Abstract: In this paper, a novel fault detection method based on sparse non-negative matrix factorization (SNMF) is proposed. NMF (non-negative matrix factorization) is a new dimension reduction technique that can find a low-rank matrix approximation from the original data. In contrast to the conventional multivariate statistical process monitoring methods, for example PCA, NMF has no assumption about the nature of latent variables, except for non-negativity. Combining linear sparse coding and NMF, SNMF can learn much sparser representation via imposing sparseness constraints. During factorization, low-rank matrix is orthogonalized to remove redundant information and concentrate information on fewer directions of projection. Then, SNMF is used to extract the latent variables that drive a process and new statistical metrics are defined for fault detection. Kernel density estimation (KDE) is adopted to calculate the confidence limits of defined statistical metrics. Afterwards, the proposed method is applied to the Tennessee Eastman process to evaluate the monitoring performance, comparing with conventional NMF and PCA. The results from the experiment show the feasibility of the new method.

Key words: fault detection, non-negative matrix factorization, PCA, sparse coding, statistical process monitoring

摘要： 提出了基于稀疏性非负矩阵分解(SNMF)的故障监测方法。非负矩阵分解(NMF)是一种新的降维方法,可以得到原始数据的低秩近似矩阵。与传统的多元统计过程监控方法如主成分分析(PCA)相比,NMF对潜变量的性质没有假设,除了非负性的要求。将稀疏编码和非负矩阵分解方法结合在一起,因为施加了稀疏性的约束,稀疏性非负矩阵分解方法可以得到对数据更稀疏的表示。在分解时对低秩近似矩阵进行正交化处理,从而在降维时除去变量中的冗余信息,将信息集中到更少的投影方向上。然后,用SNMF方法来提取过程的潜变量,并定义新的监测指标来进行故障监测。使用核密度估计(KDE)方法来计算新定义的监测指标的控制上限。最后,将提出的基于SNMF的监测方法应用于TE过程来评估其监测性能,并与基于传统NMF和PCA的方法进行比较。仿真实验结果表明了所提出新方法的可行性。

关键词: 故障监测, 非负矩阵分解, 主元分析, 稀疏编码, 统计过程监控