中文摘要：

传统非线性频谱分析方法对复杂系统进行故障诊断时,求解出的非线性频谱数据量庞大,不便于直接用于故障检测与分类识别.本文提出了一种非线性频谱特征与核主元分析（KPCA）结合的故障诊断方法,首先通过最小二乘算法估计出前3阶Volterra时域核,由多维傅立叶变换求取出广义频率响应函数,然后利用KPCA方法对谱数据进行压缩与提取谱特征,最后利用多分类最小二乘支持向量机进行多故障检测与识别.考虑到频谱数据具有非线性的特点,KPCA中的核函数选用由多项式函数与径向基函数构成的混合核函数,兼顾了局部特性与全局特性.论文基于非线性频谱数据,给出了核主元模型建立与在线故障诊断的具体算法.对非线性模拟电路和数控机床伺服传动系统进行了仿真实验,结果表明本文方法能够大幅度降低频谱数据维数,故障识别率高,是一种实用的故障诊断方法.

英文摘要：

When the traditional nonlinear frequency spectrum analysis method is applied to diagnose faults in complex systems,the amount of frequency spectrum data is very large,causing inconvenience in directly detecting and identifying faults.A novel fault diagnosis approach is proposed based on the nonlinear frequency spectrum feature and the kernel principal component analysis（KPCA）.Firstly,the first three order time domain Volterra kernels are estimated by the leastsquares algorithm,and then the generalized frequency response functions are obtained from the time domain Volterra kernels by multiple Fourier transform.Secondly,the KPCA method is used to compress frequency spectrum data and extract spectrum features.Finally,the multi-classification least-squares support vector machine is used to perform the fault detection and identification.Because of the nonlinear characteristics of frequency spectrum data,we employ the mixed function composed of the polynomial function and the radial basis function as the kernel function,so that the local characteristics and the global characteristics both are taken into considerations.Based on the nonlinear frequency spectrum data,the detailed algorithms are developed for building the kernel principal component model and for online diagnosing the faults.Simulation of fault diagnosis for a nonlinear analog circuit and a servo drive system of the numerical-control machine tool are performed.Experimental results show that the proposed method can greatly lower the data dimensions and improve the identification rate of faults.