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目的:通过Powell优化反演方法建立Winkler地基参数的反演力学模型,获得地基参数的稳定数值解。创新点:根据Bayes理论,推导广义Bayes目标函数;利用Fourier变换,推求Winkler地基上简支板的Fourier闭式解,建立地基参数的反演力学模型。方法:1.根据Bayes理论,推导广义Bayes目标函数(公式(4))及地基参数的广义Bayes均值和方差表达式(公式(9)和(11));2.引入Mindlin理论,推导Winkler地基上板的控制微分方程,推求Winkler地基上简支板的Fourier闭式解;3.提出步长的一维自动寻优方案,结合Powell优化方法建立Winkler地基参数的广义Bayes反演力学模型。结论:1.地基参数的反演迭代过程稳定收敛于参数真值;2.与Kalman滤波方法和共轭梯度法不同,Powell优化方法的迭代过程不涉及目标函数的偏导数计算;3.广义Bayes目标函数能同时考虑不同测量点和不同测量次数的位移实测资料,计算效率更高。
OBJECTIVE: To establish the inversion mechanics model of Winkler foundation parameters by the Powell optimization inversion method, and obtain the stable numerical solution of the foundation parameters. Innovative point: According to Bayesian theory, generalized Bayesian objective function is derived. Using Fourier transform, the closed-form solution of simply supported plate on Winkler foundation is deduced and the inversion mechanics model of foundation parameters is established. According to Bayesian theory, generalized Bayesian objective function (Eq. (4)) and the generalized Bayes mean and variance expression (Eqs. (9) and (11)) of subsoil parameters are deduced.2. By introducing Mindlin theory, The control differential equation of the upper plate is deduced and the Fourier closed-form solution of the simply supported plate on the Winkler foundation is deduced.3. The one-dimensional automatic optimization scheme of the step is proposed and the generalized Bayesian inversion mechanics model of the Winkler foundation parameters is established by the Powell optimization method. The results show that: 1. The iterative process of inversion of ground parameters stably converges to the true value of the parameters; 2. Unlike the Kalman filter method and the conjugate gradient method, the iterative process of the Powell optimization method does not involve the partial derivative of the objective function. The objective function can take into account the measured data of displacements of different measuring points and different measurements at the same time, and the calculation efficiency is higher.