Calibration Models Based on Reacting Mixtures
M. Amrhein, B. Srinivasan and D. Bonvin (1996-1999)
In this work, it was showed that the interpretation provided by the 3-way nonlinear decomposition to normal form using reaction and flow variants/invariants was applicable to spectroscopic data from reacting mixtures (factorization of spectroscopic data). To ensure the space-inclusion condition, i.e. the condition under which a new spectrum lies in the space spanned by the calibration set, it was proposed to build calibration models from reactive mixtures and to calibrate these data with the Reaction-Variant (RV) part only. Once the (unknown) reaction variants were predicted from a new spectrum, the (known) reaction invariants could be added to reconstruct the concentrations. Several case studies were considered such as batch, semi-batch and continuous reaction systems, as well as systems with reactions in quasi-equilibrium conditions and non-reacting mixtures with closure.
Subspace Correction Methods for Calibration Models
P. Gujral, M. Amrhein and D. Bonvin (2005-2011)
This work decomposed the prediction error of calibration models from Principal Component Regression (PCR) or Partial Least-Squares Regression (PLSR) in errors due to noise in the calibration data and bias due to truncation, and in errors due to drift and noise in the prediction data. To correct these errors, three subspace correction methods that use new information in addition to calibration data were developed: (i) latent subspace correction using unlabeled data, (ii) drift subspace correction using shrinkage or orthogonal projection, (iii) data reconciliation. These various subspace correction methods were illustrated using simulated and experimental data.
Calibration Models in Incremental Identification
Calibration models such as PCR or PLS have been used in incremental model identification to estimate concentrations from absorbance measurements. The resulting concentrations can be subsequently converted in various extents using a linear transformation. Rate parameters can then be determined by fitting each predicted reaction extent to the corresponding extent computed from the measurements. This procedure has been illustrated through simulated examples taken from homogeneous and heterogeneous chemistry.
Spectroscopy; Calibration with reacting mixtures; Reaction variants; Orthogonal projections; Unlabeled data; Drift invariance; Optimal filtering; Space inclusion; Extent-based incremental identification; Linear transformations