基于敏感稀疏主元分析的化工过程监测与故障诊断

提出敏感稀疏主元分析(SSPCA) 算法用于监测复杂的化工过程. 根据主元分析与数据矩阵奇异值分解之间的关系, 通过将??_2,1 范数作为目标函数和惩罚项得到一个获取稀疏主元负载的凸优化问题, 并通过一个迭代算法进行求解. SSPCA 算法能同时兼顾大得分主元与小得分主元在监测算法中的作用, 提高了其对故障的敏感度. 证明了SSPCA 算法的单调性和全局收敛性, 对田纳西伊斯曼过程一个算例的监测结果表明了SSPCA 算法的有效性.

Chemical process monitoring and fault diagnosis based on sensitive sparse principal component analysis

The sensitive sparse principal component analysis(SSPCA) algorithm is proposed for monitoring complex chemical process. By using the relationship between principal component analysis(PCA) and the singular value decomposition of data matrices, the convex optimization problem is presented by introducing ??2,1norm into the cost function and the regularization penality for extracting the principal components(PCs) loadings. An iterative algorithm is proposed to solve the convex optimization problem. Meanwhile, the SSPCA algorithm is capable to take into account both PCs with large scores and PCs with small scores to promote the sensitivity to the abnormal situations in the process monitoring. A case study on the Tennessee Eastman process illustrates the effectiveness of the SSPCA algorithm.