Using wavelet transform to study the Lipschitz local singular exponent in wall turbulence

In this paper, wavelet,transform is introduced to study the Lipschitz local singular exponent for characterising the local singularity behavior of fluctuating velocity in wall turbulence. I, is found that the local singular exponent is negative when the ejections and sweeps of coherent structures occur in a turbulent boundary layer.

The application of spline wavelet transform to the determination of electroosmotic mobility in capillary electrophoresis

The rule of current change was studied during capillary electrophoresis (CE) separation process while the conductivity of the sample solution was different from that of the buffer. Using a quadratic spline wavelet of compact support, the wavelet transforms (WTs) of capillary electrophoretic currents were performed. The time corresponding to the maximum of WT coefficients was chosen as the time of current inflection to calculate electroosmotic mobility. The proposed method was suitable for different CE modes, including capillary zone electrophoresis, nonaqueous CE and micellar electrokinctic chromatography. Compared with the neutral marker method, the relative errors of the developed method for the determination of electroosmotic mobility were all below 2.5%. (C) 2002 Elsevier Science B.V. All rights reserved.

Comparison of wavelet transform methods - The compression of IR spectral data

In this paper, an introduction of wavelet transform and multi-resolution analysis is presented. We describe three data compression methods based on wavelet transform for spectral information,and by using the multi-resolution analysis, we compressed spectral data by Daubechies's compactly supported orthogonal wavelet and orthogonal cubic B-splines wavelet, Using orthogonal cubic B-splines wavelet and coefficients of sharpening signal are set to zero, only very few large coefficients are stored, and a favourable data compression can be achieved.

Evaluation of a combined wavelet and a combined principal component analysis classification system for BCG diagnostic problem

Heart disease is one of the main factor causing death in the developed countries. Over several decades, variety of electronic and computer technology have been developed to assist clinical practices for cardiac performance monitoring and heart disease diagnosis. Among these methods, Ballistocardiography (BCG) has an interesting feature that no electrodes are needed to be attached to the body during the measurement. Thus, it is provides a potential application to asses the patients heart condition in the home. In this paper, a comparison is made for two neural networks based BCG signal classification models. One system uses a principal component analysis (PCA) method, and the other a discrete wavelet transform, to reduce the input dimensionality. It is indicated that the combined wavelet transform and neural network has a more reliable performance than the combined PCA and neural network system. Moreover, the wavelet transform requires no prior knowledge of the statistical distribution of data samples and the computation complexity and training time are reduced.

层析静校正技术研究和应用

Static correction is one of the indispensable steps in the conventional onshore seismic data processing, particularly in the western part of China; it is theoretically and practically significant to resolve the issue of static correction. Conventional refraction static correction is put forward under the assumption that layered medium is horizontal and evenly distributed. The complicated nature of the near surface from western part of China is far from the assumption. Therefore, the essential way to resolve the static correction problem from the complex area is to develop a new theory. In this paper, a high-precision non-linear first arrival tomography is applied to solve the problem, it moved beyond the conventional refraction algorithm based on the layered medium and can be used to modeling the complex near surface. Some of the new and creative work done is as follows: One. In the process of first arrival tomographic image modeling, a fast high-order step algorithm is used to calculate the travel time for first arrival and ray path and various factors concerning the fast step ray tracing algorithm is analyzed. Then the second-order and third-order differential format is applied to the step algorithm which greatly increased the calculation precision of the ray tracing and there is no constraint to the velocity distribution from the complex areas. This method has very strong adaptability and it can meet the needs of great velocity variation from the complicated areas. Based on the numerical calculation, a fast high-order step is a fast, non-conditional and stable high-precision tomographic modeling algorithm. Two, in the tomographic inversion, due to the uneven fold coverage and insufficient information, the inversion result is unstable and less reliable. In the paper, wavelet transform is applied to the tomographic inversion which has achieved a good result. Based on the result of the inversion from the real data, wavelet tomographic inversion has increased the reliability and stability of the inversion. Three. Apply the constrained high-precision wavelet tomographic image to the static correction processing from the complex area. During tomographic imaging, by using uphole survey, refraction shooting or other weathering layer method, weathering layer can be identified before the image. Because the group interval for the shot first arrival is relatively big, there is a lack of precision for the near surface inversion. In this paper, an inversion method of the layer constraint and well constraint is put forward, which can be used to compensate the shallow velocity of the inversion for the shot first arrival and increase the precision of the tomographic inversion. Key words: Tomography ，Fast marching method，Wavelet transform, Static corrections, First break

基于随机介质理论的多尺度储层非均质性定量描述

Application of long-term exploration for oil and gas shows that the reservoir technology of prediction is one of the most valuable methods. Quantitative analysis of reservoir complexity is also a key technology of reservoir prediction. The current reservoir technologies of prediction are based on the linear assumption of various physical relationships. Therefore, these technologies cannot handle complex reservoirs with thin sands, high heterogeneities in lithological composition and strong varieties in petrophysical properties. Based on the above-mentioned complex reservoir, this paper conducts a series of researches. Both the comprehending and the quantitative analysis of reservoir heterogeneities have been implemented using statistical and non-linear theories of geophysics. At the beginning, the research of random media theories about reservoir heterogeneities was researched in this thesis. One-dimensional (1-D) and two-dimensional (2-D) random medium models were constructed. The autocorrelation lengths of random medium described the mean scale of heterogeneous anomaly in horizontal and deep directions, respectively. The characteristic of random medium models were analyzed. We also studied the corresponding relationship between the reservoir heterogeneities and autocorrelation lengths. Because heterogeneity of reservoir has fractal nature, we described heterogeneity of reservoir by fractal theory based on analyzing of the one-dimensional (1-D) and two-dimensional (2-D) random medium models. We simulated two-dimensional (2-D) random fluctuation medium in different parameters. From the simulated results, we can know that the main features of the two-dimensional (2-D) random medium mode. With autocorrelation lengths becoming larger, scales of heterogeneous geologic bodies in models became bigger. In addition, with the autocorrelation lengths becoming very larger, the layer characteristic of the models is very obvious. It would be difficult to identify sandstone such as gritstone, clay, dense sandstone and gas sandstone and so on in the reservoir with traditional impedance inversion. According to the obvious difference between different lithologic and petrophysical impedance, we studied multi-scale reservoir heterogeneities and developed new technologies. The distribution features of reservoir lithological and petrophysical heterogeneities along vertical and transverse directions were described quantitatively using multi-scale power spectrum and heterogeneity spectrum methods in this paper. Power spectrum (P spectrum) describes the manner of the vertical distribution of reservoir lithologic and petrophysical parameters and the large-scale and small-scale heterogeneities along vertical direction. Heterogeneity spectrum (H spectrum) describes the structure of the reservoir lithologic and petrophysical parameters mainly, that is to say, proportional composition of each lithological and petrophysical heterogeneities are calculated in this formation. The method is more reasonable to describe the degree of transverse multi-scale heterogeneities in reservoir lithological and petrophysical parameters. Using information of sonic logs in Sulige oil field, two spectral methods have been applied to the oil field, and good analytic results have been obtained. In order to contrast the former researches, the last part is the multi-scale character analysis of reservoir based on the transmission character of wave using the wavelet transform. We discussed the method applied to demarcate sequence stratigraphy and also analyzed the reservoir interlayer heterogeneity.

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

Burst event detection in wall turbulence by WVITA method

Wavelet Variable Interval Time Average (WVITA) is introduced as a method incorporating burst event detection in wall turbulence. Wavelet transform is performed to unfold the longitudinal fluctuating velocity time series measured in the near wall region of a turbulent boundary layer using hot-film anemometer. This unfolding is both in time and in space simultaneously. The splitted kinetic of the longitudinal fluctuating velocity time series among different scales is obtained by integrating the square of wavelet coefficient modulus over temporal space. The time scale that related to burst events in wall turbulence passing through the fixed probe is ascertained by maximum criterion of the kinetic energy evolution across scales. Wavelet transformed localized variance of the fluctuating velocity time series at the maximum kinetic scale is put forward instead of localized short time average variance in Variable Interval Time Average (VITA) scheme. The burst event detection result shows that WVITA scheme can avoid erroneous judgement and solve the grouping problem more effectively which is caused by VITA scheme itself and can not be avoided by adjusting the threshold level or changing the short time average interval.

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

小波变换方法评价曲线的分形特征

应用小波变换对Kiesswetter工线和3种方法生成的分数维布朗运动（FBm）进行了分析，验证了该方法计算分形维数具有较高的精度。在宽广的分形维数范围内，与其他7种计算方法比较表明，小波变换方法的精确性和一致性都最好。小波变换为进一步分辨确定性信号、分形特征的信号或完全随机性的信号提供了一种有效工具，为评价精糙表面形貌的分形特征提供了前提条件。

小波多尺度跟踪技术研究

本论文研究的主要内容为基于小波多尺度特性的序列图像目标跟踪技术。目标跟踪作为一个在军事、工业和科学研究方面有着广泛应用背景的研究领域，一直以来吸引了大批国内外学者。由于小波变换具有多分辨率分析的特点，而且在时频两域都具有表征信号局部特征的能力，使得基于小波变换的目标跟踪算法具有传统算法无法比拟的优势。针对目标跟踪技术的研究现状和存在问题，本文着重从目标分割和特征检测与匹配两个角度对基于小波变换的几种新的目标跟踪方法进行了研究。 1. 采用基于多尺度Gabor小波的特征点检测算法对序列图像进行跟踪。借助图像的金字塔变换得到多尺度的Gabor小波特征图像，并对特征图像进行特征点检测，提取对图像变换具有鲁棒性的特征。针对两种特征检测方案，提出不同的特征匹配准则，按照分层匹配的策略由粗到精逐步定位目标的准确位置，具有较快的搜索速度。 2. 采用多尺度小波函数所提取的相位一致性特征进行基于目标分割和基于角点特征的跟踪。 对目标图像进行相位一致性检测，得到一个具有光照不变性的无量纲特征量—相位一致系数。利用相位一致性检测的这种特性，针对孤立目标的情况，提出了两种自适应目标分割和跟踪的算法。基于区域增长的目标分割算法利用从相位一致图像中找到的对比度最大点及其法线方向两边的灰度分布确定目标和背景的种子像素，进行自适应目标分割。基于相位一致性检测的目标分割算法只需确定一个阈值即可利用相位一致特征图像的方向性，依据目标在不同方向响应的不同将目标和背景区分开，适应于复杂纹理背景中的目标分割。最后，分别将两种算法所得的分割结果向水平和垂直方向投影即可确定各自的质心位置，实现自适应的质心跟踪。 进一步提取相位一致性图像的最小矩特征就能得到目标的角点信息。文中用实验验证了此方法检测到角点的综合性能。在此基础上，提出了利用单演相位差进行角点匹配跟踪的算法，并将其同基于灰度相关的匹配算法进行了对比，证明了本算法能够检测出更多准确匹配的角点、减少误匹配，同时具有较小的匹配运算量。 对以上提出的几种目标跟踪算法进行了大量的仿真实验，实验结果表明，这几种方法均取得了较好的跟踪效果，能够实现稳定、精确的跟踪。

小波变换在海面目标自动检测中的应用

本论文以下列课题为背景：（1）“新一代光电指挥仪关键技术研究”—中科院知识创新工程预研课题；（2）“自寻的反舰导弹电视导引头”—型号任务，针对武器系统研制在图象跟踪与制导信息处理方面的关键技术，研究了海空复杂背景下舰船目标的自动检测与定位技术。本文提出了一种基于小波变换的舰船目标自动检测方法。该方法在分析海空场景图象特征的基础上，利用小波多分辨率分析和小波变换良好的局部分析特性，研究了图象预处理和目标定位的WT方法，将小波分析的思想贯穿于自动目标检测的全过程。提出了一种海空复杂背景图象预处理方法—基于小波多尺度分析的水天线检测方法。采用多分辨率组合带通滤波，对海空场景图象进行多级小波分解，利用小波分解垂直方向上的高频分量，综合多个尺度下的模极大值信息，由粗到精定位水天线。通过构造能量函数，提出了一种目标自动检测和定位方法。在检测到水天线位置的基础上，进一步检测目标：对小波分解水平方向上的高频分量，进行互能量交叉，既突出了目标，又有效地抑制了背景噪声；依据水天线定位参数，结合加权处理与门限处理，进行海杂波抑制；构造边缘能量函数，通过能量判决完成了目标检测；利用双窗口的不相似性度量函数完成了目标的准确定位。大量的仿真实验表明，本文提出的海面目标自动检测的WT方法，能够较好地实现在单帧图象中检测出舰船目标，亮暗目标兼容，而且在如下几类复杂条件下，检测算法依然取得了较好的检测效果：水天线倾斜；有较强的海杂波干扰；存在一定的鱼鳞光干扰；天空背景干扰；海面能见度较低图象模糊；小目标情况等。