D-u关系的最小绝对值线性拟合法

The Least Absolute Value Linear Fitting of D-u Line

采用最小绝对值方法对几类物质的冲击波速度D与波后粒子速度u的关系进行了直线拟合,并将其与常用的最小二乘法拟合的结果进行了比较。结果显示:对于实验数据分散性较小的密实材料(金属、离子晶体、氧化物等),两种方法拟合的线性系数一致;而对于实验数据分散性较大的一些疏松材料(包括液体等),两种方法拟合的线性系数有差异。对所有物质,最小绝对值法拟合的平均绝对误差比最小二乘法拟合的要小,因而最小绝对值法较最小二乘法有更高的准确性。同时讨论了导致这两种拟合差异的因素。

The Linear relationship between shock wave velocity D and particle velocity u is very important to obtain high pressure equation of state and dynamic properties of materials under shock loading. In this paper,the least absolute value method is adopted to fit the D-u line of several kinds of materials,and comparing with the generally accepted least square method. Results show that for the experimental data which scatter small（e, g. ,non-porous samples）,the two methods obtain almost the same results;but for the experimental data which scatter large（e, g. ,porous samples） ,the two methods obtain different results. Anyway, the least absolute value method has small average absolute error than the least square method. The reason of the different result between the two methods was addressed.