Different approaches to multivariate calibration of nonlinear sensor data

Abstract

In this study, different approaches to the multivariate calibration of the vapors of two refrigerants are reported. As the relationships between the time-resolved sensor signals and the concentrations of the analytes are nonlinear, the widely used partial least-squares regression (PLS) fails. Therefore, different methods are used, which are known to be able to deal with nonlinearities present in data. First, the Box-Cox transformation, which transforms the dependent variables nonlinearly, was applied. The second approach, the implicit nonlinear PLS regression, tries to account for nonlinearities by introducing squared terms of the independent variables to the original independent variables. The third approach, quadratic PLS (QPLS), uses a nonlinear quadratic inner relationship for the model instead of a linear relationship such as PLS. Tree algorithms are also used, which split a nonlinear problem into smaller subproblems, which are modeled using linear methods or discrete values. Finally, neural networks are applied, which are able to model any relationship. Different special implementations, like genetic algorithms with neural networks and growing neural networks, are also used to prevent an overfitting. Among the fast and simpler algorithms, QPLS shows good results. Different implementations of neural networks show excellent results. Among the different implementations, the most sophisticated and computing-intensive algorithms (growing neural networks) show the best results. Thus, the optimal method for the data set presented is a compromise between quality of calibration and complexity of the algorithm.

Analytical evaluation of sensor measurements

“…5. Cluster analysis partial least squares and neural networks have to be used [3,[9][10][11]. The selection of chiral polymers to measure the ratio of enantiomers is of interest [12].…”

Fitting Straight Lines with Replicated Observations by Linear Regression. IV. Transforming Data

“…Box and Cox (1964) provided another general method for selecting transformations of the response that is applicable both in simple and multiple regression (Lee et al, 1999;Li and Moor, 2002). Since the seminal paper by Box and Cox in 1964, the BoxCox type of power transformations has inspired a large amount of research on its applicability as well as on the drawback arising Gu et al, 2007 The thyroid gland decision-making system developed through the logistic regression is an excellent system demonstrated 98.7% accurate by the classification table Kim and Yoon, 2007 Logistic regression was used to determine whether the probabilities of cell survival and electroporation depend on experimental conditions and cell properties Agarwal et al, 2007 A global logistic model was used to study the effects of both quantitative variables (NaCl, acid, and potassium sulfate concentrations) and dummy variables (laboratory medium or brine, and citric, lactic, or acetic acids) on growth of Saccharomyces cerevisiae López et al, 2007 Alternative method to the Arrhenius equation for termogravimetric analysis based on a logistic mixture model Naya et al, 2006 Kinetics modeling applied to predict the stability of cholecystokinin fragment CCK-4 in aqueous solution Oliva et al, 2006 Decimal logistic transformation to the sigmoidal calibration curve of ion-selective bulk optodes, for the determination of cations based on ionophore-chromoionophore chemistry Capitan-Vallvey et al, 2006 Short-term exposure data measurements of food micotoxin ochratoxin A (OTA) transformed through two-parameter Box-Cox transformation Counil et al, 2006 Log-log transformation without weighting is the simplest model to fit the calibration data for the determination of piperaquine (PC) in urine Singtoroj et al, 2006 Decimal logistic transformation to the sigmoidal calibration curve of ion-selective bulk optodes, for the determination of anions based on hydrophobic membranes containing neutral ionophore and chromoionofore Different methods are used, i.e., Box-Cox transformation, which are known to be able to deal with non-linearities present in data Dieterle et al, 2004 The minimum detectable value (MDV) of polychlorinated biphenyls (PBCs) is assessed by linearizing the calibration graph using the transformation y * = y p and y * = a + bx, the p parameter being determined iteratively Van Loco et al, 2003 Models generated when dealing with first order kinetic to profile the degradation of pest-control compounds in soil does not support the broad use of logarithmic transformation to stabilize the variance Herman and Scherer, 2003 It is necessary to transform both sides of the model, because of the nature of the relationship between the response and the mechanistic model, in order to achieve symmetry and constant variance Atkinson, 2003 Box-Cox ...…”

Ultraviolet and Visible Spectroscopy

“…These modern techniques are also used to evaluate microarrays [159], and are typically applied in food studies [160]. Modern sensors also take advantage of different data analysis methods [161].…”