MPOFI: Multichannel Partially Observed Functional Modeling for Defect
  Classification with Imbalanced Dataset via Deep Metric Learning
Yukun Xie Juan Du Chen Zhang
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.