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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。
In this paper, a method for estimating the parameters of a finite hybrid distribution based on genetic algorithm (GA) is proposed. By using this method, the stress spectrum of a typical welded node of the Tsing Ma Bridge is modeled. Firstly, the wavelet transform was used to eliminate the influence of temperature in the original strain monitoring data. The rain flow count method was used to convert the strain history curve to the daily stress spectrum. Considering the influence of traffic load (including vehicle load and train load) and typhoon, a standard Daily stress spectrum. Then, three different finite mixed distribution functions (finite mixed normal distribution function, finite mixed log normal distribution function and finite mixed Weibull distribution function) and the hybrid parameter estimation method based on genetic algorithm were used to simulate the amplitude of stress State model, and determine the best finite mixture model according to the Akaike’s information criterion (AIC). Finally, the joint probability density function of two-dimensional random variables of stress amplitude and average stress is established by using the bivariate finite mixture distribution and the genetic algorithm based hybrid parameter estimation method. The results show that the proposed method of finite mixed parameter estimation based on genetic algorithm proposed in this paper can be effectively applied to the probability modeling of two-dimensional random variables.