基于响应面的新型索拱桥非线性索力优化

Nonlinear cable force optimization of new type arch bridges with diagonal web cables based on response surface method

提出新型索拱桥非线性索力优化方法。该方法基于均匀设计与二次多项式响应面方法,构造新型索拱桥弯曲应变能与索力的非线性近似函数,并结合牛顿迭代法搜索其最优索力。以跨径为600 m的索拱桥作为算例,分别使用本文方法、线性的影响矩阵法、基于有限元的牛顿迭代优化法及随机搜索迭代优化法对该算例进行非线性索力优化分析,并在主拱圈弯矩优化结果、优化耗费时间及优化迭代次数方面进行比较,以验证本文方法的有效性及适用性。研究结果表明:本文所提的基于均匀设计响应面与牛顿迭代相结合的方法,在新型索拱桥非线性索力优化中有较好的适用性,其弯矩极值比线性的影响矩阵法所得极值小18.42%,弯曲应变能小33.47%,运算时间比基于有限元的牛顿迭代优化法的时间少85.22%,迭代次数比随机搜索优化法的次数少99.35%。

A nonlinear cable force optimization method for a new type arch bridges with diagonal web cables was proposed, whose approximate nonlinear function between bending strain energy and cable force was obtained by uniform design and quadratic polynomial response surface method. The optimal cable force was obtained by Newton iteration method at the end based on this approximate nonlinear function. A 600 m span arch bridge with diagonal web cables was used as an example to test the effectiveness and applicability of the proposed method, through the comparisons in the main arch ring bending moment optimization results, optimizing time-consuming and optimization iteration between four methods, which includes the proposed method, linear influence matrix method, Newton iteration method based on finite element model, and random search optimization method. The results show that the proposed method based on uniform design response surface method and Newton iteration method is applicable in this new type arch bridges, and the results of proposed method have 18.42% reduction in extreme bending moment and 33.47% reduction in bending strain energy compared to those of the influence matrix method, 85.22% reduction in optimizing time-consuming compared to that of Newton iteration method based on finite element model, and 99.35% reduction in optimization iterations compared to that of random search optimization method.