The present thesis concerns with a few investigations on sensing/measurement of small angle rotation/tilt using Pattern Imaging Method. The methodology involves looking at the tailored-objects located adjacent to the observer (CCD camera) through a mirror and extracts the angular position of the mirror from their images by processing the latter through object specific algorithm. Its principal advantage stems from the fact that small-angle measurement can be done using ambient light which is neither collimated nor filtered for single wavelength. This makes the associated optical configuration not only simple but also robust for the said application, in comparison to currently competing technologies based on Autocollimation and Interferometry. The present thesis elaborates specifically four new Pattern-Designs proposed for tailoring the spatial-brightness of the objects. Introducing for the first time, processing algorithms based on ‘Modified Fringe-Processing Strategy’ and ‘Phase-Only-Correlation’, the investigations demonstrate enhanced performance for small angle measurement with all the proposed pattern designs. The first three designs for the pattern are evaluated for 1-D measurement through fringe processing approach while the fourth pattern design is evaluated for 2-D measurement through Phase-only-Correlation. The results of the investigations are utilized to propose, design and develop a novel optical inclinometer which can work with any of the proposed pattern designs as the object. The first three pattern-designs rely upon sinusoidal modulation of the object surface and utilize three custom developed algorithms -Algorithm-A, Algorithm-B and Algorithm-C -to extract two quantities namely wrapped phase Δαw and unwrapped phase Δαuw , from the captured images. Each of these quantities will have an associated measurement range and accuracy corresponding to any of the three pattern designs. All measurements are carried out keeping the object/camera to mirror distance constant at 250 mm. From wrapped phase measurement, all the three designs, each with pitch of 2mm for sinusoidal modulation and held at a distance of 250 mm from the mirror, have been found to facilitate reliable angle measurement over a range of 850 arc seconds with accuracy better than 1 arc second after curve fitting the experimentally obtained data. From unwrapped phase measurement, the color coded as well as BCD coded composite patterns, when tested using five bands of sinusoidal modulation (with a pitch of 2mm) and held at a distance of 250 mm from the mirror, facilitated reliable angle measurement over a larger range of nearly 10 . The 2-D angle measurement using fourth pattern-design and the Algorithm-D, facilitated measurement over a range of 10 with an accuracy of 9 arc seconds when the distance between the mirror and the pattern is held at 250 mm. A comparison of the results from the present investigation with the best performance from other investigators reveals the following. The proposed modifications in the processing algorithms as well as the pattern designs help to achieve a measurement range of 750 arc seconds with accuracy better than 1 arc second from this method, with an object pattern whose lateral size is smaller by a factor of nearly 15. Such a size reduction in the object as well as the associated mirror would help to construct angle measuring instruments that work on this method more compactly. The results of the investigation have been utilized to propose and demonstrate a novel prototype optical inclinometer which has been experimentally found to work in a range of 0.40 with accuracy nearly 6 arc seconds.

Η εκπόνηση της συγκεκριμένης Μεταπτυχιακής Εργασίας, εξετάζει, καταρχήν, την έννοια της πιθανότητας και τις βασικές ιδιότητές της, όπως την τυχαία μεταβλητή και τη συνάρτηση κατανομής. Παράλληλα όμως, παρουσιάζει στοιχεία βασικών διακριτών και συνεχών κατανομών, όπως της κανονικής, της ομοιόμορφης, της Poisson, και άλλων κατανομών της γραμμικής στατιστικής. Στη συνέχεια, αναφέρεται στις βασικές έννοιες της περιγραφικής στατιστικής, όπως οργάνωση και γραφική αναπαράσταση στατιστικών δεδομένων, ομαδοποίηση παρατηρήσεων, ιστόγραμμα συχνοτήτων, καθώς και περιγραφικά μέτρα γραμμικών δεδομένων. Κυρίως, όμως, η παρούσα μελέτη αποτελεί μία γενική επισκόπηση των στατιστικών μεθόδων παρουσίασης και ανάλυσης των περιοδικών δεδομένων. Με τον όρο "περιοδικά δεδομένα", εννοούμε τυχαίες διευθύνσεις και κατευθύνσεις προσανατολισμού. Η παρουσίασης των τυχαίων γωνιών, των γραφικών αναπαραστάσεων των περιοδικών δεδομένων καθώς και των περιγραφικών μέτρων - μέτρα θέσεως, διασποράς, λοξότητας, κυρτώσεως - θα μας οδηγήσουν σε μία καλύτερη προσέγγιση, κατανόηση των περιοδικών κατανομών. Επιπλέον, θα παρουσιαστούν αναλυτικά οι βασικές περιοδικές κατανομές, ομοιόμορφη και Von Mises κατανομή. Όμως, θα εξεταστούν και άλλες κατανομές μονοκόρυφες ή πολυκόρυφες, όπως οι περιελιγμένες κατανομές , η συνημίτονο και η καρδιοειδής κατανομή, οι λοξές κατανομές κ.ά. Τέλος, η εργασία θα αναφερθεί σε μία οικογένεια συμμετρικών περιοδικών κατανομών που προτάθηκε από τον κύριο Παπακωνσταντίνου και αποτελεί επέκταση της καρδιοειδούς κατανομής,σύμφωνα με εργασία των επιστημόνων Toshihiro Abe,Arthur Pewsey,Kunio Shimizu, παρέχοντας σημαντικά πλεονεκτήματα σε σχέση με άλλες οικογένειες κατανομών. / The preparation of this thesis examines, in principle,the concept of probability and its basic properties, such as the random variable and distribution function and presents data of basic discrete and continuous distributions, including normal, uniform, the Poisson, and other distributions of linear statistics. Then it refers to the basic concepts of descriptive statistics, such as the organization and the graphic representation of statistical data, grouping observations Frequency histogram as well as descriptive measures of linear data. Mostly, though, this study represents an overview of statistic methods of presentation and analysis of periodic data. By the term "periodic data" we mean random addresses and directions orientation. The presentation of random angles, graphic representations of periodic data and descriptive measures - measures of location, dispersion, skewness and kurtosis - will lead us to a better approach and understanding of periodic distributions. Furthermore, we present in detail the basic periodic distributions, the uniform and the Von Mises distribution. But other unimodal and multimodal distributions will be examined such as wrapped distributions, the cosine and cardioid distribution, skewed distributions, etc. Finally, this thesis will mention a family of symmetric periodic distributions proposed by Mr. Papakonstantinou and an extension of the cardioid distribution, according to the paper published by the scientists Toshihiro Abe,Arthur Pewsey and Kunio Shimizu, where significant advantages are provided over other families of distributions.

<p> Wire-wrapped rod bundles are often used in nuclear reactors operating in a fast neutron spectrum, as designers seek to minimize neutron scattering by packing the fuel pins into a hexagonal lattice. Bundles with many rods have extensively been studied as representative of large fuel assemblies, however far fewer experiments have investigated bundles with 7 rods (7-pin bundles). The large difference in subchannel number between these bundles leads to 7-pin bundles having different pressure drop characteristics. The Versatile Test Reactor (VTR) sodium cartridge loop proposes to use a 7-pin bundle as its experimental core region, highlighting the need for additional data and models. The current work seeks to establish a better understanding of the pressure drop in 7-pin wire-wrapped rod bundles through scaled experiments and a novel pressure drop model. A scaling analysis is first performed to demonstrate the applicability of water experiments to the VTR sodium cartridge loop, before an experimental test facility is designed and constructed. Experiments are then performed at a range of Reynolds numbers to determine the pressure drop. Current models are able to predict the data well, but are complex and can be difficult to use. A comparatively simpler model is developed, based on exact laminar solutions of a simplified rod bundle, which also offers a theoretical lower bound for the pressure drop in wire-wrapped bundles. The proposed model compares well with the existing experimental database, able to predict bundle friction factor with an average absolute percent difference of 10.8%. This accuracy is also similar to existing correlations, while relying on fewer empirical coefficients. The theoretical lower bound is also used to identify several datasets in literature that may feature data that is systemically lower than the true pressure drop, which agrees with previous observations in literature. </p>

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