Modelling Nonlinear Random Vibrations Using an Amplitude-Dependent Autoregressive Time Series Model
本文提出一种振幅依赖自回归模型，能模拟非线性随机振动的振幅依赖频率特性，并用加拿大山猫数据验证了该模型可解释周期性行为背后的自激机制。
The behaviour of nonlinear deterministic vibrations has been studied by many authors, and may typically include such features as jump phenomena and limit cycles. Nonlinear random vibrations in continuous time have also been studied and these may commonly give rise to the phenomenon of amplitude-dependent frequency. A discrete time series model is introduced, which may be demonstrated to have properties similar to those of nonlinear random vibrations. This model is of autoregressive form with amplitude-dependent coefficients and may be estimated using an extension of a method for estimating linear time series models. The model is fitted to the Canadian lynx data and demonstrates that it may be possible to regard the periodic behaviour of this series as being generated by some underlying self-exciting mechanism.