  This study debuts a new spline dimensional decomposition (SDD) for
uncertainty quantification analysis of high-dimensional functions, including
those endowed with high nonlinearity and nonsmoothness, if they exist, in a
proficient manner. The decomposition creates an hierarchical expansion for an
output random variable of interest with respect to measure-consistent
orthonormalized basis splines (B-splines) in independent input random
variables. A dimensionwise decomposition of a spline space into orthogonal
subspaces, each spanned by a reduced set of such orthonormal splines, results
in SDD. Exploiting the modulus of smoothness, the SDD approximation is shown to
converge in mean-square to the correct limit. The computational complexity of
the SDD method is polynomial, as opposed to exponential, thus alleviating the
curse of dimensionality to the extent possible. Analytical formulae are
proposed to calculate the second-moment properties of a truncated SDD
approximation for a general output random variable in terms of the expansion
coefficients involved. Numerical results indicate that a low-order SDD
approximation of nonsmooth functions calculates the probabilistic
characteristics of an output variable with an accuracy matching or surpassing
those obtained by high-order approximations from several existing methods.
Finally, a 34-dimensional random eigenvalue analysis demonstrates the utility
of SDD in solving practical problems.
