Generally, in designing nonlinear energy sink (NES), only uncertainties in the ground motion parameters are considered and the unconditional expected mean of the performance metric is minimized. However, such an approach has two major limitations. First, ignoring the uncertainties in the system parameters can result in an inefficient design of the NES. Second, only minimizing the unconditional mean of the performance metric may result in large variance of the response because of the uncertainties in the system parameters. To address these issues, we focus on robust design optimization (RDO) of NES under uncertain system and hazard parameters. The RDO is solved as a bi-objective optimization problem where the mean and the standard deviation of the performance metric are simultaneously minimized. This bi-objective optimization problem has been converted into a single objective problem by using the weighted sum method. However, solving an RDO problem can be computationally expensive. We thus used a novel machine learning technique, referred to as the hybrid polynomial correlated function expansion (H-PCFE), for solving the RDO problem in an efficient manner. Moreover, we adopt an adaptive framework where H-PCFE models trained at previous iterations are reused and hence, the computational cost is less. We illustrate that H-PCFE is computationally efficient and accurate as compared to other similar methods available in the literature. A numerical study showcasing the importance of incorporating the uncertain system parameters into the optimization procedure is shown. Using the same example, we also illustrate the importance of solving an RDO problem for NES design. Overall, considering the uncertainties in the parameters have resulted in a more efficient design. Determining NES parameters by solving an RDO problem results in a less sensitive design.

通常，在设计非线性能量吸收器（NES）时，仅考虑地面运动参数的不确定性，并将性能指标的无条件预期均值最小化。但是，这种方法有两个主要局限性。首先，忽略系统参数的不确定性会导致NES的设计效率低下。其次，由于系统参数的不确定性，仅最小化性能指标的无条件平均值可能会导致响应的较大差异。为了解决这些问题，我们将重点放在不确定系统和危害参数下的NES稳健设计优化（RDO）。RDO解决为双目标优化问题，其中性能指标的均值和标准偏差同时最小化。通过使用加权和方法，该双目标优化问题已转换为单目标问题。但是，解决RDO问题在计算上可能会很昂贵。因此，我们使用了一种新颖的机器学习技术，称为混合多项式相关函数扩展（H-PCFE），以有效地解决了RDO问题。此外，我们采用了一种自适应框架，其中可重复使用在先前迭代中训练的H-PCFE模型，因此，计算成本较低。我们说明，与文献中提供的其他类似方法相比，H-PCFE在计算上高效且准确。数值研究表明了将不确定的系统参数纳入优化程序的重要性。使用相同的示例 我们还说明了解决NES设计中的RDO问题的重要性。总体而言，考虑到参数的不确定性，可以提高设计效率。通过解决RDO问题来确定NES参数会导致设计灵敏度降低。