Choice of Regularization Parameter Based on the Regularized Solution Reconstruction in Adaptive Signal Correction Problem

2021 ◽  
Vol 61 (1) ◽  
pp. 43-52
Author(s):  
M. L. Maslakov
Keyword(s):  
Regularization Parameter ◽  
Signal Correction ◽  
Correction Problem ◽  
Adaptive Signal ◽  
Regularized Solution

scholarly journals Development and Validation of an Adaptive Method to Generate High-Resolution Quadrature Encoder Signals

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Erva Ulu ◽  
Nurcan Gecer Ulu ◽  
Melih Cakmakci
Keyword(s):  
Adaptive Method ◽  
Recursive Least Squares ◽  
Position Information ◽  
Zero Crossings ◽  
Measurement Resolution ◽  
Signal Correction ◽  
Quadrature Phase ◽  
Correction Step ◽  
Development And Validation ◽  
Adaptive Signal

This paper presents a new method to increase the measurement resolution of quadrature encoders. The method contains an adaptive signal correction step and a signal interpolation step. Measured encoder signals contain imperfections including amplitude differences, mean offsets, and quadrature phase shift errors. With the proposed method, these errors are first corrected by using recursive least squares (RLS) estimation with exponential forgetting and resetting. Then, the corrected signals are interpolated to higher order sinusoids using a quick access look-up table generated offline. The position information can be obtained with the conversion of these high-order sinusoids to binary pulses and counting the zero crossings. Using the method presented here, a 10 nm measurement resolution is obtained using an encoder with 1 μm off-the-shelf resolution. Validation of the method and the practical limitations are also presented. Further increase in the resolution can be achieved by minimizing the effects of the electrical noise.

scholarly journals Two fractional regularization methods for identifying the radiogenic source of the Helium production-diffusion equation

2021 ◽  
Vol 6 (10) ◽  
pp. 11425-11448
Author(s):  
Xuemin Xue ◽  
◽  
Xiangtuan Xiong ◽  
Yuanxiang Zhang ◽  
Keyword(s):  
Diffusion Equation ◽  
Source Term ◽  
Regularization Parameter ◽  
A Priori ◽  
Regularization Methods ◽  
A Posteriori ◽  
Parameter Choice ◽  
Ill Posed ◽  
Parameter Choice Rules ◽  
Regularized Solution

<abstract><p>The predication of the helium diffusion concentration as a function of a source term in diffusion equation is an ill-posed problem. This is called inverse radiogenic source problem. Although some classical regularization methods have been considered for this problem, we propose two new fractional regularization methods for the purpose of reducing the over-smoothing of the classical regularized solution. The corresponding error estimates are proved under the a-priori and the a-posteriori regularization parameter choice rules. Some numerical examples are shown to display the necessarity of the methods.</p></abstract>

scholarly journals Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve

2007 ◽  
Vol 17 (2) ◽  
pp. 157-164 ◽  
Author(s):  
Dorota Krawczyk-Stańdo ◽  
Marek Rudnicki
Keyword(s):  
Regularization Parameter ◽  
Parameter Selection ◽  
Tikhonov Regularization Method ◽  
Smooth Solutions ◽  
Solution Versus ◽  
Regularization Parameters ◽  
Ill Posed ◽  
New Criterion ◽  
Regularization Parameter Selection ◽  
Regularized Solution

Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-CurveTo obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included.

scholarly journals Optimal control of propellant consumption during vertical lifting of rocket in homogeneous atmosphere using regularized solution of integral equation of the first kind

2020 ◽  
Vol 12 (S) ◽  
pp. 221-231
Author(s):  
Aleksey G. VIKULOV
Keyword(s):  
Optimal Control ◽  
Integral Equation ◽  
Optimal Trajectory ◽  
Regularization Parameter ◽  
Motion Equations ◽  
Suborbital Flights ◽  
Propellant Consumption ◽  
Minimal Consumption ◽  
Regularized Solution ◽  
Differential And Integral Equations

The article is devoted to the study of the optimal control of propellant consumption during vertical lifting of rocket in homogeneous atmosphere using regularized solution of integral equation of the first kind. The problem of lifting of a rocket into desired height along optimal trajectory in the view of minimal consumption of propellant leads to solving the set of differential and integral equations. Problem of optimal control of propellant consumption during lifting of rocket in homogeneous atmosphere is solved using regularized solution of integral equation of the first kind which is solution of corresponding Euler equation on discrete time net. Influence of the regularization parameter and some additional parameters on precision of discreted problem is investigated. Considered algorithm is summed up easily to the case of non-homogeneous atmosphere by introducing dependence of the ballistic coefficient on altitude of flight and to problem of putting spacecraft into determined orbit and suborbital flights by setting desired altitude and velocity and modifying of motion equations.

scholarly journals Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Le Nhat Huynh ◽  
Nguyen Hoang Luc ◽  
Dumitru Baleanu ◽  
Le Dinh Long
Keyword(s):  
Diffusion Equation ◽  
Source Term ◽  
Regularization Parameter ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Choice Rule ◽  
Parameter Choice ◽  
Landweber Method ◽  
Regularized Solution

AbstractThis article is devoted to the study of the source function for the Caputo–Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.

Adaptive Signal Analysis and Interpretation for Real-time Intelligent Patient Monitoring

1994 ◽  
Vol 33 (01) ◽  
pp. 60-63 ◽  
Author(s):  
E. J. Manders ◽  
D. P. Lindstrom ◽  
B. M. Dawant
Keyword(s):  
Computer Architecture ◽  
Real Time ◽  
Data Abstraction ◽  
Monitoring Strategy ◽  
Intelligent Monitoring ◽  
Patient Status ◽  
On Line ◽  
Main Components ◽  
And Control ◽  
Adaptive Signal

Abstract:On-line intelligent monitoring, diagnosis, and control of dynamic systems such as patients in intensive care units necessitates the context-dependent acquisition, processing, analysis, and interpretation of large amounts of possibly noisy and incomplete data. The dynamic nature of the process also requires a continuous evaluation and adaptation of the monitoring strategy to respond to changes both in the monitored patient and in the monitoring equipment. Moreover, real-time constraints may imply data losses, the importance of which has to be minimized. This paper presents a computer architecture designed to accomplish these tasks. Its main components are a model and a data abstraction module. The model provides the system with a monitoring context related to the patient status. The data abstraction module relies on that information to adapt the monitoring strategy and provide the model with the necessary information. This paper focuses on the data abstraction module and its interaction with the model.

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