Data-driven modeling of general damping systems by k-means clustering and two-stage regression
Data-driven modeling of general damping systems by k-means clustering and two-stage regression
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DOI：
10.1016/j.ymssp.2021.108572
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发表时间：
2022
影响因子：
8.4
通讯作者：
Jia Guo;Li Wang;Iori Fukuda;K. Ikago
中科院分区：
文献类型：
--
作者：
Jia Guo;Li Wang;Iori Fukuda;K. Ikago
阻尼是结构分析和设计中最复杂的现象之一。从原理上讲，阻尼是由振动中的能量耗散引起的，因此，摩擦、塑性和粘性等是常见的阻尼源。虽然已经提出了各种阻尼模型，但它们只适用于某些特定的阻尼现象，没有统一的方法来建模任意阻尼系统。最后，本文提出了一个数据驱动的框架建模的一般阻尼系统。建立这一框架有三个关键要素。首先，预先定义的基函数字典的建立来描述一般阻尼模型的滞回和粘性行为。其次，应用k-均值聚类技术从测量数据中分离对应于阻尼模型的滞回和粘性部分的两个数据集。第三，一个两阶段的回归过程调用的粘性和滞后部分的阻尼模型被确定顺序从容易分离的两个数据集。这种识别过程中的线性最小二乘回归和稀疏正则化。因此，如果一个新的阻尼系统的滞回和粘性行为完全反映在字典中，底层的模型方程可以直接和快速恢复通过所提出的数据驱动的方法。数值例子以及实验测试的研究，以证明所提出的数据驱动建模方法的有效性和效率一般阻尼系统。
Damping is one of the most complicated phenomena in structural analysis and design. In principle, damping arises with energy dissipation in the vibration and therefore, friction, plasticity and viscosity etc are common sources of damping. Though various damping models have been proposed, they are only applicable to some certain damping phenomena and there is no unified way to model an arbitrary damping system. To the end, this paper presents a data-driven framework for modeling of general damping systems. There are three key ingredients in establishing this framework. At first, pre-defined dictionaries of basis functions are built to describe the hysteretic and viscous behaviors of a general damping model. Secondly, the k-means clustering technique is applied to separate the two datasets corresponding to respective hysteretic and viscous parts of the damping model from the measured data. Thirdly, a two-stage regression procedure is invoked where the viscous and hysteretic parts of the damping model are identified sequentially from the readily separated two datasets. Such identification proceeds by means of linear least-squares regression and sparse regularization. As a consequence, if a new damping system whose hysteretic and viscous behaviors are totally reflected in the dictionary, the underlying model equation can be directly and quickly recovered through the proposed data-driven approach. Numerical examples as well as an experimental test are studied to demonstrate the effectiveness and efficiency of the proposed data-driven modeling approach for general damping systems.