Abstract:

The traditional neighborhood preserving embedding (NPE) algorithm uses the k-nearest neighbors (k-NN) method to select neighborhoods for reconstruction to achieve dimensionality reduction. However, the samples collected in the actual industrial process have time series correlation. Selecting the nearest neighbor samples only by Euclidean distance cannot fully reflect the information contained in the data, which will affect the detection performance. Therefore, a local time difference constrained neighborhood preserving embedding (LTDCNPE) algorithm is proposed, which establishes a more accurate fault detection model by fully considering the temporal and spatial relationship between samples. Firstly, the algorithm selects the neighborhoods based on the time and spatial characteristics of the samples within a fixed scale time window. Secondly, the time differences between samples are used to weight the neighborhood samples. In this way, the reconstructed samples retain the local structure of the high-dimensional space. Then, T^{\mathrm{2}} and SPE statistics are calculated for the principal component space and residual space obtained through LTDCNPE. Next, the control limits are determined to detect the process faults. Finally, the performance of LTDCNPE is described by a numerical example and Tennessee Eastman (TE) simulation study.

Key words: process control, process systems, dynamic modeling, neighborhood preserving embedding algorithm, neighborhood selection, fault detection

摘要：

传统的邻域保持嵌入(neighborhood preserving embedding，NPE)算法通过k近邻(k-nearest neighbors，k-NN)方法选择邻域进行重构来实现降维。但在实际工业过程中采集的样本具有时序相关性，仅仅通过欧氏距离选择近邻样本不能充分反映数据中包含的信息，从而影响检测效果。因此，提出一种局部时差约束邻域保持嵌入(local time difference constrained neighborhood preserving embedding，LTDCNPE)算法，充分考虑样本间的时间和空间关系，从而建立准确的故障检测模型。首先，该算法在固定尺度的时间窗内，根据样本的时序关系和空间特征挑选出邻域。其次，利用样本间的时间差异为邻域样本进行加权，使数据特征保留了高维空间的局部结构。然后，对降维后得到的主元空间和残差空间构建T^{\mathrm{2}}和SPE统计量并确定控制限。最后，通过数值例子和Tennessee-Eastman(TE)过程仿真验证LTDCNPE算法的有效性。

关键词: 过程控制, 过程系统, 动态建模, 邻域保持嵌入算法, 邻域选择, 故障检测