基于概率密度演化的复杂工程结构抗震整体可靠度研究

In order to realize the performance design and control of complex engineering structures, the randomness of external excitations and structural properties, and the nonlinearity of structural behaviors are two unavoidable basic problems. The main purpose of the research on stochastic dynamics is to solve the analysis, design and control of nonlinear stochastic systems subjected to random dynamic excitations. The research of this project is focused on the above issues. Basically, the Karhunen-Loeve(K-L)decomposition provides a second-moment characterization of random processes in terms of deterministic orthogonal functions and uncorrelated random variables. The efficiency of the K-L decomposition hinges crucially on the availability of accurate eigenvalues and eigenfunctions of the covariance function. The double orthogonal expansion method overcomes the shortcomings of the K-L decomposition. However, the above two methods need a large number of uncorrelated random variables to describe a random process in engineering. Using the idea of the homology random, an innovative triple orthogonal expansion model of random dynamic excitations, such as earthquake, strong wind and wave, can be obtained. The method of triple orthogonal expansion using a basic random variable can accurately simulate the random process from the external excitation source in second order moment characterization. In addition, structures exhibit inelastic behaviors under severe cyclic loads associated with earthquakes. The generalized Bouc-Wen differential model with 13 parameters is one of the most widely accepted phenomenological models of hysteresis in structures. It can account for strength degradation, stiffness degradation, and even pinching of an inelastic member. Through theoretical analysis, structural model test and numerical simulation, the values of insensitive parameters will be fixed and the probability distributions of sensitive parameters will be obtained in the hysteresis model of reinforced concrete structures. So, the restoring force model with coupling nonlinearity and randomness can be constructed. The recently developed probability density evolution method by Li and Chen is capable of capturing instantaneous probability density function and its evolution of linear and/or nonlinear response of structures. It is natural to combine the probability density evolution method and the foregoing triple orthogonal expansion of seismic ground motion and the hysteresis model with the nonlinearity and randomness in reinforced concrete structures to study the nonlinear stochastic seismic response and global reliability of complex engineering structures. Furthermore, based on the global reliability of structures, the optimization design and control of the structural seismic performance can be realized.

为了实现复杂工程结构的全寿命性能设计与控制，结构外部作用的随机性与结构性态的非线性及随机性耦合是两个不可回避的基本问题，随机动力系统研究的主要目的，即在于解决非线性随机系统在随机动力作用下的分析、设计与控制问题。本研究亦集中于这一问题。首先，从Karhunen-Loeve分解理论出发，在随机过程的二重正交展开基础上，采用同源随机性的思想，研究地震等随机动力激励的三重正交展开模型，达到用一个基本随机变量即可在二阶数值特征意义上精确反映外部激励源的随机性。其次，采用具有13个参数的广义Bouc-Wen模型来描述结构性态的滞回特性，通过理论分析、结构模型试验与数值模拟，研究模型参数的确定性取值或概率分布，构建具有非线性与随机性耦合的恢复力模型。最后，结合最新发展的概率密度演化理论，研究复杂工程结构的非线性随机地震反应与抗震整体可靠度，进而实现基于整体可靠度的结构抗震性能优化设计与控制目的。

为了实现复杂工程结构的全寿命性能设计与控制，结构外部作用的随机性与结构性态的非线性及随机性耦合是两个不可回避的基本问题，随机动力系统研究的主要目的，即在于解决非线性随机系统在随机动力作用下的分析、设计与控制问题。本研究亦集中于这一问题。首先，在随机过程的正交展开和谱表示方法基础上，采用随机函数的思想，建立了地震、强风及海浪等工程随机动力作用的正交展开-随机函数方法和谱表示-随机函数方法，实现了用1-2个基本随机变量即可在二阶数值特征意义上精确反映外部激励源的随机性。其次，从非平稳地震动的物理过程出发，发展了两类新的演变功率谱模型，即广义演变功率谱模型和以时-频双调制函数为核心的演变功率谱模型。同时，采用具有13个参数的广义Bouc-Wen模型来描述结构性态的滞回特性，通过理论分析、结构模型试验与数值模拟，研究了模型参数的确定性取值或概率分布，构建了具有非线性与随机性耦合的恢复力模型。最后，将非平稳地震动过程的概率模型与最新发展的概率密度演化理论相结合，研究了复杂工程结构（如大跨桥梁结构、大型渡槽结构及混凝土重力坝结构等）的非线性随机地震反应分析与抗震整体可靠度的计算，进而为实现基于整体可靠度的结构抗震性能优化设计与控制奠定了基础。