Optimal experimental design provides a way of determining a-priori the best locations at which to place accelerometers in vibrations analysis experiments. However, in practice, sensors often fail during experimentation due high mechanical accelerations. There have been limited works exploring the use of robust OED in the context of vibrations analysis, where design spaces (i.e. candidate sensor locations and orientations) are high-dimensional and the finite-element models are expensive to compute. Therefore, this work considers the application of more general robust OED formulations to such a structural dynamics problem. We employ a relaxation-based approach that enables the use of efficient gradient-based optimization. Furthermore, we leverage a binary-inducing penalty during optimization to provide a binary sensor design as an alternative to leveraging post-optimization rounding heuristics. We consider performance metrics based on the log-determinant of the parameter covariance as well those based on parameter and prediction mean-squared errors. We find that although robust and classical designs are similar for the structural dynamics problem of interest, robust designs outperform classical designs on average over relevant failure scenarios of interest.

翻译：最优实验设计提供了一种在振动分析实验中预先确定加速度计最佳布设位置的方法。然而在实际中，传感器常因高机械加速度而在实验过程中失效。目前，将鲁棒最优实验设计应用于振动分析领域的研究较为有限，该领域的设计空间（即候选传感器的位置与方位）维度高，且有限元模型计算成本高昂。因此，本文考虑将更通用的鲁棒最优实验设计公式应用于此类结构动力学问题。我们采用了一种基于松弛的方法，能够利用高效的梯度优化技术。此外，在优化过程中引入了一项二元诱导惩罚项，以替代优化后常用的舍入启发式方法，直接生成二元传感器设计方案。我们分别采用基于参数协方差矩阵对数行列式的性能指标，以及基于参数均方误差和预测均方误差的性能指标进行评估。研究发现，尽管鲁棒设计与经典设计在相关结构动力学问题中表现相似，但在所有关注的典型失效场景下，鲁棒设计的平均性能均优于经典设计。