一种检测动力系统振动频率的新方法

A NEW APPROACH TO DETECT THE CHARACTERISTIC FREQUENCY OF DYNAMICAL SYSTEMS

为了检测动力系统的振动频率，建立了动力系统的拓扑空间 u 和非平稳正弦函数空间 M．采用拓扑 反变理论把空间 u 映射到已知的空间 M 中，通过拓扑反变算子 f∶u→M 检测未知的空间 u 振动频率．求出 这个反变算子后，通过 Poincaré映射给出该反变算子稳定的存在条件．通过此方法即能够检测出动力系统振 动特征频率的瞬变性，同时该方法具有较强的抗干扰能力．实验测试结果表明该方法是可行的．

To detect the vibration frequency of dynamical systems, the corresponding topology space u and space M were founded. The topology contravariant functor was used to map the unknown space u to the known space M, and the vibration frequency of the unknown space was investigated by the contravariant functor （f： u→M）. After solving the contravariant functor, we studied its stability using the Poincaré map. By this approach the vibration frequency of dynamical systems could be detected , and the approach has strong constraint to noise immunity. The experiments showed the feasibility of the approach.