Secured PCR (sPCR) for detection and correction of PCR calibration model failures induced by uncalibrated spectral features

Abstract

Many spectroscopic monitoring techniques make use of chemometric algorithms such as principal component regression (PCR) for calibration and evaluation of optical spectra. However, standard techniques of chemometric calibration and evaluation suffer from uncalibrated spectral features which are contained in measured spectra but were not considered during the initial calibration. For two main reasons such uncalibrated spectral features have to be detected and corrected: (a) if unknown spectral features appear after calibration major errors of concentration prediction are encountered and (b) the detection of uncalibrated spectral features enables recognition and handling of failures occurring in chemical processes. Hence detection, correction and characterization of uncalibrated absorption features are of great importance in on-line spectroscopy. A novel approach is proposed here for this purpose. This algorithm performs a qualitative data analysis for detecting and correcting such uncalibrated spectral features. Following this qualitative data analysis and if necessary correction, a conventional PCR is used for calculating the concentration of the calibrated analytes. Both steps together set up a so-called secured PCR (sPCR). In the undisturbed case this sPCR algorithm is demonstrated to provide equivalent results as conventional PCR and to be superior in evaluating disturbed spectra. For testing purposes simulated spectra sets are used since the disturbance is known and the determined results can be validated with respect to the magnitude of the true disturbance. The errors averaged over 1000 disturbed test samples could be decreased up to 71% by sPCR compared with conventional PCR. In up to 94% of the test samples more accurate concentration values were obtained. The novel sPCR algorithm was also applied to experimental spectra measured with mid-infrared attenuated total reflection spectroscopy considering chlorinated hydrocarbons dissolved in water. sPCR is capable to extract uncalibrated features from these experimental data and to improve the concentration results.

Fault‐tolerant spectroscopic data evaluation based on extended principal component regression correcting for spectral drifts and uncalibrated spectral features

“…Secured PCR (sPCR) for correction of uncalibrated spectral features sPCR [3,4] takes advantage of an additional analysis of the residual spectrum e in (2). e is determined from a measurement spectrum x meas by projecting [5] x meas onto the orthogonal complement of the vector space spanned by the PCs p 1 ; .…”

“…The notation in this study follows Reference [3]. pPCR and sPCR are based on a conventional PCR deriving a set of R orthonormal PCs p 1 ; .…”

“…As was proposed in ref. [3,4], a narrow window is moved over a matrix containing the PCs and the residual spectrum. Then it is analyzed whether the residual spectrum inside this window is linearly dependent from the PCs or linearly independent.…”

“…However, as will be shown in this study, pPCR cannot determine localized uncalibrated absorption features and sPCR cannot correct for broad drifts affecting the complete spectrum (see e.g. Figure 7 in Reference [3]). Hence a combination of both methods is proposed and investigated in this study.…”

“…problems during monitored processes. Such situations are handled with a method called secured principal component regression (sPCR) which was published recently [3,4]. sPCR detects and corrects localized spectral features which are not consistent with the PCs.…”