Variational inference-based transfer learning for profile monitoring with incomplete data

Profile monitoring is a widely used tool in quality control. The rapid development of sensor technology has created unprecedented opportunities for multi-channel profile data collection, which motivates the modeling and transfer learning for multi-profile data. The Multi-output Gaussian Process (MGP) is often used for multi-profile data, due to its flexible modeling capability and elegant mathematical properties. However, two practical concerns limit the broader application of MGP for transfer learning and monitoring of multi-profile data: high computational complexity and data incompleteness. In this article, we propose a Variational Inference (VI)-based MGP framework to facilitate transfer learning and profile monitoring using incomplete profile data. The proposed framework features a specially designed convolutional structure for constructing an explicit covariance relationship between the inducing variables in VI and the MGP in multi-profile data. This structure inspires a comprehensive solution to both computational complexity and data incompleteness in modeling multi-profile data, which facilities the transfer learning for profile monitoring. Various numerical studies and one real case study are conducted to demonstrate and compare the transfer learning and monitoring performance of the proposed method. The results show the method can achieve superior monitoring performance while maintain a very low level of computational complexity.