岩石流变分数阶模型研究

以Kelvin流变模型为研究对象,提出了一种分数阶Kelvin流变模型。首先,把Kelvin模型中的整数阶导数改为分数阶导数,考虑到岩石材料的频率通常不超过1000 Hz,在分数阶拟合时,拟合频段选取为[0 1000],进而利用Oustalop滤波算法把分数阶表示为整数阶模式;其次,利用试验数据对分数阶模型进行参数识别,考虑到分数阶Kelvin模型具有强非线性的特点,引入了Levenberg-Marquardt优化算法来确定未知参数;最后,对于频域表示的流变方程,利用Laplace逆变换获得流变精确表达式。仿真实例表明本文方法可以很好地反映岩石流变特性。

Research on fractional order models of rock rheology

In the paper, the Kelvin rheological model is utilized as research object, and a Kelvin model with fractional order(FO) is suggested. First, the integer order(IO) derivative of the model is replaced by a fractional order one. The fitting frequency range of FO model is determined considering that the fundamental natural frequency of common rock is lower than 1000 Hz. And then the FO mode is transferred into IO one by Ouslop filter algorithm. Secondly, experimental data are used to identify the unknown parameters in the FO model, and Levenberg-Marquardt algorithm is adopted to solve the strong nonlinear equations. Thirdly, a precise expression is acquired by Laplace inverse transformation. Finally, an example is used to show the efficiency of presented method.