ABSTRACT

Robust parameter design (RPD) aims at reducing the effect of noise variation on quality through achieving a small expected quality loss (EQL). In RPD with time-consuming computer simulations, Gaussian process (GP) models are used to predict the EQL. Three straightforward models for predicting the EQL include a GP model for the simulator output, a GP model for the quality loss, and a lognormal process model for the quality loss (the log quality loss is modeled as a GP). Each of these models has some drawbacks as discussed in this paper. We propose the shifted log loss GP model, which includes the lognormal process model for the quality loss and the GP model for the quality loss as special cases when the shift varies from zero to infinity. The proposed model overcomes some of the limitations of the three existing models. It has a simple and accurate approximation for the posterior EQL distribution, and it gives accurate and precise predictions of the EQL. We illustrate the superior performance of the proposed model over the three existing models with a toy example and an RPD problem involving a steel beam.

摘要

稳健参数设计 (RPD) 旨在通过实现较小的预期质量损失 (EQL) 来减少噪声变化对质量的影响。在具有耗时计算机模拟的 RPD 中，高斯过程 (GP) 模型用于预测 EQL。用于预测 EQL 的三个直接模型包括用于模拟器输出的 GP 模型、用于质量损失的 GP 模型和用于质量损失的对数正态过程模型（对数质量损失建模为 GP）。正如本文所讨论的，这些模型中的每一个都有一些缺点。我们提出了移位对数损失GP模型，其中包括质量损失的对数正态过程模型和质量损失的GP模型作为移位从零到无穷大的特殊情况。所提出的模型克服了三个现有模型的一些局限性。它对后验 EQL 分布有一个简单而准确的近似值，并且它给出了对 EQL 的准确和精确的预测。我们通过一个玩具示例和一个涉及钢梁的 RPD 问题来说明所提出的模型相对于三个现有模型的优越性能。