正态信息扩散法推断岩土参数概率分布的窗宽优化和区间截尾问题研究

Research on window width optimization and interval truncation for inferring probability distribution of geotechnical parameters by normal information diffusion method

正态信息扩散法被认为是相对最优的推断岩土参数概率分布方法,但其存在窗宽选择和截尾误差问题。提出以均方差指标最小为目标,逐级改变窗宽h,获得与直方图匹配的正态信息扩散分布窗宽确定方法;在确定匹配窗宽的基础上,借助样本队列曲线,提出增大样本下界、减小样本上界的“收窄”正态信息扩散分布取值区间方法。工程实际测试样本的统计结果表明:提出的匹配窗宽下的信息扩散分布所得到的概率密度函数优于h窗宽下的概率密度函数,拟合误差更小;“收窄”样本边界后获得的正态信息扩散分布区间与样本的实际分布区间更接近,减小截尾误差,累积概率更接近1。

The Normal information diffusion method is considered to be the relatively optimal method for inferringthe probability distribution of geotechnical parameters,but there are some problems such as window width selection and truncation error.A method for determining the window width of the normal information diffusion distribution by changing the window width h step by step with the goal of minimizing the mean square error index wasproposed in this paper.On the basis of determining the matching window width,the method of“narrowing”the value interval of normal information diffusion distribution was proposedby increasing the lower bound of sample and reducing the upper bound of sample ward with the help of sample queue curve.The statistical results of engineering test samples show that the probability density function of information diffusion distribution under matching window width is better than that under h window width,and the fitting error is smaller in this paper.The diffusion distribution interval of normal information obtained after"narrowing"the sample boundary is closer to the actual distribution interval of the sample.The truncation error is reduced and the cumulative probability is closer to 1.