Nonlinear Online Multioutput Gaussian Process for Multistream Data Informatics

Abstract

The revolution of Industry 4.0 and Internet of Things facilitate large and cheap data acquisition from complex systems. However, the online processing and analytics of such multi-stream data still suffer difficulties. The key reason is that data from different sensors (multi-stream data) contain nonlinear within-and-cross sensor correlations, which poses challenges in the modeling and analysis of such data, especially for the online scenarios. To jointly model multi-stream data, multi-output Gaussian Process (MGP) has become popular and achieved great success. However, existing methods assume different outputs are linearly correlated, which significantly limits their applications. In this paper, we propose a nonlinear online MGP framework to simultaneously realize nonlinear correlation modeling and online processing of multi-stream data. Specifically, a tailored co-variance structure is developed based on the convolution process, which can capture nonlinear self-and-cross correlations. To realize online processing, Bayesian analysis and marginalized particle filter are applied to estimate function values and model parameters. Comparing to existing methods, the proposed method features superiorities in i) the non-linear characterization of self-and-cross correlations, and ii) the efficient modeling and prediction capability. These features make the proposed method especially appropriate for industrial informatics with complex relationship and large-scale data sets. The proposed method is validated with simulation studies and a real-case study of biophysical signals.