基于自适应时频分析的结构非平稳响应及动力可靠性分析方法研究

The safety of engineering structures under natural hazards is a critical important issue for structural engineers, the natural hazards such as earthquake and wind have the nonstationary properties, therefore, it is important to study the reliability of structures under nonstaionary random excitations. Based on the local stationary wavelet process model of the nonstationary stochastic process, the adaptive time-frequency analysis based nonstationary random vibration and dynamic reliability analysis method will be developed in this project. Firstly, the chirplet-based nonstationary random excitation simulation method and the evolutionary power spectral density estimation method will be developed, based on the accurate representation time-frequency characters of the random excitations, the method for determining the non-stationary responses of linear system will be also developed. Secondly, based on the orthogonal properties of the local stationary wavelet process, the adaptive time-frequency representation method for the statistical linearization will be developed, and the principle of the time-frequency transmission for the random excitations and the responses of the nonlinear systems will be also explored, the effect of the nonstationary of the excitations on the nonlinear responses of the structures will be studied. Lastly, based on the obtained nonstationary random responses of the systems, the efficient simulation method and the adaptive wavelet-frame neural network method for determining the first excursion probabilities will be developed. This project aims to provide an innovative methodology for nonstationary random vibration of structures, and the method to be developed will be widely applicable for the related disciplines.

工程结构在自然灾害下的安全性是设计中的重大问题，由于像地震、风这类常见灾害荷载具有非平稳特征，因此研究非平稳随机激励作用下结构可靠性具有重要意义。本项目基于新近提出的非平稳随机过程局部平稳小波过程模型，利用自适应时频分析探索结构非平稳随机振动及动力可靠性分析方法。首先，研究非平稳随机激励模拟及其演变功率谱密度估计的线调频小波方法，在精确表达随机激励时频非平稳特征的基础上，研究线性结构非平稳随机响应求解的线调频小波方法；其次，利用局部平稳小波过程的正交性探索统计线性化的自适应时频表达，揭示非平稳随机激励下非线性结构体系激励与响应的时频传输原理，并分析激励非平稳性对结构非线性反应的影响；最后基于得到的结构非平稳随机响应，建立结构动力可靠性分析高效数值模拟方法和自适应小波框架神经网络方法。本项目研究将为结构非平稳随机振动分析开辟一条新途径，同时对其他相关学科中实际问题的解决也具有广泛应用前景。

工程结构在自然灾害下的安全性是设计中的重大问题，由于像地震、风这类常见灾害荷载具有非平稳特征，因此研究非平稳随机激励作用下结构可靠性具有重要意义。本项目基于新近提出的非平稳随机过程局部平稳小波过程模型，利用自适应时频分析探索结构非平稳随机振动及动力可靠性分析方法。首先，研究非平稳随机激励模拟及其演变功率谱密度估计的线调频小波方法，在精确表达随机激励时频非平稳特征的基础上，研究线性结构非平稳随机响应求解的线调频小波方法；其次，利用局部平稳小波过程的正交性探索统计线性化的自适应时频表达，揭示非平稳随机激励下非线性结构体系激励与响应的时频传输原理，并分析激励非平稳性对结构非线性反应的影响；最后基于得到的结构非平稳随机响应，建立结构动力可靠性分析高效数值模拟方法和自适应小波框架神经网络方法。本项目研究将为结构非平稳随机振动分析开辟一条新途径，同时对其他相关学科中实际问题的解决也具有广泛应用前景。