Wang Yajun, Yu Hongli, Li Xiaohui
School of Electronics and Information Engineering, Liaoning University of Technology, Jinzhou 121001, China.
ACS Omega. 2021 Apr 6;6(15):9989-9997. doi: 10.1021/acsomega.0c06039. eCollection 2021 Apr 20.
The Internet environment has provided massive data to the actual industrial production process. It not only has large amounts of data but also has a high data dimension, which brings challenges to the traditional statistical process monitoring. Aiming at the nonlinearity and dynamics of industrial large-scale high-dimensional data, an efficient iterative multiple dynamic kernel principal component analysis (IMDKPCA) method is proposed to monitor the complex industrial process with super-large-scale high-dimensional data. In KPCA, a new KK matrix is first created by using kernel matrix K. According to the properties of the symmetric matrix, the newly constructed matrix has the same eigenvector as the original matrix K; hence, each column of the matrix K can be used as the input sample of the iteration algorithm. After iterative operation, the kernel principal component can be deduced fleetly without the eigen decomposition. Because the kernel matrix is not stored in the algorithm beforehand, it can effectively reduce the computation complexity of the kernel. Especially for a tremendous data scale, the traditional eigen decomposition technology is no longer appropriate, yet the presented method can be solved quickly. The autoregressive moving average (ARMA) time series model and kernel principal component analysis (KPCA) are combined to build the IDKPCA model for dealing with the dynamics and nonlinearity in the industrial process. Eventually, it is applied to monitor faults in the penicillin fermentation process and compared with MKPCA to certify the accuracy and applicability of the proposed method.
互联网环境为实际工业生产过程提供了海量数据。这些数据不仅数量庞大，而且维度很高，给传统的统计过程监控带来了挑战。针对工业大规模高维数据的非线性和动态性，提出了一种高效的迭代多重动态核主成分分析（IMDKPCA）方法，用于监控具有超大规模高维数据的复杂工业过程。在核主成分分析中，首先利用核矩阵K创建一个新的KK矩阵。根据对称矩阵的性质，新构造的矩阵与原始矩阵K具有相同的特征向量；因此，矩阵K的每一列都可以用作迭代算法的输入样本。经过迭代运算，无需进行特征分解即可快速推导出核主成分。由于算法中事先不存储核矩阵，因此可以有效降低核的计算复杂度。特别是对于巨大的数据规模，传统的特征分解技术不再适用，但所提出的方法可以快速求解。将自回归移动平均（ARMA）时间序列模型与核主成分分析（KPCA）相结合，构建了IDKPCA模型，以处理工业过程中的动态性和非线性。最终，将其应用于青霉素发酵过程的故障监测，并与MKPCA进行比较，以验证所提方法的准确性和适用性。
