WAVELETS AND TIME-DEPENDENT SPECTRAL ANALYSIS

Abstract. One of the key features of wavelet analysis is its potential use for effecting time-frequency decompositions of non-stationary signals. The relationship between wavelet analysis and time-dependent spectral analysis has so far rested mainly on heuristic reasoning:in this paper we examine the relationship in a more precise mathematical form. A crucial feature of this analysis is the need to define carefully the notion of "frequency" when applied to non-stationary signals.     

Fluctuations in instantaneous clearness index: Analysis and statistics

Solar radiation is characterized by short fluctuations introduced by passing clouds. An analysis of these fluctuations with regard to solar energy applications should focus on the instantaneous clearness index. Its probability distribution for a given mean clearness index is, as a first approximation, independent from the season and partly also from the site. This is verified for four annual datasets from three different sites.An analysis of fluctuations in solar radiation must focus on their amplitude, persistence, and frequency of occurrence rather than their location in time. The Fourier analysis cannot satisfactorily provide this information since time series of the instantaneous clearness index exhibit no periodicity. Instead, a localized spectral analysis based on wavelet bases rather than on periodic-ones has been applied. This analysis allows the decomposition of the fluctuating clearness index signal into a set of orthonormal subsignals. Each of them represents one specific scale of persistence of the fluctuation.The annual mean square values of all subsignals have been analysed, permitting the allocation of the signal’s power content to the different scales of persistence of a fluctuation. These annual mean values agree well for the different datasets, indicating the existence of statistically significant mean square values of the fluctuations as a function of their persistence.The analysis offers a valuable tool for the estimation of power flow fluctuations introduced by direct solar energy systems. With further elaboration it may be applied by power system operators for network planning in distribution grids with a high density of embedded generation.     

Numerical study of mixing of passive and reactive scalars in two-dimensional turbulent flows using orthogonal wavelet filtering

We present the application of orthogonal wavelet filtering to study mixing and chemical reaction in 2D turbulent flows. We show that the coherent vortices are responsible for the mixing dynamics. Therefore, we perform direct numerical simulation of decaying and statistically stationary homogeneous isotropic 2D turbulence. We split the flow in each time step into coherent vortices represented by few wavelet modes and containing most of the kinetic energy and an incoherent background flow. We quantify the mixing properties of both flow components and demonstrate that efficient mixing of scalars is triggered by the coherent flow, while the influence of the incoherent flow on the mixing corresponds to pure diffusion. These results hold for both passive scalars and reactive scalars with simple and multi-step kinetics.     

New wavelet-based adaptive method for the breakage equation

A new wavelet-based adaptive collocation method is formulated for the solution of breakage equations. The technique of grid adaptation is based on sparse point representation (SPR). Without loss of generality, the method is applied and tested for the cases of uniform binary breakup and multiple breakup. Accurate and convergent solutions are obtained and found to match the analytical solutions very well.     

Browsing and placement of multi-resolution images on parallel disks

Abstract. With rapid advances in computer and communication technologies, there is an increasing demand to build and maintain large image repositories. To reduce the demands on I/O and network resources, multi-resolution representations are being proposed for the storage organization of images. Image decomposition techniques such as wavelets can be used to provide these multi-resolution images. The original image is represented by several coefficients, one of them with visual similarity to the original image, but at a lower resolution. These visually similar coefficients can be thought of as thumbnails or icons of the original image. This paper addresses the problem of storing these multi-resolution coefficients on disks so that thumbnail browsing as well as image reconstruction can be performed efficiently. Several strategies are evaluated to store the image coefficients on parallel disks. These strategies can be classified into two broad classes, depending on whether the access pattern of the images is used in the placement. Disk simulation is used to evaluate the performance of these strategies. Simulation results are validated with results from experiments with real Disks, and are found to be in good qualitative agreement. The results indicate that significant performance improvements can be achieved with as few as four disks by placing image coefficients based upon browsing access patterns. Work supported by a research grant from NSF/ARPA/NASA IRI9411330 and NSF instrumentation grant CDA-9421978 and NSF Career grant No. IIS-9985019, and NSF grant 0010044-CCR.     

Extracting useful information from images

The paper presents an overview of methods for extracting useful information from digital images. It covers various approaches that utilized different properties of images, like intensity distribution, spatial frequency content and several others. A few case studies including isotropic and heterogeneous, congruent and non-congruent images are used to illustrate how the described methods work and to compare some of them.     

内燃机机体振动信号时域识别方法研究

根据内燃机在工作过程中，其机体在不同时刻受到不同激振力作用这一特点，对机体振动信号在时域上进行了分析处理与识别。首先，对内燃机在工作过程中的机体振动信号进行小波降噪处理，从而突出了其机体在不同时刻受到激振的结果。然后，对机体在不同时刻所受到激振的结果分别建立二阶AR模型，以模型系数作为模式识别参数。最后，采用感知器神经网络对模型参数进行识别与分类。由于只对振动信号进行处理与识别便可得到与不同激振力相关的信息，因此这种处理与识别方法具有形式简单，便于实现的特点，因而，对实现内燃机在线控制，监测与故障诊断均有重要的应用价值。     

基于小波BP-时间序列的齿轮箱温度预警

由于风电机组的运行条件恶劣,在运行过程中经常会出现许多不确定的外界因素,这些因素使得风电机组各部件的故障率较高。采用小波BP神经网络的时间序列方法对风电机组的齿轮箱温度进行预测,并利用滑动窗口技术对其预测残差进行统计分析,然后通过分析齿轮箱温度的残差均值和标准差来预测齿轮箱温度是否存在异常情况或是故障隐患,从而达到预警目的。     

A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share a hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping “pictures”. We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.     

Two-layered image compression using 2G bandelets and wavelets

An image can be decomposed into the structural component and the geometric textural component.Based on this idea,an efficient two-layered compressing algorithm is proposed,which uses 2nd generation bandelets and wavelets.First,an original image is decomposed into the structural component and the textural component,and then these two components are compressed using wavelets and 2nd generation bandelets respectively.Numerical tests show that the proposed method works better than the bandelets and JPEG2000 in some specific SAR scene.