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interval arithmetic and Its Application to Electrical Circuits

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Computer Technology and Application 2013年第8期4卷 424-430页

作者： Nacira Diffellah Fouzia Hamadache Khier Benmahammed Department of Electronic Faculty of Science and Technology University of Bordj Bou Arreridj 34000 Algeria LSI Intelligent Systems Laboratory Setif l 9000 Algeria Department of Electronic Faculty of Science and Technology University of Setif l 9000 Algeria

interval arithmetic is an elegant tool for practical work with inequalities, approximate numbers, error bounds, and more generally with certain convex and bounded sets. In this section we give a number of simple examples showing where intervals and ranges of functions over intervals arise naturally. interval mathematics is a generalization in which interval numbers replace real numbers, interval arithmetic replaces real arithmetic, and interval analysis replaces real analysis. interval is limited by two bounds： lower bound and upper bound. The present paper introduces some of the basic notions and techniques from interval analysis needed in the sequel for presenting various uses of interval analysis in electric circuit theory and its applications. In this article we address the representation of uncertain and imprecise information, the interval arithmetic and its application to electrical circuits.

关键词： interval arithmetic linear system uncertain information propagation of uncertainties information.

Applications of interval arithmetic in solving polynomial equations by Wu's elimination method

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Science China Mathematics 2005年第9期 110-123页

作者： CHEN Falai & YANG Wu Department of Mathematics,University of Science and Technology of China,Hefei 230026,China

Wu’s elimination method is an important method for solving multivariate poly- nomial *** this paper,we apply interval arithmetic to Wu’s method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- *** results such as zero-decomposition theorem are obtained for interval poly- nomial *** advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely ***, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically *** examples are provided to illustrate the effectiveness of the proposed algorithm.

关键词： mathematical mechanization Wu’s method polynomial equation interval arithmetic

A Fault Isolation Method Using interval arithmetic for Nonlinear Dynamic Systems

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A Fault Isolation Method Using Interval Arithmetic for Nonli...

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

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作者： Boutaieb Dahhou Boutaieb Dahhou CNRS LAAS Universite′ de Toulouse UPS INSA INP ISAE UT1 UTM LAAS

In this work interval arithmetic is used for the calculation of interval envelopes in the parameter interval based fault isolation method. Thanks the advantage of interval arithmetic of without dependence on the monotonic of model parameters, the application of the parameter interval based fault isolation method can be extended to multi-parameters fault.

关键词： Fault Isolation Parameter interval interval arithmetic Multi-Parameters Fault

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Acta Mechanica Sinica 2016年第1期32卷 170-180页

作者： Zhuang-Zhuang Liu Tian-ShuWang Jun-Feng Li School of Aerospace Tsinghua University

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

关键词： Non-intrusive hybrid interval method Dynamic response analysis Uncertain nonlinear systems Polynomial approximation interval arithmetic Derivative information

A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

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Science China(Physics,Mechanics & Astronomy) 2015年第4期58卷 45-57页

作者： LIU ZhuangZhuang WANG TianShu LI JunFeng School of Aerospace Tsinghua University

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial *** method provides tighter solution ranges compared to the existing approximation interval *** consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine ***,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval *** interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval ***,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.

关键词： non-intrusive interval method dynamic response analysis uncertain nonlinear systems trigonometric polynomial ap-proximation interval arithmetic

A Reliable and Accurate Calculation of Excitation Capacitance Value for an Induction Generator Based on interval Computation Technique

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International Journal of Automation and computing 2011年第4期8卷 429-436页

作者： Rajesh Kumar Thakur Vivek Agarwal Paluri S. V. Nataraj Systems and Control Engineering Interdisciplinary Programme (IDP)Mumbai 400076 India Department of Electrical Engineering IIT-Bombay Powai Mumbai 400076 India

A squirrel cage induction generator （SCIG） offers many advantages for wind energy conversion systems but suffers from poor voltage regulation under varying operating conditions. The value of excitation capacitance （C exct ） is very crucial for the selfexcitation and voltage build-up as well as voltage regulation in SCIG. Precise calculation of the value of C exct is, therefore, of considerable practical importance. Most of the existing calculation methods make use of the steady-state model of the SCIG in conjunction with some numerical iterative method to determine the minimum value of C exct . But this results in over estimation, leading to poor transient dynamics. This paper presents a novel method, which can precisely calculate the value of C exct by taking into account the behavior of the magnetizing inductance during saturation. interval analysis has been used to solve the equations. In the proposed method, a range of magnetizing inductance values in the saturation region are included in the calculation of C exct , required for the self-excitation of a 3-φ induction generator. Mathematical analysis to derive the basic equation and application of interval method is presented. The method also yields the magnetizing inductance value in the saturation region which corresponds to an optimum C exct（min） value. The proposed method is experimentally tested for a 1.1 kW induction generator and has shown improved results.

关键词： d-q model hull consistency induction generator interval analysis interval arithmetic optimization range of interval realpaver self-excitation transients.

Hybrid method for global optimization using more accuracy interval computation

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Journal of Shanghai University(English Edition) 2011年第5期15卷 445-450页

作者：崔中浩雷咏梅 School of Computer Engineering and Science Shanghai University

In this paper, a novel hybrid method is presented for finding global optimization of an objective function. Based on the interval computation, this hybrid method combines interval deterministic method and stochastic evolution method. It can find global optimization quickly while ensuring the deterministic and stability of the algorithm. When using interval computation, extra width constraints accuracy of interval computation results. In this paper, a splitting method to reduce the extra width is introduced. This method is easy and it can get a more precise interval computation result. When finding the global optimization, it can increase the efficiency of pruning. Several experiments are given to illustrate the advantage of the new hybrid method.

关键词： interval arithmetic global optimization interval computation extra width hybrid method

Numerical Robust Stability Estimation in Milling Process

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Chinese Journal of Mechanical Engineering 2012年第5期25卷 953-959页

作者： ZHANG Xiaoming ZHU Limin DING Han XIONG Youlun State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Shanghai 200240 China

The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment, In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.

关键词： robust stability estimation sensitivity analysis interval arithmetic decision making

Driving force planning in shield tunneling based on Markov decision processes

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Science China(Technological Sciences) 2012年第4期55卷 1022-1030页

作者： HU XiangTao HUANG YongAn YIN ZhouPing XIONG YouLun State Key Laboratory of Digital Manufacturing Equipment&Technology Huazhong University of Science&TechnologyWuhan 430074China

In shield tunneling, the control system needs very reliable capability of deviation rectifying in order to ensure that the tunnel trajectory meets the permissible criterion. To this goal, we present an approach that adopts Markov decision process (MDP) theory to plan the driving force with explicit representation of the uncertainty during excavation. The shield attitudes of possi- ble world and driving forces during excavation are scattered as a state set and an action set, respectively. In particular, an evaluation function is proposed with consideration of the stability of driving force and the deviation of shield attitude. Unlike the deterministic approach, the driving forces based on MDP model lead to an uncertain effect and the attitude is known only with an imprecise probability. We consider the case that the transition probability varies in a given domain estimated by field data, and discuss the optimal policy based on the interval arithmetic. The validity of the approach is discussed by comparing the driving force planning with the actual operating data from the field records of Line 9 in Tianjin. It is proved that the MDP model is reasonable enough to predict the driving force for automatic deviation rectifying.

关键词： shield tunneling Markov decision process automatic deviation rectifying interval arithmetic driving force planning