基于时间响应函数的结构阻尼识别方法比较

研究了3种基于时间响应函数的结构阻尼识别方法, 包括对数衰减法、希尔 伯特方法和小波方法. 给出了3种方法的实现算法, 分析了对密集模态的识别能力. 构造仿真算例, 采用3种方法识别了5{\%}, 10{\%}和30{\%}噪声条件下的模态阻尼. 结果表明, 小波方法比对数衰减法和希尔伯特方法具有更好的噪声鲁棒性. 采用小波方法分析了润扬大桥结构健康监测系统获得的实测数据, 识别出了润扬大桥悬索桥前6阶模态参数, 第2阶和第3阶模态频率相差仅为0.015\,Hz. 研究表明, 小波方法具备噪声条件下密集模态的识别能力, 是工程中阻尼识别的优选方法.     

小波级数的Bouligand维数(英)

本文讨论小波级数的上、下Buoligangd维数，在小波级数满足一定的条件下，给出了与Weierstrass函数相应的结果．     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR DUALS OF WAVELET FRAMES

（张泽银）（王建忠）ＯＮＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＦＯＲＤＵＡＬＳＯＦＷＡＶＥＬＥＴＦＲＡＭＥＳ￥ＺｈａｎｇＺｅｙｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｕｂａｉＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００６２，Ｃｈｉｎａ...     

小波系数压缩用于柴油十六烷值近红外光谱分析建模

近红外光谱分析建模中存在多变量高维数据处理问题,导致计算量大,不利于过程控制中应用.为此提出利用小波变换压缩近红外光谱数据的算法与准则,并结合柴油十六烷值定量分析研究压缩数据的建模效果.研究表明,经小波方法处理后,变量维数压缩30倍左右,光谱主要信息基本保留,而模型的预测精度和常规预处理方法分析相比有明显提高.光谱数据压缩的同时包含了噪声滤除和基线校正,简化数据处理步骤,有利于NIRS实际应用时提高建模效率.     

Multiphase Thermohaline Convection in the Earth’s Crust: I. A New Finite Element – Finite Volume Solution Technique Combined With a New Equation of State for NaCl–H2O

We present a new finite element – finite volume (FEFV) method combined with a realistic equation of state for NaCl–H₂O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity vapor phase well above the critical point of pure H₂O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation, this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl–H₂O is valid from 0 to 750°C, 0 to 4000 bar, and 0–100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is common.     

Signal enhancement of a novel multi-address coding lidar backscatters based on a combined technique of demodulation and wavelet de-noising

Multi-address coding (MAC) lidar is a novel lidar system recently developed by our laboratory. By applying a new combined technique of multi-address encoding, multiplexing and decoding, range resolution is effectively improved. In data processing, a signal enhancement method involving laser signal demodulation and wavelet de-noising in the downlink is proposed to improve the signal to noise ratio (SNR) of raw signal and the capability of remote application. In this paper, the working mechanism of MAC lidar is introduced and the implementation of encoding and decoding is also illustrated. We focus on the signal enhancement method and provide the mathematical model and analysis of an algorithm on the basis of the combined method of demodulation and wavelet de-noising. The experimental results and analysis demonstrate that the signal enhancement approach improves the SNR of raw data. Overall, compared with conventional lidar system, MAC lidar achieves a higher resolution and better de-noising performance in long-range detection.     

Solving diffusion equation using wavelet method

A wavelet-based numerical method based on wavelets of Hermite cubic splines is presented for computing singularly perturbed convection-dominated diffusion equation. The advantages of the method are explained. To improve the accuracy of singular areas, wavelets are configured hierarchically for solving algebraic equations. Numerical examples show that the proposed method has good efficiency and precision.     

A note on one-point quadrature formula for Daubechies scale function with partial support

This note is concerned with an efficient computation of integrals of products of a smooth function and Daubechies scale function with partial support by using a one-point quadrature rule. The error estimate is obtained. The rule is illustrated by considering an example from the literature.     

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.