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ON RATIONAL interpolation WITH POSITIVITY CONSTRAINTS

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 1991年第4期10卷 471-483页

作者： LEPSCHY, A MIAN, GA VIARO, U 1. Department of Electronics and Informatics University of Padova Via Gradenigo 6/A 35131 Padova Italy

The problem of interpolating a given set of points by means of a squared magnitude rational function of minimal degree is considered. In this way, the resulting interpolating function can be factorized to yield a stable and minimum-phase transference. It is shown that in the polynomial case a nonnegative solution is easily obtained by adding to the standard Hermite interpolation polynomial a suitable term of immediately higher degree. Concerning the general rational case, a computationally efficient procedure, based on a Hermite-type parametrization, is suggested. The positivity requirement may again be met by inserting suitable terms in the numerator and denominator polynomials. An example is worked out to show the practicality of the method.

关键词： rational interpolation Denominator Constraint Polynomial Numerator rational functions interpolation function Set of points interpolation

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Vibration of stiffened plates using hierarchical trigonometric functions

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JOURNAL OF SOUND AND VIBRATION 2000年第5期235卷 727-747页

作者： Barrette, M Berry, A Beslin, O Univ Sherbrooke Dept Mech Engn GAUS Sherbrooke PQ J1K 2R1 Canada

The vibration analysis of stiffened plates using hierarchical finite elements with a set of local trigonometric interpolation functions is presented. The local functions extend on the plate domain comprised between consecutive stiffeners, thereby allowing a coarse discretization of the global structure. Convergence studies as well as comparison of the present approach with the literature and experimental results are presented. The great numerical stability of the trigonometric functions and their readiness for symbolic manipulations make them potentially attractive for vibration and sound radiation analysis in the mid-frequency range. (C) 2000 Academic Press.

关键词： RADIATION ANALYSIS Vibration Vibration analysis Acoustic radiation global structures Trigonometry Stiffened plates Circular functions Readiness Medium frequency interpolation function Numerical stability

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interpolation representations of fuzzy logic systems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2003年第10-11期45卷 1683-1693页

作者： Li, HX Lee, ES Kansas State Univ Dept Ind & Mfg Syst Engn Manhattan KS 66506 USA Tsing Hua Univ Dept Automat Beijing 100084 Peoples R China

interpolation functions, which can represent fuzzy logic system (FLS) models, are investigated. Since interpolation is a basic tool for function approximation and since FLS has been shown to be a function approximator, interpolation functions can be established for these models. To establish and to explore these interpolations, some features, which are regarded as basic conditions on interpolation of FLS, are first introduced. Then, several interpolation functions of the frequently used FLS models are established and proved. Finally, a general model is suggested based on the results. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： fuzzy logic system fuzzy inference rule interpolation function base function interpolation representation

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Three types of meshless finite volume method for the analysis of two-dimensional elasticity problems

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COMPUTATIONAL & APPLIED MATHEMATICS 2017年第2期36卷 971-990页

作者： Ebrahimnejad, M. Fallah, N. Khoei, A. R. Univ Guilan Dept Civil Engn Rasht Iran Sharif Univ Technol Dept Civil Engn Tehran Iran

This paper presents three schemes of 2D meshless finite volume (MFV) method, referred to as MFV with overlapping control volumes (MFV1), MFV with irregular non-overlapping control volumes (MFV2) and MFV with regular non-overlapping control volumes (MFV3). The methods utilize the local symmetric weak form of system equation and the interpolation functions constructed using the weighted multi-triangles method (WMTM) which is recently developed by the present authors. The proposed formulation involves only integrals over the boundaries of control volumes. The performance of the proposed schemes is studied in three benchmark problems. A comparative study between the predictions of the above MFV schemes and finite element method (FEM) shows the superiority of WMTM-based MFV1 and MFV2 over FEM.

关键词： Finite volume method Meshless methods Control volume (CV) interpolation function

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Preservation of oscillations of the Runge-Kutta method for equation x′(t) plus ax(t) plus a₁x([t-1])=0

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2009年第6期58卷 1113-1125页

作者： Liu, M. Z. Gao, J. F. Yang, Z. W. Harbin Inst Technol Dept Math Harbin 150001 Peoples R China Harbin Normal Univ Sch Math Sci Harbin 150025 Peoples R China Harbin Inst Technol Acad Fundamental & Interdisciplinary Sci Ctr Sci Res Harbin 150001 Peoples R China

The paper deals with the preservation of oscillations of the Runge-Kutta method for equation x'(t)+ax(t)+a(1)x([t- 1]) = 0. It is proved that oscillations of the analytic solution are preserved by the Runge-Kutta method. Special interpolation functions of the numerical solutions are given. It turns out that zeros of the interpolation function of the numerical solution converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge-Kutta method. Some numerical experiments are presented. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Oscillation Numerical solution Delay differential equation Piecewise constant interpolation function

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EMPIRICAL MODELING END RESPONSE SURFACES FOR ELECTROLESS CO DEPOSITION PROCESS

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JOURNAL OF THE ELECTROCHEMICAL SOCIETY 1995年第5期142卷 1495-1500页

作者： PAUNOVIC, M NGUYEN, T MUKHERJEE, R SAMBUCETTI, C ROMANKIW, LT IBM CORP DIV STORAGE SYSTSAN JOSECA 95113

The electroless deposition process was studied by statistical techniques. Two types of experiments were designed: the two-factor two-level factorial and the central composite rotatable five-factor five-level experiments. The two-factor factorial experiments were used to determine the effect of each individual variable and interactions between variables. It was concluded from the analysis of data that (i) the most significant factors are citrate, the Co2+ complexing agent, pH, and temperature;and (ii) the most significant interactions are pH-citrate and pH-hypophosphite interactions. The central composite rotatable experiments were used to construct the second-order empirical model for the relationship between the Co deposition rate and five independent variables. The interpolation polynomial had 21 coefficients. The interpolation function was used to construct the 3-D response surfaces and 2-D response contours. Two types of response surfaces were found: simple maximum and rising ridge. The interpolation polynomial was used also to optimize the Co deposition process with respect to the minimized variability.

关键词： Copper deposition rotation CODEPOSITION interpolation function response surface interpolation DEPOSITION (PROCESS)

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An efficient method to reduce ill-posedness for structural dynamic load identification

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2017年 95卷 273-285页

作者： Liu, Jie Meng, Xianghua Zhang, Dequan Jiang, Chao Han, Xu Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

For the inverse problem of structural dynamic load identification, high system illposedness is a main cause leading to instability and low accuracy. In this study, an efficient interpolation-based method is proposed to reduce ill-posedness availably and identify dynamic load stably. The load history is discretized into a series of time elements, and the load profile in each time element is approximated through interpolation functions. Then, in the whole time domain, the dynamic responses under interpolation function loads are calculated through a few finite element analysis and then assembled together to form a global kernel function matrix for load identification. Using singular value decomposition (SVD), the ill-posed degree of the global kernel function matrix can be analyzed. Compared with the conventional Green kernel function method (GKFM), the illposedness of global kernel function matrix in the proposed method is significantly reduced. Especially, when the length of time element is selected appropriately, the global kernel function matrix is entirely well-posed and the corresponding dynamic load can be stably identified without any regularization operation. Numerical examples demonstrate the effectiveness of the proposed method and the correctness of identified load. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Load identification Ill-posedness interpolation function Time element Singular value decomposition

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A Lagrangian finite element model for estimating the heating and cooling demand of a residential building with a different envelope design

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APPLIED ENERGY 2015年 142卷 66-79页

作者： Seo, Dong-yeon Koo, Choongwan Hong, Taehoon Incheon Natl Univ Div Architecture & Urban Design Inchon 406772 South Korea Yonsei Univ Dept Architectural Engn Seoul 120749 South Korea

It is important for an architect or a construction manager to easily and accurately estimate the heating and cooling demand of a residential building with a different envelope design in the early design phase. To achieve this objective, this study aimed to develop a nine-node-based Lagrangian finite element model for estimating the heating and cooling demand of a residential building with a different envelope design, which can be useful for an architect or a construction manager in the early design phase. This study was conducted in the following steps: (i) definition of the building envelope design elements;(ii) establishment of a standard database through energy simulation;and (iii) development of a Lagrangian finite element model. The prediction performance of the proposed nine-node-based model was improved in comparison with the four-node-based model. It was concluded that the prediction performance of the proposed nine-node-based model was superior to that of the four-node-based model. For the heating demand, RMSE(9-node, heating) (61.2), MAE((9-node, heating)) (45.1), and MAPE((9-node, heating)) (1.18%) of the proposed nine-node-based model was lower than that of the four-node-based model (73.9, 53.2, and 1.36%). For the cooling demand, RMSE(9-node, cooling) (71.5), MAE((9-node, cooling)) (55.3), and MAPE((9-node, cooling)) (8.24%) of the proposed nine-node-based model was lower than that of the four-node-based model (84.1, 61.1, and 8.71%). The series of processes used in this study could be applied to any other energy-saving technique or to a new/renewable energy system. It could also be extended to any other country or sector in the global environment. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Building envelope design Heating and cooling demand Finite element method Shape function interpolation function Energy simulation

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A NEW interpolation THEOREM WITH APPLICATION TO PULSE TRANSMISSION

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IEEE TRANSACTIONS ON COMMUNICATIONS 1991年第10期39卷 1438-1444页

作者： LECHLEIDER, JW Bellcore Morristown NJ USA

An interpolation theorem is determined for the case when there are a finite number of arbitrarily placed sampling instants and the interpolation function is output of a known filter. They are also the interpolation functions with the specified properties that have minimum energy. The theorem is used to determine of the input to a communications channel given a finite number of samples of its output. This provides a generalization of matched filters and a new perspective on the benefits of fractionally spaced equalization. The theorem is also used to construct masks of a family of pulses that are specified by the range of pulse voltages at a finite number of sampling instants. The theory determines how the pulse mask thus constructed is transformed when the pulse family is transmitted through a filter such as a length of transmission line.

关键词： Random number sampling Vital Signs interpolation matched filters Filters interpolation function Finite Theorem Sampling Transmission Lines Pulse transmission

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A mesh-free minimum length method for 2-D problems

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COMPUTATIONAL MECHANICS 2006年第6期38卷 533-550页

作者： Liu, G. R. Dai, K. Y. Han, X. Li, Y. Natl Univ Singapore Dept Mech Engn Ctr ACES Singapore 119260 Singapore Hunan Univ Coll Mech & Automobile Engn Changsha 410082 Peoples R China

A mesh-free minimum length method (MLM) has been proposed for 2-D solids and heat conduction problems. In this method, both polynomials as well as modified radial basis functions (RBFs) are used to construct shape functions for arbitrarily distributed nodes based on minimum length procedure, which possess Kronecker delta property. The shape functions are then used to formulate a mesh-free method based on weak-form formulation. Both Gauss integration (GI) and stabilized nodal integration (NI) are employed to numerically evaluate Galerkin weak form. The numerical examples show that the MLM achieves better accuracy than the 4-node finite elements especially for problems with steep gradients. The method is easy to implement and works well for irregularly distributed nodes. Some numerical implementation issues for MLM are also discussed in detail.

关键词： mesh-free method meshless method minimum length method radial basis function (RBF) interpolation function

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