Abstract:

Process monitoring based on Geodesic Distance Statistic(GDS) is proposed in this article for that fault monitoring method based on Euclidean distance of k Nearest Neighbors (kNN) could not fully reflect the complex characteristics between data with multiple conditions. To start, the batch process data is expanded and standardized by the batch direction. Principal Component Analysis (PCA) is utilized for data dimensionality reduction. Next, Get empowered adjacency matrix in the reduced space. Improved Dijkstra (IDijkstra) algorithm is proposed based on Dijkstra algorithm for easier implement. It can better characterize the actual shortest distance of the nonlinear data and reflect the local neighborhood relations between batch data. Meanwhile, statistics D^α based on α power of Geodesic distance which could reduce the deviation of distance from the edge of the training data is structured for fault monitoring compared with D² based on quadratic sum of Euclidean distance. Finally, the effectiveness of the proposed algorithm is verified by applying it in numerical simulation and industry examples.

Key words: multiple conditions, nonlinear, batch process, geodesic distance, algorithm

摘要：

针对间歇过程数据具有非线性和多工况的特点, 提出一种基于测地线距离统计量(geodesic distance statistic, GDS)的监测方法。首先, 对多工况间歇过程数据按批次方向展开及标准化, 利用主元分析(principal component analysis, PCA)方法进行降维;然后, 在降维空间获得赋权邻接矩阵, 提出采用改进的Dijkstra (improved Dijkstra, IDijkstra)算法使Dijkstra算法更易于实现, 计算各批次之间的测地线距离, 用以表征非线性多工况数据之间的实际最短距离, 更好地体现批次数据之间的局部近邻关系。通过构造测地线距离α次方统计量D^α进行过程监测, 与欧氏距离平方和D²相比将减小边缘训练数据距离的偏离程度。最后, 通过在数值仿真和工业仿真实例中的应用, 验证所提算法的有效性。

关键词: 多工况, 非线性, 间歇过程, 测地线距离, 算法