A modular formulation for flexible multibody systems including nonlinear finite elements

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) appioach Several aspects that turned out to be crucial for the presented approach are discussed The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist In this paper the performance of several solvers is investigated regarding then suitability for the application to the usually highly stiff DAE The substructures are connected with each other by nonlinear algebraic constraint equations Furthet, partial derivatives of the constraints are tequired, which often leads, to extensive algebraic transfoimations Handcoding of analytically determined derivatives is compared to an appioach utilizing algouthmic differentiation

     

Walking pattern generation employing DAE integration method

A stable walking pattern generation method for a biped robot is presented in this paper In general, the ZMP (zero moment point) equations, which are expressed as differential equations, are solved to obtain a stable walking pattern However, the number of differential equations is less than that of unknown coordinates in the ZMP equations It is impossible to integrate the ZMP equations directly since one or more constraint equations are involved in the ZMP equations To overcome this difficulty, DAE (differential and algebraic equation) solution method is employed The proposed method has enough flexibility for various kinematic structures Walking simulation for a virtual biped robot is performed to demonstrate the effectiveness and validity of the proposed method The method can be applied to the biped robot for stable walking pattern generation     

System identification of two-dimensional continuous-time systems using wavelets as modulating functions

In this paper, parameter identification of two-dimensional continuous-time systems via two-dimensional modulating functions is proposed. In the proposed method, trigonometric functions and sine-cosine wavelets are used as modulating functions. By this, a partial differential equation on the finite-time intervals is converted into an algebraic equation linear in parameters. The parameters of the system can then be estimated using the least square algorithms. The underlying computations utilize a two-dimensional fast Fourier transform algorithm, without the need for estimating the unknown initial or boundary conditions, at the beginning of each finite-time interval. Numerical simulations are presented to show the effectiveness of the proposed algorithm.     

一类带冗余支链并联机器的运动学自标定

利用冗余支链测量信息,对一类带冗余支链并联机器的运动学参数进行自标定。通过矢量闭环微分法,建立冗余支链运动学误差模型,并通过多个位姿处误差传递矩阵的组合,得到自标定的辨识雅可比矩阵。针对部分运动学参数误差辨识性差的问题,提出一种基于辨识雅可比矩阵各列线性相关性分析的辨识性分析方法,得到可辨识的运动学参数误差线性耦合式,并简化误差辨识方程使辨识性提高。最后利用冗余支链角度编码器测量信息,完成一个4RRR冗余并联机器的运动学自标定,仿真结果显示,基于冗余支链的运动学自标定能有效提高冗余支链和机构终端运动精度。     

Three-dimensional static solutions of rectangular plates by variant differential quadrature method

An endeavor to exploit three-dimensional elasticity solutions for bending and buckling of rectangular plates via the differential quadrature (DQ) and harmonic differential quadrature (HDQ) methods is performed. Unlike other works, the priority of this paper is to examine the computational characteristics of the two methods; therefore, we focus our studies only on the simply supported and clamped rectangular plates. To start with, we first outline the basic equations and boundary conditions describing the bending and buckling of rectangular plates followed by normalizing and discretizing them according to the DQ and HDQ algorithms. The resulting algebraic equation systems are then solved to obtain the solutions. Based on these solutions, the computational characteristics of the DQ and HDQ methods are investigated in terms of their numerical performances. It is found that the DQ method displays obvious superior convergence characteristics over the HDQ method for the three-dimensional static analysis of rectangular plates.     

基于DAE-HTPF的新能源汽车电池剩余寿命预测

针对反映锂电池寿命的趋势性特征自学习与电池剩余寿命预测问题,提出了基于降噪自编码器（denoising auto-encoder,DAE）与混合趋势粒子滤波（hybrid trend particle filter,HTPF）的电池剩余寿命预测方法。利用电池使用前期的信号特征训练DAE,然后将使用中后期的电池信号特征输入DAE中,并提取重构误差。另外,利用HTPF方法对电池生命周期内的信号特征进行分析,建立自适应状态方程。分析结果表明,该方法能有效地对锂电池的性能退化趋势性特征进行自提取,从而有效地减少人为因素的干扰,同时相比于传统粒子滤波（particle filter,PF）,HTPF对电池剩余寿命预测精度更高。      

线性时滞系统区域极点配置的数值方法

介绍了一种应用于线性时滞系统的区域极点配置的数值方法,它实质上是应用于线性定常无时滞系统的传统极点配置方法的推广应用.由于时滞系统的特征方程是超越方程,故有无穷多个特征值.该方法的目标是通过进行数值方法的不断迭代,来不断整合反馈增益阵,最终把最右端的一批极点配置到指定的区域中去.通过引入对带有输入迟延和状态迟延的线性系统进行配置的实例来对这一方法进行说明.实践证明,该配置方法能取得较好的配置效果.     

Differential algebraic method for aberration analysis of typical electrostatic lenses

In this paper up to fifth-order geometric and third-order chromatic aberration coefficients of typical electrostatic lenses are calculated by means of the charged particle optics code, COSY INFINITY, based on the differential algebraic (DA) method. A two-tube immersion lens and a symmetric einzel lens have been chosen as two examples, whose axial potential distributions are numerically calculated by a FORTRAN program using the finite difference method. The DA results are in good agreement with those evaluated by the aberration integrals in electron optics. The DA method presented here can easily be extended to aberration analysis of other numerically computed electron lenses, including magnetic lenses.     

各种板边条件下大挠度圆板自由振动的分岔解

计及几何非线性,在各种板边条件下,建立圆板自由振动的非线性动力学方程.采用Galerkin法,将圆板的非线性动力学偏微分方程简化成三种标准类型的Duffing方程.提出一类强非线性动力系统的两项谐波法,将描述动力系统的二阶常微分方程,化为以频率、振幅为变量的非线性代数方程组,考虑初始条件补充约束方程,构成频率、振幅为变量的封闭非线性代数方程组.利用Maple程序可以方便地求解.结果表明,两项谐波法不仅适合于对称振动问题,而且适合于非对称振动问题.     

偏微分方程与微分代数方程的一致求解方法

Modelica 语言是一种复杂物理系统多领域统一建模语言,但目前该语言只能解决由微分代数方程（DAE）描述的问题,而不能解决由偏微分方程（PDE）表达的问题。为此,提出一种偏微分方程与微分代数方程的一致求解方法,利用所构建的径向基函数配点无网格法直接将偏微分方程在空间上离散成一系列的微分代数方程,然后采用成熟的微分代数方程求解器进行求解。实例结果表明,该方法在不改变 Modelica 语法的前提下,能较好地实现偏微分方程与微分代数方程的一致求解,且求解精度高、边界条件处理简单,有利于Modelica直接求解复杂工程系统中多领域耦合、时间域与空间域耦合的复杂问题。     

脉冲激励振动问题的高精度数值分析

利用数值稳定性好、计算精度高的重心Lagrange插值近似未知函数,得到未知函数各阶导数的微分矩阵,提出高精度数值分析任意激励下振动问题的重心插值配点法.采用附加法施加初始条件,得到一个n+2个方程n个未知量的代数方程组.利用最小二乘法求解线性方程组,得到振动位移,进而利用微分矩阵直接求得振动的速度和加速度.对于脉冲激励等复杂激励下的振动问题,将前一个时间区域末的位移和速度作为下一个时间区域的初始条件,分段进行数值分析.数值算例表明重心插值配点法在分析脉冲激励下的振动问题,具有非常高的计算精度.     

Eigenstructure assignment by the differential Sylvester equation for linear time-varying systems

This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control continues to be a major focus of research efforts. Scheduling of frozen-time, frozen-state controllers for fast time-varying dynamics is known to be mathematically fallacious and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, we i) introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ii) propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic. The scheme can be used to determine the stability of linear time-varying systems easily as well as to provide a new horizon of designing controllers for linear time-varying systems. The presented method is illustrated by a numerical example.     

A High-Precision Circular Helicoidal Surface Meshing Model for Producing High-Performance Lead Screws

This paper presents a new circular helicoidal surface meshing model for producing high transmission performance lead screws. The formulation of the meshing model includes the analytical derivation of the helicoidal surface equation and the profile equations of revolving and non-revolving conjugate elements. These surface profile equations are derived and presented using several different theories and techniques including coordinate transformation, differential geometry and meshing principles. Since the meshing model is constructed systematically by rigorous differential geometry and meshing theories instead of the simple techniques of analytical geometry, the lead screw model thus built can lead to better transmission quality and higher system performance. In order to verify the effectiveness of the proposed models and the systematic modelling procedure, the performance of the system is evaluated numerically by three major indices including the transmissivity index, the manipulability index and the lubrication angle. The results obtained by using the proposed modelling procedure are also verified by experimental data taken directly from a sample product produced on an NC machine using the proposed theory. The comparative study further indicates that the proposed circular helicoidal surface meshing model presented in this paper is accurate and efficient. The proposed theory and performance indices presented in this paper can thus be used to design for various high transmission performance lead screw systems.     

System identification with measurement noise compensation based on polynomial modulating function for fractional-order systems with a known time-delay

This study presents a system identification method based on polynomial modulating function for fractional-order systems with a known time-delay involving input and output noises in the time domain. Based on the polynomial modulating function and fractional-order integration by parts, the identified fractional-order differential equation is transformed into an algebraic equation. By using the numerical integral formula, the least squares form for the system identification is obtained. In order to reduce the effect of noises existing in the input and output measurements, the compensation method for the input and output noises is also studied by introducing an auxiliary high-order fractional-order system in the revised identification algorithm. Finally, the effectiveness of the proposed algorithm is verified by the simulation result of an illustrative example and the experimental result of temperature identification for a thermal system.     

用于连续体的间隙非线性参数辨识方法

间隙在机械系统中是不可避免的,由间隙引起的接触非线性会严重影响系统的动态响应,使其偏离理想状态,进而降低机械系统的性能和使用寿命。若能利用系统的动态信息识别出间隙非线性参数,就能为机械系统的间隙控制提供依据。针对含间隙连续体系统,提出一种改进的恢复力-位移曲线和条件逆向路径法相结合的间隙非线性参数辨识方法。将哈密尔顿原理推导得到的微分方程简化为空间缩减模型,在获取系统输入和输出的基础上,使用改进的恢复力-位移曲线方法识别连续体系统的间隙值,再利用条件逆向路径法识别间隙接触刚度。整个识别过程在Matlab软件中进行仿真,并在设计的含间隙悬臂梁试验台上进行了参数辨识试验,仿真和试验结果均显示了较高的识别精度,验证了该方法的有效性。     

Data processing in subspace identification and modal parameter identification of an arch bridge

A data-processing method concerning subspace identification is presented to improve the identification of modal parameters from measured response data only. The identification procedure of this method consists of two phases, first estimating frequencies and damping ratios and then extracting mode shapes. Elements of Hankel matrices are specially rearranged to enhance the identifiability of weak characteristics and the robustness to noise contamination. Furthermore, an alternative stabilisation diagram in combination with component energy index is adopted to effectively separate spurious and physical modes. On the basis of identified frequencies, mode shapes are extracted from the signals obtained by filtering measured data with a series of band-pass filters. The proposed method was tested with a concrete-filled steel tubular arch bridge, which was subjected to ambient excitation. Gabor representation was also employed to process measured signals before conducting parameter identification. Identified results show that the proposed method can give a reliable separation of spurious and physical modes as well as accurate estimates of weak modes only from response signals.     

Explicit motion of dynamic systems with position constraints

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier’s method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss’s principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.     

A new weighting function for solving nonlinear oscillation problems

A new approximation technique is presented for solving nonlinear oscillation problems. A solution of form x = x₀ sin ωt is assumed and put into the differential equation, which leads to an algebraic equation which can be solved for ω in terms of x₀. The new technique is to reduce the algebraic equation to an identity at ωt = π/3. This method is compared with other common approximation techniques and with the exact solution for several nonlinear problems. Overall, the new method works better than any other approximation technique. In addition, it has the very practical advantage of being purely algebraic; no integrals need be evaluated, as in several other methods.     

微分变换法在动力学响应分析及系统边界参数识别中的应用研究

引入求解非线性微分方程的微分变换法，将其推广为广义微分变换法。建立求解一般非线性振动微分方程的一般框架，将此方法用于求解著名的Vander pol方程。并且将微分变换法推广到结构边界参数识别，以一个典型的悬臂梁边界参数识别为例，对其进行数值仿真和实验研究，并将此方法的实验研究识别结果与用实测频率响应函数法的识别结果作比较。说明该方法具有良好的工程应用价值。