Sensitivity study of generalised frequency response functions

The dependence and independence of input signal amplitudes for Generalised Frequency Response Functions(GFRF’s) are discussed based on parametric modelling

Analysis of nonlinear oscillators in the frequency domain using volterra series Part II : identifying and modelling jump Phenomenon

In this the second part of the paper, a common and severe nonlinear phenomenon called jump, a behaviour associated with the Duffing oscillator and the multi-valued properties of the response solution, is investigated. The new frequency domain criterion of establishing the upper limits of the nonlinear oscillators, developed in Part I of this paper, is applied to predict the onset point of the jump, and the Volterra time and frequency domain analysis of this phenomenon are carried out based on graphical and numerical techniques

Piecewise Volterra modelling of the Duffing oscillator in the frequency domain

When analysing the nonlinear Duffing oscillator, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear oscillators, which can be transformed into the frequency domain, can generally only provide Volterra modelling and analysis in the frequency-domain over a fraction of the entire framework of weak nonlinearity. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the frequency domain, to weakly nonlinear Duffing systems at a wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address

Estimation of generalised frequency response functions

Volterra series theory has a wide application in the representation, analysis, design and control of nonlinear systems. A new method of estimating the Volterra kernels in the frequency domain is introduced based on a non-parametric algorithm. Unlike the traditional non-parametric methods using the DFT transformed input-output data, this new approach uses the time domain measurements directly to estimate the frequency domain response functions

A new frequency domain representation and analysis for subharmonic oscillation

For a weakly nonlinear oscillator, the frequency domain Volterra kernels, often called the generalised frequency response functions, can provide accurate analysis of the response in terms of amplitudes and frequencies, in a transparent algebraic way. However a Volterra series representation based analysis will become void for nonlinear oscillators that exhibit subharmonics, and the problem of finding a solution in this situation has been mainly treated by the traditional analytical approximation methods. In this paper a novel method is developed, by extending the frequency domain Volterra representation to the subharmonic situation, to allow the advantages and the benefits associated with the traditional generalised frequency response functions to be applied to severely nonlinear systems that exhibit subharmonic behaviour

Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation

Analysis of a duffing oscillator that exhibits hysteresis with varying excitation frequency and amplitude

Hysteresis, or jump phenomenon, are a common and severe nonlinear behaviour associated with the Duffing oscillator and the multi-valued properties of the response solution. Jump phenomenon can be induced by either varying the amplitude or the frequency of excitation. In this paper a new time and frequency domain analysis is applied to this class of system based on the response curve and the response spectrum map

Adaptive response to oxidative stress in the filamentous fungus Aspergillus niger B1-D

In the present study, we used a recombinant filamentous fungus strain, Aspergillus niger B1-D, as a model system, and investigated the antioxidant defences in this organism. Our findings indicate that pretreatment with low concentrations of H2O2 completely prevents killing by this oxidant at high concentrations. It shows that A. niger adapts to exposure to H2O2 by reducing growth and inducing a number of antioxidant enzyme activities, including superoxide dismutase, catalase, glutathione peroxidase, glutathione reductase, of which the induction of catalase is the most pronounced. Moreover the decline of these antioxidant enzymes activities after H2O2 detoxification, coincides with recommencement of growth. Results from monitoring the extracellular H2O2 concentration clearly indicate a very rapid detoxification rate for H2O2 in adapted A. niger cultures. A mathematical model predicts only very low concentrations of intracellular H2O2 accumulating in such cultures. Our results also show that glutathione plays a role in the oxidative defence against H2O2 in A. niger. On addition of H2O2, the intracellular pool of glutathione increases while the redox state of glutathione becomes more oxidized

Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV