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This dissertation uses spatial filtering to develop a large eddy simulation reduced order model (LES-ROM) framework for fluid flows. Proper orthogonal decomposition is utilized to extract the dominant spatial structures of the system. Within the general LES-ROM framework, two approaches are proposed to address the celebrated ROM closure problem. No phenomenological arguments (e.g., of eddy viscosity type) are used to develop these new ROM closure models. The first novel model is the approximate deconvolution ROM (AD-ROM), which uses methods from image processing and inverse problems to solve the ROM closure problem. The AD-ROM is investigated in the numerical simulation of a 3D flow past a circular cylinder at a Reynolds number $Re=1000$. The AD-ROM generates accurate results without any numerical dissipation mechanism. It also decreases the CPU time of the standard ROM by orders of magnitude. The second new model is the calibrated-filtered ROM (CF-ROM), which is a data-driven ROM. The available full order model results are used offline in an optimization problem to calibrate the ROM subfilter-scale stress tensor. The resulting CF-ROM is tested numerically in the simulation of the 1D Burgers equation with a small diffusion parameter. The numerical results show that the CF-ROM is more efficient than and as accurate as state-of-the-art ROM closure models. / Ph. D. / Numerical simulation of complex fluid flows is often challenging in many realistic engineering, scientific, and medical applications. Indeed, an accurate numerical approximation of such flows generally requires millions and even billions of degrees of freedom. Furthermore, some design and control applications involve repeated numerical simulations for different parameter values. Reduced order models (ROMs) are an efficient approach to the numerical simulation of fluid flows, since they can reduce the computational time of a brute force computational approach by orders of magnitude while preserving key features of the flow. Our main contribution to the field is the use of spatial filtering to develop better ROMs. To construct the new spatially filtered ROMs, we use ideas from image processing and inverse problems, as well as data-driven algorithms. The new ROMs are more accurate than standard ROMs in the numerical simulation of challenging three-dimensional flows past a circular cylinder.

Non-destructive testing (NDT) techniques are critical to ensure integrity and safety of engineered structures. Structural health monitoring (SHM) is considered as the next step in the field enabling continuous monitoring of structures. The first part of the thesis concerns NDT and SHM using guided waves in plates, or Lamb waves, to perform imaging of plate structures. The imaging is performed using a fixed active array setup covering a larger area of a plate. Current methods are based on conventional beamforming techniques that do not efficiently exploit the available data from the small arrays used for the purpose. In this thesis an adaptive signal processing approach based on the minimum variance distortionless response (MVDR) method is proposed to mitigate issues related to guided waves, such as dispersion and the presence of multiple propagating modes. Other benefits of the method include a significant increase in resolution. Simulation and experimental results show that the method outperforms current standard processing techniques. The second part of the thesis addresses transducer design issues for resonant ultrasound inspections. Resonant ultrasound methods utilize the shape and frequency of the object's natural modes of vibration to detect anomalies. The method considered in the thesis uses transducers that are acoustically coupled to the inspected structures. Changes in the transducer's electrical impedance are used to detect defects. The sensitivity that can be expected from such a setup is shown to highly depend on the transducer resonance frequency, as well as the working frequency of the instrument. Through simulations and a theoretical argumentation, optimal conditions to achieve high sensitivity are given.

Η σύγχρονη μελέτη της κεντρικής και αυτόνομης δραστηριότητας θεωρούνται χρήσιμες στην ανάδειξη της σχέσης των δύο συστημάτων και της φυγόκεντρου ανατροφοδότησης των περιφερικών αλλαγών. Στην εργασία αυτή διερευνώνται οι πιθανές σχέσεις μεταξύ κεντρικών και αυτόνομων απαντήσεων σε σωματαισθητικούς ερεθισμούς. Η ηλεκτροδερμική δραστηριότητα (ΗΔΑ) είναι δείκτης της αυτόνομης δραστηριότητας. Προκλητά δυναμικά και ΗΔΑ καταγράφονταν ταυτόχρονα έπειτα από μια σειρά ερεθισμών του μέσου νεύρου ,με τρείς διαφορετικές εντάσεις, σε έξι φυσιολογικά άτομα. Η χαμηλότερη ένταση ερεθισμού ρυθμίζονταν έτσι ώστε να μη γίνεται αντιληπτή από το άτομα. Τα επάρματα P40, P100, N200 και P300 των προκλητών δυναμικών εξήχθησαν από το καταγεγραμμένο σήμα. Μελετήσαμε το πλάτος και τον λανθάνοντα χρόνο και διερευνήσαμε την πιθανή συσχέτιση των μεγεθών αυτών της ΗΔΑ. Χρησιμοποιήσαμε την συνηθισμένη μέθοδο της μεσοποίησης (average), καθώς και την προσέγγιση των μοναδιαίων απαντήσεων, εξάγωντας τις απαντήσεις με την χρήση χωρικού φίλτρου. Το συμπαθητικό νευρικό σύστημα φαινόταν να απαντά ακόμα και σε ερεθισμούς μη αντιληπτούς από το υποκείμενο. Η φλοιική επεξεργασία των αντιληπτών και μη ερεθισμάτων όπως αποτυπώνονταν με τα επάρματα των προκλητών δυναμικών, φαίνεται να είναι όμοια και στις δύο περιπτώσεις κατά τη διάρκεια των πρώτων 40ms έπειτα από τον ερεθισμό, ενώ τα μακρά κύματα ήταν απόνατ στους μη αντιληπτούς ερεθισμούς. Τα πλάτη της ΗΔΑ και του P300 με την προσέγγιση των μοναδιαίων απαντήσεων παρουσίαζαν μια σημαντική θετική συσχέτιση. / Concurrent studies of central and autonomic activity are considered useful in elucidating the relationship between the two systems and indicating the centripetal feedback of peripheral changes. The SSR (sympathetic skin response) is one index of autonomic arousal. In our study we examine the possible relationships between central and autonomic responses to somatosensory stimuli. EPs (evoked potentials) and SSRs were simultaneously recorded during a series of electrical stimuli of median nerve in six normal adults using three different intensities of stimuli. The weakest of them was unperceived by subject. The P40, P100, N200 and P300 waves of EPs were extracted and their latencies and amplitudes were analysed in order to find correlations with those of the SSRs. We used the conventional method of signal averaging and the single trial (ST) approach, as the EP waves were subtracted by spatial filtering. Interestingly, sympathetic nervous system seemed to react even to stimuli unperceived by the subject. The cortical processing of consciously perceived and unperceived somatosensory stimuli as it was expressed by the evoked potentials seems to be identical during the first 40ms after the stimulus onset while later waves were absent for unperceived stimuli. SSR and P300 amplitude at the ST level had a positive correlation.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

This work deals with the problem of reverse audio engineering for active listening. The format under consideration corresponds to the audio CD. The musical content is viewed as the result of a concatenation of the composition, the recording, the mixing, and the mastering. The inversion of the two latter stages constitutes the core of the problem at hand. The audio signal is treated as a post-nonlinear mixture. Thus, the mixture is "decompressed" before being "decomposed" into audio tracks. The problem is tackled in an informed context: The inversion is accompanied by information which is specific to the content production. In this manner, the quality of the inversion is significantly improved. The information is reduced in size by the use of quantification and coding methods, and some facts on psychoacoustics. The proposed methods are applicable in real time and have a low complexity. The obtained results advance the state of the art and contribute new insights.

L'estimation de l'état mental d'un individu sur la base de son activité cérébrale et de ses activités physiologiques résultantes est devenue l'un des challenges des interfaces cerveau-machine (ICM) dites passives, dans le but notamment de répondre à un besoin en neuroergonomie. Ce travail de thèse se focalise sur l'estimation des états de fatigue et de charge mentale. Son objectif est de proposer des chaines de traitement efficaces et réalistes dans leur mise en œuvre. Ainsi, un des points à l'étude a été la modulation des indicateurs de charge ainsi que la robustesse des performances de classification en fonction du temps passé sur une tâche (TPT). L'impact de la charge et du TPT sur les marqueurs d'état attentionnel a aussi été évalué. Pour ce faire, un protocole expérimental a été mis en œuvre afin de recueillir les signaux électro-encéphalographiques (EEG), cardiaques (ECG) et oculaires (EOG) de participants volontaires sains lors de la réalisation prolongée d'une tâche combinant charge en mémoire de travail et attention sélective. Des chaînes de traitement performantes incluant une étape de filtrage spatial et une classification supervisée ont été mises en place afin de classer au mieux ces états. La pertinence de plusieurs marqueurs électrophysiologiques a été comparée, notamment l'activité EEG spontanée et les potentiels évoqués (PEs), ainsi que différentes étapes de prétraitement dont les méthodes de filtrage spatial pour PEs. Des effets d'interactions ont été mis au jour entre les différents états mentaux, dont un effet négatif du TPT sur les performances en classification de la charge mentale lorsque l'on utilise des marqueurs mesurant la puissance moyenne de l'EEG dans des bandes de fréquence d'intérêt. La chaîne basée sur les PEs est en revanche robuste à cet effet. Une comparaison du type de stimuli utilisables pour éliciter les PEs a révélé que des stimuli tâche-indépendants permettent tout de même d'obtenir des performances très élevées, ce qui montre leur pertinence pour une implémentation en situation réelle. En perspective seront présentés des travaux en cours visant à mettre en évidence des marqueurs de charge mentale robustes à la tâche, ainsi que l'utilité des potentiels évoqués auditifs en paradigme de simple stimulus. / Mental state estimation on the basis of cerebral activity and its resulting physiological activities has become a challenge for passive Brain-Computer Interfaces (BCI), in particular to address a need in neuroergonomics. This thesis work focuses on mental fatigue and workload estimation. Its purpose is to provide efficient and realistic processing chains. Thus, one issue was the modulation of workload markers as well as classification performance robustness depending on time-on-task (TOT). The impact of workload and TOT on attentional state markers was also assessed. For those purposes, an experimental protocol was implemented to collect the electroencephalographic (EEG), cardiac (ECG) and ocular (EOG) signals from healthy volunteers as they performed for a prolonged period of time a task that mixes working memory load and selective attention. Efficient signal processing chains that include spatial filtering and classification steps were designed in order to better estimate these mental states. The relevance of several electrophysiological markers was compared, among which spontaneous EEG activity and event-related potentials (ERPs), as well as various preprocessing steps such as spatial filtering methods for ERPs. Interaction effects between mental states were brought to light. In particular, TOT negatively impacted mental workload estimation when using power features. However, the chain based on ERPs was robust to this effect. A comparison of the type of stimuli that can be used to elicit the ERPs revealed that task-independent probes still allow very high performance, which shows their relevance for real-life implementation. Lastly, ongoing work that aims at assessing task-robust workload markers, as well as the usefulness of auditory ERPs in a single-stimulus paradigm will be presented as prospects.