The performance of the sequential metamodel based optimization procedure depends strongly on the chosen building blocks for the algorithm, such as the used metamodeling method and sequential improvement criterion. In this study, the effect of these choices on the efficiency of the robust optimization procedure is investigated. A novel sequential improvement criterion for robust optimization is proposed, as well as an improved implementation of radial basis function interpolation suitable for sequential optimization. The leave-one-out cross-validation measure is used to estimate the uncertainty of the radial basis function metamodel. The metamodeling methods and sequential improvement criteria are compared, based on a test with Gaussian random fields as well as on the optimization of a strip bending process with five design variables and two noise variables. For this process, better results are obtained in the runs with the novel sequential improvement criterion as well as with the novel radial basis function implementation, compared to the runs with conventional sequential improvement criteria and kriging interpolation.

Modern production systems have numerous sensors that produce large amounts of data. This data can be exploited in many ways, from providing insight into the manufacturing process to facilitating automated decision making. These opportunities are still underexploited in the metal forming industry, due to the complexity of these processes. In this work, a probabilistic framework is proposed for simultaneous model improvement and state estimation in metal forming mass production. Recursive Bayesian estimation is used to simultaneously track the evolution of process state and to estimate the deviation between the physics-based model and the real process. A sheet bending mass production process is used to test the proposed framework. A metamodel of the process is built using proper orthogonal decomposition and radial basis function interpolation. The model is extended with a deviation model in order to account for the difference between model and real process. Particle filtering is used to track the state evolution and to estimate the deviation model parameters simultaneously. The approach is tested and analysed using a large number of simulations, based on pseudo-data obtained from a numerical sheet bending model.

The Yld2004-18p yield criterion uses 18 parameters to define anisotropy for a full 3D stress state. It is demonstrated in this paper that dependencies between the parameters exist and for a given set of experimental data the parameters are not uniquely defined. Analysis of the yield function shows that two specific combinations of parameters do not contribute to the value of the yield function. Therefore, the number of parameters can be reduced to 16, without any loss of flexibility. Similarly, the number of parameters for the plane stress version of this yield criterion reduces from 14 to 12.

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