published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

In this document we review the status of existing techniques for nonlinear model order reduction by investigating how well these techniques perform for typical industrial needs. In particular the TPWL-method (Trajectory Piecewise Linear-method) and the POD-approach (Proper Orthogonal Decomposion) is taken under consideration. We address several questions that are (closely) related to both the theory and application of nonlinear model order reduction techniques. The goal of this document is to provide an overview of available methods together with a classification of nonlinear problems that in principle could be handled by these methods.

Στις υποθαλάσσιες επικοινωνίες χρησιμοποιούνται ακουστικά κύματα για τη μεταφορά της πληροφορίας. Κατά τη διαδικασία της μετάδοσης εμφανίζονται προβλήματα που σχετίζον- ται με τη καθυστέρηση διάδοσης, την εξασθένηση του σήματος, τις πολλαπλές οδεύσεις λόγω ανάκλασης καθώς και άλλα προβλήματα που παρουσιάζονται στις ασύρματες επι- κοινωνίες. Στην παρούσα εργασία αναλύεται και εξετάζεται η πλειονότητα αυτών. Στο πρώτο κεφάλαιο γίνεται μία συνοπτική περιγραφή του φαινομένου των διαλείψεων καθώς και η ανάλυση βασικών εννοιών, τις οποίες συναντάμε σε επόμενα κεφάλαια. Στο δεύτερο κεφάλαιο περιγράφεται η πολύπλεξη OFDM, η οποία χρησιμοποιείται στις περισσότερες εφαρμογές των υποθαλάσσιων επικοινωνιών. Στο τρίτο κεφάλαιο αναλύεται μαθηματικά η τυφλή εκτίμηση για συστήματα OFDM και αναφέρονται επίσης προσαρμοστικοί αλγόριθ- μοι για την εκτίμηση του καναλιού με βάση την θεωρία η οποία παρουσιάζεται. Τέλος στο τέταρτο κεφάλαιο παρατίθεται κώδικας matlab, στον οποίο γίνεται χρήση των αλγορίθμων των τρίτου κεφαλαίου με σκοπό την εκτίμηση της κρουστικής απόκρισης του καναλιού, ενώ πέραν της γενικής περίπτωσης εξετάζονται επιπλέον λύσεις sparse μορφής. / --

As the field service life of retroreflective raised pavement marker (RRPM) is much shorter than expected, it is necessary to identify the causes and thus improve the RRPM structural design to mitigate the main failure modes, such as poor retention from pavements, structural damage, and loss of retroreflectivity. One strategy for extending RRPM service life is to enhance RRPM geometric characteristics to decrease critical stresses in markers. The main purpose of this thesis is to analyze the relationship between stresses, failure modes, and RRPM profiles. Based on this research, some measures are suggested in order to avoid corresponding failure modes by optimizing RRPM profiles.

In recent years, multicarrier modulation techniques have stirred great interest among engineers and researchers working in the field of telecommunications. Multicarrier systems are characterized by the fact that constellation symbols are modulated in parallel onto several distinct subcarriers. One specific form of multicarrier modulation, referred to as OFDM (orthogonal frequency division multiplexing), has been deployed in many applications, such as in wireless LAN (local area network) routers, in high-definition television tuners, and in DSL (digital subscriber line) modems. Multicarrier and OFDM systems have proved to be much more robust against impairments such as impulse noise and sudden channel fadings than their single carrier counterparts. Moreover, channel equalization in OFDM systems can be performed at a very low computational cost by a set of per-subcarrier one-tap equalizers. / Despite their many advantages, OFDM systems have a few, but important, drawbacks. In particular, OFDM relies on the inverse FFT for modulation purposes, which leads to a very poor spectral containment and a high susceptibility to narrowband noise. To mitigate this problem, we propose in this thesis to perform multicarrier modulation using a perfect reconstruction (PR) DFT filter bank instead of employing the inverse FFT. The design of such filter banks is addressed using a novel method that guarantees the PR property to be satisfied while the spectral containment is being maximized. Equalization in the proposed DFT filter bank transceiver takes advantage of the fact that the filter banks do not contribute to any distortion due to its PR nature. Two equalization schemes are presented. The first one is based on a zero-padded block linear equalization approach, and the second one utilizes a one-tap per subcarrier configuration. The estimation of the channel coefficients in the proposed transceiver is also addressed. A blind estimation method that exploits the inherent cyclostationarity of the transmitted signal is derived. Computer experiments presented in this thesis indicate that the spectral containment of the proposed PR DFT filter bank transceiver is indeed superior to that of the OFDM system. Moreover, simulations conducted in a DSL-like environment contaminated by a narrowband noise show that the achievable bit rate of the proposed transceiver is much higher than that of a conventional OFDM system.

Diversity transmission is an effective technique to combat fading channels and this thesis introduces two main ideas. Firstly, a novel precoding technique is proposed to achieve diversity transmission and improve bit error rate (BER) performance over the existing linear constellation precoding (LCP) techniques. Experimental and theoretical results are presented to show that the proposed precoding schemes can outperform the existing LCP schemes in various fading channels and additive white Gaussian noise channels. Secondly, an interleaving technique to further improve the BER performance is proposed. The proposed diversity transmission techniques are implemented for both single-carrier and orthogonal frequency division multiplexing (OFDM) systems. The second part of the thesis focuses on the pairwise error probability analysis of the proposed and LCP schemes when receivers have imperfect channel state information (CSI). The BER performance of the proposed precoding and interleaver scheme are investigated in OFDM systems with minimum mean square error channel estimators and single-carrier systems with basis expansion model based channel estimators. It is demonstrated that while precoding schemes designed for receivers with perfect CSI yield near-optimum BER performance in the former system, the proposed phase-shift keying based precoding schemes perform well in the latter system. In both cases, the proposed precoding scheme, combined with the novel interleaving technique, outperforms the existing LCP schemes.

Šio darbo tikslas – sukurti trimačių dėžių su papildomu orientacijos erdvėje apribojimu pakavimo optimizavimo algoritmą, o realizavus jį programinėmis priemonėmis – ištirti jo efektyvumą su atsitiktinai sugeneruotų kraunamų dėžių rinkiniais ir prie skirtingų algoritmo veikimo parametrų. Taip pat sukurti ir pakavimo optimizavimo sprendinio vizualizavimo trimatėje erdvėje programinę įrangą. / Presented work covers one of the most complex areas of combinatorial optimization – three dimensional bin packing problem. Solution methods of this problem are applied in the real world from logistics, packing optimization to VLSI circuit and automobile engineering. Several heuristic packing algorithms suggested by other authors are analyzed. Approach based on tree-search and wall building strategy is chosen to create a 3D packing optimization algorithm. A bin orientation in space restriction is added to classical 3D bin packing problem to make it more complex and more suited for real world applications. A prototype of created algorithm is created and tested with randomly generated data collections. Each data sample is processed with and without bin orientation in space restriction. Influence of restriction and maximal tree width on packing efficiency and computational time is statistically analyzed. Visualization tool based on Microsoft Direct X technology is created to view results of packing optimization.

We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10^−9ms^−2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.

Modelling of human motion is used in a wide range of applications. An important aspect of accurate representation of human movement is the ability to customize models to account for individual differences. The following work proposes a methodology using Hill-based candidate functions in the Fast Orthogonal Search (FOS) method to predict translational force at the wrist from flexion and extension torque at the elbow. Within this force estimation framework, it is possible to implicitly estimate subject-specific physiological parameters of Hill-based models of upper arm muscles. Surface EMG data from three muscles of the upper arm (biceps brachii, brachioradialis and triceps brachii) were recorded from 10 subjects as they performed isometric contractions at varying elbow joint angles. Estimated muscle activation level and joint kinematic data (joint angle and angular velocity) were utilized as inputs to the FOS model. The resulting wrist force estimations were found to be more accurate for models utilizing Hill-based candidate functions, than models utilizing candidate functions that were not physiologically relevant. Subject-specific estimates of optimal joint angle were determined via frequency analysis of the selected FOS candidate functions. Subject-specific optimal joint angle estimates demonstrated low variability and fell within the range of angles presented in the literature. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2008-10-30 01:32:01.606

The recent decade has witnessed great advances in microarray and genotyping technologies which allow genome-wide single nucleotide polymorphism (SNP) data to be captured on a single chip. As a consequence, genome-wide association studies require the development of algorithms capable of manipulating ultra-large-scale SNP datasets. Towards this goal, this thesis proposes two SNP selection methods; the first using Independent Component Analysis (ICA) and the second based on a modified version of Fast Orthogonal Search. The first proposed technique, based on ICA, is a filtering technique; it reduces the number of SNPs in a dataset, without the need for any class labels. The second proposed technique, orthogonal search based SNP selection, is a multivariate regression approach; it selects the most informative features in SNP data to accurately model the entire dataset. The proposed methods are evaluated by applying them to publicly available gene SNP datasets, and comparing the accuracies of each method in reconstructing the datasets. In addition, the selection results are compared with those of another SNP selection method based on Principal Component Analysis (PCA), which was also applied to the same datasets. The results demonstrate the ability of orthogonal search to capture a higher amount of information than ICA SNP selection approach, all while using a smaller number of SNPs. Furthermore, SNP reconstruction accuracies using the proposed ICA methodology demonstrated the ability to summarize a greater or equivalent amount of information in comparison with the amount of information captured by the PCA-based technique reported in the literature. The execution time of the second developed methodology, mFOS, has paved the way for its application to large-scale genome wide datasets. / Thesis (Master, Computing) -- Queen's University, 2010-12-15 18:03:00.208