The moment quadrature method for global sensitivity analysis

This study proposes a novel direct non-sampling method, the moment quadrature method, for calculating Sobol’ sensitivity indices by formulating a deterministic computational procedure, allowing for simultaneous evaluation of all Sobol’ sensitivity indices using one pass of model evaluations. The method is different from the existing Monte Carlo (MC)-based and surrogate-based methods; therefore, it does not suffer from the inherent sampling error in MC-based methods nor from the modeling error in surrogate-based methods. Various benchmarking and engineering problems are used to examine the performance of the method, and the results are compared with the best known MC estimator reportedly available at the time of this work and/or exact solutions when available. The results show that the proposed method offers higher accuracy, faster convergence rate, and less computational demand, particularly for complex time-varying computational problems. A realistic computationally demanding time-varying fluid problem that cannot be effectively solved using MC-based methods demonstrates the advantage of the proposed method, where a total number of 8 model evaluations yields converged global sensitivity results.