基于机器学习的多时标动力系统数字孪生模型
Machine learning based digital twin for dynamical systems with multiple time-scales
摘要：
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，我们专注于一个数字孪生框架的线性单自由度结构动力系统，除了其内在的动态时间尺度在两个不同的操作时间尺度演变。我们的方法战略上分为两个组成部分-（a）基于物理的标称模型的数据处理和响应预测，和（b）数据驱动的机器学习模型的系统参数的时间演变。基于物理的标称模型是系统特定的，并且基于所考虑的问题来选择。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，我们建议利用混合专家作为数据驱动模型。在混合专家模型中，采用高斯过程（GP）作为专家模型。其主要思想是让每个专家在一个单一的时间尺度上跟踪系统参数的演变。为了学习“混合专家使用GP”的超参数，一个有效的框架，利用期望最大化和序贯蒙特卡罗采样器。数字孪生的性能示出了一个多时间尺度的动态系统的刚度和/或质量的变化。数字孪生被认为是强大的，并产生合理的准确结果。拟议中的数字孪生模型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。还调查了与数据质量和数据量有关的方面。
英文摘要：
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.
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