Surrogate modelling and robust optimization of multi-stage metal forming processes

In a world where materials are becoming more and more scarce, it is of key importance to produce with the least amount of waste as possible. This is also the case for metal forming processes. Unfortunately, metal forming processes are subjected to uncertainty, such as variations in the raw material or the production environment. These disturbances must be taken into account when designing the process in order to manufacture products with high accuracy and low scrap rates. The procedure of finding the design parameters that lead to the least variation in the final product despite the influence of the uncertain parameters, is referred to as robust optimization. To reduce the time and costs associated with process development using physical experiments, computational models are often used.

Metal forming processes are commonly modelled with transient Finite Element Analysis (FEA), which is computationally expensive, with model evaluation times usually in the order of minutes or hours. In general, optimization requires many evaluations of the objective function. Optimizing the production process based on the FE-model is therefore not computationally feasible. Surrogate models are commonly used to overcome this computational burden. A surrogate model is a cheap-to-evaluate model that mimics the output of the expensive model and is constructed using a data set of results from a limited number of evaluations of the expensive model.

In this work, methods for surrogate modelling and robust optimization of multi-stage metal forming processes using computational models are studied. The dissertation focuses on the construction of surrogate models that describe the entire output field of FE-models. Special attention is paid on how the available data should be preprocessed to get as much information as possible from them when different phyiscal quantities need to be modelled. Furthermore it is investigated how Radial Basis Function interpolation can be applied to get the best interpolation of preprocessed data. The obtained knowledge is applied in order to construct a surrogate model of a production stage of a two-stage metal forming process. The output from the surrogate model of the first stage is propagated to the FE-model of the subsequent stage and compared with the output of a surrogate model that describes both stages at once. Lastly, an adaptive sampling strategy for scalar metamodel-based robust optimization with multi-stage models is presented. For this purpose an algorithm is proposed that takes account of the simulation time of different stages.