Multilevel MVU models with localized construction for monitoring processes with large scale data

Massive amounts of data, accumulated in real time and over decades, are spread over a wide variety of the modern automation in chemical plants. However, several standard process monitoring algorithms, such as kernel-based algorithms, do not easily scale to such orders of magnitude. Particularly in their running time and memory complexity increasing dramatically with the increase in the size of the data set. This paper proposes a scalable approximate kernel based on the multilevel maximum variance unfolding (MLMVU) technique that uses low rank kernel-based MVU approximations for reducing and distributing the computational load among parallel multilevel machines to achieve time efficiency. Theoretically, it is guaranteed that the performance of the proposed MLMVU can approximate that of the centralized MVU. The mathematical framework is presented for the development of MLMVU and various aspects of their computational complexity and approximation ability are discussed. The greater time efficiency and scalability in the computation are achievable. The effectiveness of the proposed algorithm is confirmed through a simple nonlinear system and the industrial Tennessee Eastman process.