Volterra Kernels Of Nonlinear Systems Research Articles

Volterra Series identification Based on State Transition Algorithm with Orthogonal Transformation

A Volterra kernel identification method based on state transition algorithm with orthogonal transformation (called OTSTA) was proposed to solve the hard problem in identifying Volterra kernels of nonlinear systems. Firstly, the population with chaotic sequences was initialized by using chaotic strategy. Then the orthogonal transformation was used to finish the mutation operator of the selected individual. OTSTA was used on the identification of Volterra series, and compared with particle swarm optimization (called PSO) and state transition algorithm (STA). The simulation results showed that OTSTA has better identification precision and convergence than PSO and STA under non-noise interference. And when there is noise, the identification precision, convergence and anti-interference of OTSTA are also superior to PSO and STA.

Identification of Nonlinear Parameters by Using M-sequence and Harmonic Probing Method

Many classes of nonlinear systems can be represented by Volterra kernels. The authors have recently developed a method for identification of Volterra kernels of nonlinear systems by using M-sequence and correlation technique. In this paper, the authors propose a new method for identification of nonlinear mechanical systems by use of Volterra kernels. The nonlinear mechanical systems are approximated to a nonlinear vibrating system which consists of a mass, a dumper, a linear spring and nonlinear and springs. Then, the parameters, which represent the nonlinear springs are calculated by use of the Volterra kernels. From the results of computer simulation and experiment, the parameters that represent the nonlinear characteristics of the nonlinear mechanical systems can be identified by the proposed method.

Use of Meixner Functions in Estimation of Volterra Kernels of Nonlinear Systems With Delay

Volterra series representation of nonlinear systems is a mathematical analysis tool that has been successfully applied in many areas of biological sciences, especially in the area of modeling of hemodynamic response. In this study, we explored the possibility of using discrete time Meixner basis functions (MBFs) in estimating Volterra kernels of nonlinear systems. The problem of estimation of Volterra kernels can be formulated as a multiple regression problem and solved using least squares estimation. By expanding system kernels with some suitable basis functions, it is possible to reduce the number of parameters to be estimated and obtain better kernel estimates. Thus far, Laguerre basis functions have been widely used in this framework. However, research in signal processing indicates that when the kernels have a slow initial onset or delay, Meixner functions, which can be made to have a slow start, are more suitable in terms of providing a more accurate approximation to the kernels. We, therefore, compared the performance of Meixner functions, in kernel estimation, to that of Laguerre functions in some test cases that we constructed and in a real experimental case where we studied photoreceptor responses of photoreceptor cells of adult fruitflies (Drosophila melanogaster). Our results indicate that when there is a slow initial onset or delay, MBF expansion provides better kernel estimates.

非線形システムの偶数次及び奇数次Volterra核の分離同定

非線形システムの偶数次及び奇数次Volterra核の分離同定

低次M系列を用いる非線形系のVolterra核の同定法

低次M系列を用いる非線形系のVolterra核の同定法

Identification of Volterra Kernels of Nonlinear Systems by use of Μ-Sequence Correlation

A new method for obtaining Volterra kernels of nonlinear system by use of pseudo random M-sequences and correlation technique is described. The application of this method to two actual nonlinear systems (mechanical and chemical system) is carried out. The comparison is made between the actual output with estimated output which is calculated from the measured Volterra kernels, showing a good agreement between them. This method of nonlinear system identification would be useful in actual nonlinear systems.

Adaptive estimation of third-order frequency domain Volterra kernels

Techniques for adaptive estimation of frequency domain Volterra kernels of non-linear systems up to the third order are investigated. A simple adaptive algorithm for identifying the frequency domain Volterra kernels is derived based on the assumption that the input is Gaussian. Compared with the conventional adaptive method based on the recursive least squares (RLS) technique, the proposed method requires substantially less computation and computer memory. The insensitivity of the proposed method to the Gaussianity assumption of the input is also demonstrated via computer simulation and application to experimental data. The results show that the proposed adaptive method is comparable in performance with the conventional RLS-based adaptive method even when the input is non-Gaussian.

非線形システムのボルテラ核の同定

非線形システムのボルテラ核の同定

Exploitation of cyclostationarity for identifying the Volterra kernels of nonlinear systems

A class of random time-series inputs for nonlinear time-invariant systems that permit the analytical specification of a set of operators on the input that are orthonormal over all time to the Volterra operators for all orders and all lag sets is introduced. The time series in this class are cyclostationary and complex valued. The orthonormal operators are used to obtain an input-output type of cross-correlation formula for identifying the individual Volterra kernels of arbitrary order for a nonlinear system of possibly infinite order and possibly infinite memory. The real parts of the complex-valued inputs in this class comprise a class of real-valued inputs for which the same sets of specified operators apply. However, the orthogonality for different orders holds for these real inputs only for Volterra operators of order less than the order of the specified operator. Thus, these real inputs can be used to identify Volterra kernels only for finite-order systems. Frequency-domain counterparts of the time-domain methods that can utilize an FFT algorithm are developed. >

Identification of the Volterra kernels of nonlinear systems

Identification of the Volterra kernels of nonlinear systems

Multidimensional Laguerre transform

The description of the Volterra kernels of nonlinear systems leads us to define the multidimensional Laguerre transform. This transform allows the construction of the isomorphism between the continuous signal space and the discrete signal space.

Caractérisation des noyaux de Volterra d'un systéme non lineaire (Characterisation of the Volterra kernels of a nonlinear system)

A procedure is described which allows the determination of the Volterra kernels of nonlinear systems. The output of each kernel is determined and a double decomposition on a set of orthonormal functions is used to identify the kernels