We report the use of dual-domain regression models, which were built utilizing a wavelet prism decomposition and paired with transfer by orthogonal projection, for the calibration transfer of near-infrared (NIR) spectra. The new method is based on obtaining specific frequency components for a spectrum via wavelet analysis, projecting the frequency components of the primary instrument onto the subspace orthogonal to the mean instrumental difference between spectra from the primary and the secondary instrument, and weighting each frequency component model according to the cross-validation error of the frequency components of the projected primary instrument's spectra to generate a stacked ensemble model robust to contributions to the spectra from instrumental variations. The method, which does not require property values from the secondary data set, is tested on three NIR data sets, and is compared with orthogonal projection in the wavelength domain, orthogonal signal correction, and with model updating approaches. For the data sets we examined, we show that the prediction performance of the new method is competitive with orthogonal projections in the wavelength domain, as well as orthogonal signal correction and model updating approaches, both of which require property values for spectra from the secondary instrument. Examination of the spectral data reconstructed from the projected frequency components indicates that aspects of the data that may be attributable to instrumental or physical phenomena (i.e., instrumental baseline shifts or discretized intensity changes which may be attributed to scatter) are suppressed, but those associated with the chemical phenomena are retained. The benefits of orthogonal projection on each individual frequency component are further corroborated by the fact that the models based on frequency component projection generalize better to unseen instruments compared with the other methods.

No abstract

No abstract

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.

A novel, nonlinear soft sensor based on a localized, adaptive single-layer feedforward neural network with random hidden layer weights, also called an extreme learning machine, combined with the recursive partial least squares algorithm to update the linear output layer weights, is explored. The soft sensor is highly adaptive with minimal operator input, and automated mechanisms are included to self-correct numerous aspects of the underlying model.For instance, mechanisms are put in place to automatically select an optimized local model region describing the current process dynamics from the historical data when the current prediction error reaches an adaptively computed threshold. Additionally, the new soft sensor simultaneously employs an ensemble of models with diverse recursive partial least squares forgetting factors with automated and adaptive reweighting of the models in the ensemble, thus enabling real-time model memory adjustment. The validity of the method is shown by comparison with numerous other soft sensor methods for the prediction of the activity of a polymerization catalyst.