基于小波分析的滞回结构系统非平稳随机地震响应研究

The stochastic response analysis of a hysteretic MDOF system to full non-stationary excitations plays an important theoretic role in the structural seismic reliability evaluation. In this regard, a wavelet-based approach will be proposed for determining the time-varying Power Spectrum Density (PSD) of the response of hysteretic structural systems to full non-stationary earthquake excitations. Specifically, first, a reliable approach for the time-varying PSD estimation of the non-stationary engineering stochastic processes could be established via the wavelet analysis. To this purposed, the inherent relationship between the wavelet coefficients and PSD of stochastic processes shall be studied carefully. Next, considering the wavelet-based solution of differential equation of motion and based on the above-mentioned developments, a relationship between the time-varying PSDs on the local time-frequency domains of the full non-stationary excitations and of the responses could be obtained. These studies of time-varying PSD determination of linear structures could lay a complete foundation of the ensuing statistical linearization analysis. Finally, the response PSD of the hysteretic structural systems to fully non-stationary earthquake excitations is expected to be solved by combing the celebrated statistical linearization method and the time-frequency resolution of the wavelet. In this regard, the statistical linearization method shall be implemented on the local time-frequency domains, vis-a-vis the classical one is implemented only on the time domain. This treatment shall not only allow time-frequency dependent equivalent system parameters leading an important improving of the statistical linearization, but also could permit a novel approach for dealing with the full non-stationary earthquake excitations of the MDOF hysteretic structures. The proposed approach is expected to provide an alternative theoretic foundation for the further seismic reliability analysis of the hysteretic structures to the real-world stochastic earthquake excitations.

完全非平稳地震动作用下多自由度滞回系统的随机动力响应分析对工程结构的抗震性能评估有着重要理论指导作用。本研究将结合小波分析的时间-尺度（频率）联合分辨特点，研究多自由度滞回结构在完全非平稳随机地震动作用下的随机动力行为：首先将探讨非平稳随机过程小波变换与其时变功率谱密度之间的联系，建立由小波变换到时变功率谱密度过渡的途径；随后结合求解结构动力方程的小波变换方法，建立线性结构非平稳激励与响应时变功率谱密度之间的联系；在此基础上，发展适用于多自由度非线性滞回结构的局部时间-频率子域上的统计线性化方法。采用所建立的基于小波分析的统计线性化方法，能充分利用小波变换的时-频联合分辨能力与统计线性化方法的广泛适用性，从而有针对性地探索随机地震动时间-频率联合非平稳特性对多自由度非线性滞回结构随机动力响应的影响，为结构抗震可靠度评估提供理论基础。

本研究结合小波分析的时间-尺度（频率）联合分辨特点，研究了多自由度滞回结构在完全非平稳随机地震动作用下的随机动力行为。探讨了非平稳随机过程小波变换与其时变功率谱密度之间的联系，建立了由小波变换到时变功率谱密度过渡的途径；随后，结合求解结构动力方程的小波变换方法，建立了线性结构非平稳激励与响应时变功率谱密度之间的联系；在此基础上，发展了适用于多自由度非线性滞回结构的局部时间-频率子域上的统计线性化方法。采用所建立的基于小波分析的统计线性化方法，能充分利用小波变换的时.震动时间-频率联合非平稳特性对多自由度非线性滞回结构随机动力响应的影响，为结构抗震可靠度评估提供理论基础。课题研究期间，发表论文8篇，其中SCI收录论文4篇，EI3篇，中文核心期刊论文1篇。培养研究生5人，博士生1人。