Subharmonic oscillation modeling and MISO Volterra series

Subharmonic generation is a complex nonlinear phenomenon which can arise from nonlinear oscillations, bifurcation and chaos. It is well known that single-input–single-output Volterra series cannot currently be applied to model systems which exhibit subharmonics. A new modeling alternative is introduced in this paper which overcomes these restrictions by using local multiple input single output Volterra models. The generalized frequency-response functions can then be applied to interpret systems with subharmonics in the frequency domain

The Response Spectrum Map, a Frequency Domain Equivalent to the Bifurcation Diagram

The Response Spectrum Map (RSM) is introduced as a frequency domain equivalent to the Bifurcation Diagram. The RSM is a map of the energy distribution of a system in the frequency domain, where subharmonics, superharmonics and chaos generation can be revealed. The RSM is used in this paper to qualitatively analyse and detect various dynamical states exhibited by a nonlinear system

Dynamic Wavelet and Equivalent Models

The representation of nonlinear dynamic wavelet models in the form of an equivalent global model which is valid over the operating range of the system is investigated. The results are used to analyse and interpret the nonlinear wavelet models using non-linear frequency response functions

Subharmonic Oscillation Modelling and MISO Volterra Series

Subharmonic generation is a complex nonlinear phenomenon which can arise from nonlinear oscillations, bifurcation and chaos. It is well known that single input output Volterra series cannot currently be applied to model systems which exhibit subharmonics. A new modelling alternative is introduced in this paper which overcomes these restrictions by using local multiple input output Volterra models. The generalised frequency response functions can then be applied to interpret systems with subharmonics in the frequency domain

The Response Spectrum Map, Volterra Series Representations and the Duffing Equation.

The validity of Volterra series representations is assessed in the time and frequency domain for the particular example of the Duffing oscillator. The theoretical results derived in the literature associated with the existence of the Volterra series are reviewed and tested for the Duffing equation. Response Spectrum Maps are introduced for the first time as frequency domain equivalent to the Bifurcation Diagram, and these are used to qualitatively analyse and detect various dynamical states exhibited by the Duffing oscillator

Spectral Analysis of Nonlinear Wave Forces

The spectral analysis of nonlinear wave forces is investigated, based on the Morison equation and related models including the recently introduced Dynamic Morison model. An expression for the response power spectrum is initially derived in terms of the higher-order nonlinear frequency response functions and the spectrum of the input velocity. It is then shown how this can be evaluated for the Dynamic Morison model to yield an expression for the output power spectrum in terms of the coefficients of the time-domain differential equations and properties of the input. A comparison of the output spectra computed using traditional methods and the new expression of the response spectrum over several data sets is included. An interpretation of the Morison equation response spectrum is finally given

Identification of Nonlinear Processes in the Magnetospheric Dynamics and Forecasting of Dst Index

The NARMAX approach is used to analyse simultaneous measurements of the geomagnetic Dst index and VBs, the merging rate of the IMF and the geomagnetic field. The nonlinear discrete relation which describes the dynamics of the Dst index driven by VBs is identified directly from experimental measurements. This identified model is then used to forecast the evolution of the Dst index. Analysis of the identified model in the frequency domain provides information about the types of nonlinearities involved in the energy storage process in the magnetosphere. It is also shown how the nonlinear frequency response functions derived from the data can be used to validate theoretical models proposed to describe the evolution of the magnetosphere

Global Nonlinear Model for the Evolution of the Dst Index

The NARMAX (Nonlinear Auto Regressive Moving Average model with eXogenous inputs) approach is used to analyse simultaneous measurements of the geomagnetic Dst Index and the merging rate of the IMF and the geomagnetic field VBs. A nonlinear discrete relation which describes the dynamics of the Dst index driven by VBs is derived directly from experimental measurements. This relation can be used to forecast the evolution of Dst index. Higher order spectral analysis of the identified model provides information about nonlinear coupling between the various spectral components

Time and Frequency Domain Identification and Analysis of a Gas Turbine Engine

The NARMAX (Nonlinear Auto Regressive Moving Average model with eXogenous inputs) approach has been used to analyse the dynamics of a gas turbine engine. The fuel flow-shaft speed relationship is analysed by identifying both time and frequency domain models of the system. The frequency domain analysis is studied by mapping the discrete-time NARMAX models into the Generalised Frequency Response Functions (GFRF's) to reveal the nonlinear coupling between the various input spectral components and the energy transfer mechanisms in the system. A continuous-time nonlinear differential equation model is also estimated using the Generalised Frequency Response Functions