Gaussian Surrogate Dimension Reduction for Efficient Reliability-Based Design Optimization

Abstract

Reliability-based design optimization (RBDO) is commonly performed using surrogates to approximate the response due to deterministic and stochastic design variables, as well as random parameters, but is ultimately limited by the number of dimensions that can be accurately represented. In this paper, a new surrogate-centric RBDO formulation is developed to alleviate the computational expense of excessive random parameters. Nondeterministic kriging nonstationary variation estimation is used to characterize normally distributed random parameters and numerical noise rather than increasing the surrogate’s dimensionality. Simultaneously, surrogate-based uncertainty propagation is performed considering the nonnormally distributed or high nonlinear random parameters, and stochastic design variables. In this study, propagated uncertainties and the uncertainty captured by the kriging variation are recombined through the convolution of the two probability density functions. It was found that conglomerations of normally distributed random parameters allow this method to reduce the number of approximated spaces while maintaining accuracy compared to existing surrogate approaches. This paper contains a detailed description of the proposed methodology; foundational four-, five-, and six-dimensional RBDO examples with comparisons to previous methods from the literature; and the RBDO of a 10-dimensional nonlinear thermoelastic hat-stiffened panel under a frequency and stress constraint.