Metamodeling Based on the Fusion of FEM Simulations Results and Experimental Data

In this paper an innovative multistage metamodeling technique is proposed for linking data coming from two different sources: simulations and experiments. The model is hierarchical, in the sense that one set of data (the experiments) is considered to be more reliable and it is labeled as "high- resolution" and the other set (the simulations) is labeled as "low-resolution". The results of experiments is obviously fully accurate, except for the only approximation due to the measurement system and given the intrinsically aleatory nature of all real experiments. In the proposed approach, Gaussian models are used to describe results of computer experiments because they are flexible and they can easily interpolate data coming from deterministic simulations. A second stage model is used, in order to link the prediction of the first model to the real experimental data. For the linkage model, as in the first stage, a Gaussian process is used. In this second stage a random parameter can be added to the model, known as nugget, in order to take into account the process variability. This kind of metamodeling can have different purposes: adjusting or tuning the simulations, having a better tool to drive the design process, making an optimization of a parameter of interest. In the paper, its use for optimization of a single response y with two design variables x₁ and x₂ is demonstrated. The approach is applied for modeling the crash behavior in three point bending of metal foam filled tubes.