Vector-Ordering Filter Procedure for Data Reduction
The vector-ordering filter (VOF) technique involves a procedure for sampling a large population of data vectors to select a subset of data vectors that fully characterize the state space of the large population. The VOF technique enables a large reduction of the volume of data that must be handled in the automated monitoring system and method discussed in the two immediately preceding articles. In so doing, the VOF technique enables the development of data-driven mathematical models of a monitored asset from sets of data that would otherwise exceed the memory capacities of conventional engineering computers. Data-driven mathematical models have been shown to offer high fidelity for purposes of control and monitoring of assets. In practice, a collection of asset-operating observations is acquired with the intention that the collection contain observations characteristic of the full dynamic range of operation of the asset. Often, such a collection contains an extremely large number of observations, many of which are redundant. The VOF technique fills the need for a means to extract, from the original collection of observational data, a reduced data matrix that excludes redundant data while maintaining the full statistical character and dynamic range of the original data. The reduced data matrix can then be used as the input data for development of a mathematical model of the monitored asset, or as training data for a neural-network substitute for an explicit mathematical model of the asset. Alternatively, the reduced data matrix can, itself, be used directly as a mathematical model of the monitored asset, as is commonly done in multivariate state-estimation techniques. The original data are collected from the asset over a range of operating states and are put in matrix form. Each column vector in the original data matrix represents the signal values acquired at a particular operational state of the asset. Thus, the number of columns of the original data matrix equals the number of observed states and the number of rows in this matrix equals the number of signals acquired at each observation. In the VOF technique, one extracts the reduced data matrix from the original data matrix through the selection of a representative subset of the column (state) vectors.