Using GeTLS EXIN learning for the life cycle inventory problem

Life cycle assessment (LCA) is a method used to quantify the environmental impacts of a product, process, or service across its whole life cycle. One of the problems occurring when the system at hand involves processes delivering more than one valuable output (multi-functional processes) is the allotment of resources consumption and environmental burdens in the correct proportion amongst the products. Mathematically, this is represented by the solution of an overdetermined system of linear equations. In the matrix method for the solution of the inventory problem, the system is solved by resorting to mathematical tricks to transform its rectangular coefficients matrix into a square and invertible one, inevitably introducing uncertainty in the solution. The paper describes the application of an iterative algorithm (called GeTLS) for the implementation of Total Least Square (TLS) regression to solve this kind of over-determined system directly in its rectangular form. The solutions obtained with the iterative method are compared with the direct TLS solutions obtained using Singular Value Decomposition (SVD) and with the classical Ordinary Least Square (OLS) solutions. The results obtained showed that in most cases the iterative method had a higher stability with respect to perturbations of the coefficients matrix.