Time-frequency analysis of the restricted three-body problem: transport and resonance transitions

A method of time-frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem.. The method is based on the extraction of instantaneous frequencies from the wavelet transform of numerical solutions. Time-varying frequencies provide a good diagnostic tool to discern chaotic trajectories from regular ones, and we can identify resonance islands that greatly affect the dynamics. Good accuracy in the calculation of time-varying frequencies allows us to determine resonance trappings of chaotic trajectories and resonance transitions. We show the relation between resonance transitions and transport in different regions of the phase space

The 2D Continuous Wavelet Transform: Applications in Fringe Pattern Processing for Optical Measurement Techniques

Optical metrology and interferometry are widely known disciplines that study and develop techniques to measure physical quantities such as dimensions, force, temperature, stress, etc. A key part of these disciplines is the processing of interferograms, also called fringe patterns. Owing that this kind of images contains the information of interest in a codified form, processing them is of main relevance and has been a widely studied topic for many years. Several mathematical tools have been used to analyze fringe patterns, from the classic Fourier analysis to regularization methods. Some methods based on wavelet theory have been proposed for this purpose in the last years and have evidenced virtues to consider them as a good alternative for fringe pattern analysis. In this chapter, we resume the theoretical basis of fringe pattern image formation and processing, and some of the most relevant applications of the 2D continuous wavelet transform (CWT) in fringe pattern analysis

Real-World Repetition Estimation by Div, Grad and Curl

We consider the problem of estimating repetition in video, such as performing push-ups, cutting a melon or playing violin. Existing work shows good results under the assumption of static and stationary periodicity. As realistic video is rarely perfectly static and stationary, the often preferred Fourier-based measurements is inapt. Instead, we adopt the wavelet transform to better handle non-static and non-stationary video dynamics. From the flow field and its differentials, we derive three fundamental motion types and three motion continuities of intrinsic periodicity in 3D. On top of this, the 2D perception of 3D periodicity considers two extreme viewpoints. What follows are 18 fundamental cases of recurrent perception in 2D. In practice, to deal with the variety of repetitive appearance, our theory implies measuring time-varying flow and its differentials (gradient, divergence and curl) over segmented foreground motion. For experiments, we introduce the new QUVA Repetition dataset, reflecting reality by including non-static and non-stationary videos. On the task of counting repetitions in video, we obtain favorable results compared to a deep learning alternative

NOVEL METHODS FOR PERMANENT MAGNET DEMAGNETIZATION DETECTION IN PERMANENT MAGNET SYNCHRONOUS MACHINES

Monitoring and detecting PM flux linkage is important to maintain a stable permanent magnet synchronous motor (PMSM) operation. The key problems that need to be solved at this stage are to: 1) establish a demagnetization magnetic flux model that takes into account the influence of various nonlinear and complex factors to reveal the demagnetization mechanism; 2) explore the relationship between different factors and demagnetizing magnetic field, to detect the demagnetization in the early stage; and 3) propose post-demagnetization measures. This thesis investigates permanent magnet (PM) demagnetization detection for PMSM machines to achieve high-performance and reliable machine drive for practical industrial and consumer applications. In this thesis, theoretical analysis, numerical calculation as well as experimental investigations are carried out to systematically study the demagnetization detection mechanism and post-demagnetization measures for permanent magnet synchronous motors. At first a flux based acoustic noise model is proposed to analyze online PM demagnetization detection by using a back propagation neural network (BPNN) with acoustic noise data. In this method, the PM demagnetization is detected by means of comparing the measured acoustic signal of PMSM with an acoustic signal library of seven acoustical indicators. Then torque ripple is chosen for online PM demagnetization diagnosis by using continuous wavelet transforms (CWT) and Grey System Theory (GST). This model is able to reveal the relationship between torque variation and PM electromagnetic interferences. After demagnetization being detected, a current regulation strategy is proposed to minimize the torque ripples induced by PM demagnetization. Next, in order to compare the demagnetization detection accuracy, different data mining techniques, Vold-Kalman filtering order tracking (VKF-OT) and dynamic Bayesian network (DBN) based detection approach is applied to real-time PM flux monitoring through torque ripple again. VKF-OT is introduced to track the order of torque ripple of PMSM running in transient state. Lastly, the combination of acoustic noise and torque is investigated for demagnetization detection by using multi-sensor information fusion to improve the system redundancy and accuracy. Bayesian network based multi-sensor information fusion is then proposed to detect the demagnetization ratio from the extracted features. During the analysis of demagnetization detection methods, the proposed PM detection approaches both form torque ripple and acoustic noise are extensively evaluated on a laboratory PM machine drive system under different speeds, load conditions, and temperatures

A New High-Speed Foreign Fiber Detection System with Machine Vision

A new high-speed foreign fiber detection system with machine vision is proposed for removing foreign fibers from raw cotton using optimal hardware components and appropriate algorithms designing. Starting from a specialized lens of 3-charged couple device (CCD) camera, the system applied digital signal processor (DSP) and field-programmable gate array (FPGA) on image acquisition and processing illuminated by ultraviolet light, so as to identify transparent objects such as polyethylene and polypropylene fabric from cotton tuft flow by virtue of the fluorescent effect, until all foreign fibers that have been blown away safely by compressed air quality can be achieved. An image segmentation algorithm based on fast wavelet transform is proposed to identify block-like foreign fibers, and an improved canny detector is also developed to segment wire-like foreign fibers from raw cotton. The procedure naturally provides color image segmentation method with region growing algorithm for better adaptability. Experiments on a variety of images show that the proposed algorithms can effectively segment foreign fibers from test images under various circumstances

Analysis of observed chaotic data

Thesis (Master)--Izmir Institute of Technology, Electronics and Communication Engineering, Izmir, 2004Includes bibliographical references (leaves: 86)Text in English; Abstract: Turkish and Englishxii, 89 leavesIn this thesis, analysis of observed chaotic data has been investigated. The purpose of analyzing time series is to make a classification between the signals observed from dynamical systems. The classifiers are the invariants related to the dynamics. The correlation dimension has been used as classifier which has been obtained after phase space reconstruction. Therefore, necessary methods to find the phase space parameters which are time delay and the embedding dimension have been offered. Since observed time series practically are contaminated by noise, the invariants of dynamical system can not be reached without noise reduction. The noise reduction has been performed by the new proposed singular value decomposition based rank estimation method.Another classification has been realized by analyzing time-frequency characteristics of the signals. The time-frequency distribution has been investigated by wavelet transform since it supplies flexible time-frequency window. Classification in wavelet domain has been performed by wavelet entropy which is expressed by the sum of relative wavelet energies specified in certain frequency bands. Another wavelet based classification has been done by using the wavelet ridges where the energy is relatively maximum in time-frequency domain. These new proposed analysis methods have been applied to electrical signals taken from healthy human brains and the results have been compared with other studies