用于动态化工过程故障检测的T-TELPP算法

Tensor-Temporal Extension Locality Preserving Projection Algorithm for Dynamic Chemical Process Fault Detection

工业过程具有高复杂性、动态性等特点。在特征提取时,引入时滞因子扩展时序矩阵可以解决现场变量带有的自相关与互相关特性问题。特征提取算法处理三阶张量形式的扩展数据时需要将三阶张量在某一方向向量化,这将破坏原始数据内在二维结构信息。对此,本文提出了基于张量空间的时序扩展局部结构保持算法(Tensor-Temporal Extension Locality Preserving Projection,T-TELPP)。首先,改进局部保持投影(LPP)算法得到时序扩展的LPP算法(TELPP),使其充分提取欧氏空间近邻与时序近邻信息;然后,将TELPP扩展到张量空间得到T-TELPP算法。T-TELPP直接将动态扩展数据投影到特征空间与残差空间,并分别建立T2和SPE统计量。对田纳西-伊斯曼(Tennessee Eastman,TE)过程进行监测,通过与PCA、DPCA和DLPP算法对比,验证了T-TELPP算法在动态过程监测上的有效性与优越性。

The industrial process has the characteristics of high complexity and dynamics. During feature extraction, the utilization of time-delay factor for expanding the matrix of time-series data can overcome the self-correlation and cross-correlation problem of field variables. When a feature extraction algorithm is utilized to deal with the extension data of three-order tensor form, it usually needs to vectorize the three-order tensor in a certain direction, which will destroy the intrinsic two-dimensional structure information in the original data. Aiming at the above shortcoming, this paper proposes a tensor-temporal extension locality preserving projection （T-TELPP） algorithm based on tensor space. First, locality preserving projection （LPP） algorithm is modified to obtain the temporal extension locality preserving projection （TELPP） algorithm so that the Euclidean neighbors and the temporal neighbor information can be fully extracted. And then, the TELPP algorithm is extended to tensor space for obtaining the T-TELPP algorithm. A key feature of T-TELPP algorithm is that it projects dynamic extended data into feature space and residual space and establishes T2 and SPE statistics, respectively, to realize the process monitoring. Finally, the T-TELPP-based monitoring method is applied in the dynamic chemical process of Tennessee Eastman （TE）, which verifies the effectiveness and superiority of the T-TELPP fault detection algorithm in dynamic process monitoring, compared with principal component analysis （PCA）, dynamic PCA （DPCA） and dynamic locality preserving projections （DLPP）.