In this paper we present an algorithm for yield estimation and optimization exploiting Hessian based optimization methods, an adaptive Monte Carlo (MC) strategy, polynomial surrogates and several error indicators. Yield estimation is used to quantify the impact of uncertainty in a manufacturing process. Since computational efficiency is one main issue in uncertainty quantification, we propose a hybrid method, where a large part of a MC sample is evaluated with a surrogate model, and only a small subset of the sample is re-evaluated with a high fidelity finite element model. In order to determine this critical fraction of the sample, an adjoint error indicator is used for both the surrogate error and the finite element error. For yield optimization we propose an adaptive Newton-MC method. We reduce computational effort and control the MC error by adaptively increasing the sample size. The proposed method minimizes the impact of uncertainty by optimizing the yield. It allows to control the finite element error, surrogate error and MC error. At the same time it is much more efficient than standard MC approaches combined with standard Newton algorithms.

中文翻译：

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基于自适应 Newton-Monte Carlo 和多项式代理的产量优化

在本文中，我们提出了一种利用基于 Hessian 的优化方法、自适应蒙特卡洛 (MC) 策略、多项式代理和几个误差指标的产量估计和优化算法。产量估计用于量化制造过程中不确定性的影响。由于计算效率是不确定性量化的一个主要问题，我们提出了一种混合方法，其中使用代理模型评估大部分 MC 样本，而仅使用高保真有限元重新评估样本的一小部分模型。为了确定样本的这一关键部分，对替代误差和有限元误差都使用了伴随误差指标。对于产量优化，我们提出了一种自适应 Newton-MC 方法。我们通过自适应地增加样本大小来减少计算工作量并控制 MC 误差。所提出的方法通过优化产量来最小化不确定性的影响。它允许控制有限元误差、代理误差和 MC 误差。同时，它比结合标准牛顿算法的标准 MC 方法更有效。