Dynamic Modeling and Experimental Validation of a 3-PRR Parallel Manipulator with Flexible Intermediate Links

This paper presents the development of structural dynamic equations of motion for a 3-PRR parallel manipulator with three flexible intermediate links, based on the assumed mode method. Lagrange’s equation is used to derive the dynamic model of the manipulator system. Flexible intermediate links are modeled as Euler–Bernoulli beams with pinned–pinned boundary conditions. Dynamic equations of motion of a 3-PRR parallel manipulator with three flexible links are developed by adopting the assumed mode method. The effect of concentrated rotational inertia at both ends of intermediate links is included in this model. Numerical simulations of vibration responses, coupling forces and inertial forces are presented. The corresponding frequency spectra analysis is performed using the Fast Fourier Transform (FFT). Experimental modal tests are performed to validate the theoretical model through comparison and analysis of modal characteristics of the flexible manipulator system.     

Convergence of self-tuning Riccati equation with correlated noises

For the linear discrete time-invariant stochastic system with correlated noises,and with unknown model parameters and noise statistics,substituting the online consistent estimators of the model paramet...     

一类非线性船舶在随机波上的倾覆概率仿真

研究一类非线性船舶在随机波上的倾覆概率仿真。船舶在给定随机波上的、直到颠覆的大幅度横摇可用一个四元非线性方程表示;假定噪声为白噪声的情况下,该方程通过转化可被改写成对应的二阶随机微分方程;基于半离散数值解法,设计了一类非线性船舶在随机波上的倾覆概率仿真算法,该方法简单,易于工程应用;给出实例演示了方法的应用,验证了算法的有效性。     

Parameter identification of distributed parameter systems in the presence of measurement noise

A new approach to recursive parameter identification of second-order distributed parameter systems in the presence of measurement noise under unknown initial and boundary conditions is proposed. A two-dimensional low-pass filter is introduced to pre-filter the observed data corrupted by measurement noise. The low-pass filter is designed in the continuous time-space domain and discretized by bilinear transformation. Thus a discrete estimation model of the system under study is easily constructed with filtered input-output data for recursive identification algorithms. The recursive least squares method is still efficient in the presence of low measurement noise if the filter parameters are designed so that the noise effects are reduced sufficiently. Using filtered input data as instrumental variables, a recursive instrumental variable method is also presented to obtain consistent estimates when the digital low-pass filters are not designed successfully or when the output data is corrupted by high measurement noise. Illustrative examples are given to demonstrate the applicability of the proposed methods.     

Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMAX systems

An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein–Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. Two methods of separating the parameter estimates of the original parameters from the product terms are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is presented. The simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor.     

Model updating of multistory shear buildings for simultaneous identification of mass,stiffness and damping matrices using two different soft-computing methods

In this research, two novel methods for simultaneous identification of mass–damping–stiffness of shear buildings are proposed. The first method presents a procedure to estimate the natural frequencies, modal damping ratios, and modal shapes of shear buildings from their forced vibration responses. To estimate the coefficient matrices of a state-space model, an auto-regressive exogenous excitation (ARX) model cooperating with a neural network concept is employed. The modal parameters of the structure are then evaluated from the eigenparameters of the coefficient matrix of the model. Finally, modal parameters are used to identify the physical/structural (i.e., mass, damping, and stiffness) matrices of the structure. In the second method, a direct strategy of physical/structural identification is developed from the dynamic responses of the structure without any eigenvalue analysis or optimization processes that are usually necessary in inverse problems. This method modifies the governing equations of motion based on relative responses of consecutive stories such that the new set of equations can be implemented in a cluster of artificial neural networks. The number of neural networks is equal to the number of degree-of-freedom of the structure. It is shown the noise effects may partially be eliminated by using high-order finite impulse response (FIR) filters in both methods. Finally, the feasibility and accuracy of the presented model updating methods are examined through numerical studies on multistory shear buildings using the simulated records with various noise levels. The excellent agreement of the obtained results with those of the finite element models shows the feasibility of the proposed methods.     

基于模糊ARMAX模型的模糊建模

提出了一种利用MGS(modified Gram-Schmidt)算法建立模糊ARMAX模型的方法, 给出了基于MGS算法的模型结构和参数辨识的一体化方法. 利用MGS正交变换对通过GK模糊聚类的聚类结果进行变换, 确定对模型贡献大的规则, 删除对模型贡献小的规则, 同时对模型中的参数进行估计. 本文提出的方法能够实现模糊模型的结构和参数的优化. 仿真结果表明, 本文提出的方法能够建立非线性系统的模糊ARMAX模型.     

一种变步长CMAC的沉降NARMAX模型*

为了提高氧化铝生产质量和降低能耗,本文分析了氧化铝沉降工艺中影响沉降过程的各种因素,采用小脑模型神经网络(CMAC)系统辨识的方法建立沉降系统的带外部输入的自回归滑移模型(ARMAX)。针对CMAC收敛性存在的问题,提出了基于变步长小脑模型神经网络(CMAC)算法,通过双曲正割函数优化学习步长,提高了小脑模型神经网络算法的收敛速度和计算精度,进而优化了沉降槽密度ARMAX模型。仿真实验表明,该算法的ARMAX模型可以对沉降过程中的槽内密度进行准确识别,指导氧化铝的沉降生产操作。     

基于积分方程的连续模型辨识与仿真

大多数实际物理系统的模型本质上是连续的，连续时间模型为物理系统的行为提供了更好的解释。提出了一种采样数据中存在高频有色噪声的连续模型辨识方法，该方法通过引入积分运算，将连续时间系统的微分方程模型转换为积分方程模型，从而使噪声的影响可以忽略，然后直接利用传统的最小二乘法估计出系统的连续时间模型参数。该方法具有较强的抗有色噪声干扰的鲁棒性、计算方法简单、参数辨识精度高等优点。仿真实例验证了该方法的有效性和可行性。     

Spectral density based estimation of continuous‐time ARMAX process parameters

The continuous‐time ARMAX model is a standard model that can be used for describing continuous‐time stochastic dynamic systems for control purposes. In this note, the problem of estimating the parameters in such a model from discrete‐time data is considered. In the proposed solution, the parameters in the denominator polynomial are estimated using a continuous‐time Yule‐Walker equation. Thereafter, the parameters in the numerator polynomials are estimated using an approach based on the spectral density of the output signal and regularized least squares. The method is sub‐optimal but easy to apply and the given estimates can be used directly or as initial values for the maximum likelihood method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于偏差消除最小二乘估计和Durbin方法的两阶段ARMAX参数辨识

针对带有外生变量的自回归移动平均模型(Autoregressive moving average with exogenous variable, ARMAX)的参数辨识问题提出一种两阶段辨识方法. 首先通过偏差消除最小二乘方法辨识带有外生变量的自回归部分(Autoregressive part with exogenous variable, ARX),然后采用Durbin方法将移动平均部分(Moving average, MA)的参数辨识问题转换成一个长自回归模型(Long autoregressive, LAR)的参数辨识问题, 并利用MA与等价LAR的参数对应关系直接得到MA参数, 最后利用辨识出的MA参数计算出噪声方差. 与扩展最小二乘法的数值仿真比较验证了这种两阶段辨识方法的有效性.     

基于输出误差模型优化的甲板运动预报算法研究

本文提出了一种适用于多种复杂海况的大型舰船甲板运动预报方法,目的在于提高算法对不同海域复杂海况的适用性,以及对甲板运动模型的辨识精度与预报精度。该方法通过将量测数据的时间滞后处理引入输出误差模型来描述甲板运动的动力学模型,引入定阶准则确定了模型最优阶数数对。在此基础上应用了辅助模型递推最小二乘算法进行系统参数辨识并估计输出误差模型中的状态变量。实验结果表明,本文所提出的预报方法在系统参数辨识阶段可以将递推最小二乘算法的辨识精度提高5.13%,并且在预报阶段可以有效地将甲板运动的幅值与相位预测精度提高3.17%。该方法在复杂海况下具备良好的预测性能,适用于大型舰船甲板运动预报。     

不确定多传感器系统鲁棒观测融合Kalman 预报器

对于带不确定模型参数和噪声方差的线性离散时不变多传感器系统, 用虚拟噪声补偿不确定参数, 系统转化为仅带噪声方差不确定性的多传感器系统. 用加权最小二乘法和极大极小鲁棒估计准则, 基于带噪声方差保守上界的最坏情形保守系统, 提出一种鲁棒加权观测融合稳态Kalman 预报器, 并应用Lyapunov 方程方法证明了它的鲁棒性, 同时给出了与鲁棒局部和集中式融合Kalman 预报器的精度比较. 最后通过一个仿真例子说明了如何搜索参数扰动的鲁棒域, 并验证了所提出的理论结果的正确性和有效性.

     

含间隙齿轮碰振系统的全局动力学分析

为研究含间隙齿轮碰振系统的全局及周期运动的稳定性及分岔条件,建立了齿轮副主动轮的单自由度非线性动力学模型.运用非光滑系统Melnikov理论研究齿轮系统异宿轨道全局分岔条件,然后,求得各分段系统的通解,再将每个切换面作为Poincaré截面,运用组合映射的方法分析系统的周期运动特性.最后通过数值模拟,得到不同参数条件下系统的运动状态和分岔特性,验证了Melnikov方法分析齿轮非光滑系统的有效性.     

System Identification Methods for (Operational) Modal Analysis: Review and Comparison

Operational modal analysis deals with the estimation of modal parameters from vibration data obtained in operational rather than laboratory conditions. This paper extensively reviews operational modal analysis approaches and related system identification methods. First, the mathematical models employed in identification are related to the equations of motion, and their modal structure is revealed. Then, strategies that are common to the vast majority of identification algorithms are discussed before detailing some powerful algorithms. The extraction and validation of modal parameter estimates and their uncertainties from the identified system models is discussed as well. Finally, different modal analysis approaches and algorithms are compared in an extensive Monte Carlo simulation study.     

Affine Reconstruction from Translational Motion under Various Autocalibration Constraints

In this paper algorithms for affine reconstruction from translational motion under various auto calibration constraints are presented. A general geometric constraint, expressed using the camera matrices, is derived and this constraint is used in a least square solution to the problem. Necessary and sufficient conditions for critical motions are derived and shown to depend on the knowledge of the intrinsic parameters of the camera. Experiments on simulated data are performed to evaluate the noise sensitivity of the algorithms and the reconstruction quality for motions close to being critical. An experiment is performed on real data to illustrate that the method works in practice.     

A structural defect identification approach based on a continuum damage model

This paper introduces a structural identification technique built on finite element (FE) model updating. The FE model is parameterized by a structural parameter that continuously describes the damage in the structure, and besides, an evolution equation of this damage parameter is presented. The model updating is accomplished by determining the subset of this damage parameters that minimizes a global error derived from the dynamic residue vectors, which is obtained by introducing the experimental modal properties into the original model eigenproblem. A mode-shape projection technique is used in order to achieve compatibility between the dimension of the experimental and analytical models. The adjusted model maintains basic properties of the analytical model as the sparsity and the symmetry, which plays an important role in model updating-based damage identification. The verification and assessment of the current structural defect identification is performed on a analytically derived bidimensional truss structure and on a cantilever bidimensional Euler–Bernouilli beam through a virtual test simulator. This simulator is used to realistically simulate the corrupting effects of noise, filtering, digital sampling and truncation of the modal spectrum. The eigensystem realization algorithm along with the common-based normalized system identification were utilized to obtain the required natural frequencies and mode shapes.     

线性时变反馈系统的状态空间模型和模态参数递推辨识

针对闭环系统中时变状态空间模型和模态参数的辨识问题, 提出一种递推辨识格式, 将这种格式与递推子空间方法结合, 得到一种辨识方法. 该方法通过重建输入输出数据之间的关系, 递推辨识得到闭环系统的时变状态空间模型和模态参数. 算例研究了系统在模态参数突变和周期变化两种情况下的辨识问题, 仿真结果表明, 所提出算法能有效辨识线性时变反馈系统的状态空间模型和模态参数.

     

Modeling of flexible-link manipulators with prismatic joints

The axially translating flexible link in flexible manipulators with a prismatic joint can be modeled using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, we present a nondimensional form of the Euler-Bernoulli beam equation using the concept of group velocity and present conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions lead to a time-dependent frequency equation for the translating flexible beam. We present a novel method to solve this time-dependent frequency equation by using a differential form of the frequency equation. We then present a systematic modeling procedure for spatial multi-link flexible manipulators having both revolute and prismatic joints. The assumed mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. We show, using a model-based control law, that the closed-loop dynamic response of modal variables become unstable during retraction of a flexible link, compared to the stable dynamic response during extension of the link. Numerical simulation results are presented for a flexible spatial RRP configuration robot arm. We show that the numerical results compare favorably with those obtained by using a finite element-based model.     

Transfer matrix method for linear multibody system

A new method for linear hybrid multibody system dynamics is proposed in this paper. This method, named as transfer matrix method of linear multibody system (MSTMM), expands the advantages of the traditional transfer matrix method (TMM). The concepts of augmented eigenvector and equation of motion of linear hybrid multibody system are presented at first to find the orthogonality and to analyze the responses of the hybrid multibody system using modal method. If using this method, the global dynamics equation is not needed in the study of linear hybrid multibody system dynamics. The MSTMM has a small size of matrix and higher computational speed, and can be applied to linear multi-rigid-body system dynamics, linear multi-flexible-body system dynamics and linear hybrid multibody system dynamics. This method is simple, straightforward, practical, and provides a powerful tool for the study on linear hybrid multibody system dynamics. This method can be used in the following: (1) Solve the eigenvalue problem of linear hybrid multibody systems. (2) Obtain the orthogonality of eigenvectors of linear hybrid multibody systems. (3) Realize the accurate analysis of the dynamics response of linear hybrid multibody systems. (4) Find the connected parameters between bodies used in the computation of linear hybrid multibody systems. A practical engineering system is taken as an example of linear multi-rigid-flexible-body system, the dynamics model, the transfer equations and transfer matrices of various bodies and hinges; the overall transfer equation and overall transfer matrix of the system are developed. Numerical example shows that the results of the vibration characteristics and the response of the hybrid multibody system received by MSTMM and by experiment have good agreements. These validate the proposed method.