Powell inversion mechanical model of foundation parameters with generalized Bayesian theory

Abstract

The inversion mechanical model of foundation parameters based on Powell optimizing theory was studied with generalized Bayesian theory. First, the generalized Bayesian objective function for foundation parameters was deduced with maximum likelihood theory. Then, the expectation expression and the covariance expression of the foundation parameters were obtained. After selecting the Winkler foundation as representative, the governing differential equations of the typical foundation were derived. With the orthogonal series transform method, the Fourier closed form solution of a moderately-thick plate on the Winkler foundation was achieved. After the optimal step length was determined with the quadratic parabolic interpolation method, the Powell inversion mechanical model of foundation parameters was resolved, and the corresponding inversion procedure was completed. Through particular example analysis, the highlight is that the Powell inversion mechanical model of foundation parameters with generalized Bayesian theory is correct and the derived Powell inversion model has universal significance, which can be applied in other kinds of foundation parameters. Besides, the Powell inversion iterative processes of foundation parameters have excellent numerical stability and convergence. The Powell optimizing theory is unconcerned with the partial derivatives of systematic responses to foundation parameters, which undoubtedly has a satisfying iterative efficiency compared with the available Kalman filtering or conjugate gradient inversion of the foundation parameters. The generalized Bayesian objective function can synchronously take the stochastic property of systematic parameters and systematic responses into account.

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。