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A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

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Defence Technology（防务技术） 2019年第5期15卷 741-757页

作者： C.A.Rabbath D.Corriveau Defence R&D Canada Valcartier Research Centre

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

关键词： Aerodynamic coefficients piecewise polynomial functions Cubic splines Curve fitting piecewise linear functions piecewise cubic Hermite interpolating polynomial Projectile modelling and simulation Fire control inputs Precision Ballistic computer software

Method of Hill Tunneling via Weighted Simplex Centroid for Continuous piecewise Linear Programming

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Tsinghua Science and Technology 2019年第3期24卷 301-316页

作者： Zhiming Xu Yu Bai Kuangyu Liu Shuning Wang the National Laboratory for Information Science and Technology Department of Automation Tsinghua University Faculty of Air Force Engineering University

This paper works on a heuristic algorithm with determinacy for the global optimization of Continuous piecewise Linear(CPWL) programming. The widely applied CPWL programming can be equivalently transformed into D.C. programming and concave optimization over a polyhedron. Considering that the super-level sets of concave piecewise linear functions are polyhedra, we propose the Hill Tunneling via Weighted Simplex Centroid(HTWSC) algorithm, which can escape a local optimum to reach the other side of its contour surface by cutting across the super-level set. The searching path for hill tunneling is established via the weighted centroid of a constructed simplex. In the numerical experiments, different weighting methods are studied first, and the best is chosen for the proposed HTWSC algorithm. Then, the HTWSC algorithm is compared with the hill detouring method and the software CPLEX for the equivalent mixed integer programming, with results indicating its superior performance in terms of numerical efficiency and the global search capability.

关键词： global optimization piecewise linear concave minimization cutting plane method hill tunneling

Determination of pKa values of alendronate sodium in aqueous solution by piecewise linear regression based on acid-base potentiometric titration

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Journal of Pharmaceutical Analysis 2016年第6期6卷 404-409页

作者： Jing Ke Hanfei Dou Ximin Zhang Dushimabararezi Serge Uhagaze Xiali Ding Yuming Dong Institute of Pharmaceutical Analysis School of PharmacyLanzhou University Key Laboratory of Gansu Province Chinese Medicine Preparation of Solid Dispersion Gansu longshenrongfa Pharmaceutical Industry Co.Ltd.

As a mono-sodium salt form of alendronic acid,alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups.The dissociation constants of alendronate sodium were determined in this work by studying the piecewise linear relationship between volume of titrant and p H value based on acidbase potentiometric titration reaction.The distribution curves of alendronate sodium were drawn according to the determined p Ka values.There were 4 dissociation constants(pKa_1=2.43,pKa_2=7.55,pKa_3=10.80,pKa_4=11.99,respectively) of alendronate sodium,and 12 existing forms,of which 4 could be ignored,existing in different p H environments.

关键词： Dissociation constants Alendronate sodium Distribution curve piecewise linear regression Acid-base potentiometric titration

A piecewise Linear Isotropic-Kinematic Hardening Model with Semi-Implicit Rules for Cyclic Loading and Its Parameter Identification

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Computer Modeling in Engineering & Sciences 2016年第4期111卷 303-333页

作者： M.Ohsaki T.Miyamura J.Y.Zhang Department of Architecture and Architectural Engineering Kyoto UniversityKyoto-Daigaku KatsuraNishikyoKyoto 615-8540Japan Department of Computer Science Nihon University1 NakagawaraTokusadaTamuraKoriyama 963-8642Japan Department of Architecture and Urban Design Nagoya City University2-1-10 Kita-ChigusaChigusaNagoya 464-0083Japan

A simple constitutive model,called semi-implicit model,for cyclic loading is proposed for steel materials used for structures such as building frames in civil engineering.The constitutive model is implemented in the E-Simulator,which is a software package for large-scale seismic response analysis.The constitutive relation is defined in an algorithmic manner based on the piecewise linear combined isotropic-kinematic hardening.Different rules are used for the first and subsequent loading states to incorporate characteristics such as yield plateau and Bauschinger effect of rolled mild steel materials.An optimization method is also presented for parameter identification from the results of cyclic and monotonic loading tests.Therefore,the proposed model is readily applicable to practical elastoplastic analysis of building frames.Accuracy of the model is demonstrated in an example of a cantilever subjected to various types of cyclic loading.

关键词： Combined isotropic-kinematic hardening piecewise linear hardening Steel material Parameter optimization Cyclic load

piecewise算法计算超越函数及其FPGA实现

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核电子学与探测技术 2010年第6期30卷 755-758,770页

作者：杨阳王永纲都军伟物理电子学安徽省重点实验室中国科学技术大学近代物理系安徽合肥230026

使用分段逼近(piecewise approximation)算法计算超越函数,以神经网络中最常用的双曲正切型(tanh)传输函数为例来分析逼近精度同分段数、有限字长之间的关系,并给出如何最优地选取分段数和字长来达到所需的精度。还在FPGA上硬件实现了基... 详细信息

使用分段逼近(piecewise approximation)算法计算超越函数,以神经网络中最常用的双曲正切型(tanh)传输函数为例来分析逼近精度同分段数、有限字长之间的关系,并给出如何最优地选取分段数和字长来达到所需的精度。还在FPGA上硬件实现了基于piecewise算法来计算tanh函数,并且比较了几种piecewise approximation算法以及其它常见硬件算法(如CORDIC,Look-up table)的资源消耗和速度。

关键词： piecewise tanh FPGA

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

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Control Theory and Technology 2019年第1期17卷 99-111页

作者： Meng WANG Jianbin QIU Gang FENG Department of Biomedical Engineering City University of Hong Kong Kowloon Hong Kong China State Key Laboratory of Robotics and Systems & Research Institute of Intelligent Control and Systems Harbin Institute of Technology Harbin Heilongjiang 150080 China

This paper investigates the problem of event-triggered H∞state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed H∞performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler's lemma, the event-triggered H∞observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the event-triggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.

关键词： Takagi-Sugeno (T-S) fuzzy affine systems event-triggered scheme, piecewise Lyapunov-Krasovskii functional, state estimation

Exponential change of measure for general piecewise deterministic Markov processes

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Science China Mathematics 2019年第4期62卷 719-734页

作者： Zhaoyang Liu Yuying Liu Guoxin Liu School of Mathematics and Statistics Central South University Department of Mathematics and Physics Shijiazhuang Tiedao University

We consider a general piecewise deterministic Markov process(PDMP) X = {X_t}_(t≥0) with a measure-valued generator A, for which the conditional distribution function of the inter-occurrence time is not necessarily absolutely continuous. A general form of the exponential martingales that are associated with X is given by■By considering this exponential martingale to be a likelihood-ratio process, we define a new probability measure and show that the process X is still a general PDMP under the new probability measure. We additionally find the new measure-valued generator and its domain. To illustrate our results, we investigate the continuous-time compound binomial model.

关键词： exponential change of measure piecewise deterministic Markov process measure-valued generator Stieltjes exponential

Nonlinear System Monitoring with piecewise Performed Principal Component Analysis

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Nonlinear System Monitoring with Piecewise Performed Princip...

Bifurcations and Chaotic Dynamics of a piecewise Smooth Linear System

第36届中国控制会议

作者： LUO Xianxi Shuhui Li LIU Guoquan XU Menghua WANG Wei Jiangxi Province Engineering Research Center of New Energy Technology and Equipment(East China University of Technology) Electrical and Computer Engineering Department The University of Alabama

ISBN: (纸本)9781538629185

An innovated method of piecewise performed principal analysis（PCA） is proposed to monitor a nonlinear system in this article.By analyzing the highest concerned variable and critical influence variables distribution through the collected data,we separate the variable space into smaller sections and perform PCA for each section to derive the PCA model.The process is momtored by applying the new data to the model for the section in which the data locates.To demonstrate the performance,the method is applied for the monitoring of single steam pipe in a steam pipe network of an iron＆ steel plants.The simulation result shows the proposed method is effective and sensitive to the faults.

关键词： Nonlinear System Monitoring piecewise PCA

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Bifurcations and Chaotic Dynamics of a Piecewise Smooth Line...