Powell's optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell＇s optimization theory is used to perform the stochastic identification of material constants of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell＇s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element （FCSE） method. Some classical examples show that Powell＇s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell＇s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses axe simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

Dynamic Bayesian identification of mechanical parameters of multi-cell curve box girder based on conjugate gradient theory

For multi-cell curve box girder, the finite strip governing equation was derived on the basis of Novozhilov theory and orthogonal property of harmonious function series. Dynamic Bayesian error function of mechanical parameters of multi-cell curve box girder was achieved with Bayesian statistical theory. The corresponding formulas of dynamic Bayesian expectation and variance were obtained. After the one-dimensional optimization search method for the automatic determination of step length of the mechanical parameter was put forward, the optimization identification calculative formulas were also obtained by adopting conjugate gradient method. Then the steps of dynamic Bayesian identification of mechanical parameters of multi-cell curve box girder were stated in detail. Through analysis of a classic example, the dynamic Bayesian identification processes of mechanical parameters are steadily convergent to the true values, which proves that dynamic Bayesian theory and conjugate gradient theory are suitable for the identification calculation and the compiled procedure is correct. It is of significance that the foreknown information of mechanical parameters should be set with reliable practical engineering experiences instead of arbitrary selection.

基于广义Bayes理论地基参数的Powell反演力学模型（英文）

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。

基于Jeeves模式搜索理论地基参数的更新Bayes探测法（英文）

目的:通过Jeeves模式搜索理论建立弹性地基参数的更新Bayes探测分析模型,以及获得地基参数的寻优搜索结果。创新点:1.根据Bayes统计理论,推导更新Bayes误差函数。2.结合最优步长的抛物线插值理论,推求地基参数的Jeeves模式搜索寻优方法,建立地基参数的探测分析模型。方法:1.根据Bayes统计理论,推导更新Bayes误差函数(公式(4))及误差函数对地基参数的梯度表达式(公式(5))。2.根据中厚度弹性地基板理论,推求Winkler地基上板的控制微分方程(公式(19))和Fourier闭式解(公式(20))。3.提出最优步长的抛物线插值寻优方案,并结合Jeeves模式搜索理论建立弹性地基参数的更新Bayes探测分析模型。结论:1.基于更新Bayes理论,可研究地基参数的Jeeves模式搜索分析模型,且地基参数的探测迭代过程具有良好的稳定性与收敛性。2.更新Bayes误差函数能同时考虑不同量测次数和不同测点的位移实测信息,计算效率较高。3.与共轭梯度法和Kalman滤波方法不同的是,Jeeves模式搜索理论的迭代过程不涉及误差函数偏导数计算,避免了迭代过程的误差累积。

基于变尺度梯度理论地基参数的修正Bayes探索（英文）

目的:建立弹性地基参数的修正Bayes分析模型,并获得地基参数的变尺度优化结果。创新点:推求地基参数的变尺度梯度优化方法,建立地基参数的修正Bayes探索分析模型。方法:建立修正Bayes目标函数及弹性地基参数的修正Bayes探索分析模型,并利用变尺度梯度搜索方法进行参数的优化迭代计算。结论:地基参数的变尺度梯度搜索分析模型在优化过程中能够稳定地收敛于地基参数的真值(图2)。变尺度梯度优化理论能够适时地修正空间矩阵尺度以产生新的搜索方向,并有效地优化修正Bayes目标函数。