一种基于半参数回归的加速度计误差模型辨识方法

为了解决加速度计离心机试验中系统误差和未建模误差对加速度计模型辨识的影响,将统计学中的半参数回归方法引入到加速度计的模型辨识中,建立了加速度计的半参数回归模型,提出了一种基于最小二乘-半参数回归模型(LS-SPRM)的估计方法,该估计方法利用最小二乘法估计加速度计的误差模型系数,利用半参数回归方法估计加速度计测试中的系统误差,并通过检验残差是否为白噪声作为判断是否有系统误差的条件。在半参数模型的估计中,采用二阶段估计方法,利用三次样条函数进行非参数部分的估计,并讨论了光滑参数的选取方法。仿真试验结果表明,采用该方法能够较好地补偿由于系统误差和未建模误差带来的影响,使加速度计模型辨识的标准差较普通最小二乘法减小45%左右,估计的残差也减小了近一倍。     

环形桁架展开天线索网的预拉力优化技术及工程应用

针对环形桁架展开天线抛物面索网预拉力配置问题,提出了一种寻找预拉力最优配置的方法,该方法基于抛物面索网结构的平衡矩阵奇异值分解,并采用含线性不等式约束及线性等式约束的线性规划方法,寻找抛物面索网最优预拉力配置,文中对抛物面索网结构平衡矩阵的形成、奇异值分解、线性约束优化方法的数学模型、约束矩阵的集成等关键技术进行了详细的推导说明,同时,根据理论推导编写了相应的分析程序,进行了算例分析,并采用非线性有限元法对分析结果进行了验证,证明该方法的正确性.最后,通过实际的天线结构工程的设计分析,对文中提出方法的工程应用可行性进行了论证.     

面向复杂几何模型的并行四面体网格生成方法

面向大规模工程计算等数值模拟领域,提出了一种支持复杂几何模型的大规模四面体网格并行生成方法。该方法以复杂几何模型作为输入,首先采用串行网格生成方法生成初始四面体网格,然后通过两级区域分解方法将初始网格分解为多个子网格并分配到相应的进程中,进程间并行地提取出子网格的表面网格,并基于几何模型对面网格进行贴体加密,最后对加密后的面网格采用Delaunay方法重新生成四面体网格,该方法可以更好地适应高性能计算机体系结构,较好地克服了并行方法中并行性能和网格质量不能兼顾的问题。对三峡大坝模型进行测试和验证,证明该方法具有良好的并行效率和可扩展性,可以在数万处理器核上并行生成数十亿高质量四面体网格。     

捷联惯导系统最简多位置解析对准改进算法

最简多位置解析对准作为测量IMU偏置的简单方法,降低了传统多位置解析对准的工程复杂度,摆脱了伺服平台的限制,但是最简多位置解析对准目前使用的是几何方法,几何方法计算复杂,精度受先验信息的影响。针对这一问题,提出了最简多位置对准解析算法,通过解析算法可得到IMU偏置的解析解。通常两位置即可求得IMU偏置,特殊情况需要三位置,某些特殊位置可以计算特定轴向的偏置。解析法计算简单,不受先验信息的影响,并通过实例仿真证实该算法的有效性,计算误差主要由一阶近似误差和测量噪声引起。     

Constrained parameter-splitting perturbation method for the improved solutions to the nonlinear vibrations of Euler–Bernoulli cantilevers

In this paper, a new method named constrained parameter-splitting perturbation method for improving the solutions obtained from the parameter-splitting perturbation method is proposed for solving the problems in some extremal cases, such as the strongly nonlinear vibration of an Euler–Bernoulli cantilever. The proposed method takes the advantages of both the perturbation method and the harmonic balance method. The idea is that the solution obtained by the parameter-splitting perturbation method is substituted into the equation of motion and then the accumulative error of the equation is minimized for determining the unknown splitting parameters under the constraints constructed under the frame of harmonic balance method. The forced vibration of an oscillator with cubic geometric nonlinearity and inertia nonlinearity and the forced vibration of a planar microcantilever beam with a lumped tip mass are studied as examples to reveal the efficacy of the proposed method. The inspection of the steady-state response including its stability is conducted by means of comparing the frequency-response curves obtained by the proposed method with those obtained by the numerical continuation method and harmonic balance method, respectively, to show the efficacy and the advantages of the proposed method. Meanwhile, the nonlinear ordering effect on the solutions of the proposed method is also studied by comparing the results obtained by using different nonlinear orderings in the systems. In the last, we found through convergence examinations that it is necessary to have corrections to the erroneous solution which are obtained by harmonic balance method and Floquet theory in stability analysis.

     

样条配点法分析结构动力响应的无条件稳定计算格式

本文以三次B样条函数作为位移时域函数,应用配点法,在任一时间步长中列出两个时刻的结构物运动方程式残值为零的条件并使结果满足了稳定条件得到一个计算结构物动力响应无条件稳定的计算格式。 这个计算格式于参数θ符合0.15<θ<0.05时是绝对无条件稳定的,研究证明,本文所提出的格式的精度根据三项指标:振幅衰减率 AD,周期伸长率 PE 及算法阻尼比都比较Wilson-θ法,Newmark法及Houbolt法的为优,例题计算也证明此点,即本文方法精度较上述三法为高,本文格式简单,准确,工作量不多,可以作为计算结构动力响应有效方法之一。     

Pumping of a fluid through a microchannel by means of a bubble driven by a light beam

A new method of pumping a fluid through a microchannel device using a gas bubble-piston, set in motion by the thermocapillary force induced by a light beam, is proposed. To demonstrate the method, a model micropump has been assembled. The model consists of two reservoirs connected by two channels with a bubble-piston driven by a light beam. The pumping rate and the volume per piston stroke are evaluated experimentally. The method proposed is compared with known microfluid pumping methods. Some advantages of the new method are indicated.     

A hybrid immersed‐boundary and multi‐block lattice Boltzmann method for simulating fluid and moving‐boundaries interactions

A numerical method is developed for modelling the interactions between incompressible viscous fluid and moving boundaries. The principle of this method is introducing the immersed‐boundary concept in the framework of the lattice Boltzmann method, and improving the accuracy and efficiency of the simulation by refining the mesh near moving boundaries. Besides elastic boundary with a constitutive law, the method can also efficiently simulate solid moving‐boundary interacting with fluid by employing the direct forcing technique. The method is validated by the simulations of flow past a circular cylinder, two cylinders moving with respect to each other and flow around a hovering wing. The versatility of the method is demonstrated by the numerical studies including elastic filament flapping in the wake of a cylinder and fish‐like bodies swimming in quiescent fluid. Copyright © 2006 John Wiley & Sons, Ltd.     

An extended unresolved CFD-DEM coupling method for simulation of fluid and non-spherical particles

This study develops an extended unresolved CFD-DEM coupling method for simulation of the fluid–solid flow with non-spherical particles. The limitation of fluid grid size is discussed, by simulating the settling of a cylinder in a Newtonian fluid based on the resolved and unresolved CFD-DEM coupling method. Then, the calculation of porosity and the fluid–particle relative velocity based on the particle shape enlargement method for simulation of non-spherical particles is proposed. The availability of the particle shape enlargement method for the simulation of non-spherical particles with different sphericity is discussed in this work, by comparing it with the results from the equivalent diameter enlargement method. The limitation of the equivalent diameter enlargement method for non-spherical particles is revealed from the simulation results. Several typical cases are employed to elaborate and verify the extended unresolved CFD-DEM method based on particle shape enlargement method, by presenting a good consistency with the experimental results. It proves that the extended unresolved CFD-DEM method is suitable for different CFD grid size ratios, and consolidates that it is a universal calculation method for CFD-DEM coupling simulation.     

高阶边界元奇异积分的一种通用高效计算方法

针对三维边界元法中曲面单元上的(弱、强、超)奇异积分提出了一种通用高效的计算方法。经极坐标变换,将奇异积分转化为常规积分;采用数值方法计算Cauchy主值积分和Hadamard有限项积分系数;引入保角变换和反曲变换消除因单元畸形或因积分点靠近单元边界而引起的周向积分奇异性。该方法可以统一处理(弱、强、超)奇异积分,并且只需要知道核函数的奇异阶数和少数几个点上的被积函数值,不依赖于积分和函数的具体选取;所需的积分点少,精度高,并且受单元畸形程度影响较小,稳定性好。采用该方法计算了声学和弹性力学中的典型奇异积分,并结合二阶Nystrm方法求解了弹性力学的边界积分方程,验证了方法的高精度和高效性。本文数值积分程序可向作者索取。     

基于剩余推力法的地震滑坡永久位移研究

基于剩余推力法思想 ,结合Newmark有限滑动位移法 ,考虑了由于动力作用造成的孔隙水压力变化 ,对一种最为常见的边坡灾害—滑坡 ,提出了一种简便的估算地震动力永久位移的方法。对一实例用该法和快速拉格朗日元 (FLAC3D)进行对比计算 ,结果表明两者的结果基本接近 ,前者要保守一些。这就使得应用剩余推力法这一常规方法对滑坡进行真正意义上的动力时程分析成为可能.     

从钓鱼竿的变形看逐段分析求和法

本文从钓鱼竿的变形分析引入逐段分析求和法,进而得出逐段分析求和法的具体应用方法,即逐段刚化法或逐段软化法。然后,讨论了应用逐段分析求和法的前提条件,以及它与叠加法的本质区别。最后基于从离散到连续的逐步逼近,解释了逐段分析求和法与积分法的内在联系。启发学生在进行该部分内容的学习时,除了能够熟练掌握逐段分析求和法的具体应用外,还能够深入理解该方法的思想内涵和力学本质。     

Simulation of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique

Two-dimensional external viscous flows are numerically approximated by means of a domain decomposition method which combines a vortex method and a finite difference method. The vortex method is used in the flow region which is dominated by convective effects, whereas the finite difference method is used in the flow region where viscous diffusion effects are dominant. An influence matrix technique combined with the uniformity condition of the pressure is used to enforce the tangential velocity boundary condition. Comparisons between numerical and experimental data show that the method is well adapted for simulating two-dimensional flows.     

分析蜂窝夹芯板脱胶问题的片条合成-能量法

本文提出了分析蜂窝夹芯板脱胶问题的片条合成－能量法。在文献[2]建立的分析模型的基础上，根据分析蜂窝夹芯梁脱胶问题得到的位移模态，用片条合成的方法构造蜂窝夹芯脱胶板的位移模态，然后用最小势能原理进行求解，得到了位移幅值，应力分布和幅值。通过算例对本文方法的适用性和有效性进行了讨论，分析表明本文的结果与文献[2]中双三角级数解法所得的结果吻合的很好。而利用片条合成－能量法，可以得到蜂窝夹芯板脱胶问题的闭合形式解答，便于工程应用。     

High-order methods for differential equations with large first-derivative terms

A method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non-linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one-dimensional case an approximating equation is developed using just three points. The method first presented is a fourth-order approximation but is extended to become a higher-order method. Results are included for the fourth-, sixth-, eighth- and tenth-order methods. The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie. The method of this paper was also tested on the solution of some non-linear diffusion equations with concentration-dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two-dimensional problems. The method developed in this paper is accurate, easy to use and can be generalized to other problems.     

Finite element analysis of density flow using the velocity correction method

A finite element method is proposed for the analysis of density flow which is induced by a difference of density. The method employs the idea that density variation can be pursued by using markers distributed in the flow field. For the numerical integration scheme, the velocity correction method is successfully used, introducing a potential for the correction of velocity. This method is useful because one can use linear interpolation functions for velocity, pressure and potential based on the triangular finite element. The final equations can be formulated using the quasi-explicit finite element method. A flume in a tank with sloping bottom has been analysed by the present method. The computed results show extremely good agreement with the experimental observations.     

基于单位分解法的无网格数值流形方法

在数值流形方法和单位分解法的基础上，提出了无网格数值流形方法. 无网格数值流形 方法在分析时采用了双重覆盖系统，即数学覆盖和物理覆盖. 数学覆盖提供的节点形成求解 域的有限覆盖和单位分解函数；而物理覆盖描述问题的几何区域及其域内不连续性. 与原有 的数值流形方法相比，无网格数值流形方法的数学覆盖形状更加灵活，可以用一系列节点的 影响域来建立数学覆盖和单位分解函数，具有无网格方法的特性，从而摆脱了传统的数值流 形方法中网格所带来的困难. 与无网格方法相比，由于采用了有限覆盖技术，试函数的构造 不受域内不连续的影响，克服了原有的无网格方法在处理不连续问题时所遇到的困难. 详细推导了无网格数值流形方法的试函数和求解方程，最后给出了算例，验证了该方法的正 确性.     

A new method for computing turbulence in compressible laminar-turbulent transition and boundary layers--PSE＋DNS

A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers is proposed. It is especially useful for computation of laminar-turbulent transition and turbulence starting from small-amplitude disturbances. The laminar stage, up to the beginning of the breakdown in laminar-turbulent transition, is computed by parabolized stability equations (PSE). The direct numerical simulation (DNS) method is used to compute the transition process and turbulent flow, for which the inflow condition is provided by using the disturbances obtained by PSE method up to that stage. In the two test cases incfuding a subsonic and a supersonic boundary layer, the transition locations and the turbulent flow obtained with this method agree well with those obtained by using only DNS method for the whole process. The computational cost of the proposed method is much less than using only DNS method.     

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations(ODEs) are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.     

基于激光扫描法布里--珀罗干涉原理的压电常数测试系统

提出了由扫描法布里--珀罗干涉法测量微小形变的方法, 设计了一种基于激光扫描法布里--珀罗干涉原理的压电常数$d_{31}$测试系统. 文中给出了测量原理、测量装置及陶瓷样本的测量结果,并与用IEEE标准测量方法的测量结果进行了对比,测试结果表明两者相差很小.