Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty

Wavelet coefficients based on spatial wavelets are used as damage indicators to identify the damage location as well as the size of the damage in a laminated composite beam with localized matrix cracks. A finite element model of the composite beam is used in conjunction with a matrix crack based damage model to simulate the damaged composite beam structure. The modes of vibration of the beam are analyzed using the wavelet transform in order to identify the location and the extent of the damage by sensing the local perturbations at the damage locations. The location of the damage is identified by a sudden change in spatial distribution of wavelet coefficients. Monte Carlo Simulations (MCS) are used to investigate the effect of ply level uncertainty in composite material properties such as ply longitudinal stiffness, transverse stiffness, shear modulus and Poisson's ratio on damage detection parameter, wavelet coefficient. In this study, numerical simulations are done for single and multiple damage cases. It is observed that spatial wavelets can be used as a reliable damage detection tool for composite beams with localized matrix cracks which can result from low velocity impact damage.

Auditory-motivated Gammatone wavelet transform

The ability of the continuous wavelet transform (CWT) to provide good time and frequency localization has made it a popular tool in time-frequency analysis of signals. Wavelets exhibit constant-Q property, which is also possessed by the basilar membrane filters in the peripheral auditory system. The basilar membrane filters or auditory filters are often modeled by a Gammatone function, which provides a good approximation to experimentally determined responses. The filterbank derived from these filters is referred to as a Gammatone filterbank. In general, wavelet analysis can be likened to a filterbank analysis and hence the interesting link between standard wavelet analysis and Gammatone filterbank. However, the Gammatone function does not exactly qualify as a wavelet because its time average is not zero. We show how bona fide wavelets can be constructed out of Gammatone functions. We analyze properties such as admissibility, time-bandwidth product, vanishing moments, which are particularly relevant in the context of wavelets. We also show how the proposed auditory wavelets are produced as the impulse response of a linear, shift-invariant system governed by a linear differential equation with constant coefficients. We propose analog circuit implementations of the proposed CWT. We also show how the Gammatone-derived wavelets can be used for singularity detection and time-frequency analysis of transient signals. (C) 2013 Elsevier B.V. All rights reserved.

Gammatone Wavelet Cepstral Coefficients for Robust Speech Recognition

We develop noise robust features using Gammatone wavelets derived from the popular Gammatone functions. These wavelets incorporate the characteristics of human peripheral auditory systems, in particular the spatially-varying frequency response of the basilar membrane. We refer to the new features as Gammatone Wavelet Cepstral Coefficients (GWCC). The procedure involved in extracting GWCC from a speech signal is similar to that of the conventional Mel-Frequency Cepstral Coefficients (MFCC) technique, with the difference being in the type of filterbank used. We replace the conventional mel filterbank in MFCC with a Gammatone wavelet filterbank, which we construct using Gammatone wavelets. We also explore the effect of Gammatone filterbank based features (Gammatone Cepstral Coefficients (GCC)) for robust speech recognition. On AURORA 2 database, a comparison of GWCCs and GCCs with MFCCs shows that Gammatone based features yield a better recognition performance at low SNRs.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

基于梳状小波理论的颜色滤光片设计

渐变折射率薄膜因为消除了界面而克服了传统的分层介质膜的固有弊端。探讨了一种基于这种渐变膜系的设计方法。从小波理论及渐变折射率增透理论出发，以分层介质高反膜系为参照，给出了采用梳状（Rugate）滤光片设计不同类型颜色滤光片的设计原理，并以目前背投系统中使用的红、绿、蓝颜色滤光片为指标，理论设计出了具有优良光谱特性的红、绿、蓝颜色滤光片；对该设计结果进行了角度敏感性分析、偏振效应分析并与传统的反射膜叠加法得到的分层膜系进行比较，发现通过梳状滤光片理论设计的滤光片较传统的多层膜滤光片具有更小的角度敏感性和较小

Multiscale object features from clustered complex wavelet coefficients

This paper introduces a method by which intuitive feature entities can be created from ILP (InterLevel Product) coefficients. The ILP transform is a pyramid of decimated complex-valued coefficients at multiple scales, derived from dual-tree complex wavelets, whose phases indicate the presence of different feature types (edges and ridges). We use an Expectation-Maximization algorithm to cluster large ILP coefficients that are spatially adjacent and similar in phase. We then demonstrate the relationship that these clusters possess with respect to observable image content, and conclude with a look at potential applications of these clusters, such as rotation- and scale-invariant object recognition. © 2005 IEEE.

Species identification of family Lutjanidae and separation of populations of John’s snapper (Lutjanus johnii) in Persian Gulf and Oman Sea based on otolith shape analysis

The anatomical and morphometric (shape indices, contour descriptors and otolith weight) characterizations of sagittal otoliths were investigated in 13 species of Lutjanus spp. inhabiting the Persian Gulf. This is the first study that compares the efficiency of three different image analysis techniques for discriminating species based on the shape of the outer otolith contour, including elliptical Fourier descriptors (EFD), fast Fourier transform (FFT) and wavelet transform (WT). Sagittal otoliths of snappers are morphologically similar with some small specific variations. The use of otolith contour based on wavelets (WT) provided the best results in comparison with the two other methods based on Fourier descriptors, but only the combination of the all three methods (EFD, FFT and WT) was useful to obtain a robust classification of species. The species prediction improved when otolith weight was included. In relation to the shape indices, only the aspect ratio provided a clear grouping of species. Also, another study was carried on to test the possibility of application of shape analysis and comparing otolith contour of otoliths of Lutjanus johnii from Persian Gulf and Oman Sea to identify potential stocks. The results showed the otoliths have differences in contour shape and can be contribute to two different stocks.

DT-MRI data visualisation using the dual tree Complex Wavelet transform

In this paper a novel visualisation method for diffusion tensor MRI datasets is introduced. This is based on the use of Complex Wavelets in order to produce "stripy" textures which depict the anisotropic component of the diffusion tensors. Grey-scale pixel intensity is used to show the isotropic component. This paper also discusses enhancements of the technique for 3D visualisation. © 2004 IEEE.

Fractal dimension, wavelet shrinkage and anomaly detection for mine hunting

An anomaly detection approach is considered for the mine hunting in sonar imagery problem. The authors exploit previous work that used dual-tree wavelets and fractal dimension to adaptively suppress sand ripples and a matched filter as an initial detector. Here, lacunarity inspired features are extracted from the remaining false positives, again using dual-tree wavelets. A one-class support vector machine is then used to learn a decision boundary, based only on these false positives. The approach exploits the large quantities of 'normal' natural background data available but avoids the difficult requirement of collecting examples of targets in order to train a classifier. © 2012 The Institution of Engineering and Technology.

The rocking response of large flexible structures to earthquakes

The rocking response of structures subjected to strong ground motions is a problem of 'several scales'. While small structures are sensitive to acceleration pulses acting successively, large structures are more significantly affected by coherent low frequency components of ground motion. As a result, the rocking response of large structures is more stable and orderly, allowing effective isolation from the ground without imminent danger of overturning. This paper aims to characterize and predict the maximum rocking response of large and flexible structures to earthquakes using an idealized structural model. To achieve this, the maximum rocking demand caused by different earthquake records was evaluated using several ground motion intensity measures. Pulse-type records which typically have high peak ground velocity and lower frequency content caused large rocking amplitudes, whereas non-pulse type records caused random rocking motion confined to small rocking amplitudes. Coherent velocity pulses were therefore identified as the primary cause of significant rocking motion. Using a suite of pulse-type ground motions, it was observed that idealized wavelets fitted to velocity pulses can adequately describe the rocking response of large structures. Further, a parametric analysis demonstrates that pulse shape parameters affect the maximum rocking response significantly. Based on these two findings, a probabilistic analysis method is proposed for estimating the maximum rocking demand to pulse-type earthquakes. The dimensionless demand maps, produced using these methods, have predictive power in the near-field provided that pulse period and amplitude can be estimated a priori. Use of this method within a probabilistic seismic demand analysis framework is briefly discussed. © 2013 Springer Science+Business Media Dordrecht.

Construction of 2-D directional filter bank by cascading checkerboard-shaped filter pair and CMFB

In this paper, we propose a new approach to construct a 2-dimensional (2-D) directional filter bank (DFB) by cascading a 2-D nonseparable checkerboard-shaped filter pair and 2-D separable cosine modulated filter bank (CMFB). Similar to diagonal subbands in 2-D separable wavelets, most of the subbands in 2-D separable CMFBs, tensor products of two 1-D CMFBs, are poor in directional selectivity due to the fact that the frequency supports of most of the subband filters are concentrated along two different directions. To improve the directional selectivity, we propose a new DFB to realize the subband decomposition. First, a checkerboard-shaped filter pair is used to decompose an input image into two images containing different directional information of the original image. Next, a 2-D separable CMFB is applied to each of the two images for directional decomposition. The new DFB is easy in design and has merits: low redundancy ratio and fine directional-frequency tiling. As its application, the BLS-GSM algorithm for image denoising is extended to use the new DFBs. Experimental results show that the proposed DFB achieves better denoising performance than the methods using other DFBs for images of abundant textures. (C) 2008 Elsevier B.V. All rights reserved.

地震岩性与物性联合反演技术研究和应用

This paper studies how to more effectively invert seismic data and predict reservoir under complicated sedimentary environment, complex rock physical relationships and fewer drills in offshore areas of China. Based on rock physical and seismic amplitude-preserving process, and according to depositional system and laws of hydrocarbon reservoir, in the light of feature of seismic inversion methods present applied, series methods were studied. A joint inversion technology for complex geological condition had been presented, at the same time the process and method system for reservoir prediction had been established. This method consists four key parts. 1)We presented the new conception called generalized wave impedance, established corresponding inversion process, and provided technical means for joint inversion lithology and petrophysical on complex geological condition. 2)At the aspect of high-resolution nonlinear seismic wave impedance joint inversion, this method used a multistage nonlinear seismic convolution model rather than conventional primary structure Robinson seismic convolution model, and used Caianiello neural network implement inversion. Based on the definition of multistage positive and negative wavelet, it adopted both deterministic and statistical physical mechanism, direct inversion and indirect inversion. It integrated geological knowledge, rock physical theory, well data, and seismic data, and improved the resolution and anti-noise ability of wave impedence inversion. 3)At the aspect of high-resolution nonlinear reservoir physical property joint inversion, this method used nonlinear rock physical model which introduced convolution model into the relationship between wave impedance and porosity/clay. Through multistage decomposition, it handles separately the large- and small-scale components of the impedance-porosity/clay relationships to achieve more accurate rock physical relationships. By means of bidirectional edge detection with wavelets, it uses the Caianiello neural network to finish statistical inversion with combined applications of model-based and deconvolution-based methods. The resulted joint inversion scheme can integrate seismic data, well data, rock physical theory, and geological knowledge for estimation of high-resolution petrophysical parameters. 4)At the aspect of risk assessment of lateral reservoir prediction, this method integrated the seismic lithology identification, petrophysical prediction, multi-scale decomposition of petrophysical parameters, P- and H-spectra, and the match relationship of data got from seismics, well logging and geology. It could describe the complexity of medium preferably. Through applications of the joint inversion of seismic data for lithologic and petrophysical parameters in several selected target areas, the resulted high-resolution lithologic and petrophysical sections(impedance, porosity, clay) show that the joint inversion can significantly improve the spatial description of reservoirs in data sets involving complex deposits. It proved the validity and practicality of this method adequately.

砂泥岩薄互层储层预测方法与应用研究

With the deeply development of exploration and development in petroleum in China, new increasing reserves are found in old oil fields and the verge of the old ones through re-study of geological property. It is more and more important to discovery and develop thin layer or thin inter-bedded layers reservoirs. All of the targets are thin sand-shale inter-bedded reservoirs and the core technology is reservoir predictions between wells in thin sand-shale inter-bedded layers. The continuity of the thin sand-shale inter-bedded layers in space or separating and heterogeneity is the key of reservoir geology research. The seismic reflection, high resolution analysis method and inversion method to thin sand-shale inter-bedded layers are thorough discussed and deeply studied in this paper to try to find the methods and resolutions of reservoir geology research. The below is followed. 1. Based on the pre-research of other people, five models are created: the sand sphenoid body, interlay sandstone and interlay shale of the equal thickness, interlay sandstone of the equal thickness and interlay shale of the unequal thickness, interlay sandstone of the unequal thickness and interlay shale of the unequal thickness, interlay sandstone of the changing thickness in sequence and interlay shale of the changing thickness in sequence. Then the study of the forward modeling are conducted on the thin layer and thin inter-bedded layers geological characters and seismic reflections including amplitude, frequency, phase, wave shape and time-frequency responding in the domains of time and frequency. The affect of petro-physics difference of layers, single thin layer thickness, thickness of inter-bedded, layer number of inter-bedded, incident wavelet domain frequency and types, sample interval to seismic reflection characters, frequency spectrum and time-frequency respond of reflectivity is theoretically discussed. 2. Qualitatively analyzing the sedimentary rhythm of the thin inter-bedded layers in vertical orientation and computing the single layer thickness or the average thickness with the method of generalized S transform. Identifying the reflecting interface or lithology interface using the amplitude value of amplitude spectrum domain frequency. 3. Based on the seismic respond of thin sand-shale inter-bedded layers, bring out the high resolution analysis method of seismic data in thin sand-shale inter-bedded layers using wavelet analysis and the idea of affecting low and high frequency with middle frequency. Then analyzing the effect to the method and testing some wavelets in the method. This method is applied to the theoretical models and the field data. 4. Bring forward one improved very fast simulated annealing method (IVFSA) to resolve the problem nonlinearity and multi-parameters of the inversion in thin inter-bedded layers. And IVFSA is more productive and higher precision than general ways. 5. New target constrained function is used in the inversion based on the property of the inversion in thin inter-bedded layers. 6. Making the full use of geological and logging information, IVFSA and the new function are applied in the non-linear inversion to improve reservoir prediction and evaluation in thin inter-bedded formations combined with the idea of logging and seismic inversion. This method was applied to the field data and got good results.

各向同性与各向异性介质中地震波旅行时正演模拟与反演成像

By seismic tomography, interesting results have been achieved not only in the research of the geosphere with a large scale but also in the exploration of resources and projects with a small scale since 80'. Compared with traditional inversion methods, seismic tomography can offer more and detailed information about subsurface and has been being paid attention by more and more geophysicists. Since inversion based on forward modeling, we have studied and improved the methods to calculate seismic traveltimes and raypaths in isotropic and anisotropic media, and applied the improved forward methods to traveltime tomography. There are three main kinds of methods to calculate seismic traveltime field and its ray path distribution, which are ray-tracing theory, eikonal equation by the finite-difference and minimum traveltime tree algorithm. In ray tracing, five methods are introduced in the paper, including analytic ray tracing, ray shooting, ray bending, grid ray tracing and rectangle grid ray perturbation with three points. Finite-difference solution of eikonal equation is very efficient in calculation of seismic first-break, but is awkward in calculation of reflection traveltimes. We have put forward a idea to calculate traveltimes of reflected waves using a combining way of eikonal equation method and other one in order to improve its capability of dealing with reflection waves. The minimum traveltime tree algorithm has been studied with emphases. Three improved algorithms are put forward on the basis of basic algorithm of the minimum traveltime tree. The first improved algorithm is called raypath tracing backward minimum traveltime algorithm, in which not only wavelets from the current source but also wavelets from upper source points are all calculated. The algorithm can obviously improve the speed of calculating traveltimes and raypaths in layered or blocked homogeneous media and keep good accuracy. The second improved algorithm is raypath key point minimum traveltime algorithm in which traveltimes and raypaths are calculated with a view of key points of raypaths (key points of raypths mean the pivotal points which determine raypaths). The raypath key point method is developed on the basis of the first improved algorithm, and has better applicability. For example, it is very efficient even for inhomogeneous media. Another improved algorithm, double grid minimum traveltime tree algorithm, bases upon raypath key point scheme, in which a model is divided with two kinds of grids so that the unnecessary calculation can be left out. Violent undulation of curved interface often results in the phenomenon that there are no reflection points on some parts of interfaces where there should be. One efficacious scheme that curved interfaces are divided into segments, and these segments are treated respectively is presented to solve the problem. In addition, the approximation to interfaces with discrete grids leads to large errors in calculation of traveltimes and raypaths. Noting the point, we have thought a new method to remove the negative effect of mesh and to improve calculation accuracy by correcting the traveltimes with a little of additional calculation, and obtained better results.