  The application of polynomial chaos expansions (PCEs) to the propagation of
uncertainties in stochastic dynamical models is well-known to face challenging
issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a
sufficient level of long term accuracy requires the use of high-order
polynomials. In numerous cases, it is even infeasible to obtain accurate
metamodels with regular PCEs due to the fact that PCEs cannot represent the
dynamics. To overcome the problem, an original numerical approach was recently
proposed that combines PCEs and non-linear autoregressive with exogenous input
(NARX) models, which are a universal tool in the field of system
identification. The approach relies on using NARX models to mimic the dynamical
behaviour of the system and dealing with the uncertainties using PCEs. The
PC-NARX model was built by means of heuristic genetic algorithms. This paper
aims at introducing the least angle regression (LAR) technique for computing
PC-NARX models, which consists in solving two linear regression problems. The
proposed approach is validated with structural mechanics case studies, in which
uncertainties arising from both structures and excitations are taken into
account. Comparison with Monte Carlo simulation and regular PCEs is also
carried out to demonstrate the effectiveness of the proposed approach.
