基于Lyapunov指数的非线性模拟电路故障诊断方法

A Fault Diagnosis Approach for Nonlinear Analog Circuits Based on Lyapunov Exponents

本文介绍一种基于计算最大Lyapunov指数的非线性模拟电路故障诊断方法,它应用混沌方法对一个变周期的多谐振荡器的输出信号进行处理,利用数据替代法生成电路故障数据,借助于小数据量法计算相应的最大Lyapunov指数,将这种混沌特性分析应用于强非线性模拟电路的故障诊断,并对混沌时间序列相空间重构中的延迟时间间隔和嵌入维数的选取方法进行了讨论;结合实例对该方法进行了计算验证。

Based on the computation of maximum Lyapunov exponents, a new approach of fault diagnosis for the nonlinear analog circuits is presented. Chaotic analysis is employed to process the output signal of a harmonic oscillator with variable periods. A surrogate method is used to generate the fault data, and the corresponding maximum Lyapunov exponents are calculated by means of small data sets. This chaotic analysis method can be applied to the fault diagnosis of strong nonlinear analog circuits. Meanwhile, how to select a proper number of embedding dimensions and time delay for phase space reconstruction is also discussed. Finally, the proposed fault diagnosis approach is validated by the experiment on practical problems.