Study on Method of Exponential Function for Fitting Settlement Rule of Highway Tunnel Enigneeing
Zhang Zixian;
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 GuassNewton 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.
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