An improved optimal elemental method for updating finite element models

The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures, the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method.The example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.     

位温方程拉格朗日平流计算方案的改进及其在GRAPES_GFS全球模式的应用

GRAPES全球数值预报系统(GRAPES_GFS)个例试验中,模式高层垂直速度在南极大陆上空会出现较大的计算噪音,进而影响模式的积分稳定性,甚至积分中断。对GRAPES_GFS的动力框架以及动力、物理耦合方案进行诊断分析,发现位势温度在拉格朗日上游点上的垂直插值是垂直速度噪音产生的主要原因。2013年7月实际资料试验表明,在位温方程中引入垂直非插值的拉格朗日平流方案,可以减少或消除该计算噪音。使用新的方案后,北半球和热带地区模式预报的整体性能得到了明显提高,8 d预报的全球质量损失较为严重的问题也得到了缓解。     

基于FLEXPART模式对黄河源区盛夏降水异常的水汽源地及输送特征研究

依据近10年黄河源区流域气象台站的降水观测资料,提取夏季降水最强月对应的异常特征,利用拉格朗日粒子扩散模式(Flexible Particle Dispersion Model,FLEXPART),针对目标时段开展大气粒子群(气块)的后向模拟,着重分析了流域内降水正负异常状态下的水汽输送特征及其差异,并评估各水汽源地对流域内三类降水的贡献。结果表明,以“S”型跨赤道输送(“由阿拉伯海至孟加拉湾和印度半岛再由青藏高原西南侧进入黄河源区”)和“几”型输送(“由南中国海经长江中下游平原后途径四川盆地再进入黄河源区”)为代表的南支路径是2012年7月黄河源区对应的主要水汽输送路径;而以东、西风急流作用下的两条远距离输送(“由南中国海至孟加拉湾和印度半岛东北部附近后再经由青藏高原西侧或北侧进入黄河源区”以及“由欧洲平原东部和中亚地区进入青藏高原西侧或北侧后到达黄河源区”)为代表的北支路径是2015年7月黄河源区对应的主要水汽输送路径。在对气块后向模拟追踪的同时,对其运动过程中的比湿变化进行了对应经纬度网格的空间平均,变化特征显示出喜马拉雅山南麓、四川盆地周边、孟加拉湾和青藏高原北侧是黄河源区流域降水对应的潜在水汽源地。由定量评估贡献率的结果可知:青藏高原北侧的广大干旱及半干旱草原地区是2015年7月黄河源区降水的最主要水汽来源,其贡献率高达52.9%;而在2012年,三个主要源地的贡献率差异远不及2015年显著;无论对应何种类型的降水,青藏高原西南部和北侧提供了黄河源区主要可供降水的外来水汽。     

辅助纬度与大地纬度间的无穷展开

利用无穷级数理论和拉格朗日反演定理,详细推导了大地测量和制图学中常用的辅助纬度与大地纬度间的无穷展开,主要表现为参考椭球第一偏心率的幂级数形式。通过建立一系列严格的系数递推公式,得到了等量纬度反解展开式和等角纬度反解展开式;同时,推导了古德曼函数的泰勒展开式,进而得到了等角纬度正解展开式;利用级数除法公式,得到了等距离纬度正解展开式系数的行列式表示。通过比较本文方法与计算机代数系统Mathematica直接推导求得的辅助纬度正反解展开式e^0～e⁴⁰阶系数和相应的程序用时,表明本文算法是正确的、快速的。以CGCS2000参考椭球为例,对辅助纬度正反解进行了算例分析,也进一步验证了本文公式的正确性。     

A generalized frontogenesis function and its application

With the definition of generalized potential temperature, a new generalized frontogenesis function, which is expressed as the Lagrangian change rate of the magnitude of the horizontal generalized potential temperature gradient, is derived. Such a frontogenesis function is more appropriate for a real moist atmosphere because it can reflect frontogenesis processes, in which the atmosphere in a frontal zone is typically characterized by neither completely dry nor uniform saturation. Furthermore, by derivation, the expression of generalized frontogenesis function includes both temperature and humidity gradients, which is different from and superior to the traditional frontogenesis function in moist processes, which also uses equivalent potential temperature. Diagnostic studies of real cases are performed and show that the generalized frontogenesis function in non- uniformly saturated moist atmosphere indeed provides a useful tool for frontogenesis, compared to using the traditional frontogenesis function. The new frontogenesis function can be used in situations involving either a strong temperature or moisture gradient and is closely correlated with precipitation.     

基于改进低秩矩阵恢复模型的测井数据去噪方法研究

在铀矿中子测井数据处理方面,受井液、地层孔隙度、岩性等因素的影响,测井的噪声数据不一定满足稀疏性的要求,传统的低秩矩阵恢复（LRMR）模型对于测井原始数据的去噪效果不佳。作者提出一种基于低秩矩阵恢复的改进模型,以提高对含复杂噪声的测井数据的去噪能力。同时把加权m1范数和加权核范数的思想引入到传统的LRMR模型中,使用F范数作为惩罚项,得到改进的LRMR模型,并应用表现效果较好的非精确增广拉格朗日乘子法（IALM）对模型进行求解。运用传统模型和改进的模型对某铀矿的中子测井数据进行去噪,并使用支持向量机、决策树算法对去噪后的数据进行矿层分类分析;实验结果表明,经过改进模型去噪处理后的测井数据分类准确度更高。改进的LRMR模型去噪能力比传统LRMR模型更强,为铀矿中子测井数据去噪提供了技术支撑。     

广义Birkhoff方程的积分方法

场方法和最终乘子法是求解运动微分方程的基本方法. 本文将这两种方法应用于广义Birkhoff系统,求出了场方法的基本偏微分方程和该方程的完全积分; 根据Jacobi最终乘子定理求出了广义Birkhoff方程的解. 并举例说明结果的应用.     

基于拉格朗日方法的洪泽湖与巢湖河流出入湖水体追踪计算

利用耦合北斗和GPS双定位系统的拉格朗日随体法水质点追踪仪,在2018年9月至2019年10月期间开展了总数为18次的洪泽湖和巢湖主要河流河水入湖后表层、中层和底层水体运移同步追踪观测,研究了两个湖泊河水入湖后的运移轨迹和速度特征。结果表明:淮河主河道河水入洪泽湖后流向南北两侧;徐洪河河口处水体表层流速在洪泽湖5条河道出入湖口处为最大;巢湖双桥河河口处水体流速受巢湖闸运行影响强烈,各层流速在7条入湖河流中最大。洪泽湖、巢湖入湖水体流速由表层至底层逐渐降低,洪泽湖各层水体流速大于巢湖。洪泽湖河口处表层水体8次测量平均流速为6.11cm/s;巢湖为5.51cm/s;二者中层流速分别为5.32和3.85cm/s;底层则分别为4.96和3.67cm/s。     

A Lagrangian mean theory on coastal sea circulation with inter-tidal transports I. Fundamentals

A brief review is made on the theory of the Lagrangian residual circulation and inter-tidal transports in a convectively weakly nonlinear system. In the review the emphasis is put on the systematical development of the theory and its weakness of convectively weakly nonlinear approximation. The fundamentals of a Lagrangian tidally-averaged theory on circulation with inter-tidal transport processes have been proposed for a general nonlinear coastal/estuarine system. The Lagrangian residual velocity is strictly de- fined, and it has been verified to be able to embody the velocity field of circulation. A new concept of the concentration for inter- tidal transport processes is presented. The concentration describing the inter-tidal transport processes should be a ＂Lagrangian inter-tidal concentration＂ defined and named, but not the Eulcrian tidally-averaged concentration used traditionally. The circulation described here contains a set of infinite temporal-spatial fields of velocity/concentration, each of which corresponds to a specific value of tidal phases varying continuously over one tidal cycle. When the convectively weakly nonlinear condition（ with a smaller order of eddy diffusion and sources） is approximately satisfied, a set of infinite temporal-spatial fields of velocity/concentration can be reduced to a single one.. the mass transport velocity/the Eulerian tidally averaged concentration as exhibited traditionally.     

不定乘子在完整与非完整力学系统中的作用

归纳总结了不定乘子的由来、意义和作用，提出在非完整力学系统中，不定乘子的引入是解决问题的一把钥匙。