On-Line Least-Squares Method of Estimating the Coefficients of the Orthogonal-Polynomial Expansion of a Function

Traditional methods for stiffness analysis of the air spring are based on deterministic assumption that the parameters are fixed. However, uncertainties have widely existed, and the mechanic property of the air spring is very sensitive to these uncertainties. To model the uncertainties in the air spring, the interval/random variables models are introduced. For response analysis of the interval/random variables models of the air spring system, a new unified orthogonal polynomial expansion method, named as sparse quadrature-based interval and random moment arbitrary polynomial chaos method (SQ-IRMAPC), is proposed. In SQ-IRMAPC, the response of the acoustic system related to both interval and random variables is approximated by the moment-based arbitrary orthogonal polynomial expansion. To efficiently calculate the coefficient of the interval and random orthogonal polynomial expansion, the sparse quadrature is introduced. The proposed SQ-IRMAPC was employed to analyze the mechanic performance of an air spring with interval and/or random variables, and its effectiveness has been demonstrated by fully comparing it with the most recently proposed orthogonal polynomial-based interval and random analysis method.

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Orthogonal polynomial expansion of the spectral density operator and the calculation of bound state energies and eigenfunctions

Chemical Physics Letters ◽

10.1016/0009-2614(93)e1345-h ◽

1994 ◽

Vol 217 (1-2) ◽

pp. 73-79 ◽

Cited By ~ 89

Author(s):

Wei Zhu ◽

Youhong Huang ◽

D.J. Kouri ◽

Colston Chandler ◽

David K. Hoffman

Keyword(s):

Spectral Density ◽

Orthogonal Polynomial ◽

Density Operator ◽

Bound State ◽

Polynomial Expansion ◽

Orthogonal Polynomial Expansion

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Adaptive predistortion linearization based on orthogonal polynomial expansion for nonlinear power amplifiers in OFDM systems

2011 International Conference on Communications and Signal Processing ◽

10.1109/iccsp.2011.5739374 ◽

2011 ◽

Cited By ~ 1

Author(s):

Osamu Muta ◽

Isamu Kaneko ◽

Yoshihiko Akaiwa ◽

Hiroshi Furukawa

Keyword(s):

Orthogonal Polynomial ◽

Power Amplifiers ◽

Polynomial Expansion ◽

Ofdm Systems ◽

Orthogonal Polynomial Expansion ◽

Predistortion Linearization ◽

Adaptive Predistortion

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A Three-Dimensional Generalization of Reuleaux’s Method Based on Line Geometry

Volume 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2006-99153 ◽

2006 ◽

Cited By ~ 2

Author(s):

Jasem Baroon ◽

Bahram Ravani

Keyword(s):

Rigid Body ◽

Least Squares ◽

Least Squares Method ◽

Three Dimensional ◽

Line Geometry ◽

Basic Form ◽

Motion Reconstruction ◽

Linear Solution ◽

On Line

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much if not all of the previous work in this area has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. An elegant geometric method is developed based on line geometry that can be considered as a generalization of the classical Reuleaux’s method used in 2D kinematics. The case of over determined system is also considered a linear solution is presented based on least squares method.

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