Volterra series

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

Use of Higher-Order Frequency Response Functions for Identification of Nonlinear Adsorption Kinetics: Single Mechanisms under Isothermal Conditions

Abstract: The concept of higher-order frequency response functions(FRFs), which is based on Volterra series expansion of nonlinearfunctions, is used for analysis of kinetics of nonlinear adsorptionsystems. Four different kinetic mechanisms: Langmuir kinetics, filmresistance control, micropore diffusion control and pore-surfacediffusion control were analyzed and the results were compared. It wasshown that, contrary to the linear frequency response characteristicfunctions, the higher-order FRFs corresponding to different mechanismsdiffer in shape. This result offers great potential for theidentification of the adsorption-diffusion mechanism governing theprocess. It is shown that the second order FRFs give sufficientinformation for distinguishing different mechanisms.

A learning technique for Volterra series representation

Abstract: This paper presents a method of system identification based upon the techniques of pattern recognition. The method developed is an on-line error-correcting procedure which provides the coefficients of the Volterra series representation of the system. The systems considered are those with finite settling time and piecewise constant inputs. The method is extremely general, identifying both linear and nonlinear systems in the presence of noise, without the requirement of special test signals. The theoretical basis for this method lies in the observation that system identification is a special case of the general theory of pattern recognition. A system is treated as a transformation from the set of past inputs to the real line, the system output. The Volterra expansion treats this transformation as a hypersurface, the shape of which is determined by the Volterra kernels. However, the techniques of pattern recognition produce this type of surface as the discriminant function between pattern classes. Furthermore, these surfaces are iteratively obtained as more data are available. Consequently, the computational difficulties, which are encountered in obtaining the Volterra kernels, are circumvented by this iterative learning procedure.

Base-band derived volterra series for power amplifier modeling

Abstract: This paper proves that the traditional way of deriving power amplifier low-pass equivalent complex-signal Volterra models from their original band-pass RF real-signal Volterra models is too restrictive, and so does not lead to an optimal model. Then, it proposes a much richer alternative approach. Instead of deriving the base-band Volterra model from the RF Volterra model, we started by a general Volterra series expansion of a complex-signal to only then impose the restrictions of odd parity required by the low-pass equivalent polynomial approximation. This way, not only we prove that the theoretical reticence that was raised to similar approaches previously proposed for the memoryless polynomial and the memory polynomial were unfounded, as experimental results fully justified this novel approach.

Parameter estimation for nonlinear Volterra systems by using the multi-innovation identification theory and tensor decomposition

Abstract: The Volterra model can represent a wide range of nonlinear dynamical systems. However, its practical use in nonlinear system identification is limited due to the exponentially growing number of Volterra kernel coefficients as the degree increases. This paper considers the identification issue of discrete-time nonlinear Volterra systems and uses a tensorial decomposition called PARAFAC to represent the Volterra kernels which can provide a significant parametric reduction compared with the conventional Volterra model. Applying the multi-innovation identification theory, the recursive algorithm by combining the l2-norm is proposed for the PARAFAC-Volterra models with the Gaussian noises. In addition, the multi-innovation algorithm combining with the logarithmic p-norms is investigated for the nonlinear Volterra systems with the non-Gaussian noises. Finally, some simulation results illustrate the effectiveness of the proposed identification methods.