Stochastic sensitivity analysis by dimensional decomposition and score functions

This article presents a new class of computational methods, known as dimensional decomposition methods, for calculating stochastic sensitivities of mechanical systems with respect to probability distribution parameters. These methods involve a hierarchical decomposition of a multivariate response function in terms of variables with increasing dimensions and score functions associated with probability distribution of a random input. The proposed decomposition facilitates univariate and bivariate approximations of stochastic sensitivity measures, lower-dimensional numerical integrations or Lagrange interpolations, and Monte Carlo simulation. Both the probabilistic response and its sensitivities can be estimated from a single stochastic analysis, without requiring performance function gradients. Numerical results indicate that the decomposition methods developed provide accurate and computationally efficient estimates of sensitivities of statistical moments or reliability, including stochastic design of mechanical systems. Future effort includes extending these decomposition methods to account for the performance function parameters in sensitivity analysis.