Multiscale rectification of random errors without fundamental process models
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abstract
Data rectification is the task of removing errors from measured process data, and is of paramount importance for the efficient execution of other process operation tasks. Existing methods for rectification represent the measured variables at a single scale in the time or frequency domain. This representation is inefficient for rectification of data containing multiscale features such as, contributions from events of different duration in time and frequency, and non-white stochastic errors. In this paper, a new class of methods is developed for the rectification of random errors based on representing the measured variables at multiple scales by decomposition on time-frequency localized basis functions derived from orthonormal wavelets. A new technique is developed for the on-line rectification of stationary random errors in the absence of fundamental or empirical process models. This rectification method eliminates basis function coefficients smaller than a threshold, and provides better rectification than that by the widely used method of exponential smoothing. The threshold for rectification is derived from a multiscale model of the errors, which may he estimated from the mulliscalc decomposition of the measured data. If multiple redundant measured variables are available, then the data may be rectified by extracting an empirical model relating the variables, by methods such as principal components analysis. A new multiscale PCA method is developed that provides better rectification than PCA, by simultaneously extracting the relationship among the variables and among the measurements. The performance of the multiscale univariate filtering and multiscale PCA are illustrated by several examples, and areas for future research are identified.
