Ž . Chemometrics and Intelligent Laboratory Systems 37 1997 5–14 The chemical mass balance as a multivariate calibration problem Philip K. Hopke ) , Xin-Hua Song Department of Chemistry, Clarkson UniÕersity, Box 5810, Potsdam, NY 13699-5810, USA Abstract The problem of source identification and quantitative mass apportion for airborne particulate matter commonly called re- ceptor modeling can be treated in a manner analogous to the multivariate calibration problem commonly encountered in Ž . chemometrics. Partial least-squares PLS has been previously used in such a context. In this work, artificial neural networks Ž . Ž . ANN and simulated annealing SA have been applied to the sets of simulated data. The aerosol composition data gener- Ž . ated by the National Bureau of Standards NBS for the 1982 EPA workshop on mathematical and empirical receptor model- ing held at Quail Roost, NC, have been examined. From these tests of ANN and SA and earlier work on partial least-squares, it appears that multivariate calibration methods may be helpful in resolving sources and apportioning the airborne mass. ANN was better able to deal with the collinearity in the source profile matrix. For CMB and PLS, this collinearity prevented the apportionment of mass to all of the known sources. In addition, ANN could identify which sources were active when trained with a source profile library containing more sources than actually contributed to the samples. SA produced more accurate source contribution estimates than the other methods, but was also bothered by the collinearity to the same degree as the CMB or PLS results. Thus, the initial results with these methods are promising, but further development and testing are needed before they can be routinely used. Keywords: Chemical mass balance; Multivariate calibration 1. Introduction In many chemical studies, the measured proper- ties of the system can be considered to be the linear sum of the term representing the fundamental effects in that system times appropriate weighing factors. For example, the absorbance at a particular wavelength of a mixture of compounds for a fixed path length, z , is considered to be a sum of the absorbencies of the in- dividual components a l Ž . s l C q l C q ... q l C Ž . Ž . Ž . p 1 2 1 2 p z 1 Ž. ) Corresponding author. where is the molar extinction coefficient for the i i-th compound at wavelength l and C is the corre- i sponding concentration. Thus, if the absorbencies of a mixture of several absorbing species are measured at m various wavelengths, a series of equations can be obtained. p a l Ž . j s l C 2 Ž. Ž . Ý j k k z ks1 If we know what components are present and what the molar extinction coefficients are for each com- pound at each wavelength, the concentrations of each compound can be determined using a multiple linear regression fit to these data. However, over the past decade or more, there has been an increasing ten- dency to relate the composition of complex mixtures 0169-7439r97r$17.00 Copyright q 1997 Elsevier Science B.V. All rights reserved. Ž . PII S0169-7439 96 00043-3