Topic
Volterra series
About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors extend the results on the theory of realizations of finite Volterra series by exploiting the structural properties of the observation space, and show that two distinct minimal realizations can be constructed based on the properties of observation space and the Lie algebra.
Abstract: In this paper we extend the results on the theory of realizations of finite Volterra series by exploiting the structural properties of the observation space. In general, two distinct minimal realizations of a finite Volterra series may be constructed, one based on the properties of the observation space and the other based on the properties of the Lie algebra. Both these realizations display the canonical structure found earlier for such systems. The results given here also yield information on the observation algebra generated by functions in the observation space, just as previous work gave information on the Lie algebra. As an application, the structure found here is applied to the finite-dimensional filtering problem for these systems.
18 citations
18 citations
TL;DR: In this paper, a parametric identification procedure based on recursive evaluation of response harmonic amplitude series is presented for a rotor-bearing system supported in rolling element bearings and compared with analytical values and experimental results of previous works.
Abstract: Volterra series provides a structured analytical platform for modeling and identification of nonlinear systems. The series has been widely used in nonparametric identification through higher order frequency response functions or FRFs. A parametric identification procedure based on recursive evaluation of response harmonic amplitude series is presented here. The procedure is experimentally investigated for a rotor-bearing system supported in rolling element bearings. The estimates of nonlinear bearing stiffness obtained from experimentation have been compared with analytical values and experimental results of previous works.
18 citations
Posted Content•
TL;DR: In this paper, a discretization method for solving nonlinear integral equations with a Volterra series was proposed, and the existence and uniqueness of solutions were proved and convergence and estimates of the order of convergence for the numerical methods of solution were given.
Abstract: We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.
18 citations
04 Jun 1996
TL;DR: In this article, the convergence properties of the modified Volterra-like modeling approach for non-linear dynamic systems in comparison with the classical VOLTERRA series representation are analyzed.
Abstract: The paper presents a theoretical study on the convergence properties of the new modified Volterra-like modeling approach for non-linear dynamic systems in comparison with the classical Volterra series representation. In particular, the assumptions which enable a single-fold non-linear convolution integral to be adopted also in the presence of strong non-linearities are pointed out. Experimental and simulation results which confirm the theoretical considerations are also provided.
18 citations