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, within-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. Note to Practitioners—This paper was motivated by the need of implementing multichannel profile detection for Raman spectra to realize in-line process monitoring and quality control of continuous manufacturing of carbon nanotube (CNT) buckypaper. Existing approaches, such as the mixed-effects model or the smooth-sparse decomposition method, cannot separate defective information in random effects effectively. This paper develops a penalized mixed-effects decomposition which decomposes Raman spectra into four components: fixed effects, normal effects, defective effects, and signal-dependent noise, respectively. The first three components can be applied to monitor the fabrication consistency, degree of uniformity, and defect information of buckypaper, respectively. With this new approach, several quality features can be monitored simultaneously and the algorithm based on the accelerated proximal gradient (APG) method can satisfy the computation speed requirement of in-line monitoring. This paper provides a solid foundation for in-line process monitoring and quality control for scalable nanomanufacturing of CNT buckypaper. Furthermore, the developed methodology can be applied in the decomposition of other signal systems with fixed, normal, and defective effects.

中文翻译：

---

基于小波的惩罚混合效应分解用于在线拉曼光谱的多通道轮廓检测

轮廓（尤其是高维非线性轮廓）的建模和分析是统计过程控制中一个重要且具有挑战性的主题。常规的混合效应模型在解决在线拉曼光谱的多通道轮廓检测问题时有几个局限性，例如无法从随机效应中分离缺陷信息，计算效率低下以及无法处理高维提取系数。为了解决拉曼光谱中的多通道轮廓检测问题，提出了一种新的基于小波的惩罚混合效应分解（PMD）方法。提出的PMD利用线性约束的正则化高维回归将轮廓分解为四个部分：固定效应，法向效应，缺陷效应和信号相关噪声。提出了一种基于加速近端梯度（APG）的优化算法，可以对所提出的模型进行有效的参数估计。最后，分离的固定效应系数，法向效应系数和缺陷效应系数可分别用于提取制造一致性，样品内均匀性和缺陷信息的质量特征。使用替代数据分析和案例研究，我们评估了提出的PMD方法的性能，并展示了具有更少计算时间的更好检测能力。给从业者的注意-本文的动机是需要对拉曼光谱实施多通道轮廓检测，以实现在线过程监控和碳纳米管（CNT）buckypaper连续生产的质量控制。现有方法 诸如混合效果模型或平滑稀疏分解方法之类的方法，不能有效地以随机效果分离出缺陷信息。本文提出了一种惩罚混合效应分解方法，该方法将拉曼光谱分解为四个分量：固定效应，法向效应，缺陷效应和信号相关噪声。前三个组件可分别用于监视制造的一致性，均匀度和Buckypaper的缺陷信息。通过这种新方法，可以同时监视几个质量特征，并且基于加速近端梯度（APG）方法的算法可以满足在线监视的计算速度要求。本文为CNT buckypaper的可扩展纳米制造的在线过程监控和质量控制提供了坚实的基础。此外，所开发的方法可以应用于具有固定，正常和有缺陷影响的其他信号系统的分解。