基于有限曲条理论弯箱梁桥位移参数的动态Bayes-CG估计

应用Bayes-CG方法,动态地估计了弯箱梁桥位移参数.基于Novozhilov理论,推导了简支弯箱梁桥有限曲条控制方程,利用谐函数的正交性解决了曲条刚度矩阵元素的耦合问题;结合柔度理论,解决了箱横隔板的超静定求解问题;应用Bayes定理,建立了弯箱梁桥位移参数的动态Bayes误差函数,推导了相应的动态Bayes均值和方差表达式.提出步长的一维自动寻优方案后,结合CG法研究了弯箱梁桥位移参数的动态Bayes估计方法,同时给出了弯箱梁桥位移参数具体估计步骤.典型算例分析结果表明:有限曲条元法是分析弯箱梁桥的有效计算方法,所需条元少且计算精度高;Bayes-CG方法能正确地动态估计弯箱梁桥位移参数,且参数先验信息合理时,待估参数稳定地收敛于参数实际值.

Dynamic Bayes-CG estimation of displacement parameters of curved box girder bridge based on FCS theory

Displacement parameters of curved box girder bridge are dynamically estimated by applying Bayes-CG method.Based on Novozhilov theory,the FCS(finite curried strip) controlling equation of pinned curved box girder bridge is derived and the coupling problem between the elements of FCS(finite curved strip) stiffness matrix is resolved by using the orthogonal property of harmonious function.With flexibility method,the indeterminate problem of segregating slab of curved box girder bridge is solved.Dynamic Bayesian error function of displacement parameters of curved box girder bridge is founded for the first time based on Bayesian theory.The corresponding formulas of dynamic Bayesian expectation and variance are derived.After the method of solving the automatic search of step length is broached,the optimization estimation computing formulas are also obtained by adapting CG method.Then the steps of dynamic Bayesian estimation are given in detail.Through analysis of a typical example,the conclusions are drawn: FCS method with few strip elements and precise results is an efficient computational method for curved box girder bridge;displacement parameters of curved box girder bridge can be correctly estimated with Bayes-CG method and when the pre-known information is proper,displacement parameters are steadily convergent to the true values.