A direct random sampling method for the Fourier amplitude sensitivity test of nonuniformly distributed uncertainty inputs and its application in C/C nozzles

Abstract

In this paper, the applicability of the conventional random balanced design method for the Fourier amplitude sensitivity test (RBD-FAST) is extended to uncertainty parameters with nonuniform distributions. The latter is a more general premise in real-world applications. The Halton low discrepancy sequence is proposed for direct random sampling (DRS) in RBD-FAST. The correctness of the method is verified with two benchmark problems, i.e., the G function and the flood model. DRS can alleviate the cumbersome mathematical derivation of sampling functions in the conventional FAST, and a higher accuracy level is observed with the DRS-RBD-FAST. The proposed method is employed in the global sensitivity analysis (GSA) of a C/C nozzle where 24 input parameters with normal distributions are considered. The key uncertainties contributing to the transient thermal stress of the C/C nozzle are identified, including the coefficient of thermal expansion, the wall thickness of the nozzle, the coefficient of thermal conductivity, the Poisson's ratios, and Young's moduli. The Poisson's ratios are identified as more sensitive parameters than the Young's moduli, which would not be identified without the higher accuracy level of the proposed DRS method. The proposed method can be used for widespread applications.