Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

A nonlinear analysis of the relationship between rainfall and runoff for extreme floods

Abstract: The watershed response to heavy rainfall was considered as a hereditary process. A nonlinear system model was developed in terms of a Volterra integral series of the first kind, which satisfies the principle of dissipation of hereditary action as well as the requirement of time invariance. A workable and practical method was developed to compute optimal response functions or kernels of the two-term truncated Volterra series. A Galerkin-type method was used, whereby the kernels were approximated by an orthogonal function expansion in terms of Chebyshev polynomials. The kernels evaluated from historical data for the Cowanesque watershed in the Chemung River basin were tested by reconstituting the hydrograph of an unrelated and unusual flood event caused by tropical storm Agnes of June 1972. It was found that the nonlinear watershed model yields a better prediction of the hydrograph of an exceptional flood than the linear model. The performance of both nonlinear and linear models is sensitive to the assumed value of the rainfall loss rate.

A Scattering Variable Approach to the Volterra Analysis of Nonlinear Systems

Abstract: A new mathematical model is developed which extends Volterra series analysis of nonlinear systems with memory to high-frequency systems, including those containing linear distributed component devices. A generalized set of nonlinear scattering parameters is defined which can be used to describe power transfer and distortion in nonlinear multiports, and which reduce to the classical scattering parameters for linear networks. The methodology is based on Volterra functional series, and is most useful for the small-signal case where the response can be approximated by a finite number of terms of the series. Nonlinear scattering kernels, derived by extending the Volterra analysis, are simply related to previously developed nonlinear voltage and current Volterra kernels. For sinusoidal inputs nonlinear scattering parameters are defined which are shown to be particularly helpful when power relationships are studied. The principal applications are for microwave networks terminated in real-valued site reference impedances. To evaluate the average power dissipated in a load at some intermodulation frequency, the concept of nonlinear transducer gain is defined and shown to be proportional to the squared magnitude of a nonlinear scattering parameter. Examples are presented illustrating the analysis procedure for a tunnel diode reflection amplifier and for a linear lossless transmission line terminated by a non-linear network.

On Random Field Discretization in Stochastic Finite Elements

Abstract: Several traditional methods for discretizing random fields in stochastic mechanics applications are considered; they are the midpoint method, the interpolation method, and the local averaging method. A simple and computationally convenient criterion for estimating the accuracy of these discretization methods is developed. Also, the Volterra series representation of nonlinear input/output relationships is utilized to assess the effect of the random field discretization methods on the response variability of stochastic mechanics problems. The theoretical developments are elucidated by a numerical example involving a beam problem.

High-order system identification with an adaptive recursive second-order polynomial filter

Abstract: In this letter, an adaptive recursive nonlinear filter based on the Volterra series and an infinite impulse response (IIR) structure is considered. For certain types of nonlinear systems where high-order nonlinearities are recursively generated, we show that the adaptive recursive second-order polynomial filter has improved performance over the well-known (nonrecursive) adaptive second-order Volterra filter and a third-order Volterra filter. This filter represents an alternative to using a traditional Volterra filter whose order has been increased to match that of the system being modeled.