基于广义Bayes理论地基参数的Powell反演力学模型（英文）

发布时间：2018-06-07 13:18

本文选题：Powell反演 + 力学模型　；参考：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2017年07期

【摘要】：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。
[Abstract]:Aim: to establish the inversion mechanics model of Winkler foundation parameters by Powell optimization inversion method and obtain the stable numerical solution of foundation parameters. Innovation: according to Bayes theory, the generalized Bayes objective function is deduced, and the Fourier closed solution of simply supported plate on Winkler foundation is derived by Fourier transformation, and the inverse mechanics model of foundation parameters is established. Method 1: 1. Based on the Bayes theory, the generalized Bayes objective function and the expressions of the generalized Bayes mean value and variance of the foundation parameters are derived. By introducing the Mindlin theory, the governing differential equation of the plate on the Winkler foundation is derived, and the Fourier closed solution of the simply supported plate on the Winkler foundation is derived. A one-dimensional automatic optimization scheme based on step size is proposed and a generalized Bayes inverse mechanical model of Winkler foundation parameters is established by combining with Powell optimization method. Conclusion 1. The inversion iterative process of foundation parameters converges stably to the true value of the parameters. Different from the Kalman filtering method and the conjugate gradient method, the iterative process of the Kalman optimization method does not involve the calculation of the partial derivative of the objective function. The generalized Bayes objective function can take into account the measured displacement data of different measuring points and different times of measurement at the same time, so the calculation efficiency is higher.
【作者单位】： Department
【基金】：supported by the Fundamental Research Funds for the Central Universities of China(No.NS2014003)
【分类号】：TU47

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