基于特征样本的KPCA在故障诊断中的应用

KPCA Based on Feature Samples for Fault Detection

核函数主元分析(KPCA)可用于非线性过程监控.建立KPCA模型首先要计算核矩阵K,K的维数等于训练样本的数量,对于大样本集,计算K很困难.对此提出一种基于特征样本的KPCA(SKPCA),其基本思想是,首先利用非线性映射函数将输入空间映射到特征子空间,然后在特征子空间中计算主元.将SKPCA应用于监控T ennesseeE astm an过程,并与基于全体样本的KPCA作比较,仿真结果显示,二者诊断结果基本相同,然而特征样本只是训练样本中的一小部分,因此减少了K的维数,解决了K的计算问题.

Kernel principal component analysis （KPCA） has emerged in recent years as a nonlinear process monitoring technique. The KPCA is computed using a kernel matrix K, whose dimension is equivalent to the number of trained samples. For large data sets, KPCA based on feature samples （SKPCA） is proposed to solve the computation problem of K. The basic idea is to map the input space into a subspace via nonlinear mapping and then to compute the principal components in that subspace. SKPCA is used to monitor the Tennessee Eastman process. The simulation shows that the result is almost same compared to the KPCA based on the all samples. But featurc samples are only a small part of the trained sample sets. The computational problem is solved by reducing the dimensions of matrix K.