The non-intrusive polynomial chaos (NIPC) expansion method is one of the most frequently used methods for uncertainty quantification (UQ) due to its high computational efficiency and accuracy. However, the number of polynomial bases is known to substantially grow as the number of random parameters increases, leading to excessive computational cost. Various sparse schemes such as the least angle regression method have been utilised to alleviate such a problem. Nevertheless, the computational cost associated with the NIPC method is still nonnegligible in systems which consist of a high number of random parameters. This paper proposes the first versatile UQ method which requires the least computational cost whilst maintaining the UQ accuracy. We combine the hyperbolic scheme with the principal component analysis method and reduce the number of polynomial bases with the simpler procedure than currently available, keeping most information in the system. The ridge regression method is utilised to build a statistical parsimonious model to decrease the number of input samples and the leaveone- out cross-validation method is applied to improve the UQ accuracy .
- Non-intrusive polynomial chaos expansion (NIPC)
- principal component analysis (PCA)
- ridge regression (RR)
- uncertainty quantification
- finite difference time domain (FDTD)
- Debye media