Seismic Wavelet Analysis Based on Finite Element Numerical Simulation

The practice of exploration and production has proved that explosives are excited in different surrounding rocks and the seismic wavelets collected have different characteristics. In this paper, by establishing a numerical model of the explosion in the well, using finite element analysis technology for numerical simulation, the simulation calculated the stress structure in the near-source area of the earthquake excitation, and extracted the seismic wavelet. The results show that the simulation seismic wavelet characteristics of different thin interbedded sand and mudstone structures have changed significantly. Through excitation simulation, the amplitude and spectrum information of seismic wavelets can be compared and analyzed, and the excitation parameters can be optimized. .

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.

Application of Wavelet Finite Element Method to Simulation of the Temperature Field of Copier Paper

Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method, which provides a new method for improving the copier properties.

THE FINITE ELEMENT METHOD BASED ON INTERPOLATING WITH WAVELET BASIS FUNCTION

The compactly supported wavelet basis functions are introduced into the construction of interpolating function of traditional finite element method when analyzing the problems with high gradient, and the traditional interpolating method is modified. The numerical stability of the new interpolating pattern is discussed and the convergence of the new method is also discussed by patch test analysis. The additional freedom of the new interpolating pattern is eliminated by static condensation method. Finally, the wavelet finite element formulations based on variational principles are put forward.

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.

Second-generation wavelet finite element based on the lifting scheme for GPR simulation

Ground-penetrating radar(GPR)is a highly efficient,fast and non-destructive exploration method for shallow surfaces.High-precision numerical simulation method is employed to improve the interpretation precision of detection.Second-generation wavelet finite element is introduced into the forward modeling of the GPR.As the finite element basis function,the second-generation wavelet scaling function constructed by the scheme is characterized as having multiple scales and resolutions.The function can change the analytical scale arbitrarily according to actual needs.We can adopt a small analysis scale at a large gradient to improve the precision of analysis while adopting a large analytical scale at a small gradient to improve the efficiency of analysis.This approach is beneficial to capture the local mutation characteristics of the solution and improve the resolution without changing mesh subdivision to realize the efficient solution of the forward GPR problem.The algorithm is applied to the numerical simulation of line current radiation source and tunnel non-dense lining model with analytical solutions.Result show that the solution results of the secondgeneration wavelet finite element are in agreement with the analytical solutions and the conventional finite element solutions,thereby verifying the accuracy of the second-generation wavelet finite element algorithm.Furthermore,the second-generation wavelet finite element algorithm can change the analysis scale arbitrarily according to the actual problem without subdividing grids again.The adaptive algorithm is superior to traditional scheme in grid refinement and basis function order increase,which makes this algorithm suitable for solving complex GPR forward-modeling problems with large gradient and singularity.

Finite Elements Based on Deslauriers-Dubuc Wavelets for Wave Propagation Problems

This paper presents the formulation of finite elements based on Deslauriers-Dubuc interpolating scaling functions, also known as Interpolets, for their use in wave propagation modeling. Unlike other wavelet families like Daubechies, Interpolets possess rational filter coefficients, are smooth, symmetric and therefore more suitable for use in numerical methods. Expressions for stiffness and mass matrices are developed based on connection coefficients, which are inner products of basis functions and their derivatives. An example in 1-D was formulated using Central Difference and Newmark schemes for time differentiation. Encouraging results were obtained even for large time steps. Results obtained in 2-D are compared with the standard Finite Difference Method for validation.

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.

Steam turbine rotor crack detection using sifting process of EMD and B-spline wavelet on the interval element model

A high-precision identification method for steam turbine rotor crack is presented. By providing me nrst three measured natural frequencies, contours for the specified natural frequency are plotted in the same coordi- nate, and the intersection of the three curves predicts the crack location and size. The cracked rotor system is mod- eled using B-spline wavelet on the interval （BSWI） finite element method, and a method based on empirical mode decomposition （EMD） and Laplace wavelet is implemented to improve the identification precision of the first three measured natural frequencies. Compared with the classical nondestructive testing, the presented method shows its effectiveness and reliability. It is feasible to apply this method to the online health monitoring for rotor structure.

Wave propagation of laminated composite plates via GPU-based wavelet finite element method

This paper presents a novel parallel implementation technology for wave-based structural health monitoring (SHM) in laminated composite plates. The wavelet-based B-spline wavelet on he interval (BSWI) element is constructed according to Hamilton’s principle, and the element by element algorithm is parallelly executed on graphics processing unit (GPU) using compute unified device architecture (CUDA) to get the responses in full wave field accurately. By means of the Fourier spectral analysis method,the Mindlin plate theory is selected for wave modeling of laminated composite plates while the Kirchhoff plate theory predicts unreasonably phase and group velocities. Numerical examples involving wave propagation in laminated composite plates without and with crack are performed and discussed in detail. The parallel implementation on GPU is accelerated 146 times comparing with the same wave motion problem executed on central processing unit (CPU). The validity and accuracy of the proposed parallel implementation are also demonstrated by comparing with conventional finite element method (FEM) and the computation time has been reduced from hours to minutes. The damage size and location have been successfully determined according to wave propagation results based on delay-and-sum (DAS). The results show that the proposed parallel implementation of wavelet finite element method (WFEM) is very appropriate and efficient for wave-based SHM in laminated composite plates.

Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

Load identification in one dimensional structure based on hybrid finite element method

The new hybrid elements are proposed by combing modified Hermitian wavelet elements with ANASYS elements. Then hybrid elements are substituted into finite element formulations to solve the load identification. Transfer matrix can be constructed by using the inverse Newmark algorithm and hybrid finite element method. Loads can obtain through the responses and the transfer matrix. Load identification law was studied under different excitation cases in rod and Timoshenko beam.Regularization method is adopted to solve ill-posed inverse problem of load identification. Compared with ANSYS results,hybrid elements and HCSWI elements can accurately identify the applied load. Numerical results show that the algorithm of hybrid elements is effective. The accuracy of hybrid elements and HCSWI elements can be verified by comparing the load identification result of ANASYS elements with the experiment data. Hermitian wavelet finite element methods have high accuracy advantage but it is difficult to apply the engineering practice. In practical engineering, complex structure can be analyzed by using the hybrid finite element methods which can be obtained the high accuracy in the crucial component.

高模态密度结构宽频振动分析的小波有限元方法实现

高模态密度结构的宽频振动分析问题是声振分析领域内关注的重点问题之一,可实现宽频振动预测的数值分析方法是该领域内重要的研究内容,有效的宽频振动数值分析方法应在低频至高频域可同时提供精准的数值解。然而,由于明显的耗散误差和计算成本过高导致传统有限元方法(traditional finite element method,TFEM)在对高模态密度结构进行宽频振动分析时,难以在高频域提供精准的数值解,致使无法实现有效的宽频振动分析。而小波有限元分析方法(wavelet finite element method,WFEM)在进行结构分析时具有潜在的求解效率优势,并且可大幅度降低耗散误差带来的影响。为此,本文首先构造了基于小波有限元理论进行宽频振动分析时的自耦合算法,并据此介绍了小波有限元方法对高模态密度结构进行宽频振动分析的架构,形成了宽频小波有限元分析方法(wide wavelet finite element method,WWFEM)。随后,采用数值分析研究方法,基于WWFEM对具有解析解的高模态密度薄板结构进行了宽频振动分析。最后,采用实验分析研究方法,预测了高模态密度结构在宽频域内的振动响应。在此基础上,对比分析了小波有限元方法在进行高频振动分析时的收敛性和宽频振动分析的有效性等。可为依据小波有限元分析方法解决圆柱壳、曲壳等高模态密度结构宽频振动分析问题提供理论参考。

基于模态参数及小波变换的旋转梁结构损伤识别

本文采用旋转悬臂梁模型模拟旋翼直升机桨叶结构,并对其开展损伤识别问题研究.首先,基于有限元方法,采用Hamilton变分原理,建立旋转结构的动力学模型,通过对比理论和实验的结果验证模型的正确性.其次,利用不同模态参数(位移模态、应变模态)对旋转悬臂梁结构进行损伤识别研究.最后,针对位移模态,基于小波变换的奇异性分析特性,研究通过小波系数辅助损伤识别的方法.计算结果表明,对于旋转结构,应变模态的损伤识别效果较好,而位移模态若结合小波变换的奇异性分析,同样可以实现较为准确的损伤识别效果.

基于小波有限元的裂纹故障诊断

从线弹性断裂力学的角度考虑裂纹引起的局部附加柔度,进而构造了小波有限元裂纹刚度矩阵,提出了基于小波有限元的裂纹故障诊断算法,克服了裂纹奇异性给传统有限元算法造成的困难.将系统前3阶的固有频率作为输入,绘制裂纹等效刚度与裂纹位置的3条曲线,根据曲线的交点可以预测出裂纹的位置与尺寸.用于研究该算法精度的裂纹轴数值算例表明:裂纹位置与尺寸的辨识误差均不超过2%,这为工程实践中早期微弱裂纹的故障预示与诊断提供了新的方法.

基于小波有限元的悬臂梁裂纹识别

研究了悬臂梁裂纹识别中的正反问题 ,即通过裂纹位置和尺寸求解梁的固有频率以及利用梁的固有频率 ,识别裂纹位置和尺寸。以矩形截面裂纹悬臂梁为例 ,利用小波有限元方法建立了梁自由振动的有限元模型 ,其中裂纹被看作为一刚度已知的扭转线弹簧 ,求解出了系统的固有频率 ;通过行列式变换 ,将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题 ,分别做出了以不同固有频率作为输入值时裂纹位置与弹簧刚度之间的解曲线 ,曲线交点预测出裂纹的位置与尺寸。数值算例证实了算法的有效性 。

流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法

本文将小波有限元法引入到流体饱和多孔隙介质二维波动方程的正演模拟中,以二维Daubechies小波的尺度函数代替多项式函数作为插值函数,构造二维张量积小波单元.引入一类特征函数解决了Daubechies小波没有显式解析表达式所带来的基函数积分值计算问题,并推导出计算分数节点上Daubechies小波函数值的递推公式,从而构造出由小波系数空间到波场位移空间的快速小波变换.数值模拟结果表明该方法是有效的.

基于区间B样条小波有限元的裂纹故障定量诊断

研究基于模型的结构裂纹故障诊断中的正反问题,即求解含裂纹参数结构的固有频率以及利用实测固有频率,定量识别裂纹参数。构造用于求解正问题的一维区间B样条小波裂纹单元,通过求解裂纹结构有限元模型,绘制以裂纹等效刚度与裂纹位置为变量的三阶频响函数解曲线,将实际测出的系统前三阶固有频率作为输入,根据曲线的交点定量预示出裂纹的位置和深度。实验研究表明,文中构造的区间B样条小波裂纹单元有效克服了传统有限元分析在求解裂纹奇异性问题时存在的效率低、精度差甚至难以收敛到正确解的缺陷,同时具有足够的辨识精度。

电力变压器局部放电在线监测系统的研制

摘要:研制了一套新型变压器局部放电在线监测系统,该系统基于电声联合检测方法,检测出变压器局部放电产生的多路电流脉冲信号和超声波信号,在硬件上采用了光缆传输等抗干扰措施,有效抑制了监测现场的电磁干扰,在软件中采用离散二进小波变换算法滤除监测信号中的周期干扰以及电晕干扰,从而准确地区分内外放电脉冲;并基于等值声速原理,运用模糊理论和有限元数值分析方法对变压器局部放电点进行了定位。在现场运行的情况表明了该系统具有较高的检测灵敏度,可为电力变压器的状态 检修提供可信的依据。

梁类结构多裂纹微弱损伤的小波有限元定量检测方法

提出了一种定量检测梁类结构多裂纹参数的方法。利用适宜求解奇异性问题的小波有限元法,从动力学正问题入手,对裂纹梁进行有限元建模,获得裂纹故障在结构固有频率上反映的本质征兆,并利用曲面拟合技术绘制出以裂纹位置和深度作为变量的固有频率变化率曲面,然后对整个裂纹梁进行剖分,迭代求解出每个剖分单元上的结构损伤系数。损伤系数为正的单元诊断为裂纹单元,在每个裂纹单元上求出裂纹对应的前三阶固有频率变化率,并分别将其作为输入参数代入固有频率变化率曲面,做出前三阶模态的频率变化率等高线,最后通过三条等高线的交点预测出裂纹存在的位置和深度,算例分析验证了该算法的有效性。