Parameter identification of a class of nonlinear systems with numerical optimization technique

Abstract

A time domain technique for the identification of unknown parameters in the nonlinear system of some given structures is presented. The nonlinearities considered in this paper are in the forms of saturation, deadzone and backlash. The steps of the identification process are first to set the initial or guessed system parameters in a learning model, then apply the recorded input signal of the actual system to the mathematical learning model. By comparing the output errors between the model's and the system's responses, an optimization algorithm can be applied to search for the true parameters of the nonlinear system in order to meet a least mean square error criterion. The computer simulations have demonstrated the feasibility of this numerical technique.     

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.     

未知激励下的无迹卡尔曼滤波新方法

无迹卡尔曼滤波（UKF）是一种识别非线性系统的有效方法,然而传统的UKF方法需要观测外部激励,这限制了UKF的应用范围。迄今为止,国内外对未知激励情况下的UKF方法的研究还非常少。该文在传统UKF的基础上,推导出在未知激励情况下的无迹卡尔曼滤波（UKF-UI）方法的递推公式,通过对观测误差的最小化,利用非线性方程求解,识别未知外部激励,进而识别非线性结构系统状态与结构未知参数。进一步采用融合部分观测的加速度响应及位移响应,消除识别结果的漂移问题。分别通过白噪声和未知地震作用下识别非线性迟滞模型的两个数值算例,考虑观测噪声对非线性系统进行识别,从而验证提出新方法的有效性。结果表明,该文所提出的UKF-UI方法,能够在部分观测结构系统响应的情况下,有效地识别非线性结构参数和未知激励。     

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。     

基于函数连接神经网络的传感器Hammerstein模型辨识研究

针对非线性动态传感器模型辨识问题,提出利用函数连接神经网络算法对非线性系统的Hammerstein模型进行一步辨识的方法。以多项式逼近传感器中的静态非线性环节,同时结合动态线性环节的差分方程,建立关于直接输入输出的离散数据表达式,利用改进FLANN训练求解Hammerstein模型参数。采用变学习因子的方法对FLANN算法进行改进,提高了收敛速率和稳定性。实验结果表明,该辨识方法简单有效且具有更快的收敛速度。     

利用结构化神经网络识别振动系统非线性特性

本文提出了振动系统非线性特性识别的结构化神经网络方法。与传统的前馈神经网络不同的是，该法把系统分为线性和非线性两部分，学习得到的神经网络可以单独识别出系统非线性模型，而不是线性与非线性综合在一起的模型。本文将其应用于振动系统非线性特性的识别。实例表明该方法是可行的。     

基于模糊神经网络的数据融合结构损伤识别方法

为了有效利用结构健康监测系统中的多源传感器数据信息,提高损伤检测与评估的识别正确率,该文通过构造模糊神经网络分类器,提出了一种基于模糊神经网络的数据融合损伤识别方法并将之应用于结构健康诊断中。它先通过数据预处理,提取原始响应信号中的特征参数,接着将之作为模糊神经网络的输入,构造模糊神经网络模型进行识别决策,最后运用数据融合算法,计算出数据融合后的决策结果。为了验证所提方法的有效性,通过一个7自由度的建筑模型,分别用单一模糊神经网络决策器和数据融合损伤识别方法进行了损伤识别和比较。研究结果表明:该文所提方法比单一决策结果更准确、可靠。     

基于前向神经网络的非线性时变系统辨识改进EKF算法

为了克服传统扩展卡尔曼滤波算法进行参数估计时可能产生的新数据失效问题,提出了一种改进的扩展卡尔曼滤波(EKF)步骤,然后将改进步骤做为人工神经网络的学习算法用于基于前向神经网络的非线性时变系统辨识。与传统的扩展卡尔曼滤波步骤相比克服了新数据的饱和现象,可以更好地反映系统时变特征。通过一个单变量一般时变非线性系统和一个三自由度非线性时变刚度结构系统算例,仿真验证了新算法在辨识精度和计算量方面的改进特性。     

基于系统识别理论的磁流变阻尼器模型

磁流变阻尼器(MR damper)是一种新型的半主动结构振动控制装置。只要给该阻尼器输入很小的能量,它就能在极短的时间内(毫秒级)产生很大的力。这种阻尼器的性能可通过一组非线性微分方程来描述,物理参数包括位移、电压和力。给阻尼器输入位移和电压,阻尼器能产生一定的力。基于系统识别理论,采用ARX模型和优化神经网络技术对磁流变阻尼器的性能进行了仿真。训练后的神经网络能分别通过前向模型和反向模型精确地预测磁流变阻尼器的力和电压。把这样的神经网络用于控制系统,还能实现结构的主动控制。     

基于改进最小二乘步骤的NARMA模型辨识非线性时变结构系统

基于时变非线性自回归滑动平均模型利用改进的递推最小二乘算法提出一种用于非线性时变结构系统辨识的方法。利用线性变换将非线性时不变结构系统的动力学模型转化为非线性自回归滑动平均模型,然后将非线性项展开为系统输出数据的多项式的形式。利用短时时不变假设,通过改变模型的参数跟踪系统参数的变化,将非线性时变系统的辨识问题转化为线性时变系统的辨识问题,再利用改进的递推最小二乘算法实现对非线性时变结构系统的辨识。最后通过一个具有非线性时变刚度的三自由度结构系统的仿真算例表明,该方法可以有效地辨识非线性时变结构系统。     

一种非线性振动系统参数辨识模型

本文探讨了一种适用于非线性振动系统参数辨识的模型,并对该模型的建模方法,模型参数估计,模型的相关检验等作了详细叙述,并对模型进行了仿真计算。仿真考核计算表明,该模型具有结构简洁,对输入无限制,计算工作量小等优点。     

基于 ResU-Net 的三维断层识别方法及应用

断层刻画了地层的边界位置,地震成像数据中反射层的不连续性可作为断层解释的主要依据。深度神经网络的强非线性性质可作为地震数据中断层不连续特征表达的有力工具,断层识别问题可视作一个像素级别的二分类问题,并使用深度学习方法对此问题进行建模求解。据此可给出一种端到端的基于深度学习网络的三维断层自动识别方法。首先利用地震子波与反射系数卷积合成多组三维地震数据,建立用于深度网络学习断层特征的样本数据,随后搭建网络进行训练,网络训练完成后应用于实际地震数据。鉴于残差模块可很好地提升网络泛化性能,所提出的将残差网络中的残差块结构引入U-Net中的方法,可用于提升通过合成数据样本训练得到的网络模型在训练数据之外,即实际地震数据上的断层识别性能。所建立网络用于断层解释时,输入为叠后三维地震数据,输出为相同维度的三维数据体,其中每一输出值代表输入三维地震数据相同位置处断层的概率。实际算例对比测试表明,此方法可对三维地震数据中的断层进行有效识别,在合成数据集上训练精度相差不大的前提下,引入残差模块的ResU-Net在实际地震数据上的断层识别泛化性能得到提升。     

基于时变NARMA模型的非线性时变系统辨识

在非线性自回归滑动平均模型NARMA(NonlinearAutoRegressiveMovingAverage)中引入时间变量,将其扩展为时变NARMA模型,用Taylor展开将模型中的非线性函数展开为关于输入输出的多项式,得到关于参数线性时变的多项式形式的时变NARMA模型,再用基序列拟合模型的时变参数得到关于参数线性时不变的模型,最后用递推最小二乘法估计模型参数。仿真算例证明,与小波网络方法相比,辨识精度高,计算量小。     

An advanced algorithm for partitioning and parameter estimation in local model networks and its application to vehicle vertical dynamics

In this paper, advanced concepts for the identification of complex nonlinear systems are discussed. Three major problems are addressed: The nonlinearity of the system, noise in the data upon which the model has to be built, and the potential to incorporate qualitative and quantitative prior knowledge about the system. As an integrated solution approach, local model networks (LMNs) with appropriate parameter estimation schemes are proposed. LMNs generally offer a versatile structure for the identification of nonlinear dynamic systems. In order to account for a realistic situation when noise is present both in input and output data, an equality constrained generalised total least squares algorithm for the local model parameter estimation of the LMN is presented; the incorporation of equality constraints allows to mathematically enforce desired system properties. As an application and benchmark problem, the vertical dynamics of a vehicle is considered. After training the LMN on a rough road, excellent predictions of the behaviour of the vehicle at crossing a single obstacle are obtained, thus proving the effectiveness of the proposed algorithm. It is illustrated how both the application of a proper parameter estimation scheme and the integration of system constraints systematically improve the performance of the model.     

复杂动力学系统计算模型的修改

本文介绍使用输入或输出残量法的数学模型的修改.应用模态转换来减小被修改模型的自由度数,模态转换矩阵由数学模型的低阶模态组成,高阶模态的静力修改被考虑.对于不同的系统,引进相关模态坐标系和不相关的模态坐标系,前者适合于弱模态耦合系统,后者适合于高密度模态系统.在两个模态坐标系中的参数识别过程完全类似于在物理坐标系中的识别过程.     

A general identification technique for nonlinear differential equations of motion

This paper develops and demonstrates by computer simulations new nonlinear system stochastic techniques to determine the amplitude-domain and frequency-domain properties of nonlinear systems as described in nonlinear differential equations of motion. From measurements of input excitation data and output response data, this new method, based upon multiple-input/single-output (MI/SO) linear analysis of reverse dynamic systems, allows for the efficient identification of different nonlinear systems. Nonlinear systems simulated here include Duffing, Van der Pol, Mathieu, and Dead-Band systems. Features of this new method are: (1) it can be implemented using established MI/SO linear procedures and computer programs; (2) it determines nonlinear system amplitude properties separate from nonlinear system frequency properties; (3) it quantifies relative contributions from different nonlinear terms by using appropriate coherence functions; (4) it gives results that are independent of the input or output probability distributions, spectral properties, and input excitation levels.     

Neural networks to model dynamic systems with time delays

An algorithm is proposed to identify a neural network model that represents a nonlinear dynamic system with a multivariate time delay response. The algorithm consists of two major parts. The first one identifies the time delay vector for a given neural network structure. This task is accomplished by using an exhaustive integer enumeration algorithm that minimizes a statistical parameter to assess the performance of the neural network model. The second part uses a cross-validation strategy to identify the best neural network model. Since the structure that models a nonlinear system is usually unknown, the identification strategy consists of selecting several neural network structures and identifying the best time delay vector for each network. The modeling process starts with the simplest structure and progressively the complexity of the network is increased to end up with a complex structure. Finally, the network that offers the simplest structure with the best network performance is the one that exhibits the appropriate neural network structure with the corresponding optimal time delay vector. The Monte Carlo simulation technique was used to test the performance of the algorithm under the presence of linear and nonlinear relationships among several variables of dynamic systems and with a different time delay applied to each input variable. The introduced algorithm is used to detect a chemical reaction delay among enriched amyl acetate, acetic acid, water, and the pH of erythromycin sail. An appropriate neural network model was designed to model the pH of the erythromycin during a continuous extraction process. To the best of the authors knowledge the proposed algorithm is the only one currently available to identify time delay interactions in the multivariate input output variables of a system. The major drawback of the introduced algorithm is that it becomes very slow as the number of system inputs increases. This algorithm works efficiently in a system that involves five inputs or less.     

Linear approximation model network and its formation via evolutionary computation

To overcome the deficiency of ’local model network’ (LMN) techniques, an alternative ’linear approximation model’ (LAM) network approach is proposed. Such a network models a nonlinear or practical system with multiple linear models fitted along operating trajectories, where individual models are simply networked through output or parameter interpolation. The linear models are valid for the entire operating trajectory and hence overcome the local validity of LMN models, which impose the predetermination of a scheduling variable that predicts characteristic changes of the nonlinear system. LAMs can be evolved from sampled step response data directly, eliminating the need for local linearisation upon a pre-model using derivatives of the nonlinear system. The structural difference between a LAM network and an LMN is that the overall model of the latter is a parameter-varying system and hence nonlinear, while the former remains linear time-invariant (LTI). Hence, existing LTI and transfer function theory applies to a LAM network, which is therefore easy to use for control system design. Validation results show that the proposed method offers a simple, transparent and accurate multivariable modelling technique for nonlinear systems.     

基于Wiener-Hammerstein模型的一种系统辨识方法

针对工业大系统中Wiener-Hammerstein模型,提出一种新的辨识方法。该方法结合分散辨识对线性系统辨识精度高的优点与混合粒子群优化解决非线性、不可微和多峰值的复杂问题的长处,进行复合控制,并利用计量学中的动态计量方法,建立动态计量仿真模型。仿真研究与实验结果表明,该方法应用在非线性分布参数系统辨识中可有效提高辨识精度。     

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。