A Wavelet-Based Penalized Mixed-Effects Decomposition for Multichannel Profile Detection of In-Line Raman Spectroscopy

Abstract

Modeling and analysis of profiles, especially high-dimensional nonlinear profiles, is an important and challenging topic in statistical process control. Conventional mixed-effects models have several limitations in solving the multichannel profile detection problems for in-line Raman spectroscopy, such as the inability to separate defective information from random effects, computational inefficiency, and inability to handle high-dimensional extracted coefficients. In this paper, a new wavelet-based penalized mixed-effects decomposition (PMD) method is proposed to solve the multichannel profile detection problem in Raman spectroscopy. The proposed PMD exploits a regularized high-dimensional regression with linear constraints to decompose the profiles into four parts: fixed effects, normal effects, defective effects, and signal-dependent noise. An optimization algorithm based on the accelerated proximal gradient (APG) is developed to do parameter estimation efficiently for the proposed model. Finally, the separated fixed effects coefficients, normal effects coefficients, and defective effects coefficients can be used to extract the quality features of fabrication consistency, with in sample uniformity, and defect information, respectively. Using a surrogated data analysis and a case study, we evaluated the performance of the proposed PMD method and demonstrated a better detection power with less computational time.

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