Data driven optimal filtering for phase and frequency of noisy oscillations: application to vortex flowmetering

A new method for extracting the phase of oscillations from noisy time series is proposed. To obtain the phase, the signal is filtered in such a way that the filter output has minimal relative variation in the amplitude (MIRVA) over all filters with complex-valued impulse response. The argument of the filter output yields the phase. Implementation of the algorithm and interpretation of the result are discussed. We argue that the phase obtained by the proposed method has a low susceptibility to measurement noise and a low rate of artificial phase slips. The method is applied for the detection and classification of mode locking in vortex flowmeters. A novel measure for the strength of mode locking is proposed.Comment: 12 pages, 10 figure

Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

Temperature Dependence of the Dynamics of Portevin-Le Chatelier Effect in Al-2.5%Mg alloy

Tensile tests were carried out by deforming polycrystalline samples of Al-2.5%Mg alloy at four different temperatures in an intermediate strain rate regime of 2x10-4s-1 to 2x10-3s-1. The Portevin-Le Chatelier (PLC) effect was observed throughout the strain rate and temperature region. The mean cumulative stress drop magnitude and the mean reloading time exhibit an increasing trend with temperature which is attributed to the enhanced solute diffusion at higher temperature. The observed stress-time series data were analyzed using the nonlinear dynamical methods. From the analyses, we could establish the presence of deterministic chaos in the PLC effect throughout the temperature regime. The dynamics goes to higher dimension at a sufficiently high temperature of 425K but the complexity of the dynamics is not affected by the temperature.Comment: 18 pages, 8 figures; accepted in Met. Mater. Trans.

Face Processing with Whitney Reduction Networks

This paper investigates the application of the Whitney Reduction Network (WRN) to the lowdimensional characterization of digital images human faces. Motivated by Whitney's Embedding theorem from differential topology the WRN provides a nonlinear parameterization of m dimensional manifolds. Based on this, the reduction of the high-dimensional raw image data consists of two-stages. First, a lowdimensional representation is constructed using an optimal projection. Secondly, a nonlinear inverse from the image of the projection to the null-space of the projection is approximated to permit the (almost) perfect reconstruction of the data. This architecture is applied to problem of representing a family of digital images, i.e., faces. We compare this method with the wellknown eigenpicture approach, which may be viewed as a special limiting case of the WRN. 1 Introduction The application of the Karhunen-Lo`eve (KL) procedure for the representation of digital images of faces was introduced ove..

A New Approach for Dimensionality Reduction: Theory and Algorithms

This paper applies Whitney's embedding theorem to the data reduction problem and introduces a new approach motivated in part by the (constructive) proof of the theorem. The notion of a good projection is introduced which involves picking projections of the high-dimensional system that are optimized such that they are easy to invert. The basic theory of the approach is outlined and algorithms for finding the projections are presented and applied to several test cases. A method for constructing the inverse projection is detailed and its properties, including a new measure of complexity, are discussed. Finally, well-known methods of data reduction are compared with our approach within the context of Whitney's theorem. Keywords: dimensionality reduction, radial basis functions, Whitney 's embedding theorem, secant basis. AMS subject classifications: 53-04, 62H99, 65D99, 65C99 1 The Data Reduction Problem Assume that the data set A of interest is a discrete sampling of a compact m- dime..