SURROGATE MODELING CONSIDERING MEASURING DATA AND THEIR MEASUREMENT UNCERTAINTY

Virtual approaches to manufacturing processes are a common tool in developing components today. Simulations are always containing uncertainties like simplifying assumptions in computer aided modelling, material deviations, fluctuating external loads or other known and unknown influences. To integrate such uncertainties in an early design stage, the input parameters should be defined as intervals, because insufficient data may be available at this stage to provide probability distributions. To consider such epistemic uncertainties, a large number of intervals can be merged into a fuzzy number. For each interval a membership value is assigned which depends on the interval limits and an expert estimation. However, this interval modelling leads to a very high number of expensive evaluations, which is not feasible for a high number of uncertain input parameters. To reduce the calculation time, surrogate models are used. Here, the full model is evaluated only at some grid points and the system response is approximated by mathematical approaches. Design and Analysis of Computer Experiments (DACE) offers a suitable surrogate model based on the Kriging method. The system model substituted in this way can be evaluated in an efficient way, but in addition to the uncertain simulation results, the approximation error dependent on the surrogate model has to be considered. Investigations of first prototypes lead to new knowledge that can be used to improve the surrogate model. Measurements, however, also include errors that are composed of systematic and random errors. The systematic measurement errors are specific errors for each measuring system and task, which are usually corrected during the measurement. However, an estimation of the random measurement error, which represents the precision of the measurement can be taken into account. Two methods are presented. Either an additional constant term is implemented in the standard Kriging or a superposition of two standard Kriging models, which are based on the simulation data and the measurement data, is used. As an application example a cold forging process of a steel gearwheel is employed.