Abstract

Modern manufacturing systems typically involve multiple production stages, the real-time status of which can be tracked continuously using sensor networks that generate a large number of profiles associated with all process variables at all stages. The analysis of the collective behavior of the multistage multivariate profile data is essential for understanding the variance patterns of the entire manufacturing process. For this purpose, two major challenges regarding the high data dimensionality and low model interpretability have to be well addressed. This article proposes integrating Multivariate Functional Principal Component Analysis (MFPCA) with a three-level structured sparsity idea to develop a novel Hierarchical Sparse MFPCA (HSMFPCA), in which the stage-wise, profile-wise and element-wise sparsity are jointly investigated to clearly identify the informative stages and variables in each eigenvector. In this way, the derived principal components would be more interpretable. The proposed HSMFPCA employs the regression-type reformulation of the PCA and the reparameterization of the entries of eigenvectors, and enjoys an efficient optimization algorithm in high-dimensional settings. The extensive simulations and a real example study verify the superiority of the proposed HSMFPCA with respect to the estimation accuracy and interpretation clarity of the derived eigenvectors.

摘要

现代制造系统通常涉及多个生产阶段，可以使用传感器网络连续跟踪其实时状态，这些传感器网络会在各个阶段生成与所有过程变量关联的大量配置文件。多级多元轮廓数据的集体行为分析对于理解整个制造过程的差异模式至关重要。为此，必须很好地解决有关高数据维度和低模型可解释性的两个主要挑战。本文提出将多元功能主成分分析（MFPCA）与三层结构的稀疏性思想相结合，以开发一种新颖的分层稀疏MFPCA（HSMFPCA），其中分阶段，联合研究了轮廓稀疏度和元素稀疏度，以清楚地识别每个特征向量中的信息阶段和变量。这样，派生的主要成分将更具解释性。提出的HSMFPCA采用PCA的回归类型重新编制和特征向量项的重新参数化，并在高维环境中享有高效的优化算法。大量的仿真和一个实际的例子研究证明了所提出的HSMFPCA在推导特征向量的估计精度和解释清晰度方面的优越性。提出的HSMFPCA采用PCA的回归类型重新编制和特征向量项的重新参数化，并在高维环境中享有高效的优化算法。大量的仿真和一个实际的例子研究证明了所提出的HSMFPCA在推导特征向量的估计精度和解释清晰度方面的优越性。提出的HSMFPCA采用PCA的回归类型重新编制和特征向量项的重新参数化，并在高维环境中享有高效的优化算法。大量的仿真和一个实际的例子研究证明了所提出的HSMFPCA在推导特征向量的估计精度和解释清晰度方面的优越性。