基于极大似然法的雪荷载计算与分析

Calculation and Analysis of Snow Loads Based on the Maximum Likelihood Method

为了提高雪荷载评估的准确性,利用极大似然法对雪荷载平稳二项随机概率分布模型进行参数估计.通过引入似然函数,使似然函数在某组参数上达到最大值,获得模型参数的极大似然估计.然后利用柯尔莫哥洛夫检验法对分布函数进行检验,并与矩法和耿贝尔法进行对比分析.结果表明,极大似然法在剩余方差Sf和拟合相对偏差Rf指标方面最优.进一步应用上述三种方法,基于沭阳县实测的历年最大积雪深度计算雪压,并与现行规范中的基本雪压进行对比,发现极大似然法计算结果合理可靠、整体效果最好,认为规范采用极大似然法对雪荷载进行参数估计更为合适.

In order to improve the accuracy of the evaluation of snow loads, this paper estimated the parameter of stationary binomial probability distribution model for snow loads using maximum likelihood method. Firstly, the maximum likelihood estimation of the model parameters was obtained when the function reached a maximum at a certain set of parameters by introducing the likelihood function. Then the distribution function was tested through the Kolmogorov criterion. Comparison results between the maximum likelihood method, the moment method and the Gumbel method show that maximum likelihood method is better in the remaining variance Sf and indicators relative deviation R~. Furthermore, snow pressure at Shuyang was calculated according to measured maximum snow depth applying the above three methods, and it was compared with the basic snow pressure in the current code. It is found that the maximum likelihood is reasonable and reliable, and it has the best overall effect. It is advised that the basic snow pressure should he evaluated using the maximum likelihood in building code.