Antonin Novak

Nonlinear System Identification Using Exponential Swept-Sine Signal

In this paper, we propose a method for nonlinear system (NLS) identification using a swept-sine input signal and based on nonlinear convolution. The method uses a nonlinear model, namely, the nonparametric generalized polynomial Hammerstein model made of power series associated with linear filters. Simulation results show that the method identifies the nonlinear model of the system under test and estimates the linear filters of the unknown NLS. The method has also been tested on a real-world system: an audio limiter. Once the nonlinear model of the limiter is identified, a test signal can be regenerated to compare the outputs of both the real-world system and its nonlinear model. The results show good agreement between both model-based and real-world system outputs.

Nonparametric Identification of Nonlinear Systems in Series

In this paper, a method allowing the identification of two nonlinear systems in series is presented. More precisely, the identification of the second nonlinear subsystem under test is achieved by considering the effects of the nonlinearities of the first subsystem. The method is based on the estimation of the higher harmonic frequency responses from the measurement of distorted input and output signals. The second nonlinear system is then modeled by nonparametric generalized Hammerstein model made up of power series associated with linear filters. The method is experimentally validated in the well-known framework of nonlinear propagation of acoustic waves.

Comparison of non linear system identification methods : the example of non linear propagation of acoustic waves in ducts

The weakly non linear propagation of travelling acoustic waves in ducts is a well known problem leading to approximated analytical solutions. From an experimental point of view, the classical way for estimating the non linear parameters of propagation is to generate sine waves and to analyse the higher order harmonics as a function of the amplitude and the frequency of the excitation. In this work, new methods for estimating the non linear parameters of propagation are developed and compared to the sine excitation based method. The excitation signals associated to these new methods can be stationary noise or logarithmic chirps. For these excitation signals, the data processing is based on Multiple Input Single Output (MISO) direct path method. The comparison is made in terms of signal to noise ratio robustness and computation time. Experimental and theoretical results are also compared. We particularly show that a measurement using only one logarithmic chirp allows estimating accurate results for a broad ...

Modeling of a one-dimensional acoustic device composed of a planar beam and fluid gap with discontinuity in thickness

Precise modeling of 1D acoustic devices (passive or active, miniaturized or not) containing a planar beam loaded by a fluid gap and cavities is of interest in a variety of applications (transducers, acoustic filters, metamaterials, etc.). An analytical approach presented herein enables the description of the vibration of the planar elastically supported rigid beam of rectangular crossection surrounded by very thin slits and loaded by the fluid gap, which is divided in three parts of different thicknesses (the central part being the thinner one), the thermoviscous losses originating in the fluid being taken into account. Comparing to the case of the fluid gap of uniform thickness, such a geometry provides more parameters which can be adjusted in order to achieve the required behavior (resonant or damped, etc.). The analytically calculated beam displacement is presented and compared to the numerical solution provided by finite element method (a reference against which the analytical results are tested).

Modeling of 1D acoustic device composed of a planar beam and a fluid gap with discontinuity in thickness

Precise modeling of 1D acoustic devices (passive or active, miniaturized or not) containing a planar beam loaded by a fluid gap and cavities is of interest in a variety of applications (transducers, acoustic filters, metamaterials, etc.). An analytical approach presented herein enables to describe the vibration of the planar elastically supported rigid beam of rectangular cross-section surrounded by very thin slits and loaded by the fluid gap, which is divided in three parts of different thicknesses (the central part being the thinner one), the thermoviscous losses originating in the fluid being taken into account. Comparing to the case of the fluid gap of uniform thickness, such a geometry provides more parameters which can be adjusted in order to achieve the required behavior (resonant or damped, etc.). The analytically calculated beam displacement is presented and compared to the numerical solution provided by finite element method (a reference against which the analytical results are tested).