本文選題：Powell反演 + 力學(xué)模型　； 參考：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2017年07期

【摘要】：目的:通過(guò)Powell優(yōu)化反演方法建立Winkler地基參數(shù)的反演力學(xué)模型,獲得地基參數(shù)的穩(wěn)定數(shù)值解。創(chuàng)新點(diǎn):根據(jù)Bayes理論,推導(dǎo)廣義Bayes目標(biāo)函數(shù);利用Fourier變換,推求Winkler地基上簡(jiǎn)支板的Fourier閉式解,建立地基參數(shù)的反演力學(xué)模型。方法:1.根據(jù)Bayes理論,推導(dǎo)廣義Bayes目標(biāo)函數(shù)(公式(4))及地基參數(shù)的廣義Bayes均值和方差表達(dá)式(公式(9)和(11));2.引入Mindlin理論,推導(dǎo)Winkler地基上板的控制微分方程,推求Winkler地基上簡(jiǎn)支板的Fourier閉式解;3.提出步長(zhǎng)的一維自動(dòng)尋優(yōu)方案,結(jié)合Powell優(yōu)化方法建立Winkler地基參數(shù)的廣義Bayes反演力學(xué)模型。結(jié)論:1.地基參數(shù)的反演迭代過(guò)程穩(wěn)定收斂于參數(shù)真值;2.與Kalman濾波方法和共軛梯度法不同,Powell優(yōu)化方法的迭代過(guò)程不涉及目標(biāo)函數(shù)的偏導(dǎo)數(shù)計(jì)算;3.廣義Bayes目標(biāo)函數(shù)能同時(shí)考慮不同測(cè)量點(diǎn)和不同測(cè)量次數(shù)的位移實(shí)測(cè)資料,計(jì)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.
【作者單位】： Department
【基金】：supported by the Fundamental Research Funds for the Central Universities of China(No.NS2014003)
【分類號(hào)】：TU47

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