Modelling Crowd Load for Floor Vibration Analysis

The dynamic floor loads induced by crowds in gymnasium or stadium structures are commonly modelled by superposition of the individual contributions using reduction factors for the different Fourier coefficients. These Fourier coefficients and the reduction factors are calculated using full scale measurements. Generally the testing is performed on platforms or structures that can be considered rigid, such that the natural frequencies are higher than the frequencies of the spectator movement. In this paper we shall present the testing done on a structure that used to be a gymnasium as well as the procedure used to identify its dynamic properties and a first evaluation of the socalled “group effect”.

A review of load models for the prediction of footfall-induced vibration in structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadium, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lag among individuals inside the crowd. This paper presents the testing done on a structure designed to be a gymnasium. Two series of dynamic test were performed on the gym slab. For the first test an electrodynamic shaker was placed at several locations and during the second one people located inside a marked area bounced and jumped guided by different metronome rates. A finite element model (FEM) is presented and a comparison of numerically predicted and experimentally observed vibration modes and frequencies has been used to assess its validity. The second group of measurements will be compared with predictions made using the FEM model and three alternatives for crowd induced load modelling.

Model of human rhythmic activities on structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadiums, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these Fourier coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lags among individuals inside the crowd. Generally the testing is performed on platforms or structures that can be considered rigid because their natural frequencies are higher than the excitation frequencies associated with crowd loading. In this paper we shall present the testing done on a structure designed to be a gymnasium, which has natural frequencies within that range. In this test the gym slab was instrumented with acceleration sensors and different people jumped on a force plate installed on the floor. Test results have been compared with predictions based on the two abovementioned load modelling alternatives and a new methodology for modelling jumping loads has been proposed in order to reduce the difference between experimental and numerical results at high frequency range.

Casamento de modelos baseado em projeções radiais e circulares invariante a pontos de vista.

Este trabalho aborda o problema de casamento entre duas imagens. Casamento de imagens pode ser do tipo casamento de modelos (template matching) ou casamento de pontos-chaves (keypoint matching). Estes algoritmos localizam uma região da primeira imagem numa segunda imagem. Nosso grupo desenvolveu dois algoritmos de casamento de modelos invariante por rotação, escala e translação denominados Ciratefi (Circula, radial and template matchings filter) e Forapro (Fourier coefficients of radial and circular projection). As características positivas destes algoritmos são a invariância a mudanças de brilho/contraste e robustez a padrões repetitivos. Na primeira parte desta tese, tornamos Ciratefi invariante a transformações afins, obtendo Aciratefi (Affine-ciratefi). Construímos um banco de imagens para comparar este algoritmo com Asift (Affine-scale invariant feature transform) e Aforapro (Affine-forapro). Asift é considerado atualmente o melhor algoritmo de casamento de imagens invariante afim, e Aforapro foi proposto em nossa dissertação de mestrado. Nossos resultados sugerem que Aciratefi supera Asift na presença combinada de padrões repetitivos, mudanças de brilho/contraste e mudanças de pontos de vista. Na segunda parte desta tese, construímos um algoritmo para filtrar casamentos de pontos-chaves, baseado num conceito que denominamos de coerência geométrica. Aplicamos esta filtragem no bem-conhecido algoritmo Sift (scale invariant feature transform), base do Asift. Avaliamos a nossa proposta no banco de imagens de Mikolajczyk. As taxas de erro obtidas são significativamente menores que as do Sift original.

Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

An inverse method for designing loaded RF coils in MRI

Radio-frequency ( RF) coils are designed such that they induce homogeneous magnetic fields within some region of interest within a magnetic resonance imaging ( MRI) scanner. Loading the scanner with a patient disrupts the homogeneity of these fields and can lead to a considerable degradation of the quality of the acquired image. In this paper, an inverse method is presented for designing RF coils, in which the presence of a load ( patient) within the MRI scanner is accounted for in the model. To approximate the finite length of the coil, a Fourier series expansion is considered for the coil current density and for the induced fields. Regularization is used to solve this ill-conditioned inverse problem for the unknown Fourier coefficients. That is, the error between the induced and homogeneous target fields is minimized along with an additional constraint, chosen in this paper to represent the curvature of the coil windings. Smooth winding patterns are obtained for both unloaded and loaded coils. RF fields with a high level of homogeneity are obtained in the unloaded case and a limit to the level of homogeneity attainable is observed in the loaded case.

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Congruences in modular, Jacobi, Siegel, and mock modular forms with applications

We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the Fourier expansion. We have several applications. We describe the Ramanujan congruences in the counting functions for overparitions, overpartition pairs, crank differences, and Andrews' two-coloured generalized Frobenius partitions. We also study Ramanujan congruences in the Fourier coefficients of certain ratios of Eisenstein series. We also determine the exact number of holomorphic modular forms with Ramanujan congruences when the weight is large enough. In a chapter based on joint work with Olav Richter, we study Ramanujan congruences in the coefficients of Jacobi forms and Siegel modular forms of degree two. Finally, the last chapter contains a completely unrelated result about harmonic weak Maass forms.

Applications of perceptual sparse representation (Spikegram) for copyright protection of audio signals

Chaque année, le piratage mondial de la musique coûte plusieurs milliards de dollars en pertes économiques, pertes d’emplois et pertes de gains des travailleurs ainsi que la perte de millions de dollars en recettes fiscales. La plupart du piratage de la musique est dû à la croissance rapide et à la facilité des technologies actuelles pour la copie, le partage, la manipulation et la distribution de données musicales [Domingo, 2015], [Siwek, 2007]. Le tatouage des signaux sonores a été proposé pour protéger les droit des auteurs et pour permettre la localisation des instants où le signal sonore a été falsifié. Dans cette thèse, nous proposons d’utiliser la représentation parcimonieuse bio-inspirée par graphe de décharges (spikegramme), pour concevoir une nouvelle méthode permettant la localisation de la falsification dans les signaux sonores. Aussi, une nouvelle méthode de protection du droit d’auteur. Finalement, une nouvelle attaque perceptuelle, en utilisant le spikegramme, pour attaquer des systèmes de tatouage sonore. Nous proposons tout d’abord une technique de localisation des falsifications (‘tampering’) des signaux sonores. Pour cela nous combinons une méthode à spectre étendu modifié (‘modified spread spectrum’, MSS) avec une représentation parcimonieuse. Nous utilisons une technique de poursuite perceptive adaptée (perceptual marching pursuit, PMP [Hossein Najaf-Zadeh, 2008]) pour générer une représentation parcimonieuse (spikegramme) du signal sonore d’entrée qui est invariante au décalage temporel [E. C. Smith, 2006] et qui prend en compte les phénomènes de masquage tels qu’ils sont observés en audition. Un code d’authentification est inséré à l’intérieur des coefficients de la représentation en spikegramme. Puis ceux-ci sont combinés aux seuils de masquage. Le signal tatoué est resynthétisé à partir des coefficients modifiés, et le signal ainsi obtenu est transmis au décodeur. Au décodeur, pour identifier un segment falsifié du signal sonore, les codes d’authentification de tous les segments intacts sont analysés. Si les codes ne peuvent être détectés correctement, on sait qu’alors le segment aura été falsifié. Nous proposons de tatouer selon le principe à spectre étendu (appelé MSS) afin d’obtenir une grande capacité en nombre de bits de tatouage introduits. Dans les situations où il y a désynchronisation entre le codeur et le décodeur, notre méthode permet quand même de détecter des pièces falsifiées. Par rapport à l’état de l’art, notre approche a le taux d’erreur le plus bas pour ce qui est de détecter les pièces falsifiées. Nous avons utilisé le test de l’opinion moyenne (‘MOS’) pour mesurer la qualité des systèmes tatoués. Nous évaluons la méthode de tatouage semi-fragile par le taux d’erreur (nombre de bits erronés divisé par tous les bits soumis) suite à plusieurs attaques. Les résultats confirment la supériorité de notre approche pour la localisation des pièces falsifiées dans les signaux sonores tout en préservant la qualité des signaux. Ensuite nous proposons une nouvelle technique pour la protection des signaux sonores. Cette technique est basée sur la représentation par spikegrammes des signaux sonores et utilise deux dictionnaires (TDA pour Two-Dictionary Approach). Le spikegramme est utilisé pour coder le signal hôte en utilisant un dictionnaire de filtres gammatones. Pour le tatouage, nous utilisons deux dictionnaires différents qui sont sélectionnés en fonction du bit d’entrée à tatouer et du contenu du signal. Notre approche trouve les gammatones appropriés (appelés noyaux de tatouage) sur la base de la valeur du bit à tatouer, et incorpore les bits de tatouage dans la phase des gammatones du tatouage. De plus, il est montré que la TDA est libre d’erreur dans le cas d’aucune situation d’attaque. Il est démontré que la décorrélation des noyaux de tatouage permet la conception d’une méthode de tatouage sonore très robuste. Les expériences ont montré la meilleure robustesse pour la méthode proposée lorsque le signal tatoué est corrompu par une compression MP3 à 32 kbits par seconde avec une charge utile de 56.5 bps par rapport à plusieurs techniques récentes. De plus nous avons étudié la robustesse du tatouage lorsque les nouveaux codec USAC (Unified Audion and Speech Coding) à 24kbps sont utilisés. La charge utile est alors comprise entre 5 et 15 bps. Finalement, nous utilisons les spikegrammes pour proposer trois nouvelles méthodes d’attaques. Nous les comparons aux méthodes récentes d’attaques telles que 32 kbps MP3 et 24 kbps USAC. Ces attaques comprennent l’attaque par PMP, l’attaque par bruit inaudible et l’attaque de remplacement parcimonieuse. Dans le cas de l’attaque par PMP, le signal de tatouage est représenté et resynthétisé avec un spikegramme. Dans le cas de l’attaque par bruit inaudible, celui-ci est généré et ajouté aux coefficients du spikegramme. Dans le cas de l’attaque de remplacement parcimonieuse, dans chaque segment du signal, les caractéristiques spectro-temporelles du signal (les décharges temporelles ;‘time spikes’) se trouvent en utilisant le spikegramme et les spikes temporelles et similaires sont remplacés par une autre. Pour comparer l’efficacité des attaques proposées, nous les comparons au décodeur du tatouage à spectre étendu. Il est démontré que l’attaque par remplacement parcimonieux réduit la corrélation normalisée du décodeur de spectre étendu avec un plus grand facteur par rapport à la situation où le décodeur de spectre étendu est attaqué par la transformation MP3 (32 kbps) et 24 kbps USAC.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

Statistical properties of fast Fourier transform coefficients computed from real-valued, covariance-stationary, periodic random sequences /

"July 1976."

On the Fourier refinement of protein structures

The situation normally encountered in the high-resolution refinement of protein structures is one in which the inaccurate positions of P out of a total of N atoms are known whereas those of the remaining atoms are unknown. Fourier maps with coefficients (FN -- F'P) × exp (i[alpha]'P) and (mFN -- nF'P) exp (i[alpha]'P), where FN is the observed structure factor and F'P and [alpha]'P are the magnitude and the phase angle of the calculated structure factor corresponding to the inaccurate atomic positions, are often used to correct the positions of the P atoms and to determine those of the Q unknown atoms. A general theoretical approach is presented to elucidate the effect of errors in the positions of the known atoms on the corrected positions of the known atoms and the positions of the unknown atoms derived from such maps. The theory also leads to the optimal choice of parameters used in the different syntheses. When the errors in the positions of the input atoms are systematic, their effects are not taken care of automatically by the syntheses.

On Fast Bilateral Filtering Using Fourier Kernels

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.

A new high-order Fourier continuation-based elasticity solver for complex three-dimensional geometries

This thesis presents a new approach for the numerical solution of three-dimensional problems in elastodynamics. The new methodology, which is based on a recently introduced Fourier continuation (FC) algorithm for the solution of Partial Differential Equations on the basis of accurate Fourier expansions of possibly non-periodic functions, enables fast, high-order solutions of the time-dependent elastic wave equation in a nearly dispersionless manner, and it requires use of CFL constraints that scale only linearly with spatial discretizations. A new FC operator is introduced to treat Neumann and traction boundary conditions, and a block-decomposed (sub-patch) overset strategy is presented for implementation of general, complex geometries in distributed-memory parallel computing environments. Our treatment of the elastic wave equation, which is formulated as a complex system of variable-coefficient PDEs that includes possibly heterogeneous and spatially varying material constants, represents the first fully-realized three-dimensional extension of FC-based solvers to date. Challenges for three-dimensional elastodynamics simulations such as treatment of corners and edges in three-dimensional geometries, the existence of variable coefficients arising from physical configurations and/or use of curvilinear coordinate systems and treatment of boundary conditions, are all addressed. The broad applicability of our new FC elasticity solver is demonstrated through application to realistic problems concerning seismic wave motion on three-dimensional topographies as well as applications to non-destructive evaluation where, for the first time, we present three-dimensional simulations for comparison to experimental studies of guided-wave scattering by through-thickness holes in thin plates.

Graft chain propagation rate coefficients of acrylic acid in melt graft copolymerization with linear low density polyethylene

Graft chain propagation rate coefficients (k(p.g)) for grafting AA onto linear low density polyethylene (LLDPE) in the melt in ESR tubes have been measured via Fourier transform infrared (FTIR) spectroscopy and electron spin resonance (ESR) spectroscopy in the temperature range from 130 to 170 degrees C. To exclude the effect of homopolymerization on the grafting. the LLDPE was pre-irradiated in the air by electron beam to generate the peroxides and then treated with iodide solution to eliminating one kind of peroxides, hydroperoxide. The monomer conversion is determined by FTIR and the chain propagation free-radical concentration is deduced from the double integration of the well-resolved ESR spectra, consisting nine lines in the melt. The temperature dependence of k(p.g) is expressed:The magnitude of k(p.g) from FTIR and ESR analysis is in good agreement with the theoretical data deduced from ethylene-AA copolymerization, suggesting this method could reliably and directly provide the propagation rate coefficient. The comparison of k(p.g) with the data extrapolated from solution polymerization at modest temperature indicates that the extrapolated data might not be entirely fitting to discuss the kinetics behavior in the melt.