Second-Order Analytical Uncertainty Analysis in Life Cycle Assessment

Life cycle assessment (LCA) results
are inevitably subject to uncertainties.
Since the complete elimination of uncertainties is impossible, LCA
results should be complemented by an uncertainty analysis. However,
the approaches currently used for uncertainty analysis have some shortcomings:
statistical uncertainty analysis via Monte Carlo simulations are inherently
uncertain due to their statistical nature and can become computationally
inefficient for large systems; analytical approaches use a linear
approximation to the uncertainty by a first-order Taylor series expansion
and thus, they are only precise for small input uncertainties. In
this article, we refine the analytical uncertainty analysis by a more
precise, second-order Taylor series expansion. The presented approach
considers uncertainties from process data, allocation, and characterization
factors. We illustrate the refined approach for hydrogen production
from methane-cracking. The production system contains a recycling
loop leading to nonlinearities. By varying the strength of the loop,
we analyze the precision of the first- and second-order analytical
uncertainty approaches by comparing analytical variances to variances
from statistical Monte Carlo simulations. For the case without loops,
the second-order approach is practically exact. In all cases, the
second-order Taylor series approach is more precise than the first-order
approach, in particular for large uncertainties and for production
systems with nonlinearities, for example, from loops. For analytical
uncertainty analysis, we recommend using the second-order approach
since it is more precise and still computationally cheap.