ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.

A Study on Precipitation Products with High Resolution in Anhui Province Based on Thin Plate Smoothing Spline

In order to achieve refined precipitation grid data with high accuracy and high spatial resolution,hourly precipitation grid dataset with 1 km spatial resolution in Anhui Province from May to September (in the rainy season) in 2016 and from August 2017 to July 2018 was established based on thin plate smoothing spline (TPS),which meets the needs of climate change research and meteorological disaster risk assessment.The interpolation errors were then analyzed.The grid precipitation product obtained based on thin plate smoothing spline,CLDAS-FAST and CLDAS-FRT were evaluated.The results show that the interpolated values of hourly precipitation by thin plate smoothing spline are close to the observed values in the rainy season of 2016.The errors are generally below 0.9 mm/h.However,the errors of precipitation in the mountainous areas of eastern Huaibei and western Anhui are above 1.2 mm/h.On monthly scale,the errors in June and July are the largest,and the proportion of absolute values of the errors ≥2 mm/h is up to 2.0% in June and 2.2% in July.The errors in September are the smallest,and the proportion of absolute values of the errors ≥2 mm/h is only 0.6%.The root mean square (RMSE) is only 0.37 mm/h,and the correlation coefficient (COR) is 0.93.The interpolation accuracy of CLDAS-FRT is the highest,with the smallest RMSE (0.65 mm/h) and mean error ( ME =0.01 mm/h),and the largest COR (0.81).The accuracy of the precipitation product obtained by thin plate smoothing spline interpolation is close to that of CLDAS-FAST.Its RMSE is up to 0.80 mm/h,and its ME is only -0.01 mm/h.Its COR is 0.73,but its bias (BIAS) is up to 1.06 mm/h.

COMPACT SUPPORT THIN PLATE SPLINE ALGORITHM

Common tools based on landmarks in medical image elastic registration are Thin Plate Spline (TPS) and Compact Support Radial Basis Function (CSRBF). TPS forces the corresponding landmarks to exactly match each other and minimizes the bending energy of the whole image. However, in real application, such scheme would deform the image globally when deformation is only local. CSRBF needs manually determine the support size, although its deformation is limited local. Therefore, to limit the effect of the deformation, new Compact Support Thin Plate Spline algorithm (CSTPS) is approached, analyzed and applied. Such new approach gains optimal mutual information, which shows its registration result satisfactory. The experiments also show it can apply in both local and global elastic registration.

Development of quadrilateral spline thin plate elements using the B-net method

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.

CUBLIC SPLINE SOLUTIONS OF AXISYMMETRICALNONLINEAR BENDING AND BUCKLING OFCIRCULAR SANDWICH PLATES

Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.

ISOTROPICALIZED SPLINE INTEGRAL EQUATION METHOD FOR THE ANALYSIS OF ANISOTROPIC PLATES

In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.

THE SOLUTION OF RECTANGULAR PLATES WITH LARGE DEFLECTION BY SPLINE FUNCTIONS

In this paper, Von Karman's set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point (SFP) method and by the spline finite element (SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.

黄土高原降雨量空间插值精度比较——KRIGING与TPS法

黄土高原地域广阔,降雨量时空分布复杂多变,插值方法将影响降雨量的时空变化特征分析,进而影响水文及土壤侵蚀模拟效果。采用黄土高原河龙区间及毗邻地区50余个气象站点20年(1981—2000年)的降雨量数据,分别利用KR IG ING(克里金)和TPS(薄板光滑样条)方法对多年平均、年和月降雨量进行插值,对研究区内27个站点进行交叉验证,比较和分析其插值精度变化特征。结果表明:1)无论多年平均,还是年和月尺度,KR IG ING与TPS方法降雨量插值结果都能正确反映河龙区间降雨量的空间变化趋势,2种方法交叉验证平均一致性指标(A)绝对值相差均在±0.01范围内,2种方法面平均插值精度均没有显著性差异。2)不同时间尺度的插值精度,KR IG ING与TPS 2种插值方法的交叉验证平均一致性指标(A)均表现出多年均值优于4月约14%,优于年值约19%,优于7月约35%。

基于改进薄板样条运动模型的人脸动画算法

面部动画在电影、游戏、虚拟现实等领域起着关键作用,对于实现逼真、生动的人脸动画和情感传达至关重要。当面临面部形状、姿态、表情等多个变化因素时,虽然通过薄板样条非线性变换可以获得较好的运动估计结果,但在处理面部复杂纹理和嘴部运动时存在运动估计不精细的问题,需要更强大的图像修复能力。因此,提出一种基于改进薄板样条运动模型(TPSMM)的人脸动画算法。首先,在TPSMM的基础上引入一种Farneback光流金字塔算法,通过与薄板样条变换和背景仿射变换相结合,使得人脸局部运动估计更精准;其次,为了更真实地恢复缺失区域的细节纹理信息,提出一种多尺度细节感知网络,该网络在编码器中通过嵌入通道注意力(ECA)模块减少源图像因多层下采样而导致的人脸细节信息丢失,在解码器中利用坐标注意力(CA)模块来有效捕获运动估计特征图中不同位置的重要特征,提高人脸图像的生成质量。实验结果表明,相比一阶段运动模型(FOMM)、关节动画的运动表示法(MRAA)、TPSMM等,该算法在MUG、UvA-Nemo和Oulu-CASIA数据集上的L1、平均关键点距离(AKD)、平均欧氏距离(AED)数值均达到最优,平均分别为0.0129、0.923、0.00099。

基于TPS模板的弹性形变指纹的匹配算法的研究

为了克服指纹图像获取过程中的非线性形变 ,本文提出一种新的细节点匹配算法。该算法基于TPS(thethin platespline)模板 ,分为局部匹配和全局匹配两部分。通过建立与该模板一致的匹配算法 ,用很小的匹配阈值算出匹配细节点的数目 ,得到较高的匹配分数。实验表明 ,这种算法能很好的校准弹性形变指纹 ,提高了指纹识别系统的实用性。

基于小波分析的智能电能表动态测试信号模型与误差分析

针对电能表动态误差测试问题,文章采用小波分析对采集到的加热炉负载等三种实际工况信号进行了分解,提取了时域及时频域的特征,从幅值和频率两个维度总结提取了包括幅值变化、低频稳态、高频稳态、高频暂态在内的四类测试信号,能够全面表征多种动态信号的特性,并且采用薄板样条插值建立了包络信号,幅值上升、下降、中断、谐波、间谐波、冲击的七种单一测试信号模型,在搭建好的动态信号测试平台上实验并分析了单一测试信号的参数对误差的影响,结果表明幅值变化和包络、间谐波对电能表计量误差影响较大。通过单一测试信号的参数调整以及多种信号的复合进一步建立了复合测试信号模型,可逼近现实工况信号,遍历各种工作模态,对采集到的激光切割机负荷进行误差预测与补偿,模型预测误差的结果验证了复合测试信号模型的正确性,可为电能表动态误差研究提供依据。

基于3D TPS空间插值的中国降水量空间分布响

常用的空间插值模型通常仅考虑地理位置坐标而忽略高程值,针对这一不足,本研究以中国年均降水量空间分布为例,将高程值作为重要的自变量因子用于三维薄板样条(3DTPS)模型的空间插值,旨在减少因高程值变化较大造成的影响,提高空间数据插值精度。基于Visual Basic.Net和ArcGIS Engine二次开发工具,通过提取中国数字高程模型(DEM)图中的高程值以及中国气象站分布图中气象站的地理坐标和年均降水量,再以DEM图中的格网为模板,用3DTPS模型进行空间插值,得到中国年均降水量空间分布图。最后,与其他不同模型进行对比分析,证明3DTPS的插值精度最高,标准误差为113.95,尤其在高程值变化较大的区域优势明显。

基于部件组合的连衣裙款式图快速生成研究

款式图作为真实服装的一种平面表达方式,在服装生产过程中起着重要的作用。为了简化服装款式设计过程,提高款式设计的效率与服装信息表达的准确率,并针对不同体型生成个性化的款式图,以连衣裙为对象,基于部件数字化对款式图快速生成进行了研究。首先,采用薄板样条插值算法以使服装款式图拟合不同人体体型,使衣身能够快速达到满足特定体型的尺寸;其次,通过基于关键点的矩阵变形实现部件之间的自适应组合;最后,选用参数驱动和交互式修正关键点2种方法实现对服装款式细节的调整。以连腰鱼尾裙为例,阐述并实现了连衣裙款式图快速生成过程,验证了基于部件组合的款式图快速生成的可行性,为个性化定制和智能化款式设计提供理论支持。

基于TPS变形的3D面皮层次点对应方法

在统计模型的颅面复原中,针对如何建立三维面皮间顶点的生理一致对应关系的问题,提出一种面皮层次点对应方法(HPCM)。根据Frankfurt坐标系下特征点的严格对应关系对样本面皮进行薄板样条变形,使其与模板面皮近似重合。在此基础上分别建立体素模型,结合顶点的欧式距离、局部相对位置与几何特征等多重约束确定最优对应点。实验结果表明,HPCM提高了点对应的精度,可有效建立颅面统计复原所需的具备生理点对应关系的面皮样本。

基于姿势引导下的虚拟试穿网络

针对现有的基于姿势引导下的虚拟试穿方法存在着服装纹理过度变形、生成的图像出现遮挡等问题,提出了一种基于姿势引导下的虚拟试穿网络(pose-guidedvirtualtry-on network,PG-VTON).首先,使用基于U-Net的网络对人物图像进行姿势转换,生成目标姿势下的人物解析图,引入信息增强模块提高解析图的准确性,减少试穿中的错误遮挡;然后,通过薄板样条变换(thin platespline,TPS)方法将目标服装变形为与人物身体相贴合的形状,引入网格变形约束项来保留目标服装的纹理和细节特征;最后,将解析图和变形服装结合起来,生成最终的虚拟试穿图像.实验结果表明,该方法不仅比Downto(downtothelast detail)网络试穿图像的平均结构相似性(structural similarity,SSIM)提高了2.83%,初始得分(inception score,IS)提高了6.74%,与其他最新的虚拟试穿方法相比减少了试穿过程中的错误遮挡,能生成更加清晰真实的结果.

基于形状增强和纹理插值的三维脑部MRI数据增强算法

针对医学伦理和人工标注的成本高昂,目前公开的数据集中标记的医学图像数据量不足的问题,许多研究者提出了不同的算法来增强医学数据.使用卷积神经网络(Convolutional Neural Networks,CNN)对阿尔茨海默症(Alzheimer's Disease,AD)的诊断和研究只有在数据丰富时,才能得到更好的分析结果.本文提出一种基于形状增强和纹理插值的三维脑部MRI(Magnetic Resonance Imaging,MRI)数据增强算法,将脑部MRI图像的属性分解为形状和纹理,先通过GAN(Generative Adversarial Nets,GAN)增强MRI数据的形状,再通过三维薄板样条插值对所得的增强形状进行纹理插值,得到三维脑部MRI增强图像.通过实验可得生成数据的分布与真实数据的分布相似,验证了本文提出的数据增强算法的有效性.

Convergence and exact solutions of spline finite strip method using unitary transformation approach

The spline finite strip method （FSM） is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems. To date, no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such, in this paper, the mathematical exact solutions of spline finite strips in the plate analysis are derived using a unitary transformation approach （abbreviated as the U-transformation method herein）. These exact solutions are presented for the first time in open literature. Unlike the conventional spline FSM which involves assembly of the global matrix equation and its numerical solution, the U-transformation method decouples the global matrix equation into the one involving only two unknowns, thus rendering the exact solutions of the spline finite strip to be derived explicitly. By taking Taylor＇s series expansion of the exact solution, error terms and convergence rates are also derived explicitly and compared directly with other numerical methods. In this regard, the spline FSM converges at the same rate as a non-conforming finite element, yet involving a smaller number of unknowns compared to the latter. The convergence rate is also found superior to the conventional finite difference method.

基于曲面样条插值的压力敏感涂料测压数据修正方法

压力敏感涂料(Pressure Sensitive Paint,PSP)试验结果修正方法多基于最小二乘法实现,通常忽视了翼面上弦向和展向的流动特性。利用无限平板样条(Infinite Plate Spline,IPS)插值技术,建立了适用于压力敏感涂料试验结果修正的混合修正方法与流程。使用传统测压试验的全展长飞机模型,在2.4 m量级跨声速风洞中同时开展了完整机翼的PSP测压和PSI(Pressure Scanner Instrument)测压试验,试验马赫数为0.735,迎角范围为-6.38°~10.59°。试验结果与修正结果表明:PSP试验结果与PSI试验结果整体吻合较好,但PSP试验系统对机翼前缘流场捕获精度较差;混合修正方法有效,且兼顾了翼面前缘、中部和后缘的压强分布特点,修正后的压强分布数据能够更好地反映翼面流场的变化规律。

采煤沉陷区地形插值方法精度对比分析及改进

为探究采煤沉陷区精确的地形特征,在常用地形插值模型的基础上提出一种改良插值模型。运用图像对比、交叉验证、相关性分析等方法对各插值方法进行精度分析,选取最合适该区域的插值方法;再根据非充分采动区沉陷地质结构和无法保留地形细节的情况,采用合适的插值法、使用K-means聚类法将整个研究区域分块,选取地表粗糙度Sr较大的区域,用薄板样条插值法重构局部地形DEM。线性三角网法插值曲面与真实的沉陷地形更吻合且连续性和趋势符合性良好,其评价指标精度最高。采用拟合度为0.9的薄板样条插值法重构Sr>1.50的地形DEM,并计算得整个区域的决定系数R2为0.981 5。结果表明,该组合插值方法在保持高精度的同时,具有可靠的平滑性,可以保留更多的地形细节。结论可为无人船数据构建沉陷区水下地形DEM选择最佳的插值方法及相关工作提供一定的参考。