scholarly journals A Modification of Gustavsen and Semlyen’s vector fitting algorithm for overestimated model order

2021 ◽  
Author(s):  
Andrew Mackay
Keyword(s):  
Control Parameter ◽  
Infinite Order ◽  
Null Space ◽  
Original Function ◽  
Model Order ◽  
Vector Fitting ◽  
Fitting Algorithm ◽  
Improve Accuracy ◽  
Space Method

Gustavsen and Semlyen’s vector fitting algorithm (VFA) is popular for the determination of the poles and residues of a sampled response function, modeled as a finite order rational function. However, it does not always perform well when the original function is of infinite order and/or the model order is overestimated. This article is concerned with a novel “null-space” modification of the VFA that provides an accurate representation of the original function when the model order is large and when the original VFA performs poorly. The null-space method is parameterized by a single control parameter, L, which can be adjusted to improve accuracy. Comparisons are made with the original VFA and another of Gustavsen’s modifications

scholarly journals A Modification of Gustavsen and Semlyen’s vector fitting algorithm for overestimated model order

2021 ◽  
Author(s):  
Andrew Mackay
Keyword(s):  
Control Parameter ◽  
Infinite Order ◽  
Null Space ◽  
Original Function ◽  
Model Order ◽  
Vector Fitting ◽  
Fitting Algorithm ◽  
Improve Accuracy ◽  
Space Method

Gustavsen and Semlyen’s vector fitting algorithm (VFA) is popular for the determination of the poles and residues of a sampled response function, modeled as a finite order rational function. However, it does not always perform well when the original function is of infinite order and/or the model order is overestimated. This article is concerned with a novel “null-space” modification of the VFA that provides an accurate representation of the original function when the model order is large and when the original VFA performs poorly. The null-space method is parameterized by a single control parameter, L, which can be adjusted to improve accuracy. Comparisons are made with the original VFA and another of Gustavsen’s modifications

Analytic Determination of Wrench Closure Workspace of Spatial Cable Driven Parallel Mechanisms

2015 ◽  
Author(s):  
Zhiyu Sheng ◽  
Joon-Hyuk Park ◽  
Paul Stegall ◽  
Sunil K. Agrawal
Keyword(s):  
Simulation Study ◽  
Null Space ◽  
Boundary Surface ◽  
Parallel Mechanisms ◽  
Analytic Determination ◽  
Structure Matrix ◽  
Feasible Solutions

This paper proposes an efficient way of determining analytically the Wrench Closure Workspace (WCW) of spatial redundant cable-driven parallel mechanisms (CDPM). The method builds upon the boundary surface equations obtained from the null space of the structure matrix of CDPM. The set of feasible solutions is obtained that satisfies positive tension in the cables. This method was applied to characterize the WCW of spatial CDPM which has redundancy of 1 or 2. A simulation study was carried out to validate the accuracy and efficiency of the method. Several advantages over conventional approaches for determining the WCW were identified through simulation.

Time-Differentiable Null Space Method for Constrained Mechanical Systems (Application to a Rheonomic System)

2013 ◽  
Author(s):  
Keisuke Kamiya
Keyword(s):  
Lagrange Multipliers ◽  
Null Space ◽  
Constraint Equation ◽  
Coefficient Matrix ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Accurate Analysis ◽  
Constrained Mechanical Systems ◽  
Space Matrix ◽  
Space Method

The governing equations of multibody systems are, in general, formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. For efficient and accurate analysis, it is desirable to eliminate the Lagrange multipliers and dependent variables. Methods called null space method and Maggi’s method eliminate the Lagrange multipliers by using the null space matrix for the coefficient matrix which appears in the constraint equation in velocity level. In a previous report, the author presented a method to obtain a time differentiable null space matrix for scleronomic systems, whose constraint does not depend on time explicitly. In this report, the method is generalized to rheonomic systems, whose constraint depends on time explicitly. Finally, the presented method is applied to four-bar linkages.

scholarly journals Multivariate Distributions in Hydrology and River Regulation

1976 ◽  
Vol 7 (5) ◽  
pp. 265-280
Author(s):  
N.A. Kartvelishvili ◽  
L.T. Gottschalk
Keyword(s):  
Markov Process ◽  
Finite Difference ◽  
Difference Scheme ◽  
River Runoff ◽  
Finite Difference Scheme ◽  
River Regulation ◽  
Distribution Functions ◽  
Multivariate Distributions ◽  
Model Order

It is assumed that the river runoff process can be approximated by a Markov process. The process is thus described by M distribution functions: Fn (qt, t ; qt-1; t-1;…;qt-n, t-n), t ≡ 1, 2, …, M where M is the number of time intervals within the year, n - the order of the Markov process and qt, in general, is a vector representing runoff at several sites in a river or neighbouring rivers. Fundamental hypothesis of relations between multivariate distributions and corresponding marginal distributions is given. A finite difference scheme for multisite and multilag generation of river runoff is derived. The derivation is based on the multivariate normal distribution. Different methods for determination of the order of the finite difference scheme are discussed as well as the influence of model order and method of parameter estimation on properties of the model.

Sign in / Sign up

Export Citation Format

Share Document