Abstract The quality and stability of products are seriously influenced by the process conditions. A large number of modern production processes can be considered as batch processes, with nonlinear relationships between the process variables. How to troubleshoot batch processes has attracted considerable attention in the literature. The research object of batch processes is expressed as the third-order tensor data of batch × variable × time. The traditional methods convert the tensors into second-order forms through matrix expansion. A novel method named improved chordal kernel tensor locality preserving projections (ICK-TLPP) is proposed for fault detection of batch processes. First, the chordal distance is introduced as a measurement of the similarity of matrix, and an improved method is proposed for describing the variation of time series data. Then, the chordal kernel function is introduced to preserve the spatial structure of the tensor data without the information loss caused by vectorization, and describe the nonlinear correlation during the multivariate control system. Next, the locality preserving projections algorithm is applied to detect the intrinsic manifold structure. Parallel analysis is applied to optimize the hyper-parameters in the model. Finally, Granger causality analysis is performed to locate the root cause of the process fault. The proposed method is validated on two datasets, penicillin fermentation process and the hot strip rolling process. The best results of false alarm rate and fault detection rate are 16% and 94% respectively. The proposed method performs better compared with the traditional algorithms.

中文翻译：

---

通过改进的弦核张量局部保持投影对批处理进行非线性故障检测

摘要 工艺条件严重影响产品的质量和稳定性。大量的现代生产过程可以被视为批处理过程，过程变量之间存在非线性关系。如何对批处理过程进行故障排除在文献中引起了相当大的关注。批处理的研究对象表示为批处理×变量×时间的三阶张量数据。传统方法通过矩阵展开将张量转换为二阶形式。提出了一种名为改进的弦核张量局部保持投影（ICK-TLPP）的新方法，用于批处理过程的故障检测。首先，引入弦距作为矩阵相似度的度量，提出了一种描述时间序列数据变化的改进方法。然后，引入和弦核函数来保留张量数据的空间结构，避免矢量化造成的信息丢失，描述多元控制系统中的非线性相关性。接下来，应用局部保持投影算法来检测内在流形结构。应用并行分析来优化模型中的超参数。最后，进行格兰杰因果关系分析，定位过程故障的根本原因。所提出的方法在两个数据集上得到验证，青霉素发酵过程和热轧带钢过程。误报率和故障检测率的最佳结果分别为16%和94%。与传统算法相比，所提出的方法性能更好。引入和弦核函数，保留张量数据的空间结构，避免矢量化造成的信息丢失，描述多元控制系统中的非线性相关性。接下来，应用局部保持投影算法来检测内在流形结构。应用并行分析来优化模型中的超参数。最后，进行格兰杰因果关系分析，定位过程故障的根本原因。所提出的方法在两个数据集上得到验证，青霉素发酵过程和热轧带钢过程。误报率和故障检测率的最佳结果分别为16%和94%。与传统算法相比，所提出的方法性能更好。引入和弦核函数，保留张量数据的空间结构，避免矢量化造成的信息丢失，描述多元控制系统中的非线性相关性。接下来，应用局部保持投影算法来检测内在流形结构。应用并行分析来优化模型中的超参数。最后，进行格兰杰因果关系分析，定位过程故障的根本原因。所提出的方法在两个数据集上得到验证，青霉素发酵过程和热轧带钢过程。误报率和故障检测率的最佳结果分别为16%和94%。与传统算法相比，所提出的方法性能更好。