Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

1990 ◽  
Author(s):  
K. PARK ◽  
W. BELVIN
Keyword(s):  
Kalman Filtering ◽  
Second Order ◽  
Structural Systems ◽  
Time Invariant ◽  
Discrete Integration

Order Reduction of Parametrically Excited Linear and Nonlinear Structural Systems

2005 ◽  
Vol 128 (4) ◽  
pp. 458-468 ◽  
Author(s):  
Venkatesh Deshmukh ◽  
Eric A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Order Reduction ◽  
Second Order ◽  
Degree Of Freedom ◽  
Structural Systems ◽  
Parametrically Excited ◽  
Reduced Models ◽  
Linear And Nonlinear ◽  
Time Invariant ◽  
Time Periodic

Order reduction of parametrically excited linear and nonlinear structural systems represented by a set of second order equations is considered. First, the system is converted into a second order system with time invariant linear system matrices and (for nonlinear systems) periodically modulated nonlinearities via the Lyapunov-Floquet transformation. Then a master-slave separation of degrees of freedom is used and a relation between the slave coordinates and the master coordinates is constructed. Two possible order reduction techniques are suggested. In the first approach a constant Guyan-like linear kernel which accounts for both stiffness and inertia is employed with a possible periodically modulated nonlinear part for nonlinear systems. The second method for nonlinear systems reduces to finding a time-periodic nonlinear invariant manifold relation in the modal coordinates. In the process, closed form expressions for “true internal” and “true combination” resonances are obtained for various nonlinearities which are generalizations of those previously reported for time-invariant systems. No limits are placed on the size of the time-periodic terms thus making this method extremely general even for strongly excited systems. A four degree-of-freedom mass- spring-damper system with periodic stiffness and damping as well as two and five degree-of-freedom inverted pendula with periodic follower forces are used as illustrative examples. The nonlinear-based reduced models are compared with linear-based reduced models in the presence and absence of nonlinear resonances.

scholarly journals Tuning of a time-delayed controller for a general class of second-order linear time invariant systems with dead-time

2019 ◽  
Vol 13 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Raul Villafuerte-Segura ◽  
Francisco Medina-Dorantes ◽  
Leopoldo Vite-Hernández ◽  
Baltazar Aguirre-Hernández
Keyword(s):  
General Class ◽  
Dead Time ◽  
Linear Time ◽  
Second Order ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Successive linearizations of second order multidimensional time-invariant systems

2004 ◽  
Vol 162 (2) ◽  
pp. 79-88 ◽  
Author(s):  
Fethi Belkhouche ◽  
Boumediene Belkhouche
Keyword(s):  
Second Order ◽  
Time Invariant

scholarly journals L2 and L1Trend Filtering: A Kalman Filter Approach a

2021 ◽  
Author(s):  
Arman Kheirati Roonizi
Keyword(s):  
Image Processing ◽  
Kalman Filtering ◽  
Nonlinear Filtering ◽  
Linear Time ◽  
Piecewise Linear ◽  
Additive White Gaussian Noise ◽  
Signal And Image Processing ◽  
Linear Time Invariant ◽  
Filter Approach ◽  
Time Invariant

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

scholarly journals Second-Order Kalman Filtering Application to Fading Channels Supported by Real Data

2016 ◽  
Vol 07 (02) ◽  
pp. 61-74 ◽  
Author(s):  
Azra Kapetanovic ◽  
Redhwan Mawari ◽  
Mohamed A. Zohdy
Keyword(s):  
Fading Channels ◽  
Kalman Filtering ◽  
Real Data ◽  
Second Order

scholarly journals L2 and L1Trend Filtering: A Kalman Filter Approach a

2021 ◽  
Author(s):  
Arman Kheirati Roonizi
Keyword(s):  
Image Processing ◽  
Kalman Filtering ◽  
Nonlinear Filtering ◽  
Linear Time ◽  
Piecewise Linear ◽  
Additive White Gaussian Noise ◽  
Signal And Image Processing ◽  
Linear Time Invariant ◽  
Filter Approach ◽  
Time Invariant

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

scholarly journals L2 and L1Trend Filtering: A Kalman Filter Approach amodification

2022 ◽  
Author(s):  
Arman Kheirati Roonizi
Keyword(s):  
Image Processing ◽  
Kalman Filtering ◽  
Nonlinear Filtering ◽  
Linear Time ◽  
Piecewise Linear ◽  
Additive White Gaussian Noise ◽  
Signal And Image Processing ◽  
Linear Time Invariant ◽  
Filter Approach ◽  
Time Invariant

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

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