指向Lyapunov指数及其在单输入单输出系统故障检测中的应用

Directional Lyapunov exponent and its application to fault detection of the single input single output system

针对单输入单输出系统的故障检测，采用混沌振荡器作为激励源，并利用非一致延迟时间法对被测系统输出时间序列进行相空间重构。在相空间中平衡点附近定义了指向Lyapunov指数，并用其对被测系统输出在相空间中平衡点附近特征结构进行分析，实现了对单输入单输出系统的故障检测。仿真结果表明，被测系统的参数变化将会引起相空间中平衡点附近特征结构的改变，指向Lyapunov指数对其变化敏感。

In this paper, for the fault detection of a single-input single-output （SISO） system, we use chaotic oscillator to generate the excitation of the system under test （SUT）, and use non-uniform method to reconstruct the phase space of the output time series. Directional Lyapunov exponent is defined around the equilibrium point in the phase space, and it is used to analyze the eigen-structure of the output phase space around its equilibrium point, thus the fault detection of the SISO system is realized. The simulation results show that parameter changes of the SUT will affect the phase space structure around its equilibrium point, and the directional Lyapunov exponent is sensitive to these changes.