弹性体非线性振动系统参数辨识的一种时域法

A Nonlinear Time-domain Method for Parameter Identification and Prediction of Elastomer's Nonlinear Oscillation

提出了对弹性体非线性振动系统参数辨识与预测的一种时域模型法。它可视为时间序列分析中的 AR模型法在非线性领域内的一种推广。该方法首先将非线性振动系统中的非线性恢复力和非线性阻尼力用某一函数级数(例如幂级数 )表示 ,然后 ,先用线性模型来逼近原系统 ,应用线性系统辨识方法确定系统阶次 ,再确定系统中非线性恢复力、阻尼力的结构 ,建立非线性模型并辨识各项参数 ,最后进行预测。算例表明 ,用该方法建立的模型能够较好地反映系统的非线性特性 ,并能提高模型预测的准确性。

Linear methods are usually used in nonlinear oscillation system's parameter identification. But these methods often suffer form many shortcomings. For example, they cannot show the system's nonlinear characteristics. Based on time series methods, this paper presents a new nonlinear method to overcome these shortcomings. First, the existing linearization methods are used to determine the system's order. Then, nonlinear damp force and nonlinear elasticity force are supposed to get the nonlinear differential form of the model; by numericial differential, the nonlinear differential form are dispersed to nonlinear difference form. and the input and output time series are used to predict the coefficient of the nonlinear difference form by direct prediction method. Finally, the difference form are transformed to differential form again, so the parameters of the nonlinear model are identified. this method is applied to a SDOF system and a simply supported beam. The results shown in Figs. 2 to 5 prove that very good approximation is obtained.