摘要:
针对数据信息的特征提取和降维问题, 提出一种局部保持最大方差投影 (Locality preserving maximum varianceprojections, LPMVP) 新算法. 该算法综合考虑了主元分析(Principalcomponent analysis, PCA)和局部保持投影(Locality preservingprojections, LPP)算法的优点和不足, 提出了新的优化目标, 使投影得到的低维空间不仅和原始变量空间有相似的局部近邻结构, 而且有相似的整体结构, 因而可以包含更多的特征信息. 在此基础上, 本文使用LPMVP算法把原始变量空间划分为特征空间和残差空间, 分别构造了T2和SPE统计量对过程进行监测, 建立了一种新的故障检测方法. 通过数值例子以及TE过程的仿真研究, 表明了LPMVP算法可以有效地提取数据信息, 同时也体现了较强的故障检测能力.
Abstract:
In order to handle the feature extraction anddimensionality reduction problem, a new method named as localitypreserving maximum variance projections (LPMVP) is developed. Thisalgorithm can be considered as a linear approach with a newoptimizing target, which takes the excellence and limitation ofprincipal component analysis (PCA) and locality preservingprojections (LPP) into account. Comparing to original variablespace, this low-dimension projection space enjoys similar localityneighborhood structure and global one. As a result, more featureinformation can be extracted. Moreover, a new fault detection methodis also proposed. The LPMVP algorithm is used to divide the originalvariable space into two parts: feature space and residual space.Then, T2 and SPE statistics can be built to monitor theprocess. Case studies of a numerical example and Tennessee-Eastman(TE) process illustrate the efficiency of the LPMVP algorithm oninformation extraction. Besides, the new method also shows its faultdetection ability.
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