Multivariate estimation of the limit of detection by orthogonal partial least squares in temperature-modulated MOX sensors

Abstract

Metal oxide semiconductor (MOX) sensors are usually temperature-modulated and calibrated with multivariate models such as partial least squares (PLS) to increase the inherent low selectivity of this technology. The multivariate sensor response patterns exhibit heteroscedastic and correlated noise, which suggests that maximum likelihood methods should outperform PLS. One contribution of this paper is the comparison between PLS and maximum likelihood principal components regression (MLPCR) in MOX sensors. PLS is often criticized by the lack of interpretability when the model complexity increases beyond the chemical rank of the problem. This happens in MOX sensors due to cross-sensitivities to interferences, such as temperature or humidity and non-linearity. Additionally, the estimation of fundamental figures of merit, such as the limit of detection (LOD), is still not standardized in multivariate models. Orthogonalization methods, such as orthogonal projection to latent structures (O-PLS), have been successfully applied in other fields to reduce the complexity of PLS models. In this work, we propose a LOD estimation method based on applying the well-accepted univariate LOD formulas to the scores of the first component of an orthogonal PLS model. The resulting LOD is compared to the multivariate LOD range derived from error-propagation. The methodology is applied to data extracted from temperature-modulated MOX sensors (FIS SB-500-12 and Figaro TGS 3870-A04), aiming at the detection of low concentrations of carbon monoxide in the presence of uncontrolled humidity (chemical noise). We found that PLS models were simpler and more accurate than MLPCR models. Average LOD values of 0.79 ppm (FIS) and 1.06 ppm (Figaro) were found using the approach described in this paper. These values were contained within the LOD ranges obtained with the error-propagation approach. The mean LOD increased to 1.13 ppm (FIS) and 1.59 ppm (Figaro) when considering validation samples collected two weeks after calibration, which represents a 43% and 46% degradation, respectively. The orthogonal score-plot was a very convenient tool to visualize MOX sensor data and to validate the LOD estimates.