wiener modelling using HLCPWL functions

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2011年第1-2期14卷 13-26页

作者： Alvarez, Marcela P. Castro, Liliana R. Agamennoni, Osvaldo E. Univ Nacl Sur Dept Matemat Av Alem 1253B8000CPB Bahia Blanca Buenos Aires Argentina Univ Nacl Sur Dept Matemat CONICET Inst Invest Ingn Elect Bahia Blanca Buenos Aires Argentina Univ Nacl Sur Dept Ingn Elect & Comp CONICET Inst Invest Ingn Elect Bahia Blanca Buenos Aires Argentina

In this paper, we propose a Wiener-like model structure where the dynamic linear part is represented by a finite set of discrete Laguerre or Kautz transfer functions, while the non-linear static part is realised by high level canonical piecewise linear basis functions (HLCPWL). In control applications, Laguerre functions are commonly used when dealing with overdamped systems, while Kautz systems are suitable for weakly damped ones. The approximation of the static non-linear functions using HLCPWL functions is based on that this representation uses the least number of parameters and the algorithm for computing the approximation is very efficient. In this model, we estimate the parameters of the HLCPWL using set membership estimation theory, under mild error constraints. It is shown that this structure allows to uniformly approximate any causal, time-invariant, non-linear discrete dynamic system with fading memory.

关键词： identification non-linear systems estimation theory piecewise linear functions set membership estimation theory Wiener modelling block oriented models orthonormal basis functions Kautz functions Laguerre functions HLCPWL functions

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