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本文给出一个比较简单的非参数识别方法,用于识别广泛的一类非线性集总参数振动系统的非线性(包括线性,下同)特性。方法的要点是用若干个幂级数来表示系统的非线性特性,然后用回归——最小二乘法确定该幂级数的未知系数。系统各集中质量的加速度、速度和位移的强追响应或自由响应假定为已知。在自由响应的情况下,如果知道系统的总质量,则亦可识别出各个质量的大小。文中通过两个计算实例说明本方法在响应数据中包含噪声干扰时的识别精度。与本领域内目前已知的方法相比,本方法更为通用且简单。
In this paper, a relatively simple non-parametric identification method is given to identify the nonlinear (including linear, same below) characteristics of a wide range of nonlinear systems with lumped parameters. The point of the method is to express the nonlinear characteristic of the system by several power series, and then determine the unknown coefficient of the power series by regression-least squares method. The strong chase or free response of accelerations, velocities and displacements of the concentrated mass systems is assumed to be known. In the case of free response, the size of each mass can also be identified if the total mass of the system is known. In this paper, two examples are given to illustrate the recognition accuracy of this method when noise is included in the response data. This method is more general and simpler than the methods currently known in the art.