High Dimensional Process Monitoring Using Robust Sparse Probabilistic Principal Component Analysis

High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However, in many cases, data sets have underlying structures, such as in advanced manufacturing systems. If extracted correctly, efficient methods for process control can be developed. This paper proposes a robust sparse dimensionality reduction approach for correlated high-dimensional process monitoring to address the aforementioned issues. The developed monitoring technique uses robust sparse probabilistic PCA to reduce the dimensionality of the data stream while retaining interpretability. The proposed methodology utilizes Bayesian variational inference to obtain the estimates of a probabilistic representation of PCA. Simulation studies were conducted to verify the efficacy of the proposed methodology. Furthermore, we conducted a case study for change detection for in-line Raman spectroscopy to validate the efficiency of our proposed method in a practical scenario

Learning the Treatment Effects on FTIR Signals Subject to Multiple Sources of Uncertainties

Fourier-transform infrared spectroscopy (FTIR) is a versatile technique for characterizing the chemical composition of the various uncertainties, including baseline shift and multiplicative error. This study aims at analyzing the effect of certain treatment on the FTIR responses subject to these uncertainties. A two-step method is proposed to quantify the treatment effect on the FTIR signals. First, an optimization problem is solved to calculate the template signal by aligning the pre-treatment FTIR signals. Second, the effect of treatment is decomposed as the pattern of modification $\mathbf{g}$ that describes the overall treatment effect on the spectra and a vector of effect $\boldsymbol{\delta}$ that describes the degree of modification. $\mathbf g$ and $\boldsymbol{\delta}$ are solved by another optimization problem. They have explicit engineering interpretations and provide useful information on how the treatment effect change the surface chemical components. The effectiveness of the proposed method is first validated in a simulation. In a real case study, it's used to investigate how the plasma exposure applied at various heights affects the FTIR signal which indicates the change of the chemical composition on the composite material. The vector of effects indicates the range of effective plasma height, and the pattern of modification matches existing engineering knowledge well.Comment: \{copyright} 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work