基于Cayley变换的紧支撑二元正交小波滤波器组的构造

构造正交滤波器组,在多相域里就等价于构造仿酉矩阵,而仿酉矩阵的构造涉及到非线性方程组的求解.通过对Cayley变换的研究,把仿酉矩阵的构造转换为更易构造的仿斜厄米特矩阵,基于这种变换构造了二元紧支撑正交小波滤波器组,并给出了算例.     

Acoustic detection and classification of river boats

We present a robust algorithm to detect the arrival of a boat of a certain type when other background noises are present. It is done via the analysis of its acoustic signature against an existing database of recorded and processed acoustic signals. We characterize the signals by the distribution of their energies among blocks of wavelet packet coefficients. To derive the acoustic signature of the boat of interest, we use the Best Discriminant Basis method. The decision is made by combining the answers from the Linear Discriminant Analysis (LDA) classifier and from the Classification and Regression Trees (CART) that is also accompanied with an additional unit, called Aisles, that reduces false alarms rate. The proposed algorithm is a generic solution for process control that is based on a learning phase (training) followed by an automatic real time detection while minimizing the false alarms rate.     

3D particle positioning by using the Fraunhofer criterion

In particle tracking velocimetry, the necessary information is the 3D location of a given particle in space. This information can be obtained by examining the real image or by analyzing the interference fringe recorded on a digital camera. In this work, we measure the three-dimensional position of spherical particles by calculating the Central Spot Size of the interference pattern of a particle diffraction image. The Central Spot Size is obtained by combining the Continuous Wavelet transform and circle Hough transform. The Continuous Wavelet transform allow us in only one step enhanced quality of particle images and sets a threshold to select properly places where a Central Spot Size appear in order to determine its size via the Hough transform. The size and centroid of the Central Spot Size render z and x-y position of a particle image, respectively. The Central Spot Size is related to a criterion of a simplified theory given by the Fraunhofer theory in order to obtain z particle position. Our approach has been applied to simulated and experimental particle images. Simulated particle images show good agreement between actual and calculated Central Spot Size. An average relative error of 0.5% and 1.12% for x-y and z directions, respectively, was found in the analysis. Our experimental particle images were obtained from particle motion inside a channel. The quality of the particle images determines the accuracy of the calculation of the Central Spot Size of a particle image.     

Nonlinear approximation with general wave packets

We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.     

Modified wavelet based morphological correlation for rotation-invariant recognition

A wavelet-based rotation invariant morphological correlation (WBRIMC) is proposed as a new architecture to improve the properties of the classical rotation invariant morphological correlation (RIMC). For the WBRIMC, the JPS of the RIMC is filtered by an appropriately dilated power spectrum function of wavelet. Simulation results confirm that the WBRIMC has higher discrimination capability with sharp and intense correlation signals, and is more tolerant to the salt-and-pepper noise and white additive Gaussian noise than is the Circular harmonic filter (CHF), the phase only CHF (POCHF) and the RIMC.     

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。     

Identification of time-varying hysteretic structures using wavelet multiresolution analysis

In this paper, a wavelet multiresolution technique is proposed to identify time-varying properties of hysteretic structures. It is well known that arbitrary transient functions can be effectively and accurately approximated using wavelet multiresolution expansions due to wavelet's good time-frequency localization property. By decomposing the time-varying parameters with wavelet multiresolution expansion, a time-varying parametric identification problem can be transformed into a time-invariant non-parametric one. The identification in the time-invariant wavelet multiresolution domain can be achieved by choosing a wavelet basis function and performing a suitable parameter estimation technique. Since wavelet representation of arbitrary signal uses only a small number of terms, the orthogonal forward regression algorithm can be adopted for significant term selection and parameter estimation. Single and multiple degrees of freedom Bouc-Wen hysteretic structures with gradual and abrupt varying properties are used to illustrate the proposed approach. Results show that the wavelet multiresolution technique can identify and track the time-varying hysteretic parameters quite accurately. The effect of measurement noise is also studied. It is found that the presence of noise would affect more on the damping ratios and the Bouc-Wen parameters but less on the equivalent stiffness coefficients.     

Large deflection and post-buckling analysis of non-linearly elastic rods by wavelet method

We propose a wavelet method in the present study to analyze the large deflection bending and post-buckling problems of rods composed of non-linearly elastic materials, which are governed by a class of strong non-linear differential equations. This wavelet method is established based on a modified wavelet approximation of an interval bounded L²-function, which provides a new method for the large deflection bending and post-buckling problems of engineering structures. As an example, in this study, we considered the rod structures of non-linear materials that obey the Ludwick and the modified Ludwick constitutive laws. The numerical results for both large deflection bending and post-buckling problems are presented, illustrating the convergence and accuracy of the wavelet method. For the former, the wavelet solutions are more accurate than the finite element method and the shooting method embedded with the Euler method. For the latter, both bifurcation and limit loads can be easily and directly obtained by solving the extended systems. On the other hand, for the shooting method embedded with Runge–Kutta method, to obtain these values usually needs to choose a good starting value and repeat trial solutions many times, which can be a tough task.     

小波变换基线扣除对激光诱导等离子体温度计算的改善

温度是激光诱导等离子体特性研究最重要的参数之一,为降低光谱连续背景对Boltzmann平面法计算等离子体温度的精密度的影响,利用小波变换对等离子体光谱进行分解,并采用软阈值法对代表光谱基线的低频信号进行扣除。选择合适的小波分解层数L及阈值系数α能有效提高Boltzmann图的线性相关度,即有更高的拟合系数R2,从而提高等离子体温度的计算精密度。对低合金钢样品417～445 nm波段LIBS光谱采用db4小波函数进行分解、基线扣除和信号重构,选用12条Fe原子谱线建立Boltzmann图,由Boltzmann图拟合直线的斜率计算得到等离子体温度。对L和α系数进行了优化选择,研究发现,采用8层小波分解时Boltzmann图具有较高的R2,而α的选择与时延t_d有关,t_d≤4.0 μs时,α=0.3可获得最佳R2值,之后随t_d的增大,α逐渐减小; 在t_d≥6.5 μs后,α=0,即光谱低频信号被完全扣除,说明基线对光谱特征谱线的干扰随时延的增加逐渐减弱。基线扣除后各时延的等离子体温度降低约2 000～3 000 K,温度随时延的增加逐渐降低,与等离子体膨胀过程中温度逐渐下降的物理过程相吻合,且变化过程中的波动变小。