A frequency‐localized recursive partial least squares ensemble for soft sensing

We report the use of a frequency‐localized adaptive soft sensor ensemble using the wavelet coefficients of the responses from the physical sensors. The proposed method is based on building recursive, partial least squares soft sensor models on each of the wavelet coefficient matrices representing different frequency content of the signals from the physical sensors, combining the predictions from these models via static weights determined from an inverse‐variance weighting approach, and recursively adapting each of the soft sensor models in the ensemble when new data are received. Wavelet‐induced boundary effects are handled by using the undecimated wavelet transform with the Haar wavelet, an approach that is not subject to wavelet boundary effects that would otherwise arise on the most recent sensor data. An additional advantage of the undecimated wavelet transform is that the wavelet function is defined for a signal of arbitrary length, thus avoiding the need to either trim or pad the training signals to dyadic length, which is required with the basic discrete wavelet transform. The new method is tested against a standard recursive partial least squares soft sensor on 3 soft‐sensing applications from 2 real industrial processes. For the datasets we examined, we show that results from the new method appear to be statistically superior to those from a soft sensor based only on a recursive partial least squares model with additional advantages arising from the ability to examine performance of each localized soft sensor in the ensemble.

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