scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: In this correspondence, closed-form expressions for the blind identification of linear-quadratic Volterra systems are established and Cumulant-based formulas are developed demonstrating that the system is uniquely identifiable.
Abstract: In this correspondence, closed-form expressions for the blind identification of linear-quadratic Volterra systems are established. The system is excited by a complex valued random sequence and the output cumulants (of order up to 4) are employed. It is assumed that the memory of the linear part is greater than or equal to the memory of the quadratic part. Cumulant-based formulas are developed demonstrating that the system is uniquely identifiable. An SVD based variant with improved performance is also derived. Simulations and comparisons with existing techniques are presented.

16 citations

Proceedings ArticleDOI
27 Apr 1993
TL;DR: It is shown that PRMS are persistently exciting for a Volterra series model with nonlinearities of polynomial degree N if and only if the sequence takes on N+1 or more distinct levels.
Abstract: The authors consider pseudorandom multilevel sequences (PRMS) for the identification of nonlinear systems modeled via a truncated Volterra series with a finite degree of nonlinearity and finite memory length. It is shown that PRMS are persistently exciting (PE) for a Volterra series model with nonlinearities of polynomial degree N if and only if the sequence takes on N+1 or more distinct levels. A computationally efficient least squares identification algorithm based on PRMS inputs is developed that avoids forming the inverse of the data matrix. Simulation results comparing identification accuracy using PRMS and Gaussian white noise are given. >

16 citations

Journal ArticleDOI
TL;DR: In this article, an approach for nonlinear system identification using output-only data is proposed, where the outputs of the system are computed by multiple convolutions between the excitation force and the Volterra kernels.
Abstract: The operational modal analysis methods based on output-only measurements are well-known and applied in linear systems. However, they are not so well developed for nonlinear systems. Thus, this paper proposes an approach for nonlinear system identification using output-only data. In the conventional Volterra series, the outputs of the system are computed by multiple convolutions between the excitation force and the Volterra kernels. However, in this paper at least two time series measured in different placements are used to compute the multiple convolutions and the excitation signals are not required. The novel kernels identified can be used to characterize nonlinear behavior through a model using only output data. A numerical example based on a Duffing oscillator with two degrees-of-freedom (2DOF) and experimental vibration data from a buckled beam with hardening nonlinearities are used to illustrate the proposed method. The prediction results using output-only data are similar to the conventional Volterra kernels based on input and output data.

16 citations

Journal ArticleDOI
TL;DR: The theoretical analysis of the effects of nonlinear viscous damping on vibration isolation using the output frequency response function approach reveals that the force transmissibility of the oscillator is suppressed due to the existence of the fractional order damping, but the results can be used as designing parameters for vibration isolation systems.
Abstract: Motivated by the theoretical analysis of the effects of nonlinear viscous damping on vibration isolation using the output frequency response function approach, the output frequency response function approach is employed to investigate the effects of the nonlinear fractional order damping on vibration isolation based on Volterra series in the frequency domain. First, the recursive algorithm which is proposed by Billings et al. is extended to deal with the system with fractional order terms. Then, the analytical relationships are established among the force transmissibility, nonlinear characteristic coefficients and fractional order parameters for the single degree of freedom oscillator. Consequently, the effects of the nonlinear system parameters on the force transmissibility are discussed in detail. The theoretical analysis reveals that the force transmissibility of the oscillator is suppressed due to the existence of the fractional order damping, but presents different effects on suppressing the ...

16 citations

Journal ArticleDOI
TL;DR: In this article, the radial basis function (RBF) neural network is proposed to model the dynamics underlying the fMRI data and the equivalence of the proposed method to the existing Volterra series method has been demonstrated.
Abstract: Functional magnetic resonance imaging (fMRI) is an important technique for neuroimaging. The conventional system identification methods used in fMRI data analysis assume a linear time-invariant system with the impulse response described by the hemodynamic responses (HDR). However, the measured blood oxygenation level-dependent (BOLD) signals to a particular processing task (for example, rapid event-related fMRI design) show nonlinear properties and vary with different brain regions and subjects. In this paper, radial basis function (RBF) neural network (a powerful technique for modelling nonlinearities) is proposed to model the dynamics underlying the fMRI data. The equivalence of the proposed method to the existing Volterra series method has been demonstrated. It is shown that the first- and second-order Volterra kernels could be deduced from the parameters of the RBF neural network. Studies on both simulated (using Balloon model) as well as real event-related fMRI data show that the proposed method can accurately estimate the HDR of the brain and capture the variations of the HDRs as a function of the brain regions and subjects.

16 citations


Network Information
Related Topics (5)
Linear system
59.5K papers, 1.4M citations
80% related
Amplifier
163.9K papers, 1.3M citations
77% related
Control theory
299.6K papers, 3.1M citations
77% related
Robustness (computer science)
94.7K papers, 1.6M citations
77% related
Nonlinear system
208.1K papers, 4M citations
75% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202315
202246
202146
202057
201983
201881