X-parameters and Volterra theory

X-Parameters ◽  
2013 ◽  
pp. 196-201
Author(s):  
David Root ◽  
Jason Horn ◽  
Jan Verspecht ◽  
Mihai Marcu
Keyword(s):  
Volterra Theory

Application of Multi-Input Volterra Theory to Nonlinear Multi-Degree-of-Freedom Aerodynamic Systems

AIAA Journal ◽  
2010 ◽  
Vol 48 (1) ◽  
pp. 56-62 ◽  
Author(s):  
Maciej Balajewicz ◽  
Fred Nitzsche ◽  
Daniel Feszty
Keyword(s):  
Degree Of Freedom ◽  
Volterra Theory

Fractional rheological models for thermomechanical systems. Dissipation and free energies

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Mauro Fabrizio
Keyword(s):  
Fractional Derivative ◽  
Heat Propagation ◽  
Free Energies ◽  
Compatibility Conditions ◽  
Rheological Models ◽  
Fractional Models ◽  
Volterra Theory ◽  
Definition Of ◽  
Thermodynamic Restrictions ◽  
With Memory

AbstractWithin the fractional derivative framework, we study thermomechanical models with memory and compare them with the classical Volterra theory. The fractional models involve significant differences in the type of kernels and predicts important changes in the behavior of fluids and solids. Moreover, an analysis of the thermodynamic restrictions provides compatibility conditions on the kernels and allows us to determine certain free energies, which in turn enables the definition of a topology on the history space. Finally, an analogous analysis is carried out for the phenomenon of heat propagation with memory.

Analytical Volterra-based models for nonlinear low order flight dynamics approximation systems

2012 ◽  
Vol 116 (1185) ◽  
pp. 1123-1153 ◽  
Author(s):  
A. Omran ◽  
B. Newman
Keyword(s):  
Nonlinear Response ◽  
Volterra Series ◽  
Design Tool ◽  
Analytical Methodology ◽  
Single Degree Of Freedom ◽  
Response Characteristics ◽  
Nonlinear Responses ◽  
Volterra Theory ◽  
Dynamics Approximation ◽  
Low Order

AbstractAnalytical methodology is presented to conduct dynamical assembly of simple low order nonlinear responses for system synthesis and prediction using Volterra theory. The procedure is set forth generically and then applied to several atmospheric flight examples. A two-term truncated Volterra series, which is enough to capture the quadratic and bilinear nonlinearities, is developed for first and second order generalised nonlinear single degree of freedom systems. The resultant models are given in the form of first and second kernels. A parametric study of the influence of each linear and nonlinear term on kernel structures is investigated. A step input is then employed to quantify and qualify the nonlinear response characteristics. Uniaxial surge and pitch motions are presented as examples of the low order flight dynamic systems. These examples show the ability of the proposed analytical Volterra-based models to predict, understand, and analyse the nonlinear aircraft behaviour beyond that attainable by linear-based models. The proposed analytical Volterra-based model offers an efficient nonlinear preliminary design tool in qualifying the aircraft responses before computer simulation is available or invoked.

Limits to growth from Volterra theory of population

1974 ◽  
Vol 16 (2) ◽  
pp. 113-118 ◽  
Author(s):  
A. Borsellino ◽  
V. Torre
Keyword(s):  
Limits To Growth ◽  
Volterra Theory

A Unifying View of Wiener and Volterra Theory and Polynomial Kernel Regression

2006 ◽  
Vol 18 (12) ◽  
pp. 3097-3118 ◽  
Author(s):  
Matthias O. Franz ◽  
Bernhard Schölkopf
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Polynomial Kernel ◽  
Implicit Representation ◽  
Weakly Nonlinear ◽  
The Past ◽  
Volterra Theory ◽  
Low Dimensional ◽  
Polynomial Kernels

Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series can be represented implicitly as elements of a reproducing kernel Hilbert space by using polynomial kernels. The estimation complexity of the implicit representation is linear in the input dimensionality and independent of the degree of nonlinearity. Experiments show performance advantages in terms of convergence, interpretability, and system sizes that can be handled.

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