Data Decomposition for Analytics of Engineering Systems: Literature Review, Methodology Formulation, and Future Trends

Data decomposition is an important step for high-dimensional data analytics of complex engineering systems, but it is less emphasized in our current data analytics domain. This paper summarizes the key techniques for data decomposition, and separates them into two categories. One is deterministic decomposition, and the other is stochastic decomposition. The deterministic decomposition captures geometric or algebraic shape from the high-dimensional datasets directly, which is efficient for feature extraction and dimensionality reduction; while the stochastic decomposition provides probabilistic descriptions, and corresponding statistical distributions are estimated from the datasets. A novel methodology framework of data decomposition is proposed to formulate the existing approaches. Based on this methodology framework, some future research opportunities for new methodology development are discussed for data analytics of engineering systems.