区间参数结构动力优化的改进方法

Improved Dynamic Optimization Method for Uncertain Structures with Interval Parameters

针对区间参数结构,提出一种改进的动力响应的区间优化方法。由于区间优化问题一般要比确定性优化问题的求解复杂得多,因此,通过优化结构动力响应区间值的上界,将区间优化问题转化为近似的确定性优化问题。为了得到结构动力响应更加准确的区间值,把结构动力响应Taylor展开式中的一阶导数也看成区间的,这样得到的区间值能近似包含精确值。在区间优化方法中,设计变量的中值和半径都被选为优化变量,可以得到比传统确定性优化方法更多的优化信息。把该方法应用于典型刚架结构,优化结果表明,区间优化方法不仅能得到与传统优化方法大致相当的设计变量最优值,还能得到实际问题中当设计变量取不到最优值而有微小变化时,目标函数值的一个变化范围。

An improved interval dynamic optimization method is presented for uncertain structures with interval parameters. Due to the complexity of the interval optimization problem, it is transformed into an approximate deterministic one through optimizing the upper bound of the structural interval response. To obtain more accurate interval value of the structural response, the derivatives in the Taylor series expansion of the structural response are also considered to be interval. As a result, the approximate interval almost includes the exact structural response. Because mean values and uncertainties of the design variables are selected as optimization variables, more optimization information can be obtained by the interval optimization method. A typical frame structure is used to demonstrate the effectiveness of the method. Optimization results show that the proposed method can obtain the optimal design variables which are almost the same as that obtained by the traditional optimization method. Furthermore, an interval value of the objective function corresponding to the variation of the optimal design variables can be obtained.