International Journal of Wavelets, Multiresolution and Information Processing

This paper describes the application of discrete wavelet transforms to the analysis of condensation jets in order to clarify the associated fluid and heat transfer phenomena. An experimentally-obtained, two-dimensional image of the condensation particle density around the jet was decomposed into 7 levels of resolution with their respective wavelengths. Based on the known physical characteristics of turbulent flow around the jet, levels 0 and 1 were shown to represent the large-scale components of the condensation particle density and the higher levels represent the small-scale components. From the wavelet-analyzed images, the width of the condensation zone was obtained and this compared well with the width inferred from temperature measurements. Thus, the method was verified and also provided data not available experimentally.

Particle concentration distribution images of a dense solid-air two-phase (plug) flow have been obtained at 10 ms intervals at a bend pipe upstream in a horizontal pipeline by means of a capacitance computed tomography. The three-dimensional images (time and two-dimensional space images) have been decomposed to the wavelet time levels to extract the dominant particle concentration distribution using three-dimensional discrete wavelet multiresolution. As a result, the time dominant particle distribution with specific time frequency level is visualized in a cross-section. In detail, the high concentration of the particle spatial distribution at the dense flow front, which composes high-time frequency levels 6 and 7, is located at the center above the stationary layer.

The author's peculiarity in Ekuni's short story Duke is visualized in the reader-story fusion world by analyzing the conversation; the inner, direct and indirect speeches. Voices and sounds as conversations and onomatopoeias play an interesting role in her story world. Structures of expression in conversation in her two books are visualized by wavelet multiresolution analysis. In this study, the visualization of Duke is compared with that of Rakka-suru Yugata. As a result, the author's peculiarity and literary genre differences are extracted.

A discrete wavelet transform is one of the effective methodologies for compressing the image data and extracting the major characteristics from various data, but it always requires a number of target data composed of a power of 2. To overcome this difficulty without losing any original data information, we propose here a novel approach based on the Fourier transform. The key idea is simple but effective because it keeps all of the frequency components comprising the target data exactly. The raw data is firstly transformed to the Fourier coefficients by Fourier transform. Then, the inverse Fourier transform makes it possible to the number of data comprising a power of 2. We have applied this interpolation for the wind vector image data, and we have tried to compress the data by the multiresolution analysis by using the three-dimensional discrete wavelet transform. Several examples demonstrate the usefulness of our new method to work out the graphical communication tools.

This paper describes a wavelet-based preconditioning technique for conjugate gradient method for linear systems derived from the Poisson equation. The linear systems solved with a conventional iterative matrix solver resulted in a marked increase in computing time with respect to an increase in grid points. Use of our wavelet-based technique leads to a matrix with a bounded condition number so that computing time is reduced significantly. In this study, one of the simplest wavelets, the Haar wavelet, is used for the purpose of developing a simple but efficient preconditioning algorithm. Simple wavelets having low data communication property such as the Haar wavelet are expected to be suitable for the purpose of improving computing performance. In this study, we also pay attention to the basic characteristics of the Haar-wavelet-based preconditioning method for a Poisson equation solver.

This paper describes an application of the wavelet transform in in-line solder paste inspection. In the development of a three-dimensional (3D) automatic inspection device of solder paste, it is necessary to detect the characteristic positions in images. In this paper, on the basis of the property of local wavelet transform modulus maximum (WTMM) and the deference filter, a practical algorithm is proposed for the detection of the characteristic positions. The proposed algorithm is applied to more than 20 actual images obtained from the 3D automatic inspection device. The detected errors are smaller than the maximum permissible error of 5 pixels. Also, the proposed algorithm is verified in-line. The experimental results show that the quality of solder paste can be successfully judged in-line. The proposed algorithm is superior to other possible techniques reported so far because of its implementation in assembly lines.

We propose a hybrid expansion that consists of a multiresolution approximation (MRA) and a proper orthogonal decomposition (POD) to analyze turbulent flow structures in open-channel flows with complex geometries. The open-channel cavity flows are examined here and their velocity vectors are measured by using particle image velocimetry (PIV). In the first step of the hybrid expansion, the velocity time-series are classified into three distinct components using the MRA, i.e. pseudo-mean velocity, organized turbulence in a mixing shear layer, and incoherent turbulence. In the next step, these velocity components are decomposed by applying the POD. The principal components of the pseudo-mean velocity and the organized turbulence disclose the predominant flow characteristics, such as spatial structures of recirculating flows in the cavity and organized turbulent motions along the mixing shear layer, hysteretic behavior in modal time-series, and so forth. The results strongly support that the present hybrid analysis is effective for detecting spatiotemporal hierarchical structures in turbulent flows with complex geometries.

The flow feature of the jet issuing from the circular pipe with the rotating inclined section has been investigated by the methods of flow visualization and image processing. It has been found that the jet diffusion is affected by the inclined angle and the rotating speed. The coherent structure of the jet has also been studied by using wavelet multiresolution analysis. The multiscale turbulent structures were visualized and the core and edge of the vortex were identified at different broad scales.

The high Reynolds number wake topology of a square prism is experimentally investigated using wavelet analysis. It is shown that a systematic application of one-dimensional continuous wavelet techniques, including a relatively new wavelet pattern recognition technique can reveal important three-dimensional features of the flow, assessing the validity of previously proposed wake topological models. Present results suggest that the high Reynolds number turbulent wakes are topologically similar, but not identical, to their laminar counterparts.

We present a new wavelet-based adaptive multiresolution representation (WAMR) algorithm for the numerical solution of multiscale evolution problems. Key features of the algorithm are fast procedures for grid rearrangement, computation of derivatives, as well as the ability to minimize the degrees-of-freedom for a prescribed solution accuracy. To demonstrate the efficiency and accuracy of the algorithm, we use it to solve the two-dimensional benchmark problem of incompressible fluid-flow in a lid-driven cavity at large Reynolds numbers. The numerical experiments demonstrate the great ability of the algorithm to adapt to different scales at different locations and at different times so as to produce accurate solutions at low computational cost. Specifically, we show that solutions of comparable accuracy as the benchmarks are obtained with more than an order of magnitude reduction in degrees-of-freedom.

A method of information processings based on the classical field theory is outlined to derive the modal-wavelet transform (MWT) as a wavelet-like orthonormal transform. The theoretical background and application of MWT are described. The bases of MWT are derived from modal analysis of the potential field equations. Namely, a principal idea of MWT is that a numerical data set is regarded as a set of the field potentials or source densities. A modal matrix, constituting characteristic vectors, derived from the discretized field equations enables us to carry out an orthonormal transform inasmuch as the same way as those of conventional discrete wavelets. MWT is based on this data modeling to provide multiresolution analysis in an efficient manner. Three-dimensional MWT demonstrates a classification of a weather satellite infrared animation into background and cloud-moving frame images.

Wavelet multiresolution analysis has been applied to digital images of ethanol sprays injected into air at atmospheric pressure and at room temperature. The imaging was performed with laser-sheet imaging using the 308 nm light from a XeCl excimer laser. Image capturing was performed with a CCD camera. The importance of different scales in the turbulent structure of the sprays was easily recognized using wavelet multiresolution analysis. It was observed that the intermediate and small scale levels contained information of such important phenomena as the spray break-up. This was not easily recognized in the original images, due to averaging over all scales.

Rotating stall is usually the first symptom of approaching compressor instability. It consists of zones of a turbulent flow, which rotate slower than the compressor impeller. The wavelet cross-correlation function was applied to detect rotating objects, whereas the continuous wavelet transform was used to identify different phases of the compressor operation. These methods of signal analysis enabled the identification of rotating pressure waves that appear during all phases of operation. Some of them have several times shorter wavelength than these manifested by the rotating stall. What is more, rotating pressure waves, though very weak, appear also during the stable compressor operation.