WAVELET ANALYSIS OF COHERENT STRUCTURES IN A THREE-DIMENSIONAL MIXING LAYER

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists.

Detecting Near-Surface Coherent Structure Characteristics Using Wavelet Transform with Different Meteorological Elements

In the present study, three wavelet basis functions, i.e., Mexican-hat, Morlet, and Wave, were used to analyze the atmospheric turbulence data obtained from an eddy covariance system in order to determine the effect of six meteorological elements including three-dimensional wind speed, temperature, and CO2and H2O concentrations on the time scale of coherent structures. First, we used the degree of correlation between original and reconstructed waveforms to test the three wavelets’performance when determining the time scale of coherent structures. The Wave wavelet’s reconstructed coherent structure signal best matched the original signal;thus, it was used to further analyze the time scale, number, and time cover of the meteorological elements. We found similar results for all elements, though there was some internal variation, suggesting that coherent structures are not inherently dependent on these elements. Our results provide a basis for proper coherent structure detection in atmospheric turbulence and improve the understanding of similarities and differences between coherent structure characteristics of different meteorological elements, which is helpful for further research into atmospheric turbulence and boundary layers.

GAP STRUCTURE ANALYSIS OF FOREST TRANSECT USINGTHE 1-D DISCRETE WAVELET TRANSFORM

Wavelets is a very effective technique for time-frequency analysis with the ability of preserving loeal information, applied to many areas such as nonlinear science, information processing.quantum physics etc.. In this paper. from the view of ecology spatial pattern, the authors try to process the sample data of Larix forest transects to identify the canopy gap structures by wavelet analysis. The caleulation of wavelet variance, derived from the transtform facilitates comparison based on dominant scale of pattern between multiple datasets such as the stands described.

Recognition of vortex structures in turbulent refractive index field using wavelet transformation

When the light wave propagates through the hypersonic flow field, the aero-optic distortion happens. It is necessary to recognize the vortex structure for studying the light propagation model. A new vortex structure recognition method is proposed in this paper. Firstly, the refractive index field, which is transformed from the turbulent density field, is changed to gray scale images with a- bundant texture information equivalently. Then, wavelet transform is performed to decompose these images and the entropy values of the wavelet base coefficients are calculated. Comparing the entropy value to a given threshold, the modules with lower entropy are considered to be the large-scale vortex modules while those with higher entropy are small-scale vortex modules. The computer simulation results show that the proposed method is valid to recognize the vortex structures. This paper provides basis for investigation on the optics propagation model in terms of the turbulence vortex structures.

Image Coding Using Wavelet Transform and EntropyConstrained Vector Quantization with Quadtree Structure Vectors

This paper presents a new wavelet transform image coding method. On the basis of a hierarchical wavelet decomposition of images, entropy constrained vector quantization is employed to encode the wavelet coefficients at all the high frequency bands with

Discrete wavelet structure and discrete energy of classical plane light waves

We find by the wavelet transform that the classical plane light wave of linear polarization can be decomposed into a series of discrete Morlet wavelets.In the theoretical frame,the energy of the classical light wave becomes discrete;interestingly,the discretization is consistent with the energy division of P portions in Planck radiation theory,where P is an integer.It is shown that the changeable energy of a basic plane light wave packet or wave train is H_(0k)=nP0 kω(n=1,2,3,...;k=|k|),with discrete wavelet structure parameter n,wave vector k and idler frequency ω,and a constant p0 k.The wave-particle duality from the Mach-Zehnder interference of single photons is simulated by using random basic plane light wave packets.

MULTIVARIATE PROBABILISTIC APPROXIMATION IN WAVELET STRUCTURE

Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These approximate F(x,y)in the supnorm.The degree of this approximation is estimated by establishing a Jackson type inequality.Furthermore we give generalizations for the case of a mother wavelet ≠,which is just any distribution function on R^2,also we extend these results in R^r,r>2.

Damage Characterization of Composite Structures Using Difference Peak Signal-to-Noise Ratio as a Function of Variable Wavelets (ΔPSNR-ΔW)

A novel approach employs the principles of medical image analysis using Wavelet Transform (WT) and Difference Peak Signal-to-Noise Ratio (ΔPSNR). Both techniques are combined as a function of different decomposing levels of wavelets and various image search through and slicing levels, which is implemented under MATLAB environment. In this new approach, the structural change due to damage in the component or the presence of foreign bodies appearing in an image taken for a specific structure is uncovered with its extent determined after applying the search through algorithm. Such alteration of the composite structure, which could be masked by the presence of noise, is accounted for using combined WT and PSNR. Effect of Artifacts and Blurring caused by different wavelet types is investigated before choosing an appropriate wavelet, namely Sym8. This new approach, which also reduces the required layers of search within an image, produces a pattern matrix per damaged area and is an excellent way in tracing and modeling damage in structures with ability to predict effects of further damage on components and further application to artificial limbs that could suffer damage and affect users mobility.

Theoretical research on structural damage alarming of long-span bridges using wavelet packet analysis

The state equation and observation equation of the structural dynamic systems under various analysis scales are derived based on wavelet packet analysis. The time-frequency properties of structural dynamic response under various scales are further formulated. The theoretical analysis results reveal that the wavelet packet energy spectrum （WPES） obtained from wavelet packet decomposition of structural dynamic response will detect the presence of structural damage. The sensitivity analysis of the WPES to structural damage and measurement noise is also performed. The transfer properties of the structural system matrix and the observation noise under various analysis scales are formulated, which verify the damage alarming reliability using the proposed WPES with preferable damage sensitivity and noise robusticity.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

Output only modal identification and structural damage detection using time frequency & wavelet techniques

The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

Application of wavelet transform in structural health monitoring

Structural health monitoring(SHM)is a process of implementing a damage detection strategy in existing structures to evaluate their condition to ensure safety.The changes in the material,geometric and/or structural properties affect structural responses,which can be captured and analyzed for condition assessment.Various vibration-based damage detection algorithms have been developed in the past few decades.Among them,wavelet transform(WT)gained popularity as an efficient method of signal processing to build a framework to identify modal properties and detect damage in structures.This article presents the state-of-the-art implementation of various WT tools in SHM with a focus on civil structures.The unique features and limitations of WT,and a comparison of WT and other signal processing methods,are further discussed.The comprehensive literature review in this study will help interested researchers to investigate the use of WT in SHM to meet their specific needs.

Identification of Coherent Structures of Turbulence at the Atmospheric Surface Layer

A parameter-free method based on orthonormal wavelet transforms is recommended for calculating the principal time scale of coherent structures in atmospheric boundary-layer measurements. First, the atmospheric turbulent signal is decomposed into the small scale vortex that has approximate isotropy and the large scale vortex with the digital filter. Then, the large scale vortex is used to detect coherent structures with this method. The principal time scale and profile of coherent structures for velocity components (u, v, w above rice fields are obtained. In order to testify the validity of this method, the correlation of coherent structures and non-coherent structures are also calculated.

Crustal structure beneath Cameroon from EGM2008

We used the Earth Gravitational Model （EGM2008） data sets to analyze the regional gravity anoma- lies and to study the underground structures in Cameroon. We first created a high-resolution Free-Air anomaly database, then corrected the gravity field of the topographic effect by using ETOPO1 DEM with a resolution of 0.01~ to obtain the Bouguer anomaly, then applied a multi-scale wavelet-analysis technique to separate the gravity-field components into different parts of shallow-to-deep origins, and finally used the logarithmic power spectrum technique to obtain detailed images and corresponding source depths as well as certain lateral inho- mogeneity of structure density. The anomalies of shallow origin show successive elongated gravity ＂highs＂ and ＂lows＂ attributable to subsurface Tertiary and lower Cretaceous undulations. Our results are in good agreement with previous investigations.

The spatial-temporal evolution of coherent structures in log law region of turbulent boundary layer

The spatial-temporal evolution of coherent structures （CS） is significant for turbulence control and drag re- duction. Among the CS, low and high speed streak structures show typical burst phenomena. The analysis was based on a time series of three-dimensional and three-component （3D-3C） velocity fields of the flat plate turbulent boundary layer （TBL） measured by a Tomographic and Time-resolved PIV （Tomo TRPIV） system. Using multi-resolution wavelet transform and conditional sampling method, we extracted the intrinsic topologies and found that the streak structures appear in bar-like patterns. Furthermore, we seized locations and velocity information of transient CS, and then calculated the propagation velocity of CS based on spatial-temporal cross-correlation scanning. This laid a foundation for further studies on relevant dynamics properties.

Crustal structure beneath Beijing and its surrounding regions derived from gravity data

In this paper we use gravity data to study fine crustal structure and seismogenic environment beneath Beijing and its surrounding regions. Multi-scale wavelet analysis method is applied to separating gravity fields. Logarithmic power spectrum method is also used to calculate depth of gravity field source. The results show that the crustal structure is very complicated beneath Beijing and its surrounding areas. The crustal density exhibits laterally inhomogeneous. There are three large scale tectonic zones in North China, i.e., WNW-striking Zhangjiakou-Bohai tectonic zone （ZBTZ）, NE-striking Taihang piedmont tectonic zone （TPTZ） and Cangxian tectonic zone （CTZ）. ZBTZ and TPTZ intersect with each other beneath Beijing area and both of them cut through the lithosphere. The upper and middle crusts consist of many small-scale faults, uplifts and depressions. In the lower crust, these small-scale tectonic units disappear gradually, and they are replaced by large-scale tectonic units. In surrounding regions of Beijing, ZBTZ intersects with several other NE-striking tectonic units, such as Cangxian uplift, Jizhong depression and Shanxi Graben System （SGS）. In west of Taihangshan uplift, gravity anomalies in upper and middle crusts are correlated with geological and topographic features on the surface. Compared with the crust, the structure is comparatively simple in uppermost mantle. Earthquakes mainly occurred in upper and middle crusts, especially in transitional regions between high gravity anomaly and low gravity anomaly. Occurrence of large earthquakes may be related to the upwelling of upper mantle and asthenosphere heat flow materials, such as Sanhe earthquake （Ms8.0） and Tangshan earthquake （Ms7.8）.

Wind Vibration Study of Long-span Steel Arch Structure of Beijing Capital International Airport

The wind-induced dynamic response of long-span light-weight steel arch structure of the global transportation center (GTC) of Beijing Capital International Airport was studied. A composite technique with combination of WAWS(Weighted Amplitude Wavelet Superposition) and FFT(Fast Fourier Transformation) was introduced to simulate wind velocity time series of hundreds of spatial points simultaneously. The structural shape factors of wind load was obtained from wind tunnel model test. The wind vibration factor based on structural displacement response was investigated. After comparing the computational results with wind tunnel model test data, it was found out that the two results accord with each other if wind comes from 0° direction angle, but are quite different if wind comes from 180° direction angle in the area blocked off by airport terminals. The possible reasons of this difference were analyzed. Haar wavelet was used to transform and analyze wind velocity time series and structural wind-induced dynamic responses. The relationship between exciting wind loads and structural responses was studied in time and frequency domains.

Effects of excitation frequency on detection accuracy of orthogonal wavelet decomposition for structural health monitoring

Accurate estimation of stiffness loss is a challenging problem in structural health monitoring.In this studyorthogonal wavelet decomposition is used for identifying the stiffness loss in a single degree of freedom spring-mass-dampersystem.The effects of excitation frequency on accuracy of damage detection is investigated.Results show that pseudo-aliaseffects caused by the orthogonal wavelet decomposition(OWD),affect damage detectability.It is demonstrated that theproposed approach is sunable for damage detection when the excitation frequency is relatively low.This study shows how apriori knowledge about the signal and ability to control the sampling frequency can enhance damage detectability.

Crustal density structure of the southern segment of the Liaocheng-Lankao fault, China

The 1:200,000 middle-large scale Bouguer gravity anomaly data covering the southern segment of the Liaocheng-Lankao fault(SLLF)and its vicinity are analyzed with two methods.First,the Bouguer gravity anomaly data are decomposed by two-dimensional(2 D)wavelet to make the family of multi-scale modes correspond with density structure at different depths.Second,a two and half dimension(2.5 D)human-computer interaction inversion of the Bouguer gravity anomaly data are conducted with the constraints provided by two deep seismic sounding profiles(DSS1 and DSS2)crossing the study area to get the crustal density profiles.Based on the integrated study,we can draw the following conclusions:1)SLLF appears to be a deep fault with almost vertical dipping and rooted into the uppermost mantle;2)In the middle to upper crust SLLF shows an clear turning patterns and segmentation features;3)In the study area the epicentral distributions of the precisely re-located small earthquakes and the historical large earthquakes have a good correspondence with the turning patterns and segmentation features of SLLF;and 4)The results of the horizontal slices from 2 D wavelet decomposition show that there are significant differences in the density structure on the two sides of the fault.A well-defined concave structure with low density exists in the upper crust of the Dongming Depression on the west side of the fault,with the concave center being estimated at a depth of about 8 km.In contrast,the upper crust on the east side presents a relative thinner pattern in depth with a bit higher density.Meanwhile,the low-density structure in the middle crust underneath the fault is presumably caused by the uplift of the upper mantle materials and their intrusion along the deep rupture system.This paper clarified the inconsistency of fault system and epicenters of small earthquakes from upper to lower crust.The results indicated that the fault system plays an important governing role to the seismicity in this area.

APPLICATION OF WAVELET TRANSFORM IN STRUCTURAL OPTIMIZATION

It is very common in structural optimization that the optima lie at or in the vicinities of the singular points of feasible domain. Therefore it is very reasonable to introduce wavelet transform that is advantageous in singularity detection. The principle and algorithm of the application of wavelet transform in structural optimization are discussed The feasibility is demonstrated by some typical examples.