Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Wavelet method is a recently developed tool in applied mathematics. Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools at various places to provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction–diffusion equations. This review intends to provide the great utility of wavelets to science and engineering problems which owes its origin to 1919. Also, future scope and directions involved in developing wavelet algorithm for solving reaction–diffusion equations are addressed.     

Approximation of Gaussian Random Fields: General Results and Optimal Wavelet Representation of the Lévy Fractional Motion

We investigate the approximation rate for certain centered Gaussian fields by a general approach. Upper estimates are proved in the context of so–called Hölder operators and lower estimates follow from the eigenvalue behavior of some related self–adjoint integral operator in a suitable L ₂(μ)–space. In particular, we determine the approximation rate for the Lévy fractional Brownian motion X _H with Hurst parameter H∈(0,1), indexed by a self–similar set T?? ^N of Hausdorff dimension D. This rate turns out to be of order n ^?H/D (log?n)^1/2. In the case T=[0,1] ^N we present a concrete wavelet representation of X _H leading to an approximation of X _H with the optimal rate n ^?H/N (log?n)^1/2.     

基于小波的一维线性波动方程的数值解法

小波的紧支性，正交性和二阶以上的Daubechies尺度函数及小波函数的可微性，很适合作为Galerkin方法的基函数。加上快速小波变换，这已成为数值求解偏微分方程的有力工具，本文利用微分算子的小波表示。对一维线性波动方程的小波数值解法进行了讨论。最后用实例说明了波波方法的有效性和快速性。     

基于小波变换的激光光刀图像去噪技术

介绍了激光线扫描测量系统的测量原理,以及图像去噪处理在系统中的必要性;以现代数学小波分析为依据,提出了基于小波变换的激光光刀图像去噪技术.通过实验与分析,说明使用小波变换进行光刀图像去噪处理提高了激光扫描测量系统的测量精度.     

基于小波分析的马铃薯地上生物量估算

地上生物量(AGB)是作物长势评价及产量预测的重要指标,因此快速准确地估算AGB至关重要.由于传统植被指数(VIs)估算多生育期的AGB存在饱和现象,因此,利用VIs结合基于离散小波转换(DWT)的影像小波分解(IWD)技术提取的高频信息和连续小波转换(CWT)技术提取的小波系数,探究VIs,VIs+IWD和VIs+C...     

一种新的活动星系光谱红移自动测量方法

星系红移的自动测量对进行大样本天文学研究如宇宙学大尺度结构研究具有重要意义。星系一般分为正常星系和活动星系两种,活动星系光谱一般具有较明显的发射线特征。文章提出了一种不用精确提取谱线而快速测量活动星系光谱红移的方法。该方法包括步骤：(1)对待测光谱进行去噪;(2)利用小波变换提取低频成分光谱,并用去噪后光谱减去低频谱得到残差谱;(3)计算残差谱的均方差,并保留大于阈值的波长集合(4)根据标准谱线表计算所有候选红移;(5)利用Parzen窗估计方法计算红移密度最大点,并在邻域内求均值确定最终红移。对模拟数据和SDSS DR7部分实测数据的测试表明,该方法是鲁棒的并且具有较高的红移测量正确率。     

Detection of rolling bearing defects using discrete wavelet analysis

In the detection of bearing faults the so much desired objective remains the extraction of the defect vibratory signature from the measured signal in which immerses the random noise and other components of the machine. In this article a denoising method of the measured signals is presented. Based on the optimization of wavelet multiresolution analysis, it uses the kurtosis as an optimization and evaluation criterion, several parameters were then selected. The experimental results show the validity of this method within the detection of several defects simulated on ball bearings. The various configurations, in which the signals were measured, allow leading to optimum conditions of its application. The application of WMRA on filtered signals allows better results than its application on wide bands signals or a simple band pass filtering.     

Reconstruction of signals from multiscale edges

We present a method for signal reconstruction based upon the location of its singularities which are identified by a wavelet transform technique. The reconstructed signal is an infconvolution spline approximant. The data for the interpolation problem which we solve comes from a compact signal coding procedure. Error bounds and convergence results for the calculated signal are given.     

多菌灵农药的激光拉曼光谱分析

实验采集多菌灵农药的固体和液体拉曼光谱信号,对固体的原始拉曼光谱信号进行小波去噪预处理,利用正交试验方法筛选小波去噪参数的最优组合。结果表明,采用db2小波基函数、分解层数为2、阈值方案选择为rigrsure、重调方式为sln时,去噪效果最好,信噪比为62.483。根据不同官能团的振动模式,对去噪后的拉曼光谱分3个波数段(1 400～2 000,700～1 400,200～700 cm-1)进行谱峰归属和分析,得到了多菌灵农药分子在不同波数范围内的特征振动模式,其中,在619,725,964,1 022,1 265,1 274和1 478 cm-1处的拉曼信号较强,可作为固体多菌灵农药的特征峰。从多菌灵农药的液体拉曼光谱中,找到了629,727,1 001,1 219,1 258和1 365 cm-1特征峰,这些特征峰跟固体多菌灵农药的特征峰基本吻合。研究结果可为拉曼光谱分析技术在食品及农产品中农药残留的快速筛选提供判别依据。     

A wavelet-based methodology for monitoring thermoelastic structures

A wavelet-based methodology for detecting critical events in displacement and temperature histories, obtained by monitoring in-situ thermoelastic structures, is proposed. It is based on the wavelet analysis of thermoelastic potentials furnishing also the possibility to detect separately cases in which sudden jumps occur in the displacement history from those in which they occur on temperature history.