CAJ | 학술논문

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Dα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。
침대간헐과정수거구유비선성화다공황적특점，제출일충기우측지선거리통계량（geodesic distance statistic, GDS）적감측방법。수선，대다공황간헐과정수거안비차방향전개급표준화，이용주원분석（principal component analysis，PCA）방법진행강유；연후，재강유공간획득부권린접구진，제출채용개진적Dijkstra (improved Dijkstra， IDijkstra)산법사 Dijkstra 산법경역우실현，계산각비차지간적측지선거리，용이표정비선성다공황수거지간적실제최단거리，경호지체현비차수거지간적국부근린관계。통과구조측지선거리α차방통계량Dα진행과정감측，여구씨거리평방화D2상비장감소변연훈련수거거리적편리정도。최후，통과재수치방진화공업방진실례중적응용，험증소제산법적유효성。
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 Dαbased onαpower 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.