Power series expansion and structural analysis for life cycle assessment |
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Authors: | Sangwon Suh Reinout Heijungs |
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Institution: | (1) Department of Bio-based Products, College of Natural Resources, University of Minnesota, 2004 Folwell Ave., Saint Paul, MN 55108, USA;(2) Institute of Environmental Sciences (CML), Leiden University, PO Box 9518, 2300 RA Leiden, The Netherlands |
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Abstract: | Goal, Scope and Background The usefulness of power series expansion for an LCA system has often been doubted, as those systems may not possess the unique
properties that enable power series expansion and analyses based on the power series. This paper surveys the existing literature
on power series expansion of monetary input-output system and discusses how the power series expansion can be utilized for
more general systems including the LCA model.
Methods The inherent properties of matrices that are capable of producing power series forms for their inverse and, further, can utilize
structural path analysis are analyzed. Using these analyses, the way how a matrix that is not eligible for structural analyses
is converted into an eligible form is investigated. A numerical example is presented to demonstrate the findings.
Results The necessary and sufficient condition for an indecomposable, real square technology matrix can be expressed using power series
was identified. Two additional conditions for a technology matrix to be utilized for structural analyses using power series
expansion are discussed as well. It was also shown that an LCA system that fulfills the Hawkins-Simon condition can be easily
converted into the form that is eligible for structural analysis by rescaling the columns and rows.
Discussion As a numerical example, an application of accumulative structural path analysis for an LCA system is shown. The implications
of the results are discussed in a more plain language as well.
Conclusions The survey presented in this paper provides not only the conditions under which a linear system is expressed using a power
series form but also the way to appropriately convert a system to utilize the rich analytical tools using power series expansion
for structural analyses.
Recommendations and Perspectives Widely used LCA databases and software tools have employed the linear systems approach as the basis. Much of these developments
in the domain of LCA have been made, however, in isolation of the rich findings of IOA. There will be much to benefit LCA
through an active dialogue between the two disciplines.
There are rich analytical tools available through the use of power series expansion. The current survey will help software
developers and LCA practitioners to apply such tools in LCA. |
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Keywords: | Input-output analysis IOA LCA practitioners LCA software developers monetary input-output system power series expansion structural path analysis |
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