Abstract 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.

中文翻译：

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基于不完全非平稳数据的具有分数阶导数项的非线性多自由度结构系统的谱识别

摘要 开发了一种新的光谱识别技术，用于基于可用的输入-输出（激励-响应）实现来确定非线性和时变多自由度 (MDOF) 结构系统的参数。该技术的一个显着优势在于它可以很容易地解释系统控制方程中分数导数项的存在，以及非平稳、不完整和/或噪声损坏数据的情况。具体来说，该技术依赖于将控制方程重铸为小波域中的一组多输入/多输出系统。接下来，采用基于压缩采样理论的 l 1 -范数最小化程序来确定可用的不完整非平稳输入输出数据的小波系数。最后，这些小波系数用于重建非平稳不完整信号，从而确定系统相关的时间和频率相关的基于小波的频率响应函数和相关参数。在数值例子中考虑了两个说明性的 MDOF 系统，以证明技术的可靠性。第一个涉及具有分数导数项的非线性时变系统，而第二个涉及受流动诱导力影响的非线性海上结构系统。值得注意的是，对于离岸系统，最近提出的广泛使用的 JONSWAP 谱的一种新的演化版本被用于模拟随时间变化的海况下的非平稳自由表面高程。