Multilevel surrogate modeling approach for optimization problems with polymorphic uncertain parameters

Abstract

The solution of optimization problems with polymorphic uncertain data requires combining stochastic and non-stochastic approaches. The concept of uncertain a priori parameters and uncertain design parameters quantified by random variables and intervals is presented in this paper. Multiple runs of the nonlinear finite element model solving the structural mechanics with varying a priori and design parameters are needed to obtain a solution by means of iterative optimization algorithms (e.g. particle swarm optimization). The combination of interval analysis and Monte Carlo simulation is required for each design to be optimized. This can only be realized by substituting the nonlinear finite element model by numerically efficient surrogate models. In this paper, a multilevel strategy for neural network based surrogate modeling is presented. The deterministic finite element simulation, the stochastic analysis as well as the interval analysis are approximated by sequentially trained artificial neural networks. The approach is verified and applied to optimize the concrete cover of a reinforced concrete structure, taking the variability of material parameters and the structural load as well as construction imprecision into account.