Extension of self-modeling curve resolution to mixtures of more than three components: Part 2. Finding the complete solution

Abstract

The previous paper [R.C. Henry, B.M. Kim, Extension of self-modeling curve resolution to mixtures of more than three components: Part 1. Finding the basic feasible region, Chemometrics and Intelligent Laboratory Systems 8 (1990) 205–216] explained an extension of self-modeling curve resolution for an arbitrary number of components. A method was described to determine the basic feasible region that is formed with certain natural physical constraints in eigenspace. This basic feasible region is not a complete solution. It is still necessary to find where components are located in the basic feasible region. For a complete solution, a priori information is required and this is incorporated into the natural physical constraints as additional physical constraints. In this paper, the use of additional physical constraints is described. Once the location of one component has been determined from the additional physical constraints in the basic feasible region, this information further restricts the possible locations for other components. To incorporate this restriction into the model, a method has been developed similar to that used to determine the inner boundary. This algorithm was implemented in Fortran 77, and a new model, Source Apportionment by Factors with Explicit Restrictions (SAFER), was developed. As a first attempt, the SAFER model was applied to an error-free four-component problem to examine the new model's performance when there are no random measurement errors. The results of the simulation study show that the new model successfully resolves the feasible ranges of the source compositions and estimates source compositions with some bias. In addition, the feasible region of one unknown component was also resolved.