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.

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.

ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.

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.

FWNN for Interval Estimation with Interval Learning Algorithm

In this paper, a wavelet based fuzzy neural network for interval estimation of processed data with its interval learning algorithm is proposed. It is also proved to be an efficient approach to calculate the wavelet coefficient.

基于WPD-ARIMA-GARCH组合模型的酱卤肉制品安全风险区间预测

针对传统确定性预测不能提供不确定性信息的难题,本研究提出了一种点估计和区间估计组合预测模型,并将其创新性地应用在食品安全风险预警领域。在点估计部分,使用小波包分解(wavelet packet decomposition,WPD)对周风险等级序列分解后,应用差分自回归移动平均(autoregressive integrated moving average,ARIMA)模型进行预测;在区间估计部分,使用广义自回归条件异方差(generalized autoregressive conditional heteroskedast,GARCH)模型对残差进行预测。本实验将建立的WPD-ARIMA-GARCH组合模型运用于某地区酱卤肉制品的风险预测,结果表明2019年的3月底和7月底该地区的酱卤肉制品安全风险较高,与实际情况相符;同时,该模型在10个不同地区的酱卤肉制品风险预测中,均方误差、平均绝对误差和平均绝对百分比误差分别为1.626、0.806和20.824;其90%置信区间的预测区间平均宽度和覆盖宽度标准值均为0.024,可以覆盖所有真实值。该模型具有较高的预测精度和较低的误差,能对酱卤肉制品质量安全起到风险防控作用,可为日常食品安全监管提供相应的技术支持。

基于连续小波变换和高阶统计量的心律失常识别算法

针对可变持续时间心电图(ECG)数据信号的非平稳性和时序性问题,提出一种基于连续小波变换(CWT)和高阶统计量(HOS)的心律失常识别算法。首先,针对可变持续时间ECG数据中每个样本的数据点数量不同,采用RR间期插值法预处理数据,并通过CWT将信号分解为不同的时频分量,从而使网络能够更好地提取心电信号中的时间和频率特征。其次,针对时序信息利用不充分的问题,提出基于HOS和长短期记忆网络的时序挖掘模块,以捕捉和学习ECG信号中的长期依赖关系,从而有助于识别和理解特定的心律失常类别。通过在公开的ECG数据集MIT-BIN上进行的大量实验,验证所提方法的有效性和优越性。

基于Mask R-CNN的电力关键设备载波运行状态检测

为解决因载波信号大幅波动造成的电力设备运行状态检测失准问题,提出基于Mask R-CNN的电力关键设备载波运行状态检测方法。在Mask R-CNN网络模型中,通过定义小波基向量的方法确定电力载波暂态系数的计算结果。联合电量阻抗特征,求解连续阈值区间表达式,将获取到的电力载波信号放置在已定义阈值区间内。计算奇异值检测系数的取值条件,完成电力关键设备载波运行状态检测。对比实验结果表明,所提方法可以将电力载波信号波动幅值控制在±17 dB之间,对载波信号波动行为起到了明显的抑制作用,能够提升电网主机对电力设备运行状态检测的准确性。

Wavelet Numerical Solutions for Weakly Singular Fredholm Integral Equations of the Second Kind

Daubechies interval cally weakly singular Fredholm kind. Utilizing the orthogonality equation is reduced into a linear wavelet is used to solve nurneriintegral equations of the second of the wavelet basis, the integral system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse, while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally, numerical example is presented to show the application of the wavelet method.

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.

Minimum-energy wavelet frame on the interval

The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows： 1） give the definition of interval minimum-energy wavelet frame; 2） give the necessary and sufficient conditions for the minimum-energy frames for L^2[0,1]; 3） present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support y; 4） give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1],

Interval interpolating wavelets with robust boundary filters

This paper studies the mathematical mechanism of the generalized interpolating filters and gives the corresponding parametric representations. On the basis of the parametric representations, a novel criterion and algorithm are proposed to design interval interpolating wavelets with robust boundary filters. Furthermore, some examples are designed and their performances in data compression are investigated. Both the theoretical analysis and the experimental results show that such an interval interpolating wavelet can effectively suppress the boundary effect.

Impact of spectral interval on wavelet features for detecting wheat yellow rust with hyperspectral data

Detection of yellow rust using hyperspectral data is of practical importance for disease control and prevention.As an emerging spectral analysis method,continuous wavelet analysis(CWA)has shown great potential for the detection of plant diseases and insects.Given the spectral interval of airborne or spaceborne hyperspectral sensor data differ greatly,it is important to understand the impact of spectral interval on the performance of CWA in detecting yellow rust in winter wheat.A field experiment was conducted which obtained spectral measurements of both healthy and disease-infected plants.The impacts of the mother wavelet type and spectral interval on disease detection were analyzed.The results showed that spectral features derived from all four mother wavelet types exhibited sufficient sensitivity to the occurrence of yellow rust.The Mexh wavelet slightly outperformed the others in estimating disease severity.Although the detecting accuracy generally declined with decreasing of spectral interval,relatively high accuracy levels were maintained(R^(2)>0.7)until a spectral interval of 16 nm.Therefore,it is recommended that the spectral interval of hyperspectral data should be no larger than 16 nm for the detection of yellow rust.The relatively loose spectral interval requirement permits extensive applications for disease detection with hyperspectral imagery.

一种新型日前光伏功率概率区间预测方法研究

面对大量光伏出力并网,其带来的波动性和不确定性给智能微电网的控制和设计带来了很大的挑战。因此,文章提出一种基于WD-BiLSTM-NPKDE的日前光伏功率概率区间预测方法。首先,利用小波分解方法进行数据信号分解,进一步消除随机性、波动性对预测精度的影响;其次,将分解后的分量输入到BiLSTM模型进行训练;再次,采用非参数核密度估计求解概率预测结果;最后,得到给定置信水平下的光伏功率预测区间。算例结果表明,该方法能有效得到光伏功率区间。

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。

传感器网络中基于数据压缩的汇聚算法

结合传感器网络的节点特性和位置信息,提出了一种基于连通支配集的传感器网络定向传播模型,以及一种基于“域”的分布式数据汇聚模型DDAM(distributeddataaggregationmodel).DDAM把传感器网络按“域”划分来构建连通核,传感节点只需在连通核中寻径,因而可明显减少寻径时间复杂度并且具有更好的分布性;然后在该定向传播与数据汇聚模型基础上,考虑传感器网络的数据特性及小波变换在流数据压缩方面的良好性能,提出了一种基于区间小波变换的混合熵数据压缩方法.理论分析和实验仿真结果表明:对比传统的DC算法-DD路由算法相结合的算法,新算法能对传感器网络中的流数据进行有效压缩,可更大程度地降低传感器节点数据传输的能耗,从而进一步延长整个网络的生命周期.

金堆城露天矿生产爆破合理微差时间的探讨

基于金堆城钼业公司现场的爆破振动试验的实测数据,利用小波分析技术,对不同微差间隔以及相同微差间隔不同爆心距的振动信号进行能量分析,获得了2种情况下爆破振动信号频带的能量分布规律,从能量的角度探索了适合金堆城露天矿生产爆破的合理微差时间,达到降低爆破振动的目的。

偏微分方程的区间小波自适应精细积分法

利用插值小波理论构造了拟Shannon区间小波,并结合外推法给出了一种求解非线性常微分方程组的时间步长自适应精细积分法,在此基础上构造了求解非线性偏微分方程的区间小波自适应精细积分法(AIWPIM)· 数值结果表明,该方法在计算精度上优于将小波和四阶Runge＿Kutta法组合得到的偏微分方程的数值求解方法,而计算量则相差不大· 该文方法通过Burgers方程给出。

基于小波变换和ICA的滚动轴承早期故障诊断

滚动轴承早期故障诊断的关键在于如何从低信噪比混合信号中检测出显著的轴承故障特征频率。提出以连续小波变换(CWT)和独立分量分析(ICA)相结合的方法来诊断单通道信号的滚动轴承早期故障,提出按频谱等间隔选取伪中心频率的小波分解尺度,并对ICA处理后的信号进行包络频谱分析以确定故障类型。最后,利用实际的滚动轴承实验数据对该方法进行了验证。

模式自适应小波构造与添加及其在爆破振动信号分析中的应用

小波分析中所用到的小波基既不是任意的也不是唯一的,同一信号使用不同的小波基进行分析时会产生不同的结果,如何解决适合爆破振动信号特征的小波基构造、添加及其实现等问题,始终是困扰广大研究者的难题。针对爆破振动信号具有持时短、突变快等特点,通过对从实测微差爆破振动信号中分离出的子信号进行模式自适应匹配,构造与实测爆破振动信号波形相似度高的小波基函数,然后将该爆破振动信号小波基添加到MATLAB小波分析工具箱中,并用于对微差起爆延时间隔的精确定位,结果表明所构造的模式自适应连续小波具有良好的应用效果,从而为爆破振动信号分析在实际工程中的应用提供了参考。