随机动力系统非平稳响应和可靠性的小波算法及应用研究—以地震输入为例

Applications of wavelet analysis in engineering has become a hot research both at Domestic and abroad, it has practical significance for earthquake wave localization, the non-stationary response and reliability analysis on civil engineering. This study adopts wavelet theory on seismic wave time-frequency characteristics, response and dynamic reliability of random vibration for further study, analysis time-frequency characteristics of seismic wave, combination its time domain and frequency domain, then wavelet evolutionary spectrum model which fits to random non-stationary process for earthquake input will be constructed. Meanwhile, seismic random response for particle displacement, velocity and acceleration's moments of multi degree of freedom MDOF dynamic systems will be estimated to calculate dynamic reliability in practical engineering. Finally, the wavelet algorithm which is simple and practical will be researched. The subject explains characteristics of non-stationary earthquake input of dynamic response from the point of view in time domain and frequency domain theory the random response. Dynamic reliability optimal algorithm will be given based on mother wavelet's mathematical properties with dynamic nonlinear system; this research will provide new ideas and theoretical basis of wavelet theory application in engineering nonlinear random vibration analysis for the further study。

小波分析在工程中的应用已成为国内外研究热点，它对于土木工程输入的地震波局部化分析，非平稳响应，可靠性分析等有重要的实际意义。本课题采用小波理论对地震波时频特性、随机振动响应及动力可靠度等问题进行深入探索，通过地震波的时频特性分析，并采用小波理论解决时域和频域的有机联合问题，从而构造出适用工程地震输入的随机非平稳小波演变谱模型。同时以输入的小波演变谱模型及其时频联合分布函数为基础，深入探讨工程中动力学系统中单、多自由度体系质点的位移、速度和加速度等随机响应的各阶谱矩，解决地震波输入单、多自由度体系的动力可靠度工程实际问题；研究简便实用的算法。课题从时频域理论角度阐明非平稳信号输入工程中动力体系响应特性，从选择的母小波本身数学特性和动力体系非线性的角度提出随机响应和动力可靠度最优算法，为小波理论在工程中随机振动非线性分析的进一步研究提供新思路和理论依据。

小波分析在工程中的应用已成为国内外研究热点，它对于土木工程输入的地震波局部化分析，非平稳响应，可靠性分析等有重要的实际意义。本课题采用小波理论对地震波时频特性、随机振动响应及动力可靠度等问题进行了深入探索，通过对地震波的时频特性进行分析，解决了地震波在结构动力分析中时域和频域的有机联合问题，构造出适用工程地震输入的随机非平稳小波演变谱模型。同时以输入的小波演变谱模型及其时频联合分布函数为基础，深入探讨了工程中动力学系统中单、多自由度体系质点的位移、速度和加速度等随机响应的各阶谱矩，解决地震波输入单、多自由度体系的动力可靠度工程实际问题；得到简便实用的算法。课题从时频域理论角度阐明非平稳信号输入工程中动力体系响应特性，从选择的母小波本身数学特性和动力体系非线性的角度提出随机响应和动力可靠度最优算法，为小波理论在工程中随机振动非线性分析的进一步研究提供新思路和理论依据。