Estimating prediction uncertainties in PLS models based on NIR data: application in process water quality monitoring
Introduction
Membrane technology has been used for a long time in the production of dairy ingredients. At Arla Foods Ingredient (AFI) cheese whey proteins are up concentrated by ultrafiltration membranes, while the permeate is further processed with a two-stage reverse osmosis plant (RO and RO-polisher) to collect lactose. The potential for re-using the RO-polisher permeate as process water is our interest.
In order to assess the risk of (re-)using the process water the quality must be monitored. By implementing the principles of process analytical technology the risk can be monitored continuously and real-time. In the present study, urea has been identified to be the main chemical compound in the RO water at AFI. Urea can be quantified with high accuracy by enzymatic assays but this approach is time-consuming and slow. Urea can also be detected by NIR spectroscopy, which opens the opportunity for real-time measurements.
The reduced concentration of urea pushes the detection and quantification limits for NIR applications and increases prediction uncertainty. Prediction uncertainty estimation has been described previously in literature. Unfortunately, a proper strategy and justification for the determination of the parameters that go into the uncertainty estimates are seldom given, which has resulted in a limited use of confidence limits for PLS-based predictions in industrial applications.
Experimental
Forty process water samples were collected from three sampling points simultaneously over ten hours of production at AFI. Ten laboratory samples were prepared by combining stock solutions of lactose, urea, and demineralized water. NIR spectra were measured with ABB Bomem MB Series FT-NIR (CA) with a custom made, temperature controlled sample cell. Sample was introduced into the cell and measured five times in a row, each the average of 128 scans over the spectral range 700-2500 nm with a spectral resolution of 8 cm-1. Temperature was set to 27 ˚C. All samples were measured over the course of three days, and the same background – demineralized water - was used for all spectra obtained. As spectral range for urea calibration 2083 – 2257 nm was selected, and the spectra were preprocessed using Savitzky-Golay second order polynomial, second derivative, with a window size of app. 62 nm. For all samples two of the five replicate measurements were excluded based on the norm of the difference between the average of all five preprocessed spectra and the given preprocessed spectra. The three remaining spectra were included with a common reference value. Independent urea concentration determinations were made using a Urea+ammonia enzyme assay (Megazymes, GB) as described by the vendor.
Results and discussion
Two separate PLS models were built relating the NIR spectra to the concentration of urea: One model based on laboratory samples made of known amounts of urea and lactose, and one model based on urea concentration estimated by the enzyme assay reference method applied to process samples. Prediction error variance (Vpe) is calculated and compared to the RMSEP obtained from an independent test set. The Vpe is decomposed into the individual the variance components and discussed.