公路桥梁车辆荷载截尾分段概率模型及应用

Piecewise Truncation Probability Distribution Model of Vehicle Loads for Highway Bridges and Its Application

为了准确描述实际公路桥梁车辆荷载多峰厚尾的分布特征,利用分段函数结合多个高斯分布函数,并采用数据拟合方法,求得了车辆荷载的概率密度函数和概率分布函数表达式,建立了车辆荷载的分段截尾的多重混合高斯概率分布模型,并进一步推导了基于EM算法的多重混合高斯分布模型求解方法。根据中国实测车辆荷载的轴组特征,获得了各典型地区该分段截尾车辆荷载模型的概率分布参数。分析结果表明:该分布函数模型的拟合精度较高,能准确反映荷载分布的多峰厚尾特征;各典型地区车辆荷载轴质量分布呈现不同特点,但各地区单轴质量的首峰分布基本一致,各轴组荷载普遍超载,特别是贵州、湖北和湖南地区超载较严重;各地区双联轴、三联轴的平均轴质量超出汽车国标规定值约2倍,双联轴平均轴质量超出现行公路工程规范标准值的15%以上;实测数据显示三联轴在95%保证率下的平均轴质量约为50t。

In order to accurately describe the distribution characteristics of multiple-peaks and fat tails of actual vehicle loads of highway bridges, the probability density function and probability distribution expression of vehicle loads were obtained by data fitting method. And the multiple- gaussian mixture distribution model of piecewise truncation was established by piecewise function combined with multiple-gaussian distribution ~unctions. The solving method of multiple-gaussian mixture distribution model was further derived based on EM algorithm. On the basis of characteristics of axial configuration, the probability distribution parameters of the piecewise truncation probability distribution models in typical areas were obtained. The results show that the fitting with high precision of the distribution function model can accurately reflect the load region presents different features, but the first peak distribution of single axle weight in each region is basically similar. Almost all the axial configurations overload, especially in the regions of Guizhou, Hubei and Hunan. The average axle weights of tandem axles and tridem axles are about twice more than national standard values of vehicles in each region, and the average axle weight of tandem axles exceed 15% of the standard value of the current technical standard of highway engineering. The measured data shows that the average tridem-axle weight is about 50 tons at 95 % guarantee rate.