Journal of Zhejiang University-SCIENCE A

, Volume 19, Issue 9, pp 691–703

# Updated Bayesian detection of foundation parameter with Jeeves pattern search theory

• Jian Zhang
• Chao Jia
• Chu-wei Zhou
Article

## Abstract

Updated Bayesian detection of foundation parameters in the specific foundation mechanical model was studied based on Jeeves pattern search theory. Firstly, the updated Bayesian objective function for general foundation parameters was derived which could synchronously take the stochastic property of systematic parameters and systematic responses into account. Then the governing differential equations for the Winkler foundation model were gained with elastic Mindlin plate theory and the Fourier close form solution of the foundation model was achieved with the Fourier transform method. After the step length of pattern movement was determined with the quadratic parabolic interpolation method, the updated Bayesian detection of stochastic foundation parameters was resolved with Jeeves pattern search theory and then the corresponding detection procedure was completed. Through particular example analysis, the updated Bayesian detection of stochastic foundation parameters has excellent numerical stability and convergence during iterative processes. Jeeves pattern search theory is unconcerned with the partial derivatives of systematic responses to foundation parameters, and undoubtedly has satisfactory iterative efficiency compared with the available Kalman filtering or conjugate gradient detections of the significant foundation parameters. If the iterative processes are efficiently convergent, it is an important prerequisite that the systematic response assignment should be accurate enough. The derived Jeeves pattern search method with updated Bayesian theory can be applied in other kinds of foundation parameters.

## Key words

Jeeves pattern search theory Updated Bayesian objective function Detection Foundation parameters Fourier close form solution

# 基于Jeeves模式搜索理论地基参数的更新Bayes探测法

## 摘要

### 创新点

1. 1.

根据Bayes统计理论, 推导更新Bayes误差函数。

2. 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. 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. 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. 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. 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. 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. 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。

## 关键词

Jeeves 模式搜索理论 更新 Bayes 误差函数 探测 地基参数 Fourier 闭式解

TU470

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© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

1. 1.Department of Mechanics and Structural EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
2. 2.School of Civil EngineeringShandong UniversityJinanChina