scholarly journals On the accuracy and convergence of the hybrid FE-meshfree Q4-CNS element in surface fitting problems

2018 ◽  
Vol 147 ◽  
pp. 01002
Author(s):  
Foek Tjong Wong ◽  
Richo Soetanto ◽  
Januar Budiman
Keyword(s):  
Convergence Rates ◽  
Least Squares Method ◽  
Hybrid Methods ◽  
Numerical Study ◽  
Surface Fitting ◽  
Shape Functions ◽  
Distorted Mesh ◽  
Gradient Fields ◽  
Elasticity Problems ◽  
Better Than

In the last decade, several hybrid methods combining the finite element and meshfree methods have been proposed for solving elasticity problems. Among these methods, a novel quadrilateral four-node element with continuous nodal stress (Q4-CNS) is of our interest. In this method, the shape functions are constructed using the combination of the ‘non-conforming’ shape functions for the Kirchhoff’s plate rectangular element and the shape functions obtained using an orthonormalized and constrained least-squares method. The key advantage of the Q4-CNS element is that it provides the continuity of the gradients at the element nodes so that the global gradient fields are smooth and highly accurate. This paper presents a numerical study on the accuracy and convergence of the Q4-CNS interpolation and its gradients in surface fitting problems. Several functions of two variables were employed to examine the accuracy and convergence. Furthermore, the consistency property of the Q4-CNS interpolation was also examined. The results show that the Q4-CNS interpolation possess a bi-linier order of consistency even in a distorted mesh. The Q4-CNS gives highly accurate surface fittings and possess excellent convergence characteristics. The accuracy and convergence rates are better than those of the standard Q4 element.

scholarly journals Semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices

2021 ◽  
Author(s):  
Hongxia Wang ◽  
Xuehong Luo ◽  
Long Ling
Keyword(s):  
Convergence Rates ◽  
Least Squares Method ◽  
Linear Method ◽  
Trend Function ◽  
Autoregressive Coefficient ◽  
New Class ◽  
Temporal Models ◽  
Local Linear Method ◽  
Spatio Temporal ◽  
Better Than

We consider a new class of semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule-Walker equation to estimate trend function and spatio-temporal autoregressive coefficient matrices respectively. We also balance the over-determined and under-determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. The proposed methods are further illustrated using both simulation and case studies, the results also show that our estimator is stable among different sample size, and it performs better than the traditional method with known spatial weight matrices.

scholarly journals Reinforcement learning versus swarm intelligence for autonomous multi-HAPS coordination

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Ogbonnaya Anicho ◽  
Philip B. Charlesworth ◽  
Gurvinder S. Baicher ◽  
Atulya K. Nagar
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Swarm Intelligence ◽  
Performance Indicators ◽  
Convergence Rates ◽  
Tuning Parameters ◽  
Continuous State Space ◽  
Continuous State ◽  
User Coverage ◽  
Better Than

AbstractThis work analyses the performance of Reinforcement Learning (RL) versus Swarm Intelligence (SI) for coordinating multiple unmanned High Altitude Platform Stations (HAPS) for communications area coverage. It builds upon previous work which looked at various elements of both algorithms. The main aim of this paper is to address the continuous state-space challenge within this work by using partitioning to manage the high dimensionality problem. This enabled comparing the performance of the classical cases of both RL and SI establishing a baseline for future comparisons of improved versions. From previous work, SI was observed to perform better across various key performance indicators. However, after tuning parameters and empirically choosing suitable partitioning ratio for the RL state space, it was observed that the SI algorithm still maintained superior coordination capability by achieving higher mean overall user coverage (about 20% better than the RL algorithm), in addition to faster convergence rates. Though the RL technique showed better average peak user coverage, the unpredictable coverage dip was a key weakness, making SI a more suitable algorithm within the context of this work.

scholarly journals On the optimal control force applied to tuned mass dampers for multi-degree-of-freedom systems

2004 ◽  
Vol 26 (1) ◽  
pp. 1-10
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Chi Sang
Keyword(s):  
Optimal Control ◽  
Numerical Study ◽  
Degree Of Freedom ◽  
Control Force ◽  
Linear Quadratic ◽  
Tuned Mass Dampers ◽  
Coloured Noise ◽  
Optimal Theory ◽  
The One ◽  
Better Than

The design of active TMD for multi-degree-of-freedom systems subjected to second order coloured noise excitation is considered using the linear quadratic optimal theory. A detailed numerical study is carried out for a 2-DOF system. It is shown that the effectiveness of active TMD is better than the one of passive TMD.

scholarly journals A numerical study for convection in a cylindrical model with continuously varying viscosity

1996 ◽  
Vol 39 (3) ◽  
Author(s):  
F. Fanucci ◽  
A. Megna ◽  
S. Santini ◽  
F. Vetrano
Keyword(s):  
Viscosity Solutions ◽  
Numerical Study ◽  
Viscosity Coefficient ◽  
Cylindrical Symmetry ◽  
The Earth ◽  
Realistic Representation ◽  
Convective Motions ◽  
Constant Viscosity ◽  
Varying Viscosity ◽  
Better Than

In the framework of a cylindrical symmetry model for convective motions in the asthenosphere, a new profile for the viscosity coefficient depending on depth is suggested here. The numerical elaboration of the above mentioned model leads to interesting results which fit well with experimental observations. In particular these continuously varying viscosity solutions probably describe the convective motions within the Earth better than simple constant viscosity solutions. Consequently the temperature values seem to be a realistic representation of the possible thermal behaviour in the upper mantle.

scholarly journals GM(1,1;λ) with Constrained Linear Least Squares

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Model Fitting ◽  
Ordinary Least Squares ◽  
Linear Least Squares ◽  
Unknown Parameters ◽  
Constrained Problems ◽  
Linear Least Squares Problems ◽  
Ordinary Least Squares Method ◽  
Better Than

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

scholarly journals Error Estimate and Adaptive Refinement in Mixed Discrete Least Squares Meshless Method

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
J. Amani ◽  
A. Saboor Bagherzadeh ◽  
T. Rabczuk
Keyword(s):  
Convergence Rate ◽  
Error Estimate ◽  
Least Squares ◽  
Meshless Method ◽  
Least Square ◽  
Adaptive Refinement ◽  
Error Estimator ◽  
Shape Functions ◽  
Numerical Errors ◽  
Elasticity Problems

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.

scholarly journals Parabolic Pulse Generation Using Tapered Microstructured Optical Fibres

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Natasha Vukovic ◽  
Neil G. R. Broderick ◽  
Francesco Poletti
Keyword(s):  
Pulse Shape ◽  
Pulse Shaping ◽  
Numerical Study ◽  
Pulse Generation ◽  
Optical Fibres ◽  
Step Index ◽  
Index Fibre ◽  
Microstructured Optical Fibres ◽  
Misfit Parameter ◽  
Better Than

This paper presents a numerical study of parabolic pulse generation in tapered microstructured optical fibres (MOFs). Based on our results and the algorithms presented, one can determine the linear taper profile (starting and finishing pitch values and taper length) needed to achieve parabolic pulse shaping of an initial Gaussian pulse shape with different widths and powers. We quantify the evolution of the parabolic pulse using the misfit parameter and show that it is possible to reach values significantly better than those obtained by a step index fibre.

scholarly journals Multi-Dimensional Moving Least Squares Method for Elasticity Problems

2012 ◽  
Vol 78 (786) ◽  
pp. 142-151
Author(s):  
Kohei SAKIHARA ◽  
Hitoshi MATSUBARA ◽  
Takaaki EDO ◽  
Hisao HARA ◽  
Genki YAGAWA
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Moving Least Squares Method ◽  
Elasticity Problems

The Optimization of the PID Controller Using the Least Squares Method and the Improved Lbest PSO Algorithm

2013 ◽  
Vol 397-400 ◽  
pp. 1296-1303 ◽  
Author(s):  
Chuan Gui Yang ◽  
Zhao Jun Yang ◽  
Fei Chen ◽  
Yan Zhu ◽  
Ying Nan Kan ◽  
...  
Keyword(s):  
Least Squares ◽  
Pid Controller ◽  
Least Squares Method ◽  
Dynamic Performance ◽  
Pso Algorithm ◽  
Pid Tuning ◽  
Loading System ◽  
Hydraulic Servo ◽  
Tuning Scheme ◽  
Better Than

A self-adaptive PID tuning scheme is presented for the electro-hydraulic servo loading system. It requires the least squares method to identify the parameters of the transfer function of the electro-hydraulic servo loading system and utilizes the improved lbest PSO algorithm to optimize the PID controller. The scheme can provide the optimal PID parameters so that the dynamic performance and stability of the electro-hydraulic servo loading system are improved. Results show the fact that the dynamic performance and stability of the system are improved by the scheme. And in terms of optimization of PID controller, the improved lbest PSO algorithm is better than the lbest PSO algorithm and Ziegler-Nichols method.

scholarly journals An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection

2019 ◽  
Vol 56 (4) ◽  
pp. 773-794 ◽  
Author(s):  
Mårten Gulliksson ◽  
Stepan Mazur
Keyword(s):  
Covariance Matrix ◽  
Portfolio Selection ◽  
Numerical Study ◽  
Asset Returns ◽  
Positive Definite ◽  
Convergence Properties ◽  
Good Convergence ◽  
Optimal Portfolio Selection ◽  
Singular Covariance Matrix ◽  
Better Than

AbstractCovariance matrix of the asset returns plays an important role in the portfolio selection. A number of papers is focused on the case when the covariance matrix is positive definite. In this paper, we consider portfolio selection with a singular covariance matrix. We describe an iterative method based on a second order damped dynamical systems that solves the linear rank-deficient problem approximately. Since the solution is not unique, we suggest one numerical solution that can be chosen from the iterates that balances the size of portfolio and the risk. The numerical study confirms that the method has good convergence properties and gives a solution as good as or better than the solutions that are based on constrained least norm Moore–Penrose, Lasso, and naive equal-weighted approaches. Finally, we complement our result with an empirical study where we analyze a portfolio with actual returns listed in S&P 500 index.

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