Nonlinearity Mode Theory Foundation Research of EMP Coupling by Volterra Series

2014 ◽  
Vol 511-512 ◽  
pp. 1022-1026
Author(s):  
Yong Sheng Gao ◽  
Sha Wu ◽  
Jiu He Ma ◽  
Jiu Liang Xiong
Keyword(s):  
Volterra Series ◽  
Electromagnetic Coupling ◽  
Nonlinear Behavior ◽  
Coupling Model ◽  
Kernel Functions ◽  
Volterra Kernel ◽  
Coupling Process ◽  
Electric System ◽  
Model Research ◽  
Theory Foundation

Strong Electromagnetic Pulses (EMP) as a new idea weapon has caused many effects like malfunctions, performance degradation, interferences, and destructions in electronic and electrical systems. EMP coupling model research is the foundation of effect evolution and protection. In this paper, a new modeling method on the base of combination system identification theory and Volterra series algorithm was utilized to analyze the electromagnetic coupling process from an external field to an inner electric system. First, we will analyze the theory foundation of non-parameters model evolution. And then, using input and output test data, we presented commonly Voleterra series expression of EMP electromagnetic coupling model. Then, we analyze coupling models several important characteristics in detail. Finally, we approach High Order Spectrum algorithms to identify Volterra kernel functions. Theoretical results show that the Volterra kernel function will be used as an efficient method in EMP coupling model research and can apply this method to character the nonlinear behavior of the EMP electromagnetic coupling. The model described above was assigned under certain assumptions, moreover describes the effects in theory only and does not consider the time variation of the parameters of the system. From this reason it appears as more convenient to characterize the electromagnetic coupling process, by a more universal mathematical approach.

Parametric Estimation of Volterra Kernel for the Dynamic Response of an Offshore Structure Using Laguerre Polynomials

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Jae-Hyeon Son ◽  
Yooil Kim
Keyword(s):  
Volterra Series ◽  
Laguerre Polynomials ◽  
Nonlinear Dynamic System ◽  
Least Square Method ◽  
Time Domain Analysis ◽  
Engineering Problem ◽  
Least Square ◽  
Parametric Estimation ◽  
Volterra Kernel ◽  
Offshore Structure

Abstract The behavior of a nonlinear dynamic system under arbitrary excitation can be represented by the Volterra series if the Volterra kernels of different orders are known. This study presents a methodology for a direct estimation of the Volterra kernel coefficients up to the second-order using prepared data obtained by running a time-domain analysis of the system of interest. To avoid potential problems during kernel estimation, the Volterra kernel is expanded into a polynomial series using the Laguerre polynomials, and the coefficients of the Laguerre polynomials are then estimated using a least-square method. A nonlinear oscillator with a quadratic stiffness term is introduced, and the methodology is applied to check the applicability and accuracy. The methodology is applied to a more realistic engineering problem of a simplified riser under irregular wave excitation.

scholarly journals On the detection of a nonlinear damage in an uncertain nonlinear beam using stochastic Volterra series

2019 ◽  
Vol 19 (4) ◽  
pp. 1137-1150 ◽  
Author(s):  
Luis GG Villani ◽  
Samuel da Silva ◽  
Americo Cunha ◽  
Michael D Todd
Keyword(s):  
Volterra Series ◽  
Novelty Detection ◽  
Nonlinear Behavior ◽  
System Response ◽  
Baseline Model ◽  
Nonlinear Beam ◽  
Stochastic Version ◽  
Nonlinear Components ◽  
Baseline State ◽  
Data Variation

In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a baseline model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed “healthy”) and damaged. The studied system exhibits nonlinear behavior even in the reference condition, and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.

Correlation Techniques for the Identification of Non-Linear Systems

1972 ◽  
Vol 5 (8) ◽  
pp. 316-321 ◽  
Author(s):  
R. J. Simpson ◽  
H. M. Power
Keyword(s):  
Linear System ◽  
Frequency Domain ◽  
Recent Work ◽  
Cross Correlation ◽  
Volterra Series ◽  
Kernel Functions ◽  
Non Linear ◽  
Non Linear Systems ◽  
Correlation Techniques ◽  
Non Linear System

The Volterra series expansion of the response of a non-linear system is described, along with its counterpart in the frequency domain. Cross-correlation methods for identifying the kernel functions which occur in this expansion are reviewed, with particular emphasis on techniques for obtaining the linear approximant to a non-linear system. Some recent work which appears to be unrelated to the Volterra approach is also discussed.

Nonlinear analysis of VCO jitter generation using Volterra series

2018 ◽  
Vol 37 (2) ◽  
pp. 755-771
Author(s):  
Hadi Dehbovid ◽  
Habib Adarang ◽  
Mohammad Bagher Tavakoli
Keyword(s):  
Phase Noise ◽  
Volterra Series ◽  
Nonlinear Behavior ◽  
Voltage Controlled Oscillator ◽  
Degree Polynomial ◽  
Content Type ◽  
Practical Model ◽  
Oscillator Phase Noise ◽  
Oscillator Phase ◽  
Second Degree

PurposeCharge pump phase locked loops (CPPLLs) are nonlinear systems as a result of the nonlinear behavior of voltage-controlled oscillators (VCO). This paper aims to specify jitter generation of voltage controlled oscillator phase noise in CPPLLs, by considering approximated practical model for VCO. Design/methodology/approachCPPLL, in practice, shows nonlinear behavior, and usually in LC-VCOs, it follows second-degree polynomial function behavior. Therefore, the nonlinear differential equation of the system is obtained which shows the CPPLLs are a nonlinear system with memory, and that Volterra series expansion is useful for such systems. FindingsIn this paper, by considering approximated practical model for VCO, jitter generation of voltage controlled oscillator phase noise in CPPLLs is specified. Behavioral simulation is used to validate the analytical results. The results show a suitable agreement between analytical equations and simulation results. Originality/valueThe proposed method in this paper has two advantages over the conventional design and analysis methods. First, in contrast to an ideal CPPLL, in which the characteristic of the VCO’s output frequency based on the control voltage is linear, in the present paper, a nonlinear behavior was considered for this characteristic in accordance with the real situations. Besides, regarding the simulations in this paper, a behavior similar to the second-degree polynomial was considered, which caused the dependence of the produced jitter’s characteristic corner frequency on the jitter’s amplitude. Second, some new nonlinear differential equations were proposed for the system, which ensured the calculation of the produced jitter of the VCO phase noise in CPPLLs. The presented method is general enough to be used for designing the CPPLL.

VOLTERRA FUNCTIONAL SECURE COMMUNICATION SYSTEMS

2003 ◽  
Vol 13 (01) ◽  
pp. 123-146 ◽  
Author(s):  
A. D. IRVING ◽  
T. DEWSON
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Secure Communication ◽  
Communication Systems ◽  
Additive Noise ◽  
Kernel Functions ◽  
Volterra Kernel ◽  
Functional Expansion ◽  
Coupled Differential Equations ◽  
Transmitted Signal

Two methods, based on nonlinear dynamics, are described for broad- and narrow-band communication systems. The first approach employs hyperchaotic discrete time series carrier sequences generated with mixed linear–nonlinear coupled differential equations [Irving & Dewson, 1997]. In this first approach it is assumed that the solution of the coupled ordinary differential equations can be represented as a multichannel Volterra functional expansion. Identification, synchronization and the potential unmasking of hyperchaotic communications systems, are achieved by generating a tractable hierarchy of ascending order time series moment equations by operating on a suitably truncated Volterra functional expansion. The estimated moment hierarchy facilitates the calculation of the coefficients of the coupled differential equations that generate the multichannel carrier that is to be modulated by the message. Due to its ability to easily and accurately estimate the coefficients of the governing differential equations the method is applied to the multichannel carrier sequences of data generated by a set of hyperchaotic equations. The inherent problem of resynchronization in chaotic communication systems cannot be avoided in general because of the evolutionary, time dependent, nature of the time series carriers used. This time dependence problem that results in repeated resynchronization can be avoided by considering an alternative and innovative approach that employs time series carrier sequences generated by an input–output multichannel Volterra kernel expansion [Dewson & Irving, 1996]. In this second method, mixed order multichannel Volterra kernel functions are used to generate the carrier sequence that is then modulated by the message. The Volterra kernel function values used to generate the carrier can be identified with the moment hierarchy method [Dewson & Irving, 1996] enabling the message to be deconvolved from the transmitted signal. The modulated nonlinear multichannel signal is transmitted to the receiver. The effect of transmission is to distort and corrupt the signal. In this work it is assumed that the distortions to the transmitted signal remain small, with the case where they become significant being treated elsewhere. First, the case where the signal is received free from both noise and distortion, for example the decryption of an encrypted e-mail, is first considered. Then signal reception in the presence of additive noise is considered. Each of the two proposed methods has been investigated to determine their accuracy and robustness in the presence of additive noise.

Numerical Coupling Analysis of Droplets’ Behaviors in GMAW

2010 ◽  
Vol 139-141 ◽  
pp. 981-985
Author(s):  
Yan Lu Huang ◽  
Xin You Ke ◽  
Yi Bin Li
Keyword(s):  
Electric Current ◽  
Current Density ◽  
Electromagnetic Force ◽  
Electromagnetic Coupling ◽  
Gas Metal Arc Welding ◽  
Coupling Model ◽  
Metal Transfer ◽  
Electric Current Density ◽  
Forming Process ◽  
Metal Arc Welding

The forming process and dynamic behaviors of droplets in gas metal arc welding (GMAW) were numerically simulated by using weak electromagnetic coupling method, with considering the gravity, the electromagnetic force, the free surface and the turbulent flow in the droplets. The shape update of the droplets was calculated on basis of VOF and CSF theories. The Gaussian electric current density was identified as boundary conditions for calculating electromagnetic force. A weak electromagnetic coupling model was used to study the characteristics of relevant physical variables and their roles in metal transfer. The simulation results suggest that the maximal value of electric current density lies in the neck of droplets, and the electromagnetic force has great effects of accelerating droplets’ contraction and shortening their falling time. Under the action of strong electromagnetic force, the metal transfer is in a spray form rather than a globular one in GMAW process. The simulated results agree well with theoretical analyses and predecessors’ experiments.

De-Noising, Clustering, Classification, and Representation of Microarray Data for Disease Diagnostics

2014 ◽  
pp. 149-174
Author(s):  
Nitin Baharadwaj ◽  
Sheena Wadhwa ◽  
Pragya Goel ◽  
Isha Sethi ◽  
Chanpreet Singh Arora ◽  
...  
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Fourier Transform ◽  
Microarray Data ◽  
Diagnostic Tool ◽  
Volterra Series ◽  
Nonlinear Behavior ◽  
Gene Signature ◽  
Disease Diagnosis

A microarray works by exploiting the ability of a given mRNA molecule to bind specifically to the DNA template from which it originated under specific high stringency conditions. After this, the amount of mRNA bound to each DNA site on the array is determined, which represents the expression level of each gene. Qualification of the mRNA (probe) bound to each DNA spot (target) can help us to determine which genes are active or responsible for the current state of the cell. The probe target hybridization is usually detected and quantified using dyes/flurophore/chemiluminescence labels. The microarray data gives a single snapshot of the gene activity profile of a cell at any given time. Microarray data helps to elucidate the various genes involved in the disease and may also be used for diagnosis /prognosis. In spite of its huge potential, microarray data interpretation and use is limited by its error prone nature, the sheer size of the data and the subjectivity of the analysis. Initially, we describe the use of several techniques to develop a pre-processing methodology for denoising microarray data using signal process techniques. The noise free data thus obtained is more suitable for classification of the data as well as for mining useful information from the data. Discrete Fourier Transform (DFT) and Autocorrelation were explored for denoising the data. We also used microarray data to develop the use of microarray data as diagnostic tool in cancer using One Dimensional Fourier Transform followed by simple Euclidean Distance Calculations and Two Dimensional MUltiple SIgnal Classification (MUSIC). To improve the accuracy of the diagnostic tool, Volterra series were used to model the nonlinear behavior of the data. Thus, our efforts at denoising, representation, and classification of microarray data with signal processing techniques show that appreciable results could be attained even with the most basic techniques. To develop a method to search for a gene signature, we used a combination of PCA and density based clustering for inferring the gene signature of Parkinson’s disease. Using this technique in conjunction with gene ontology data, it was possible to obtain a signature comprising of 21 genes, which were then validated by their involvement in known Parkinson’s disease pathways. The methodology described can be further developed to yield future biomarkers for early Parkinson’s disease diagnosis, as well as for drug development.

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