Two-dimensional Wavelet Analysis Research Articles

A hybrid two-dimensional orthogonal wavelet multiresolution and proper orthogonal decomposition technique for the analysis of turbulent wake flow

A hybrid two-dimensional orthogonal wavelet multiresolution and proper orthogonal decomposition technique is developed to analyze the wake flow behind a semi cylinder. The two-dimensional orthogonal wavelet analysis is first applied to decompose the measured velocity fields into four wavelet components based on their spatial scales. Then the extracted multi-scale structures are further investigated based on proper orthogonal decomposition. The modal energy distributions of multi-scale flow structures suggest that the dominance of first two POD modes is reduced and the relative energy becomes more distributed as the flow structure changes from large-scale to small-scale. The first two POD modes of intermediate-scale structure also appear in a mode pair and they are related to secondary resonance accompanied with large-scale flow oscillation. The POD mode 3 of intermediate-scale structure suggest the existence of symmetric vortex shedding pattern. The first two POD modes of small-scale structure also display a symmetrically distributed vortex pair and the distance between adjacent vortices is about half of the case of mode 3 of intermediate-scale structure. The PSD distributions of POD modes of multi-scale structures suggest that the bandwidth of PSD becomes less concentrated as the flow structure varies from large-scale to small-scale. Distinctive flow patterns associated with first and second order harmonics of fundamental flow oscillation can be successfully extracted from the dominating POD modes of intermediate-scale and small-scale structures. The proposed hybrid technique provides a tool for relate the most energetic flow events over a period of time with multi-scale structures cascaded in the turbulence flow.

(Retracted) Deep graph convolutional network-based high-performance detection method for spectral domain gesture image stream

The use of vision-based high-performance detection technology has become an innovative technical methodology. Gestures can express more actions and even emotions, which is more in line with the design idea of large-scale integrated human–computer interaction software, and then assists the development of emotion recognition and other fields. The emerging deep graph convolutional network can capture the interdependence between instances, and then infer the complete information of the image based on specific features. The two-dimensional discrete wavelet and multi-resolution analysis are used to replace the traditional Fourier transform to realize the convolution operation, which improves the accuracy of the generated graph data. This work studies the spectral clustering method of Graph Wavelet Neural Network and adds the local correlation preserving support vector machine as a classifier. This classifier has a simplified structure compared with the cascade classifier and can achieve faster and stable classification results. On the test set, the average accuracy of the algorithm is 93.40%, the recall rate is 96.27%, and the average detection time per frame is 359 ms.

Multi-Scale Identification of Urban Landscape Structure Based on Two-Dimensional Wavelet Analysis: The Case of Metropolitan Beijing, China

Scale dependence is one of the major characteristics of landscape. Urban landscape is highly affected by human activities with a multi-scale structure, which makes the multi-scale identification of urban structure an obligation for urban spatial studies. Although there have been many previous studies on urban landscape structure, most of them have been conducted on a single scale, and the multi-scale effects of landscape patterns were rarely involved. Two-dimensional wavelet transforms can link spatial structures to scale and spatial locations, and maybe an effective method for the multi-scale analysis of landscape. In this paper, we applied two-dimensional discrete wavelet transform and wavelet variance to analyze the multi-scale spatial structure characteristics and the nested hierarchical structure of the metropolitan Beijing area. The results indicated that the spatial distribution and configuration of the patches were highly scattered at small scales, and the urban landscape exhibited a relatively complicated structure. At medium scales, a combination of the polycentric and sectorial structure was identified due to the prominence of dominant patches within each administrative district. At larger scales, the urban landscape pattern exhibits typical concentric ring characteristics. Two characteristic scales were detected by the wavelet variance in the south-north direction of the main urban zones, scale 4 (112m) and 8 (1792m) in Dongcheng District, scale 3 (56m) and 6 (448m) in Xicheng District, which were corresponding to the extent of middle-small blocks and large blocks respectively. One characteristic scale was detected in each of the suburb areas (Chaoyang, Haidian, and Fengtai District). The spatial structure of the main urban zones is more complex than that of the suburb areas, and it presents a typical hierarchical structure in the south-north direction. In general, the spatial structure of Beijing metropolitan area appears polycentric and concentric ring structure at large scales, the main urban area has nested hierarchies at different characteristic scales, and the wavelet method can effectively identify multi-scale characteristics of urban spatial structure.

Identification of the minimum chip thickness based on the two-dimensional wavelet analysis

In this paper, authors take attempt to adapt the two-dimensional wavelet transform to assess the value of the minimum chip thickness for the face milling process of C45 steel. The images of surface layer from selected measuring devices were analyzed using a mother wavelet bior6.8. The analysis based on the wavelet transform revealed in signals three characteristics zones of the impact of cutting insert on the workpiece during initiation of the cutting process. The obtained values allowed to determine the relative method accuracy and to evaluate the possibility of application the particular measuring machines to assess the value of hmin parameter.

A persistent quiet-Sun small-scale tornado

Context. Recently, the appearance, characteristics, and dynamics of a persistent 1.7 h vortex flow, resembling a small-scale tornado, have been investigated with observations both from the ground and from space in a quiet-Sun region in several lines and channels and for the first time in the Hα line centre. The vortex flow showed significant substructure in the form of several intermittent chromospheric swirls. Aims. We investigate the oscillatory behaviour of various physical parameters in the vortex area in an attempt to better understand the physics of the reported vortex flow. This is the first analysis of this extent. Methods. We used the same data set of high spatial and temporal resolution CRisp Imaging SpectroPolarimeter (CRISP) observations in several wavelengths along the Hα and Ca II 8542 Å line profiles, as well as Doppler velocities and full-width at half-maximum (FWHM) derived from the Hα line profiles. The spectral analysis of oscillations is based on a two-dimensional wavelet analysis performed within the vortex flow area and in a quiet-Sun region (used for comparison), as well as along line and circular slices. Results. The vortex flow shows significant oscillatory power in the range of 3–5 min, peaking around 4 min. This power behaves differently than the reference quiet-Sun region. The derived oscillations reflect the cumulative action of different components such as swaying motions, rotation, and waves. The derived periods for swaying motions are in the range of 200–220 s, and the rotation periods are ∼270 s for Hα and ∼215 s for Ca II 8542 Å. Periods increase with atmospheric height and seem to decrease with radial distance from the vortex centre, suggesting a deviation from a rigid rotation. The behaviour of power within the vortex flow as a function of period and height implies the existence of evanescent waves. Moreover, considerable power is obtained even for periods as long as 10 min, not only at photospheric but also at chromospheric heights, while the formation of vortexes is related to turbulent convection or to twisting motions exercised in the magnetic field concentrations. These imply that different types of waves may be excited, such as magnetoacoustic (e.g. kink) or Alfvén waves. Conclusions. The vortex flow seems to be dominated by two motions: a transverse (swaying) motion, and a rotational motion. The obtained oscillations point to the propagation of waves within it. Nearby fibril-like flows could play an important role in the rotational modulation of the vortex flow. There also exists indirect evidence that the structure is magnetically supported, and one of the swirls, close to its centre, seems to be acting as a “central engine” to the vortex flow.

Gravity waves excited during a minor sudden stratospheric warming

Abstract. An exceptionally deep upper-air sounding launched from Kiruna airport (67.82∘ N, 20.33∘ E) on 30 January 2016 stimulated the current investigation of internal gravity waves excited during a minor sudden stratospheric warming (SSW) in the Arctic winter 2015/16. The analysis of the radiosonde profile revealed large kinetic and potential energies in the upper stratosphere without any simultaneous enhancement of upper tropospheric and lower stratospheric values. Upward-propagating inertia-gravity waves in the upper stratosphere and downward-propagating modes in the lower stratosphere indicated a region of gravity wave generation in the stratosphere. Two-dimensional wavelet analysis was applied to vertical time series of temperature fluctuations in order to determine the vertical propagation direction of the stratospheric gravity waves in 1-hourly high-resolution meteorological analyses and short-term forecasts. The separation of upward- and downward-propagating waves provided further evidence for a stratospheric source of gravity waves. The scale-dependent decomposition of the flow into a balanced component and inertia-gravity waves showed that coherent wave packets preferentially occurred at the inner edge of the Arctic polar vortex where a sub-vortex formed during the minor SSW.

Self-dissimilar landscapes: Revealing the signature of geologic constraints on landscape dissection via topologic and multi-scale analysis

Climatic or geologic controls, such as tectonics or glacial drainage, might impose constraints on landscape self-organization resulting in spatial patterns of rivers and valleys which do not obey the typical self-similar relationships found in most landscapes. The goal of this study is to quantify how such geologic constraints express themselves on channel network topology, spatial heterogeneity of drainage patterns, and emergence of preferred scales of landscape dissection. We use as an example a basin located in the Upper Midwestern United States where successive glaciations over the past thousand years have led to a pronounced spatially anisotropic channel network structure which defeats most scaling laws of fluvial landscapes. This is contrasted with another river basin in the North-Central U.S. which has been organized under the absence of major geologic influences and follows a typical self-similar channel network organization. We show how the geologic constraints have imposed a competition for space which is captured in the slope–local drainage density probabilistic structure, in the failure of self-similarity in basin-wide river network topology, and in the length-area scaling relationship being not typical of fluvial landscapes. Via a two-dimensional wavelet analysis and synthesis, we demonstrate the occurrence of a gap in the power spectrum which corresponds to the presence of preferred scales of organization, and characterize them through multi-scale detrending. The developed methodologies can be useful in advancing our geomorphologic understanding of how external controls might manifest themselves in creating a landscape dissection that is outside the norm and how this dissection can be studied objectively for understanding cause and effect.

Observational indications of downward-propagating gravity waves in middle atmosphere lidar data

Two Rayleigh lidars were employed at a southern-hemisphere mid-latitude site in New Zealand (45°S) and a northern-hemisphere high-latitude site in Finland (67°N) in order to observe gravity waves between 30 and 85km altitude under wintertime conditions. Two-dimensional wavelet analysis is used to analyze temperature perturbations caused by gravity waves and to determine their vertical wavelengths and phase progression. In both datasets, upward phase progression waves occur frequently between 30 and 85km altitude. Six cases of large-amplitude wave packets are selected which exhibit upward phase progression in the stratosphere and/or mesosphere. We argue that these wave packets propagate downward and we discuss possible wave generation mechanisms. Spectral analysis reveals that superpositions of two or three wave packets are common. Furthermore, their characteristics often match those of upward-propagating waves which are observed at the same time or earlier. In the dataset means, the contribution of upward phase progression waves to the potential energy density Ep is largest in the lower stratosphere above Finland. There, Ep of upward and downward phase progression waves is comparable. At 85km one third of the potential energy carried by propagating waves is attributed to upward phase progression waves. In some cases Ep of upward phase progression waves far exceeds Ep of downward phase progression waves. The downward-propagating waves might be generated in situ in the middle atmosphere or arise from reflection of upward-propagating waves.

Two-dimensional orthogonal wavelet multi-resolution analysis on multi-scale flow structures behind triangle cylinder

This study focuses on the multi-scale turbulent structures of triangle cylinder wake flow measured by high-speed particle image velocimetry (PIV). The measured turbulent structures were spatially extracted into large-, intermediate-, relatively small-, and small-scale components using two-dimensional orthogonal wavelet analysis. Then the features of multi-scale turbulent structures were analyzed in terms of two-point auto correlation, power spectra, turbulent kinetic energy and Reynolds shear stress. It is found that the large-scale structure attributed to coherent motions in the wake flow makes largest contribution to the total fluctuating energy and maximum Reynolds shear stress, accounting for 84% and 92% respectively. The intermediate scale structures, which are unidentifiable by PIV measurement, are found to shed into the separated shear layer due to Kelvin–Helmholtz instability, and the central frequency of intermediate scale vortex is approximately twice of Kármán vortex shedding frequency. Besides, two symmetric regions of intensive velocity fluctuations having relatively small-scale are observed near the cylinder surface and the boundary of separation region, and they are not dominant.

Investigation of fractal properties of the magnetic survey data array in the Pechenga ore region using two-dimensional wavelet analysis

The article deals with a study of the fractal properties of geophysical data arrays obtained by areal geophysical works over hierarchically organized geologic systems. It was shown by the example of magnetic survey data in the Pechenga ore region that two-dimensional wavelet analysis is a useful tool for investigating the fractal properties of geophysical data arrays. The application of wavelet analysis allows detecting the hierarchical structure of organization of the whole ore region, estimating the degree of the system inhomogeneity, and concluding about local properties of a geologic system, for example, the ore potential of separate sites.

Two-Dimensional Wavelet Analysis of Supraorbital Margins of the Human Skull for Characterizing Sexual Dimorphism

The accurate determination of the sex of human skeletal remains is a critical challenge in forensic pathology and skeletal anthropology. The pelvis and the skull are the most commonly used skeletal sites for determining the sex of skeletons. In the skull, the supraorbital region, which includes the supraorbital margin, is considered a specific sexually dimorphic trait. In the traditional approach, sex is determined through visual and tactile assessment. This paper introduces a methodology for the objective quantification of sexually dimorphic features using wavelet transform, which is a multiscale mathematical tool that allows for the measurement of shape variations that are hidden at different scales of resolution. The method was successfully applied for the sex determination of a pilot sample of 3D meshes—digital records of supraorbital morphology. This information can be used by experts to improve the accuracy of biologic profile assessment of a human skeleton, and to describe the geographic and temporal variations within and among populations.

Research on Plate Damage Detection by Two-Dimensional Wavelet Analysis

Wavelet analysis has the characteristics of timing and frequency adapting to each other. Two-dimensional wavelet analysis can rotate and amplify the signal in frequency domain. So, in this paper, two-dimensional wavelet analysis is used to detect the position of the injury of simply supported plate. This article simulates an injury and two injuries in a simply supported plate and the detection of the location of the injury. This article verifies that the feasibility of this method.

Two-dimensional wavelet analysis of spruce budworm host basal area in the Border Lakes landscape

Increases in the extent and severity of spruce budworm (Choristoneura fumiferana Clem.) outbreaks over the last century are thought to be the result of changes in forest structure due to forest management. A corollary of this hypothesis is that manipulations of forest structure and composition can be used to reduce future forest vulnerability. However, to what extent historical forest management has influenced current spatial patterns of spruce budworm host species is unknown. To identify landscape-scale spatial legacies of forest management in patterns of spruce budworm host species (i.e., Abies balsamea and Picea spp.), we analyzed remotely sensed forest data from the Border Lakes landscape of northern Minnesota and northwestern Ontario. Our study area contains three regions with different management histories: (1) fine-scale logging patterns in Minnesota, (2) coarse-scale logging patterns in Ontario, and (3) very limited logging history in the Boundary Waters Canoe Area and adjacent Quetico Provincial Park. We analyzed forest basal-area data using wavelets and null models to identify: (1) at which scales forest basal area is structured, (2) where those scales of pattern are significantly present, and (3) whether regions of local significance correspond to regional boundaries that separate the study area. Results indicate that spatial patterns in host basal area are created by nonstationary processes and that these processes are further constrained by lakes and wetlands. Wavelet analysis combined with significance testing revealed a bimodal distribution of scale-specific wavelet variance and separate zones of host species basal area that partially correspond with regional boundaries, particularly between Minnesota and the Wilderness region. This research represents one of the first comparisons of forest spatial structure in this region across an international border and presents a novel method of two-dimensional wavelet analysis that can be used to identify significant scale-specific structure in spatial data.

Damage detection in stiffened plates by wavelet transform

In this study, numerical analysis was carried out by using the finite element method to construct the first mode shape of damaged stiffened plates, and the damage locations were detected with two-dimensional discrete wavelet analysis. In the experimental analysis, four different damaged stiffened structures were observed. Firstly, each damaged structure was hit with a shaker, and then accelerometers were used to measure the vibration responses. Secondly, the first mode shape of each structure was obtained by using the wavelet packet, and the location of cracks were also determined by two-dimensional discrete wavelet analysis. The results of the numerical analysis and experimental investigation reveal that the proposed method is applicable to detect single crack or multi-cracks of a stiffened structure. The experimental results also show that fewer measurement points are required with the proposed technique in comparison to those presented in previous studies.

Damage detection in stiffened plates by wavelet transform

In this study, numerical analysis was carried out by using the finite element method to construct the first mode shape of damaged stiffened plates, and the damage locations were detected with two-dimensional discrete wavelet analysis. In the experimental analysis, four different damaged stiffened structures were observed. Firstly, each damaged structure was hit with a shaker, and then accelerometers were used to measure the vibration responses. Secondly, the first mode shape of each structure was obtained by using the wavelet packet, and the location of cracks were also determined by two-dimensional discrete wavelet analysis. The results of the numerical analysis and experimental investigation reveal that the proposed method is applicable to detect single crack or multi-cracks of a stiffened structure. The experimental results also show that fewer measurement points are required with the proposed technique in comparison to those presented in previous studies.

Two-dimensional discrete wavelet analysis of multiparticle event topology in heavy ion collisions

The event-by-event analysis of multiparticle production in high energy hadron and nuclei collisions can be performed using the discrete wavelet transformation. The ring-like and jet-like structures in two-dimensional angular histograms are well extracted by wavelet analysis. For the first time the method is applied to the jet-like events. The jet positions are located quite well by the discrete wavelet transformation of angular particle distribution even in the presence of soft process background in nucleus-nucleus collisions at LHC energies.

Two-Dimensional Continuous Wavelet Analysis and Its Application to Meteorological Data

AbstractThe two-dimensional continuous wavelet transform (2D CWT) has become an important tool to examine and diagnose nonstationary datasets on the plane. Compared with traditional spectral analysis methods, the 2D CWT provides localized spectral information of the analyzed dataset. It also has the advantage over the 2D discrete wavelet transform (DWT) in that it covers the domain of the analyzed data with a continuous analysis from which detailed, shift-invariant spectral information of different positions and orientations can be obtained. In this paper, a brief introduction of the 2D CWT and some of the most common wavelet mother functions are given, and some practical issues arising from the implementation and applications of the 2D CWT are discussed. The 2D CWT is applied to several test functions to illustrate the effects of the transforms. To demonstrate its practical application, the 2D CWT is used to analyze a set of meteorological data obtained from a numerical model stimulation.

Regeneration pattern analysis of Quercus liaotungensis in a temperate forest using two-dimensional wavelet analysis

This paper introduces the two-dimensional (2D) wavelet analysis as a general interrogative technique for the detection of spatial structure in lattice data. The 2D wavelet analysis detects components of hierarchical structure and displays the locational information of the components. Patches and gaps of different spatial scales in graphical presentation of wavelet coefficients can be linked to the local ecological processes that determine patterns at stand or landscape scales. Derived from the 2D wavelet transform function, the calculation of wavelet variance can reduce the four-dimensional data of wavelet coefficients to a two-dimensional wavelet variance function and quantify the contribution of the given scale to the overall pattern. We illustrate the use of the 2D wavelet analysis by analyzing two simulated patterns and identifying the regeneration pattern of the Quercus liaotungensis in a warm temperate forest in north China. Our results indicate that the recruitment of Q. liaotungensis occurs in an overlapping area between the patch of adult and canopy gap at scales of 45 m×45 m–70 m×70 m and 20 m×20 m–30 m×30 m. The regeneration pattern of Q. liaotungensis can be mainly ascribed to a trade-off between two ecological processes: recruitment around parent trees and the physiological light requirements of seedlings and saplings. Our results provide a general portrayal of the regeneration pattern for the dispersal-limited and shade-intolerant Quercus species. We find that the two-dimensional wavelet analysis efficiently characterizes the scale-specific pattern of Q. liaotungensis at different life-history stages.

Two-dimensional wavelet analysis based classification of gas chromatogram differential mobility spectrometry signals

This study introduces two-dimensional (2-D) wavelet analysis to the classification of gas chromatogram differential mobility spectrometry (GC/DMS) data which are composed of retention time, compensation voltage, and corresponding intensities. One reported method to process such large data sets is to convert 2-D signals to 1-D signals by summing intensities either across retention time or compensation voltage, but it can lose important signal information in one data dimension. A 2-D wavelet analysis approach keeps the 2-D structure of original signals, while significantly reducing data size. We applied this feature extraction method to 2-D GC/DMS signals measured from control and disordered fruit and then employed two typical classification algorithms to testify the effects of the resultant features on chemical pattern recognition. Yielding a 93.3% accuracy of separating data from control and disordered fruit samples, 2-D wavelet analysis not only proves its feasibility to extract feature from original 2-D signals but also shows its superiority over the conventional feature extraction methods including converting 2-D to 1-D and selecting distinguishable pixels from training set. Furthermore, this process does not require coupling with specific pattern recognition methods, which may help ensure wide applications of this method to 2-D spectrometry data.

Two-dimensional discrete wavelet analysis of multiparticle event topology in heavy-ion collisions

The event-by-event analysis of multiparticle production in high energy hadron and nuclei collisions can be performed using the discrete wavelet transformation. The ring-like and jet-like structures in two-dimensional angular histograms are well extracted by wavelet analysis both for toy models and in Monte Carlo simulated events of nucleus–nucleus collisions at LHC energies. For the first time the method is applied to the jet-like events. The jet positions are located quite well by the discrete wavelet transformation of angular particle distribution even in the presence of the underlying soft process background in nucleus–nucleus collisions at LHC energies.