地下隧洞结构区间分析的优化方法

Interval analysis of underground tunnel structure by optimization method

工程中的不确定性问题可以用区间理论、随机理论或模糊理论进行求解。采用区间分析方法来处理地下隧洞结构开挖支护过程中的不确定性问题时。将结构系统中的不确定性参数用区间数来表示,用有限元方法建立系统的控制方程。该控制方程是一个包含不确定性几何参数的复杂的非线性区间方程组。讨论了两种优化计算模型,分别将方程组中的所有区间数作为设计变量,区间量的变化区间作为相应的设计变量的边界约束,运用遗传模拟退火算法求出位移和应力等响应量的最大值和最小值。通过工程算例验证了文中方法的合理性及可行性,并与端点组合方法的结果进行了比较分析。

The uncertain problem in engineering can be solved by using interval,probabilistic or fuzzy theories. Interval analysis method is used to simulate the uncertainty in excavation and shoring of underground tunnels. By representing the uncertain parameters as interval numbers,the governed equations of structural system are obtained by means of the finite element method. These equations are complicated nonlinear interval equations which comprise uncertain geometric parameters. There are two optimization models which are discussed in this paper. Taking all the interval numbers in the equations as optimal design variables and representing the lower and upper bounds of each interval number as the boundary constrain of the variable respectively,the maximum and minimum of response components such as displacements and stresses are achieved by using the genetic and simulated annealing algorithms. The numerical results demonstrate the rationality and feasibility of the present method. As a contrast,the corresponding outputs of the boundary combination are analyzed.