中文摘要：

为解决PCA（Principal Component Analysis）因样本数目少而无法得到稳健协方差矩阵问题,根据主元分析的几何意义,引入CS分解贝叶斯空间估计的思想,将协方差矩阵问题转化成特征子空间估计问题.首先根据大量历史数据运用PCA离线建立SPE（Squard Prediction Error）统计量阈值和故障模式特征子空间矩阵库,当在线检测到系统存在异常情况时,由于受一定的环境影响只能得到小样本故障数据,利用本文方法可估计出小样本数据的特征子空间矩阵;然后通过对比特征子空间与故障模式特征子空间的相似性,完成故障诊断.最后通过仿真验证了此方法的可行性和有效性.

英文摘要：

To solve the problem that a robust covariance matrix cannot be obta samples in principal component analysis, the covariance matrix was transforme ined because of insufficient d into the feature subspace estimation problem by introducing the idea of CS decomposition Bayesian spatial estimation. First, the SPE （squard prediction error） statistic threshold and failure mode feature subspace matrix library were es- tablished using a large number of historical data using PCA offline. When there exists an abnormal condi- tion in the online system, only a small sample of failure data can be obtained due to the effect of a certain environment. However, the feature subspace matrix can be obtained using a small sample data. Then, fault diagnosis was completed by comparing the similarity between the feature subspace and the failure mode subspace. Finally, the feasibility and effectiveness of this method was verified by simulation.