指数函数拟合公路隧道工程沉降规律的方法研究  

Study on Method of Exponential Function for Fitting Settlement Rule of Highway Tunnel Enigneeing

作　　者：张子贤[1] 

机构地区：[1]江苏建筑职业技术学院,江苏徐州221116

出　　处：《城市道桥与防洪》2017年第12期157-160,共4页Urban Roads Bridges & Flood Control

基　　金：住房与城乡建设部项目(2015-K7-009)

摘　　要：对于指数函数回归,只当采用乘积随机误差时才能够线性化。导出了采用乘积随机误差及采用线性化回归方法时,指数函数因变量的数学期望的表达式,该式表明,该因变量的估计值并非是其数学期望的估值。分析表明,采用线性化回归方法所求指数函数的回归系数不满足该因变量的残差平方和为最小。基于上述不合理现象,对指数函数的回归计算应采用非线性回归方法求解。文中给出了采用高斯-牛顿法或借助MATLAB软件中nlinfit函数求解指数函数非线性回归的方法。实例进一步表明,采用非线性回归方法拟合效果显著优于线性化的回归方法,且借助MATLAB软件易于实现。The regression of exponential function can be linearized only when using the product random error. The formula of mathematical expectation of dependent variable of exponential function is deduced when using the product random error and using regression method of linearization. The formula indicates that the estimated value of this dependent variable is not its estimated value of mathematical expectation.The analysis indicates that the calculated regression coefficient of exponential function using regression method of linearization does not make residual sum of squares of the dependent variable to be minimum.The regression calculation of exponential function should be solved by nonlinear regression method based on the above unreasonable phenomenon. In this paper, the methods of solved nonlinear regression for exponential function are proposed using Guass-Newton method or using MATLAB software nlinfit function. The example further shows that the fitting effect of nonlinear regression method is notably better than the regression method of linearization, and the method is easy to achieve using MATLAB software.

关 键 词：指数函数 线性化回归方法 非线性回归方法 沉降规律拟合 拟合精度 

分 类 号：U456.3[建筑科学—桥梁与隧道工程]