基于Krylov子空间的微混合器宏模型设计与仿真

获得宏模型是微混合器设计与仿真的关键。将Navier-Stokes方程和对流扩散方程用有限元方法进行离散化处理,应用Krylov子空间的Arnoldi过程对得到的微分-代数方程组降阶处理,提取出宏模型。仿真结果表明,经过降阶处理得到的宏模型保证了微混合器的输出精度,降低了计算复杂度。     

动力缩聚及缩聚模型修正

工程应用中,往往需要对有限元分析得到的结构大阶模型进行降阶,但对降阶后的模型进行动力分析时,常嫌精度不足。本文提出一种新的方法,首先由缩聚法得到降阶的刚度、质量阵,再以实测频响函数拟合降阶系统频响函数的理论预示值,从而得到降阶系统的质量、刚度阵。此法既对大阶有限元模型进行了有效的降阶,又使降阶后的数学模型与实际系统的动力特性相近。仿真计算与实物试验结果表明,本文方法有效且具有很好的精度。     

一种基于多端口组件网络的MEMS系统级建模方法

以多端口组件及其网络的研究作为理论基础,创建了专门针对MEMS的系统级建模方法———用单个组件 表示MEMS的各功能结构部件,组件的端口表征与部件有关的各种物理量,依据一定规则联结组件形成的网络表 征整个微系统。该方法采用常微分和代数方程描述组件的行为,混合信号硬件描述语言作为组件及其网络的建模 语言。以梁为例,阐述了如何建立其行为方程,以得到参数化、可供重用的组件模型。上述研究结合微加速度计的 系统级设计应用实例,表明该方法是实现MEMS系统级建模的有效手段,能针对MEMS固有的多能量域耦合行为 等进行快速建模与仿真。     

复杂齿轮耦合转子-轴承系统动力学的规范建模方法

由于齿轮的耦合作用,齿轮-转子-轴承系统中各个转子的振动是相互耦合、相互影响的,研究齿轮-转子-轴承系统动力学,必须基于系统的、整体的观念进行分析。因此,齿轮-转子-轴承耦合系统动力学建模和模型降阶一直是人们普遍关注的问题。基于齿廓啮合基本定理,给出了直齿轮、斜齿轮、直齿锥齿轮、弧齿锥齿轮共4种齿轮的几何耦合模型（或称运动耦合模型）;利用耦合模型矩阵,给出了含以上4种齿轮副的复杂齿轮转子-轴承系统纵-弯-扭耦合动力学研究的统一、方便、规范的建模方法。为复杂齿轮-转子-轴承耦合系统动力学分析研究提供了方便。     

基于神经网络观测器的机械臂力/位置控制

针对机械臂末端运动受约束的力/位置控制中无法精确建模、模型具有外界干扰和关节角速度不可测等问题，设计一种基于神经网络观测器的补偿控制系统。首先，通过解耦力和位置控制，得到降阶动态模型。然后，利用神经网络速度观测器对关节速度在线估计，并用神经网络对降阶动力学模型中的不确定项进行逼近补偿滑模控制器。最后，基于Lyapunov稳定性理论证明系统稳定性，并对二连杆机械臂进行仿真。仿真结果表明所设计的控制系统的有效性。     

基于灰色辨识的光刻机恒温控制系统建模

针对光刻机媒质远传温控系统的大惯性、多重时滞和多重扰动特点,采用理论建模与系统辨识相结合的建模方法,运用大系统解耦理论实现高阶模型的降阶分解,设计多态抗失真试验采集输出数据序列,采用系统辨识方法估计数学模型参数,建立分散时滞、扰动的温控系统动态数学模型.此模型已被成功运用于光刻机投影物镜高精度恒温控制系统中,达到了0.006℃的温度稳定度,并表现出较强的鲁棒性和自适应性.     

微机电系统(MEMS)的仿真和模型分析

微机电系统 (MEMS)器件及系统仿真正日益受到MEMS研究者的重视。其仿真内容涉及力学、电子学、热学、光学、流体学等许多学科。MEMS和其他微系统可看作为一个多域物理系统。本文从方法学观点讨论了建模方法、计算机辅助模拟工具、多域模型库以及不同仿真器的耦合问题。将电网络概念引入到不同域系统仿真中以及等效电路被应用到不同的物理域系统。对于系统模拟和仿真来说,元件模型库的建立非常重要,引入多端口元件,并用线性和非线性微分方程加以描述。另外,本文也简单分析了系统仿真中涉及的降阶问题、模型优化方法以及相关的仿真工具和仿真器间的耦合问题。     

大型带式输送机动态建模及模型降阶

通过有限元方法建立大型带式输送机的动态模型,并通过基于系数矩阵的有序实Schur分解的模型降阶法对带式输送机系统模型进行降阶处理,得到低阶模型,绘出其频率特性Bode图,比较降阶前后系统的频率特性。     

微机电系统光学组件的系统级建模

为提高微机电系统(MEMS)中光学系统整体仿真的准确性和效率,解决光学组件系统级建模存在的问题,提出了一种光学组件系统级建模方法,该方法可同时支持与MEMS系统级机械组件和电路组件共同仿真.首先,介绍了多端口组件网络方法、高斯光束特点和空间坐标系变换理论.接着,以微平面镜为例,介绍了光学组件系统级建模方法的流程.最后,采用Verilog-A硬件描述语言建立了包含多个典型光学组件的系统级光学库.使用该库的光学组件在MEMS集成设计工具MEMSGarden中搭建微扫描系统进行了仿真与测试.与商业软件CoventorWare的分析结果相比,提出的建模方法解决了扫描盲区问题,且非差分电压分析的误差小于3％.结果显示,本文提出的建模方法精确有效,对MEMS的系统级设计有参考价值.     

高阶累积量的子空间模态参数辨识方法研究

基于传统的高阶累积量降阶方法的子空间模态参数辨识方法具有一定的缺陷.提出采用2种降阶方法用于改善高阶累积量的子空间模态参数辨识方法,并对该方法进行了实验验证,证明了方法的可靠性.该方法的计算量较小,能够用于一般结构的模态参数辨识.     

Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction

In this paper, we examine an efficient calculation of the approximate frequency response (FR) for large-size finite element (FE) models using the Krylov subspace-based model order reduction (MOR) and its direct design sensitivity analysis with respect to design variables for sizing. Information about both the FR and its design sensitivity is necessary for typical gradient-based optimization iterations; therefore, the problem of high computational cost may occur when FRs of a large-size FE models are involved in the optimization problem. In the method suggested in this paper, reduced order models, generated from the original full-order FE models through the Arnoldi process, are used to calculate both the FR and FR sensitivity. This maximizes the speed of numerical computation of the FR and its design sensitivity. Assuming that the Krylov basis vectors remain constant with respect to the perturbation of a design variable, the FR sensitivity analysis is performed in a more efficient manner. As numerical examples, a car body with 535,992 degrees of freedom (DOF) and a 6 × 6 micro-resonator array with 368,424 DOF are adopted to demonstrate the numerical accuracy and efficiency of the suggested approach. Using the reduced-order models, we found that the FR and FR sensitivity are in a good agreement with those using the fullorder FE model. The reduction in computation time is also found to be significant because of the use of Krylov subspace-based reduced models.     

宏微观跨尺度下的锥套运行力学机理研究

为揭示薄壁锥套在运行过程中产生损伤的运行力学机理,提高其运行可靠性,提出一种用于解决具有宏微观跨尺度问题和大规模非线性接触问题的流固耦合方法。通过对薄壁锥套和轧辊所形成的固体域进行三维静电多极离散,采用改进后的Krylov子空间广义极小残值法(GMRES(m))对其进行优化迭代。其中,弹性摩擦接触域进行点面接触非线性数学规划,耦合界面处采用非匹配网格数,并对微米级油膜进行弹性润滑解析和无厚度处理,同时引入Lagrange族内插函数,建立薄壁锥套在宏微观跨尺度下的运行力学模型。通过薄壁锥套运行力学机理试验,验证计算方法在揭示薄壁锥套运行力学行为的正确性。结果表明,薄壁锥套在运行过程中的油膜力场和接触应力场呈三维动态非均匀分布,在复杂交变力场作用下,位于薄壁锥套两端密封槽处的应力奇异性是造成其发生粘结、断裂等破坏的力学原因。在设计阶段必须考虑轧制工况状态,通过设计合适的过盈量和锥套厚度来减小疲劳损伤,提高可靠性。     

基于改进共轭梯度法的ERT图像重建

针对电阻层析成像(ERT)图像重建中灵敏度矩阵的病态特性导致共轭梯度法的收敛率低的问题,提出了改进的共轭梯度算法,ERT图像重建前先对数据进行归一化预处理,将解空间映射到Krylov子空间中,再通过共轭梯度法求解低维子空间中的反问题。分别利用共轭梯度法、预处理共轭梯度法和改进共轭梯度法对典型的气水两相流模型做了仿真实验。实验结果表明,改进共轭梯度法能够提高重建图像的质量,并且相对于其他算法,降低了计算时间。     

Model Order Reduction for Coupled Dynamic Characterization of Torsional Micromirrors

Numerical solutions could not perform rapid system-level simulation of the behavior of micro-electro-mechanical systems(MEMS) and analytic solutions for the describing partial differential equations are only available for simple geometries.Model order reduction(MOR) can extract approximate low-order model from the original large scale system.Conventional model order reduction algorithm is based on first-order system model,however,most structure mechanical MEMS systems are naturally second-order in time.For the purpose of solving the above problem,a direct second-order system model order reduction approach based on Krylov subspace projection for the coupled dynamic study of electrostatic torsional micromirrors is presented.The block Arnoldi process is applied to create the orthonormal vectors to construct the projection matrix,which enables the extraction of the low order model from the discretized system assembled through finite element analysis.The transfer functions of the reduced order model and the original model are expanded to demonstrate the moment-matching property of the second-order model reduction algorithm.The torsion and bending effect are included in the finite element model,and the squeeze film damping effect is considered as well.An empirical method considering relative error convergence is adopted to obtain the optimal choice of the order for the reduced model.A comparison research between the full model and the reduced model is carried out.The modeling accuracy and computation efficiency of the presented second-order model reduction method are confirmed by the comparison research results.The research provides references for MOR of MEMS.     

Calculation of design sensitivity for large-size transient dynamic problems using Krylov subspace-based model order reduction

Nowadays, transient dynamic responses of a large-size finite element (FE) model can be solved within a reasonable computation time owing to rapid improvement in both numerical schemes and computing resources. However, increasing demands for accurate simulation and complicated modeling have led to larger and more complex finite element models, which consequently result in considerably high computational cost. In addition, when structural optimizations include transient responses such as displacement, velocity, and acceleration, the optimizations often do not end within a reasonable process time because the large-size simulation must be repeated many times. In order to reduce the computational cost in this respect, model order reduction (MOR) for the original full-order model (FOM) can be used for the transient response simulation. In this paper, a transient dynamic response analysis using Krylov subspace-based MOR and its design sensitivity analysis with respect to sizing design variables is suggested as an approach to the handling of large-size finite element models. Large-size finite element models can incur the problem of a long computation time in gradient-based optimization iterations because of the need for repeated simulation of transient responses. In the suggested method, the reduced order models (ROMs) generated from the original FOMs using implicit moment-matching via the Arnoldi process are used to calculate the transient response and its design sensitivity. As a result, the speed of numerical computation for the transient response and its design sensitivity is maximized. Newmark’s time integration method is employed to calculate transient responses and their design sensitivities. In the case of the transient sensitivity analysis, we apply a temporal discretization scheme to the design sensitivity equation derived by directly differentiating the governing equation with respect to design variables. This methodology has been programmed on the MATLAB with the FE information extracted from the FE package ANSYS. Two application examples are provided to demonstrate the numerical accuracy and efficiency of the suggested approach. The relative errors of transient response and design sensitivity between the FOMs and ROMs are also compared according to the orders of the reduced model. Calculation of transient dynamic responses and their sensitivities using Krylov subspacebased MOR shows a sizeable reduction in computation time and a good agreement with those provided by the FOM.     

Discriminative sparse subspace learning and its application to unsupervised feature selection

In order to efficiently use the intrinsic data information, in this study a Discriminative Sparse Subspace Learning (DSSL) model has been investigated for unsupervised feature selection. First, the feature selection problem is formulated as a subspace learning problem. In order to efficiently learn the discriminative subspace, we investigate the discriminative information in the subspace learning process. Second, a two-step TDSSL algorithm and a joint modeling JDSSL algorithm are developed to incorporate the clusters׳ assignment as the discriminative information. Then, a convergence analysis of these two algorithms is provided. A kernelized discriminative sparse subspace learning (KDSSL) method is proposed to handle the nonlinear subspace learning problem. Finally, extensive experiments are conducted on real-world datasets to show the superiority of the proposed approaches over several state-of-the-art approaches.     

卡尔曼滤波在MEMS惯性姿态测量中的应用

由于测控成本和有效载荷的限制,一般采用微机电系统(MEMS)惯性传感器来测量小型无人机的飞行姿态。在MC9S12XS128单片机上通过嵌入式软件编程实现了卡尔曼滤波算法,并在JZJ-1型自准直仪转台上对MEMS加速度计和陀螺仪的输出信号进行了数据融合试验,较好地解决了MEMS惯性测量系统的零漂和机械振动干扰问题。     

基于修正粒子滤波的MEMS传感器飞行器姿态解算

针对单一采用 MEMS传感器解算飞行器姿态无法克服系统非线性噪声干扰的问题,提出了一种基于修正粒子滤波的 MEMS传感器飞行器姿态解算方法.首先,利用共轭梯度法减小陀螺仪漂移误差,然后,利用加权粒子构造概率密度函数以更新粒子权值,得到优化状态估计值;再将共轭梯度法与修正粒子滤波进行融合,确定加权因子,同时以 STM32与 MEMS传感器为核心设计姿态解算系统.实验结果表明,该方法优化了飞行器静态与动态性能,姿态解算性能良好,系统过渡时间短,跟踪特性较好,且增强了系统的鲁棒性与稳定性.     

用于线性时变系统辨识的固定长度平移窗投影估计递推子空间方法

给出了一个新的用于线性时变参数结构系统模态参数识别的基于固定长度平移窗投影估计的递推子空间方法。首先推得基于平移窗投影估计的子空间跟踪算法,以代替奇异值分解,再推得系统数据矩阵的一阶修正形式,从而得到新的基于平移窗投影估计的递推子空间方法。该方法可有效地降低算法的计算量。最后通过刚度随时间变化的3自由度系统和一具有移动质量的机械臂系统的时变模态频率辨识仿真表明该方法可有效地辨识线性时变系统的伪模态参数。