非线性回归法求解爆破振动速度衰减公式参数

准确分析场地爆破振动衰减规律是爆破工程设计的基本依据。通过考察爆破振动速度衰减公式中参数的线性回归方法和非线性回归方法,提出了线性残差平方和与非线性（亦即标准残差平方和）的概念,给出了求解衰减公式参数的非线性回归法,并详述了该方法的实现过程。结合工程实例,以标准残差平方和作为爆破振动实测数据与衰减公式拟合值偏差大小的判断依据,分析了线性和非线性回归分析方法得到的萨道夫斯基公式和其修正公式的标准残差平方和。分析结果表明,非线性回归分析方法的准确度明显高于线性回归分析方法;分别采用线性回归和非线性回归方法得到的萨道夫斯基公式和其修正公式的标准残差平方和非常接近,因此,采用两种形式的公式拟合爆破振动衰减规律都是可行的。

Study on attenuation parameters of blasting vibration by nonlinear regression analysis

Determination of the blasting attenuation characteristics is of most importance for blasting design.The linear and nonlinear regression analysis methods to evaluate the parameters in the S formula and revised S formula are investigated.Based on the investigation,the concept for the residual sum of squares and nonlinear residual sum of squares(standard residual sum of squares) are proposed.The algorithm of nonlinear residual sum of squares is also introduced in detail.In accordance with the engineering case,the standard residual sum of squares is used to evaluate the deviation of vibration velocity acquired by the site monitoring and the regression analysis results by S and revised formula.It is shown that the accuracy of the nonlinear regression analysis method is significantly better than the linear regression analysis method.It is also reported the residual sum of squares and the standard residual sum of squares obtain by S formulas and revised S formula are almost similar;for this case,the two blasting attenuation formulas are available.