Multimodal regression and mode recognition via an integrated deep neural network

Deep learning has emerged as a powerful tool to model complicated relationships between inputs and outputs in manufacturing systems. Existing deep learning approaches in manufacturing are often used to directly predict the Variables of Interest (VoI) such as the system status from a set of sensor measurements by supervised learning. However, in various complex manufacturing systems, components are operated under multiple modes that are not well known beforehand. The mapping of the VoI from sensor measurements highly depends on the mode information given that sensor measurements under different operation modes usually present different patterns. Therefore, predicting the VoI under multiple operation modes given sensor measurements is urgently necessary. This study develops a novel deep learning method for multimodal regression and mode recognition to predict the VoI under multiple modes and recognize the specific mode of a component from its sensor measurements. Specifically, we establish a deep neural network (DNN)-based regression- and classification-integrated framework. For model training, our innovative idea is to develop an Expectation-Maximum (EM)-based backpropagation algorithm, where the modes of components are set as latent variables, given that the mode information cannot be provided. Numerical experiments and a case study of degraded gas turbine engines are presented to validate the proposed model performance.