基于遗传算法和有限混合分布的应力谱多模态建模

该文提出了一种基于遗传算法(genetic algorithm, GA)的有限混合分布参数估计方法, 应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先, 采用小波变换消除原始应变监测数据中的温度影响, 利用雨流计数法将应变时程曲线转化为日应力谱, 考虑到交通荷载(包括汽车荷载和火车荷载)和台风的影响, 建立标准日应力谱。然后, 采用三种不同的有限混合分布函数(有限混合正态分布函数、有限混合对数正态分布函数和有限混合威布尔分布函数)以及基于遗传算法的混合参数估计方法对应力幅进行多模态建模, 根据赤池信息准则(Akaike’s information criterion, AIC)确定最佳的有限混合模型。最后, 采用双变量有限混合分布和基于遗传算法的混合参数估计方法建立了应力幅和平均应力二维随机变量联合概率密度函数。结果表明, 该文提出的基于遗传算法的有限混合分布参数估计方法可以有效应用于二维随机变量的概率建模。

MULTI-MODAL MODELING OF STRESS SPECTRUM USING GENETIC ALGORITHM AND FINITE MIXTURE DISTRIBUTIONS

In this study, a genetic algorithm-based (GA-based) method for the estimation of the parameters in the finite mixture distributions is proposed and applied to the multi-modal modeling of the stress spectrum of a typical welded joint of Tsing Ma Bridge. Firstly, the temperature effect on the original strain monitoring data is eliminated by wavelet transform. The rainflow counting algorithm is employed to transfer the strain stress histories into daily stress spectra. A standard daily stress spectrum accounting for highway traffic, railway traffic, and typhoon effects is derived. Then, the multi-modal modeling of the stress range is conducted by use of three types of finite mixture distributions (normal, lognormal, and Weibull) in conjunction with the GA-based mixture parameter estimation method. The optimal finite mixed model is determined by the Akaike’s information criterion (AIC). Finally, the joint probability density function (PDF) of the stress range and the mean stress is obtained using the bivariate finite mixture distributions and the GA-based mixture parameter estimation method. The results show that the proposed GA-based mixture parameter estimation method is adequate in the probabilistic modeling of two random variables.