Spectral identification of nonlinear multi-degree-of-freedom structural systems with fractional derivative terms based on incomplete non-stationary data
Spectral identification of nonlinear multi-degree-of-freedom structural systems with fractional derivative terms based on incomplete non-stationary data
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DOI：
10.1016/j.strusafe.2020.101975
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发表时间：
2020-09
影响因子：
5.8
通讯作者：
K. D. Santos;Olga Brudastova;I. Kougioumtzoglou
中科院分区：
文献类型：
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作者：
K. D. Santos;Olga Brudastova;I. Kougioumtzoglou
提出了一种基于输入-输出（激励-响应）实现的非线性时变多自由度（MDOF）结构系统参数谱识别方法。该技术的一个显著优点涉及这样的事实，即它可以很容易地考虑分数阶导数项在系统控制方程中的存在，以及非平稳，不完整和/或噪声破坏数据的情况。具体而言，该技术依赖于重铸的控制方程作为一组多输入/多输出系统在小波域。其次，采用基于压缩采样理论的l 1范数最小化方法来确定可用的不完全非平稳输入输出数据的小波系数。最后，这些小波系数被用来重建非平稳不完整的信号，从而确定系统相关的时间和频率依赖的基于小波的频率响应函数和相关参数。数值算例中考虑了两个典型的多自由度系统，验证了方法的可靠性。第一个是指一个非线性时变系统的分数阶导数项，而第二个地址的非线性海洋结构系统受到流诱导力。值得注意的是，对于海上系统，最近提出的一种新的进化版本的广泛使用的JONSWAP频谱用于建模的非平稳的自由表面高程的情况下，随时间变化的海况。
A novel spectral identification technique is developed for determining the parameters of nonlinear and time-variant multi-degree-of-freedom (MDOF) structural systems based on available input-output (excitation-response) realizations. A significant advantage of the technique relates to the fact that it can readily account for the presence of fractional derivative terms in the system governing equations, as well as for the cases of non-stationary, incomplete and/or noise corrupted data. Specifically, the technique relies on recasting the governing equations as a set of multiple-input/multiple-output systems in the wavelet domain. Next, an l 1-norm minimization procedure based on compressive sampling theory is employed for determining the wavelet coefficients of the available incomplete non-stationary input-output data. Finally, these wavelet coefficients are utilized to reconstruct the non-stationary incomplete signals, and consequently, to determine system related time-and frequency-dependent wavelet-based frequency response functions and associated parameters. Two illustrative MDOF systems are considered in the numerical examples for demonstrating the reliability of technique. The first refers to a nonlinear time-variant system with fractional derivative terms, while the second addresses a nonlinear offshore structural system subjected to flow-induced forces. It is worth noting that for the offshore system, a novel recently proposed evolutionary version of the widely used JONSWAP spectrum is employed for modeling the non-stationary free-surface elevation in cases of time-dependent sea states.