中文摘要：

阐述了并联随机共振、混沌振子、差分振子的基本原理和数学模型。并联随机共振利用相关分析从多个随机共振输出结果中提取出相同成分，在一定程度上减小了对参数设置的依赖性。当混沌振子从混沌状态向大尺度周期状态转变时，其相图的Hu氏不变矩值将发生明显的跃变，利用Hu氏不变矩的跃变对混沌振子的状态进行自动定量识别。差分振子相图的大小与待检测信号幅值之间呈现出一种线性比例关系，弥补了差分振子不能检测信号幅值的缺陷。将这三种非线性方法应用于机电设备故障诊断中，成功地提取出了设备早期故障的微弱特征信息，取得了理想的效果。

英文摘要：

The basic theory and mathematic model of parallel stochastic resonance （PSR）, chaotic oscillator and difference res- onance were expounded. The correlation analysis was applied to extract the same components from the output of difference SR in the PSR, thereby reduce the dependence on the system parameters. When the chaotic oscillator changing from chaos state to large-scale periodic state, the Hu moment invariant will have a distinct change. So the nu moment invariant can be used to automatically quantify the phase state of chaotic oscillator. The linear relationship between the phase diagram size and signal amplitude is presented to make up for the shortage that differential oscillator can＇t detect the signal amplitude. Apply- ing the three nonlinear methods to the fault diagnosis of mechanical equipments, the weak feature information of incipient fault was successfully extracted.