Balancing Resolution with Analysis Time for Biodiesel–Diesel Fuel Separations Using GC, PCA, and the Mahalanobis Distance

Abstract

In this work, a statistical metric called the Mahalanobis distance (MD) is used to compare gas chromatography separation conditions. In the two-sample case, the MD computes the distance between the means of the multivariate probability distributions of two groups. Two gas chromatography columns of the same polarity but differing length and film thickness were utilized for the analysis of fatty acid methyl esters in biodiesel fuels. Biodiesel feedstock samples representing classes of canola, coconut, flaxseed, palm kernal, safflower, soy, soyabean, sunflower, tallow, and waste grease were used in our experiments. Data sets measured from each column were aligned with the correlated optimized warping (COW) algorithm prior to principal components analysis (PCA). The PC scores were then used to compute the MD. Differences between the data produced by each column were determined by converting the MD to its corresponding p-value using the F-distribution. The combination of COW parameters that maximized the p-value were determined for each feedstock separately. The results demonstrate that chromatograms from each column could be optimally aligned to minimize the MD derived from the PC-transformed data. The corresponding p-values for each feedstock type indicated that the two column conditions could produce data that were not statistically different. As a result, the slight loss of resolution using a faster column may be acceptable based on the application for which the data are used.

Recent applications of chemometrics in one‐ and two‐dimensional chromatography

“…An interesting application of PCA in combination with COW within the field of chromatography is to compare columns [136]. The chromatograms are first aligned with a COW algorithm prior to the PCA, such as to maximize the probability (p-) values.…”