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Polynomial chaos expansions (PCE) have proven efficiency in a number offields for propagating parametric uncertainties through computational models ofcomplex systems, namely structural and fluid mechanics, chemical reactions andelectromagnetism, etc. For problems involving oscillatory, time-dependentoutput quantities of interest, it is well-known that reasonable accuracy ofPCE-based approaches is difficult to reach in the long term. In this paper, wepropose a fully non-intrusive approach based on stochastic time warping toaddress this issue: each realization (trajectory) of the model response isfirst rescaled to its own time scale so as to put all sampled trajectories inphase in a common virtual time line. Principal component analysis is introducedto compress the information contained in these transformed trajectories andsparse PCE representations using least angle regression are finally used toapproximate the components. The approach shows remarkably small predictionerror for particular trajectories as well as for second-order statistics of thelatter. It is illustrated on different benchmark problems well known in theliterature on time-dependent PCE problems, ranging from rigid body dynamics,chemical reactions to forced oscillations of a non linear system.

Surrogate models for oscillatory systems using sparse polynomial chaos expansions and stochastic time warping