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
2021 ◽  
pp. 107754632110191
Author(s):  
Fereidoun Amini ◽  
Elham Aghabarari

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.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhiming Zhou ◽  
Zhengyun Zhou ◽  
Liang Wu

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.


2021 ◽  
Vol 2131 (2) ◽  
pp. 022132
Author(s):  
Lidia V Azarova

Abstract The features of approximation of empirical data by functional dependence with nonlinear parameters using the two-stage least squares method are considered in this paper. A method of simplified parameter estimation by constructing a new expression that depends on the parameters in a linear way is described. To obtain the final solution, the least squares estimation of the main dependence linearized in terms of parameters is performed. The influence of various forms of noise imposed on the theoretical dependence on the approximations is modeled.


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