Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.

A new three-phase transformer modeling for three-phase harmonic analysis in distribution systems

This work presents a new three-phase transformer modeling suitable for simulations in Pspice environment, which until now represents the electrical characteristics of a real transformer. It is proposed the model comparison to a three-phase transformer modeling present in EMTP - ATP program, which includes the electrical and magnetic characteristics. In addition, a set including non-linear loads and a real three-phase transformer was prepared in order to compare and validate the results of this new proposed model. The three-phase Pspice transformer modeling, different from the conventional one using inductance coupling, is remarkable for its simplicity and ease in simulation process, since it uses available voltage and current sources present in Pspice program, enabling simulations of three-phase network system including the most common configuration, three wires in the primary side and four wires in the secondary side (three-phases and neutral). Finally, the proposed modeling becomes a powerful tool for three-phase network simulations due to its simplicity and accuracy, able to simulate and analyze harmonic flow in three-phase systems under balanced and unbalanced conditions.

On the harmonic analysis of cup anemometer rotation speed: A principle to monitor performance and maintenance status of rotating meteorological sensors

The calibration results of one anemometer equipped with several rotors, varying their size, were analyzed. In each case, the 30-pulses pert turn output signal of the anemometer was studied using Fourier series decomposition and correlated with the anemometer factor (i.e., the anemometer transfer function). Also, a 3-cup analytical model was correlated to the data resulting from the wind tunnel measurements. Results indicate good correlation between the post-processed output signal and the working condition of the cup anemometer. This correlation was also reflected in the results from the proposed analytical model. With the present work the possibility of remotely checking cup anemometer status, indicating the presence of anomalies and, therefore, a decrease on the wind sensor reliability is revealed.

A new algorithm to accelerate harmonic analysis of time series

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.

Statistical and harmonic analysis of gravity /

Project no. MO-011.

Harmonic analysis and the theory of probability.

"Notes and references": p. 168-172.

Expedition in Data and Harmonic Analysis on Graphs

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors are nonzero on the i’th node. Because of this dependency on the support of eigenvectors we study the characteristic set of Laplacian eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish on large neighborhoods and then explicitly construct a family of non-planar graphs that do exhibit this property. We then prove original results in modern analysis on graphs. We extend results on spectral graph wavelets to create vertex-dyanamic spectral graph wavelets whose support depends on both scale and translation parameters. We prove that Spielman’s Twice-Ramanujan graph sparsifying algorithm cannot outperform his conjectured optimal sparsification constant. Finally, we present numerical results on graph conditioning, in which edges of a graph are rescaled to best approximate the complete graph and reduce average commute time.

Innovative layout design and radiated harmonic analysis for advanced frequency-diverse array solutions

Wireless power transfer is becoming a crucial and demanding task in the IoT world. Despite the already known solutions exploiting a near-field powering approach, far-field WPT is definitely more challenging, and commercial applications are not available yet. This thesis proposes the recent frequency-diverse array technology as a potential candidate for realizing smart and reconfigurable far-field WPT solutions. In the first section of this work, an analysis on some FDA systems is performed, identifying the planar array with circular geometry as the most promising layout in terms of radiation properties. Then, a novel energy aware solution to handle the critical time variability of the FDA beam pattern is proposed. It consists on a time-control strategy through a triangular pulse, and it allows to achieve ad-hoc and real time WPT. Moreover, an essential frequency domain analysis of the radiating behaviour of a pulsed FDA system is presented. This study highlights the benefits of exploiting the intrinsic pulse harmonics for powering purposes, thus minimising the power loss. Later, the electromagnetic design of a radial FDA architecture is addressed. In this context, an exhaustive investigation on miniaturization techniques is carried out; the use of multiple shorting pins together with a meandered feeding network has been selected as a powerful solution to halve the original prototype dimension. Finally, accurate simulations of the designed radial FDA system are performed, and the obtained results are given.

Experimental analysis of harmonic distortions in the excitation currents of double-excited three-phase transformers

This paper shows the results of experimental investigations of three-phase banks composed of single-phase transformers and three-phase three-limb core transformers under simultaneous alternating and direct current excitations, for several winding connections. Harmonic analysis of excitation currents for different de saturation levels is performed.

Harmonic propagation analysis in electric energy distribution systems

An important alteration of the equivalent loads profile has been observed in the electrical energy distribution systems, for the last years. Such fact is due to the significant increment of the electronic processors of electric energy that, in general, behave as nonlinear loads, generating harmonic distortions in the currents and voltages along the electric network. The effects of these nonlinear loads, even if they are concentrated in specific sections of the network, are present along the branch circuits, affecting the behavior of the entire electric network. For the evaluation of this phenomenon it is necessary the analysis of the harmonic currents flow and the understanding of the causes and effects of the consequent voltage harmonic distortions. The usual tools for calculation the harmonic flow consider one-line equivalent networks, balanced and symmetrical systems. Therefore, they are not tools appropriate for analysis of the operation and the influence/interaction of mitigation elements. In this context, this work proposes the development of a computational tool for the analysis of the three-phase harmonic propagation using Norton modified models and considering the real nature of unbalanced electric systems operation. © 2011 IEEE.

Aerodynamic Analysis of Cup Anemometers Performance: The Stationary Harmonic Response

The effect of cup anemometer shape parameters, such as the cups’ shape, their size, and their center rotation radius, was experimentally analyzed.This analysis was based on both the calibration constants of the transfer function and the most important harmonic termof the rotor’smovement,which due to the cup anemometer design is the third one.This harmonic analysis represents a new approach to study cup anemometer performances. The results clearly showed a good correlation between the average rotational speed of the anemometer’s rotor and the mentioned third harmonic term of its movement.

A descriptive analysis of the seasonal variation of physical oceanographic characteristics in the northern region of the Todos os Santos Bay (Bahia, Brazil)

The results obtained in the August and December 2003, August 2004 and January 2005 oceanographic campaigns in the northern region of the Todos os Santos Bay (lat. 12º44.5'S; long. 038º35.00'W) between the Madre de Deus and Maré islands are analyzed. Instruments of continuous and discrete samplings were used to measure hydrographic properties currents and tides. The water mass of the northern region of the bay is forced by semidiurnal and mesotides of form number 0.08 and the lunar component M2 height was estimated at 91cm. The time series of the surface currents indicated movements in the N/S direction, forced by the tide with maximum magnitudes of 0.73 m.s-1 on the December 2003 campaign. However, in August 2004 the currents were dominated by the wind stress forcing, with a maximum speed of 1.85 m.s-1 and SE direction. Near the bottom, the influence of the tide is not as evident, with a decrease in intensity due to internal and bottom friction, with a maximum velocity of 0.17 m.s-1. The thermal and haline structures were weakly horizontally, as well as vertically stratified, with extreme values varying in the intervals 23ºC (August, 2004) to 28ºC (December, 2003) and 31.0 psu (August, 2003) to 36.0 psu (December, 2003), respectively. Some conclusions may be drawn from these results: i) The signs of the dilution of the fresh water discharges of the Caípe, Mataripe and São Paulo rivers in the region under the influence of the RLAM were observed only during the winter periods, but in the summer the region was flooded by waters of oceanic origin and the salinities above 36.0 indicated TW mass intrusion; ii) The N-S circulation near the RLAM is strongly dominated by the tide, and the importance of the M2 component was unequivocal, however, the E-W component presented some tidal modulation away from abrupt bottom topographical changes, and iii) The residual series, calculated as the difference between the original and modeled, is about ¼ of the original and confirmed its semidiurnal character.

Objective analysis of gait coordination for total knee arthroplasty outcome

Introduction: Coordination is a strategy chosen by the central nervous system to control the movements and maintain stability during gait. Coordinated multi-joint movements require a complex interaction between nervous outputs, biomechanical constraints, and pro-prioception. Quantitatively understanding and modeling gait coordination still remain a challenge. Surgeons lack a way to model and appreciate the coordination of patients before and after surgery of the lower limbs. Patients alter their gait patterns and their kinematic synergies when they walk faster or slower than normal speed to maintain their stability and minimize the energy cost of locomotion. The goal of this study was to provide a dynamical system approach to quantitatively describe human gait coordination and apply it to patients before and after total knee arthroplasty. Methods: A new method of quantitative analysis of interjoint coordination during gait was designed, providing a general model to capture the whole dynamics and showing the kinematic synergies at various walking speeds. The proposed model imposed a relationship among lower limb joint angles (hips and knees) to parameterize the dynamics of locomotion of each individual. An integration of different analysis tools such as Harmonic analysis, Principal Component Analysis, and Artificial Neural Network helped overcome high-dimensionality, temporal dependence, and non-linear relationships of the gait patterns. Ten patients were studied using an ambulatory gait device (Physilog®). Each participant was asked to perform two walking trials of 30m long at 3 different speeds and to complete an EQ-5D questionnaire, a WOMAC and Knee Society Score. Lower limbs rotations were measured by four miniature angular rate sensors mounted respectively, on each shank and thigh. The outcomes of the eight patients undergoing total knee arthroplasty, recorded pre-operatively and post-operatively at 6 weeks, 3 months, 6 months and 1 year were compared to 2 age-matched healthy subjects. Results: The new method provided coordination scores at various walking speeds, ranged between 0 and 10. It determined the overall coordination of the lower limbs as well as the contribution of each joint to the total coordination. The difference between the pre-operative and post-operative coordination values were correlated with the improvements of the subjective outcome scores. Although the study group was small, the results showed a new way to objectively quantify gait coordination of patients undergoing total knee arthroplasty, using only portable body-fixed sensors. Conclusion: A new method for objective gait coordination analysis has been developed with very encouraging results regarding the objective outcome of lower limb surgery.