B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.

THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.

Edge detection of molten pool and weld line for CO_2 welding based on B-spline wavelet

Due to the disturbances of spatters, dusts and strong arc light, it is difficult to detect the molten pool edge and the weld line location in CO_2 welding processes. The median filtering and self-multiplication was employed to preprocess the image of the CO_2 welding in order to detect effectively the edge of molten pool and the location of weld line. The B-spline wavelet algorithm has been investigated, the influence of different scales and thresholds on the results of the edge detection have been compared and analyzed. The experimental results show that better performance to extract the edge of the molten pool and the location of weld line can be obtained by using the B-spline wavelet transform. The proposed edge detection approach can be further applied to the control of molten depth and the seam tracking.

Two Dimensional Tensor Product B-Spline Wavelet Scaling Functions for the Solution of Two-Dimensional Unsteady Diffusion Equations

The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions,4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.

A Study on B-Spline Wavelets and Wavelet Packets

In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.

Analysis of a Gyroscope′s Rotor Nonlinear Supported Magnetic Field Based on the B-Spline Wavelet-FEM

A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.

具有空间-通道重构卷积模块的肺音分类模型

目的探究肺音数据的准确识别及分类。方法本文提出了一种结合空间-通道重构卷积(SCConv)模块的卷积网络架构以及双可调Q因子小波变换(DTQWT)与三重Wigner-Ville变换(WVT)结合的肺音特征提取方法,通过自适应地聚焦于重要的通道和空间特征,提高模型对肺音关键特征的捕捉能力。基于ICBHI2017数据集,进行正常音、哮鸣音、爆裂音、哮鸣音和爆裂音结合的分类。结果方法在分类的准确率、敏感性、特异性以及F1分数上分别达到85.68%、93.55%、86.79%、90.51%。结论所提方法在ICBHI 2017肺音数据库上取得了优异的性能,特别是在区分正常肺音和异常肺音方面。

Wavelet-Based Fractal Function Approximation

In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.

4TH-ORDER SPLINE WAVELETS ON A BOUNDED INTERVAL

The 4th-order spline wavelets an a bounded interval are constructed by the 4th-order truncated B-spline functions. These wavelets consist of inner and boundary wavelets. They are bases of wavelet space with finite dimensions. Arty function on an interval will be expanded as the sum of finite items of the scaling functions and wavelets. It plays an important role for numerical analysis of partial differential equations, signal processes, and other similar problems.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Wavelet Collocation Method for Solving Elliptic Singularly Perturbed Problem

Wavelet collocation method is used to solve an elliptic singularly perturbed problem with two parameters. The B-spline function is used as a single mother wavelet, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problem and the result shows the reliability and efficiency of the method.

Multiresolution for Closed Curves and Surfaces Using Wavelets

Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline curves and surfaces are concentrated on open ones. In this paper, we focus on the multiresolution representations and editing of closed B-spline curves and surfaces using wavelets. A repetition approach is adopted for the multiresolution analysis of closed B-spline curves and surfaces. Since the closed curve or surface itself is periodic, it can overcome the drawback brought by the repetition method, i.e. introducing the discontinuities at the boundaries. Based on the models at different multiresolution levels, the multiresolution editing methods of closed curves and surfaces are introduced. Users can edit the overall shape of a closed one while preserving its details, or change its details without affecting its overall shape.

小波分析和RBF神经网络在地基沉降预测中的应用研究

地基沉降是一种危害很大的环境灾害。地基沉降的监测数据经常受降雨及工程施工等诸多外界因素的干扰,故而在沉降曲线中存在许多数据突变点。为此,提出基于小波分析与RBF神经网络相结合的新的地基沉降预测方法,首先采用小波分析对对原始监测数据进行数据去噪处理,进而得到反映实际变化的地基沉降曲线,然后采用径向基函数(RBF)神经网络方法对其进行预测,为工程设计提供依据。最后结合工程实例分析,通过多种小波去噪与预测结果的对比研究,表明3次B样条小波的去噪及预测效果最好,与实测值能较好地吻合,具有较好的工程应用前景。

Hamilton体系下压电材料层合板特征值灵敏度分析

在Hamilton体系下,基于区间B(B-spline wavelet on the interval)-样条小波有限元法研究压电材料特征值的灵敏度分析问题,推导压电材料特征值响应灵敏度系数的控制方程。利用二分法求得压电材料层合板前4阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明所提方法的可靠性。结果表明,在Hamilton体系下求解特征值的灵敏度系数是可行的。

小波包消噪在Compass电离层三频二阶改正中的应用

针对Compass电离层二阶改正存在的问题,提出利用小波包分析算法对观测值进行消噪,再进行三频二阶改正的方法。利用Compass仿真数据的试验表明,小波消噪算法能够大大削弱观测噪声,有利于提高Compass三频二阶改正的精度,增强其可行性和有效性。

声表面波式小波变换器件的三次行程反射信号的研究

本文提出了用同相位法减小三次行程反射信号的方法.当信号频率与叉指换能器中心频率相等,并且主信号的相位等于三次行程反射信号的相位时,从可达到减小三次行程反射信号的影响.并且探讨了双接收叉指换能器并联法,要求双接收叉指换能器要完全对称,否则声表面波式小波变换器件频率特性曲线不光滑.

离散小波变换快速探测卫星机动算法

针对卫星机动直接影响导航系统的导航、定位和授时服务性能,当导航卫星发生机动时,需要对机动卫星单独处理以生成高精度轨道信息。载波相位三差法可用于卫星机动探测,但受差分测量噪声影响,通过多历元累积方式可减小噪声的影响,但其机动探测结果可能受基线选取的影响。基于此提出了一种离散小波变换的卫星机动快速探测及周期确定方法,在载波相位三差模型基础上,提取载波相位三差残差量,挖掘卫星机动开始及结束时刻载波相位三差残差的先验信息,基于多分辨分析的尺度特性对载波相位三差残差进行分解,分解层数由细节系数和近似系数探测结果确定,通过分析不同频率特性的近似系数和细节系数,获取载波相位三差残差隐含的卫星机动信息,实现对卫星机动的快速探测及周期确定。实验结果表明,相比于传统载波相位三差探测方法,离散小波变换法采用单历元处理方式可更快探测卫星机动,且不同基线探测到的机动结果一致,能更准确地探测卫星机动并确定其周期。

低信噪比下的一种信号检测方法

针对低信噪比情况下的信号检测问题 ,利用 Morlet小波变换在时间、频率局部化信号的能力 ,提出了一种信号检测方法。运用该方法对雷达信号进行小波变换和三重自相关处理 ,由相关函数的峰值对目标信号进行检测。仿真结果表明 ,该方法能够有效地抑制噪声 。

基于Harr小波的动态场景全频阴影绘制算法

针对现有的预计算辐射传递算法对三维场景限制严格、适合于低频光照环境等问题,提出了一种动态场景的全频阴影绘制算法.在预处理阶段使用球体对三维物体进行拟合,同时对光照函数和BRDF(bidirectional reflectance distribution function)函数进行Harr小波变换;在运行时阶段利用不同基函数的优势,在像素基空间进行多个球体可见性函数的快速合并,在小波基空间进行光照函数、BRDF函数和可见性函数的三乘积分,得到最终的光照值.使用CUDA(computed unified device architecture)实现了该算法,充分利用了图形硬件的最新功能.实验结果表明,阴影绘制质量有很大的提高,可以基本达到实时绘制.

基于多不变量特征的遥感影像小地物识别

重点研究应用多门限检验方法识别中、高分辨率遥感图像上的小型地物。该方法首先通过基于知识特征的小波多分辨理论分割图像,得到目标所在区域。然后通过使用标准像素大小(30×30)的窗口提取图像中目标的7个不变矩特征,以此作为BP神经网络的输入向量。在得到目标的初步识别结果后,再利用“零片”三阶相关量特征[2]这一门限值对识别结果进行精确检验。实验结果表明,该方法对识别中、高分辨率遥感影像上的小型地物是一种有效的方法。