基于同伦方法的路面模量反算研究

根据最优化问题的极值条件 ,将模量反算转化为非线性映射求零点的问题 ,结合数值微分计算弯沉对模量的一阶和二阶偏导数 ,建立了基于同伦方法反算路面模量的数学模型 ;并采用 LI-YORKE算法求解微分方程初值问题跟踪同伦曲线 ,获得模量的反算结果 ,在此基础上编制了相应的模量反算程序。通过对 3种路面结构的落锤式弯沉仪 ( FWD)的实测弯沉盆进行模量反算 ,并与国内外其它反算程序比较 ,验证了同伦方法反算结果的精度和可靠性。同时 ,通过选取不同初始值进行反算比较 ,验证了同伦方法的大范围收敛性和反算结果的稳定性。结果表明 ,采用同伦方法进行路面模量反算有效地解决了常规最优化算法的初始值和局部收敛的问题 ,是一种精度好、速度快、效率高、结果稳定且大范围收敛的模量反算方法。

Backcalculation of modulus for pavements based on homotopy method

Firstly, the backcalculation of modulus is transferred into finding zero points of nonlinear maps according to extreme conditions of optimization problems. A mathematical model for backcalculation of pavement layer modulus based on the homotopy method is established with partial derivatives of the l st and 2nd order for deflections to modulus computed by numerical derivative methods. Secondly, partial differential equations are solved with LI YORKE algorithms to follow homotopy paths, and backcalculated results are obtained. A program for backcalculation of modulus is written. Thirdly,3 measured deflection basins of 3 kinds of pavements from falling weight deflectometers(FWD) are backcalculated. Modulus results of homotopy method are compared to ones of other programs. Accuracy and reliability of the results are validated. Lastly,convergency of wide range and stability of backcalculated results for homotopy method are checked through selecting different initial values. It shows that the problems of initial values and partial convergences for conventional optimum algorithms are solved efficiently by using homotopy method to backcalculate layer modulus of pavements.Therefore,using homotopy method to backcalculate layer modulus of pavements is great in accuracy, fast in speed,high in efficiency,stable in result and wide in convergency.