基于凸模型和伪概率分布的不确定性结构响应分析

针对传统基于凸模型的方法分析不确定性结构时仅能给出结构响应边界的局限性, 本文结合基于体积比的伪概率度量和一次二阶矩提出一种结构响应不确定性量化的新方法. 该方法在精确求解不确定性结构响应上下界的同时, 给出了结构响应在上下界内的伪概率分布. 首先利用椭球凸模型对结构不确定性进行建模, 结构响应关于不确定性参数的状态方程将椭球分割成两个区域, 则分割区域体积与椭球域总体积之比可作为伪概率来度量结构响应的不确定性; 其次, 用一次二阶矩法序列求解结构响应不确定性传播方程, 获得最可能展开点及相应分割区域的近似体积. 最后, 通过一个典型的六杆桁架结构算例与传统凸模型方法和蒙特卡洛法进行比较, 验证该方法对不确定性结构响应分析和量化的有效性和优越性.

Uncertainty Analysis of Structural Response Based on Convex Model and Pseudo-probability Distribution

Through the traditional response analysis method for uncertain structures based on non-probabilistic convex model, only the bounds can be obtained. So, in this paper a new uncertainty propagation method which combined volume ratio with first order second moment is proposed. Using this uncertainty propagation method, not only the bounds but also the pseudo-probability distribution of the structural response can be accurately evaluated. First, the uncertainty of structure parameter is modeled by multidimensional ellipsoid convex set. The ellipsoid is separated two parts by the state equation of the structural response with respect to uncertain parameters. So, the volume ratio of separated domain and the whole ellipsoid domain can be used to quantify the uncertainty of structural response. Second, in order to obtain the most probable expansion point and the approximate volume of the separated domain, the propagation equation of uncertain response is sequentially solved through First order second moment (FOSM) method. Finally, the uncertain response analysis of a typical six-bar truss is applied using the proposed method, Monte Carlo simulation and traditional method. The comparisons of the results demonstrate that the proposed method is more effective and accurate.