Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics

Analysis and synthesis techniques of nonlinear dynamical systems with applications to diagnostic of controlled thermonuclear fusion reactors

Nonlinear dynamical systems are of wide interest to engineers, physicists and mathematicians, and this is due to the fact that most of physical systems in nature are inherently non-linear. The nonlinearity of these systems has consequences on their time-evolution, which in some cases can be completely unpredictable, apparently random, although fundamentally deterministic. Chaotic systems are striking examples of this. In most cases, there are no hard and fast rules to analyse these systems. Often, their solutions cannot be obtained in closed form, and it is necessary to resort to numerical integration techniques, which, in case of high sensitivity to initial conditions, lead to ill-conditioning problems and high computational costs. The dynamical system theory, the branch of mathematics used to describe the behaviour of these systems, focuses not on finding exact solutions to the equations describing the dynamical system, but rather on knowing if the system stabilises to a steady state in the long term, and what are the possible attractors, e.g. a quasi-periodic or chaotic attractors. Regarding the synthesis, from both a practical and a theoretical standpoint, it is very desirable to develop methods of synthesizing these systems. Although extensive theory has been developed for linear systems, no complete formulation for nonlinear systems synthesis is present today. The main topic of this thesis is the solution of engineering problems related to the analysis and synthesis of nonlinear and chaotic systems. In particular, a new algorithm which optimizes Lyapunov exponents estimation in piecewise linear systems has been applied to PWL and polynomial chaotic systems. In the field of complex systems synthesis, a systematic method to project systems of order 2n characterized by two positive Lyapunov exponents, has been proposed. This procedure couples nth-order chaotic systems with a suitable nonlinear coupling function. Furthermore, a method for the fault detection has been developed. In the field of time series analysis, a new denoising method, based on the wavelet transform of the noisy signal, has been described. The method implements a variable thresholding, whose optimal value is determined by analysing the cross-correlation between the denoised signal and the residuals and by applying different criteria depending on the particular decomposition level. Finally, a study of dynamical behaviour of Type I ELMs has been performed for a future modelization of the phenomenon. In this context, a statistical analysis of time intervals between successive Type I ELMs has been proposed.---------------------------------- Il tema principale di questa tesi è la soluzione di problemi ingegneristici legati all’analisi e alla sintesi di sistemi dinamici non lineari. I sistemi dinamici non lineari sono di largo interesse per ingegneri, fisici e matematici, e questo è dovuto al fatto che la maggior parte dei sistemi fisici in natura è intrinsecamente non lineare. La non linearità di questi sistemi ha conseguenze sulla loro evoluzione temporale, che in certi casi può rivelarsi del tutto imprevedibile, apparentemente casuale, seppure fondamentalmente deterministica. I sistemi caotici sono un esempio lampante di questo comportamento. Nella maggior parte dei casi non esistono delle regole standard per l’analisi di questi sistemi. Spesso, le soluzioni non possono essere ottenute in forma chiusa, ed è necessario ricorrere a tecniche di integrazione numerica, che, in caso di elevata sensibilità alle condizioni iniziali, portano a problemi di mal condizionamento e di elevato costo computazionale. La teoria dei sistemi dinamici, la branca della matematica usata per descrivere il comportamento di questi sistemi, non si concentra sulla ricerca di soluzioni esatte per le equazioni che descrivono il sistema dinamico, ma piuttosto sull’analisi del comportamento a lungo termine del sistema, per sapere se questo si stabilizzi in uno stato stabile e per sapere quali siano i possibili attrattori, ad esempio, attrattori quasi-periodici o caotici. Per quanto riguarda la sintesi, sia da un punto di vista pratico che teorico, è molto importante lo sviluppo di metodi in grado di sintetizzare questi sistemi. Sebbene per i sistemi lineari sia stata sviluppata una teoria ampia e esaustiva, al momento non esiste alcuna formulazione completa per la sintesi di sistemi non lineari. In questa tesi saranno affrontati problemi di caratterizzazione, analisi e sintesi, legati allo studio di sistemi non lineari e caotici. La caratterizzazione dinamica di un sistema non lineare permette di individuarne il comportamento qualitativo a lungo termine. Gli esponenti di Lyapunov sono degli strumenti che permettono di determinare il comportamento asintotico di un sistema dinamico. Essi danno informazioni circa il tasso di divergenza di traiettorie vicine, caratteristica chiave delle dinamiche caotiche. Le tecniche esistenti per il calcolo degli esponenti di Lyapunov sono computazionalmente costose, e questo fatto ha in qualche modo precluso l’uso estensivo di questi strumenti in problemi di grandi dimensioni. Inoltre, durante il calcolo degli esponenti sorgono dei problemi di tipo numerico, per ciò il calcolo deve essere affrontato con cautela. L’implementazione di algoritmi veloci e accurati per il calcolo degli esponenti di Lyapunov è un problema di interesse attuale. In molti casi pratici il vettore di stato del sistema non è disponibile, e una serie temporale rappresenta l’unica informazione a disposizione. L’analisi di serie storiche è un metodo di analisi dei dati provenienti da serie temporali che ha lo scopo di estrarre delle statistiche significative e altre caratteristiche dei dati, e di ottenere una comprensione della struttura e dei fattori fondamentali che hanno prodotto i dati osservati. Per esempio, un problema dei reattori a fusione termonucleare controllata è l’analisi di serie storiche della radiazione Dα, caratteristica del fenomeno chiamato Edge Localized Modes (ELMs). La comprensione e il 16 controllo degli ELMs sono problemi cruciali per il funzionamento di ITER, in cui il type-I ELMy H-mode è stato scelto come scenario di funzionamento standard. Determinare se la dinamica degli ELM sia caotica o casuale è cruciale per la corretta descrizione dell’ELM cycle. La caratterizzazione dinamica effettuata sulle serie temporali ricorrendo al cosiddetto spazio di embedding, può essere utilizzata per distinguere serie random da serie caotiche. Uno dei problemi più frequenti che si incontra nell’analisi di serie storiche sperimentali è la presenza di rumore, che in alcuni casi può raggiungere anche il 10% o il 20% del segnale. È quindi essenziale , prima di ogni analisi, sviluppare una tecnica appropriata e robusta per il denosing. Quando il modello del sistema è noto, l’analisi di serie storiche può essere applicata al rilevamento di guasti. Questo problema può essere formalizzato come un problema di identificazione dei parametri. In questi casi, la teorie dell’algebra differenziale fornisce utili informazioni circa la natura dei rapporti fra l’osservabile scalare, le variabili di stato e gli altri parametri del sistema. La sintesi di sistemi caotici è un problema fondamentale e interessante. Questi sistemi non implicano soltanto un metodo di realizzazione di modelli matematici esistenti ma anche di importanti sistemi fisici reali. La maggior parte dei metodi presentati in letteratura dimostra numericamente la presenza di dinamiche caotiche, per mezzo del calcolo degli esponenti di Lyapunov. In particolare, le dinamiche ipercaotiche sono identificate dalla presenza di due esponenti di Lyapunov positivi

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks

Nondestructive Testing in Composite Materials

In this era of technological progress and given the need for welfare and safety, everything that is manufactured and maintained must comply with such needs. We would all like to live in a safe house that will not collapse on us. We would all like to walk on a safe road and never see a chasm open in front of us. We would all like to cross a bridge and reach the other side safely. We all would like to feel safe and secure when taking a plane, ship, train, or using any equipment. All this may be possible with the adoption of adequate manufacturing processes, with non-destructive inspection of final parts and monitoring during the in-service life of components. Above all, maintenance should be imperative. This requires effective non-destructive testing techniques and procedures. This Special Issue is a collection of some of the latest research in these areas, aiming to highlight new ideas and ways to deal with challenging issues worldwide. Different types of materials and structures are considered, different non-destructive testing techniques are employed with new approaches for data treatment proposed as well as numerical simulations. This can serve as food for thought for the community involved in the inspection of materials and structures as well as condition monitoring

Early characterisation of neurodegeneration with high-resolution magnetic resonance elastography

This thesis contributes to recent interest within medical imaging regarding the development and clinical application of magnetic resonance elastography (MRE) to the human brain. MRE is a non-invasive phase-contrast MRI technique for measurement of brain mechanical properties in vivo, shown to reflect the composition and organisation of the complex tissue microstructure. MRE is a promising imaging biomarker for the early characterisation of neurodegeneration due to its exquisite sensitivity to variation among healthy and pathological tissue. Neurodegenerative diseases are debilitating conditions of the human nervous system for which there is currently no cure. Novel biomarkers are required to improve early detection, differential diagnosis and monitoring of disease progression, and could also ultimately improve our understanding of the pathophysiological mechanisms underlying degenerative processes. This thesis begins with a theoretical background of brain MRE and a description of the experimental considerations. A systematic review of the literature is then performed to summarise brain MRE quantitative measurements in healthy participants and to determine the success of MRE to characterise neurological disorders. This review further identified the most promising acquisition and analysis methods within the field. As such, subsequent visits to three brain MRE research centres, within the USA and Germany, enabled the acquisition of exemplar phantom and brain data to assist in discussions to refine an experimental protocol for installation at the Edinburgh Imaging Facility, QMRI (EIF-QMRI). Through collaborations with world-leading brain MRE centres, two high-resolution - yet fundamentally different - MRE pipelines were installed at the EIF-QMRI. Several optimisations were implemented to improve MRE image quality, while the clinical utility of MRE was enhanced by the novel development of a Graphical User Interface (GUI) for the optimised and automatic MRE-toanatomical coregistration and generation of MRE derived output measures. The first experimental study was performed in 6 young and 6 older healthy adults to compare the results from the two MRE pipelines to investigate test-retest agreement of the whole brain and a brain structure of interest: the hippocampal formation. The MRE protocol shown to possess superior reproducibility was subsequently applied in a second experimental study of 12 young and 12 older cognitively healthy adults. Results include finding that the MRE imaging procedure is very well tolerated across the recruited population. Novel findings include significantly softer brains in older adults both across the global cerebrum and in the majority of subcortical grey matter structures including the pallidum, putamen, caudate, and thalamus. Changes in tissue stiffness likely reflect an alteration to the strength in the composition of the tissue network. All MRE effects persist after correcting for brain structure volume suggesting changes in volume alone were not reflective of the detected MRE age differences. Interestingly, no age-related differences to tissue stiffness were found for the amygdala or hippocampus. As for brain viscosity, no group differences were detected for either the brain globally or subcortical structures, suggesting a preservation of the organisation of the tissue network in older age. The third experiment performed in this thesis finds a direct structure-function relationship in older adults between hippocampal viscosity and episodic memory as measured with verbal-paired recall. The source of this association was located to the left hippocampus, thus complementing previous literature suggesting unilateral hippocampal specialisation. Additionally, a more significant relationship was found between left hippocampal viscosity and memory after a new procedure was developed to remove voxels containing cerebrospinal fluid from the MRE analysis. Collectively, these results support the transition of brain MRE into a clinically useful neuroimaging modality that could, in particular, be used in the early characterisation of memory specific disorders such as amnestic Mild Cognitive Impairment and Alzheimer’s disease

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity