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Nonlinear system identification : NARMAX methods in the time, frequency, and spatio-temporal domains
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: * The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model * The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term * Statistical and qualitative model validation methods that can be applied to any model class * Generalised frequency response functions which provide significant insight into nonlinear behaviours * A completely new class of filters that can move, split, spread, and focus energy * The response spectrum map and the study of sub harmonic and severely nonlinear systems * Algorithms that can track rapid time variation in both linear and nonlinear systems * The important class of spatio-temporal systems that evolve over both space and time * Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
eBook
Migrating photon avalanche in different emitters at the nanoscale enables 46th-order optical nonlinearity
A photon avalanche (PA) effect that occurs in lanthanide-doped solids gives rise to a giant nonlinear response in the luminescence intensity to the excitation light intensity. As a result, much weaker lasers are needed to evoke such PAs than for other nonlinear optical processes. Photon avalanches are mostly restricted to bulk materials and conventionally rely on sophisticated excitation schemes, specific for each individual system. Here we show a universal strategy, based on a migrating photon avalanche (MPA) mechanism, to generate huge optical nonlinearities from various lanthanide emitters located in multilayer core/shell nanostructrues. The core of the MPA nanoparticle, composed of Yb
3+
and Pr
3+
ions, activates avalanche looping cycles, where PAs are synchronously achieved for both Yb
3+
and Pr
3+
ions under 852 nm laser excitation. These nanocrystals exhibit a 26th-order nonlinearity and a clear pumping threshold of 60 kW cm
−2
. In addition, we demonstrate that the avalanching Yb
3+
ions can migrate their optical nonlinear response to other emitters (for example, Ho
3+
and Tm
3+
) located in the outer shell layer, resulting in an even higher-order nonlinearity (up to the 46th for Tm
3+
) due to further cascading multiplicative effects. Our strategy therefore provides a facile route to achieve giant optical nonlinearity in different emitters. Finally, we also demonstrate applicability of MPA emitters to bioimaging, achieving a lateral resolution of ~62 nm using one low-power 852 nm continuous-wave laser beam.
A general mechanism, migrating photon avalanche, can generate large optical nonlinearity from various lanthanides emitters at the nanoscale.
Journal Article
Semiclassical standing waves with clustering peaks, for nonlinear Schrödinger equations
We study the following singularly perturbed problem
eBook
Nonlinear forced vibrations of FGM sandwich cylindrical shells with porosities on an elastic substrate
The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied. A step function and a porosity volume fraction are introduced to describe the porosities in FGM layers of sandwich shells. Using the Donnell’s nonlinear shallow shell theory and Hamilton’s principle, an energy approach is employed to gain the nonlinear equations of motion. Afterwards, the multi-degree-of-freedom nonlinear ordinary differential equations are carried out by using Galerkin scheme, and subsequently the pseudo-arclength continuation method is utilized to perform the bifurcation analysis. Finally, the effects of the core-to-thickness ratio, porosity volume fraction, power-law exponent, and external excitation on nonlinear forced vibration characteristics of FGM sandwich shells with porosities are investigated in detail.
Journal Article
Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities
The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: complex nonlinear mode (CNM) and extended periodic motion concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: extended energy balance method (E-EBM) and nonlinear modal synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail.
Journal Article