三轴液压仿真转台非线性多输入多输出QFT控制器设计

三轴液压仿真转台本质上是非线性变参数多输入多输出系统.系统负载、油源压力、增益的变化及耦合作用随速度,加速度的变化造成很大的参数不确定性.针对液压转台提出一种基于SIMULINK模型线性化的多输入多输出非线性定量反馈设计方法.其本质是找到液压伺服系统一系列控制特性最差的运行点,直接用它们的频率响应集合来综合非线性定量反馈控制器.这种方法简化了目前的QFT多输入多输出控制系统设计方法,显示了很大的优越性.文中举例说明这种方法的效果.     

多自由度系统自然激励技术的统一模型

结构运行状态下的模态参数提取是结构健康监测系统需要解决的关键问题之一.自然激励技术的提出为大型复杂工程结构运行状态下的模态参数提取提供了一条新的途径.原始自然激励技术给出了单输入白噪声激励下利用结构位移响应的互相关函数进行模态识别的理论模型,对于多输入情况则缺乏相应的理论模型.本文在单输入理论模型的基础上进一步发展了自然激励技术:推导了多输入独立白噪声激励下多自由度系统结构位移响应的互相关函数的解析公式,并分析了它与单输入情况下互相关函数之间的关系;基于此互相关函数定义了一个新函数,证明它含有结构各阶模态信息,可以表达为一系列衰减正弦函数之和,并且各个组分正弦函数的频率等于各阶模态的有阻尼固有圆频率;提出了以新函数为核心的同时适用于单输入和多输入情况的模态识别算法,建立了自然激励技术的统一模型.     

多尺度法的设解形式之探讨

当采用多尺度法研究非线性振动问题时，经常会遇到不同情形下系统响应的设解形式不同的问题，不同的设解形式得到的结果是否相同，用哪种设解形式更为好一些，在其他文献中尚未见到有关讨论．本文针对一类具有平方和立方非线性项的单自由度和多自由度非线性系统，得到不同设解形式下的一次近似解和二次近似解，并与数值解相比较，发现两种设解形式的近似解与数值仿真解的解曲线吻合的很好，表明传统的各种设解形式在研究弱非线性系统时都有很好的近似性。     

一种辩识多输入多输出振动系统参数的方法

本文讨论的是多输入、多输出串联振动系统传递函数的辩识问题.本文表明:从系统结构来看,多输入、多输出串联振动系统可以化成为多重交叉闭环系统.本文将这类振动系统的传递函数分解成多个二阶子系统.从系统辩识的角度出发,提出了一种通过辩识子系统传递函数,实现对整个系统传递函数辩识的新方法.仿真结果及模型实验结果表明:这种方法是可行的,且具有较高的精度.     

多自由度非线性随机系统的响应与稳定性

响应与稳定性分析一直是随机动力学研究的热点, 发展预测随机响应及判定系统响应性态的方法具有重要的科学意义与广阔的应用前景. 本文综述了有关多自由度非线性随机系统的响应与稳定性的研究. 首先简介用于随机系统响应预测的Fokker-Planck-Kolmogorov方程法、随机平均法、等效线性化法、等效非线性系统法和Monte Carlo模拟法, 评述其优缺点, 进而讨论了多自由度非线性随机系统响应的精确平稳解、近似瞬态解的研究现状. 然后介绍了随机系统稳定性分析的两类方法, 即Lyapunov函数法及Lyapunov指数法,并综述了多自由度非线性随机系统稳定性分析的研究现状. 最后给出几点发展建议.     

链状柔性多体机器人系统动力学研究

本文基于Ｊｏｕｒｄａｉｎ变分原理建立了具有链状拓扑结构柔性多体机器人系统动力学通用模型，用在一致质量有限单元法及正则模态分析基础上引入的模态坐标描述构件的弹性形，用独立坐标描述相邻板件间的大位移运动，每个铰容许１－６个自由度，组强非线性惯性耦合的封闭形式的系统动力学微分方程组，文末对单弹性臂和双弹性臂机器人操作手进行动力学仿真。     

多自由度非线性系统的同伦分析方法

大部分工程实际问题可以用多自由度非线性系统来描述,这些系统的数学模型是许多个耦合的两阶常微分方程.一般地,要精确求解这些方程非常困难,因此可以考虑它们的解析近似解.同伦分析方法是解非线性系统响应的有用工具,本文将它应用于多自由度非线性系统的求解中.利用求两自由度耦合van del Pol振子周期解的实例,展示了同伦分析方法的有效性和巨大潜力.同时,把得到的解析近似解与系统的Runge-Kutta数值解作了比较,结果表明同伦分析方法是求解多自由度非线性系统的有效方法.     

非线性系统参数辩识的一种频域模型

本文基于对非线性系统的可分离性假设，将非线性弹性力和阻尼力分别分解为物理坐标下各点间相对位移和相对速度的幂级数函数，导出了一般多自由度非线性系统在恒幅激励下的广义频率响应函数与输入输出之间的迭代关系式，提出了非线性系统中基本线性部分的概念，进而了一种在实验条件下的系统物理参数辩识方法。     

多输入——多输出实验模态参数识别(3)——频域识别法及其内在联系

本文从文献[1]中所建立的多输入多输出实验模态参数识别的统一模型出发,推导出几种近十几年最常见的多输入多输出实验模态参数频域识别法,阐明了它们之间的内在联系,统一了频域识别技术的理论基础。     

复内积平均法在多自由度非光滑振动系统中的应用

本文以多自由度非光滑非线性振动系统为例，采用复内积的平均法，借助Maple应用程序，完全借助计算机得到了系统在二阶主共振情况下的分岔方程，在给定的一组参数条件下，所得分岔方程的计算结果与原实数平均法、数值法和实验结果吻合较好。为更为普遍的非线性系统用计算机推导解析解提供了一种简便的方法。     

Wavelet basis expansion-based spatio-temporal Volterra kernels identification for nonlinear distributed parameter systems

In practical industries, there are many systems belong to nonlinear distributed parameter systems (DPS); unfortunately, modeling of nonlinear DPS is a challenging task because of the infinite-dimensional and nonlinear properties. To model the nonlinear DPS, a spatio-temporal Volterra model is presented with a series of spatio-temporal kernels. It can be considered as a spatial extension of the traditional Volterra model. One question involved in modeling a spatio-temporal functional relationship between the input and output of nonlinear distributed parameter systems using spatio-temporal Volterra series is to identify the spatio-temporal Volterra kernel functions. In addition, in order to derive a low-order model, the Karhunen–Loève (KL) decomposition is used for the time/space separation. The basic routine of the approach is that, first, from the system outputs, KL decomposition is used for the time/space separation, where the spatio-temporal output is decomposed into a few dominant spatial basis functions with temporal coefficients. Second, according to temporal coefficients of outputs under multilevel excitations, the Volterra series outputs of different orders are estimated with the wavelet balance method. Third, the Volterra kernel functions of different orders are separately estimated through their corresponding Volterra series outputs by expanding them with four-order B-spline wavelet on the interval (BSWI). Finally, the spatio-temporal Volterra model can be reconstructed using the time/space synthesis. The simulation studies verify the effectiveness of the presented identification method.     

单自由度参数振动系统非线性响应的若干特征

用数值积分方法，分析了无阻尼单自由度参数振动系统在给定的单频刚度激励和单频外载荷激振时的非线性动力学响应特性。研究表明了参数振动问题的主要特征：1)单频激励多频响应；2)多频响应中各谐波的分布具有特殊的规律；3)系统具有多频共振特性。     

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density(PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.     

Newton iterative identification method for an input nonlinear finite impulse response system with moving average noise using the key variables separation technique

This paper studies parameter identification problems for input nonlinear finite impulse response systems with moving average noise (i.e., input nonlinear finite impulse response moving average systems). Since the identification model of the system contains the product of the parameters of the nonlinear part and the linear part, we use the key variables separation technique and express the output of the system as the linear combination of all parameters, and then derive a Newton iterative identification method. The simulation results show that the proposed algorithm is effective.     

广义概率密度演化方程的再生核质点加密算法

采用一般质点近似和再生核质点近似表示系统响应量,给出了动力系统响应量的一般表达式。在此基础上,发展了一类求解广义概率密度演化方程的再生核质点加密算法,给出了详细求解步骤。以单自由度系统为例,从响应概率密度的角度考察了再生核质点加密算法的精度。以多自由度框架结构为例,验证了再生核质点加密算法求取非线性随机动力系统响应概率密度的正确性。     

Finite memory quadratic Volterra model for the response prediction of a slender marine structure under a Morison load

A quadratic Volterra model with a finite nonlinear memory effect was introduced and applied to the time series prediction of a slender marine structure exposed to the Morison load. First, the unknown nonlinear single-input–single-output dynamic system was identified using the nonlinear autoregressive with exogenous input (NARX) technique based on the prepared datasets of the wave elevation and system response, which was obtained by running nonlinear time domain analysis for a certain short term sea state. The structure of NARX was designed in such a way that the linear part had infinite memory, whereas the nonlinear part had finite memory of a certain length. Second, the frequency domain Volterra kernels, both linear and quadratic, were derived analytically by applying the harmonic probing method to the identified system. To derive the frequency response functions, the sigmoidal function used in NARX to realize the nonlinear relationship between the input and output was expanded to polynomials based on the Taylor series expansion, so that the harmonics of same frequencies were easily matched between the input and output. Finally, the time series of the system response under arbitrarily given short term sea states were predicted using the quadratic Volterra series. The proposed methodology was used to predict the nonlinear dynamic response of a 2-dimentional free standing catenary riser exposed to a random ocean wave load, and the comparison between the prediction and simulation results was made on the probability distribution of the maximum excursion of riser top. The results show that the proposed methodology can successfully capture the nonlinear effects of the dynamic response of a slender marine structure induced by the quadratic term of the Morison formula.     

一类非线性系统的随机振动频率响应分析研究

Volterra级数是研究非线性系统的一种重要数学工具, 它可看作线性系统理论中的卷积运算在非线性系统分析中的推广. 基于Volterra级数, 给出了受高斯白噪声激励下的非线性系统输出功率谱的计算公式. 公式表明, 该系统输出功率谱可用激励强度的多项式函数来表示, 其结果为研究激励强度对非线性系统输出功率谱的影响提供了有效途径.      

Wavelet basis expansion-based Volterra kernel function identification through multilevel excitations

Volterra series is a powerful mathematical tool for nonlinear system analysis, which extends the convolution integral for linear system to nonlinear system. There is a wide range of nonlinear engineering systems and structures which can be modeled as Volterra series. One question involved in modeling a functional relationship between the input and output of a system using Volterra series is to identify the Volterra kernel functions. In this article, a wavelet balance method-based approach is proposed to identify the Volterra kernel functions from observations of the in- and outgoing signals. The basic routine of the approach is that, from the system outputs under multilevel excitations, the Volterra series outputs of different orders are first estimated with the wavelet balance method, and then the Volterra kernel functions of different orders are separately estimated through their corresponding Volterra series outputs by expanding them with four-order B-spline wavelet on the interval. The simulation studies verify the effectiveness of the proposed Volterra kernel identification method.     

IDENTIFICATION AND PREDICTION OF UNSTEADY TRANSONIC AERODYNAMIC LOADS BY MULTI-LAYER FUNCTIONALS

Nonlinear unsteady aerodynamic effects present major modelling difficulties in the analysis and control of aeroelastic response. A rigorous mathematical framework, that can account for the complex nonlinearities and time-history effects of the unsteady aerodynamic response, is provided by the use of functional representations. A recent development, based on functional approximation theory, has achieved a new functional form; namely, multi-layer functionals. The development of a multi-layer functional for discrete-time, finite memory, causal systems has been shown to be realizable via finite impulse response neural networks. Identification of an appropriate temporal neural network model of the nonlinear transonic aerodynamic response is facilitated via a supervised training process using multiple input–output sets, with data obtained by an Euler CFD code. The training process is based on a genetic algorithm to optimize the network architecture, combined with a random search algorithm to update weight and bias values. The approach is examined for two different multiple aerodynamic input–output data sets, and in both cases, the prediction properties of the network model establish the multi-layer functional as a suitable representation of unsteady aerodynamic response.