多点激励下减震桥梁结构抗震可靠度分析的哈密顿蒙特卡洛子集模拟法

Hamiltonian Monte Carlo based subset simulation for reliability analysis of energy-dissipation bridge structures with viscous dampers under multi-support seismic excitations

减震桥梁结构在地震激励下的可靠度分析为一典型的局部非线性动力可靠度问题。随机模拟法对于求解非线性动力可靠度问题具有普遍适用性,但对于实际工程问题,其应用存在计算工作量巨大的问题。随机模拟法计算时间主要取决于所需样本数目及单次样本计算效率。为提高减震桥梁结构抗震可靠度计算效率,基于精细时程积分法、Newton迭代法建立了多点激励下减震桥梁的运动方程及相应的时域显式降维迭代解格式,提高了单次样本的计算效率;引入基于哈密顿蒙特卡洛算法的子集模拟法,减少了所需样本个数。数值算例表明:与传统随机模拟法相比,所建立的方法可有效地提高减震桥梁结构非线性动力可靠度计算效率。

The reliability analysis of energy-dissipation bridge structures with viscous dampers under multi-support seismic excitations is a typical local nonlinear dynamic problem.The Monte Carlo simulation method has the general applicability to solve the nonlinear dynamic reliability problem,but with the problem of huge computational cost for engineering practice.The computational cost is determined by the number of samples and the efficiency of a single run of deterministic structural dynamic analysis.In order to improve the efficiency of the seismic reliability analysis of the energy-dissipation bridge structures with viscous dampers,an explicit time-domain dimension-reduced iteration scheme is established using precise time-integration method and Newton-Raphson method,so that the efficiency of dynamic analysis is improved.A subset simulation method using Hamiltonian Monte Carlo is introduced to improve the sampling efficiency of random ground motion in failure domain.Numerical results show that the high efficiency of the present approach for solving nonlinear dynamic reliability problems of energy-dissipation bridge structures with viscous dampers.