A Spline Least Squares Method for Numerical Parameter Estimation in Differential Equations

1982 ◽  
Vol 3 (1) ◽  
pp. 28-46 ◽  
Author(s):  
J. M. Varah
Keyword(s):  
Parameter Estimation ◽  
Differential Equations ◽  
Least Squares ◽  
Least Squares Method ◽  
Numerical Parameter

Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Fractional Differential Equations ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Variable Order ◽  
Polynomial Solutions ◽  
Fractional Differential ◽  
Approximate Polynomial

AbstractIn this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

Online parameter estimation and adaptive control with limited information in structures

2021 ◽  
pp. 107754632110191
Author(s):  
Fereidoun Amini ◽  
Elham Aghabarari
Keyword(s):  
Parameter Estimation ◽  
Adaptive Control ◽  
Least Squares ◽  
Control Algorithm ◽  
Least Squares Method ◽  
Recursive Least Squares ◽  
Limited Information ◽  
Online Identification ◽  
Recursive Least Squares Method ◽  
Adaptive Control Algorithm

An online parameter estimation is important along with the adaptive control, that is, a time-dependent plant. This study uses both online identification and the simple adaptive control algorithm with velocity feedback. The recursive least squares method was used to identify the stiffness and damping parameters of the structure’s stories. Identification was carried out online without initial estimation and only by measuring the structural responses. The limited information regarding sensor measurements, parameter convergence, and the effects of the covariance matrix is examined. The integration of the applied online identification, the appropriate reference model selection in simple adaptive control, and adopting the proportional integral filter was used to limit the structural control response error. Some numerical examples are simulated to verify the ability of the proposed approach. Despite the limited information, the results show that the simultaneous use of online identification with the recursive least squares method and simple adaptive control algorithm improved the overall structural performance.

Structural System Parameter Estimation by Two-Stage Least Squares Method

1976 ◽  
Vol 102 (5) ◽  
pp. 883-899
Author(s):  
Will Gersch ◽  
George T. Taoka ◽  
Robert Liu
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
System Parameter ◽  
Least Squares Method ◽  
Structural System ◽  
Two Stage ◽  
Two Stage Least Squares

Least Squares Parameter Estimation in Chaotic Differential Equations

1993 ◽  
pp. 353-371
Author(s):  
Josef Kallrath ◽  
Johannes P. Schlöder ◽  
Hans Georg Bock
Keyword(s):  
Parameter Estimation ◽  
Differential Equations ◽  
Least Squares

scholarly journals Polynomial Least Squares Method for Fractional Lane–Emden Equations

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 479 ◽  
Author(s):  
Bogdan Căruntu ◽  
Constantin Bota ◽  
Marioara Lăpădat ◽  
Mădălina Paşca
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Least Squares Method ◽  
Polynomial Solution ◽  
Approximate Polynomial

This paper applies the Polynomial Least Squares Method (PLSM) to the case of fractional Lane-Emden differential equations. PLSM offers an analytical approximate polynomial solution in a straightforward way. A comparison with previously obtained results proves how accurate the method is.

Generalized phase-shifting interferometry by parameter estimation with the least squares method

2013 ◽  
Vol 51 (5) ◽  
pp. 626-632 ◽  
Author(s):  
Rigoberto Juarez-Salazar ◽  
Carlos Robledo-Sánchez ◽  
Cruz Meneses-Fabian ◽  
Fermin Guerrero-Sánchez ◽  
L.M. Arévalo Aguilar
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Least Squares Method ◽  
Phase Shifting ◽  
Phase Shifting Interferometry

scholarly journals Calibration for Parameter Estimation of Signals with Complex Noise via Nonstationarity Measure

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhiming Zhou ◽  
Zhengyun Zhou ◽  
Liang Wu
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Least Squares Method ◽  
Random Noise ◽  
Calibration Method ◽  
Numerical Studies ◽  
Chaotic Signals ◽  
Inaccurate Estimation ◽  
Non Gaussian ◽  
First Time

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex (such as non-Gaussian noise, strong noise, and chaotic noise). This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of the stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types (including random noise and chaotic noise) and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations.

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