Wavelet-based multiresolution analysis of Wivenhoe Dam water temperatures

Water temperature measurements from Wivenhoe Dam offer a unique opportunity for studying fluctuations of temperatures in a subtropical dam as a function of time and depth. Cursory examination of the data indicate a complicated structure across both time and depth. We propose simplifying the task of describing these data by breaking the time series at each depth into physically meaningful components that individually capture daily, subannual, and annual (DSA) variations. Precise definitions for each component are formulated in terms of a wavelet-based multiresolution analysis. The DSA components are approximately pairwise uncorrelated within a given depth and between different depths. They also satisfy an additive property in that their sum is exactly equal to the original time series. Each component is based upon a set of coefficients that decomposes the sample variance of each time series exactly across time and that can be used to study both time-varying variances of water temperature at each depth and time-varying correlations between temperatures at different depths. Each DSA component is amenable for studying a certain aspect of the relationship between the series at different depths. The daily component in general is weakly correlated between depths, including those that are adjacent to one another. The subannual component quantifies seasonal effects and in particular isolates phenomena associated with the thermocline, thus simplifying its study across time. The annual component can be used for a trend analysis. The descriptive analysis provided by the DSA decomposition is a useful precursor to a more formal statistical analysis.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Wavelet transform analysis of truncated fringe patterns in 3-D surface profilometry

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe images do not satisfy periodicity. Three specific cases that give raise to non-periodicity of fringe image are simulated and leakage effects caused by each one of them are analyzed with continuous complex Morlet wavelet transform. Same images are analyzed with FFT method to make a comparison of the reconstructed profiles with both methods. Simulation results revealed a significant advantage of wavelet transform profilometry (WTP), that the distortions that arise due to leakage are confined to the locations of discontinuity and do not spread out over the entire projection as in the case of Fourier transform profilometry (FTP).

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

Wave propagation analysis in adhesively bonded composite joints using the wavelet spectral finite element method

A wavelet spectral finite element (WSFE) model is developed for studying transient dynamics and wave propagation in adhesively bonded composite joints. The adherands are formulated as shear deformable beams using the first order shear deformation theory (FSDT) to obtain accurate results for high frequency wave propagation. Equations of motion governing wave motion in the bonded beams are derived using Hamilton's principle. The adhesive layer is modeled as a line of continuously distributed tension/compression and shear springs. Daubechies compactly supported wavelet scaling functions are used to transform the governing partial differential equations from time domain to frequency domain. The dynamic stiffness matrix is derived under the spectral finite element framework relating the nodal forces and displacements in the transformed frequency domain. Time domain results for wave propagation in a lap joint are validated with conventional finite element simulations using Abaqus. Frequency domain spectrum and dispersion relation results are presented and discussed. The developed WSFE model yields efficient and accurate analysis of wave propagation in adhesively-bonded composite joints. (C) 2014 Elsevier Ltd. All rights reserved.

Delineation of homogeneous hydrometeorological regions using wavelet-based global fuzzy cluster analysis

Identification of homogeneous hydrometeorological regions (HMRs) is necessary for various applications. Such regions are delineated by various approaches considering rainfall and temperature as two key variables. In conventional approaches, formation of regions is based on principal components (PCs)/statistics/indices determined from time series of the key variables at monthly and seasonal scales. An issue with use of PCs for regionalization is that they have to be extracted from contemporaneous records of hydrometeorological variables. Therefore, delineated regions may not be effective when the available records are limited over contemporaneous time period. A drawback associated with the use of statistics/indices is that they do not provide effective representation of the key variables when the records exhibit non-stationarity. Consequently, the resulting regions may not be effective for the desired purpose. To address these issues, a new approach is proposed in this article. The approach considers information extracted from wavelet transformations of the observed multivariate hydrometeorological time series as the basis for regionalization by global fuzzy c-means clustering procedure. The approach can account for dynamic variability in the time series and its non-stationarity (if any). Effectiveness of the proposed approach in forming HMRs is demonstrated by application to India, as there are no prior attempts to form such regions over the country. Drought severity-area-frequency (SAF) curves are constructed corresponding to each of the newly formed regions for the use in regional drought analysis, by considering standardized precipitation evapotranspiration index (SPEI) as the drought indicator.

Evaluation of a combined wavelet and a combined principal component analysis classification system for BCG diagnostic problem

Heart disease is one of the main factor causing death in the developed countries. Over several decades, variety of electronic and computer technology have been developed to assist clinical practices for cardiac performance monitoring and heart disease diagnosis. Among these methods, Ballistocardiography (BCG) has an interesting feature that no electrodes are needed to be attached to the body during the measurement. Thus, it is provides a potential application to asses the patients heart condition in the home. In this paper, a comparison is made for two neural networks based BCG signal classification models. One system uses a principal component analysis (PCA) method, and the other a discrete wavelet transform, to reduce the input dimensionality. It is indicated that the combined wavelet transform and neural network has a more reliable performance than the combined PCA and neural network system. Moreover, the wavelet transform requires no prior knowledge of the statistical distribution of data samples and the computation complexity and training time are reduced.

Analysis of Fixed-Speed Wind Farm Low-Frequency Power Pulsations using a Wavelet-Prony Method

The increasing penetration of wind generation on the Island of Ireland has been accompanied by close investigation of low-frequency periodic pulsations contained within the active power flow from different wind farms. A primary concern is excitation of existing low-frequency oscillation modes already present on the system, particularly the 0.75 Hz mode as a consequence of the interconnected Northern and Southern power system networks. Recently grid code requirements on the Northern Ireland power system have been updated stipulating that wind farms connected after 2005 must be able to control the magnitude of oscillations in the range of 0.25 - 1.75 Hz to within 1% of the wind farm's registered output. In order to determine whether wind farm low-frequency oscillations have a negative effect (excite other modes) or possibly a positive impact (damping of existing modes) on the power system, the oscillations at the point of connection must be measured and characterised. Using time - frequency methods, research presented in this paper has been conducted to extract signal features from measured low-frequency active power pulsations produced by wind farms to determine the effective composition of possible oscillatory modes which may have a detrimental effect on system dynamic stability. The paper proposes a combined wavelet-Prony method to extract modal components and determine damping factors. The method is exemplified using real data obtained from wind farm measurements.

A Wavelet Approach to the Selective Computation of Eigenvalues for Small Signal Stability Analysis

This paper proposes a method to assess the small signal stability of a power system network by selective determination of the modal eigenvalues. This uses an accelerating polynomial transform, designed using approximate eigenvalues
obtained from a wavelet approximation. Application to the IEEE 14 bus network model produced computational savings of 20%,over the QR algorithm.