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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。
The Levenberg-Marquit optimization method using differential method to calculate the partial derivative of the calculation accuracy and low efficiency shortcomings, the use of complex variable method instead of the commonly used differential method of partial derivative calculation, so as to achieve the Leven-berg-Marquit The optimization method is improved. An improved algorithm is proposed to optimize the elastic displacement of underground roadway. In this method, the complex variable differential method is constructed on the basis of the complex function Taylor series expansion, and the direct derivative is obtained through the function calculation. Thus, an improved Levenberg-Marquit optimization inverse analysis method is formed and the relevant calculation program is compiled. Finally, the practical examples of optimal back analysis through the elastic displacement of underground tunnels show that the proposed improved back analysis method is obviously superior to the previous methods in accuracy and speed of calculation, and can be used in engineering practice.