Digital twin technology has a huge potential for widespread applications in different industrial sectors such as infrastructure, aerospace, and automotive. However, practical adoptions of this technology have been slower, mainly due to a lack of application-specific details. Here we focus on a digital twin framework for linear single-degree-of-freedom structural dynamic systems evolving in two different operational time scales in addition to its intrinsic dynamic time-scale. Our approach strategically separates into two components -- (a) a physics-based nominal model for data processing and response predictions, and (b) a data-driven machine learning model for the time-evolution of the system parameters. The physics-based nominal model is system-specific and selected based on the problem under consideration. On the other hand, the data-driven machine learning model is generic. For tracking the multi-scale evolution of the system parameters, we propose to exploit a mixture of experts as the data-driven model. Within the mixture of experts model, Gaussian Process (GP) is used as the expert model. The primary idea is to let each expert track the evolution of the system parameters at a single time-scale. For learning the hyperparameters of the `mixture of experts using GP', an efficient framework the exploits expectation-maximization and sequential Monte Carlo sampler is used. Performance of the digital twin is illustrated on a multi-timescale dynamical system with stiffness and/or mass variations. The digital twin is found to be robust and yields reasonably accurate results. One exciting feature of the proposed digital twin is its capability to provide reasonable predictions at future time-steps. Aspects related to the data quality and data quantity are also investigated.

中文翻译：

---

基于机器学习的多时标动态系统数字孪生

数字孪生技术在基础设施、航空航天和汽车等不同工业领域具有广泛应用的巨大潜力。然而，这项技术的实际采用速度较慢，主要是由于缺乏特定于应用程序的细节。在这里，我们专注于线性单自由度结构动力系统的数字孪生框架，除了其固有的动态时间尺度外，还可以在两个不同的操作时间尺度上演进。我们的方法战略性地分为两个部分——（a）用于数据处理和响应预测的基于物理的标称模型，以及（b）用于系统参数时间演化的数据驱动机器学习模型。基于物理的标称模型是特定于系统的，并根据所考虑的问题进行选择。另一方面，数据驱动的机器学习模型是通用的。为了跟踪系统参数的多尺度演化，我们建议利用专家的混合作为数据驱动模型。在混合专家模型中，高斯过程（GP）被用作专家模型。主要思想是让每个专家在单个时间尺度上跟踪系统参数的演变。为了学习“使用 GP 的专家混合”的超参数，使用了利用期望最大化和顺序蒙特卡罗采样器的有效框架。数字孪生的性能在具有刚度和/或质量变化的多时间尺度动力系统上进行了说明。数字孪生被发现是健壮的并且产生相当准确的结果。提议的数字孪生的一个令人兴奋的功能是它能够在未来的时间步长提供合理的预测。还研究了与数据质量和数据数量相关的方面。