岩石疲劳损伤模型的参数估计方法研究

岩石是一种非均质的复杂地质材料，其疲劳损伤演化具有明显的3阶段发展规律。倒S型非线性疲劳累积损伤模型可以很好地描述这一规律。应用倒S型模型开展损伤计算和疲劳寿命分析的先决条件是确定出不同应力水平下的模型参数，而运用Levenberg-Marquardt法进行倒S型曲线拟合的结果表明，不用任何优化方法而随意选取参数初始值时迭代收敛到最优解的概率很低。因此，提出运用有限组合法估算初始值，即在参数可行域中均匀布点，以这些点为起始点分别实施一次Levenberg-Marquardt优化计算，取残差平方和最小的一组参数作为第2次Levenberg-Marquardt拟合计算的初始值。试验结果表明，以有限组合法估算参数初始值，Levenberg-Marquardt迭代计算总能收敛到最优解。

Parameter estimation method of fatigue damage model of rock

Rock is a complex heterogeneous geological material with three-phase law in fatigue damage evolution. This law can be described well by inverted S-shaped nonlinear fatigue cumulative model. The parameters of this model under different stress levels must be determined before using it to calculate damage or analyze fatigue life. However, the calculating result indicates that the probability is very low for Levenberg-Marquardt method converging to optimal solution with arbitrary initial parameters. Therefore, a finite combination method is proposed to estimate initial parameters for Levenberg-Marquardt calculation. Initial points uniformly distributed in the feasible region of parameters are inputted for Levenberg-Marquardt calculation; and the set of parameters with minimum residual sum of squares is taken as final initial parameters. The results show that the set of initial parameters estimated by finite combination method is always effective for Levenberg-Marquardt method converging to optimal solution.