Yield Estmation Using Surrogate Modelling in Industry
Most manufacturing processes suffer from small deviations, which may lead to rejections of some products due to malfunctioning. In this context, malfunctioning is commonly understood as violating a given performance feature specification. In order to quantify the impact of the uncertainty one defines the yield as the percentage of realizations in a manufacturing process that fulfill the specification. Thus, yield is mathematically equivalent to the concept of reliability and the relation between yield and failure probability is given in the form yield = 1 – failure probability.
To this end, a new effcient error controlled method for yield estimation and optimization was recently proposed in arXiv:1912.09908 and arXiv:2003.13278. The yield estimation combines the reliability and accuracy of a high fidelity Monte Carlo analysis and the efficiency of surrogate based techniques such as stochastic collocation or Gauß process regression. In case the accuracy of the surrogate model is not sufficient, sample points are re-evaluated employing a high fidelity model. For example adjoint error indicators can be applied to quantify the accuracies of the models. Finally, for the yield optimization a globalized Newton method is used that autmatically chooses computational models based on their fidelity.
Using an industrial example from Dassault systems (a lowpass filter model from the examples library of CST Studio Suite) it was shown that such an uncertainty quantification and optimization workflow is computaionally feasible and significantly more reliable than linearizing the model w.r.t. the uncertain parameters.