基于复变量微分法的改进反分析方法及其验证

Improved Back Analysis Method Based on Complex Variable Differentiation Method and Its Verification

对Levenberg-Marquit优化方法中利用差分法计算偏导数带来的计算精度与效率偏低等缺点,通过采用复变量微分法取代常用的差分法进行偏导数计算,从而实现了对Leven-berg-Marquit优化方法的改进,对地下巷道弹性位移优化反分析构造了一种改进算法。该方法以复函数泰勒级数展开为理论基础构造复变量微分法,通过函数计算直接求得偏导数,由此形成了改进的Levenberg-Marquit优化反分析方法,并编制相关计算程序。最后,通过地下巷道弹性位移优化反分析实际算例表明,建立的改进反分析方法在计算的精度与速度方面都明显优于以往的方法,可用于工程实际。

To avoid the inefficiency and poor precision of difference method in calculating partial derivatives of the displacement with respect to the parameters, the complex-variable-differentiation method is introduced to replace the Levenberg-Marquit method, and an improved calculating method for back analysis of elastic displacement for un- derground tunnel is established. The complex-variable-differentiation method is based on complex function Taylor se- ries expansion, and the partial derivatives is directly obtained after calculating the function, then the improved Leven- berg-Marquit method for back analysis is established. Also, the relevant computer program is gotten in the paper. Fi- nally, an example about back analysis of elastic displacement for underground tunnel shows that the improved Leven- berg-Marquit method based on complex variable differentiation method has much more evident advantages on calculat- ing accuracy and speed compared with existed method, and it can be used extensively in the actual engineering pro- ject.