Development of a new SMP model satisfying all known physical constraints in environmental application

A new Solver for Mixture Problem (SMP) model has been developed that satisfies all known fundamental natural physical constraints identified in environmental application. Previously, nonnegative matrix factorization (NMF) models were developed and applied successfully in chemometrics application and aerosol source apportionment studies. NMF models are based on nonnegativity constraints of loadings and scores that are equivalent to source compositions and source apportionments, respectively, in aerosol source apportionment study. In environmental applications of aerosol source apportionment studies, however, more physical constraints must be satisfied in addition to nonnegativity constraints of loadings and scores. A new model has been developed based on alternating primal-dual interior point nonlinear programming, subject to inequality constraints of all known fundamental physical constraints. Previous multivariate receptor models have been partial implementations; they have not been able to satisfy meaningful physical constraints when estimating both source compositions and source apportionments from ambient data. The SMP model, however, successfully estimates both source apportionments and source compositions while satisfying all physical constraints. Source compositions estimated by the SMP model can be used in other source apportionment studies using the Chemical Mass Balance (CMB) receptor model. The SMP model has been applied to an error free data set to examine the capability of estimating source compositions and source apportionments. Two sets of simulations were conducted and the results are compared and discussed. Simulation results show that SMP estimated pairs of source compositions and source apportionments satisfy all known physical constraints and are in good agreement with true values.

► SMP model is based on alternating primal–dual interior point nonlinear programming.
► SMP model satisfies all physical constraints identified in environmental application.
► SMP-estimated source compositions can be used in other CMB analysis.
► SMP-estimated source profiles and contributions satisfy all identified constraints.
► The SMP model can be applied to any mixture problem.