Abstract:

Total kernel projection to latent structures (T-KPLS) has been widely used in the fault detection control field, its core idea is to conduct the covariance matrix decomposition of the data matrix, without using the higher-order statistics and other useful information of the data, which will cause an information loss in the feature extraction process, then result in a bad fault recognition performance. Aiming to solve the problem, a statistics pattern analysis (SPA) combing with the T-KPLS based multi-way statistics pattern analysis total kernel projection to latent structures (MSPAT-KPLS) is proposed. First, different order statistics of the data samples are constructed to map the data from the original data space into the statistic sample space, then utilize kernel function to map the statistic sample space into the higher dimensional kernel space, and according to the quality variable, the feature space will be divided into 4 subspaces, namely: process variable related to quality variable space, process variable not related to quality variable space, process variable orthogonal to quality variable space and residual error space; Lastly, aiming at the process variable related to quality variable subspace and the residual error space, different detection models are constructed, which will trace the fault variables when faults are detected. In the end, apply the proposed method on the microbial fermentation process, and the comparison results with the traditional methods show that the proposed method could achieve a better detection.

Key words: fault monitoring, total kernel projection to latent structrues, statistics pattern analysis

摘要：

核函数的全影结构投影(total kernel projection to latent structures,T-KPLS)最近在故障监控领域取得了广泛应用, 其实质是对数据矩阵的协方差矩阵进行分解, 没有利用数据的高阶统计量等有用信息, 在进行特征提取时会造成数据有用信息的丢失, 导致故障识别效果差。为了解决此问题, 提出了统计量模式分析(statistics pattern analysis, SPA)与核函数的全影结构投影法(total kernel projection to latent structures, T-KPLS)相结合的多向统计量模式分析的核函数的全影结构投影法(multi-way statistics pattern analysis total kernel projection to latent structures, MSPAT-KPLS)。该方法首先构造样本的不同阶次统计量, 将数据从原始的数据空间映射到统计量样本空间, 然后利用核函数将统计量样本空间映射到高维核空间并在质量变量的引导下将特征空间分为过程变量与质量变量相关、过程变量与质量变量无关、过程变量与质量变量正交和残差4个子空间;最后针对与质量变量相关和残差空间建立联合监控模型, 当监控到有故障发生时进行故障变量追溯。最后将该方法应用到微生物发酵过程中, 并与传统方法进行比较, 发现该方法具有更好的监控性能。

关键词: 故障监控, 核函数全影结构投影, 统计量模式分析