Uncertainty propagation in stochastic fractional order processes using spectral methods: A hybrid approach

Stochastic spectral methods are widely used in uncertainty propagation thanks to its ability
to obtain highly accurate solution with less computational demand. A novel hybrid
spectral method is proposed here that combines generalized polynomial chaos (gPC) and
operational matrix approaches. The hybrid method takes advantage of gPC’s efficient handling
of large parameter uncertainties and overcomes its limited applicability to systems
with relatively highly correlated inputs. The hybrid method’s use of operational matrices
allows analyses of systems with low input correlations without suffering its restriction
to small parameter uncertainties. The hybrid method is aimed to propagate uncertainties
in fractional order systems with random parameters and random inputs with low correlation lengths. It is validated through several examples with different stochastic uncertainties.Comparison with Monte Carlo and gPC demonstrates the superior computational efficiency of the proposed method.