MPOFI: Multichannel Partially Observed Functional Modeling for Defect Classification with Imbalanced Dataset via Deep Metric Learning

In modern manufacturing, most of the product lines are conforming. Few products are nonconforming but with different defect types. The identification of defect types can help further root cause diagnosis of production lines. With the sensing development, continuous signals of process variables can be collected in high resolution, which can be regarded as multichannel functional data. They have abundant information to characterize the process and help identify the defect types. Motivated by a real example from the pipe tightening process, we target at detect classification when each sample is a multichannel functional data. However, the available samples for each defect type are limited and imbalanced. Moreover, the functions are partially observed since the pre-tightening process before the pipe tightening process is unobserved. To classify the defect samples based on imbalanced, multichannel, and partially observed functional data is very important but challenging. Thus, we propose an innovative framework known as "Multichannel Partially Observed Functional Modeling for Defect Classification with an Imbalanced Dataset" (MPOFI). The framework leverages the power of deep metric learning in conjunction with a neural network specially crafted for processing functional data. This paper introduces a neural network explicitly tailored for handling multichannel and partially observed functional data, complemented by developing a corresponding loss function for training on imbalanced datasets. The results from a real-world case study demonstrate the superior accuracy of our framework when compared to existing benchmarks.