Adaptive kriging for simulation-based design under uncertainty development of metamodels in augmeted input space and adaptive tuning of their characteristics

This investigation focuses on design-under-uncertainty problems that employ a probabilistic performance as objective function and consider its estimation through stochastic simulation. This approach puts no constraints on the computational and probability models adopted, but involves a high computational cost especially for design problems involving complex, high-fidelity numerical models. A framework relying on kriging metamodeling to approximate the system performance in an augmented input space is considered here to alleviate this cost. A sub region of the design space is defined and a kriging metamodel is built to approximate the system response (output) with respect to both the design variables and the uncertain model parameters (random variables). This metamodel is then used within a stochastic simulation setting (addressing uncertainties in the model parameters) to approximate the system performance when estimating the objective function for specific values of the design variables. This information is then used to search for a local optimum within the previously established design sub domain. Only when the optimization algorithm drives the search outside this domain, a new metamodel is generated. The process is iterated until convergence is established and an efficient sharing of information across these iterations is established to adaptively tune characteristics of the kriging metamodel.