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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.

Covers theoretical and practical aspects related to the behavioral modelling and predistortion of wireless transmitters and power amplifiers. It includes simulation software that enables the users to apply the theory presented in the book. In the first section, the reader is given the general background of nonlinear dynamic systems along with their behavioral modelling from all its aspects. In the second part, a comprehensive compilation of behavioral models formulations and structures is provided including memory polynomial based models, box oriented models such as Hammerstein-based and Wiener-based models, and neural networks-based models. The book will be a valuable resource for design engineers, industrial engineers, applications engineers, postgraduate students, and researchers working on power amplifiers modelling, linearization, and design.

Much work on analysis and synthesis problems relating to the multiple model approach has already been undertaken. This has been motivated by the desire to establish the problems of control law synthesis and full state estimation in numerical terms. In recent years, a general approach based on multiple LTI models (linear or affine) around various function points has been proposed. This so-called multiple model approach is a convex polytopic representation, which can be obtained either directly from a nonlinear mathematical model, through mathematical transformation or through linearization around various function points. This book concentrates on the analysis of the stability and synthesis of control laws and observations for multiple models. The authors’ approach is essentially based on Lyapunov’s second method and LMI formulation. Uncertain multiple models with unknown inputs are studied and quadratic and non-quadratic Lyapunov functions are also considered.

Process engineering became, recently in historical terms, an extension of food engineering principles to other fields of manufacturing as the food biotechnology and beverage industry is. This article proposes a non-linear mathematical model that makes possible the simulation of the batch alcoholic fermentation of white wine. The model was developed based on the zone modelling principle, considering the physiological states of the yeast cells. The nonlinear mathematical model led to a good qualitative and quantitative description of the alcoholic fermentation process. The model was implemented as a Matlab S-function and the results were compared with the existing experimental data. Further on, the mathematical model was used for the investigation of the dynamic behaviour of a batch fermentation process through direct sensitivity analysis method (DSA). The DSA of dynamic model allowed the calculus of the matrix of the sensitivity functions in order to determine the influence of the small deviations of initial state and parameters from their nominal values on the state trajectory and system output over the time.

This book aims to propose the implementation and application of Fractional Order Systems (FOS). It is well known that FOS can be utilized in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductory chapters are included on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material will have applications in robotics, aerospace and biomedicine.

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

This paper focuses on the influence of radial internal clearance on the dynamics of a rolling-element bearing. In the beginning, the 2—Degree of Freedom (DOF) model was studied, in which the clearance was treated as a bifurcation parameter. The derived nonlinear mathematical model is based on Hertzian contact theory and takes into consideration shape errors of rolling surfaces and eccentricity reflecting real operating conditions. The analysis showed characteristic dynamical behavior by specific clearance range, which reflects others in a low or high amplitude and can refer to the optimal clearance. The experimental validation was conducted with the use of a double row self-aligning ball bearing (SABB) NTN 2309SK in which the acceleration response was measured by various rotational velocities. The time series obtained from the mathematical model and the experiment were analyzed with the recurrence quantification analysis.

This study explores optical solitons in the Biswas–Arshed equation within birefringent fibers. Employing the unified solver method, the 1 φ ( η ) , φ ′ ( η ) φ ( η ) method, and new Kudryashov’s method, we extract various optical soliton solutions, encompassing dark, singular, bright, and periodic forms. These solutions deepen our understanding of dynamic phenomena in birefringent fibers, showcasing their potential practical applications. The results, effectively visualized in 3D and 2D plots, reveal intricate patterns. Our research underscores the efficacy and simplicity of these approaches in obtaining optical solitons for diverse nonlinear evolution equations. The novelty lies in the advanced methodologies applied to investigate the Biswas–Arshed equation, yielding a diverse array of soliton solutions and their practical implications. This study not only presents a variety of solutions but also highlights their applicability across disciplines and real-world scenarios. Consequently, our research significantly contributes to advancing our understanding of optical solitons in birefringent fibers, offering a methodological breakthrough in engineering and applied physics.

The objective of this paper is to propose a mathematical model representing the hydraulic behavior of a generic three-tank aquaponic system, capable to support future research on optimized sizing and suited control algorithms. The components of the system are a fish tank, a hydroponic reservoir, and a multi-task buffer water tank. The mathematical model is structural, representing the water-tanks and the water-flows between them, by differential equations, implemented in Matlab-Simulink.