磁流变阻尼器参数辨识方法研究

应用修正的Dahl模型,通过能量积分分批识别出不同电流下的参数,确定参数与电流的关系。提出的参数辨识方法,将含有滞迟环节的非线性参数识别转化为线性识别问题,达到了较高的识别精度。     

基于遗传算法的非线性迟滞系统参数识别

研究了非线性迟滞系统的参数识别问题。在识别过程中,将非线性迟滞系统的记忆复力用双折线模型来描述,并由此模型写出非线性迟滞系统的参数识别方程。利用相干函数,把关于模型参数非线性的参数识别方程转化线性参数识别前提下的非线性函数优化问题。     

包装系统非线性特性识别方法

目的建立一种能同时识别包装系统中非线性弹性和非线性阻尼特性的方法。方法首先将单自由度包装系统运动方程式推导为第1类Volterra非线性积分方程式,为在包含噪声的条件下准确求出方程的解,采用Landweber迭代正则化方法求解该积分方程,由于迭代次数对求解结果的准确性有很大的影响,文中采用L曲线准则确定迭代的次数。在求解Volterra方程后,利用方程的解和系统自由响应数据同时识别包装系统非线性弹性和非线性阻尼。结果文中采用一个数字实例验证了该方法的准确性。结论文中提出的方法可有效识别包装系统的非线性特性。     

含铰柔性结构的非线性模态分析

建立了含铰柔性结构的非线性动力学模型,利用打靶法和伪弧长法计算该结构的非线性模态和频率-能量关系图,研究含铰柔性结构的非线性特性。其次,考虑非线性铰链刚度对结构动态特性的影响,讨论了不同线性/非线性刚度与结构的非线性模态及频率-能量曲线的关系。利用非线性三自由度保守系统的模态分析,阐释频率-能量曲线能够直观反映结构的非线性特性:固有频率变化及分叉、模态转换及内共振。对含铰柔性结构的非线性模态分析及参数影响研究表明:1)含铰柔性结构的固有频率与输入能量存在明显非线性特性;2)铰链非线性刚度的增加,使得含铰柔性结构的固有频率和模态在较低的振动能量下即可发生较大变化;其次,随着线性刚度的增加,非线性特性减弱,各阶固有频率的相对变化降低,频率-能量关系图由曲线变为直线;3)较高的振动能量在结构模态之间发生转换,使得结构出现明显的内共振非线性特性。     

对接机构非线性物理参数辨识方法

采用直接参数识别方法(DPE)由系统的输入、输出数据识别空间对接机构的物理参数:惯量矩阵、阻尼矩阵和刚度系数矩阵。首先建立了对接机构简化非线性动力学方程,然后利用系统已知的对称性和非满阵信息将机构的非线性物理方程变形为参数线性的辨识模型,分别采用同时需要位移、速度和加速度数据的DPE方法和只需要位移数据的四阶差分DPE方法识别机构的物理参数。六自由度对接机构仿真算例验证了两种方法的可行性。     

阻尼对耦合非线性能量阱系统影响研究

研究了耦合非线性能量阱的非保守系统的定向能量传递现象。基于复变量平均法推导含有阻尼参数的系统慢变方程,求解出系统能量与各参数近似关系,获得了系统能够实现定向能量传递时阻尼必须满足的条件,并给出了非线性能量阱具有吸振能力时线性振子阻尼有效范围,最后数值分析验证上述研究结果。     

含分层损伤复合材料层合板非线性动力稳定性

采用Reddy 的板高阶剪切变形简化理论研究了含分层损伤复合材料层合板的非线性动力稳定性问题。建立了分层模型, 推导了考虑几何非线性和阻尼效应的Methieu 方程, 给出了该方程的解析解表达式; 研究了参数振动解的稳定性; 然后通过典型数例讨论了分层损伤对层合板固有频率、屈曲临界力以及动力稳定区域的影响; 研究了保守与非保守体系的外载荷的激励频率对层合板第一参数振动的振幅的影响, 以及线性、非线性阻尼对非保守体系的最大牵引深度的影响。由典型算例讨论可知, 随着复合材料层合板分层损伤的扩大, 其动力稳定性能逐渐减弱, 特别是损伤接近层合板的中面时, 分层损伤对其动力稳定性能的影响最大。      

结构分析的非线性模态综合法

本文导出了一种适用于具有分块线性的复杂结构的非线性振动问题的非线性模态综合法。该法以连接各块的非线性元件的变形量为广义坐标,应用各分块构成的线性子系统的模态特性和非线性连接元件的本构关系建立了积分型的综合方程组。为了提高综合精度,方程组中考虑了各子系统的由高阶模态影响所形成的剩余柔度矩阵。由于以连接元件的变形量为广义坐标,使方程的数目与元件数目相同,从而缩小了解题的规模,提高了效率。文中给出了几个典型的应用算例,证明了本文理论的正确性。     

基于离散呼吸子理论的靶能量传递研究

研究了一个具有非线性能量阱的两自由度线性振子耦合系统,确定了其产生靶能量传递的条件和传递频率。建立了无量纲形式的振动方程,利用复变量——平均法推导了保守系统的慢变动力流和哈密顿函数。基于哈密顿力学和相空间中的离散呼吸子理论确定了系统产生靶能量传递的质量比条件和初值条件,并采用椭圆积分计算得到靶能量传递的频率。通过数值仿真验证了有阻尼系统中靶能量传递的不可逆性。     

一种基于离散变分原理的非线性动力系统参数识别方法

提出了一种辨识非线性动力系统模型参数的方法。首先将待辨识参数的导数引入到系统输出误差代价函数中;然后利用离散变分原理导出关于待辨识参数的差分方程,并与系统方程一同求解;最后通过迭代运算使待辨识参数从给定的初值收敛到稳定真值。利用本方法对线性和非线性振动系统的模型参数分别进行了参数识别仿真,数值计算结果证明了方法的有效性。     

Monte Carlo filters for identification of nonlinear structural dynamical systems

The problem of identification of parameters of nonlinear structures using dynamic state estimation techniques is considered. The process equations are derived based on principles of mechanics and are augmented by mathematical models that relate a set of noisy observations to state variables of the system. The set of structural parameters to be identified is declared as an additional set of state variables. Both the process equation and the measurement equations are taken to be nonlinear in the state variables and contaminated by additive and (or) multiplicative Gaussian white noise processes. The problem of determining the posterior probability density function of the state variables conditioned on all available information is considered. The utility of three recursive Monte Carlo simulation-based filters, namely, a probability density function-based Monte Carlo filter, a Bayesian bootstrap filter and a filter based on sequential importance sampling, to solve this problem is explored. The state equations are discretized using certain variations of stochastic Taylor expansions enabling the incorporation of a class of non-smooth functions within the process equations. Illustrative examples on identification of the nonlinear stiffness parameter of a Duffing oscillator and the friction parameter in a Coulomb oscillator are presented. This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

系统非线性参数识别的松驰法

研究了非线性参数系统模型的识别问题,通过引入求解线性方程的松驰法思想,构造了一类新的迭代识别算法。算例表明此方法具有很好的参数识别精度,并且具有概念清楚,易于编程等特点,为非线性系统模型参数的识别问题提供了新的思路。     

An adaptive algorithm for nonlinear system identification

There are several methods — fixed, adaptive, recursive — for the identification of linear and bilinear systems from input-output measurements that are noisy. However, literature is rather scarce as far as such techniques are concerned for the identification of nonlinear systems. The objective of this paper, therefore, is to suggest an iterative technique for the identification of nonlinear system parameters from measurements that are noisy. This technique requires the transformation of a nonlinear system in the state variable form into an input-output autoregressive moving average exogenous (armax) model. The pseudo linear regression algorithm, which has been extensively used for the identification of linear systems, can then be used to identify the nonlinear system parameters. Using this technique simulation studies were carried out which, indeed, confirm the efficacy of the method.     

多个关键部件产品的破损边界

目的 得到矩形冲击下具有多个关键部件产品的破损边界，并分析破损边界在线性和非线性（正切型和双曲正切型）情况下的变化规律以及影响因素。方法 首先，使用集中质量法建立多自由度离散包装系统模型；然后，运用牛顿第二定律推导系统动力学方程，经无量纲处理后获得系统的无量纲动力学方程；最后，应用四阶龙格库塔法进行求解，获得系统的动力学响应，得到破损边界。结果 相较于线性包装材料，双曲正切型缓冲包装材料可以扩大包装件的非破损区，而正切型缓冲包装材料则相反，且影响程度与非线性参数成正比；在特定情况下，不同关键部件的破损边界曲线存在相交情况。结论 不同类型的冲击会导致不同关键部件的破损，实际物流过程中要考虑所有关键部件的保护。     

A closed form solution for linear and nonlinear free vibrations of composite and fiber metal laminated rectangular plates

In this paper, the nonlinear equations of motion for laminated composite rectangular plates based on first order shear deformation theory, which include shear deformation and rotary inertia, have been derived. Then, through introducing a force function, these equations reduced to a set of coupled nonlinear partial differential equations and a compatibility equation. By using the Galerkin method, for the first time, a nonlinear ordinary differential equation is obtained, which includes nonlinear inertia and stiffness terms. By using the multiple time scales method, analytical relations for nonlinear frequency and transverse displacement have been obtained. Results are compared with the literature and good agreement is achieved for both linear and nonlinear frequencies. After proving the validity of our work for isotropic rectangular plates and laminated rectangular plates, linear and nonlinear free vibration of a Fiber Metal Laminate panel have been investigated. Also the effects of some system parameters on the nonlinear frequency have been investigated.     

有限维线性系统参数辨识问题

本文考虑一维输入输出有限维线性系统参数辨识问题。该问题源于电机系统的参数辨识。首先我们对简单参数形式的线性时不变动态系统,给出了一种精确辨识方法,并给出了这种辨识方法的误差界。这种方法能够保证辨识出的参数是最佳的；而且不用求解对应的非线性最小二乘问题,只需求一元多项式的根,从而大大减少计算量。接着我们考虑了复合参数形式的线性时变系统参数辨识问题,给出了一种近似辨识方法,并导出了该方法的误差界；该方法本质是通过求解非线性最小二乘问题来辨识参数。对于测量存在误差、误差服从区间分布的线性系统,我们给出了其等价的确定性问题,并给出了几个算例。计算结果表明,本文给出的参数辨识方法是有效的。     

Nonlinear random vibration analysis: A Bayesian nonparametric approach

Random vibration analysis aims to estimate the response statistics of dynamical systems subject to stochastic excitations. Stochastic differential equations (SDEs) that govern the response of general nonlinear systems are often complicated, and their analytical solutions are scarce. Thus, a range of approximate methods and simulation techniques have been developed. This paper develops a hybrid approach that approximates the governing SDE of nonlinear systems using a small number of response simulations and information available a priori. The main idea is to identify a set of surrogate linear systems such that their response probability distributions collectively estimate the response probability distribution of the original nonlinear system. To identify the surrogate linear systems, the proposed method integrates the simulated responses of the original nonlinear system with information available a priori about the number and parameters of the surrogate linear systems. There will be epistemic uncertainty in the number and parameters of the surrogate linear systems because of the limited data. This paper proposes a Bayesian nonparametric approach, called a Dirichlet Process Mixture Model, to capture these uncertainties. The Dirichlet process models the uncertainty over an infinite-dimensional parameter space, representing an infinite number of potential surrogate linear systems. Specifically, the proposed method allows the number of surrogate linear systems to grow indefinitely as the nonlinear system observed dynamic unveil new patterns. The quantified uncertainty in the estimates of the unknown model parameters propagates into the response probability distribution. The paper then shows that, under some mild conditions, the estimated probability distribution approaches, as close as desired, to the original nonlinear system’s response probability distribution. As a measure of model accuracy, the paper provides the convergence rate of the response probability distribution. Because the posterior distribution of the unknown model parameters is often not analytically tractable, a Gibbs sampling algorithm is presented to draw samples from the posterior distribution. Variational Bayesian inference is also introduced to derive an approximate closed-form expression for the posterior distribution. The paper illustrates the proposed method through the random vibration analysis of a nonlinear elastic and a nonlinear hysteretic system.     

《橡胶隔振移动硬盘非线性系统的冲击研究》

在橡胶隔振移动硬盘构成的非线性系统中引入了频率硬化系数,建立了非线性振动微分方程,并构造了相应的仿真计算模型。使用该模型计算了具有不同脉冲加速度幅值和脉冲时间宽度的冲击响应,分析并讨论了脉冲信号参数对隔振效果的影响。理论分析与数值模拟表明：与传统的线性振动模型相比,引入频率硬化系数的橡胶隔振模型更符合实际,且具有良好的冲击响应。仿真模型简单,计算方便,可以用于快速确定非线性隔振系统的固有频率。     

Estimating parameterized scalable models from the best linear approximation of nonlinear systems for accurate high-level simulations

System designers of communication systems need to compare the simulated behavior of a system with the linear and nonlinear specifications. They need high-level models to perform these simulations fast. The existing high-level models for nonlinear components do not scale smoothly with external parameters like the input power. To overcome this problem, a modeling technique based on the best linear approximation is developed. The parameterized models describe trajectories of the poles and zeros as a function of the input power. The resulting models accurately describe both the linear and nonlinear behavior of the system components. They can easily be implemented in modern simulators.