Identification of first order volterra kernels of M-sequence correlation method for nonlinear system

2007 ◽  
Author(s):  
Eiji Nishiyama
Keyword(s):  
Nonlinear System ◽  
Correlation Method ◽  
Volterra Kernels ◽  
First Order ◽  
Sequence Correlation ◽  
M Sequence

scholarly journals Estimation of Parameters of Nonlinear System by Using M-sequence and Volterra Kernels

2008 ◽  
Vol 74 (740) ◽  
pp. 766-772
Author(s):  
Hiroshi HARADA ◽  
Yukio TOYOZAWA ◽  
Masahiko SHIGAKI ◽  
Hiroshi KASHIWAGI ◽  
Teruo YAMAGUCHI
Keyword(s):  
Nonlinear System ◽  
Estimation Of Parameters ◽  
Volterra Kernels ◽  
M Sequence

scholarly journals Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jin-yan Hu ◽  
Gang Yan ◽  
Tao Wang
Keyword(s):  
Nonlinear System ◽  
Cross Correlation ◽  
Correlation Method ◽  
Kernel Functions ◽  
Third Order ◽  
Mathematical Properties ◽  
M Sequence ◽  
System Output ◽  
Even Order ◽  
Order Kernel

The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length sequence (m-sequence) can be used to estimate nonlinear binary kernel slices using cross-correlation method. In this study, we examine the relevant mathematical properties of kernel slices, particularly their shift-and-product property and overlap distortion problem caused by the irregular shifting of the estimated kernel slices in the cross-correlation function between the input m-sequence and the system output. We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance of kernel-slice overlapping. An instance of third-order Wiener nonlinear model is simulated to justify the proposed method.

scholarly journals Achieving Seventh-Order Amplitude Accuracy in Leapfrog Integrations

2013 ◽  
Vol 141 (9) ◽  
pp. 3037-3051 ◽  
Author(s):  
Paul D. Williams
Keyword(s):  
Nonlinear System ◽  
Third Order ◽  
First Order ◽  
Time Stepping ◽  
The Third ◽  
Numerical Integrations ◽  
Seventh Order ◽  
Ocean Models ◽  
Stability And Accuracy ◽  
Fifth Order

Abstract The leapfrog time-stepping scheme makes no amplitude errors when integrating linear oscillations. Unfortunately, the Robert–Asselin filter, which is used to damp the computational mode, introduces first-order amplitude errors. The Robert–Asselin–Williams (RAW) filter, which was recently proposed as an improvement, eliminates the first-order amplitude errors and yields third-order amplitude accuracy. However, it has not previously been shown how to further improve the accuracy by eliminating the third- and higher-order amplitude errors. Here, it is shown that leapfrogging over a suitably weighted blend of the filtered and unfiltered tendencies eliminates the third-order amplitude errors and yields fifth-order amplitude accuracy. It is further shown that the use of a more discriminating (1, −4, 6, −4, 1) filter instead of a (1, −2, 1) filter eliminates the fifth-order amplitude errors and yields seventh-order amplitude accuracy. Other related schemes are obtained by varying the values of the filter parameters, and it is found that several combinations offer an appealing compromise of stability and accuracy. The proposed new schemes are tested in numerical integrations of a simple nonlinear system. They appear to be attractive alternatives to the filtered leapfrog schemes currently used in many atmosphere and ocean models.

Energies and hyperfine structures of the 1s22s2p 3Po state of Be-like ions with Z = 11–18

2017 ◽  
Vol 95 (8) ◽  
pp. 720-724 ◽  
Author(s):  
Kai Kai Li ◽  
Lin Zhuo ◽  
Chun Mei Zhang ◽  
Chao Chen ◽  
Bing Cong Gou
Keyword(s):  
Hyperfine Coupling ◽  
Reference Data ◽  
Correlation Method ◽  
Theoretical Data ◽  
Coupling Constants ◽  
Isoelectronic Sequence ◽  
Excitation Energies ◽  
First Order ◽  
Hyperfine Structures ◽  
Good Agreement

Nonrelativistic energies and wave functions of the 1s22s2p 3Po states of Be isoelectronic sequence (Z = 11–18) are calculated using the full core plus correlation method (FCPC). To obtain the accurate energy level, the relativistic corrections and mass polarization effect are included by using the first-order perturbation theory. The calculated excitation energies (relative to the 1s22s2 ground state) are compared with the experiment. Most of the calculated [Formula: see text] energies agree with the experiment to within a few inverse centimetres. The calculated hyperfine coupling constants are in good agreement with the latest theoretical data in the literature. Our results may provide valuable reference data for spectral analysis and identification in the future.

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