动三轴试验滞回曲线的椭圆拟合分析

Analysis on Ellipse Fitting of Hysteresis Curve in Dynamic Rriaxial Test

采用正弦波形循环荷载动三轴试验获取土的动剪切模量和阻尼比的数据处理过程中通常存在两个困难:一是因为试验中存在各种噪声使滞回曲线椭圆形态不明显;二是椭圆拟合会因方法不当出现不收敛或者误差大等情况。为了在一定程度上克服第一个困难,本文将滤波技术引入到对应力应变时间序列的处理中来;为了更好地拟合滞回曲线椭圆,本文结合了主成份分析技术与椭圆的几何拟合方法,通过计算椭圆焦点位置、长半轴长度等来确定拟合椭圆,结果表明,该方法容易线性化且相对稳定,值得在动三轴数据处理中进行推广。

There exist two difficulties in the data processing of dynamic tri-axial tests when we use sinusoidal cyclic loading to obtain dynamic shear modulus and damping ratio. One difficulty is that the elliptic hysteresis curve is not clear enough due to various noises, and another one is that the procedure of fitting ellipse is divergent or the results of fitting with larger uncertainty because selected ellipse fitting method is improper. In this study, in order to overcome these difficulties to some extents, we processed time series of dynamical stress and stain with filtering technology. To fit the elliptic hysteresis curve well, we calculated the fitted ellipse by determining the two focuses and the length of the long axis of ellipse which we obtained by combining principal component analysis with ellipse geometrical fitting method. The result shows that this method is easy to linearize the nonlinear ellipse fitted problem and relatively stable, and it is worth popularizing in the dynamical tri-axial test data processing.