Comparison of the Accuracy of the Minimum-Variance Grid Method and the Least Squares Method — a Non-linear Extension

2002 ◽  
pp. 95-104
Author(s):  
Kwong Wing Chau ◽  
Wei Huang ◽  
Fung Fai Ng ◽  
Hin Man Louise Ng-Mak
Keyword(s):  
Least Squares ◽  
Linear Extension ◽  
Least Squares Method ◽  
Grid Method ◽  
Minimum Variance ◽  
Non Linear

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals Minimum variance-embedded deep kernel regularized least squares method for one-class classification and its applications to biomedical data

2020 ◽  
Vol 123 ◽  
pp. 191-216 ◽  
Author(s):  
Chandan Gautam ◽  
Pratik K. Mishra ◽  
Aruna Tiwari ◽  
Bharat Richhariya ◽  
Hari Mohan Pandey ◽  
...  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Minimum Variance ◽  
Biomedical Data ◽  
Regularized Least Squares ◽  
One Class Classification

scholarly journals Electrical Dipole Source Localization using Hybrid Least Squares Method in combination with ICA

2019 ◽  
Vol 5 (1) ◽  
pp. 361-363
Author(s):  
Fars Samann ◽  
Andreas Rausch ◽  
Thomas Schanze
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Source Localization ◽  
Biomedical Engineering ◽  
Least Squares Method ◽  
Dipole Source ◽  
Dipole Source Localization ◽  
Initial Values ◽  
Non Linear ◽  
Eeg Inverse Problem

AbstractIn biomedical engineering, dipole source localization is commonly used to identify brain activities from scalp recorded potentials, which is known as inverse problem of electroencephalography (EEG) source localization. However, this problem is fundamental in biomedical engineering, medicine and neuroscience. The EEG inverse problem is non-linear, in addition, it is ill-posed and the solver can be unstable, i.e. the solution is non-unique and it is highly sensitive to small changes of the measured signal (noise). For solving the EEG inverse problem iterative methods, like Levenberg-Marquardt algorithm, are usually considered. However, these techniques require good initial values and many electrodes N, since a large redundancy supports the finding of the right solution. Therefore, in this paper, a hybrid method of linear and non-linear modelling and least squares approach are proposed to overcome of these problems: the solutions calculated by means of a linear approximation of EEG inverse problems serve as initial values for solving the original non-linear model. In addition, independent component analysis (ICA) is combined with the proposed hybrid least squares method to separate different dipole sources from multiple EEG signals. The performance of the hybrid least squares method with and without ICA is measured in term of root mean square error. The simulation results show that the proposed method can estimate the location of dipole source with acceptable accuracy under high noise condition and small N comparing with linear least squares method considering larger N. Finally, it should be mentioned that the proposed method promises advantages in finding solutions of the EEG inverse problem effectively.

Modeling and identification of rotational joint driven by polymer fiber actuator

2020 ◽  
Author(s):  
João R. C. de Araújo ◽  
Saulo O. D. Luiz ◽  
Antonio M. N. Lima
Keyword(s):  
Least Squares ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Linear Optimization ◽  
Viscous Friction ◽  
Joint Model ◽  
Polymer Fiber ◽  
Polymer Actuators ◽  
Non Linear ◽  
Rotational Joint

Coiled polymer actuators have the characteristic to generate power by contracting when heated under strain. This work presents a project of a rotational joint driven by such actuators. Furthermore, the thermmomechanical model of the CPAs is identified by means of the least squares method. In addition, a model of the joint considering a viscous friction is suggested. Finally, the joint model is identified by means of a non linear optimization algorithm.

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